Atoms of recognition in human and computer vision

Discovering the visual features and representations used by the brain to recognize objects is a central problem in the study of vision. Recently, neural network models of visual object recognition, including biological and deep network models, have shown remarkable progress and have begun to rival human performance in some challenging tasks. These models are trained on image examples and learn to extract features and representations and to use them for categorization. It remains unclear, however, whether the representations and learning processes discovered by current models are similar to those used by the human visual system. Here we show, by introducing and using minimal recognizable images, that the human visual system uses features and processes that are not used by current models and that are critical for recognition. We found by psychophysical studies that at the level of minimal recognizable images a minute change in the image can have a drastic effect on recognition, thus identifying features that are critical for the task. Simulations then showed that current models cannot explain this sensitivity to precise feature configurations and, more generally, do not learn to recognize minimal images at a human level. The role of the features shown here is revealed uniquely at the minimal level, where the contribution of each feature is essential. A full understanding of the learning and use of such features will extend our understanding of visual recognition and its cortical mechanisms and will enhance the capacity of computational models to learn from visual experience and to deal with recognition and detailed image interpretation.The human visual system makes highly effective use of limited information (1, 2). As shown below (Fig. 1 and Figs. S1 and ​andS2),S2), it can recognize consistently subconfigurations that are severely reduced in size or resolution. Effective recognition of reduced configurations is desirable for dealing with image variability: Images of a given category are highly variable, making recognition difficult, but this variability is reduced at the level of recognizable but minimal subconfigurations (Fig. 1B). Minimal recognizable configurations (MIRCs) are useful for effective recognition, but, as shown below, they also are computationally challenging because each MIRC is nonredundant and therefore requires the effective use of all available information. We use them here as sensitive tools to identify fundamental limitations of existing models of visual recognition and directions for essential extensions.Open in a separate windowFig. 1.Reduced configurations. (A) Configurations that are reduced in size (Left) or resolution (Right) can often be recognized on their own. (B) The full images (Upper Row) are highly variable. Recognition of the common action can be obtained from local configurations (Lower Row), in which variability is reduced.Open in a separate windowFig. S1.MIRCs. Discovered MIRCs for each of the 10 original images (10 object classes) are ordered from large to small image coverage within each class. Below each MIRC are the recognition rate (Left) and size in image samples (Right).Open in a separate windowFig. S2.MIRCs coverage. Each colored frame outlines a MIRC (which may be at a reduced resolution). Together, they provide a redundant representation because recognition can be obtained from a single MIRC. Warmer colors of the MIRC frame outline areas of larger coverage.A MIRC is defined as an image patch that can be reliably recognized by human observers and which is minimal in that further reduction in either size or resolution makes the patch unrecognizable (below criterion) (Methods). To discover MIRCs, we conducted a large-scale psychophysical experiment for classification. We started from 10 greyscale images, each showing an object from a different class (Fig. S3), and tested a large hierarchy of patches at different positions and decreasing size and resolution. Each patch in this hierarchy has five descendants, obtained by either cropping the image or reducing its resolution (Fig. 2). If an image patch was recognizable, we continued to test the recognition of its descendants by additional observers. A recognizable patch in this hierarchy is identified as a MIRC if none of its five descendants reaches a recognition criterion (50% recognition; results are insensitive to criterion) (Methods and Fig. S4). Each human subject viewed a single patch from each image with unlimited viewing time and was not tested again. Testing was conducted online using the Amazon Mechanical Turk (MTurk) (3, 4) with about 14,000 subjects viewing 3,553 different patches combined with controls for consistency and presentation size (Methods). The size of the patches was measured in image samples, i.e., the number of samples required to represent the image without redundancy [twice the image frequency cutoff (5)]. For presentation to subjects, all patches were scaled to 100 × 100 pixels by standard interpolation; this scaling increases the size of the presented image smoothly without adding or losing information.Open in a separate windowFig. 2.MIRCs discovery. If an image patch was recognized by human subjects, five descendants were presented to additional observers: Four were obtained by cropping 20% of the image (Bottom Row) and one by 20% reduced resolution (Middle Row, Right). The process was repeated on all descendants until none of the descendants reached recognition criterion (50%). Detailed examples are shown in Fig. S4. The numbers next to each image indicate the fraction of subjects that correctly recognized the image.Open in a separate windowFig. S3.Original images used in the human study. The image stimuli in the human study were extracted from these 10 original images (10 object categories). In the experiment, the size of each original image was 50 × 50 image samples, or a cutoff spatial frequency of 25 cycles per image.Open in a separate windowFig. S4.MIRC hierarchical trees. Examples of MIRCs (in red boxes) and their hierarchical trees, including subimage descendants (sub-MIRCs) and superimage ancestors (super-MIRCs). At the top of each tree is a depiction of the MIRC’s position in the original image marked in a red-bordered box. The human recognition rate is shown below the image patches.     

Manipulating electronic phase separation in strongly correlated oxides with an ordered array of antidots

The interesting transport and magnetic properties in manganites depend sensitively on the nucleation and growth of electronic phase-separated domains. By fabricating antidot arrays in La_0.325Pr_0.3Ca_0.375MnO₃ (LPCMO) epitaxial thin films, we create ordered arrays of micrometer-sized ferromagnetic metallic (FMM) rings in the LPCMO films that lead to dramatically increased metal–insulator transition temperatures and reduced resistances. The FMM rings emerge from the edges of the antidots where the lattice symmetry is broken. Based on our Monte Carlo simulation, these FMM rings assist the nucleation and growth of FMM phase domains increasing the metal–insulator transition with decreasing temperature or increasing magnetic field. This study points to a way in which electronic phase separation in manganites can be artificially controlled without changing chemical composition or applying external field.Electronic phase separation (EPS) is a striking phenomenon that commonly occurs in strongly correlated materials such as high-Tc oxides and colossal magnetoresistive (CMR) manganites (1, 2). Because EPS originates from strong coupling between spin, charge, orbital, and lattice, studies of EPS may reveal the fundamentals of strong electronic interactions in complex oxides (3, 4). Moreover, physical properties of complex oxides often depend sensitively on the details of EPS domains, including their size, density, and growth kinetics upon changing physical parameters. Therefore, a great effort has been devoted to study the EPS phenomena and engineer the domains in complex oxides (5, 6).With the help of real-space imaging methods, the size of EPS domains of oxide films has been shown to range from ∼10 nm to a few hundred nanometers, depending on the material (7, 8). The spatial distribution of the EPS domains is often random, and their shape can be tuned by external strain (9, 10) or the symmetry of substrates (11). Recently, it has been shown that the nucleation and growth of EPS domains in manganites are controllable by applying local external fields (magnetic or electric) (12, 13). What has not been explored is the effect of ordered arrays of artificially structured domains on EPS.In this work, we show that ordered arrays of EPS domains can be created with controllable size, shape, and density in La_0.325Pr_0.3Ca_0.375MnO₃ (LPCMO), a prototypical CMR material. Specifically, we fabricate patterned arrays of holes, often referred to as negative dots or “antidots,” (14–16) in the epitaxial LPCMO thin films. Ferromagnetic metallic (FMM) rings were observed surrounding the edges of the antidots, which is consistent with the recent discovery of FMM edge state in manganite strips (17). The magnetic measurements indicate that the magnetization of these rings is ∼16% higher than that of the film. With the increase of antidot density, the LPCMO thin films exhibit considerably higher metal–insulator transition (MIT) temperature and lower resistivity. We propose a model that includes the nucleation effect of the FMM rings to explain the observed transport phenomena.LPCMO films with 60-nm thickness are grown epitaxially on (001)-oriented SrTiO₃ substrates by ultrahigh vacuum pulsed-laser deposition. During the growing process, the system pressure is set to 3 × 10⁻³ torr with flowing oxygen and 8% ozone; the substrate temperature is kept at 800 °C (18). The layer-by-layer growth is monitored by reflection high-energy electron diffraction. The film is postannealed ex situ in flowing oxygen at 900 °C for 3 h. The antidots are fabricated by UV optical lithography and KI:HCl:H₂O (1:1:1) wet etching (17). For consistency, six samples, including five samples with different densities of uniform circular antidot (radius 1.2 μm) arrays and one control sample with no antidot, are fabricated from one single 5-mm × 5-mm film. Au electrodes with Cr buffer layers are patterned by optical lithography and grown by sputtering and lift-off method. Their resistances are measured by the four-point probe method (19) in a physical property measurement system, as illustrated in Fig. 1A. The effective area for all transport measurements is 500 μm × 1,000 μm (uniformly and fully filled with antidots) and the distances between the centers of the nearest antidots from lowest density to highest density (labeled D1 to D5) are 20, 10, 5, 4.1, and 3.3 μm, respectively. As an example, an SEM image of the second highest density antidot sample (D4) is shown in Fig. 1B.Open in a separate windowFig. 1.(A) Schematic of the samples with different densities of antidot arrays. The golden square represents Au electrodes and the ammeter and voltmeter show the four-point probe method. (B) SEM image of the second highest density antidot sample (D4); the circles are the antidot holes fabricated by optical lithography and wet etching. The radius of the antidot is approximately 1.2 μm.Fig. 2 A–D shows the temperature dependence of normalized resistance (with respect to the resistance at 300 K) (6, 20) of different samples measured at 0-, 1-, 2-, and 5-T magnetic fields, respectively. The effect of imperfect shape of antidots, which is temperature-independent, can be excluded by using the normalized resistance. At zero and small fields, the samples with higher density antidots show considerably higher MIT temperatures, especially in the cooling process (solid line in Fig. 2). For instance, at zero field (Fig. 2A), the MIT temperature of the highest density sample (D5) is about 40 K higher than that of the control sample. This enhancement is dramatic considering the fact that it is achieved with no change of doping concentration and no external field. In addition, samples with higher density antidots show smaller normalized resistance. In particular, the normalized resistance of the highest antidot density sample (D5) at the MIT temperature is about 60× smaller than that of the controlling film. By applying stronger magnetic field, the MIT temperatures of all samples increase and the differences between them become smaller. For example, the difference of MIT temperatures between the highest density sample (D5) and the controlling sample is less than 10 K at 5 T, as shown in Fig. 2D. The differences of the normalized resistance between samples also become smaller at large field, similar to the behavior of the MIT temperature.Open in a separate windowFig. 2.Temperature dependence of normalized resistance for different density samples measured at (A) 0 T, (B) 1 T, (C) 2 T, and (D) 5 T. D1-5 represent the antidot samples with density from low to high. The solid lines show the cooling process and dashed lines show the warming process. In A, the samples with higher antidot density show higher MIT temperature and lower resistance. With increasing magnetic field in B–D, the differences become much smaller.Magnetic measurements indicate that the presence of antidots induces enhanced magnetization in the LPCMO films, which is consistent with the transport studies. Fig. 3 A and B shows the in-plane and out-of-plane initial magnetization (dashed line) and hysteresis loops (solid line) at 10 K of a 60-nm-thick LPCMO film with and without the highest density (D5) antidots. With antidots, the saturation magnetization (M_s) of the film increases by 12% and 13% at low temperatures in the in-plane and out-of-plane directions, respectively. The steep rise of the initial magnetization at low field of the sample with antidots ends up with a plateau that is considerably higher than that of the film sample without antidots in both the in-plane and out-of-plane directions. Obviously, the antidots produce a larger portion of ferromagnetic phases and higher magnetization during the phase separation process (21, 22).Open in a separate windowFig. 3.Hysteresis loop (solid line) and initial magnetization (dashed line) of a 60-nm LPCMO film is measured in the in-plane (A) and out-of-plane (B) direction, before and after the highest density antidots (D5) fabricated in it. Stronger magnetizations in antidot samples than in the film in both directions are shown. (A and B, Insets) Detailed information of the hysteresis loop around zero field.The antidot-induced dramatic increase of the MIT temperature, decrease of the normalized resistance, and increase of magnetization appear to correlate strongly with the preferred FMM phase around their edges. Fig. 4 shows the magnetic force microscopy (MFM) images of the second lowest density antidot sample (D2) acquired at 200, 140, 80, and 20 K under 5-T field cooling and the corresponding resistivity vs. temperature (R–T) cooling curve. Whereas submicrometer ferromagnetic domains can be seen in regions away from the antidots (8, 17), clear preference of ferromagnetic phase can be observed at the edges of the antidots. We note that the observed ferromagnetic domains by MFM should correspond to the FMM phase in the LPCMO system with the particular Pr and Ca doping chosen in this work (7). The preferred FMM edge phase becomes even more distinguishable when the sample is cooled to low temperature, which is in stark contrast compared with the MFM images acquired from LPCMO films with no antidots (Fig. S1). Whereas nearly the whole sample area becomes ferromagnetic at 20 K and 5 T, ferromagnetic phase with much stronger signal appears around the edge of the antidots, forming arrays of ferromagnetic rings in the film. As clearly seen from the MFM image at 20 K in Fig. 4, the magnetization signal decays with distance away from the edge of the antidots, which implies that the FMM rings serve as nuclei for the growth of ferromagnetic domains (for detailed analysis, see the Supporting Information, Fig. S2). It is important to note here that the 5-T perpendicular field is used to get a better MFM imaging contrast because the easy magnetization axis is parallel to the surface. Even with a 2-T perpendicular field, there is enough perpendicular component of magnetization that allows us to view the FMM rings in MFM (Fig. S3), although with an understandably weaker imaging contrast. Based on the percentage of the antidot-induced enhancement of the saturation magnetization and the volume ratio of the ferromagnetic rings, we estimate that the saturation magnetization of the ferromagnetic rings is about 16% higher than that of the film without antidots.Open in a separate windowFig. 4.MFM images acquired during 5-T field cooling show four antidots in the second lowest density antidot sample (D2) at 200, 140, 80, and 20 K. The color scales are set as −45°, −24°, −20°, and −15°, respectively. The colored scales are set with the same zero point but not the same value because the signals at low temperature are much stronger than that at high temperature. The R–T curve is the corresponding cooling curve in Fig. 2D. Preference of ferromagnetic states around the antidots is shown in the MFM images at 200 and 140 K and the FMM rings become clear at 80 and 20 K. Around these FMM rings, these stronger magnetic signals slowly spread and decay to the values of the normal film.Open in a separate windowFig. S1.MFM images for the LPCMO film with no antidots under 5-T cooling at 200, 140, 80, and 20 K in A–D, respectively. The color scales are the same as those in main text, Fig. 4 for each temperature, which are −45°, −24°, −20°, and −15°.Open in a separate windowFig. S2.Average value of magnetic signal per pixel at the same distance from the center of the antidots. (Inset) MFM image of the second lowest density (D2) antidots at 20 K and 5 T.Open in a separate windowFig. S3.MFM images acquired during 2-T field cooling show four antidots in the second lowest density antidot sample (D2) at (A) 200 K and (B) 20 K.To explain the experimental observations, we establish a model and carry out numerical simulations. The FMM rings around the antidots serve as nuclei sites for the expansion of FMM phase during the cooling process and assist the percolation process.We divide the film into 350 × 350 pixels and define their magnetic states with a spin s. For simplicity, we use the Ising model and the Monte Carlo method for studies of the phase transition (23),H=−J∑〈ij〉sisj+∑[ik]Jik′sisk−B∑isi,[1]where s_i are the Ising variables, B is the external magnetic field, J is the nearest-neighbor ferromagnetic coupling, and J_ik′ is the next-nearest-neighbor antiferromagnetic coupling. As known, LPCMO films tend to have stronger magnetization at the edge, which can be described by an enhanced J or reduced J′ in those regions. In the present work, the edge ferromagnetism is incorporated by setting J^′ = 0 for pixels that are within three rows near the edge (16). In the interior region, J_ik′ is calculated from a random field, J_ik′ = J^′(1 + ε_ik), with ε_ik reflecting the effect of long-range correlation of the disorder in the following manner (23):εik=∑jhjk(1+dij2)α/2,[2]where h_jk stands for the random fields at four next-nearest-neighbors k around the pixel j. The best agreement with experiment is found when α = 6.For transport studies, we define that a pixel belongs to a metallic domain if more than 70% of its neighboring pixels are aligned in the same direction at the end of Monte Carlo steps following the Metropolis algorithm, otherwise it belongs to the insulating domain. The conductivity of the metallic domain varies with temperature as σ_M = σ₀/(1 + cT) while that of the insulating domain is σ_I = exp(?E_t/k_BT), with an assumption E_t = 10J. The total resistance of the network is solved from the current continuity equation, ??σ??=0, where ϕ is the potential with the boundary condition supplied by the bias voltage. The current density across the pixels is calculated from σ?? and the total resistance can be obtained from the ratio between the bias voltage and current. Hysteresis is an important aspect of CMR R–T curves. However, unlike magnetic hysteresis curves of ferromagnetic materials, the R–T curves of CMR materials are strongly time dependent, which means that for infinitely slow measurements the hysteresis can be very small. To use the simplest possible model to explain our experiment, we will neglect hysteresis in our model, thus removing the need to assume an energy barrier for switching the spins.The results of simulations for samples of high and low antidot densities are shown in Fig. 5 A and C for B = 0, 0.2J, and 0.67J, respectively (for simulated patterns see Fig. S4). The fluctuations reflect intrinsic noise in Monte Carlo simulation. For the low-density configuration, the distance between adjacent antidots is 10× the antidot radius, whereas for the high-density one this ratio is 6. For ease of comparison, the resistance is also normalized with respect to the value at 300 K. Obviously, our simulations capture the main essences of experimental observations, i.e., the higher MIT temperature and lower resistance for samples with antidot arrays and the convergence of transport behaviors of different samples in large magnetic field.Open in a separate windowFig. 5.Monte Carlo simulation of the temperature dependence of normalized resistance for different density of antidot samples at (A) B = 0, (B) B = 0.2J, and (C) B = 0.67J. In the low-density model, the distance between adjacent antidots is 10× the antidot radius, whereas in the high-density one this ratio is 6. Simulation results are consistent with transport measurement data both in the MIT temperature and normalized resistance behavior.Open in a separate windowFig. S4.Simulated patterns of film (A and B), low density (C and D), and high density (E and F) at zero field and 300 K (A, C, and E) and 60 K (B, D, and F) during the simulation in Fig. 5 of the main text. The definitions of low density and high density are as described there. The red color represents the FMM states and green represents the charge order insulator states.The MFM data indicate that antidots facilitate the growth of FMM phase around them due to the enhancements of magnetization and magnetic ordering around the edges of antidots. Simulations verify these FMM rings are the reasons for the higher MIT temperature. In turn, the expansion of the FMM phase offers more connecting channels for the percolation, which leads to lower resistance of samples with high-density antidots at zero and small fields. The convergence of the MIT temperatures and resistances at large fields is natural because the external magnetic field plays the major role for the population of ferromagnetic phase and the effect of FMM rings becomes minor (24, 25).In summary, we designed and studied LPCMO films with antidots and found strongly enhanced MIT temperature and reduced resistance, particularly in samples with higher antidot density. Based on Monte Carlo simulations with a simple model Hamiltonian, we attributed the mechanism to the enhancement of magnetization and magnetic ordering around the edges of antidots in LPCMO films. This work offers a way to control the physical properties of CMR manganites without changing the doping concentration, introducing new materials, or applying external fields. Moreover, the successful creation of ordered arrays of FMM rings in manganites opens an avenue to electronically pattern complex oxides for better tunability of their performance in electronic and spintronic devices.     

Little evidence for enhanced phenotypic evolution in early teleosts relative to their living fossil sister group

Since Darwin, biologists have been struck by the extraordinary diversity of teleost fishes, particularly in contrast to their closest “living fossil” holostean relatives. Hypothesized drivers of teleost success include innovations in jaw mechanics, reproductive biology and, particularly at present, genomic architecture, yet all scenarios presuppose enhanced phenotypic diversification in teleosts. We test this key assumption by quantifying evolutionary rate and capacity for innovation in size and shape for the first 160 million y (Permian–Early Cretaceous) of evolution in neopterygian fishes (the more extensive clade containing teleosts and holosteans). We find that early teleosts do not show enhanced phenotypic evolution relative to holosteans. Instead, holostean rates and innovation often match or can even exceed those of stem-, crown-, and total-group teleosts, belying the living fossil reputation of their extant representatives. In addition, we find some evidence for heterogeneity within the teleost lineage. Although stem teleosts excel at discovering new body shapes, early crown-group taxa commonly display higher rates of shape evolution. However, the latter reflects low rates of shape evolution in stem teleosts relative to all other neopterygian taxa, rather than an exceptional feature of early crown teleosts. These results complement those emerging from studies of both extant teleosts as a whole and their sublineages, which generally fail to detect an association between genome duplication and significant shifts in rates of lineage diversification.Numbering ∼29,000 species, teleost fishes account for half of modern vertebrate richness. In contrast, their holostean sister group, consisting of gars and the bowfin, represents a mere eight species restricted to the freshwaters of eastern North America (1). This stark contrast between teleosts and Darwin''s original “living fossils” (2) provides the basis for assertions of teleost evolutionary superiority that are central to textbook scenarios (3, 4). Classic explanations for teleost success include key innovations in feeding (3, 5) (e.g., protrusible jaws and pharyngeal jaws) and reproduction (6, 7). More recent work implicates the duplicate genomes of teleosts (8–10) as the driver of their prolific phenotypic diversification (8, 11–13), concordant with the more general hypothesis that increased morphological complexity and innovation is an expected consequence of genome duplication (14, 15).Most arguments for enhanced phenotypic evolution in teleosts have been asserted rather than demonstrated (8, 11, 12, 15, 16; but see ref. 17), and draw heavily on the snapshot of taxonomic and phenotypic imbalance apparent between living holosteans and teleosts. The fossil record challenges this neontological narrative by revealing the remarkable taxonomic richness and morphological diversity of extinct holosteans (Fig. 1) (18, 19) and highlights geological intervals when holostean taxonomic richness exceeded that of teleosts (20). This paleontological view has an extensive pedigree. Darwin (2) invoked a long interval of cryptic teleost evolution preceding the late Mesozoic diversification of the modern radiation, a view subsequently supported by the implicit (18) or explicit (19) association of Triassic–Jurassic species previously recognized as “holostean ganoids” with the base of teleost phylogeny. This perspective became enshrined in mid-20th century treatments of actinopterygian evolution, which recognized an early-mid Mesozoic phase dominated by holosteans sensu lato and a later interval, extending to the modern day, dominated by teleosts (4, 20, 21). Contemporary paleontological accounts echo the classic interpretation of modest teleost origins (22–24), despite a systematic framework that substantially revises the classifications upon which older scenarios were based (22–25). Identification of explosive lineage diversification in nested teleost subclades like otophysans and percomorphs, rather than across the group as a whole, provides some circumstantial neontological support for this narrative (26).Open in a separate windowFig. 1.Phenotypic variation in early crown neopterygians. (A) Total-group holosteans. (B) Stem-group teleosts. (C) Crown-group teleosts. Taxa illustrated to scale.In contrast to quantified taxonomic patterns (20, 23, 24, 27), phenotypic evolution in early neopterygians has only been discussed in qualitative terms. The implicit paleontological model of morphological conservatism among early teleosts contrasts with the observation that clades aligned with the teleost stem lineage include some of the most divergent early neopterygians in terms of both size and shape (Fig. 1) (see, for example, refs. 28 and 29). These discrepancies point to considerable ambiguity in initial patterns of phenotypic diversification that lead to a striking contrast in the vertebrate tree of life, and underpins one of the most successful radiations of backboned animals.Here we tackle this uncertainty by quantifying rates of phenotypic evolution and capacity for evolutionary innovation for the first 160 million y of the crown neopterygian radiation. This late Permian (Wuchiapingian, ca. 260 Ma) to Cretaceous (Albian, ca. 100 Ma) sampling interval permits incorporation of diverse fossil holosteans and stem teleosts alongside early diverging crown teleost taxa (Figs. 1 and ​and2A2A and Figs. S1 and ​andS2),S2), resulting in a dataset of 483 nominal species-level lineages roughly divided between the holostean and teleost total groups (Fig. 2B and Fig. S2). Although genera are widely used as the currency in paleobiological studies of fossil fishes (30; but see ref. 31), we sampled at the species level to circumvent problems associated with representing geological age and morphology for multiple congeneric lineages. We gathered size [both log-transformed standard length (SL) and centroid size (CS); results from both are highly comparable (Figs. S3 and ​andS4);S4); SL results are reported in the main text] and shape data (the first three morphospace axes arising from a geometric morphometric analysis) (Fig. 2A and Figs. S1) from species where possible. To place these data within a phylogenetic context, we assembled a supertree based on published hypotheses of relationships. We assigned branch durations to a collection of trees under two scenarios for the timescale of neopterygian diversification based on molecular clock and paleontological estimates. Together, these scenarios bracket a range of plausible evolutionary timelines for this radiation (Fig. 2B). We used the samples of trees in conjunction with our morphological datasets to test for contrasts in rates of, and capacity for, phenotypic change between different partitions of the neopterygian Tree of Life (crown-, total-, and stem-group teleosts, total-group holosteans, and neopterygians minus crown-group teleosts), and the sensitivity of these conclusions to uncertainty in both relationships and evolutionary timescale. Critically, these include comparisons of phenotypic evolution in early crown-group teleosts—those species that are known with certainty to possess duplicate genomes—with rates in taxa characterized largely (neopterygians minus crown teleosts) or exclusively (holosteans) by unduplicated genomes. By restricting our scope to early diverging crown teleost lineages, we avoid potentially confounding signals from highly nested radiations that substantially postdate both genome duplication and the origin of crown teleosts (26, 32). This approach provides a test of widely held assumptions about the nature of morphological evolution in teleosts and their holostean sister lineage.Open in a separate windowFig. 2.(A) Morphospace of Permian–Early Cretaceous crown Neopterygii. (B) One supertree subjected to our paleontological (Upper) and molecular (Lower) timescaling procedures to illustrate contrasts in the range of evolutionary timescales considered. Colors of points (A) and branches (B) indicate membership in major partitions of neopterygian phylogeny. Topologies are given in Datasets S4 and S5. See Dataset S6 for source trees.Open in a separate windowFig. S1.Morphospace of 398 Permian–Early Cretaceous Neopterygii. Three major axes of shape variation are presented. Silhouettes and accompanying arrows illustrate the main anatomical correlates of these principal axes, as described in Open in a separate windowFig. S2.Morphospace of 398 Permian–Early Cretaceous Neopterygii, illustrating the major clades of (A) teleosts and (B) holosteans.Open in a separate windowFig. S3.Comparisons of size rates between (A) holosteans and teleosts, (B) crown teleosts and all other neopterygians, (C) crown teleosts and stem teleosts, (D) crown teleosts and holosteans, and (E) stem teleosts and holosteans. Comparisons were made using the full-size SL dataset, a CS dataset, and a smaller SL dataset pruned to exactly match the taxon sampling of the CS dataset. Identical taxon sampling leads the CS and pruned SL datasets to yield near identical results. Although the larger SL dataset results often differ slightly, the overall conclusion from each pairwise comparison (i.e., which outcome is the most likely in an overall majority of trees) is identical in all but one comparison (E, under molecular timescales).Open in a separate windowFig. S4.Comparisons of size innovation between (A) holosteans and teleosts, (B) crown teleosts and all other neopterygians, (C) crown teleosts and stem teleosts, (D) crown teleosts and holosteans, and (E) stem teleosts and holosteans. Comparisons were made using the full-size SL dataset, a CS dataset, and a smaller SL dataset pruned to exactly match the taxon sampling of the CS dataset. Comparisons of size innovation are presented for K value distributions of the three datasets resemble each other closely.     

Resolving the HONO formation mechanism in the ionosphere via ab initio molecular dynamic simulations

Solar emission produces copious nitrosonium ions (NO⁺) in the D layer of the ionosphere, 60 to 90 km above the Earth’s surface. NO⁺ is believed to transfer its charge to water clusters in that region, leading to the formation of gaseous nitrous acid (HONO) and protonated water cluster. The dynamics of this reaction at the ionospheric temperature (200–220 K) and the associated mechanistic details are largely unknown. Using ab initio molecular dynamics (AIMD) simulations and transition-state search, key structures of the water hydrates—tetrahydrate NO⁺(H₂O)₄ and pentahydrate NO⁺(H₂O)₅—are identified and shown to be responsible for HONO formation in the ionosphere. The critical tetrahydrate NO⁺(H₂O)₄ exhibits a chain-like structure through which all of the lowest-energy isomers must go. However, most lowest-energy isomers of pentahydrate NO⁺(H₂O)₅ can be converted to the HONO-containing product, encountering very low barriers, via a chain-like or a three-armed, star-like structure. Although these structures are not the global minima, at 220 K, most lowest-energy NO⁺(H₂O)₄ and NO⁺(H₂O)₅ isomers tend to channel through these highly populated isomers toward HONO formation.The ionosphere is the largest layer in the Earth''s atmosphere, ranging in altitude from ∼60 to 1,000 km and includes the thermosphere and parts of the mesosphere and exosphere. The ionosphere contains a high concentration of electrons and ions because of the ionization of gases in that region by short wavelength radiation from the Sun. Therefore, these species play an important role in atmospheric electricity, influencing radio propagation to different regions on the Earth’s surface and space-based navigational systems (1). The D layer is the innermost layer of the ionosphere, ranging from 60 to 90 km in altitude, where Lyman series-α hydrogen radiation from the Sun gives rise to abundant nitrosonium ions (NO⁺). In addition to the ionospheric reaction between NO⁺ and water, explorations of the chemical reactivity of NO⁺ and water clusters (2–4) have implications for understanding the mechanisms of atmospherically relevant reactions in water clusters (5–9).Over the past two decades, several experimental and theoretical studies (10–13) have focused on understanding the chemical and physical properties of the small-sized hydrated nitrosonium ion NO⁺(H₂O)_n, where n = 1–5. Two key processes have been proposed for HONO formation:NO⁺(H₂O)_n + H₂O → {(HONO)H⁺(H₂O)_n}? → H⁺(H₂O)_n + HONO?.[1]Lee and coworkers (14) used vibrational spectroscopy to obtain clear evidence of the rearrangement of the NO⁺(H₂O)_n cluster by observing the appearance of new hydrogen (H)-bonded OH stretching lines. Using quantum molecular dynamics, Ye and Cheng (15) suggested possible structures and corresponding IR spectra for NO⁺(H₂O)_n (n = 1–3) clusters. In a major experimental breakthrough, Relph et al. (16) showed that the extent to which reaction 1 produces HONO and H⁺(H₂O)_n depends on the size and shape of the water clusters. Another key finding was that the reactions for HONO production start with the n = 4 water cluster. Later, the importance of the tetrahydrate isomer NO⁺(H₂O)₄ to its conversion to proton hydrate and HONO at temperature beyond 150 K was further demonstrated experimentally by Eyet et al. (11). Indeed, before Eyet’s study, Siefermann and Abel (17) had already noted that the configurations of the trihydrate and tetrahydrate isomers examined in Relph et al.’s experiment were frozen because of the very low temperature used (5 K). At this low temperature, the most abundant water cluster structures are those found at the global minima of the potential energy surface. At temperatures that are relevant to the ionosphere (200–220 K), these lowest-lying isomers may not directly contribute to the interconversion processes involving the hydrated NO⁺(H₂O)_n ion.An early study suggested that the low rate of reaction 1 can be attributed to the fact that the reactive species responsible for HONO formation include a higher-energy isomer of NO⁺(H₂O)_n that is responsible to the release of a proton (12). Asada et al. (18) reported high-level ab initio molecular-orbital calculations and identified tens of low-energy isomers of NO⁺(H₂O)₄ and NO⁺(H₂O)₅. They also pointed out that relatively higher-energy reactant, transition-state, and product isomers are involved in the formation of HONO from NO⁺(H₂O)_n (n = 4 and 5) clusters. But, the nature of the mechanism by which these relatively higher-energy isomers (in the frozen state at 0 K) can directly contribute to the interconversion processes at temperatures relevant to the ionosphere is little studied.In light of the lack of experimental studies of the dynamics of isomer transformation, we performed Born–Oppenheimer ab initio molecular dynamics (AIMD) simulations to explore the dynamic behaviors of trihydrate NO⁺(H₂O)₃, tetrahydrate NO⁺(H₂O)₄, and pentahydrate NO⁺(H₂O)₅ clusters at 220 K. Our results suggest that 220 K is adequate to drive the isomer interconversion from the lowest-lying isomers to the critical chain-like isomers. Furthermore, based on the climbing image nudged-elastic-band method, a more realistic transition state for the formation of hydrated protons and HONO (coexisting in the tetrahydrate) was identified, with the reactant being the critical tetrahydrate NO⁺(H₂O)₄ isomer. For pentahydrate, two reaction pathways are revealed by the AIMD simulations. Furthermore, the distribution of low-lying isomers at 220 K, including both highly populated critical and less-populated local-minimum isomers, is obtained. In agreement with the results of Relph et al. (16), there is no observed charge transfer between the NO⁺ and the water clusters in the n = 1 or n = 2 NO⁺(H₂O)_n clusters, indicating that these small clusters are inert. The charge transfer observed for clusters with n ≥ 3 suggests the possible formation of HONO from the NO⁺(H₂O)_n clusters. However, the population of water clusters decreases rapidly with increasing n because of the scarcity of the water molecules in the D layer of the ionosphere (17). Therefore, the trihydrate, tetrahydrate, and pentahydrate clusters are most likely the prevailing reactive species for HONO formation in the ionosphere and thus constitute the focus of our AIMD simulations. All the AIMD simulations in this work are performed in the form of the Beche–Lee–Yang–Parr functional (19, 20) with Grimme’s dispersion correction (21) (denoted as BLYP-D method) which can well describe the trend of the charge variation of the NO⁺ hydrates systems (see Fig. S1). Note that our study here is mainly focused on the formation of the HONO species in the hydrates, corresponding to the first step in reaction 1. The detachment of the HONO species from the hydrated proton, which is an endothermic process, is not considered here.Open in a separate windowFig. S1.Charge on the NO varies with the isomers for tetrahydrates on the basis of the Mullikan charge analysis at the BLYP-D and the CCSD(T)/aug-cc-pVTZ//MP2/aug-cc-pVTZ levels of theory [here, CCSD(T) and MP2 refer to the coupled-cluster method with singlet, doublet, and triplet excitations and the second-order Møller–Plesset perturbation theory, respectively]. The CCSD(T)//MP2 denotes that the structure is optimized at the MP2/aug-cc-pVTZ level, whereas the charge analysis is performed at the CCSD(T)/aug-cc-pVTZ level.For the trihydrate cluster, the three experimentally detected low-lying isomers (18) are called 3-α, 3-β, and 3-γ (Fig. 1). Notably, our AIMD simulation shows the isomer interconversion from the two lowest-lying isomers, 3-α and 3-β, to 3-γ (Fig. S2). In the course of AIMD simulation, the N–O₁ distance decreases from ∼2.20 to ∼1.90 Å, concurrent with a slight elongation of the O₁–H₁ and O₁–H₂ bonds, implying the conversion of isomer 3-α or 3-β to the 3-γ isomer (Movies S1A and S1B). No isomerization events are observed in the AIMD simulation with the initial 3-γ configuration, indicating the high thermal stability of 3-γ at 220 K. Hence, the 3-γ isomer is expected to exhibit the highest abundance among trihydrate clusters in the D layer of the ionosphere. Moreover, for the 200-ps AIMD simulation of 3-γ, no evidence of dissociation of the O–H bonds in water molecules was observed, consistent with the previous experiment-based conclusion (16) that trihydrate clusters do not play a major role in reaction 1.Open in a separate windowFig. 1.Illustration of the dynamic-driven isomer interconversion observed in AIMD simulations of the trihydrates and tetrahydrates of NO⁺. The highlighted structures in brackets represent the most likely reaction pathway from the critical (highly populated) isomer 4E to the product isomer 4ii. White, blue, and red spheres represent hydrogen, nitrogen, and oxygen atoms, respectively.Open in a separate windowFig. S2.N–O₁ distance change with time for isomers 3-α (black), 3-β (red), and 3-γ (blue). Time required for the structural transformation from 3-α and 3-β to 3-γ. The atomic label is given. Note that both H₁ and H₂ bind with two different water molecules via H-bond arrangement, which is the so-called “symmetrical H bond.”For the tetrahydrate cluster, the four lowest-lying isomers 4A, 4B, 4C, and 4E (Fig. 1) (18) were selected to investigate their dynamic behaviors at 220 K. As shown in Fig. S3, the O–H bonds of the water molecule directly bound to the NO⁺ are <1.20 Å during the 200-ps AIMD simulations, indicating the absence of HONO-forming reactions in that time period. In contrast, sudden changes in the N–O distance (e.g., at ∼26 ps in Fig. S3A; the definition of N–O distance is given in the caption of Fig. S3) are observed in all four independent AIMD simulations (black lines in Fig. S3), indicating isomer interconversion. To characterize the degree of isomer interconversion, the bond-orientational order parameter (Ψ) given byΨ=1n|∑j=1neinφij|is computed, where n is the total number of atoms j within a given radius cutoff and φ_i?j is the angle between the vector connecting the target atom i with the neighboring atom j and the reference vector connecting the target atom i and the system’s center of mass (marked by the black solid circle in the Inset of Fig. 2A). Two different target atoms with their corresponding neighboring (source) atom j were selected to characterize the structural variation: (i) the N atom in the NO⁺ motif with the O atoms in the water molecules as the source of atom j, and (ii) the O atom (shown by the green sphere in Fig. 2A, Inset) in the water molecule located at the longer end of the chain structure with the O atoms in the other water molecules that forms a hydrogen bond with the target O atom as the source of atom j. In chain-like structures, such as isomer 4E, only one O atom exists within 2.80 Å of the N atom, whereas the target O atom only forms one hydrogen bond with the neighboring water molecule. Hence, the logarithms of Ψ_N?O and Ψ_O?O take values of zero for isomer 4E. For other isomers, either Ψ_N?O or Ψ_O?O is nonzero. Fig. 2A shows the time-dependent order parameters given by the logarithms of Ψ_N?O (red line) and Ψ_O?O (black line), with isomer 4A as the initial structure. The disappearance of the red peaks at ∼26 ps clearly results from the isomer transformation from 4C to 4E (Figs. S3A and ​andS4S4 and Movie S2A). The cyclization of 4E leads to the formation of an additional hydrogen bond with the target O atom, resulting in nonzero values of the logarithm of Ψ_O?O for the ∼50–70-ps time period (see c-4E isomer in Fig. S4). The proximity of the N and O atoms of two nearest water molecules (the corresponding isomer is denoted as d-4E in Fig. S4) results in a small red peak at ∼120 ps. Similar isomer interconversion is also observed in other AIMD simulations with 4B, 4C, or 4E as the initial structure. The corresponding time-evolution data for Ψ_N?O or Ψ_O?O and associate isomer structures are shown in Figs. S5 and ​andS4,S4, respectively.Open in a separate windowFig. 2.(A) Time evolution of the logarithms of the bond-orientational order parameters Ψ_N?O (red line) and Ψ_O?O (black line). (Inset) Illustration of the angle φ_i?j used to calculate Ψ_N?O and Ψ_O?O, where white and red spheres represent oxygen and hydrogen atoms, respectively, and blue and green spheres represent the target nitrogen and oxygen atoms, respectively, used to calculate the bond-orientational order parameter. The pie charts in B–E denote the populations of various isomers observed in four independent AIMD simulations with initial structures of 4A, 4B, 4C, and 4E, respectively. The geometric structures of the isomers are given in Fig. S4.Open in a separate windowFig. S3.Time evolution of the N–O (black line) (where O is the O atom of the nearest H₂O molecule next to the N atom of the NO⁺ ion) and the O–H (red line) (where O–H refers to the averaged O–H bond length for the water molecule nearest to the NO⁺ ion) distances for the AIMD simulations of NO⁺(H₂O)₄ clusters with different initial isomer: (A) isomer 4A, (B) isomer 4B, (C) isomer 4C, and (D) isomer 4E. (Inset) Images represent the initial structures used in each AIMD simulation.Open in a separate windowFig. S4.Geometrical structures of the observed isomers in the AIMD simulation with isomer 4A as the initial structure. The white, blue, and red spheres represent the hydrogen, nitrogen, and oxygen atoms. The arrows and three pairs of circled numbers indicate several possible shifting directions of molecules and corresponding interconversion of isomers.Open in a separate windowFig. S5.Time evolution of the logarithm of the bond-orientational order parameterΨ_N?Ο (red lines) and Ψ_O?O (black lines) for the AIMD simulations starting from isomer 4B (Top), 4C (Middle), and 4E (Bottom), respectively.The chain-like water structure is the critical structure bridging two different isomers during isomer interconversion. As shown in Fig. 2A and Fig. S5, the zero-value interval between two peaks indicates the appearance of isomer 4E during the isomer conversion. More importantly, the population analysis of each isomer over the entire 200-ps AIMD simulation suggests that the chain-like water structure of 4E is much more abundant than the other isomers (Fig. 2 B–E). Specifically, in the four independent AIMD simulations with initial structures of 4A, 4B, 4C, and 4E, the obtained population values are highest for 4E: ∼62.25%, 77.66%, 61.49%, and 86.89%, respectively. Note that at 0 K, BLYP-D functional (19, 20; see Supporting Information, Computational Details) predicts that 4E is lower in energy than 4A (i.e., BLYP-D introduces some biases toward 4E over 4A, see Fig. S6 for MP2 results). But, 4E is still about 1 kcal/mol higher in energy than 4B or 4C at the BLYP-D level. At 220 K, 4E becomes the most thermodynamically favorable isomer at the BLYP-D level. Hence, the 4E isomer can be viewed as the critical isomer among the tetrahydrate clusters and plays a critical role in the D layer of the ionosphere.Open in a separate windowFig. S6.Electronic energies (ΔE), zero-point-energy corrected electronic energies (ΔE+ZPE), and the Gibbs free energies (ΔG) relative to isomer 4A for tetrahydrate isomers at the MP2 level of theory.The HONO-containing tetrahydrate isomer detected experimentally at 5 K (named 4-ii in ref. 16) has nearly the same structure as 4G (Fig. S7). The interconversion between isomer 4-ii and 4G through HONO rotation and flipping of the H₃O⁺ groups was frequently observed in the AIMD simulations (Movie S2B). More importantly, no breaking down of the N–O bonds in HONO was observed in the course of the 200-ps AIMD simulation, suggesting that both isomers are highly stable at 220 K. Therefore, the 4-ii isomer can be viewed as the final product of HONO formation, consistent with the experimental detection of 4-ii at 5 K. To confirm this interpretation, we used climbing image nudge-elastic-band calculations (22) to search for the transition state that bridges the 4E and 4-ii isomers. As shown in Fig. 1, the movement of the water molecule at the short end of the chain-like structure toward the long end and the subsequent formation of two H bonds with two neighboring water molecules led to proton transfer between the two neighboring water molecules, giving rise to the transition state (TS in Fig. 1). Upon passing over the TS, the original water molecule near the short end breaks one hydrogen bond while retaining the other hydrogen bond with the protonated species, concurrent with the formation of HONO species. In this cooperative process, the movement of the water molecule at the short end leads to the formation of a cyclic structure, where the two water molecules and the HONO species act as hydrogen-bond acceptors and form a complete solvation shell around the H₃O⁺ ion. The formation of such a solvation shell can effectively stabilize the central H₃O⁺ ion, a well-established fact in the gas-phase reaction involving ionic clusters (23–26). Due to the stabilization effect, the formation of HONO-containing isomer 4-ii, from the highly populated isomer 4E, entails a low-energy barrier of ∼2.1 kcal/mol. Thus, at the ionospheric temperatures (200–220 K), a chemical equilibrium between 4E and the HONO-containing isomers 4-ii is expected to be an important dynamic channel for HONO formation. Note that in our AIMD simulations, the nuclear quantum effect and the hydrogen tunneling effect are not included. In general, the nuclear quantum effect is equivalent to the lowering of density-functional theory (e.g., BLYP-D) temperature of water by certain degrees (27), whereas the hydrogen tunneling would speed up the proton transfer process in our system not included in the AIMD simulations. Nevertheless, the two effects seem to somewhat offset each other and, as a result, may not affect the qualitative reaction mechanism concluded from the AIMD simulations.Open in a separate windowFig. S7.Geometrical structures of the isomer 4-ii and 4G.Another channel for HONO formation can occur through the pentahydrate NO⁺(H₂O)₅, although the population of pentahydrate clusters is expected to be much lower than that of the tetrahydrate clusters. Here, the lowest-lying four isomers, 5A, 5B, 5D, and 5M (23), are selected as the initial structures in four independent AIMD simulations. In the simulation starting with isomer 5A, no HONO formation or appreciable changes in the N–O and O–H distances were observed within the 200-ps simulation, suggesting that 5A is a highly stable isomer. In contrast, the formation of HONO species is directly observed in the AIMD simulations with initial structures of 5B, 5D, and 5M, indicating that in this case, the HONO-forming reaction has a very low energy barrier. Moreover, as shown in Fig. 3, the final HONO-containing products obtained in the three independent AIMD simulations exhibit the same structure, named 5Γ, which contains a chain-like water structure similar to that found in 4E. To the best of our knowledge, the pentahydrate isomer 5Γ has not been reported in the literature, likely because pentahydrate isomers were previously modeled without considering dynamic effects at 220 K.Open in a separate windowFig. 3.Snapshots of AIMD simulations at different time stages (unit, ps) with initial structures of (A) 5B, (B) 5D, and (C) 5M. White, blue, and red spheres represent hydrogen, nitrogen, and oxygen atoms, respectively. As shown in Fig. 4A, 5C indicates a group of isomers with similar structures. Isomers 5Λ and isomer 5Y are highly populated isomers before the final product 5Γ.As shown by the time evolution of the N–O and O–H distances (Fig. S8), the N–O distance exhibited two sudden decreases, accompanied by sudden increases in the O–H distance. This result suggests that two reaction steps are likely involved in HONO formation in pentahydrate clusters. As shown in Fig. 3A, at ∼13.8 ps, 5B evolves into a group of four intermediate isomers (named isomers 5C-i to 5C-iv) whose structures can all be viewed as derivative from the tetrahydrate isomer 4C (with the addition of one water molecule to different sites of 4C). The added water molecule can move around, thus leading to interconversion of the four isomers as shown in Fig. 4A. The isomer 5C can evolve to a chain-like structure, named 5Λ (e.g., at ∼97.16 ps in Fig. 3A), corresponding to a sudden change in the N–O and O–H distances (Movie S3A). Detailed population analysis of isomers before the formation of HONO (<207.56 ps) indicates high population of both isomer groups 5C (38.63%) and 5Λ (53.19%) (Fig. 4B). Such a population distribution is akin to that for tetrahydrates where the chain-like structure 4E entails the highest population, followed by the isomer 4C (Fig. 2 B and D). The addition of one water molecule can effectively promote the movement of one tail water molecule toward the other end of the chain structure. Meanwhile, proton transfer is observed between the two neighboring water molecules, as shown in Fig. 3A, generating the final product 5Γ (Movie S3B), while the water molecules persist in a chain-like structure similar to that of 4E.Open in a separate windowFig. 4.(A) Schematic illustration of the relocation of one water molecule (with green sphere) around the 4C structure in four different sites, resulting in a group of four different isomers (5C-i to 5C-iv). (B and C) Population of major intermediate isomer observed before the formation of HONO in the AIMD simulation, starting with isomer 5B and 5D, respectively. The isomer structures of 5σ, 5Σ, and 5M′ are illustrated in Fig. S9.Open in a separate windowFig. S8.Time evolution of N–O (black line) and O–H (red line) distance during the AIMD simulation with isomer 5B (Top), 5D (Middle),and 5M (Bottom) as the initial structure.Open in a separate windowFig. S9.Geometry structures for the isomer 5σ, 5Σ, and 5M′ of pentahydrates.In the AIMD simulation starting with the 5D isomer, isomer 5C-i has the highest population before the formation of HONO (<22. 71 ps, Figs. 3B and ​and4C).4C). Here, 5C-i evolves to a three-armed, star-like structure (named 5Y) with the H₃O⁺ at the center, while the N–O distance shortened to ∼1.60 Å and the O–H distance increased to 1.51 Å; The isomer 5Y entails HONO formation (Movie S3C). The HONO-containing 5Y lasts >130 ps during the AIMD simulations, and at ∼155.99 ps the water molecule next to HONO approaches the chain-like structure, further increasing the O–H distance (Fig. S8), and then forms the final product 5Γ (Movie S3D). In the AIMD simulation starting with isomer 5M, which entails a planar cyclic structure, the HONO formation proceeds with a similar path (Fig. 3C) as 5D (Movies S3E and S3F). The same reaction is also observed when a much shorter AIMD time step (0.1 fs) was used in an independent AIMD simulation (Movie S3G). Notably, it converts to the HONO-containing isomer 5Y within 5 ps. Such fast conversion is probably attributed to the initial cyclic water structure which is also observed in the other two cases (Fig. 3). Again, 5Y changes to 5Γ after a relatively longer period of AIMD run.In conclusion, we have shown that the tetrahydrate and pentahydrate structures located at the global minima of potential-energy surface cannot be converted directly to HONO species at the 220-K ionospheric temperature. To achieve HONO formation, the lowest-lying isomers of tetrahydrates must first be converted to the highly populated critical isomer 4E in a dynamic fashion at 220 K. Subsequently, the critical isomer 4E can be converted to the HONO-containing product with encountering very low barriers at 220 K, consistent with previous experiment (11, 17). We also confirmed another experimental finding (18) that the 3γ trihydrate cluster is a highly stable nonreactive cluster, even at 220 K (Fig. 1). However, the addition of one water molecule to 3γ can directly lead to the critical 4E isomer. Thus, the chemical equilibrium between 4E and the product 4ii coupled with the thermodynamically favorable conversion process from the three lowest-lying isomers at 0 K—4A, 4B, and 4C—to the 4E isomer at 220 K represents an important dynamic channel for HONO formation in the ionosphere.Another dynamic channel for HONO formation involves pentahydrate isomers. Upon the addition of one extra water molecule, the formation of HONO can be significantly much faster (11), for example, via a pathway similar to that proposed in the tetrahydrates, namely, via the isomer 5C which contains the motif 4C, followed by the formation of a chain-like water structure akin to 4E and by the bending of the chain to form the product 5Γ. In comparison with the tetrahydrates, the extra water molecule promotes the movement of water molecules, thus leading to the much faster formation of HONO in AIMD simulations. Another possible channel for the formation of HONO could be through the three-armed, star-like precursor isomer 5Y, followed by the combination of a single water molecule with the chain-like water structure to form the product 5Γ. The chemical equilibrium between highly populated 5Λ or 5Y and 5Γ corresponds to the second dynamic channel for HONO formation in the ionosphere. The discovery of these two dynamic channels brings previously unidentified insights into the HONO formation in the 200–220-K temperature range, a key reaction in the D layer of the ionosphere (17).     

Anomalous scaling law of strength and toughness of cellulose nanopaper

The quest for both strength and toughness is perpetual in advanced material design; unfortunately, these two mechanical properties are generally mutually exclusive. So far there exists only limited success of attaining both strength and toughness, which often needs material-specific, complicated, or expensive synthesis processes and thus can hardly be applicable to other materials. A general mechanism to address the conflict between strength and toughness still remains elusive. Here we report a first-of-its-kind study of the dependence of strength and toughness of cellulose nanopaper on the size of the constituent cellulose fibers. Surprisingly, we find that both the strength and toughness of cellulose nanopaper increase simultaneously (40 and 130 times, respectively) as the size of the constituent cellulose fibers decreases (from a mean diameter of 27 μm to 11 nm), revealing an anomalous but highly desirable scaling law of the mechanical properties of cellulose nanopaper: the smaller, the stronger and the tougher. Further fundamental mechanistic studies reveal that reduced intrinsic defect size and facile (re)formation of strong hydrogen bonding among cellulose molecular chains is the underlying key to this new scaling law of mechanical properties. These mechanistic findings are generally applicable to other material building blocks, and therefore open up abundant opportunities to use the fundamental bottom-up strategy to design a new class of functional materials that are both strong and tough.The need for engineering materials that are both strong and tough is ubiquitous. However, the design of strong and tough materials is often inevitably a compromise as these two properties generally contradict each other (1). Toughness requires a material’s ability of dissipating local high stress by enduring deformation. Consequently, hard materials tend to be brittle (less tough); lower-strength materials, which can deform more readily, tend to be tougher (2, 3). For example, the toughness of metals and alloys is usually inversely proportional to their strength (4). Acknowledging such a necessary compromise, one would expect that research on advanced material design would be focused on achieving an optimum combination of these two properties. Indeed much research effort is focused on pursuing higher strength, with rather limited corresponding regard for toughness (5–10). One example is the enthusiasm sparked by the discovery of carbon nanotubes (CNTs), which exhibit remarkably high strength. However, it still remains uncertain how such a strong material can be incorporated with bulk materials to benefit from its high strength without sacrificing toughness.There have been tremendous efforts recently to develop materials with higher strength using smaller material structures. For example, by decreasing the grain size of metals, dislocation motions (thus plasticity) are more restricted, leading to a higher strength (5–10). However, such treatments also minimize possible mechanisms (e.g., crack-tip blunting) to relieve local high stress, resulting in lower toughness. The atomic scale origins of high strength of a material, e.g., strong directional bonding and limited dislocation mobility, are also essentially the roots for brittleness of the material. In short, the well-recognized scaling law of “the smaller, the stronger” comes at a price of sacrificing toughness (Fig. 1).Open in a separate windowFig. 1.An anomalous but desirable scaling law of mechanical properties requires defeating the conventional conflict between strength and toughness.The prevailing toughening mechanisms can be categorized into two types: intrinsic and extrinsic. Intrinsic toughening operates ahead of a crack tip to suppress its propagation; it is primarily related to plasticity, and thus the primary source of fracture toughness in ductile materials. Recent progress involves introducing high-density nanotwin boundaries in metals to achieve high strength and toughness (11–15). Intrinsic toughening mechanisms are essentially ineffective with brittle materials, e.g., ceramics, which invariably must rely on extrinsic toughening (2). Extrinsic toughening acts mainly behind the crack tip to effectively reduce the crack-driving force by microstructural mechanisms, e.g., crack bridging and meandering and crack surface sliding (16–18). A counterintuitive but successful example is the development of bulk metallic glass (BMG)-based composites, in which a crystalline dendrite second phase is introduced into the BMG matrix to promote the formation of multiple shear bands, leading to a strong and also tough material (3, 9, 16, 19–21). Intrinsic and extrinsic toughening mechanisms are also found to be effective in natural materials (e.g., bones and nacres), which often involve the hierarchical structure and/or a “brick-and-mortar” hybrid microstructure of the material (22–26). Nature-inspired toughening mechanisms are also used to synthesize biomimetic structural materials. Nonetheless, so far, there exists only rather limited success in attaining both strength and toughness, which often involve material-specific, complicated (e.g., growing high density nanotwins), or expensive (e.g., BMG-dendrite composites) synthesis processes and thus are hardly applicable to other materials. A general and feasible mechanism to address the conflict between strength and toughness still remains elusive.Aiming to shed insight on the long-sought strategy addressing the conflict between strength and toughness, we rationally design cellulose-based nanopaper and investigate the dependence of their mechanical properties on constituent cellulose fiber size. Surprisingly, we find that both the strength and toughness of the nanopaper increase simultaneously (40 and 130 times, respectively) as the size of the constituent cellulose building blocks decreases (from a mean diameter of 27 µm to 11 nm). These stimulating results suggest the promising potential toward a new and highly desirable scaling law: the smaller, the stronger and the tougher (Fig. 1). Though the increasing strength as the diameter of cellulose fiber decreases can be attributed to reduced intrinsic defect size, and the dependence is well captured by a continuum fracture mechanics model, our atomistic simulations reveal that facile formation and reformation of strong hydrogen bonding among cellulose chains is the key to the simultaneously increasing toughness. These mechanistic findings that underpin the highly desirable scaling law of mechanical properties suggest a fundamental bottom-up material design strategy generally applicable to other material building blocks as well, and therefore open up abundant opportunities toward a novel class of engineering materials that are both strong and tough.Cellulose is the most abundant biopolymer on Earth and has long been used as the sustainable building block for conventional paper. Cellulose has appealing mechanical properties, with specific modulus [∼100 GPa/(g/cm³)] and specific strength [∼4 GPa/(g/cm³)] higher than most metals and composites, and many ceramics, making it as a promising building block for functional and structural materials (27). Wood fibers are the main natural source of cellulose and have an intrinsically hierarchical structure (Fig. 2). A 20- to ∼50-µm-thick native wood fiber comprises thousands of nanofibrillated cellulose (CNF) fibers (5–50 nm in diameter), each of which can be disintegrated into finer elementary fibrils consisting of cellulose molecular chains (27–36). Cellulose molecule is a linear chain of ringed glucose molecules, with a repeat unit (Fig. S1) comprising two anhydroglucose rings (C₆H₁₀O₅) linked through C–O–C covalent bond. Rich hydroxyl groups in cellulose molecule (six in each repeat unit) enable facile formation of hydrogen bonds, both intrachain and interchain (Fig. 2). Whereas the intrachain hydrogen bonding stabilizes the linkage and results in the linear configuration of the cellulose chain, interchain hydrogen bonding among neighboring cellulose molecules plays a pivotal role in the deformation and failure behaviors of cellulose-based materials.Open in a separate windowFig. 2.Hierarchical structure of wood fibers and the characteristic of cellulose fibrils. Note the rich interchain hydrogen bonds among neighboring cellulose molecular chains.Open in a separate windowFig. S1.Atomic structure of a cellulose chain repeat unit. Note the six hydroxyl groups (red circles) in each repeat unit.In this study, cellulose fibers of different mean diameters [27 μm (native fiber), 28 nm, and 11 nm, respectively] are isolated from wood cell walls using a top-down approach and characterized (SI Text and Figs. S2 and ​andS3).S3). Cellulose nanopaper is made of a highly entangled random network of CNF fibers (Fig. 3A; Materials and Methods). Regular paper made of 27-μm native cellulose fibers with the same mass per area as the nanopaper is also fabricated as the control. The mechanical properties of both the cellulose nanopaper and regular paper are measured according to ASTM Standard D638 (details in SI Text).Open in a separate windowFig. 3.An anomalous scaling law of strength and toughness of cellulose nanopaper. (A) Schematic of cellulose nanopaper, made of a random network of CNF fibers. (Inset) High-resolution transmission electron microscopy (HRTEM) image of an ∼11-nm CNF fiber. (B) Stress–strain curves of cellulose paper made of cellulose fibers of various mean diameters. As the cellulose fiber diameter decreases from micrometer scale to nanometer scale, both tensile strength and ductility of the cellulose paper increases significantly, leading to an anomalous scaling law (C): the smaller, the stronger and the tougher. (D) Reveals that the ultimate tensile strength scales inversely with the square root of cellulose fiber diameter.Open in a separate windowFig. S2.(A) Optical microscope image of native cellulose fiber with a mean diameter of 27 μm. (B) Size distribution histogram. (C) AFM image of cellulose fibers with mean diameters of 28 nm. (D) Size distribution histogram. (E) HRTEM crystalline lattice image of fiber with a mean diameter of 11 nm. (F) Size distribution histogram.Open in a separate windowFig. S3.(A) A picture of a transparent cellulose nanopaper (made of CNF fibers of a mean diameter of 11 nm) on the university logo (Left). A schematic of fibrous nanostructure of the nanopaper is also shown (Right). (B) Optical transmittance of transparent cellulose nanopaper in visible and near-infrared range. (C) AFM image of cellulose nanopaper made of CNF fibers of a mean diameter of 28 nm. (D) AFM image and height scan of cellulose nanopaper made of CNF fibers of a mean diameter of 11 nm, showing rms at 1 × 1-μm scan size is 1.5 nm.     

Universal features in the photoemission spectroscopy of high-temperature superconductors

The energy gap for electronic excitations is one of the most important characteristics of the superconducting state, as it directly reflects the pairing of electrons. In the copper–oxide high-temperature superconductors (HTSCs), a strongly anisotropic energy gap, which vanishes along high-symmetry directions, is a clear manifestation of the d-wave symmetry of the pairing. There is, however, a dramatic change in the form of the gap anisotropy with reduced carrier concentration (underdoping). Although the vanishing of the gap along the diagonal to the square Cu–O bond directions is robust, the doping dependence of the large gap along the Cu–O directions suggests that its origin might be different from pairing. It is thus tempting to associate the large gap with a second-order parameter distinct from superconductivity. We use angle-resolved photoemission spectroscopy to show that the two-gap behavior and the destruction of well-defined electronic excitations are not universal features of HTSCs, and depend sensitively on how the underdoped materials are prepared. Depending on cation substitution, underdoped samples either show two-gap behavior or not. In contrast, many other characteristics of HTSCs, such as the dome-like dependence of on doping, long-lived excitations along the diagonals to the Cu–O bonds, and an energy gap at the Brillouin zone boundary that decreases monotonically with doping while persisting above (the pseudogap), are present in all samples, irrespective of whether they exhibit two-gap behavior or not. Our results imply that universal aspects of high- superconductivity are relatively insensitive to differences in the electronic states along the Cu–O bond directions.Elucidating the mechanism of high-temperature superconductivity in the copper–oxide materials remains one of the most challenging open problems in physics. It has attracted the attention of scientists working in fields as diverse as materials science, condensed matter physics, cold atoms, and string theory. To clearly define the problem of high-temperature superconductors (HTSCs), it is essential to establish which of the plethora of observed features are universal, namely, qualitatively unaffected by material-specific details.An important early result concerns the universality of the symmetry of the order parameter for superconductivity. The order parameter was found to change sign under a 90° rotation (1, 2), which implies that the energy gap must vanish along the diagonal to the Cu–O bonds, i.e., the Brillouin zone diagonal. This sign change is consistent with early spectroscopic studies of near-optimally-doped samples (those with the highest in a given family), where a energy gap (3, 4) was observed (ϕ being the angle from the Cu–O bond direction), the simplest functional form consistent with d-wave pairing. More recently, there is considerable evidence (5–8) that, with underdoping, the anisotropy of the energy gap deviates markedly from the simple form. Although the gap node at is observed at all dopings, the gap near the antinode (near and 90°) is significantly larger than that expected from the simplest d-wave form. Further, the large gap continues to persist in underdoped (UD) materials as the normal-state pseudogap (9–11) above . This suggests that the small (near-nodal) and large (antinodal) gaps are of completely different origin, the former related to superconductivity and the latter to some other competing order parameter.This two-gap picture has attracted much attention (8), raising the possibility that multiple energy scales are involved in the HTSC problem. There is mounting evidence for additional broken symmetries (12–14) in UD cuprates, once superconductivity is weakened upon approaching the Mott insulating state. The central issue is the role of these additional order parameters in impacting the universal properties of high- superconductivity.In this paper we use angle-resolved photoemission (ARPES) to examine the universality of the two-gap scenario in HTSCs by addressing the following questions. To what extent are the observed deviations from a simple d-wave energy gap independent of material details? How does the observed gap anisotropy correlate, as a function of doping, with other spectroscopic features such as the size of the antinodal gap, and the spectral weights of the nodal and antinodal quasiparticle excitations?We systematically examine the electronic spectra of various families of cation-substituted Bi₂Sr₂CaCu₂O_8+δ single crystals as a function of carrier concentration to elucidate which properties are universal and which are not. We present ARPES data on four families of float-zone-grown Bi₂Sr₂CaCu₂O_8+δ single crystals, where was adjusted by both oxygen content and cation doping. As-grown samples, labeled Bi2212, have an optimal of 91 K. These crystals were UD to by varying the oxygen content. Ca-rich crystals (grown from material with a starting composition Bi_2.1Sr_1.4Ca_1.5Cu₂O_8+δ) with an optimal of 82 K are labeled Ca. Two Dy-doped families grown with starting compositions Bi_2.1Sr_1.9Ca_{1 − x}Dy_xCu₂O_8+δ with x = 0.1 and 0.3 are labeled Dy1 and Dy2, respectively. A full list of the samples used and their determined from magnetization measurements are shown in SI Text, where we also show high-resolution X-ray data that give evidence for the excellent structural quality of our samples.Our main result is that the Dy1 and Dy2 samples show clear evidence of a two-gap behavior in the UD regime , with loss of coherent quasiparticles in the antinodal region of k space where the gap deviates from a simple d-wave form. In marked contrast, the UD Bi2212 samples and the Ca samples show a simple d-wave gap in the superconducting state and sharp quasiparticles over the entire Fermi surface in a similar range of the UD regime. We conclude by discussing the implications of the nonuniversality of the two-gap behavior for the phenomenon of high superconductivity.We begin our comparison of the various families of samples by focusing in Fig. 1 on the superconducting state antinodal spectra as a function of underdoping. The antinode is the Fermi momentum k_F on the Brillouin zone boundary, where the energy gap is a maximum and, as we shall see, the differences between the various samples are the most striking. We show data at optimal doping, corresponding to the highest in each family, in Fig. 1A. Increasing Dy leads to a small suppression of the optimal compared with Bi2212, together with an increase in the antinodal gap and a significant reduction of the quasiparticle weight. This trend continues down to moderate underdoping, as seen in Fig. 1B, where we show UD Bi2212 and Dy2 samples with very similar . For more severely UD samples, with , spectral changes in the Dy-substituted samples are far more dramatic. In Fig. 1C, we see that quasiparticle peaks in the Dy samples are no longer visible, even well below , consistent with earlier work on Y-doped Bi2212 and also Bi2201 and La_1.85Sr_0.15CuO₄ (5, 15–18). In contrast, Bi2212 and Ca-doped samples with comparable continue to exhibit quasiparticle peaks. In this respect the latter two are similar to epitaxially grown thin-film samples that exhibit quasiparticle peaks all of the way down to the lowest (19).Open in a separate windowFig. 1.Superconducting state antinodal ARPES spectra. We use the label “Bi2212” for samples without cation doping, “Dy1” for 10% Dy, “Dy2” for 30% Dy, and “Ca” for Ca-doped samples. The temperature is indicated along with . OP denotes optimal doped, UD underdoped, and OD overdoped samples. (A) Antinodal spectra for OP samples of three different families: Bi2212 (blue), Dy1 (green), and Dy2 (red), showing an increase in gap and a decrease in quasiparticle weight with increasing Dy content. (B) Antinodal spectra for UD samples with similar (≃66 K) for Bi2212 (blue) and Dy2 (red). As in A, there is a larger gap and smaller coherent weight in the Dy-substituted sample. (C) Same as in B, but for four UD samples with near 55 K for Bi2212 (dark blue), Ca (light blue), Dy1 (green), and Dy2 (red). The Bi2212 and Ca spectra are very similar to each other and quite different from those of the Dy1 and Dy2 materials. (D) Doping evolution of the antinodal spectra of four Dy1 samples from OP to UD . (E) Doping evolution of the antinodal spectra of four Dy2 samples from OP to UD . We see in D and E the sudden loss of quasiparticle weight for below 60 K. (F) Doping evolution of the antinodal spectra of three Bi2212 samples and three Ca samples, showing well-defined quasiparticle peaks in all cases.A significant feature of the highly UD Dy samples in Fig. 1C is that, in addition to the strong suppression of the quasiparticle peak, there is severe loss of low-energy spectral weight. To clearly highlight this, we show the doping evolution of antinodal spectra for the Dy1 (Fig. 1D) and Dy2 (Fig. 1E) samples. These observations are in striking contrast with the Bi2212 and Ca-doped data in Fig. 1F, where we do see a systematic reduction of the quasiparticle peak with underdoping, but not a complete wipeout of the low-energy spectral weight. To the extent that the superconducting state peak–dip–hump line shape (20, 21) originates from one broad normal-state spectral peak, the changes in spectra of the Dy materials are not simply due to a loss of coherence, but more likely a loss of the entire spectral weight near the chemical potential.The doping evolution of the k-dependent gap is illustrated in Figs. 2 and​and 3. 3. In Fig. 2 we contrast the optimally doped Dy1 (T_c = 86 K) sample (Fig. 2 A and B) with a severely UD Dy1 (T_c = 38 K) sample (Fig. 2 C and D ), the spectra being particle–hole-symmetrized to better illustrate the gap. The OP 86 K sample shows a well-defined quasiparticle peak over the entire Fermi surface (Fig. 2A) with a simple d-wave gap of the form (blue curve in Fig. 2B). For the UD 38 K sample, we see in Fig. 2C well-defined quasiparticles near the node (red spectra), but not near the antinode (blue spectra). The near-nodal gaps (red triangles in Fig. 2D) are obtained from the energy of quasiparticle peaks and continue to follow a d-wave gap (blue curve in Fig. 2D). However, once the quasiparticle peak is lost closer to the antinode, one has to use some other definition of the gap scale. We identify a break in the slope of the spectrum, by locating the energy scale at which it deviates from the black straight lines (Fig. 2C), which leads to the gap estimates (blue squares) in Fig. 2D.Open in a separate windowFig. 2.Superconducting state spectra and energy gap for OD and highly UD Dy1 samples. (A) Symmetrized spectra at k_F, from the antinode (Upper) to the node (Lower) for an OP 86 K Dy1 sample. (B) Gap as a function of Fermi surface angle (0° is the antinode and 45° the node). The blue curve is a d-wave fit to the data. (C) Same as A for an UD 38 K Dy1 sample. Curves, near the node, with discernible quasiparticle peaks are shown in red; those near the antinode are shown in blue. (D) Gap along the Fermi surface from data of C.Open in a separate windowFig. 3.Energy gap anisotropies of various samples. (A) OD 79 K Ca (where ); (B) UD 54 K Ca; (C) OP 81 K Dy2; and (D) UD 59 K Dy2. The two near-optimal samples in A and C both show a simple d-wave gap. This behavior persists in the UD Ca sample of B, but the UD Dy2 sample of D has a two-gap behavior despite having a similar to the UD Ca sample.Despite the larger error bar associated with gap scale extraction in the absence of quasiparticles, it is nevertheless clear (Fig. 2D) that the UD 38 K Dy1 sample has an energy gap that deviates markedly from the simple d-wave form. This observation is called two-gap in the UD regime, in contrast with a single gap near optimality (Fig. 2B). It is easy to observe from Fig. 2 that the Fermi surface angle at which the energy gap starts to deviate from the form matches the one at which the spectral peak gets washed out. This is very similar to the two-gap behavior demonstrated in refs. 5, 15–18. From this, one might conclude that two-gap behavior is directly correlated with a loss of well-defined quasiparticle excitations in the antinodal region. However, we point to recent ARPES data on Y-doped Bi2212 (6, 7), where two-gap behavior has been observed despite the presence of small antinodal quasiparticle peaks.We next show that the two-gap behavior is not a universal feature of all UD samples. To make this point, we compare in Fig. 3 the gap anisotropies of the Ca-doped samples (Fig. 3 A and B) with the Dy2 samples (Fig. 3 C and D) with essentially identical , where both families have the same optimal . The near-optimal samples, OD 79 K Ca (Fig. 3A) and OP 81 K Dy2 (Fig. 3C) samples, both have a simple d-wave anisotropy (although different maximum gap values at the antinode). However, upon underdoping to similar values, the two have markedly different gap anisotropies. The UD 59 K Dy2 sample (Fig. 3D) shows two-gap behavior, and an absence of quasiparticles near the antinode (similar to the discussion in connection with Fig. 2 above). However, the UD 54 K Ca sample (Fig. 3B) continues to exhibit sharp spectral peaks and a single-gap, despite a very similar as the UD 59 K Dy2.Having established the qualitative differences in the gap anisotropies for various samples as a function of underdoping, we next summarize in Fig. 4 the doping evolution of various spectroscopic features. Instead of estimating the carrier concentration in our samples using an empirical equation (22) (that may or may not be valid for various cation substitutions), we prefer to use the measured to label the doping. In Fig. 4A we show the doping evolution of the antinodal energy gap, which is consistent with the known increase in the gap with underdoping.Open in a separate windowFig. 4.Antinodal gaps and quasiparticle weights. (A) Antinodal energy gap as a function of doping for various samples is seen to grow monotonically with underdoping. Here, and in B and C, the doping is characterized by the measured quantity , with UD samples shown to the left of and OD samples to the right. All results are at temperatures well below . (B) Coherent spectral weight for antinodal quasiparticles as a function of doping. Dy-doped samples exhibit a rapid suppression of this weight to zero for UD , whereas the Ca-doped samples show robust antinodal peaks even for . (C) Coherent spectral weight for nodal quasiparticles as a function of doping, which is seen to be much more robust than the antinodal one.The coherent spectral weight Z for antinodal quasiparticles is plotted in Fig. 4B (for details on the procedure used to estimate this weight, from a ratio of spectral areas, see SI Text). The Dy1 and Dy2 samples both show a sudden and complete loss of Z with underdoping (23), which coincides with the appearance of two-gap behavior. In marked contrast with the Dy samples, the Bi2212 and Ca samples that exhibit a single d-wave gap show a gradual drop in the antinodal Z. On the other hand, we find that the nodal excitations are much less sensitive to how the sample is UD compared with the antinodal ones. Similar sharp nodal excitations have been observed in Dy-doped Bi2212 samples in ref. 7 as well. The nodal quasiparticle weight Z in Fig. 4C decreases smoothly with underdoping for all families of samples, as expected for a doped Mott insulator (24).The two-gap behavior and the attendant loss of quasiparticle weight near the antinode imply a nodal–antinodal dichotomy, aspects of which have been recognized in k space (25–27) and in real space (28–30). Two possible, not mutually exclusive, causes of this behavior are disorder and competing orders.It is known that antinodal states are much more susceptible to impurity scattering, whereas near-nodal excitations are protected (31). However, it is not a priori clear why certain cation substitutions (Dy) should lead to more electronic disorder than others (Ca). As shown by our X-ray studies in SI Text, there is no difference in the structural disorder in Dy and Ca samples. One possibility is that Dy has a local moment, but there is no direct experimental evidence for this.The two-gap behavior in UD materials, with a large antinodal gap that persists above , is suggestive of an order parameter, distinct from d-wave superconductivity, which sets in at the pseudogap temperature . There are several experiments (12–14) that find evidence for a broken symmetry at . However, it is not understood how the observed small, and often subtle, order parameter(s) could lead to large antinodal gaps of , with a loss of spectral weight over a much larger energy range (Fig. 1 D and E).We now discuss the pertinence of competing order parameters based on our measurements. First, in our ARPES data, we have not found any direct evidence for density wave ordering (say, from zone folding). Second, our X-ray data did not provide any signature for additional diffraction peaks expected for long-range density wave ordering. However, none of these null results provide definitive evidence for the absence of a density wave ordering, particularly if it were short range. In contrast, in previously published work (5, 15–18), two-gap behavior has been conjectured to be a direct consequence of phase competition between d-wave superconductivity and some type of density wave ordering. As we have demonstrated, two-gap behavior in and of itself is a sample-specific issue and hence, even if we assume a linkage between competing order and two-gap behavior, it cannot be central to the question of superconductivity in HTSC systems.Whatever the mechanism leading to qualitatively different gap anisotropies for the UD Dy and Ca samples, it only produces relatively small, quantitative changes in key aspects of these materials, such as the dependence of on doping, the presence of sharp nodal quasiparticles, and the pseudogap. We thus conclude that antinodal states do not make a substantial contribution to the universal features of HTSCs. Clearly, two gaps are not necessary for high-temperature superconductivity.     

Laser-based three-dimensional multiscale micropatterning of biocompatible hydrogels for customized tissue engineering scaffolds

Light-induced material phase transitions enable the formation of shapes and patterns from the nano- to the macroscale. From lithographic techniques that enable high-density silicon circuit integration, to laser cutting and welding, light–matter interactions are pervasive in everyday materials fabrication and transformation. These noncontact patterning techniques are ideally suited to reshape soft materials of biological relevance. We present here the use of relatively low-energy ( <  2 nJ) ultrafast laser pulses to generate 2D and 3D multiscale patterns in soft silk protein hydrogels without exogenous or chemical cross-linkers. We find that high-resolution features can be generated within bulk hydrogels through nearly 1 cm of material, which is 1.5 orders of magnitude deeper than other biocompatible materials. Examples illustrating the materials, results, and the performance of the machined geometries in vitro and in vivo are presented to demonstrate the versatility of the approach.The ability to controllably shape biomaterials on the microscale in two, and especially three, dimensions is important given the utility of these structures in guiding cellular growth, differentiation, gene expression, and regeneration (1–4). The use of soft, biocompatible materials, however, poses challenges in fabrication due to their mechanical characteristics. Widely adopted biomaterial microfabrication techniques such as soft- and photolithography are largely limited to two dimensions. The recent advent of 3D printing technology has exploited the interaction of light with materials to rapidly prototype parts for a variety of industries, and has expanded to significantly impact the biomedical field (5–7). Microscale 3D printing has also shown promise for tissue engineering and regenerative medicine applications (8, 9). Here we will present a technique for generating voids as small as 5 μm in diameter within a biocompatible hydrogel using multiphoton absorption (MPA) of light that shares many similarities with 3D printing. Furthermore, we demonstrate that this technique functions in the absence of exogenous photoinitiators or chemical cross-linkers, thereby avoiding potentially biologic incompatibility that can otherwise limit the utility of such processes.MPA is a process that occurs under extremely intense illumination where two or more low-energy photons are absorbed simultaneously by a material (10). To achieve photon densities high enough for MPA, very short laser pulses must be tightly focused within a material. If the material is transparent to the low-energy photons, very little of the light is absorbed at the surface, allowing a focal spot to be formed, and MPA to occur, deep within the material. Multiphoton-induced structural modification leading to void formation has been investigated in a variety of biocompatible materials including collagen, poly(vinyl-alcohol) (PVA), poly(methyl methacrylate), and gelatin hydrogels (11–13). Poly(ethylene glycol) hydrogels cross-linked with a photolabile bond can be selectively degraded to induce 3D structures (14). Collagen, due to its turbidity, is unsuitable for 3D patterning with features limited to a few tens of micrometers below the surface (15). Transparent materials such as PVA have very high threshold power requirements necessitating the use of high numerical aperture objectives, or amplified femtosecond pulses to initiate MPA for void formation. Extremely high light intensities found in these amplified pulses can locally change a material’s refractive index, resulting in self-focusing of the beam. Self-focusing limits the depth at which a tight focal spot can be formed and has limited MPA-induced void formation to less than 200 μm below the surface of the material (12). Some natural proteins including amyloid (16) and silk fibroin (17) are much more efficient multiphoton absorbers than their amino acid composition would suggest. The hypothesis here was that the large multiphoton cross-section of these natural materials will allow the initiation of MPA at low threshold powers, potentially reducing the effects of self-focusing.Silk fibroin collected from the domesticated Bombyx mori silkworm has been under steady investigation for decades because of its suitability as a material for biomaterials and tissue engineering. Silk is cytocompitable, biodegradable, and able to stabilize labile compounds such as enzymes and drugs (18). Silk fibroin has also been studied as an optical material due to its transparency to visible light and low surface roughness, giving it the ability to conform to nanoscale structures such as diffraction gratings (19–21) or to generate 3D photonic crystals (22). Previous work involving photomodification of silk has thus far only considered surface modification of dried films (23). Extending this work into the third dimension requires silk to take on a different form. Recently, a highly transparent elastomeric silk fibroin hydrogel has been developed, which is ideally suited to multiphoton laser micromachining (Fig. 1A, Inset) (24). These gels are robust enough to be easily handled, amenable to cell growth, and well tolerated upon implantation. Importantly, these gels are greater than 90% water, which allows material disrupted during MPA to be deposited around the outside of the machined region without fouling.Open in a separate windowFig. 1.Overview of the micromachining process. (A) Schematic of the multiphoton micromachining workstation. (Inset) Photograph of the transparent silk hydrogel. (B) Three-dimensional AFM image of one of the lines in D. (C) Graph relating line dimensions with pulse energy. Error bars represent 1 SD (n = 4). (D) Microphotograph of lines machined into the upper surface of a silk gel at pulse energies ranging from 0.25 nJ (Bottom) to 5 nJ (Top). (E) End-on view of 30-μm-wide lines machined into a silk gel. Light was incident from the bottom of the image. Ruler on right side measures depth from the surface of the sample. Due to the large area involved, this image was stitched together from a series of microphotographs. (Inset) Detail of the cross-section of one line.Here we present the exploration of laser-induced void formation in silk hydrogels (hereafter referred to as multiphoton micromachining). We find that relatively low-energy (sub-2 nJ per pulse) infrared (λ = 810 nm) pulses at a high repetition rate (80 MHz) can be used to form voids within the hydrogels in three dimensions. The gels have a linear absorption peak at 270 nm, suggesting this to be a three-photon absorption process (Fig. S1). The short time between pulses (12.5 ns) implies that the heat deposited by the first pulse that arrives does not have time to diffuse away before another pulse hits, leading to thermal accumulation at the focus of the beam which disrupts the silk structure forming voids. The voids formed survive the rigors of handling, cell growth, and subdermal implantation. We further find that it is possible to form voids within the gels nearly 1 cm below the gel surface. To our knowledge, this represents the greatest depth of multiphoton-induced void generation reported, exceeding by 1.5 orders of magnitude the deepest ablation in any material yet tested (12).Open in a separate windowFig. S1.Linear absorption spectrum of silk gel with background subtracted. The vertical line at 810 nm indicates the wavelength used for multiphoton micromachining. Pump/2 and Pump/3 lines indicate the wavelengths associated with a two-photon and three-photon absorption process, respectively. Linear absorption is driven by tyrosine and tryptophan residues in the silk. Spectrum was filtered by a five-point moving average to reduce noise.A custom-built 3D laser writing workstation was constructed to study multiphoton micromachining (Fig. 1A). Ultrashort ( ～  100 fs) laser pulses at a pulse repetition frequency of 80 MHz were focused into the bulk of a silk hydrogel using a 10× (N.A. = 0.3) microscope objective (Fig. S2). The sample was mounted on a three-axis micropositioning stage. The sample could then be moved so the beam was focused in different locations within the material. Generation of complex 3D patterns within the material was achieved by computer control over the stage translation.Open in a separate windowFig. S2.Results from the knife edge measurement of the laser spot size. (Top) Results in the X direction. (Bottom) Results from the Y direction. Propagation was in the Z direction. The full width at half maximum spot size was calculated to be 5 μm in the X direction and 6 μm in the Y direction.The relationship between pulse energy and void size was characterized by micromachining a series of lines on the top surface of a gel ∼1 mm thick (Fig. 1D). Each line was made by a single pass of the laser at a constant speed of 50 μm/s with varying pulse energies. After machining, the lines were imaged via atomic force microscopy (AFM). We found the minimum pulse energy necessary to observe structural changes in the silk gel to be ∼0.25 nJ per pulse. At this power, the average trench dimensions were 1.5-μm full width at half maximum (FWHM) in width and 100 nm in depth. These dimensions increased to 2.5-μm FWHM and 600 nm in depth when the pulse energy was raised to 5 nJ (Fig. 1C). AFM measurements confirmed that the change in appearance of the machined region was due to material removal and not local changes in refractive index (Fig. 1B).The depth at which features could be micromachined was tested by forming a gel inside a plastic fluorescence cuvette. Features were micromachined inside the gel at various depths and subsequently imaged by rotating the cuvette 90° and examining the features using bright-field microscopy. Visible features were found in the gel up to 8 mm below the surface (Fig. 1E and Fig. S3). Deeper features should be possible using a longer working distance objective with a similar numerical aperture. We attribute this large maximum machining depth to the clarity of the silk and the large multiphoton cross-section of the protein, which allows low-powered pulses to be used to initiate MPA without significant self-focusing (Fig. S3). We estimated the critical power for self-focusing to be greater than 6 MW, which is more than 100× more power than is found in the pulses used for micromachining (Fig. S4). This combination of qualities is, to the best of our knowledge, unique to silk and enables multiphoton micromachining to occur at such large depths. Deep, high-resolution features such as these, combined with the ability to dope the silk with growth factors and other compounds, could be used for the generation of complex 3D patterned cell scaffolds to form microenvironments for different cell types within the same scaffold.Open in a separate windowFig. S3.Light incident from the left of the image was used to micromachine features at various depths in a gel. Each feature was made by a single pass of the laser scanning into the page at ∼10 nJ per pulse of power and a rate of 75 μm/s. Large boxes show a zoomed-in view of the outlined area around each individual feature. The shape of each feature remains constant at each depth, indicating that self-focusing is not significantly deflecting the beam in the material. Due to the large area involved, this image was stitched together from several different photomicrographs.Open in a separate windowFig. S4.Amplified laser pulses incident from the bottom were used to create voids in the silk hydrogels at various pulse energies. Symmetrical features using 1-μJ pulses (Left) indicate that self-focusing is negligible. Strong self-focusing effects are evident in the asymmetrical shape from 10-μJ pulses (Center) and 20-μJ (Right) pulse energies. All features were made by a single pulse at each location.With maximum penetration depth of nearly 1 cm and a lateral resolution on the order of 5 μm, silk hydrogels are an excellent substrate for multiphoton micromachining. Given the limits of travel of the micropositioning stage, the total addressable volume of our workstation was greater than 100 cm³. Within this volume, individual voxels as small as 125 μm³ could be removed at will, with the removed material deposited along the outer edges of the machined regions.To explore the practicality of this technique to generate complex 3D structures, test patterns were micromachined into the bulk of the silk gel. The first was a helix consisting of two turns with an outer diameter of 200 μm (Fig. 2A). The structure started roughly 500 μm below the surface and extended 400 μm further into the gel. The second pattern chosen was a blood-vessel–like branching pattern (Fig. 2E). This structure was situated 300 μm from the surface and had a vertical extent of 100 μm. To image these patterns, the silk was stained with Rhodamine B after multiphoton micromachining and tomographic images were collected using confocal microscopy. The Rhodamine-stained silk fluoresced brightly whereas the machined regions were dark, indicating removal of the hydrogel in these regions. In most cases, the edges of the machined features showed evidence of greater material removal than the bulk of the features. This pattern was due to the control program, which paused lateral motion of the micropositioning stage at the end of each line before closing the shutter so the edges of the features were always exposed to more pulses than the center. Increased fluorescence was also visible around the edges of the features, which we attribute to the deposition of removed material along the borders. We also observed this phenomenon when imaging using the autofluorescence of silk for contrast rather than exogenous stains (Fig. S5).Open in a separate windowFig. 2.Overview of two test patterns machined into the gel. (A) Three-dimensional model of a helical pattern input into the control program. (B) Confocal microscope image of a cross-section of the helix showing the machined region in black. (Scale bar, 100 μm.) Please see video reconstruction in Movie S1. (C) Reslice of the confocal stack along the dashed line in B. (Scale bar, 100 μm.) (D) Three-dimensional reconstruction of the segmented confocal data showing the machined feature. (E) Three-dimensional model of a branching pattern input into the machining control program. (F) Three-dimensional reconstruction of resulting machined region made by segmenting the confocal images. (G) Confocal slice showing a cross-section of the micromachined region. (Scale bar, 100 μm; same for H and I.) (H and I) Cross-sections of the confocal volumes at the indicated lines.Open in a separate windowFig. S5.Confocal cross-section (Left) of the vascular-like pattern described in Fig. 2 using only the autofluorescence of silk fibroin for contrast. An increase in autofluorescence can be appreciated immediately surrounding the machined region which suggests that an increased density of silk is present in those locations. (Right) The two panels are reslices of the confocal stack along the indicated lines. (Scale bar applies to all panels.)To be useful in biomedical applications, a material must be nontoxic and support cell growth. To ensure that the machined regions were not harmful to cells in culture, we prepared sterile gels by filtering the silk through a 0.22-μm pore filter and mixed the solution in a 35-mm-diameter plastic Petri dish under sterile conditions for gelation. Before removing the dishes from the hood the lids were covered with parafilm to maintain sterility. All machining of the gels was done within the sealed Petri dishes in ambient conditions.Parallel lines ∼3 μm in width separated by about 20 μm were micromachined onto the top surface of a gel through the bulk. Human foreskin fibroblasts were seeded on the surface and observed using phase contrast microscopy as they attached and spread over the dish. We observed that the cells tended to align with the grooves machined into the gel and grew parallel with these surface features (Fig. 3 A–D). This contact guidance phenomenon is well-known and has previously been used to induce alignment of various cell types (25, 26). Because features can be machined onto the gel through a sealed dish, we hypothesize that this could be a convenient method to reorient or disrupt already established cell cultures.Open in a separate windowFig. 3.Micromachined features in vitro. (A–D) Machined lines on the surface of a gel at day 1, 3, 5, and 8, respectively. Arrows indicate cells growing along the machined lines. D shows a fluorescently labeled cells growing in the lines. (Scale bar, 100 μm long.) D shows a slightly different region of the gel as high cell density obscured the features at the location of the other images. (E) Cartoon showing micromachining of a gel laden with hMSCs. (Inset) Bright-field image of the machined region. (Scale bar, 250 μm.) (F–H) Confocal images of the cell-laden gel following live/dead staining 76 μm below, 62 μm above, and in the plane of machining, respectively. Dashed lines outline the micromachined region. (Scale bar, 250 μm.) (I and J) Close-up of living cells irradiated by the beam above (I) and below (J) the focal plane.In tissue engineering, access to oxygen and nutrients within an artificial tissue is a major challenge that limits cell density within tissue engineered constructs (27). To address this issue, researchers have generated scaffolds with interconnected porous networks (28). However, such pores are randomly distributed, limiting the amount of control of cell growth and infiltration that is possible. Multiphoton micromachining allows fully predetermined micrometer-scale features to be generated within a construct, allowing spatial control over cell infiltration. To test whether micromachined features within the silk hydrogels could be used to direct cell growth in three dimensions, Y-shaped branching patterns were machined into the gels such that the main branch intersected the surface, allowing cells and media to penetrate the bulk of the gel (Fig. 4A). Cells were stained with a fluorescent dye and confocal images were taken of each feature at days 5, 9, and 14 postseeding. Cell density was assessed at three locations within each feature: the main branch, the transition region, and the lower branch. By day 9 and continuing to day 14, cells were observed in all three regions in 100% of the small features. The larger features were less well populated with cells found in 100% of the main branches, 86% of the transition regions, and only 14% of the lower branches by day 9. On day 14, 71% of the large features had cells in the lower branches. One of the large features did not intersect the surface of the gel and was omitted from this analysis. No subsurface cells were observed in areas that were not laser machined (Fig. 4A).Open in a separate windowFig. 4.Cell infiltration into machined features. (A, Top) Three-dimensional model of the pattern machined into hydrogels that were subsequently seeded with cells in vitro. (A, Bottom) Series of confocal images of fibroblasts growing within a Y-shaped machined feature on day 9 after seeding. Each image is separated by 10 μm in the Z direction. (Scale bar, 100 μm.) (B, Top) Three-dimensional model of the pattern machined into a hydrogel that was subsequently implanted s.c. in mice. Lines marked “(i–iii)” indicate the confocal cross-sections shown in the panels below. The white circles in (B, i) and (B, ii) correspond to the main branch diameter and approximate location in the construct. The smaller circles in (B, iii) correspond to the secondary branch diameters. Cells had infiltrated to the bottom of the main branch (B, ii) and had begun extending down one of the secondary branches (B, iii). (All scale bars, 100 μm.)Rather than providing a means for cells to infiltrate a material from the surface, it is often easier to encapsulate cells within the material itself. It has been shown that human mesenchymal stem cells (hMSCs) can be encapsulated within this type of silk hydrogel (24). When cells are encapsulated in this way, the concentrations of oxygen, nutrients, and growth factors are governed by diffusion, limiting the size of such constructs. Three-dimensional patterned cell-laden hydrogels would have more surface area for the diffusion of oxygen and well-defined patterns could provide an artificial microvasculature, greatly increasing the maximum size at which cell growth could be supported. To investigate the ability of multiphoton micromachining to pattern cell-laden hydrogels, we embedded hMSCs in the bulk of a thin gel. The word “Tufts” was micromachined into the gel (Fig. 3E) and, less than 4 h after machining, cells were stained with a live/dead fluorescence assay. Following staining the dishes were examined using confocal microscopy. We found dead cells in the plane of micromachining with living cells present both directly above and below the machined volume (Fig. 3 F–J). This was expected as cells are largely transparent to 810-nm light so they should be unaffected by the beam far from the focus. The high temperatures at the focus of the beam are likely responsible for the dead cells found in the micromachined regions.Finally, we conducted a pilot in vivo study in which three mice were implanted with two machined gels each. One gel contained a branching pattern with a main branch diameter of 200 μm; the second gel contained a branching pattern with a main branch diameter of 400 μm. One mouse was killed at 2, 3, and 4 wk. Upon subsequent imaging we were able to identify the machined features in four of the six samples with at least one feature identified at each timepoint. Cells were found to penetrate the gels via the machined features in the 2- and 3-wk sample (Fig. 4 and Figs. S6 and ​andS7).S7). In the 4-wk sample, cells were found to have overgrown the machined feature and not penetrate into the gel. It is likely that the overgrowth in the 4-wk case was not due to the extra time of implantation as no cells were seen to penetrate the gel, but rather occurred relatively soon after implantation.Open in a separate windowFig. S6.Confocal images of micromachined gel containing a feature with main branch diameter of 400 μm. A is on the surface of the gel and B is 74 μm below the gel surface. Dashed white lines indicate the diameter and approximate location of the main branch of the feature. No cells are present in the micromachined region on the surface, but are found in high concentrations at the bottom of the main branch. This sample was recovered 3 wk after implantation.Open in a separate windowFig. S7.Confocal images of micromachined gel containing a feature with main branch diameter of 200 μm. A is taken from the top surface of the gel, B is 50.5 μm below the surface, and C is 70 μm below the surface of the gel. A relative absence of cells can be seen at the surface whereas cells conforming to the shape of the feature are visible below the surface of the gel. This sample was recovered 3 wk after implantation. (Scale bar, 100 μm.)These results are significant as they show that multiphoton micromachining in silk fibroin hydrogels was capable of directing cell growth and speeding infiltration into an artificial construct. Patterned biocompatible constructs are of great interest in the field of tissue engineering, which seeks to artificially recapitulate natural structures in the body. One promising avenue to do so is the use of decellularization as a means to replace damaged organs (29). This technique involves the harvest of a healthy organ and the removal of all cellular material, leaving behind a structured extracellular matrix. The resulting decellularized scaffold acts as a template for new cell growth. However, this technique requires access to a healthy organ as well as time for cell culture. Whereas this method could be used to reduce rejection of donated organs, it does little to help those who are still waiting for an organ transplant. Whereas the micropatterning described here is too small-scale to be used to replicate an entire organ, it provides a unique combination of high-resolution (micrometer-scale) structuring with the possibility of generating large (nearly millimeter-scale) features. We believe this combination of high resolution with large volume of modification could prove useful to link large-scale 3D patterning of biological materials using techniques like 3D bioprinting (8), with techniques to produce random voids in a material on the 0.1-m scale (28).In conclusion, silk hydrogels were found to be an attractive substrate for photoinitiator-free multiphoton micromachining. Using only moderate laser power it was possible to generate voids within the bulk material at depths of nearly 1 cm. This approach enabled rapid formation of high-resolution structures over multiple length scales in three dimensions and could be carried out in cell-laden hydrogels without damage to living cells in the volume immediately adjacent to the micromachined region. The features are formed in a soft, biocompatible matrix which enables the guidance of cells in three dimensions and appears to promote infiltration of cells in vivo without loss of the pattern’s structural integrity. All-aqueous processing of the material and machining at ambient temperatures without harsh solvents or toxic photoinitiators should make it possible to further promote cell infiltration and differentiation using growth factors or other chemical signals. Whereas there are many options to improve the resolution and utility of the micromachining workstation, the technique described here allows for rapid prototyping of mesoscale features in a robust, simple to use, biocompatible substrate. Three-dimensional patterns that are suitable for guiding cell growth can be produced over large volumes with high resolution. Such patterned gels allow control over cell growth and implantation on the 10-μm scale, allowing the recapitulation of native micrometer-scale structures in tissue engineering scaffolds. This approach for the generation of programmable structures using multiphoton micromachining in biocompatible silk hydrogels is virtually impossible to produce using any other method, opening numerous new avenues of investigation into the 2D and 3D patterning of soft materials.     

Structure and control of charge density waves in two-dimensional 1T-TaS2

The layered transition metal dichalcogenides host a rich collection of charge density wave phases in which both the conduction electrons and the atomic structure display translational symmetry breaking. Manipulating these complex states by purely electronic methods has been a long-sought scientific and technological goal. Here, we show how this can be achieved in 1T-TaS₂ in the 2D limit. We first demonstrate that the intrinsic properties of atomically thin flakes are preserved by encapsulation with hexagonal boron nitride in inert atmosphere. We use this facile assembly method together with transmission electron microscopy and transport measurements to probe the nature of the 2D state and show that its conductance is dominated by discommensurations. The discommensuration structure can be precisely tuned in few-layer samples by an in-plane electric current, allowing continuous electrical control over the discommensuration-melting transition in 2D.Layered 1T-TaS₂ exhibits a number of unique structural and electronic phases. At low temperature and ambient pressure, the ground state is a commensurate (C) charge density wave (CDW). On heating, it undergoes a sequence of first-order phase transitions to a nearly commensurate (NC) CDW at 225 K, to an incommensurate (IC) CDW at 355 K, and finally to a metallic phase at 545 K. Each transition involves both conduction electron and lattice degrees of freedom—large changes in electronic transport properties occur, concomitant with structural changes to the crystal. By either chemical doping or applying high pressures, it is possible to suppress the CDWs and induce superconductivity (1–3). For device applications, it is desirable to control these phases by electrical means, but this capability is difficult to achieve in bulk crystals due to the high conduction electron density. Recent efforts to produce thin samples by mechanical exfoliation provide a new avenue for manipulating the CDWs in 1T-TaS₂ (4–8). These studies have demonstrated the suppression of CDW phase transitions using polar electrolytes, as well as resistive switching between the different phases. As the material approaches the 2D limit, however, significant changes have been observed in the transport properties (4, 5, 8). However, the microscopic nature of the 2D state remains unclear. In this work, we use transmission electron microscopy (TEM) together with transport measurements to develop a systematic understanding of the CDW phases and phase transitions in ultrathin 1T-TaS₂. We find that charge ordering disappears in flakes with few atomic layers due to surface oxidation. When samples are instead environmentally protected, the CDWs persist and their transitions can be carefully tuned by electric currents.Both the atomic and CDW structure of 1T-TaS₂ can be visualized in reciprocal space by TEM electron diffraction (9, 10). In Fig. 1A, we show diffraction images taken from a bulk-like, 50-nm-thick crystal at low and room temperature (C phase, blue panel; NC phase, red panel). The bright peaks (connected by dashed lines) correspond to Bragg scattering from a triangular lattice of Ta atoms with lattice constant a = 3.36 Å. Additional weaker diffraction peaks appear from the periodic atomic displacements of the CDW. In the low-temperature C phase, Ta atoms displace to make Star-of-David clusters (blue inset, Fig. 1B). The outer 12 atoms within each star displace slightly inward toward the atom at the center, giving rise to a commensurate superstructure with wavelength λ_C = 13a that is rotated ϕ_C = 13.9° with respect to the atomic lattice. The NC phase at room temperature also consists of such 13-atom distortions. Scanning tunneling microscope (STM) measurements have revealed, however, that such ordering is only preserved in quasi-hexagonal domains consisting of tens of stars (11, 12), with domain periodicity 60–90 Å depending on temperature (13, 14). The domains are separated by a discommensuration network forming a Kagome lattice, inside of which the Ta displacements are substantially reduced (15). A schematic of this structure is shown in the red inset of Fig. 1B.Open in a separate windowFig. 1.NC-C CDW phase transition in bulk 1T-TaS₂ and CDW suppression by oxidation in thin flakes. (A) TEM diffraction images of 50-nm-thick 1T-TaS₂ at 295 K (red, NC phase) and 100 K (blue, C phase). Weaker peaks are due to CDW distortion. (B) Resistivity vs. temperature of bulk 1T-TaS₂ crystal around the first-order, NC-C transition. (Insets) Real space schematics of CDW structure. (C) (Left) TEM diffraction of few-layer 1T-TaS₂ flake shows absence of CDW order. (Right) High-resolution, cross section electron microscopy image reveals presence of amorphous oxide. (D) Free energy schematic of CDW evolution with temperature. Vertical and horizontal axis represent free energy (E) and reaction coordinate (q), respectively. NC domains grow slowly upon cooling until abrupt transition into the C phase. Energy barrier increases in 2D samples protected from oxidation.When ultrathin 1T-TaS₂ crystals (approximately <5 nm thickness) are exfoliated in an ambient air environment, the CDW structure is not observed by the TEM electron diffraction. In the left panel of Fig. 1C, we show a room temperature electron diffraction pattern taken on a few-layer flake. The presence of Bragg peaks without CDW scattering suggests that the 1T-TaS₂ layers are in a phase that is not observed in bulk crystals at this temperature. High-resolution electron microscopy and energy dispersive spectroscopy on fully suspended samples reveal a strong presence of oxidation as well as an amorphous layer on the surface (Figs. S1 and ​andS2).S2). The amorphous oxide (∼2 nm thickness) can be clearly seen atop both surfaces of the 1T-TaS₂ layers in cross section (Fig. 1C, Right). It is possible that oxidation leads to strong surface pinning, which destroys charge ordering in ultrathin samples. Recent resistivity measurements on exfoliated 1T-TaS₂ crystals have also reported the disappearance of CDWs in sufficiently thin flakes (5). It is not clear, however, whether these are intrinsic effects related to dimensionality or extrinsic consequences of oxidation.Open in a separate windowFig. S1.High-resolution STEM image of ultrathin 1T-TaS₂ prepared in air. (A) Amorphous layers appear on the top and bottom surfaces. (B) Overview of a curled sheet providing in-plane (A) and planar (C) and viewing. (C) High-resolution STEM image of the 1T-TaS₂ sheet shows the high-frequency atomic structure and a lower frequency intensity variation corresponding to the amorphous surface layers. The amorphous surfaces are more clearly visualized in D, which uses Lab Color space to create blue/yellow contrast of the amorphous (low-frequency) intensity variation.Open in a separate windowFig. S2.Chemical analysis with STEM-spectroscopy of ultrathin 1T-TaS₂ exfoliated in air. In addition to the expected presence of Ta and S, oxygen and trace amounts of carbon are present in both the (A) dispersive X-ray and (B) electron energy loss spectroscopy. The sample was suspended such that all detected elements represent chemical species present in the specimen.To prevent surface oxidation, we exfoliated 1T-TaS₂ crystals within a nitrogen-filled glove box with under 2-ppm oxygen concentration. The flakes were protected by a capping layer of thin hexagonal boron nitride (hBN) before transfer out into the ambient environment (Methods). TEM diffraction performed on these protected samples reveals that CDW formation persists down to the lowest thicknesses measured (2 nm), as we discuss in detail in Fig. 4. This finding indicates that the absence of charge order in ultrathin, uncovered flakes is most likely caused by the effects of oxidation. The study and utilization of CDWs in 2D 1T-TaS₂ thus requires careful sample preparation in inert atmosphere.Open in a separate windowFig. 4.Dimensional dependence of phase transition—electron diffraction. (A) Overlaid TEM diffraction images of ultrathin 1T-TaS₂ covered with hBN taken at 295 K (red peaks) and 100 K (blue peaks) for two flake thicknesses. hBN preserves CDW order (circled peaks) but introduces additional diffraction spots. (B) (Upper Right) Zoom-in schematic of CDW diffraction peaks showing temperature evolution. Position of NC spot can be used to estimate commensurate domain periodicity D_NC (Upper Left). (Lower) D_NC vs. temperature with cooling measured for the two covered samples compared with data reproduced from ref. 14. Reduced thickness pushes NC to C phase transition to lower temperature.The different structural phases of 1T-TaS₂ exhibit distinct electronic transport properties that may be exploited for device applications. In the main panel of Fig. 1B, we show temperature-dependent resistivity of a bulk crystal measured across the NC-C phase transition. Resistivity abruptly increases (decreases) by over an order of magnitude on entering the C (NC) phase. The hysteresis loop between cooling and warming defines the temperature region of metastability between the two phases and can be understood by a free energy picture (Fig. 1D). In a first-order transition, an activation barrier separates the stable energy minima corresponding to the NC and C states. With cooling from the NC phase, both the C state energy and the height of the barrier decrease with respect to the NC energy. When the C state has lower energy, the NC phase becomes metastable, but the system only transitions into the C phase when the activation barrier becomes comparable to the thermal energy. The situation is reversed when warming from the C phase. In oxidation-free 2D samples, this electronic transition is qualitatively unchanged.Fig. 2A shows an example of hBN-encapsulated 1T-TaS₂ flakes before (Upper) and after device fabrication (Lower). To make electrical contact to the covered samples, we used a technique of edge metallization developed for graphene/hBN heterostructures (Methods) (16). A side-view device schematic is shown in the Inset of the lower panel. In the main panel of Fig. 2B (I = 0, black curve), we plot resistance as a function of temperature for a 4-nm-thick sample measured across the NC-C phase transition. The behavior is similar to that of the bulk crystal (Fig. 1B); however, the hysteretic region between cooling and warming is substantially widened, indicating that one or both of the CDW phases become more metastable.Open in a separate windowFig. 2.Electrical control of NC-C transition in oxidation-free, 2D devices. (A) Optical images of 1T-TaS₂ flakes on a SiO₂/Si wafer covered by hBN in inert atmosphere before (Upper) and after (Lower) side electrical contact. (Inset) Side-view device schematic. (B) ac resistance vs. temperature for 4-nm-thick device as a function of dc current. Continuous current flow stabilizes NC phase at low temperature. Normalized resistance difference between cooling and warming is plotted as a function of dc current in Inset. (C) (Upper) Current vs. voltage sweep at 150 K starting in NC phase shows abrupt decreases in current and transition to the C phase. (Lower) Same at 200 K starting in C phase shows abrupt increase in current and transition to NC phase. Sweep rate is 3–6 V/min. Free energy schematics of electrically induced transitions are plotted in Insets.Metastable phases of a CDW system are generally more susceptible to electronic perturbations, because CDWs directly couple to electric field (6–8, 17). In our device, we observe that continuous current flow stabilizes the NC phase at low temperatures. In Fig. 2B (main panel), we show ac resistance with temperature while also applying a continuous, in-plane dc current, starting at room temperature (300 K). As the dc current I is increased, the final resistance at low temperature is monotonically lowered. Concomitant with this trend, the resistance jump resulting from the NC-C phase transition also decreases with increasing I. In the Inset, we plotted the ratio of the resistance difference between cooling and warming, ∆R, to resistance R in the more conducting state at T = 180 K, the temperature in the middle of the hysteresis region, as a function of the dc current level. For I = 35 μA (blue curve in main panel), the NC-C phase transition is completely absent. This measurement indicates that C phase formation in the current driven sample is very different compared with the zero-current, equilibrium condition. Current flow hinders the formation of the C phase and maintains the sample in the more conductive NC state at low temperature. We exclude Joule heating of the sample as a possible explanation by slowly turning off the current at low temperature and verifying that the resistance does not change. We also note that cooling and warming the sample again without dc current flow reproduces the original phase transitions (Fig. S3), indicating that the currents have not damaged the flake irreversibly.Open in a separate windowFig. S3.Resistance vs. temperature before and after dc current measurements. Trace for I = 0 (after) reproduces original phase transitions suppressed by large dc current.Our observation suggests that it is possible to maintain the NC phase in a temperature region where it is not thermodynamically stable. We now show that the opposite phenomenon is also possible, i.e., we can drive a transition toward the thermodynamically stable state, if we apply an in-plane current after cooling or warming the sample in equilibrium. Fig. 2C shows the current induced phase transitions in the same device (4 nm thickness). Here, we start in the NC phase at room temperature and cool the sample down to 150 K without current flow. At this temperature, although the sample remains in the NC state, the NC phase is now metastable, and the C phase is the thermodynamically stable state. As we increase the voltage across the device (upper panel, dark green curve), the measured current through the device decreases in abrupt steps (marked by red arrows) when it reaches a critical current I_c ∼ 30 μA (marked by red dashed line). On sweeping the bias current back to zero (light green curve), the device remains in a more insulating state. Warming up the sample after this point produces a temperature curve similar to the C phase, and a transition to the NC phase is observed. We have demonstrated that a bias current applied to the sample can be used to drive the metastable NC phase toward the thermodynamically preferred C state. The dashed green arrow in Fig. 2B marks the direction of this current-induced NC to C phase transition and a free energy schematic of this process is shown in the Inset of the upper panel of Fig. 2C.Similarly, the metastable C state can also be driven toward the NC phase with current. Here, we start in the C phase at 50 K and warm up to 200 K. The sample remains in the C phase, but now the NC phase is the thermodynamic ground state. As shown in the lower panel of Fig. 2C, sweeping the voltage in this case results in a sharp increase in current and drives the sample toward the more conducting NC state. We have used the dashed orange arrow in Fig. 2B and the free energy picture in the inset of the lower panel of Fig. 2C to represent this opposite C to NC transition. Interestingly, both induced transitions occur when the current reaches about I_c ∼ 30 μA, indicating that indeed current flow rather than electric field is the underlying mechanism that drives the transition. We repeated this measurement at various temperatures and initial conditions. In all cases, whenever the initial system is metastable, reaching a current threshold of 30 to 40 μA drives the system toward the thermodynamically stable state, regardless of device resistance. In contrast, we observe no induced transition up to 45 μA at 260 K, where a metastable phase ceases to exist.Taken together, the results of Fig. 2 demonstrate that it is possible to electrically control the NC-C transition in 2D 1T-TaS₂, where the temperature region of metastability is significantly enhanced. A more detailed study of this phase transition in 2D samples, however, can provide a better understanding of our experimental observations. The key structural difference between the two CDW phases is the presence of the discommensuration network in the NC phase (Fig. 1B, red inset). The NC-C transition can then be interpreted as a discommensuration-melting transition, which can be significantly affected by dimensionality (18, 19). The discommensurations have a striking effect on the electronic transport properties in 1T-TaS₂. The NC phase is an order of magnitude more conductive than the C phase. If we assume that the interior of each commensurate domain has similar transport properties as the C phase, this then implies the discommensuration regions in the NC phase are at least 10 times more conductive than the domain interior (3). Such a view is supported by the fact that the atomic structure within the discommensurations is close to the high-temperature metallic phase (15). With this interpretation, we can use transport measurements to better understand the role of dimensionality on the discommensuration-melting transition.As the number of 1T-TaS₂ layers decreases, the resistivity change corresponding to the NC-C phase transition evolves in a continuous manner down to 2 nm thickness in environmentally protected samples. Fig. 3A shows resistivity as a function of temperature for four hBN-covered 1T-TaS₂ flakes, all measured using a 1 K/min sweep rate. Their thicknesses are 2, 4, 6, and 8 nm as determined using an atomic force microscope. For comparison, we show data from an unprotected, 20-nm-thick flake, which exhibits characteristics similar to the bulk crystal, indicating that the effects of oxidation are less pronounced in thicker samples. The temperature hysteresis associated with the phase transition between cooling and warming is substantially increased in thinner samples, consistent with our earlier observations of the device in Fig. 2A. The progressive widening of the hysteresis loop continues down to the 4-nm-thick device, below which there is no longer a detectable transition. A guide to the eye for the expansion of this metastable region is shown by the colors in Fig. 3A. In the upper panel of Fig. 3B, we plot ∆T = T_c,warm – T_c,cool as a function of flake thickness, where T_c,warm and T_c,cool are the experimentally observed NC to C or C to NC transition temperature during the warming or cooling process, respectively. Here, T_c is determined by the temperature at which the first derivative peaks in the temperature sweep. ∆T is 60 K for the 20-nm flake, slightly larger than that for the bulk crystal (40 K), and grows to 120 K for the 4-nm device. In the same panel, we also plot the average temperature T_c,avg = (T_c,warm + T_c,cool)/2 of the transition. T_c,avg does not change substantially with thickness and remains between 180 and 190 K, which then implies that lower dimensionality does not stabilize either the NC or C phase. Instead, the NC (C) phase becomes increasingly metastable during cooling (warming) for thinner samples, indicating that the size of the energy barrier separating the NC and C phases increases (Fig. 1D).Open in a separate windowFig. 3.Dimensional dependence of phase transition—electron transport. (A) Thickness evolution of temperature-dependent resistivity around NC-C phase transition measured on hBN-covered ultrathin samples and 20-nm-thick flake. (B) Average transition temperature and temperature hysteresis (Upper) and normalized resistivity difference (Lower) between cooling and warming as a function of sample thickness. Open squares are corrections from contact resistance (Fig. S4). Hysteresis widens and resistivity difference decreases in thinner samples, whereas average transition temperature remains constant. Resistivity change can be used to estimate the discommensuration density 1/d at low temperature. (C) Circuit model of discommensuration network.Although ∆T increases when sample thickness is reduced, the resistivity jump associated with the phase transition decreases with decreasing thickness. In the bottom panel of Fig. 3B, we plot the resistivity difference ∆ρ between cooling and warming at T = 180 K, normalized to ρ in the more conducting state as a function of flake thickness. The closed circles are extracted directly from the data in Fig. 3A, whereas the open squares are corrections due to the effects of contact resistance (Fig. S4). For the 20-nm device, resistivity changes by an order of magnitude. The change is smaller for thinner devices and disappears completely for the 2-nm device, which indicates that more conducting NC discommensurations persist at low temperatures for thinner samples, consistent with the larger energy barriers required to remove them. Also, the resistivity jump becomes less abrupt, which is a reflection that the phase transition has slowed, as larger energy barriers generally act also to impede the kinetics of a phase transition. A simple circuit model presented in Fig. 3C allows us to connect the measured resistance jump in the NC-C transition, ∆R, with the estimated density of discommensurations 1/d left in the low temperature phase. We assume that the device resistance at low temperature is dominated by conduction through a random network of discommensuration channels (shown as white lines), which is generally sensitive to the particular microstructure formed. However, for device sizes much larger than d, we find the resistance with discommensuration channels would be R ∼ ρ_DC d, where ρ_DC is the resistivity per unit length of each discommensuration channel. Similarly, in the high temperature NC phase with a well-defined discommensuration network, we have R_NC ∼ ρ_DC D_NC, where we assume D_NC ∼ 80 Å (13, 14). From this, we can use the resistivity change in Fig. 3B to determine d: (ΔR/R_NC) ～ (d/D_NC) ? 1. On the right axis, we plotted d extracted for the different sample thicknesses. For the 2-nm sample, d ∼ D_NC, whereas it grows to 70–160 nm for the 20-nm sample.Open in a separate windowFig. S4.Extracting contact resistivity. Two- and four-terminal resistivity vs. temperature for 4-nm-thick flakes. The difference is proportional to resistivity of edge contacts.We can further substantiate the microscopic picture presented above by providing atomic structural analysis based on TEM. As before, the CDW structure is preserved by environmentally controlled hBN encapsulation. In Fig. 4A, we show diffraction images taken from two 1T-TaS₂ flakes of different thicknesses (12 and 2 nm). To highlight their temperature dependence, we have overlaid the diffraction patterns for each flake at 295 K (red peaks) and 100 K (blue peaks), our lowest achievable temperature. Ta Bragg peaks are again connected by a dashed triangle. Multiple scattering from hBN creates additional discernable peaks. The CDW peaks have been circled for easy identification. Although the peaks circled in gray appear qualitatively similar for both flakes, only the thicker flake displays additional peaks (circled in blue) at 100 K, indicating that it makes the transition to the C phase (compare with blue panel in Fig. 1A), whereas the thinner flake remains in the NC phase. This observation is consistent with our transport data as larger energy barriers in thinner samples require lower temperatures to realize the C phase.The movement of the gray-circled peaks with cooling (denoted by arrows, Fig. 4A) can be understood more quantitatively with reference to the zoom-in schematic shown in Fig. 4B (Upper Right). The position of this CDW peak is related to the periodicity D_NC of the NC domains (Upper Left) by a simple geometric expression (14): DNC=a/(2πΔϕ/360°)2+(Δλ/λC)2, where ∆ϕ is the difference in degrees between ϕ and ϕ_C = 13.9°, and ∆λ is the difference between the apparent wavelength averaged over many domains and λ_C = 13a. Thus, as the domain size grows, the NC peaks move closer to the C phase positions. We explicitly measured the position and angle of the CDW wave vectors for these two samples at several different temperatures during cooling to determine the domain period D_NC using the expression above. The results are plotted in the lower panel of Fig. 4B. For comparison, we also reproduce STM results obtained by Thomson et al. on the surface of a bulk crystal (14). For bulk samples, D_NC grows steadily from 60 to 90 Å on cooling from 340 to 215 K and then jumps to an arbitrarily large value on transition into the C phase at ∼180 K. At the same time, the width of the discommensuration regions remains relatively constant (∼22 Å) in all of the NC phase (13). As with our transport results, we find that reducing sample thickness suppresses the NC to C phase transition to lower temperatures during cooling and slows the CDW domain growth rate during the transition. For both of the thin flakes, the initial domain size at room temperature is similar to that that of the bulk crystal (D_NC = 60–70 Å). D_NC increases slightly upon cooling in the NC phase. For the 12-nm flake, the C phase is formed between 100 and 150 K, whereas the 2-nm flake remains in the NC phase even at 100 K. Its domain size here is much larger (D_NC ∼ 500 Å), however, indicating that the phase transition has begun to take place. This result is in clear contrast to bulk samples where the transition is abrupt.Our transport and TEM measurements both indicate that reduced dimensionality increases the energy barrier separating the NC and C CDW phases and thus widens the metastable region of the phase transition. The transition into the C phase involves melting or removal of the NC discommensuration network. Microscopically, energy barriers to discommensuration motion have been attributed to the presence of defects or impurities in the material, which act to pin them locally (20). Even in nominally pure CDW samples, clusters of localized defects have been observed by STM (21, 22), where the distance between defects is on the order of ∼10 nm. In bulk 1T-TaS₂, the interlayer stacking of NC domains make the discommensuration walls extended planar objects (15, 23), which are generally more difficult to pin. In two dimensions, however, the discommensurations become lines, which may be more easily immobilized. We have constructed a model of discommensuration pinning for a 2D system of thickness t (Fig. S5). We find that in the ultrathin limit where t is smaller than the mean distance between impurities, the pinning energy for a discommensuration plane scales as E_pin ∼ t^−2/3, corresponding to a cross-over from collective weak pinning to strong individual pinning. These strong pinning centers stabilize the NC discommensuration network at low temperatures during cooling and will also hinder the nucleation and growth of discommensurations when warming from the C phase, thus increasing the temperature region of metastability for both CDW phases in accordance with our experimental observation.Open in a separate windowFig. S5.Schematic picture of a DC plane and important length scales. A shows 3D view and B shows 2D projection. Red dots denote the location of impurities inside a dc plane. The effective mean impurity distance is l for t > l, whereas it is l_1D for t < l.By using this microscopic understanding of the NC-C phase transition in 2D samples, we may further elucidate the role of dc current in the measurements of Fig. 2 B and C. When the sample is cooled in equilibrium starting in the NC phase, the activation barrier between the NC and C states is continuously lowered, and therefore discommensurations are driven away and domain size grows steadily. Near the transition temperature, the small barrier can then be overcome with sufficient current flow, which depins the discommensurations to form the C phase ground state (Fig. 2C). On the other hand, when the sample is cooled out of equilibrium in the presence of a large dc current, it is likely that the domain size does not grow—the activation barrier remains large and the small-domain NC state persists on cooling to the lowest temperatures (Fig. 2B). The dc current is thus effectively a way to control the activation barrier between the NC and C phases.Although a spatially resolved study is still needed to fully understand these effects, our results have both clarified the nature of the 2D state in 1T-TaS₂ and demonstrated clear electrical control over the NC-C phase transition in ultrathin samples, further establishing the material’s relevance for device applications. We also expect our environmentally controlled techniques to be applicable for the study of other 2D transition-metal dichalcogenides that may be unstable under ambient conditions (24).     

Myriad manifestations of Williams syndrome

4 months male child presented with failure to thrive. On general examination child had normal O2 saturation with characterstic elfin facies. Further evaluation of the patient showed major manifestations of Williams syndrome in form of supravalvar aortic stenosis, branched pulmonary artery stenosis along with cardiomyopathy. Although the entity is known, this article shows comprehensive diagnostic workup with the aid of multimodality imaging techniques. The genetic diagnosis of Williams syndrome was confirmed using fluroscent in situ hybridisation techniques (FISH). In this patient most of the manifestations of elastin vasculopathy were noted in the form of involvement of ascending aorta, pulmonary arteries and myocardium. We also want to emphasis the importance of echocardiography in newborn patients with dysmorphic facies as Williams syndrome can be easily missed in neonatal period.A 4 month old male child presented with symptoms of heart failure and poor weight gain. On examination, O₂ saturation in both limbs was 99% and there was no significant blood pressure difference in all four limbs. He had a characterstic ‘elfin facies’ with a sunken nasal bridge, a long philtrum, wide mouth, prominent lower lip, small chin and low set ears (Fig. 1). 2D echocardiography showed situs solitus, concentric left ventricular hypertrophy with mild narrowing in the supravalvular region (Fig. 2) with systolic gradients of 26 mm Hg across the segment (Fig. 3) (Online Video 1). The right pulmonary artery (RPA) after its origin showed significant short segment stenosis with peak systolic gradients of 32 mmHg. The left pulmonary artery (LPA) after its origin showed mild narrowing (Figs. 4 and 5) (Online Video 2). Cardiac CT demonstrated supravalvular aortic stenosis (SVAS) with hour glass appearance of the aorta (Figs. 6 and 7) with bilateral pulmonary artery stenosis (PAS) involving RPA more than LPA (Figs. 8 and 9). Fluorescent in-situ hybridization (FISH) studies (Fig. 10) showed heterozygous deletion of elastin gene (Chromosome 7q11.23) and confirmed the diagnosis of Williams syndrome (WS).Open in a separate windowFig. 1Characterstic elfin facies.Open in a separate windowFig. 22D echocardiography showing mild narrowing in the supravalvular region.Open in a separate windowFig. 3Doppler showing gradients of 26 mm Hg across narrowed supravalvular region.Open in a separate windowFig. 42D echocardiography with color Doppler showing bilateral PAS.Open in a separate windowFig. 5Doppler investigation showing peak systolic gradients of 32 mmHg across the narrowed segment of RPA.Open in a separate windowFig. 6Cardiac CT with 3D reconstruction showing supravalvular aortic stenosis (SVAS).Open in a separate windowFig. 7Cardiac CT (Coronal section) showing SVAS.Open in a separate windowFig. 8Cardiac CT (Transverse section) showing bilateral PAS.Open in a separate windowFig. 9Cardiac CT with 3D reconstruction showing bilateral pulmonary artery stenosis (PAS) involving RPA more than LPA.Open in a separate windowFig. 10Fluorescent in-situ hybridization studies showing deletion of elastin gene (Chromosome 7q11.23).Supplementary data related to this article can be found online at http://dx.doi.org/10.1016/j.ihj.2015.02.026.The following are the Supplementary data related to this article:Video 1: Subcostal view showing turbulence in supravalvar region of aorta and the branched pulmonary arteries.Click here to view.^{(1.3M, mp4)}Video 2: High parasternal view showing confluent pulmonary arteries with turbulence across the branched pulmonary arteries.Click here to view.^{(853K, mp4)}WS is a genetic disorder occurring with a frequency of 1 in 20,000–50,000 live births. Manifestations of WS include congenital heart disease, hypertension, dysmorphic facial features, infantile hypercalcaemia and mental retardation. Apart from supravalvular AS and branched PA stenosis other cardiac abnormalities observed are bicuspid aortic valve, mitral valve regurgitation, coarctation of the aorta, ventricular or atrial septal defects. In neonates, cardiovascular symptoms were evident in 47% of WS children.1 PA stenosis often tends to regress spontaneously and SVAS tends to progress with time. In this patient most of the manifestations of elastin vasculopathy were noted in the form of involvement of ascending aorta and pulmonary arteries. The concentric left ventricular hypertrophy observed in our patient may be an expression of hypertrophic cardiomyopathy which is known to be associated with WS.1 In neonatal period all newborn patients with dysmorphic facies should be evaluated with echocardiography so that the cardiac abnormalities are not missed.     

Sinuous flow in metals

Annealed metals are surprisingly difficult to cut, involving high forces and an unusually thick “chip.” This anomaly has long been explained, based on ex situ observations, using a model of smooth plastic flow with uniform shear to describe material removal by chip formation. Here we show that this phenomenon is actually the result of a fundamentally different collective deformation mode—sinuous flow. Using in situ imaging, we find that chip formation occurs via large-amplitude folding, triggered by surface undulations of a characteristic size. The resulting fold patterns resemble those observed in geophysics and complex fluids. Our observations establish sinuous flow as another mesoscopic deformation mode, alongside mechanisms such as kinking and shear banding. Additionally, by suppressing the triggering surface undulations, sinuous flow can be eliminated, resulting in a drastic reduction of cutting forces. We demonstrate this suppression quite simply by the application of common marking ink on the free surface of the workpiece material before the cutting. Alternatively, prehardening a thin surface layer of the workpiece material shows similar results. Besides obvious implications to industrial machining and surface generation processes, our results also help unify a number of disparate observations in the cutting of metals, including the so-called Rehbinder effect.A typical cutting process involves removal of material in the form of a continuous chip in plane–strain (2D) (Fig. S1). When the material being cut (workpiece) is in an initially annealed state, an unusually thick chip results and the forces involved in the process are very large. This difficulty in cutting, well known in industrial practice (1, 2), has hitherto eluded fundamental explanation. At the mesoscale ( ～ 100 μm), the structure of the chip is assumed homogeneous, resulting from laminar plastic flow (3, 4). Using such a framework, augmented by ex situ observations (5), the high forces are attributed to the thick chip developed in the process, without an explanation of the cause of such anomalous chip formation. In this work, we revisit this long-held hypothesis using in situ observations and analysis, in the process unearthing a collective mode of plastic deformation.Open in a separate windowFig. S1.Schematic of idealized plane–strain cutting showing chip formation by smooth laminar flow, with simple shear. The deformation zone is highlighted in blue. Initial chip thickness h₀ is measured from free surface to the surface of material separation. The workpiece material undergoes plastic shape transformation to form a chip with final thickness h_c. The velocity of bulk material flow against the tool is V₀.Our model system consists of an annealed oxygen-free high-conductivity (OFHC) copper workpiece (grain size  ～ 500 μm) cut by a hard steel wedge (tool) at a velocity of V₀ = 0.42 mm/s. Temperature effects are negligible at this low velocity. Part of the workpiece material undergoes plastic (irreversible) shape transformation to form the chip (Fig. S1). The tool face is fixed to be normal to V₀, whereas the cutting depth (initial chip thickness) is maintained at h₀ = 50 μm. This model system mimics many natural (6) and industrial cutting (2) processes. The flow of metal against the tool face is observed in situ and photographed using a high-speed camera. The images are postprocessed using particle image velocimetry (PIV) to obtain a comprehensive record of velocity, strain rate, and strain field histories. This enables quantitative characterization of material flow past the tool edge. Additional experimental details are provided in Materials and Methods.Much to our surprise, the flow responsible for the shape transformation of the workpiece material into the chip, as revealed by the streakline pattern, bore little resemblance to any reported in classical plasticity. Fig. 1A, derived from a high-speed image sequence, shows streaklines that reveal a highly unsteady, sinuous flow with significant vorticity. The streaklines are extensively folded over in the chip, with peak-to-peak amplitudes in a single fold being as much as two-thirds of the chip thickness. Small surface protuberances, which form in the compressive field just ahead of the tool face, appear to trigger the folding; one such bump is bounded by two arrows (1 and 2) in Fig. 1. These arrows demarcate pinning points which are central to fold growth. The entire chip thus forms by repeated folding of the incoming material, i.e., sinuous flow—a collective plastic deformation mode, in the same genre as kinking (7) and shear banding (8, 9). In addition to Cu, sinuous flow was observed in other systems such as α-brass and commercially pure aluminum, showing that it is a truly mesoscopic mode, independent of the material’s crystal structure. Note that sinuous flow is not to be confused with the transition between laminar and rotational dislocation motion (10), which occurs at a much smaller scale.Open in a separate windowFig. 1.Sinuous flow mode of deformation in annealed copper. (A) Streakline pattern illustrating the underlying folding. Points 1 and 2 (red arrows) are pinning locations—the material between them forms a surface bulge while continuously rotating due to differential displacements. This is seen by the inclination of the fold peak with respect to the horizontal. (B) Optical micrograph of the chip. The back surface of the chip shows regular mushroom-like corrugations, separated by gaps. These are often misinterpreted as surface cracks. (C) Strain distribution in the chip, with mean ??? = 5.62. The highly inhomogeneous strain distribution inside the chip is clearly reflective of multiple folds during deformation. The figures in A–C correspond to different instants of time.The occurrence of sinuous flow cannot be inferred purely from postmortem structural observations in the chip or force measurements. As an illustration, an optical micrograph of the removed chip is shown in Fig. 1B. The surface of the chip shows repeated mushroom-like formations, with gaps in between. This structure has been (erroneously) described as resulting from homogeneous flow, supplemented by cracking on the chip free surface (1). In situ analysis reveals that the strain field in the chip is actually highly nonhomogeneous (Fig. 1C). Interestingly, this inhomogeneity is not reflected in the measured forces; no detectable oscillations occur at the fold frequency of around 1.7 Hz (Fig. S2).Open in a separate windowFig. S2.Energies and force in cutting annealed copper. A comparison between the cutting energy computed from force (E_force) measurements and PIV (E_PIV) analysis is shown. E_PIV = E_sin + E_sub, is obtained by integrating the stress along pathlines in the PIV flow field. E_sin and E_sub are the energies dissipated in the chip and the subsurface, respectively. The specific energy U_sin for sinuous flow (see main text) is E_sin per unit volume. The cutting force F_C is also shown. Interestingly, no fluctuations are observed in the force trace at the fold formation frequency  ～ 1.7 Hz.The kinematics of fold nucleation and development is clear from the motion of the initial bump and its boundaries (compare Fig. 1A). The set of four frames in Fig. 2 shows the evolution of such a bump into a fold. The two points P₁ and P₂, bounding the initial bump, move along with the material in each frame. A white dotted line—the bump axis—joins the peaks of adjacent streaklines, indicating the orientation of the impending fold. The color scheme depicts the underlying strain rate field, from PIV calculations. The development of multiple such folds in sinuous flow, along with superimposed streaklines and strain field, is also shown in Movie S1.Open in a separate windowFig. 2.Sequence of images with superimposed streaklines showing development of folds. The underlying strain rate field (with color bar inset) captures regions of local deformation. (A) P₁ and P₂ (marked by white arrows) are material locations that delimit the initial bump. These provide the pinning points for the surface bulge in B. As shear occurs closer to the tool face (C), this bulge rotates and is stretched diagonally, before finally forming an impending fold in D. Local shear is evident from the underlying strain rate field as well as the change in orientation of the bump axis (dashed white line) between B, C, and D.In Fig. 2A, P₁ and P₂, likely grain boundaries, delimit the initial bump and act as the local pinning points. They force the bump to deform plastically, resulting in a pronounced bulge on the free surface in Fig. 2B. The underlying strain rate field reflects this deformation in the two local colored zones surrounding the initial bump (Fig. 2 A and B). The bump axis is nearly parallel in both frames. Simultaneously with surface bulging, the workpiece material is also constantly forced against the vertical tool face. This constraint imparts a vertical velocity to each material point. The bulge in Fig. 2B is hence sheared, causing the axis to rotate in a counterclockwise direction (Fig. 2C). The magnitude of shear increases as the material nears the tool face; see the strain rate field in Fig. 2C. The bulge is amplified while also reducing its original width (Fig. 2D), with the material between P₁ and P₂ now constituting a single impending fold. Folding is complete once the original bump axis is rotated by nearly 90°, at which time another bulge is initiated ahead of the tool face and the process repeats.The chip hence comprises a series of folds, developed one after another in the manner above. Corresponding folds in the streakline pattern provide quantitative geometric fold characteristics as well as variations along the chip thickness. The results of this analysis are summarized in Fig. 3 (see SI Materials and Methods for details).Open in a separate windowFig. 3.Geometric parameters characterizing the observed folds. (A) Two adjacent streaklines (blue, red) are shown, demarcating a single fold. P is the fold peak (curve maximum), M₁, M₂ are fold troughs (curve minima), M is the midpoint of M₁M₂. P^′ is the maximum of the second streakline, the axial line PP^′ and the line PM subtend angles ϕ and θ with M₁M₂. The fold amplitude A and width W are the lengths of PM and M₁M₂, respectively. (B) Scatter plot of ϕ and θ. Data shown for the first (○), second (?), and third (□) streaklines from the free surface. Marker color indicates fold width W: red (cyan) corresponding to large (small) W. The values fall around the 45° line, deviation from which implies nonuniform streakline spacing. All of the wide folds undergo large shear whereas smaller ones remain upright (θ, ? ～ 90°) (C) Histogram of fold widths W. The mean width (dashed line) W_m ? 50 μm and one SD (dotted lines) are also shown. The mean wavelength of the folds is  ～ 200 μm at the point of formation.Inhomogeneous shear in the material can easily be seen in a plot of ϕ vs. θ, as shown in Fig. 3B. For symmetrically sheared folds, maxima of adjacent streaklines are expected to lie on the line PM, corresponding to the 45° line (dashed) in Fig. 3B. However, local shear results in varying distance between adjacent streaklines, as indicated in Fig. 3A. Additionally, both ϕ- and θ-values are clustered near 0° and 180°, which indicate large shear. Geometrically, this brings fold peaks P closer to the extrapolated minima line M₁M₂. Most wide folds undergo large shear, whereas a minor fraction (small folds) remain upright (θ, ? ? 90°) and form over existing larger folds.The distribution for W, including the mean W_m ? 50 μm and one SD, is shown in Fig. 3C. The wider folds (W ≥ 150 μm) occur near the beginning of the streaklines, getting progressively narrower as material flows past the tool. Subsequently, the small folds, constituting  ～ 10% of the total, are developed. The mean and maximum fold widths are smaller than the initial grain size in the material ( ～ 500 μm). The average fold wavelength is  ～  200 μm at the point of formation.The immediate consequence of this sinuous flow mechanism is that the resulting chip is quite thick—its final thickness h_c being 14× the initial thickness h₀. However, this significant thickening is not a priori indicative of the actual unsteady folding phenomenon, for such a shape change can also be envisaged in the framework of ideal smooth laminar flow (Fig. S1). Characteristically, however, the sinuous flow also produces a highly nonuniform strain field in the chip, fluctuating between 4 and 8, that reflects the underlying fold pattern (Fig. 1C). It is interesting to note that the representative (volume-weighted) strain for sinuous flow, ? ～ 5.6, is actually much lower than for an equivalent shape change by laminar flow, where ? ～ 8.1. This latter value is obtained if only the chip thickness ratio (h_c/h₀) is considered, without accounting for the actual flow process (2).Like the strain, the specific energy U (energy per unit volume) for chip formation, i.e., shape transformation, is also significantly smaller for the sinuous flow. By the usual integration of stress and strain along path lines in the sinuous flow field, U_sin is obtained as 2.9 J/mm³ (SI Materials and Methods and Fig. S2). In comparison, the corresponding value for an equivalent laminar flow (with ? = 8.1) is U_lam = 4.2 J/mm³, which is 45% greater than U_sin.Based on the strain and specific energy, the shape transformation into a chip is thus much more efficiently achieved by sinuous flow than by laminar flow. This is counterintuitive because, at first sight, the highly folded, sinuous flow appears quite inefficient, involving extensive redundant deformation. But, because selection of collective deformation modes is in general governed by their relative stability, the material’s preference for sinuous flow is likely the result of a flow instability in smooth laminar flow. Whereas there are other instances where large-strain plastic deformation occurs via nonhomogeneous modes, e.g., shear banding, kinking, and buckling, we are not aware of any prior observations of large shape changes being effected by the sinuous flow mode demonstrated here.Our observations have uncovered a previously unidentified mesoscopic flow mode in the plastic deformation of ductile metals, in the process also explaining a longstanding problem in cutting. The mechanism of fold formation appears to be strongly tied in with the large grain size and ductility common to such annealed metals and is driven primarily by the ability of the material to undergo large plastic deformation. Microscopically, each grain roughly constitutes a single fold, consistent with both the formation mechanism (Fig. 2) and fold width distributions (Fig. 3C). In this respect, it seems to have a similar origin as the folding mechanism reported in sliding wear (11), although the resulting flow here is significantly different—there is actual material removal, and folds of very large amplitude occur. Fold patterns observed in the sinuous flow show remarkable resemblance with other well-studied folding phenomena in geophysics (12), thin films (13), fluid flow (14, 15), and non-Newtonian plastics (16).The mechanism of fold development suggests that the difficulty in cutting annealed metals can be resolved if the sinuous flow mode is suppressed or eliminated altogether. Prestraining a thin surface layer (thickness  ～ h₀) of the annealed material to strains ? ≥ 1 causes refinement of the grain size and a reduction in the ductility. Doing so removes the two main triggers for sinuous flow, viz. bulge formation and the establishment of pinning points. Thus, prestraining should suppress the sinuous flow, a fact confirmed experimentally (Fig. 4A). The streakline pattern in the figure shows that the folding is eliminated, with an almost 70% reduction in both the cutting force and strain. Additionally, the flow is completely laminar, with a sharp, well-defined deformation zone and thin chip, as in the classical plasticity model. This surface prestraining can be accomplished by a suitable surface deformation process (17, 18).Open in a separate windowFig. 4.Suppression of sinuous flow. (A) Strain rate field with superimposed streaklines when cutting hardened copper. A sharply defined narrow shear zone is seen, as assumed in conventional plasticity models. The flow is laminar with insignificant bump formation ahead of the tool–chip interface. (B) Comparison of cutting forces (force in the direction of V₀) for different surface conditions. An annealed Cu sample (Inset, brown) is surface-coated over half its length with marking ink (Inset, blue). The cutting force in the uncoated region is very large (brown). A drastic reduction ( > 50%) is seen when cutting the material coated with ink (blue), due to sinuous flow suppression. Cutting a Cu sample with a thin prestrained (hardened) surface layer (Inset, red) results in low cutting force (red), reflective of laminar flow. The application of ink on the free surface of such a hardened layer shows no measurable effect on forces, consistent with the explanation based on sinuous flow.In light of the above observations, an intriguing possibility now presents itself—can sinuous flow be suppressed also by the simple application of a thin coating to the workpiece surface? Presumably, such a coating could be expected to modify the surface mechanical state (ductility, stiffness), thereby preventing the triggers for sinuous flow. To test this hypothesis, a layer of ink (Dykem) was painted onto the free surface of the annealed workpiece (Fig. 4B, Inset, and Fig. S1), before the cutting. Dykem ink, consisting of colored pigments in an alcohol (propanol + diacetone alcohol) medium, is commonly used to mark metals. Note that the surface of ink application is above the surface along which material separation occurs (Fig. S1), and away from the tool–chip contact. Interestingly, the bump formation ahead of the tool was much reduced by this ink application, with concomitant suppression of the folding and significantly lower forces resulting. Fig. 4B shows the large force drop observed when cutting an annealed Cu sample with the ink coated along half its length. When cutting the annealed workpiece region with no surface application (brown), sinuous flow occurs as expected, and the cutting force is very large. The force decreases by more than 50% when cutting over the workpiece region with the ink coating (blue), owing to sinuous flow suppression. This effect of the ink is very similar to that due to the prestrained surface layer, also shown for comparison (red). Application of a variety of other substances such as resins and nail polish, and even marking the surface with a sketch pen, was found to suppress the sinuous flow to various degrees. Such surface layer applications, however, did not have any noticeable influence on the forces and flow when cutting prestrained Cu, where the flow is intrinsically laminar. We hope to further explore this suppression hypothesis via additional controlled experiments and modeling.These results also offer a coherent picture of the Rehbinder effect (19) in the cutting of metals. This phenomenon concerns the small reduction ( < 10%) in cutting forces upon application of a suitable volatile fluid (e.g., CCl₄) on the workpiece free surface (20, 21). The effect has traditionally been attributed to either “microcracks” on the workpiece surface promoting a physicochemical effect (21, 22) or a fundamental change in the dislocation structure near the surface (20). Besides the speculative nature of these explanations, the reports of the force reductions have been inconsistent (23, 24). Sinuous flow provides a natural explanation for this effect—any surface application, including volatile CCl₄, will modify the surface mechanical state of the workpiece and inhibit initial bump formation ahead of the tool. Consequently, the folding will be diminished, resulting in lower forces. The inconsistent force reductions observed are hence most certainly due to the large variability in the initial state (annealed, partially/fully hardened) of the workpiece arising from the specific preparation procedures.Two important and contrasting implications of our observations involve the utility and suppression of sinuous flow. The highly “redundant” nature of the flow pattern suggests its use in designing new materials for energy absorption applications. This can be viewed as being complementary to materials with a tendency to form shear bands, such as metallic glasses (25). Chip structures, similar to those in Fig. 1B, have been reported in other metallic systems such as low carbon steels and pure iron (1, 5, 21), and microtomy of metals (26). This, together with our in situ observations in Cu, brass, and Al, points to the widespread occurrence of sinuous flow in annealed metals. Hence, this flow mode will also play an important role in micromachining (27) and surface deformation (17, 18) processes. On the other hand, as we have shown, a suitable surface treatment can suppress sinuous flow, thereby enabling easier processing of annealed metals. The large reduction in forces translates directly into an equivalent energy reduction. Furthermore, the reduced forces and energy dissipation should have favorable consequences for industrial machining, e.g., avoiding chatter-vibration instability across a broader range of process conditions, improved component surface quality, and enhanced tool life.     

Choosing experiments to accelerate collective discovery

A scientist’s choice of research problem affects his or her personal career trajectory. Scientists’ combined choices affect the direction and efficiency of scientific discovery as a whole. In this paper, we infer preferences that shape problem selection from patterns of published findings and then quantify their efficiency. We represent research problems as links between scientific entities in a knowledge network. We then build a generative model of discovery informed by qualitative research on scientific problem selection. We map salient features from this literature to key network properties: an entity’s importance corresponds to its degree centrality, and a problem’s difficulty corresponds to the network distance it spans. Drawing on millions of papers and patents published over 30 years, we use this model to infer the typical research strategy used to explore chemical relationships in biomedicine. This strategy generates conservative research choices focused on building up knowledge around important molecules. These choices become more conservative over time. The observed strategy is efficient for initial exploration of the network and supports scientific careers that require steady output, but is inefficient for science as a whole. Through supercomputer experiments on a sample of the network, we study thousands of alternatives and identify strategies much more efficient at exploring mature knowledge networks. We find that increased risk-taking and the publication of experimental failures would substantially improve the speed of discovery. We consider institutional shifts in grant making, evaluation, and publication that would help realize these efficiencies.A scientist’s choice of research problem directly affects his or her career. Indirectly, it affects the scientific community. A prescient choice can result in a high-impact study. This boosts the scientist’s reputation, but it can also create research opportunities across the field. Scientific choices are hard to quantify because of the complexity and dimensionality of the underlying problem space. In formal or computational models, problem spaces are typically encoded as simple choices between a few options (1, 2) or as highly abstract “landscapes” borrowed from evolutionary biology (3–5). The resulting insight about the relationship between research choice and collective efficiency is suggestive, but necessarily qualitative and abstract.We obtain concrete, quantitative insight by representing the growth of knowledge as an evolving network extracted from the literature (2, 6). Nodes in the network are scientific concepts and edges are the relations between them asserted in publications. For example, molecules—a core concept in chemistry, biology, and medicine—may be linked by physical interaction (7) or shared clinical relevance (8). Variations of this network metaphor for knowledge have appeared in philosophy (9), social studies of science (10–12), artificial intelligence (13), complex systems research (14), and the natural sciences (7, 15, 16). Nevertheless, networks have rarely been used to measure scientific content (2, 11, 17, 18) and never to evaluate the efficiency of scientific problem selection.In this paper, we build a model of scientific investigation that allows us to measure collective research behavior in a large corpus of scientific texts and then compare this inferred behavior with more and less efficient alternatives. We define an explicit objective function to quantify the efficiency of a research strategy adopted by the scientific community: the total number of experiments performed to discover a given portion of an unknown knowledge graph. Comparing the modal pattern of “real-science” investigations with hypothetical alternatives, we identify strategies that appear much more efficient for scientific discovery. We also demonstrate that the publication of experimental failures would increase the speed of discovery. In this analysis, we do not focus on which strategies tend to receive high citations or scientific prizes, although we illustrate the relationship between these accolades and research strategies (2).Our model represents science as a growing network of scientific claims that traces the accumulation of observations and experiments (see Figs. S1–S3). Earlier scientific choices influence subsequent exploration of the network (19). The addition of one redundant link is inconsequential for the topology of science. By contrast, a well-placed new link could radically rewire this network (20). Our model incorporates two key features of problem selection, importance and difficulty, which have received repeated attention in qualitative and quantitative investigations of science. We map these features onto two network properties, degree and distance, which are central to foundational models of network formation and search (21–23). First, scientists typically select “important,” central, or well-studied topics on which to anchor their findings and signal their relevance to others’ work (10, 24). Our model uses the degree of a concept in the network of claims (i.e., the number of distinct links in which it participates) as a measure of its importance (see Figs. S4–S6). In assuming that scientists’ research choices are influenced by concept degree, we posit that scientists are influenced by the choices of others, a well-attested choice heuristic (25, 26). Second, scientists introduce novelty into their work by studying understudied topics and by combining ideas and technologies that others are unlikely to connect (17, 20). Henri Poincaré (27) and many since (28) have observed that the most generative combinations are “drawn from domains that are far apart” (ref. 27, p. 24). When the concepts under study are more distant, more effort is required to imagine and coordinate their combinations (29). More risk is involved in testing distant claims, because no similar claims have been successful (30).^* We operationalize the “cognitive distance” between concepts using their topological distance in the knowledge network. If two concepts are not mutually reachable through the network (i.e., in two distinct components of the network), there is no way a scientist could hypothesize a connection simply by wandering through the literature; conceptual jumps must be made. If two molecules are distant in the network but can reach one another (i.e., they are in the same component), scientists would need to read a range of research articles—likely spread across several journals and subfields—to infer a possible connection (32). Drawing together these insights, we model unlikely combinations as connections between neglected (i.e., low degree), distant, or disconnected concepts within the network of scientific claims.Open in a separate windowFig. S1.Chemical examples from the published network. Central estradiol and cholesterol molecules were linked when hormone therapies were found to have no effect on reducing heart disease (PMID 10954759 and 12904517). RNA and zinc (PMID 4040853) were recombined in the discovery of “zinc fingers” of amino acids, which are essential for gene regulation and ribosome synthesis. Bromodeoxyuridine, which replaced thymidine in DNA and so “labeled” replicated DNA, allowed scientists to discover cell division in the adult hippocampus (PMID 9809557). HIV therapeutics zidovudine, indinavir, stavidine, and lamivudine were combined in clinical trials of promising antiretroviral mixtures (PMID 9287227). Commercially available protein kinase inhibitors, including KT 5720, rottlerin, quercetin, wortmannin, and the more recently discovered Y 27632, were tested against an array of protein kinases (PMID 10998351).Open in a separate windowFig. S3.(A, Top and Middle) The distribution of node degrees for each pair of chemicals in MEDLINE abstracts and in abstracts authored by prize-winning scientists (SI Text). The (log-)degree of the most and least central chemicals of each pair is normalized to [0,1] and the height of the figure represents the frequency with which each pair of chemical degrees appears in the literature. All degrees are evaluated on the full (2010) network. (A, Bottom)The “Citations” subplot shows citation counts greater and smaller than average in red and blue, respectively; the red scale has been set to the same maximum value as the blue to improve contrast. (A, Middle) The combined figure reveals how less common degree–degree combinations are more intensely cited than common degree–degree combinations. (B) Distribution of network distances between each pair of chemicals in MEDLINE abstracts and in abstracts written by prize winners. All distances were evaluated at time of linking; frequencies have been transformed to log₁₀-scale. ∞ distance indicates two chemicals that are mutually unreachable—disconnected—in the current network. The red and purple bands tracing the distributions are the 95% confidence intervals, constructed by considering the actual distribution of shortest paths as a sample from an underlying multinomial distribution (SI Text). Prize winners combine disconnected molecules significantly more frequently than others.Open in a separate windowFig. S4.(A) Annotated version of the generative model. (B) A simple network example, which calculates the probability associated with possible node connections. (C) The probability of choosing nodes separated by distance d_i,j, given different values of β and γ. (D) The probability that a scientist would investigate the relationship between X and Y, X and Z, and Y and Z in Fig. S4B, given different values of α_μ, α_ι, β, γ, and δ.Open in a separate windowFig. S6.(A) Infinite distances (δ parameter, estimated separately) over time. (B) Entropy of distance distributions (bits) as a function of time. As both distance distributions become more concentrated near distance 1, entropy decreases with time. Note that there are bursts of entropy that correlate across patents and biomedical publications and correspond with the bursts of jumps pictured in A. (C) Estimated preferences for finite distances (defined by β and γ parameters) in model estimated from data. (D) Distribution of measured distances as a function of time. MEDLINE and Patents become more conservative over time, restricting distance between chemicals selected. Researchers patent pairs with shorter distances than articles (相似文献   

The structure of tropical forests and sphere packings

The search for simple principles underlying the complex architecture of ecological communities such as forests still challenges ecological theorists. We use tree diameter distributions—fundamental for deriving other forest attributes—to describe the structure of tropical forests. Here we argue that tree diameter distributions of natural tropical forests can be explained by stochastic packing of tree crowns representing a forest crown packing system: a method usually used in physics or chemistry. We demonstrate that tree diameter distributions emerge accurately from a surprisingly simple set of principles that include site-specific tree allometries, random placement of trees, competition for space, and mortality. The simple static model also successfully predicted the canopy structure, revealing that most trees in our two studied forests grow up to 30–50 m in height and that the highest packing density of about 60% is reached between the 25- and 40-m height layer. Our approach is an important step toward identifying a minimal set of processes responsible for generating the spatial structure of tropical forests.Forests are one of the world’s best investigated ecosystems (1–4). However, despite all of the studies devoted to forests, mechanistic connections among important features of forest physiognomy are not fully understood. Of crucial importance for this are tree diameter distributions, which have been used for decades in ecology and forestry to characterize the state of forests. Tree diameter distributions are available for many forests of the world and allow together with tree allometries prediction of other important forest attributes like leaf area (5), basal area (6), above-ground biomass (7), tree density, and the presence or absence of disturbances (8). Tropical forests usually include many small trees and far fewer large ones (1, 9). Diameter distributions can also be predicted from dynamic forest models (10–13) in which the forest structure emerges from the interplay between the dynamic processes of mortality, regeneration, competition, and growth.In this study, we argue that tree diameter distributions of natural tropical forests can be predicted by stochastic packing theory—a method usually used in physics or chemistry—together with site-specific tree allometries. Packing systems have a long history of use across a wide range of disciplines, going back as far as Kepler’s analysis of regular packing of spheres (i.e., with a maximum of 74% filled volume). Irregular stochastic packing of spheres has been analyzed in the last decades and shows lower maximal packing densities (e.g., jammed sphere packing systems in physics, with 55–64% filled volume) (14, 15). We show here that simple principles of stochastic packing theory together with tree allometries and other simple structural rules allow for an accurate prediction of observed tree diameter distributions and related structural attributes for two tropical forests in Barro Colorado Island (BCI, Panama) and Sinharaja (Sri Lanka). Both forests show major differences in climate, soil, and topography that affect forest structure and dynamics (16, 17).Our approach consists of three parts. First, we use tree allometries to transform size data of a tree (including the position x and the stem diameter d, which are available from forest inventories or from the packing model) into a simplified tree with a crown modeled as sphere with radius c(d) and height h(d) (Fig. 1). We use the simple allometric relationships c(d) = c₀ d^p_c and h(d) = h₀ d^p_h with parameters c₀, h₀, p_h, and p_c determined from independent datasets (18, 19) (for details, see Methods). Other height-diameter relationships saturating in maximum tree height (7) could be used alternatively. However, because only few trees become large enough to experience this saturation, this has little influence on our results. The approximation of crowns as spheres is a simplification, given that crowns might shape differently during growth (20) (Fig. S1). In SI Results, we examined the influence of the assumed crown shape on our results (Fig. S2C).Open in a separate windowFig. 1.Representations of a tropical forest on BCI as a sphere packing system. Comparison of the sphere packing systems predicted by the model (A and B) and derived from the field data (C and D). We show 1-ha plots (A and C) and corresponding 100 × 10-m plot-transects (B and D) through the simulated and observed BCI forest. The higher canopy is only sparsely filled with tree crowns (B and D).Open in a separate windowFig. S1.Comparison of the modeled geometry of trees in different static and dynamic models. (A) Our approach of a packing of tree crowns in forests. (B) Macroecological models (27) that assume equal space filling (and resource use) across growth classes. (C) The perfect plasticity approximation including phototropism where tree crowns can shape differently and aside from their stem location (20, 24). (D) Thinning in crowded stands as simulated in dynamic forest gap models (11).Open in a separate windowFig. S2.Sensitivity of the chosen height discretization (A and B) for the leaf area distribution on BCI (50 ha). (A) Logarithmic binning with exponentially increasing height class widths. (B) Linear binning with constant height class widths of 1 m. (C) Sensitivity concerning crown geometry, i.e., a comparison of the original spherical crown and a cylindrical crown is shown. (D) Sensitivity of leaf area distribution dependent on the assumed individual tree’s leaf area within its crown (leaf area homogenous in full sphere vs. upper semisphere).Second, we simulate the static forest packing system (FPM) based on the following rules:

• i)A tree with a stem diameter d is randomly determined from a uniform distribution within the interval [d_min, d_max] (with d_min = 1 cm and d_max corresponding to the maximal tree height). Fig. S3 shows that our results are insensitive to the selection of d_min and d_max.Open in a separate windowFig. S3.Sensitivity of regional leaf area and tree diameter distribution concerning tree sizes. (A) Minimum (i.e., h_min) and (B) maximum tree height (i.e., h_max) are varied for BCI (50 ha). Simulation results show a single run of the forest packing model.
• ii)We accept a tree of stem diameter d only with probability p(d) (i.e., the survival probability of a tree growing from stem diameter d_min to diameter d). This rule thus considers average tree mortality and growth. For simplicity, we assumed constant annual stem diameter growth rates g and constant annual mortality rates m that yield a probability p(d) = p₀ exp[−(m/g)d] (Methods). For comparison, we investigated in this study two versions of our model: one without mortality (i.e., m = 0) and one with mortality.
• iii)Based on the allometric relationships between tree height h(d) and crown radius c(d), the stem diameter d is translated into a crown with center h(d) − c(d) above ground (Fig. 1 A and B). Thus, in contrast to irregular stochastic packing, each crown is located in a given height layer (depending on d). This height constraint will reduce the packing density.
• iv)We tentatively locate the stem and crown (and thus the tree) at a random position within the study area.
• v)The tree is retained if it does not overlap with an already placed tree (i.e., their crowns and stems).
• vi)The algorithm stops if the observed number of individual trees is placed.

Thus, the spatially explicit crown packing system emerges from model rules and simple site-specific tree allometries that are parameterized from the data or the literature (for details, see Methods). Results of a sensitivity analysis are provided in SI Results.Finally, in the third step, the crown packing systems are analyzed with methods of classical packing theory in terms of the space occupied by crowns (Fig. 2A), local forest height (Fig. 2B), and the distribution of leaf area and packing density at different heights and spatial scales (Fig. 2 C–E). To calculate the leaf area of crowns, we assumed for simplicity that they are homogeneously filled with leaves (see SI Results for results if we modify this assumption; Fig. S2D).Open in a separate windowFig. 2.Analysis of structural attributes for the BCI forest (based on inventory data). (A) Frequency distribution of the local crown packing density φ (in %) where φ is the proportion of space occupied by tree crowns (analysis of 20 × 20-m subplots, n = 1,250; using 2% class widths). (B) Frequency distribution of local forest height (in % of assumed maximum tree height) estimated for 20 × 20-m subplots (using 4% class widths). Green solid vertical lines represent mean values. (C) The average local packing density (dots) and SD (gray horizontal lines), estimated for different height layers (20 × 20-m subplots, using 1-m layer widths). (D) Same as C, but for the estimated leaf area distribution. (E) Leaf area distribution at different heights (using 1-m layer widths) estimated for the entire 50-ha forest.     

Dietary options and behavior suggested by plant biomarker evidence in an early human habitat

The availability of plants and freshwater shapes the diets and social behavior of chimpanzees, our closest living relative. However, limited evidence about the spatial relationships shared between ancestral human (hominin) remains, edible resources, refuge, and freshwater leaves the influence of local resources on our species’ evolution open to debate. Exceptionally well-preserved organic geochemical fossils—biomarkers—preserved in a soil horizon resolve different plant communities at meter scales across a contiguous 25,000 m² archaeological land surface at Olduvai Gorge from about 2 Ma. Biomarkers reveal hominins had access to aquatic plants and protective woods in a patchwork landscape, which included a spring-fed wetland near a woodland that both were surrounded by open grassland. Numerous cut-marked animal bones are located within the wooded area, and within meters of wetland vegetation delineated by biomarkers for ferns and sedges. Taken together, plant biomarkers, clustered bone debris, and hominin remains define a clear spatial pattern that places animal butchery amid the refuge of an isolated forest patch and near freshwater with diverse edible resources.Spatial patterns in archaeological remains provide a glimpse into the lives of our ancestors (1–5). Although many early hominin environments are interpreted as grassy or open woodlands (6–8), fossil bones and plant remains are rarely preserved together in the same settings. As a result, associated landscape reconstructions commonly lack coexisting fossil evidence for hominins and local-scale habitat (microhabitat) that defined the distribution of plant foods, refuge, and water (7). This problem is exacerbated by the discontinuous nature and low time resolution often available across ancient soil (paleosol) horizons, including hominin archaeological localities. One notable exception is well-time-correlated 1.8-million-y-old paleosol horizons exposed at Olduvai Gorge. Associated horizons contain exceptionally preserved plant biomarkers along with many artifacts and fossilized bones. Plant biomarkers, which previously revealed temporal patterns in vegetation and water (8), are well preserved in the paleosol horizon and document plant-type spatial distributions that provide an ecosystem context (9, 10) for resources that likely affected the diets and behavior of hominin inhabitants.Plant biomarkers are delivered by litter to soils and can distinguish plant functional type differences in standing biomass over scales of 1–1,000 m² (11). Trees, grasses, and other terrestrial plants produce leaf waxes that include long-chain n-alkanes such as hentriacontane (nC₃₁), whereas aquatic plants and phytoplankton produce midchain homologs (e.g., nC₂₃) (12, 13). The ratio of shorter- versus long-chain n-alkane abundances distinguish relative organic matter inputs from aquatic versus terrestrial plants to sediments (13):P_aq = (nC₂₃ + nC₂₅)/(nC₂₃ + nC₂₅ + nC₂₉ + nC₃₁).Sedges and ferns are prolific in many tropical ecosystems (14). These plants both have variable and therefore nondiagnostic n-alkane profiles. However, sedges produce distinctive phenolic compounds [e.g., 5-n-tricosylresorcinol (ⁿR₂₃)] and ferns produce distinctive midchain diols [e.g., 1,13-dotriacontanediol (C₃₂-diol)] (SI Discussion).Lignin monomers provide evidence for woody and nonwoody plants. This refractory biopolymer occurs in both leaves and wood, serves as a structural tissue, and accounts for up to half of the total organic carbon in modern vegetation (11). Lignin is composed of three phenolic monomer types that show distinctive distributions in woody and herbaceous plant tissues. Woody tissues from dicotyledonous trees and shrubs contain syringyl (S) and vanillyl (V) phenols (12), whereas cinnamyl (C) phenols are exclusively found in herbaceous tissues (12). The relative abundance of C versus V phenols (C/V) is widely used to distinguish between woody and herbaceous inputs to sedimentary and soil organic matter (15).Plant biomarker ¹³C/¹²C ratios (expressed as δ¹³C values) are sensitive indicators of community composition, ecosystem structure, and climate conditions (8). Most woody plants and forbs in eastern Africa use C₃ photosynthesis (6), whereas arid-adapted grasses use C₄ photosynthesis (8, 14). These two pathways discriminate differently against ¹³C during photosynthesis, resulting in characteristic δ¹³C values for leaf waxes derived from C₃ (about –36.0‰) and C₄ (–21.0‰) plants (16). Carbon isotopic abundances of phenolic monomers of lignin amplify the C₃–C₄ difference and range between ca. –34.0‰ (C₃) and –14.0‰ (C₄) in tropical ecosystems (15). Terrestrial C₃ plant δ¹³C values decrease with increased exposure to water, respired CO₂, and shade (8), with lowest values observed in moist regions with dense canopy (17). Although concentration and δ¹³C values of atmospheric CO₂ can affect C₃ plant δ¹³C values (17), this influence is not relevant to our work here, which focuses on a single time window (SI Discussion). The large differences in leaf-wax δ¹³C values between closed C₃ forest to open C₄ grassland are consistent with soil organic carbon isotope gradients across canopy-shaded ground surfaces (6) and serve as a quantitative proxy for woody cover (f_woody) in savannas (8).As is observed for nonhuman primates, hominin dietary choices were likely shaped by ecosystem characteristics over habitat scales of 1–1,000 m² (3–5). To evaluate plant distributions at this small spatial scale (9), we excavated 71 paleosol samples from close-correlated trenches across a ∼25,000-m² area that included FLK Zinjanthropus Level 22 (FLK Zinj) at Olduvai Gorge (Fig. 1). Recent excavations (18–21) at multiple trenches at four sites (FLK^NN, FLK^N, FLK, and FLK^S, Fig. 1D) exposed a traceable thin (5–50 cm), waxy green to olive-brown clay horizon developed by pedogenic alterations of playa lake margin alluvium (22). Weak stratification and irregular redox stains suggest initial soil development occurred during playa lake regression (18, 22), around 1.848 Ma (ref. 23 and SI Discussion). To date, craniodental remains from at least three hominin individuals (18–20), including preadolescent early Homo and Paranthropus boisei, were recovered from FLK Zinj. Fossils and artifacts embedded in the paleosol horizon often protrude into an overlying airfall tuff (18, 19), which suggests fossil remains were catastrophically buried in situ under volcanic ash. Rapid burial likely fostered the exceptional preservation of both macrofossils (10) and plant biomarkers across the FLK Zinj land surface.Open in a separate windowFig. 1.Location and map of FLK Zinj paleosol excavations. (A and B) Location of FLK Zinj as referenced to reconstructed depositional environments at Olduvai Gorge during the early Pleistocene (18, 22) and the modern gorge walls. The perennial lake contained shallow saline–alkaline waters that frequently flooded the surrounding playa margin (i.e., floodplain) flats. (C) Outline of FLK Zinj paleosol excavation sites used for our spatial biomarker reconstructions. (D) Concentric (5 m) gridded distribution map of FLK Zinj paleosol excavations relative to previous archaeological trenches (18–21). Major aggregate complexes (FLK^NN, FLK^N, FLK, and FLK^S) are color-coded to show excavation-site associations.Plant biomarker signatures reveal distinct types of vegetation juxtaposed across the FLK Zinj land surface (Figs. 2–4 and Fig. S1). In the northwest, FLK^NN trenches show high nC₂₃ δ¹³C values (Fig. 2B) as well as high C/V and P_aq values (Figs. 3 and ​and4A).4A). They indicate floating or submerged aquatic plants (macrophytes) in standing freshwater (13), a finding that is consistent with nearby low-temperature freshwater carbonates (tufa), interpreted to be deposited from spring waters (22). Adjacent FLK^N trenches have lower P_aq values (Fig. 4A) with occurrences of fern-derived C₃₂-diol and sedge-derived ⁿR₂₃ (Fig. 2 C and D). These biomarker distributions indicate an abrupt (around 10 m) transition from aquatic to wetland vegetation. Less than 100 m away (Fig. 1C), low nC₃₁ δ¹³C values (Fig. 2A) and low C/V and very low P_aq values (Figs. 3 and ​and4A)4A) collectively indicate dense woody cover (Fig. 4B). In the farthest southeastern (FLK^S) trenches, high C/V values and high δ¹³C values for C lignin phenols (Fig. 3) indicate open C₄ grassland.Open in a separate windowFig. 2.Spatial distributions and δ¹³C values for plant biomarkers across FLK Zinj. Measured and modeled δ¹³C values (large and smaller circles, respectively) are shown for (A) nC₃₁ from terrestrial plants, (B) nC₂₃ from (semi)aquatic plants, (C) C₃₂-diol from ferns, and (D) ⁿR₂₃ from sedges (see refs. 12 and 13 and SI Discussion). Modeled values [inverse distance-weighted (9)] account for spatial autocorrelation (15-m radius) in standing biomass (35) over scales of soil organic matter accumulation (11). Black dots represent paleosols with insufficient plant biomarker concentrations for isotopic analysis.Open in a separate windowFig. 3.Molecular and isotopic signatures for lignin phenols across FLK Zinj. Bivariate plots are shown for diagnostic lignin compositional parameters (see refs. 12 and 15 and Fig. 1C). Symbols are colored according to respective δ¹³C values for the C lignin phenol, p-coumaric acid. FLK symbols are uncolored due to insufficient p-coumaric acid concentrations for isotopic analysis. Representative lignin compositional parameters (12, 15) are shown for monocotyledonous herbaceous tissues (G), dicotyledonous herbaceous tissues (H), cryptogams (N), and dicotyledonous woody tissues (W).Open in a separate windowFig. 4.Spatial relationships shared between local plant resources and hominin remains. Measured and modeled values (large and smaller circles, respectively) are shown for (A) P_aq (13) and (B) f_woody (8). Modeled values [inverse distance-weighted (9)] account for spatial autocorrelation (15-m radius) in standing biomass (35) over scales of soil organic matter accumulation (11). (C) Kernel density map of cut-marked bones (18–21) across the FLK Zinj land surface (Fig. S4). High estimator values indicate hotspots of hominin butchery (Fig. S5). A shaded rectangle captures the area (ca. 0.68 probability mass) with highest cut-marked bone densities and is shown in A and B for reference.Open in a separate windowFig. S1.Total ion chromatograms for saturated hydrocarbons in representative paleosols at (A) FLK^NN, (B) FLK^N, (C) FLK, and (D) FLK^S. C₂₃, tricosane; C₂₅, pentacosane; C₂₉ nonacosane; C₃₁, hentriacontane.Biomarkers define a heterogeneous landscape at Olduvai and suggest an influence of local resources on hominin diets and behavior. It is recognized (2, 24–26) that early Homo species and P. boisei had similar physiological characteristics. These similarities in physical attributes suggest behavioral differences were what allowed for overlapping ranges and local coexistence (sympatry) of both hominins. For instance, differences in seasonal subsistence strategies or different behavior during periods of drought and limited food could have reduced local hominin competition and fostered diversification via niche specialization (27–29).Physical and isotopic properties of fossil teeth indicate P. boisei was more water-dependent [low enamel δ¹⁸O values (24)] and consumed larger quantities of abrasive, ¹³C-enriched foodstuffs [flat-worn surfaces (25) and high enamel δ¹³C values (26)] than coexisting early Homo species. Although ¹³C-enriched enamel is commonly attributed to consumption of C₄ grasses or meat from grazers (14), this was not likely, because P. boisei craniodental features are inconsistent with contemporary gramnivores (24, 25) or extensive uncooked flesh mastication (26). Numerous scholars have proposed the nutritious underground storage organs (USOs) of C₄ sedges were a staple of hominin diets (14, 24, 26, 27). Consistent with this suggestion, occurrences of ⁿR₂₃ attest to the presence of sedges at FLK^NN and FLK^N (Fig. 2D). However, the low δ¹³C values measured for ⁿR₂₃ at these same sites (Fig. 2D and Fig. S2) indicate C₃ photosynthesis (12, 16), a trait common in modern sedges that grow in alkaline wetlands and lakes (30) (Fig. S3). Thus, biomarker signatures support the presence of C₃ sedges in the wetland area of FLK Zinj.Open in a separate windowFig. S2.Total ion chromatogram [TIC (A)] and selected ion chromatograms for derivatized 5-n-alkylresorcinols [m/z 268 (●)] and midchain diols [m/z 369 (○)] from a representative paleosol at FLK^N. Also shown are δ¹³C values for homologous (B) 5-n-alkylresorcinols and (C) midchain diols. C₃₂-diol, dotriacontanediol; ⁿR₂₃, tricosylresorcinol.Open in a separate windowFig. S3.Summary phyogenetic consensus tree of Cyperaceae (sedges) based on nucleotide (rcbL and ETS1f) sequence data (50–54, 95, 96). Important taxonomic distinctions discussed in SI Discussion, Fern Alkyldiols are shown explicitly. Triangle-enclosed digits represent the number of additional branches at different levels of taxonomic classification. CEFA, Cypereae Eleocharideae Fuireneae Abildgaardieae; CSD, Cariceae Scirpeae Dulichieae.Alternative foodstuffs with abrasive, ¹³C-enriched biomass include seedless vascular plants (cryptogams), such as ferns and lycophytes [e.g., quillworts (27, 30)]. Ferns are widely distributed throughout eastern Africa in moist and shaded microhabitats (31) and are often found near dependable sources of drinking water (32). Today, ferns serve as a dietary resource for humans and nonhuman primates alike (27), and fiddlehead consumption is consistent with the inferred digestive physiology [salivary proteins (33)] and the microwear on molars (34) of P. boisei in eastern Africa (25, 26). Ferns were present at FLK^N, based on measurements of C₃₂-diol (Fig. 2D). Further, the high δ¹³C values measured for these compounds are consistent with significant fern consumption by P. boisei at Olduvai Gorge.Ferns and grasses were not the only plant foods present during the time window documented by FLK Zinj. Further, the exclusive reliance on a couple of dietary resources was improbable for P. boisei, because its fossils occur in diverse localities (24–26). Aquatic plants are an additional candidate substrate, as evidenced by high P_aq values at FLK^NN and FLK^N (Fig. 4A). Floating and submerged plants proliferate in wetlands throughout eastern Africa today (13, 14), and many produce nutritious leaves and rootstock all year long (27, 28). Although C₄ photosynthesis is rare among modern macrophytes (30), they can assimilate bicarbonate under alkaline conditions, which results in C₄-like isotope signatures in their biomass (30). Their leaf waxes, such as nC₂₃ (13), are both present and carry ¹³C-enriched signatures at FLK^NN and FLK^N (Fig. 2B). It is also likely that aquatic macrophytes sustained invertebrates and fish with comparably ¹³C-enriched biomass, as they do in modern systems (14), and we suggest aquatic animal foods could have been important in P. boisei diets (27, 28).Biomarkers across the FLK Zinj soil horizon resolve clear patterns in the distribution of plants and water and suggest critical resources that shaped hominin existence at Olduvai Gorge. The behavioral implications of local conditions require understanding of regional climate and biogeography (3–5, 7), because hominin species likely had home ranges much larger than the extent of excavated sites at FLK Zinj. Lake sediments at Olduvai Gorge include numerous stacked tuffs with precise radiometric age constraints (23). These tephrostratigraphic correlations (21) tie the FLK Zinj landscape horizon to published records of plant biomarkers in lake sediments that record climate cycles and catchment-scale variations in ecology. Correlative lake sediment data indicate the wet and wooded microhabitats of FLK Zinj sat within a catchment dominated by arid C₄ grassland (8). Under similarly arid conditions today, only a small fraction of landscape area (ca. 0.05) occurs within 5 km of either forest or standing freshwater (35). Given a paucity of shaded refuge and potable water in the catchment, the concentration of hominin butchery debris (18–21) exclusively within the forest microhabitat and adjacent to a freshwater wetland (Fig. 4) is notable. We suggest the spatial patterns defined by both macro- and molecular fossils reflect hominins engaged in social transport of resources (1–5), such as bringing animal carcasses and freshwater-sourced foods from surrounding grassy or wetland habitats to a wooded patch that provided both physical protection and access to water.     

Self-removal of condensed water on the legs of water striders

The ability to control drops and their movements on phobic surfaces is important in printing or patterning, microfluidic devices, and water-repellent materials. These materials are always micro-/nanotextured, and a natural limitation of repellency occurs when drops are small enough (as in a dew) to get trapped in the texture. This leads to sticky Wenzel states and destroys the superhydrophobicity of the material. Here, we show that droplets of volume ranging from femtoliter (fL) to microliter (μL) can be self-removed from the legs of water striders. These legs consist of arrays of inclined tapered setae decorated by quasi-helical nanogrooves. The different characteristics of this unique texture are successively exploited as water condenses, starting from self-penetration and sweeping effect along individual cones, to elastic expulsion between flexible setae, followed by removal at the anisotropic leg surface. We envision that this antifogging effect at a very small scale could inspire the design of novel applicable robust water-repellent materials for many practical applications.When a vapor condenses on a rough hydrophobic surface, liquid nuclei naturally appear within the roughness, forming tiny droplets stuck in the texture (1–3). Without the assistance of external forces, dew tightly adheres to the surface in the so-called Wenzel state, which most often destroys the superhydrophobicity of the material (4, 5). An applicable robust water-repellent surface thus requires an additional mechanism to expel these condensates from the texture (6). It has been reported in the literature that nanotextures (such as found on the surface of lotus leaves or cicada wings) might generate adhesion forces small enough to permit an efficient conversion of surface energy (coming from droplet coalescence) into kinetic energy, so that droplets can be mobilized (7–9). However, contact angle hysteresis effects are generally dominant at a small scale, so that a key challenge for antifogging materials lies in the generation of a force able to expel droplets from microtextures.Water striders (Gerris remigis, Fig. 1A) living at the water surface in a highly humid environment offer a remarkably simple solution to this problem. Without any external force, tiny condensed droplets in the range of femtoliters (fL) to microliters (μL) get removed from striders’ legs, owing to the presence of oriented conical setae. A Gerris leg is a centimeter-size cylinder (of typical diameter 150 μm) decorated by an array of inclined tapered hairs characterized in Fig. 1 B and C by micro X-ray computed tomography (XCT) and scanning electron microscopy (SEM). Individual setae have a length L = 40–50 μm, a maximum diameter of ∼3 μm, and an apex angle of ∼5°. They make regular arrays with a mutual distance of 5–10 μm, and are tilted by an angle β = 25–35° to the base of the leg (Fig. 1 B and C and Fig. S1). In addition, longitudinal or quasi-helicoidal nanogrooves are found on the seta surface (10), as shown in Fig. 1C, Inset.Open in a separate windowFig. 1.Cascade of self-motions for water droplets condensing on a leg of water strider. (A) G. remigis, an insect commonly called water strider, lives at the surface of water in a highly humid environment. (B) Micro-XCT and (C) SEM images of a strider’s leg. It is composed of tilted conical setae, and nanogrooves decorate each seta (Inset). (D–G) Water condensation in a leg placed in a fog: as we follow the drop pointed out by a yellow arrow, three successive dynamical steps are observed, eventually leading to the expulsion of water. Magnification is kept constant (scale bar, 15 μm), and time is indicated in each picture. Corresponding movie is Movie S1. (D and E, step 1) Tiny droplets self-propel on single setae, before stopping when contacting another seta. Then, droplets grow by merging with neighbors (red arrows) (F, step 2) As condensation proceeds, a growing drop deforms the surrounding setae enough to generate an elastic force able to expel it at t = 3.6 s out of the structures (red arrow). Image persistence is used to give the feeling of this quick motion. (G, step 3) At the leg surface, coalescence between neighboring drops produces directional motion at t = 6.48 s (red arrow). Again, image persistence is used to suggest fast motion. Hence droplets at a micrometric scale can be self-removed, a key fact for keeping legs dry in a humid atmosphere.Open in a separate windowFig. S1.Microstructure of water strider leg. (A and B) Micro-XCT images indicate that the surface of water strider leg is composed of setae array, which is oriented toward the tip of the leg with ∼27° tilt angle. (C and D) SEM images of water strider leg reveal that the setae are all conical with an apex angle of ∼5°, in a periodicity of 5–10 μm between the neighboring setae. (E and F) Magnified SEM images show that the setae are composite of nanogrooves in longitudinal or quasi-helix orientation.Fig. 1 D–G and Movie S1 show what happens when a Gerris leg is placed in a mist. Micrometric drops condense at the setae surface, and it is first observed that these droplets slowly move away from the seta tip and sink inside the texture (Fig. 1D). This motion stops when the liquid reaches proximal setae, and drops keep on growing owing to condensation and coalescence (Fig. 1E)––the usual growth events in a breath (Fig. 1). Drops above a critical size push away the setae they contact, as revealed by their shape: they slightly elongate in the direction parallel to the setae, until they get suddenly expelled out of the hairs (Fig. 1F). Once at the top of the setae, drops still grow but coalescence is biased, and water moves along a preferred direction, which also contributes to remove it from the leg surface (Fig. 1G).This sophisticated mechanism of drop expulsion can be divided into three steps, as proposed in Fig. 1. In step 1, droplets self-propel along the surface of single conical hairs (Movie S2) and then grow. In step 2, the growth deforms the setae array, which leads to expulsion (Movie S3). In step 3, coalescence at the leg surface results in a rapid anisotropic motion of the merged drops along the surface or away from it (Movies S4 and S5). Gerris live at the water surface in a highly humid environment, and they must repel water not only at a large scale to keep floating, but also at the scale of microdrops forming from the surrounding atmosphere, in particular on the side of the leg directly facing water. By exploiting the unique design of their legs, water striders seem to be able to remove dew at a femtoliter scale, a key condition for avoiding a gradual penetration of water in the leg textures, which would lead to failure of the superhydrophobicity needed by insects to stay at the water surface.To follow the trajectory X(t) of drops and the associated dynamical phenomena during condensation, we used high-speed imaging (films shot at 1,000 frames per second) mounted on a microscope. Small water droplets (below 3 fL) from the mist randomly condense on the setae and start moving along them, from tip to base (step 1, Fig. 2A). The velocity in this phase can reach about 1 mm/s before decreasing: The drop stopped after it traveled by typically 10 μm, a distance comparable yet smaller than the setae length (Fig. 2B). We statistically analyzed the size distribution of 200 such mobile droplets (Fig. 2C), and found diameters ranging from 2 to 9 μm, with an average size of 5.7 ± 0.9 μm at the beginning of motion, and 6.2 ± 0.9 μm at the end (blue and red distributions in Fig. 2C, respectively). These drops generally do not coalesce with each other, but just move individually along the seta, which explains why both distributions nearly overlap. Fig. 2C also shows that droplets need to be large enough (around 3–4 μm) to move––at smaller scales, pinning forces can overcome the force driving the motion; hence continuous condensation triggers movement. Another way of capturing these different facts consists of comparing the position X and diameter D of 10 droplets between beginning and end of motion (Fig. 2C, Inset, where each symbol corresponds to a drop). This plot confirms that the volume does not change significantly during motion and that droplets stop at a well-defined position, typically 10–15 μm away from the seta tip. This first dynamical step seems to contradict dew expulsion, and it may be exploited by creatures to sweep tiny drops or contaminants along the setae.Open in a separate windowFig. 2.Droplets self-propelling along single conical setae (step 1). (A) As a strider leg is exposed to a fog, tiny droplets first condense at the tip of setae, before spontaneously moving toward their base. We follow the drop pointed out by a yellow arrow, and observe that it self-propels and sinks within the texture by 10 μm in less than 20 ms. Corresponding movie is Movie S2. (B) Typical plot of droplet position X as a function of time t: Water travels by a distance comparable to the seta length at a roughly constant velocity (around 0.5 mm/s) before stopping. Origin of X is chosen at the seta tip. (C) Statistics of 200 self-propelling droplets, of diameter ranging from 2 to 9 μm. Their average sizes at beginning and end of motion are 5.7 ± 0.9 μm (in blue) and 6.2 ± 0.9 μm (in red), respectively. (Inset) The diameter and position of 10 droplets (each one designated by a symbol) before and after moving confirm that drops generally do not coalesce with others, but just move individually along setae and stop at a well-defined position, typically 10–15 μm away from the seta tip. (D) For a droplet at the surface of a single seta, the conical geometry provides an asymmetric surface energy landscape, which generates a motion (see text).Self-propulsion is remarkable at this scale, where surface effects and specifically contact angle hysteresis could impede motion. Three facts facilitate mobility. (i) Setae are hydrophobic, so that drops are naturally ejected on one side of the cone (as seen in Fig. 2A), instead of being axisymmetric (11), which minimizes the solid–liquid contact and the associated pinning. (ii) Substructures (nanogrooves; Fig. 1C, Inset) should amplify the hydrophobicity of setae, and contribute to drop mobility. (iii) The cone geometry provides curvature gradients (Fig. 2D and Fig. S2), and thus an asymmetric surface energy landscape, which permits a motion (12–15). A simple argument allows us to understand the origin of the driving force. Let us consider a conical substrate with a Young contact angle close to 90° (a typical hydrophobicity). In such a case, a comparison between surface energies as drops move along the cone reduces to liquid–vapor energies, because solid–liquid and solid–vapor interfaces have common surface tensions. A drop on a seta tip, that is, on a substrate of radius r much smaller than its own radius R, has a surface energy E ∼ 4πR²γ, denoting γ as the surface tension of water. When water moves to regions of larger and larger r (Fig. 2D), its shape becomes closer and closer to a hemisphere of radius R′ = 2^1/3R, which it becomes on a substrate of infinite radius. Then its surface energy simply writes E′ ∼ 2πR′²γ ∼ 2^5/3πR²γ, that is, an energy smaller than E by 2^−1/3, i.e., about 25%: Drops in this case are drawn by surface tension. The driving force should be smaller if the apparent angle θ is larger than 90°, owing to the presence of nanogrooves: then, the liquid far from the tip forms a spherical cap of radius R^′ = R(1/2?(3?cosθ/4)+(cos³θ/4))^?(1/3) sitting on a cylinder (12, 16–18), of corresponding surface energy E′:E′=E[1−(1+cosθ)24R′21H2],[1]denoting H as the mean curvature of the solid. Curvature decreases as water goes from the tip to the seta base, and so does the energy E′ (Figs. S3–S5).Open in a separate windowFig. S2.Conical structure of setae and their nanogrooves. (A and B) The diameters of setae (D) in different positions away from the tip (L₁) present conical structures with conicity (D/2L) of 0.035. (C and D) The diameters of V-shaped nanogrooves (D) in different positions away from the tip of V-shape (L₂) present similar conical structures with conicity (D/2L) of 0.249.Open in a separate windowFig. S3.Drop motion on a single conical seta. When placed in fog, very tiny droplets (identified by numbers 1 and 2) could be condensed on the tip of seta (0 s). As water condensation continues, droplet 1 spontaneously rolled on a single conical seta from the tip to the base (0.163 s), and coalesced with droplet 2 to form larger water drops (droplet 1 + 2, 0.199 s). Similarly, this new larger drop could also move directionally to the base of setae (from 0.316 to 0.444 s), showing a self-propelled motion behavior.Open in a separate windowFig. S5.Drop motion on a superhydrophobic conical copper wire. For a superhydrophobic conical copper wire, drops could move toward the base of the wire when placed in mist.Open in a separate windowFig. S4.Drop motion on a hydrophobic conical copper wire. For a hydrophobic conical copper wire, condensed drops could coalesce anisotropically toward the base of the wire when placed in mist.Once drops stop within the setae, they grow owing to further condensation and coalescence with neighbors (Fig. 1E). We show in Fig. 3A the sudden dynamical event following this stage, corresponding to step 2 in Fig. 1F. Water moves (or jumps) in the direction opposite to the one in step 1, until its complete expulsion from the array of setae. Big droplets (about 1 pL) eventually sit at the tips of setae, from which they can be easily removed. Drop anisotropy in step 2 first increases, as guessed in Fig. 3A and observed in Fig. 3B, where we plot transverse and longitudinal diameters D₁ and D₂ as a function of time (blue and red data). The anisotropy factor D₂/D₁ increases from 1 to about 1.3, while drop position X remains fixed, until the anisotropy factor relaxes to 1, which corresponds to the jump (fast increase of X). The isotropic drop observed after expulsion always has a diameter larger than its transverse diameter before expulsion, because averaging on 200 drops shows an increase from ∼6.5 μm to ∼12.5 μm, as reported in Fig. 3C with blue and red distributions, respectively. This can also be seen in Fig. 3C, Inset, where 10 individual drop sizes are followed as they are expelled out of the array of setae. All these features can be understood by the ability of hairs to deform as a trapped drop grows. Drop elongation is a signature of this process, and we indeed observe that the typical diameter of expelled drops compares with the average distance between setae: Elastic deformation provides the energy necessary to expel the liquid out of the texture (Fig. 3D).Open in a separate windowFig. 3.Expulsion of water out of the setae (step 2). (A) As condensation proceeds, drops inside the texture grow and deform the array of setae, so that the arising elastic force can expel them out of the hairs. Here, we follow the drop pointed out by a yellow arrow, and note that it is deformed when it jumps. Corresponding movie is Movie S3. (B) Position X (empty symbols) and principal diameters D₁ (in blue) and D₂ (in red, D₁ < D₂) of the drop, as a function of time t. Just before its expulsion, the drop becomes strongly anisotropic. Origin of time is defined at the onset of anisotropy. (C) Diameter distribution of 200 drops: The drop after expulsion (in red) is always larger than before expulsion (in blue). Diameter and position changes of 10 droplets (each one designated by a symbol) confirm the drop deformation and its expulsion in step 2 (C, Inset). (D) As a growing drop gets larger than the distance between hairs, elastic energy arising from the setae deformation can generate a force F able to expel the drop out of the texture.As a condensing drop gets larger than the distance between setae (Fig. 3D), setae get distorted. The bending energy E of a single seta scales as KC², denoting K and C as the bending constant and the seta curvature, respectively (19). For a hair of Young''s modulus Y and typical radius r, K scales as Yr⁴L. Because of the high stiffness of setae, we expect the deformation to be small (ε << L) and the curvature to vary as ε/X², where X is now the distance between the bottom of the cone and the drop. Hence we get E ∼ Yr⁴Lε²/X⁴. Simply assuming that drops are larger than the space between setae, we can write ε ∼ D and deduce that the force F expelling the drop out of the grass scales as Yr⁴LD²/X ⁵. The main force opposing drop ejection is the sticking force due to contact angle hysteresis Δθ, because the weight is negligible at such scale. The corresponding resisting force is F_r ∼ γD(cosθ_r – cosθ_a), where advancing and receding angles are written θ_a = θ + Δθ/2 and θ_r = θ − Δθ/2, respectively (20). For Δθ << θ, we get F_r ∼ γDsinθΔθ. Water can be expelled from the setae provided that F(X = L) is larger than F_r, which yields an ejection criterion based on drop diameter:D>Dc=γL4Yr4sinθ Δθ.[2]This criterion is highly sensitive to the geometry of setae: it varies as the fourth power of their aspect ratio L/r, which shows that flexible hairs can accurately “select” drops of a given size. This is especially true in more general cases where L and r are tuned independently, allowing in principle the selection of droplet size in a wide range. Here (with γ ∼ 72 mN/m, L ∼ 40 μm, r ∼ 1 μm, and Y ∼ 10⁸ J/m³), we expect from Eq. 2 a critical diameter D_c on the order of 10 μm, comparable to our observations.Once expelled, drops can be evacuated by leg vibrations, or by directly contacting the water surface. However, note that a third regime of propulsion along the texture is observed during condensation, which also participates in the evacuation of dew (step 3 in Fig. 1). When droplets (at a picoliter or nanoliter scale) merge at the leg surface, the center of gravity of the resulting drop is found in Fig. 4A to be shifted, in the direction of “easy” motion––that is, in the direction favored by the anisotropic contact angle hysteresis at the setae surface. Tilted setae form a kind of ratchet that promotes directional movement in the direction of smaller adhesion (21–24) (Fig. S6), when activated by vibrations or coalescence. The amplitude of the jump is one drop size, as expected for an anisotropic coalescence. Drops sometimes can even take off and jump out of the leg (Fig. 4B), a direct expulsion event such as encountered on cicada wings or lotus leaves (8, 25). Contrasting with the latter examples, water here takes off with an oblique angle, a consequence of anisotropic adhesion: One droplet remains pinned while the other one moves to it, which yields horizontal momentum as drops merge and thus explains the oblique trajectory at takeoff.Open in a separate windowFig. 4.Directional removal of drop on the anistropic setae array (step 3). (A and B) Coalescence at the leg surface results in a rapid directional motion of merged drops along the surface (A) or away from it (B). On the ratchet made by tilted setae, liquid–solid adhesion is anisotropic, which drives the liquid along the inclined cones. Droplets involved in coalescence are pointed out by yellow arrows. Corresponding movies are Movies S4 and S5.Open in a separate windowFig. S6.Anisotropic wetting behavior of water strider leg: force curves for water strider''s leg in both (A) against-scale (AS) and (B) with-scale (WS) orientations show different wetting behavior influenced by the oriented setae contributions.The sophisticated textures of the legs of G. remigis provide a unique ensemble of functions. Robust superhydrophobicity is first necessary to deform the water surface in such a way that creatures’ weight can be opposed by Laplace pressure. The anisotropy of textures is also exploited to have gliding and resisting directions, allowing the strider to control its movements (23, 26). Here we showed that the texture also provides expulsion of condensed droplets, which prevents a major source of risk for the creature, whose hydrophobicity would reverse (in a fatal way) if setae were impregnated by water as humid air condenses. Compared with the few cases of natural antifogging materials reported in the literature, the observed behavior is original: Paradoxically, the droplets first migrate inside the texture, which might help to capture microdroplets condensed there, and possibly contaminants; this sweeping step is followed by a sudden expulsion of the liquid out of the hairs, found to be caused by elastic deformations in the network of setae around the growing water drop. Adding textures to a solid surface can provide multifunctions, such as for cicada wings, where both antireflective and water-repellent properties are generated at once (8). We have here a remarkable example where the conjunction of hydrophobicity, geometry, and flexibility provides both water repellency at a large scale (the pond) and at a very small scale (the dew). We anticipate that the self-removal behavior of droplets on Gerris legs will inspire the design of novel robust superhydrophobic materials for many practical applications, such as self-cleaning surfaces, antidew materials, dropwise condensers, and microfluidic devices.     

Exceptionally strong easterly wind burst stalling El Ni?o of 2014

Intraseasonal wind bursts in the tropical Pacific are believed to affect the evolution and diversity of El Niño events. In particular, the occurrence of two strong westerly wind bursts (WWBs) in early 2014 apparently pushed the ocean–atmosphere system toward a moderate to strong El Niño—potentially an extreme event according to some climate models. However, the event’s progression quickly stalled, and the warming remained very weak throughout the year. Here, we find that the occurrence of an unusually strong basin-wide easterly wind burst (EWB) in June was a key factor that impeded the El Niño development. It was shortly after this EWB that all major Niño indices fell rapidly to near-normal values; a modest growth resumed only later in the year. The easterly burst and the weakness of subsequent WWBs resulted in the persistence of two separate warming centers in the central and eastern equatorial Pacific, suppressing the positive Bjerknes feedback critical for El Niño. Experiments with a climate model with superimposed wind bursts support these conclusions, pointing to inherent limits in El Niño predictability. Furthermore, we show that the spatial structure of the easterly burst matches that of the observed decadal trend in wind stress in the tropical Pacific, suggesting potential links between intraseasonal wind bursts and decadal climate variations.El Niño, the warm phase of the El Niño–Southern Oscillation (ENSO), is characterized by anomalously warm water appearing in the central and eastern equatorial Pacific every 2–7 years, driven by tropical ocean–atmosphere interactions with far-reaching global impacts (recent reviews are in refs. 1–3). These interactions and El Niño development involve several important feedbacks, including the positive Bjerknes feedback [zonal wind relaxation leads to the reduction of the zonal sea surface temperature (SST) gradient and further wind relaxation] (4). Since the year 2000, there has been a shift in the observed properties of El Niño, including its magnitude, frequency, and spatial structure of temperature anomalies (5, 6). For example, El Niño events occurred more frequently than during the previous two decades, but all were weak, and none reached the extreme magnitude of the 1982 and 1997 events. Concurrently, the rise of global mean surface temperature has slowed down with the so-called global warming hiatus (7–9). The stalled development of the 2014 El Niño presents a showcase to explore the relevant connection and mechanisms of these changes.At the beginning of 2014, many in the scientific community anticipated that a moderate to strong El Niño could develop by the end of the year (10–14) (Fig. S1). In March, the National Oceanic and Atmospheric Administration (NOAA) Climate Prediction Center announced an “El Niño watch” based on predictions made by dynamical and statistical models (12), attracting attention of the general public. Admittedly, these predictions encompassed large uncertainties because of the stochastic nature of the tropical climate system (15–17). In May, the National Aeronautics and Space Administration (NASA) suggested that 2014 could potentially rival the strongest on-record event of 1997/19998 (Fig. 1B), while acknowledging the large existing uncertainty (14); their projection was supported by satellite observations of strong Kelvin waves evident in sea surface height (SSH) (Fig. 2C). The spread of spring forecast plumes from some climate models, for example that of the European Centre for Medium-Range Weather Forecasts (ECMWF), included the possibility of a failed El Niño (Fig. S1) but only as a low-probability outcome involving unusual instances of weather noise. The observed development fell near the limit of these forecast possibilities after June and July, and eventually, the 2014 warm event barely qualified as El Niño (Fig. 1A).Open in a separate windowFig. 1.El Niño development in (A and C) 2014 and (B and D) 1997. (A and B) Evolution of the Niño3, Niño4, and Niño3.4 indices; the first two indices describe SST anomalies (in degrees Celsius) in the eastern and central equatorial Pacific, respectively, whereas the last index covers the region in between. (C and D) Variation in the zonal wind stress indices. These indices are obtained by averaging wind stress anomalies (in 10⁻² newtons per meter²) in the equatorial Pacific zonally and between 5 °S and 5 °N and then selecting negative (blue; easterly anomalies), positive (red; westerly anomalies), or full values (black) (Materials and Methods). The spatial averaging is intended to take into account both the magnitude and the fetch of the wind bursts. During 2014, two early year WWBs were followed by an exceptional EWB in June (highlighted by pink and blue, respectively). This easterly burst apparently led to a rapid decrease of the Niño indices (A). In contrast, the 1997 El Niño exhibited persistent westerly wind activity throughout the year. The graphs start on January 1.Open in a separate windowFig. 2.Spatiotemporal evolution of the 2014 El Niño. (A–D) Hovmöller diagrams for anomalies in (A) SST, (B) zonal wind stress, (C) SSH, and (D) surface zonal currents in the equatorial Pacific. Time goes downward. The SSH and surface velocity plots highlight the eastward propagating downwelling Kelvin waves, especially pronounced early in the year, and a strong upwelling Kelvin wave midyear. (E and F) El Niño development in 2014 (black line) compared with several historical (E) EP and (F) CP events. The diagrams show the position of the Warm Pool Eastern Edge (degrees of longitude) vs. the Niño3 SST (degrees Celsius) for different months of the year. The Warm Pool Eastern Edge is defined as the position of the 29 °C isotherm at the equator. Numbers indicate monthly averages (1, January; 2, February, etc.). The light vertical line marks the Dateline. In 2014, both the warm pool displacement and Niño3 SST anomalies were exceptionally large during May (month 5), were similar to those in 1997 and 1982 (the strongest events of the 20th century), and then, rapidly decreased by August (month 8).Open in a separate windowFig. S1.The El Niño spring forecasts of the Niño3.4 index from the European Centre for Medium-Range Weather Forecasts (ECMWF). Red lines show 50 ensemble members of the forecast plume initiated in March of 2014; the black dotted line indicates the observed Niño3.4 index. The observed development fell outside the forecast plume in June and July and remained beyond the typical forecast spread after that. Adapted from ref. 13.The question then arises as to which dynamic factors controlled the temporal and spatial development in the tropical Pacific in 2014. This warm event began with a rapid growth, such that, in early June, all major Niño indices (Materials and Methods) along the equator were nearly identical to those during the same time of 1997 (Fig. 1 A and B). A substantial warming also developed along the Peruvian coast (Fig. 3A). Then, the event’s progression slowed down or even reversed. By year end, the equatorial warming barely exceeded 1 °C, but the SST anomaly stretched uncharacteristically across the entire equatorial Pacific almost uniformly (Figs. 1A and ​and2A).2A). Accordingly, the major goal of this study is to investigate this unusual development, identify the main factors that impeded this event, and explore its broad implications.Open in a separate windowFig. 3.The June of 2014 EWB in satellite-based data. (A) The spatial structure of anomalies in surface winds (vectors; in meters per second) and SST (colors; in degrees Celsius) on June 12, 2014, when the burst was strongest. (B) Daily vs. weekly mean values of the zonal wind stress index (10⁻² newtons per meter²) for the period 1988–2014. The blue cross marks the peak value of the June of 2014 EWB. The wind stress index is defined as anomalous zonal wind stress averaged in the equatorial Pacific zonally and between 5 °S and 5 °N (Materials and Methods). Black circles are for the year 2014, red circles are for all El Niño years before 2014, and gray circles are for all other years (La Niña or neutral). Note that the June of 2014 EWB appears strongest in the satellite record for not only daily data but also, weekly averaged values, which confirms that the observations are robust.