On randomly changing conformity bias in cultural transmission

Humans and nonhuman animals display conformist as well as anticonformist biases in cultural transmission. Whereas many previous mathematical models have incorporated constant conformity coefficients, empirical research suggests that the extent of (anti)conformity in populations can change over time. We incorporate stochastic time-varying conformity coefficients into a widely used conformity model, which assumes a fixed number n of “role models” sampled by each individual. We also allow the number of role models to vary over time (nt). Under anticonformity, nonconvergence can occur in deterministic and stochastic models with different parameter values. Even if strong anticonformity may occur, if conformity or random copying (i.e., neither conformity nor anticonformity) is expected, there is convergence to one of the three equilibria seen in previous deterministic models of conformity. Moreover, this result is robust to stochastic variation in nt. However, dynamic properties of these equilibria may be different from those in deterministic models. For example, with random conformity coefficients, all equilibria can be stochastically locally stable simultaneously. Finally, we study the effect of randomly changing weak selection. Allowing the level of conformity, the number of role models, and selection to vary stochastically may produce a more realistic representation of the wide range of group-level properties that can emerge under (anti)conformist biases. This promises to make interpretation of the effect of conformity on differences between populations, for example those connected by migration, rather difficult. Future research incorporating finite population sizes and migration would contribute added realism to these models.

Cavalli-Sforza and Feldman (1) studied the finite population dynamics of a trait whose transmission from one generation to the next depended on the mean value of that trait in the population. This “group transmission” constrained the within-group variability but could lead to increasing variance in the average trait value between groups. Other analyses of cultural transmission biases have incorporated characteristics of trait variation, such as the quality, and characteristics of transmitters, including success and prestige (2). Another class of transmission biases is couched in terms of the frequencies of the cultural variants in the population (3). These “frequency-dependent” biases include conformity and anticonformity, which occur when a more common variant is adopted at a rate greater or less than its population frequency, respectively (4).Humans have exhibited conformity in mental rotation (5), line discrimination (6), and numerical discrimination tasks (7). Anticonformity has been exhibited by young children performing numerical discrimination (7). Unbiased frequency-dependent transmission, known as random copying (8), has been suggested to account for choices of dog breeds (9), Neolithic pottery motifs, patent citations, and baby names (10, 11). However, baby name distributions appear more consistent with frequency-dependent (8, 12) and/or other (13, 14) biases.In nonhuman animals, conformity has been observed in nine-spined sticklebacks choosing a feeder (15) and great tits solving a puzzle box (16, 17) (but see ref. 18). Fruit flies displayed both conformist and anticonformist bias with respect to mate choice (19) (but these authors used a different definition of anticonformity from that of ref. 4, which we use, and therefore did not consider these behaviors to be anticonformist).Asch (20, 21) used a different definition of conformity from ref. 4, namely “the overriding of personal knowledge or behavioral dispositions by countervailing options observed in others” (ref. 22, p. 34). Aschian conformity (22) has been observed in chimpanzees (23, 24), capuchin monkeys (25, 26) (but see ref. 27), vervet monkeys (28), and great tits (16). It has also been empirically tested in at least 133 studies of humans and, in the United States, has declined from the 1950s to the 1990s (29).Temporal variation may also occur in forms of conformity other than Aschian. In ref. 12, popular US baby names from 1960 to 2010 show a concave turnover function indicative of negative frequency-dependent bias, but male baby names from earlier decades (1880 to 1930) show a convex turnover indicative of positive frequency-dependent or direct bias. However, most previous mathematical models of conformity have incorporated constant, rather than time-dependent, conformity coefficients.Cavalli-Sforza and Feldman (ref. 3, chap. 3) and Boyd and Richerson (ref. 4, chap. 7) studied models of frequency-dependent transmission of a cultural trait with two variants. Boyd and Richerson (4) incorporated conformist and anticonformist bias through a conformity coefficient denoted by D. In their simplest model, if the frequency of variant A is p and that of variant B is 1−p, then the frequency of variant A in the offspring generation, p′, isp′=p+Dp(1−p)(2p−1),[1]where D>0 entails conformity (A increases if its frequency is p>12), D<0 entails anticonformity, D=0 entails random copying, and −2<D<1. In this model, each offspring samples the cultural variants of n=3 members of the parental generation (hereafter, role models). Sampling n>3 role models requires different constraints and, if n>4, there are multiple conformity coefficients (Eq. 19).Many subsequent models have built upon Boyd and Richerson’s (4) simplest model (Eq. 1). These have incorporated individual learning, information inaccuracy due to environmental change (30–34), group selection (35), and other transmission biases, including payoff bias (36), direct bias, and prestige bias (37). Other models, which include a single conformity coefficient and preserve the essential features of Eq. 1, incorporate individual learning, environmental variability (32, 38), group selection (39), and multiple cultural variants (38).In agent-based statistical physics models, the up and down spins of an electron are analogous to cultural variants A and B (40, 41). Individuals are nodes in a network and choose among a series of actions with specified probabilities, such as independently acquiring a spin, or sampling neighboring individuals and adopting the majority or minority spin in the sample. The number of sampled role models can be greater than three (42, 43). (Anti)conformity may occur if all (42–47), or if at least r (40, 48), sampled individuals have the same variant. In contrast, Boyd and Richerson’s (4) general model (Eq. 19) allows, for example, stronger conformity to a 60% majority of role models and weaker conformity or anticonformity to a 95% majority (in humans, this might result from a perceived difference between “up-and-coming” and “overly popular” variants).In Boyd and Richerson’s (4) general model, individuals sample n role models, which is more realistic than restricting n to 3 (as in Eq. 1); individuals may be able to observe more than three members of the previous generation. With n>4, different levels of (anti)conformity may occur for different samples j of n role models with one variant. In addition to the example above with 60 and 95% majorities, other relationships between the level of conformity and the sample j of n are possible. For example, the strength of conformity might increase as the number of role models with the more common variant increases. In a recent exploration of Boyd and Richerson’s (4) general model, we found dynamics that departed significantly from those of Eq. 1 (49). If conformity and anticonformity occur for different majorities j of n role models (i.e., j>n2), polymorphic equilibria may exist that were not possible with Eq. 1. In addition, strong enough anticonformity can produce nonconvergence: With as few as 5 role models, stable cycles in variant frequencies may arise, and with as few as 10 role models, chaos is possible. Such complex dynamics may occur with or without selection.Here, we extend both Boyd and Richerson’s (4) simplest (Eq. 1) and general (Eq. 19) models to allow the conformity coefficient(s) to vary randomly across generations, by sampling them from probability distributions. Although some agent-based models allow individuals to switch between “conformist” and “non-” or “anticonformist” states over time (40, 42, 47, 50, 51), to our knowledge, random temporal variation in the conformity coefficients themselves has not been modeled previously. In reality, the degree to which groups of individuals conform may change over time, as illustrated by the finding that young children anti-conformed while older children conformed in a discrimination task (7); thus, it seems reasonable to expect that different generations may also exhibit different levels of conformity. Indeed, generational changes have occurred for Aschian conformity (29) and possibly in frequency-dependent copying of baby names (12). Our stochastic model may therefore produce more realistic population dynamics than previous deterministic models, and comparisons between the two can suggest when the latter is a reasonable approximation to the former.We also allow the number of role models, nt, to vary over time. Agent-based conformity models have incorporated temporal (43) and individual (43, 45, 46) variation in the number of sampled individuals, whereas here, all members of generation t sample the same number nt of role models. Causes of variation in nt are not explored here, but there could be several. For instance, different generations of animals may sample different numbers of role models due to variation in population density. In humans, changes in the use of social media platforms or their features may cause temporal changes in the number of observed individuals. For example, when Facebook added the feature “People You May Know,” the rate of new Facebook connections in a New Orleans dataset nearly doubled (52).In the stochastic model without selection, regardless of the fluctuation in the conformity coefficient(s), if there is conformity on average, the population converges to one of the three equilibria present in Boyd and Richerson’s (4) model with conformity (D(j)>0 for n2<j<n in Eq. 19). These are p*=1 (fixation on variant A), p*=0 (fixation on variant B), and p*=12 (equal representation of A and B). However, their stability properties may differ from those in the deterministic case. In Boyd and Richerson’s (4) model with random copying, every initial frequency p0 is an equilibrium. Here, with random copying expected and independent conformity coefficients, there is convergence to p*=0,12, or 1. In this case, and in the case with conformity expected, convergence to p*=0,12, or 1 also holds with stochastic variation in the number of role models, nt. With either stochastic or constant weak selection in Boyd and Richerson’s (4) simplest model (Eq. 1) and random copying expected, there is convergence to a fixation state (p*=0 or 1). Finally, with anticonformity in the deterministic model or anticonformity expected in the stochastic model, nonconvergence can occur.     

Layering transitions and metastable structures of cholesteric liquid crystals in cylindrical confinement

Our study of cholesteric lyotropic chromonic liquid crystals in cylindrical confinement reveals the topological aspects of cholesteric liquid crystals. The double-twist configurations we observe exhibit discontinuous layering transitions, domain formation, metastability, and chiral point defects as the concentration of chiral dopant is varied. We demonstrate that these distinct layer states can be distinguished by chiral topological invariants. We show that changes in the layer structure give rise to a chiral soliton similar to a toron, comprising a metastable pair of chiral point defects. Through the applicability of the invariants we describe to general systems, our work has broad relevance to the study of chiral materials.

Chiral liquid crystals (LCs) are ubiquitous, useful, and rich systems (1–4). From the first discovery of the liquid crystalline phase to the variety of chiral structures formed by biomolecules (5–9), the twisted structure, breaking both mirror and continuous spatial symmetries, is omnipresent. The unique structure also makes the chiral nematic (cholesteric) LC, an essential material for applications utilizing the tunable, responsive, and periodic modulation of anisotropic properties.The cholesteric is also a popular model system to study the geometry and topology of partially ordered matter. The twisted ground state of the cholesteric is often incompatible with confinement and external fields, exhibiting a large variety of frustrated and metastable director configurations accompanying topological defects. Besides the classic example of cholesterics in a Grandjean−Cano wedge (10, 11), examples include cholesteric droplets (12–16), colloids (17–19), shells (20–22), tori (23, 24), cylinders (25–29), microfabricated structures (30, 31), and films between parallel plates with external fields (32–40). These structures are typically understood using a combination of nematic (achiral) topology (41, 42) and energetic arguments, for example, the highly successful Landau−de Gennes approach (43). However, traditional extensions of the nematic topological approach to cholesterics are known to be conceptually incomplete and difficult to apply in regimes where the system size is comparable to the cholesteric pitch (41, 44).An alternative perspective, chiral topology, can give a deeper understanding of these structures (45–47). In this approach, the key role is played by the twist density, given in terms of the director field n by n⋅∇×n. This choice is not arbitrary; the Frank free energy prefers n⋅∇×n≈−q0=2π/p0 with a helical pitch p0, and, from a geometric perspective, n⋅∇×n≠0 defines a contact structure (48). This allows a number of new integer-valued invariants of chiral textures to be defined (45). A configuration with a single sign of twist is chiral, and two configurations which cannot be connected by a path of chiral configurations are chirally distinct, and hence separated by a chiral energy barrier. Within each chiral class of configuration, additional topological invariants may be defined using methods of contact topology (45–48), such as layer numbers. Changing these chiral topological invariants requires passing through a nonchiral configuration. Cholesterics serve as model systems for the exploration of chirality in ordered media, and the phenomena we describe here—metastability in chiral systems controlled by chiral topological invariants—has applicability to chiral order generally. This, in particular, includes chiral ferromagnets, where, for example, our results on chiral topological invariants apply to highly twisted nontopological Skyrmions (49, 50) (“Skyrmionium”).Our experimental model to explore the chiral topological invariants is the cholesteric phase of lyotropic chromonic LCs (LCLCs). The majority of experimental systems hitherto studied are based on thermotropic LCs with typical elastic and surface-anchoring properties. The aqueous LCLCs exhibiting unusual elastic properties, that is, very small twist modulus K2 and large saddle-splay modulus K24 (51–56), often leading to chiral symmetry breaking of confined achiral LCLCs (53, 54, 56–61), may enable us to access uncharted configurations and defects of topological interests. For instance, in the layer configuration by cholesteric LCLCs doped with chiral molecules, their small K2 provides energetic flexibility to the thickness of the cholesteric layer, that is, the repeating structure where the director n twists by π. The large K24 affords curvature-induced surface interactions in combination with a weak anchoring strength of the lyotropic LCs (62–64).We present a systematic investigation of the director configuration of cholesteric LCLCs confined in cylinders with degenerate planar anchoring, depending on the chiral dopant concentration. We show that the structure of cholesteric configurations is controlled by higher-order chiral topological invariants. We focus on two intriguing phenomena observed in cylindrically confined cholesterics. First, the cylindrical symmetry renders multiple local minima to the energy landscape and induces discontinuous increase of twist angles, that is, a layering transition, upon the dopant concentration increase. Additionally, the director configurations of local minima coexist as metastable domains with point-like defects between them. We demonstrate that a chiral layer number invariant distinguishes these configurations, protects the distinct layer configurations (45), and explains the existence of the topological defect where the invariant changes.     

Modeling the instantaneous normal mode spectra of liquids as that of unstable elastic media

We study the instantaneous normal mode (INM) spectrum of a simulated soft-sphere liquid at different equilibrium temperatures T. We find that the spectrum of eigenvalues ρ(λ) has a sharp maximum near (but not at) λ=0 and decreases monotonically with |λ| on both the stable and unstable sides of the spectrum. The spectral shape strongly depends on temperature. It is rather asymmetric at low temperatures (close to the dynamical critical temperature) and becomes symmetric at high temperatures. To explain these findings we present a mean-field theory for ρ(λ), which is based on a heterogeneous elasticity model, in which the local shear moduli exhibit spatial fluctuations, including negative values. We find good agreement between the simulation data and the model calculations, done with the help of the self-consistent Born approximation (SCBA), when we take the variance of the fluctuations to be proportional to the temperature T. More importantly, we find an empirical correlation of the positions of the maxima of ρ(λ) with the low-frequency exponent of the density of the vibrational modes of the glasses obtained by quenching to T=0 from the temperature T. We discuss the present findings in connection to the liquid to glass transformation and its precursor phenomena.

The investigation of the potential energy surface (PES) V(r1(t)…rN(t)) of a liquid (made up of N particles with positions r1(t)…rN(t) at a time instant t) and the corresponding instantaneous normal modes (INMs) of the (Hessian) matrix of curvatures has been a focus of liquid and glass science since the appearance of Goldstein’s seminal article (1) on the relation between the PES and the liquid dynamics in the viscous regime above the glass transition (2–27).The PES has been shown to form a rather ragged landscape in configuration space (8, 28, 29) characterized by its stationary points. In a glass these points are minima and are called “inherent structures.” The PES is believed to contain important information on the liquid–glass transformation mechanism. For the latter a complete understanding is still missing (28, 30, 31). The existing molecular theory of the liquid–glass transformation is mode-coupling theory (MCT) (32, 33) and its mean-field Potts spin version (28, 34). MCT predicts a sharp transition at a temperature TMCT>Tg, where T_g is the temperature of structural arrest (glass transition temperature). MCT completely misses the heterogeneous activated relaxation processes (dynamical heterogeneities), which are evidently present around and below T_MCT and which are related to the unstable (negative-λ) part of the INM spectrum (28, 30).Near and above T_MCT, apparently, there occurs a fundamental change in the PES. Numerical studies of model liquids have shown that minima present below T_MCT change into saddles, which then explains the absence of activated processes above T_MCT (2–24). Very recently, it was shown that T_MCT is related to a localization–delocalization transition of the unstable INM modes (25, 26).The INM spectrum is obtained in molecular dynamic simulations by diagonalizing the Hessian matrix of the interaction potential, taken at a certain time instant t:Hijαβ(t)=∂2∂xi(α)∂xj(β)V{r1(t)…rN(t)},[1]with ri=(xi(1),xi(2),xi(3)). For large positive values of the eigenvalues λ_j (j=1…N, N being the number of particles in the system) they are related to the square of vibrational frequencies λj=ωj2, and one can consider the Hessian as the counterpart of the dynamical matrix of a solid. In this high-frequency regime one can identify the spectrum with the density of vibrational states (DOS) of the liquid viag(ω)=2 ωρ(λ(ω))=13N∑jδ(ω−ωj) .[2]For small and negative values of λ this identification is not possible. For the unstable part of the spectrum (λ<0) it has become common practice to call the imaginary number λ=iω˜ and define the corresponding DOS asg(ω˜)≡2 ω˜ρ(λ(ω˜)).[3]This function is plotted on the negative ω axis and the stable g(ω), according to [2], on the positive axis. However, the (as we shall see, very interesting) details of the spectrum ρ(λ) near λ = 0 become almost completely hidden by multiplying the spectrum with |ω|. In fact, it has been demonstrated by Sastry et al. (6) and Taraskin and Elliott (7) already 2 decades ago that the INM spectrum of liquids, if plotted as ρ(λ) and not as g(ω) according to [2] and [3], exhibits a characteristic cusp-like maximum at λ = 0. The shape of the spectrum changes strongly with temperature. This is what we find as well in our simulation and what we want to explore further in our present contribution.In the present contribution we demonstrate that the strong change of the spectrum with temperature can be rather well explained in terms of a model, in which the instantaneous harmonic spectrum of the liquid is interpreted to be that of an elastic medium, in which the local shear moduli exhibit strong spatial fluctuations, which includes a large number of negative values. Because these fluctuations are just a snapshot of thermal fluctuations, we assume that they are obeying Gaussian statistics, the variance of which is proportional to the temperature.Evidence for a characteristic change in the liquid configurations in the temperature range above T_g has been obtained in recent simulation studies of the low-frequency vibrational spectrum of glasses, which have been rapidly quenched from a certain parental temperature T*. If T* is decreased from high temperatures toward T_MCT, the low-frequency exponent of the vibrational DOS of the daughter glass (quenched from T* to T = 0) changed from Debye-like g(ω)∝ω2 to g(ω)∝ωs with s > 2. In our numerical investigation of the INM spectra we show a correlation of some details of the low-eigenvalue features of these spectra with the low-frequency properties of the daughter glasses obtained by quenching from the parental temperatures.The stochastic Helmholtz equations (Eq. 7) of an elastic model with spatially fluctuating shear moduli can be readily solved for the averaged Green’s functions by field theoretical techniques (35–37). Via a saddle point approximation with respect to the resulting effective field theory one arrives at a mean-field theory (self-consistent Born approximation [SCBA]) for the self-energy of the averaged Green’s functions. The SCBA predicts a stable spectrum below a threshold value of the variance. Restricted to this stable regime, this theory, called heterogeneous elasticity theory (HET), was rather successful in explaining several low-frequency anomalies in the vibrational spectrum of glasses, including the so-called boson peak, which is an enhancement at finite frequencies over the Debye behavior of the DOS g(ω)∝ω2 (37–41). We now explore the unstable regime of this theory and compare it to the INM spectrum of our simulated soft-sphere liquid.^*We start Results by presenting a comparison of the simulated spectra of the soft-sphere liquid with those obtained by the unstable version of HET-SCBA theory. We then concentrate on some specific features of the INM spectra, namely, the low-eigenvalue slopes and the shift of the spectral maximum from λ = 0. Both features are accounted for by HET-SCBA. In particular, we find an interesting law for the difference between the slopes of the unstable and the stable parts of the spectrum, which behaves as T−2/3, which, again, is accounted for by HET-SCBA.In the end we compare the shift of the spectral maximum with the low-frequency exponent of the DOS of the corresponding daughter glasses and find an empirical correlation. We discuss these results in connection with the saddle to minimum transformation near T_MCT.     

From hidden order to antiferromagnetism: Electronic structure changes in Fe-doped URu2Si2

In matter, any spontaneous symmetry breaking induces a phase transition characterized by an order parameter, such as the magnetization vector in ferromagnets, or a macroscopic many-electron wave function in superconductors. Phase transitions with unknown order parameter are rare but extremely appealing, as they may lead to novel physics. An emblematic and still unsolved example is the transition of the heavy fermion compound URu2Si2 (URS) into the so-called hidden-order (HO) phase when the temperature drops below T0=17.5 K. Here, we show that the interaction between the heavy fermion and the conduction band states near the Fermi level has a key role in the emergence of the HO phase. Using angle-resolved photoemission spectroscopy, we find that while the Fermi surfaces of the HO and of a neighboring antiferromagnetic (AFM) phase of well-defined order parameter have the same topography, they differ in the size of some, but not all, of their electron pockets. Such a nonrigid change of the electronic structure indicates that a change in the interaction strength between states near the Fermi level is a crucial ingredient for the HO to AFM phase transition.

The transition of URu2Si2 from a high-temperature paramagnetic (PM) phase to the hidden-order (HO) phase below T0 is accompanied by anomalies in specific heat (1–3), electrical resistivity (1, 3), thermal expansion (4), and magnetic susceptibility (2, 3) that are all typical of magnetic ordering. However, the small associated antiferromagnetic (AFM) moment (5) is insufficient to explain the large entropy loss and was shown to be of extrinsic origin (6). Inelastic neutron scattering (INS) experiments revealed gapped magnetic excitations below T0 at commensurate and incommensurate wave vectors (7–9), while an instability and partial gapping of the Fermi surface was observed by angle-resolved photoemission spectroscopy (ARPES) (10–16) and scanning tunneling microscopy/spectroscopy (17, 18). More recently, high-resolution, low-temperature ARPES experiments imaged the Fermi surface reconstruction across the HO transition, unveiling the nesting vectors between Fermi sheets associated with the gapped magnetic excitations seen in INS experiments (14, 19) and quantitatively explaining, from the changes in Fermi surface size and quasiparticle mass, the large entropy loss in the HO phase (19). Nonetheless, the nature of the HO parameter is still hotly debated (20–23).The HO phase is furthermore unstable above a temperature-dependent critical pressure of about 0.7 GPa at T=0, at which it undergoes a first-order transition into a large moment AFM phase where the value of the magnetic moment per U atom exhibits a sharp increase, by a factor of 10 to 50 (6, 24–30). When the system crosses the HO → AFM phase boundary, the characteristic magnetic excitations of the HO phase are either suppressed or modified (8, 31), while resistivity and specific heat measurements suggest that the partial gapping of the Fermi surface is enhanced (24, 27).As the AFM phase has a well-defined order parameter, studying the evolution of the electronic structure across the HO/AFM transition would help develop an understanding of the HO state. So far, the experimental determination of the Fermi surface by Shubnikov de Haas (SdH) oscillations only showed minor changes across the HO → AFM phase boundary (32). Here, we take advantage of the HO/AFM transition induced by chemical pressure in URu2Si2, through the partial substitution of Ru with Fe (33–37), to directly probe its electronic structure in the AFM phase using ARPES. As we shall see, our results reveal that changes in the Ru 4d–U 5f hybridization across the HO/AFM phase boundary seem essential for a better understanding of the HO state.     

Dynamic rupture initiation and propagation in a fluid-injection laboratory setup with diagnostics across multiple temporal scales

Fluids are known to trigger a broad range of slip events, from slow, creeping transients to dynamic earthquake ruptures. Yet, the detailed mechanics underlying these processes and the conditions leading to different rupture behaviors are not well understood. Here, we use a laboratory earthquake setup, capable of injecting pressurized fluids, to compare the rupture behavior for different rates of fluid injection, slow (megapascals per hour) versus fast (megapascals per second). We find that for the fast injection rates, dynamic ruptures are triggered at lower pressure levels and over spatial scales much smaller than the quasistatic theoretical estimates of nucleation sizes, suggesting that such fast injection rates constitute dynamic loading. In contrast, the relatively slow injection rates result in gradual nucleation processes, with the fluid spreading along the interface and causing stress changes consistent with gradually accelerating slow slip. The resulting dynamic ruptures propagating over wetted interfaces exhibit dynamic stress drops almost twice as large as those over the dry interfaces. These results suggest the need to take into account the rate of the pore-pressure increase when considering nucleation processes and motivate further investigation on how friction properties depend on the presence of fluids.

The close connection between fluids and faulting has been revealed by a large number of observations, both in tectonic settings and during human activities, such as wastewater disposal associated with oil and gas extraction, geothermal energy production, and CO₂ sequestration (1–11). On and around tectonic faults, fluids also naturally exist and are added at depths due to rock-dehydration reactions (12–15) Fluid-induced slip behavior can range from earthquakes to slow, creeping motion. It has long been thought that creeping and seismogenic fault zones have little to no spatial overlap. Nonetheless, growing evidence suggests that the same fault areas can exhibit both slow and dynamic slip (16–19). The existence of large-scale slow slip in potentially seismogenic areas has been revealed by the presence of transient slow-slip events in subduction zones (16, 18) and proposed by studies investigating the physics of foreshocks (20–22).Numerical and laboratory modeling has shown that such complex fault behavior can result from the interaction of fluid-related effects with the rate-and-state frictional properties (9, 14, 19, 23, 24); other proposed rheological explanations for complexities in fault stability include combinations of brittle and viscous rheology (25) and friction-to-flow transitions (26). The interaction of frictional sliding and fluids results in a number of coupled and competing mechanisms. The fault shear resistance τres is typically described by a friction model that linearly relates it to the effective normal stress σ^n via a friction coefficient f:τres=f σ^n=f (σn−p),[1]where σn is the normal stress acting across the fault and p is the pore pressure. Clearly, increasing pore pressure p would reduce the fault frictional resistance, promoting the insurgence of slip. However, such slip need not be fast enough to radiate seismic waves, as would be characteristic of an earthquake, but can be slow and aseismic. In fact, the critical spatial scale h* for the slipping zone to reach in order to initiate an unstable, dynamic event is inversely proportional to the effective normal stress (27, 28) and hence increases with increasing pore pressure, promoting stable slip. This stabilizing effect of increasing fluid pressure holds for both linear slip-weakening and rate-and-state friction; it occurs because lower effective normal stress results in lower fault weakening during slip for the same friction properties. For example, the general form for two-dimensional (2D) theoretical estimates of this so-called nucleation size, h*, on rate-and-state faults with steady-state, velocity-weakening friction is given by:h*=(μ*DRS)/[F(a,b)(σn−p)],[2]where μ*=μ/(1−ν) for modes I and II, and μ*=μ for mode III (29); DRS is the characteristic slip distance; and F(a, b) is a function of the rate-and-state friction parameters a and b. The function F(a, b) depends on the specific assumptions made to obtain the estimate: FRR(a,b)=4(b−a)/π (ref. 27, equation 40) for a linearized stability analysis of steady sliding, or FRA(a,b)=[π(b−a)2]/2b, with a/b>1/2 for quasistatic crack-like expansion of the nucleation zone (ref. 30, equation 42).Hence, an increase in pore pressure induces a reduction in the effective normal stress, which both promotes slip due to lower frictional resistance and increases the critical length scale h*, potentially resulting in slow, stable fault slip instead of fast, dynamic rupture. Indeed, recent field and laboratory observations suggest that fluid injection triggers slow slip first (4, 9, 11, 31). Numerical modeling based on these effects, either by themselves or with an additional stabilizing effect of shear-layer dilatancy and the associated drop in fluid pressure, have been successful in capturing a number of properties of slow-slip events observed on natural faults and in field fluid-injection experiments (14, 24, 32–34). However, understanding the dependence of the fault response on the specifics of pore-pressure increase remains elusive. Several studies suggest that the nucleation size can depend on the loading rate (35–38), which would imply that the nucleation size should also depend on the rate of friction strength change and hence on the rate of change of the pore fluid pressure. The dependence of the nucleation size on evolving pore fluid pressure has also been theoretically investigated (39). However, the commonly used estimates of the nucleation size (Eq. 2) have been developed for faults under spatially and temporally uniform effective stress, which is clearly not the case for fluid-injection scenarios. In addition, the friction properties themselves may change in the presence of fluids (40–42). The interaction between shear and fluid effects can be further affected by fault-gauge dilation/compaction (40, 43–45) and thermal pressurization of pore fluids (42, 46–48).Recent laboratory investigations have been quite instrumental in uncovering the fundamentals of the fluid-faulting interactions (31, 45, 49–57). Several studies have indicated that fluid-pressurization rate, rather than injection volume, controls slip, slip rate, and stress drop (31, 49, 57). Rapid fluid injection may produce pressure heterogeneities, influencing the onset of slip. The degree of heterogeneity depends on the balance between the hydraulic diffusion rate and the fluid-injection rate, with higher injection rates promoting the transition from drained to locally undrained conditions (31). Fluid pressurization can also interact with friction properties and produce dynamic slip along rate-strengthening faults (50, 51).In this study, we investigate the relation between the rate of pressure increase on the fault and spontaneous rupture nucleation due to fluid injection by laboratory experiments in a setup that builds on and significantly develops the previous generations of laboratory earthquake setup of Rosakis and coworkers (58, 59). The previous versions of the setup have been used to study key features of dynamic ruptures, including sub-Rayleigh to supershear transition (60); rupture directionality and limiting speeds due to bimaterial effects (61); pulse-like versus crack-like behavior (62); opening of thrust faults (63); and friction evolution (64). A recent innovation in the diagnostics, featuring ultrahigh-speed photography in conjunction with digital image correlation (DIC) (65), has enabled the quantification of the full-field behavior of dynamic ruptures (66–68), as well as the characterization of the local evolution of dynamic friction (64, 69). In these prior studies, earthquake ruptures were triggered by the local pressure release due to an electrical discharge. This nucleation procedure produced only dynamic ruptures, due to the nearly instantaneous normal stress reduction.To study fault slip triggered by fluid injection, we have developed a laboratory setup featuring a hydraulic circuit capable of injecting pressurized fluid onto the fault plane of a specimen and a set of experimental diagnostics that enables us to detect both slow and fast fault slip and stress changes. The range of fluid-pressure time histories produced by this setup results in both quasistatic and dynamic rupture nucleation; the diagnostics allows us to capture the nucleation processes, as well as the resulting dynamic rupture propagation. In particular, here, we explore two injection techniques: procedure 1, a gradual, and procedure 2, a sharp fluid-pressure ramp-up. An array of strain gauges, placed on the specimen’s surface along the fault, can capture the strain (translated into stress) time histories over a wide range of temporal scales, spanning from microseconds to tens of minutes. Once dynamic ruptures nucleate, an ultrahigh-speed camera records images of the propagating ruptures, which are turned into maps of full-field displacements, velocities, and stresses by a tailored DIC) analysis. One advantage of using a specimen made of an analog material, such as poly(methyl meth-acrylate) (PMMA) used in this study, is its transparency, which allows us to look at the interface through the bulk and observe fluid diffusion over the interface. Another important advantage of using PMMA is that its much lower shear modulus results in much smaller nucleation sizes h* than those for rocks, allowing the experiments to produce both slow and fast slip in samples of manageable sizes.We start by describing the laboratory setup and the diagnostics monitoring the pressure evolution and the slip behavior. We then present and discuss the different slip responses measured as a result of slow versus fast fluid injection and interpret our measurements by using the rate-and-state friction framework and a pressure-diffusion model.     

Grain boundary formation through particle detachment during coarsening of nanoporous metals

Grain boundary formation during coarsening of nanoporous gold (NPG) is investigated wherein a nanocrystalline structure can form by particles detaching and reattaching to the structure. MicroLaue and electron backscatter diffraction measurements demonstrate that an in-grain orientation spread develops as NPG is coarsened. The volume fraction of the NPG sample is near the limit of bicontinuity, at which simulations predict that a bicontinuous structure begins to fragment into independent particles during coarsening. Phase-field simulations of coarsening using a computationally generated structure with a volume fraction near the limit of bicontinuity are used to model particle detachment rates. This model is tested by using the measured NPG structure as an initial condition in the phase-field simulations. We predict that up to ∼5% of the NPG structure detaches as a dealloyed Ag75Au25 sample is annealed at 300 °C for 420 min. The quantity of volume detached is found to be highly dependent on the volume fraction and volume fraction homogeneity of the nanostructure. As the void phase in the experiments cannot support independent particles, they must fall and reattach to the structure, a process that results in the formation of new grain boundaries. This particle reattachment process, along with other classic processes, leads to the formation of grain boundaries during coarsening in nanoporous metals. The formation of grain boundaries can impact a variety of applications, including mechanical strengthening; thus, the consideration and understanding of particle detachment phenomena are essential when studying nanoporous metals.

Nanoporous metals are prototypical bicontinuous structures with a network of pores and ligaments. They are created by a number of metallic dealloying processes (1–6) allowing nearly any bulk metal to be transformed into a bicontinuous two-phase mixture of metal and void phase (7). These metals have a large interfacial area per volume enabling exciting applications in oxygen reduction (8), electromechanical devices (9), battery electrodes (10), actuators (11), and catalysts (12). Given the large surface area per volume, nanoporous structures frequently undergo coarsening when annealed at elevated temperatures. Nanoporous metals coarsen by surface diffusion (13–15), a process where the characteristic length, L, increases in time, t, according to the power law L∼t1/4 (16). Coarsening decreases the total interfacial energy of the structure, which greatly affects its material properties. For instance, coarsening is used to select the length scale in the structure, which alters the sizes of pores and ligaments (7, 17–20), ultimately impacting optical, chemical, and mechanical properties (21, 22), such as the elastic modulus (23). Nanoporous gold (NPG) often serves as a prototype for studying nanoporous metals (7). This paper investigates grain boundary formation as NPG coarsens and shows that the formation of a significant number of these boundaries is from particle detachment and subsequent reattachment.Metallic samples prior to dealloying have grain sizes on the order of 10 to 100 μm (24). Dealloying and annealing of bulk nanoporous metals are typically believed to preserve the grain orientation of the original metallic sample. This was demonstrated through electron backscatter diffraction (EBSD) measurements (1) and scanning electron microscopy (SEM) images (25) for NPG. However, these techniques provide information only about the external surfaces, not the bulk structure. The formation of an in-grain orientation spread would demonstrate that nanoporous metals can develop nanocrystallinity. Some recent work has observed a developed nanocrystalline structure in nanoporous metallic samples after dealloying and annealing. Sun et al. (26) observed grain boundary formation during annealing of NPG but assumed that the varying orientations formed due to the small grain size in the original alloy. High-resolution transmission electron microscopy (HRTEM) (27) and X-ray diffraction (28) were used to identify a nanocrystalline structure in NPG postdealloying. Nanocrystalline structures have also been identified in nanoporous platinum (29) and copper (30) postdealloying. Theories of how these grain boundaries form during dealloying and annealing have not been fully investigated. Dealloyed NPG samples have been shown to contain lattice dislocations (24). It is possible that there are driving forces for dislocations to form low-angle grain boundaries in the structure when coarsening at elevated temperatures.Coarsening of nanoporous metals is often compared to simulations that coarsen computationally generated (CG) bicontinuous structures, e.g., those formed in simulations of spinodal decomposition (31). Evolution of these structures has been studied with phase-field (31–35) and kinetic Monte Carlo (KMC) (36–38) methods. In certain volume fraction ranges, particle detachment is observed during simulations of coarsening, altering the topology of the structure. This breaking of ligaments in the structure is due to a Rayleigh–Plateau instability (38), the same mechanism causing ligament pinch-off (a ligament breaking in one place) during coarsening of nanoporous metals (13, 39, 40). The topology of an object in three dimensions (3D) is quantified by the Betti numbers: β0, the number of independent objects; β1, the number of handles (genus); and β2, the number of enclosed voids in the structure. Assuming no enclosed voids, the Euler characteristic of a 3D structure is given by χ=β0−β1 (41). When a particle detaches from the microstructure, β0 increases by 1. As particles detach from the end of ligaments, β1 remains the same. If a ligament breaks in one place (a process that is referred to as a ligament pinch-off), β1 decreases by 1 and β0 remains the same. Here we define particle detachment as the process of creating small (in size when compared to the main bicontinuous structure) isolated bodies.Simulations have demonstrated that the topology of a structure has a strong dependence on the minority phase volume fraction, ϕ, and can vary drastically within a small range of ϕ (34, 38). Using KMC, Li et al. (38) investigated coarsening via surface diffusion of structures initialized as leveled Gaussian random fields with ϕ of 22, 25, and 27% and increments of 5% from 30 to 50%. By investigating the topology, they found that structures with a ϕ lower than 30% are evolving toward a particle-dominated system, while structures with a ϕ higher than 40% are evolving as a fully connected system (β0=1). As the topological changes are related to how particles detach, we establish two regimes of topological evolution. In the particle-dominated regime (low ϕ), the structure evolves toward a state where the number of handles (β1) is either zero or low compared to the number of particles (β0). In the ligament-dominated regime (high ϕ), the structure evolves toward a state where there is a low number of particles (β0) compared to the number of handles (β1). In between these regimes (intermediate ϕ), the structure evolves to a state with an intermediate number of particles and handles, and any transition to the particle-dominated regime or the ligament-dominated regime occurs too slowly to be feasibly observed. We define this approximate boundary between regimes as the limit of bicontinuity, as the structure begins to break up while still maintaining a high degree of connectivity. Due to the approximate nature of this definition, a range of ϕ (e.g., 30 to 35%) may be considered to be “at” the limit of bicontinuity. We are most likely to observe particle detachment in structures with a ϕ at the limit of bicontinuity, where β0 might be stable or increasing throughout coarsening (signifying particle detachment) while a majority of the solid volume is contained in the main bicontinuous structure. Simulations with a ϕ in the range 30 to 35% have not yet been extensively studied despite the many coarsening experiments of nanoporous metals that are within this range.Experiments commonly study NPG samples with a ϕ between 25 and 36% postdealloying and report fully connected bicontinuous structures (17, 19, 20, 42–47). In this case, the minority phase volume fraction, ϕ, corresponds to the gold volume fraction. These ϕ values are just below or at the limit of bicontinuity predicted by simulation. However, the stability of the structures during coarsening is not always investigated, especially at lower ϕ. Detachment of particles from the bicontinuous structure can be kinetically inhibited due to short coarsening times or slow coarsening rates. However, experiments that coarsen NPG for sufficiently long times such that the mean ligament diameter increased by a factor of 16 have still reported fully connected bicontinuous structures (19, 20). The bicontinuity does not necessarily indicate that disconnections do not occur during the evolution; since the vapor phase cannot support independent particles, any particles that detach would presumably fall under their own weight and reattach elsewhere, leading to a fully connected bicontinuous structure and the formation of grain boundaries.As the ϕ of many NPG samples is at the limit of bicontinuity, we show that particles detach as NPG coarsens, and we hypothesize that the reattachment of particles leads to the formation of many of the grain boundaries that are observed in the microstructure. The results of microLaue and EBSD measurements of coarsened NPG samples with a ϕ at the limit of bicontinuity identify large in-grain orientation spreads that develop during coarsening. Phase-field simulations of coarsening of a CG bicontinuous structure with a ϕ at the limit of bicontinuity are conducted to investigate how particle detachment occurs in this regime. Subsequently, the morphology of the CG and NPG structures is characterized to search for evidence of particle reattachment phenomena. A coarsened NPG structure is then used as an initial condition in a phase-field simulation to observe how particle detachment would occur if the sample had continued to coarsen. These calculations that begin with the experimentally measured structure have identified the critical role of volume fraction homogeneity in particle detachment phenomena.     

Structures and topological defects in pressure-driven lyotropic chromonic liquid crystals

Lyotropic chromonic liquid crystals are water-based materials composed of self-assembled cylindrical aggregates. Their behavior under flow is poorly understood, and quantitatively resolving the optical retardance of the flowing liquid crystal has so far been limited by the imaging speed of current polarization-resolved imaging techniques. Here, we employ a single-shot quantitative polarization imaging method, termed polarized shearing interference microscopy, to quantify the spatial distribution and the dynamics of the structures emerging in nematic disodium cromoglycate solutions in a microfluidic channel. We show that pure-twist disclination loops nucleate in the bulk flow over a range of shear rates. These loops are elongated in the flow direction and exhibit a constant aspect ratio that is governed by the nonnegligible splay-bend anisotropy at the loop boundary. The size of the loops is set by the balance between nucleation forces and annihilation forces acting on the disclination. The fluctuations of the pure-twist disclination loops reflect the tumbling character of nematic disodium cromoglycate. Our study, including experiment, simulation, and scaling analysis, provides a comprehensive understanding of the structure and dynamics of pressure-driven lyotropic chromonic liquid crystals and might open new routes for using these materials to control assembly and flow of biological systems or particles in microfluidic devices.

Lyotropic chromonic liquid crystals (LCLCs) are aqueous dispersions of organic disk-like molecules that self-assemble into cylindrical aggregates, which form nematic or columnar liquid crystal phases under appropriate conditions of concentration and temperature (1–6). These materials have gained increasing attention in both fundamental and applied research over the past decade, due to their distinct structural properties and biocompatibility (4, 7–14). Used as a replacement for isotropic fluids in microfluidic devices, nematic LCLCs have been employed to control the behavior of bacteria and colloids (13, 15–20).Nematic liquid crystals form topological defects under flow, which gives rise to complex dynamical structures that have been extensively studied in thermotropic liquid crystals (TLCs) and liquid crystal polymers (LCPs) (21–29). In contrast to lyotropic liquid crystals that are dispersed in a solvent and whose phase can be tuned by either concentration or temperature, TLCs do not need a solvent to possess a liquid-crystalline state and their phase depends only on temperature (30). Most TLCs are shear-aligned nematics, in which the director evolves toward an equilibrium out-of-plane polar angle. Defects nucleate beyond a critical Ericksen number due to the irreconcilable alignment of the directors from surface anchoring and shear alignment in the bulk flow (24, 31–33). With an increase in shear rate, the defect type can transition from π-walls (domain walls that separate regions whose director orientation differs by an angle of π) to ordered disclinations and to a disordered chaotic regime (34). Recent efforts have aimed to tune and control the defect structures by understanding the relation between the selection of topological defect types and the flow field in flowing TLCs. Strategies to do so include tuning the geometry of microfluidic channels, inducing defect nucleation through the introduction of isotropic phases or designing inhomogeneities in the surface anchoring (35–39). LCPs are typically tumbling nematics for which α2α3 < 0, where α2 and α3 are the Leslie viscosities. This leads to a nonzero viscous torque for any orientation of the director, which allows the director to rotate in the shear plane (22, 29, 30, 40). The tumbling character of LCPs facilitates the nucleation of singular topological defects (22, 40). Moreover, the molecular rotational relaxation times of LCPs are longer than those of TLCs, and they can exceed the timescales imposed by the shear rate. As a result, the rheological behavior of LCPs is governed not only by spatial gradients of the director field from the Frank elasticity, but also by changes in the molecular order parameter (25, 41–43). With increasing shear rate, topological defects in LCPs have been shown to transition from disclinations to rolling cells and to worm-like patterns (25, 26, 43).Topological defects occurring in the flow of nematic LCLCs have so far received much more limited attention (44, 45). At rest, LCLCs exhibit unique properties distinct from those of TLCs and LCPs (1, 2, 4–6, 44). In particular, LCLCs have significant elastic anisotropy compared to TLCs; the twist Frank elastic constant, K2, is much smaller than the splay and bend Frank elastic constants, K1 and K3. The resulting relative ease with which twist deformations can occur can lead to a spontaneous symmetry breaking and the emergence of chiral structures in static LCLCs under spatial confinement, despite the achiral nature of the molecules (4, 46–51). When driven out of equilibrium by an imposed flow, the average director field of LCLCs has been reported to align predominantly along the shear direction under strong shear but to reorient to an alignment perpendicular to the shear direction below a critical shear rate (52–54). A recent study has revealed a variety of complex textures that emerge in simple shear flow in the nematic LCLC disodium cromoglycate (DSCG) (44). The tumbling nature of this liquid crystal leads to enhanced sensitivity to shear rate. At shear rates γ˙<1 s−1, the director realigns perpendicular to the flow direction adapting a so-called log-rolling state characteristic of tumbling nematics. For 1 s−1<γ˙<10 s−1, polydomain textures form due to the nucleation of pure-twist disclination loops, for which the rotation vector is parallel to the loop normal, and mixed wedge-twist disclination loops, for which the rotation vector is perpendicular to the loop normal (44, 55). Above γ˙>10 s−1, the disclination loops gradually transform into periodic stripes in which the director aligns predominantly along the flow direction (44).Here, we report on the structure and dynamics of topological defects occurring in the pressure-driven flow of nematic DSCG. A quantitative evaluation of such dynamics has so far remained challenging, in particular for fast flow velocities, due to the slow image acquisition rate of current quantitative polarization-resolved imaging techniques. Quantitative polarization imaging traditionally relies on three commonly used techniques: fluorescence confocal polarization microscopy, polarizing optical microscopy, and LC-Polscope imaging. Fluorescence confocal polarization microscopy can provide accurate maps of birefringence and orientation angle, but the fluorescent labeling may perturb the flow properties (56). Polarizing optical microscopy requires a mechanical rotation of the polarizers and multiple measurements, which severely limits the imaging speed. LC-Polscope, an extension of conventional polarization optical microscopy, utilizes liquid crystal universal compensators to replace the compensator used in conventional polarization microscopes (57). This leads to an enhanced imaging speed and better compensation for polarization artifacts of the optical system. The need for multiple measurements to quantify retardance, however, still limits the acquisition rate of LC-Polscopes.We overcome these challenges by using a single-shot quantitative polarization microscopy technique, termed polarized shearing interference microscopy (PSIM). PSIM combines circular polarization light excitation with off-axis shearing interferometry detection. Using a custom polarization retrieval algorithm, we achieve single-shot mapping of the retardance, which allows us to reach imaging speeds that are limited only by the camera frame rate while preserving a large field-of-view and micrometer spatial resolution. We provide a brief discussion of the optical design of PSIM in Materials and Methods; further details of the measurement accuracy and imaging performance of PSIM are reported in ref. 58.Using a combination of experiments, numerical simulations and scaling analysis, we show that in the pressure-driven flow of nematic DSCG solutions in a microfluidic channel, pure-twist disclination loops emerge for a certain range of shear rates. These loops are elongated in the flow with a fixed aspect ratio. We demonstrate that the disclination loops nucleate at the boundary between regions where the director aligns predominantly along the flow direction close to the channel walls and regions where the director aligns predominantly perpendicular to the flow direction in the center of the channel. The large elastic stresses of the director gradient at the boundary are then released by the formation of disclination loops. We show that both the characteristic size and the fluctuations of the pure-twist disclination loops can be tuned by controlling the flow rate.     

Glasses denser than the supercooled liquid

When aged below the glass transition temperature, Tg, the density of a glass cannot exceed that of the metastable supercooled liquid (SCL) state, unless crystals are nucleated. The only exception is when another polyamorphic SCL state exists, with a density higher than that of the ordinary SCL. Experimentally, such polyamorphic states and their corresponding liquid–liquid phase transitions have only been observed in network-forming systems or those with polymorphic crystalline states. In otherwise simple liquids, such phase transitions have not been observed, either in aged or vapor-deposited stable glasses, even near the Kauzmann temperature. Here, we report that the density of thin vapor-deposited films of N,N′-bis(3-methylphenyl)-N,N′-diphenylbenzidine (TPD) can exceed their corresponding SCL density by as much as 3.5% and can even exceed the crystal density under certain deposition conditions. We identify a previously unidentified high-density supercooled liquid (HD-SCL) phase with a liquid–liquid phase transition temperature (TLL) ∼35 K below the nominal glass transition temperature of the ordinary SCL. The HD-SCL state is observed in glasses deposited in the thickness range of 25 to 55 nm, where thin films of the ordinary SCL have exceptionally enhanced surface mobility with large mobility gradients. The enhanced mobility enables vapor-deposited thin films to overcome kinetic barriers for relaxation and access the HD-SCL state. The HD-SCL state is only thermodynamically favored in thin films and transforms rapidly to the ordinary SCL when the vapor deposition is continued to form films with thicknesses more than 60 nm.

Glasses are formed when the structural relaxations in supercooled liquids (SCLs) become too slow, causing the system to fall out of equilibrium at the glass transition temperature (Tg). The resulting out-of-equilibrium glass state has a thermodynamic driving force to evolve toward the SCL state through physical aging (1). At temperatures just below Tg, the extent of equilibration is limited by the corresponding SCL state, while at much lower temperatures, equilibration is limited by the kinetic barriers for relaxation. As such, the degree of thermodynamic stability achieved through physical aging is limited (2).Physical vapor deposition (PVD) is an effective technique to overcome kinetic barriers for relaxation to produce thermodynamically stable glasses (3–10). The accelerated equilibration in these systems is due to their enhanced surface mobility (11–14). During PVD, when the substrate temperature is held below Tg, molecules or atoms can undergo rearrangements and adopt more stable configurations at the free surface and proximate layers underneath (13). After the molecules are buried deeper into the film, their relaxation dynamics significantly slow down, which prevents further equilibration. Through this surface-mediated equilibration process, stable glasses can achieve low-energy states on the potential energy landscape that would otherwise require thousands or millions of years of physical aging (2, 3, 15, 16).As such, the degree of enhanced surface mobility and mobility gradients are critical factors in the formation of stable glasses (3, 11, 17, 18). While the effect of film thickness on the surface mobility and gradients of liquid-quenched (LQ) glasses has been studied in the past (19, 20), there are limited data on the role of film thickness in the stability of vapor-deposited glasses. In vapor-deposited toluene, it has been shown that decreasing the film thickness from 70 to 5 nm can increase the thermodynamic stability but decrease the apparent kinetic stability (5, 6). In contrast, thin films covered with a top layer of another material do not show a significant evidence of reduced kinetic stability (21), indicating the nontrivial role of mobility gradients in thermal and kinetic stability.Stable glasses of most organic molecules, with short-range intramolecular interactions, have properties that are indicative of the same corresponding metastable SCL state as LQ and aged glasses, without any evidence of the existence of generic liquid–liquid phase transitions that can potentially provide a resolution for the Kauzmann entropy crisis (22). The Kauzmann crisis occurs at the Kauzmann temperature (TK), where the extrapolated SCL has the same structural entropy as the crystal, producing thermodynamically impossible states just below this temperature. Recently, Beasley et al. (16) showed that near-equilibrium states of ethylbenzene can be produced using PVD down to 2 K above TK and hypothesized that any phase transition to an “ideal glass” state to avoid the Kauzmann crisis must occur at TK.In some glasses of elemental substances (23, 24) and hydrogen-bonding compounds (25, 26), liquid–liquid phase transitions can occur between polyamorphic states with distinct local packing structures that correspond to polymorphic crystalline phases. For example, at high pressures, high- and low-density supercooled water phases are interconvertible through a first-order phase transition (27, 28). Recent studies have demonstrated that such polyamorphic states can also be accessed through PVD in hydrogen-bonding systems with polymorphic crystal states at depositions above the nominal Tg (29, 30). However, these structure-specific transitions do not provide a general resolution for the Kauzmann crisis.Here, we report the observation of a liquid–liquid phase transition in vapor-deposited thin films of N,N′-bis(3-methylphenyl)-N,N′-diphenylbenzidine (TPD). TPD is a molecular glass former with only short-range intermolecular interactions. When thin films of TPD are vapor deposited onto substrates held at deposition temperatures (Tdep) below the nominal glass transition temperature of bulk TPD, Tg (bulk), films in the thickness range of 25 nm<h<55 nm achieve a high-density supercooled liquid (HD-SCL) state, which has not been previously observed. The liquid–liquid phase transition temperature (TLL) between the ordinary SCL and HD-SCL states is measured to be TLL≃Tg(bulk)−35 K. The density of thin films deposited below TLL tangentially follows the HD-SCL line, which has a stronger temperature dependence than the ordinary SCL. When vapor deposition is continued to produce thicker films (h>60 nm), the HD-SCL state transforms into the ordinary SCL state, indicating that the HD-SCL is only thermodynamically favored in the thin-film geometry. This transition is qualitatively different from the previously reported liquid–liquid phase transitions, as it is not related to a specific structural motif in TPD crystals, and it can only be observed in thin films, indicating that the energy landscape of thin films is favoring this high-density state.We observe an apparent correlation between enhanced mobility gradients in LQ thin films of TPD and the thickness range where HD-SCL states are produced during PVD. We hypothesize that enhanced mobility gradients are essential in providing access to regions of the energy landscape corresponding to the HD-SCL state, which are otherwise kinetically inaccessible. This hypothesis should be further investigated to better understand the origin of this phenomenon.     

Entropic barrier of topologically immobilized DNA in hydrogels

The single most intrinsic property of nonrigid polymer chains is their ability to adopt enormous numbers of chain conformations, resulting in huge conformational entropy. When such macromolecules move in media with restrictive spatial constraints, their trajectories are subjected to reductions in their conformational entropy. The corresponding free energy landscapes are interrupted by entropic barriers separating consecutive spatial domains which function as entropic traps where macromolecules can adopt their conformations more favorably. Movement of macromolecules by negotiating a sequence of entropic barriers is a common paradigm for polymer dynamics in restrictive media. However, if a single chain is simultaneously trapped by many entropic traps, it has recently been suggested that the macromolecule does not undergo diffusion and is localized into a topologically frustrated dynamical state, in apparent violation of Einstein’s theorem. Using fluorescently labeled λ-DNA as the guest macromolecule embedded inside a similarly charged hydrogel with more than 95% water content, we present direct evidence for this new state of polymer dynamics at intermediate confinements. Furthermore, using a combination of theory and experiments, we measure the entropic barrier for a single macromolecule as several tens of thermal energy, which is responsible for the extraordinarily long extreme metastability. The combined theory–experiment protocol presented here is a determination of single-molecule entropic barriers in polymer dynamics. Furthermore, this method offers a convenient general procedure to quantify the underlying free energy landscapes behind the ubiquitous phenomenon of movement of single charged macromolecules in crowded environments.

Movement of charged macromolecules in aqueous media with crowded spatial constraints is ubiquitous in biology, biotechnology, and separation science (1–7). A familiar scenario is the movement of messenger RNA inside the milieu of a nucleus of a mammalian cell, which is a thick Coulomb soup, toward the nuclear pore complex in the process of initiating protein synthesis. Another well-known example is the gel electrophoresis used to identify and separate polynucleotides of different lengths. Furthermore, hydrogel-based technology is extensively implemented to perform targeted delivery of drugs and genes (2–6). Parallel to these aqueous systems, movement of macromolecules in congested nonaqueous polymer melts containing nanoparticles, and infiltration of polymer melts through restricted media, are of tremendous interest in terms of fundamental understanding and applications (8–15). Although entropic barriers associated with conformational changes of the moving macromolecules are often invoked in the above examples of both aqueous and nonaqueous polymer systems, the quantitative nature of such entropic barriers remains to be established (16–42). Despite the above-mentioned now-standard experimental protocols and substantial applications, an understanding of how macromolecules navigate themselves in crowded environments continues to be a persistent challenge.Adding fuel to the flames, a recent discovery (41, 42) shows that large charged macromolecules such as λ-DNA and sodium poly(styrene sulfonate) can be immobilized in hydrogels which are essentially water at ambient temperatures, as a strong deviation from Einstein’s theorem on diffusion. In this paper, we present a combination of theory and fluorescence-based single-molecule tracking to directly observe the movement of guest macromolecules and quantify the entropic barriers associated with their movement. We provide direct evidence for the emergence of the recently proposed nondiffusive topologically frustrated dynamical state at intermediate confinements and determine the associated entropic barrier responsible for extraordinarily long-lived metastable dynamical states.The difficulty in attaining an adequate understanding of entropically driven movement of large macromolecules in soft background media stems from the interdependence between the conformational fluctuations of the macromolecule subjected to transport and the spatial correlation of spatial constraints in the crowded background medium. As an example, consider a large macromolecule (guest) embedded inside a host hydrogel (Fig. 1A). Let the radius of gyration of the guest molecule of N monomers be Rg and the cross-link density of the hydrogel be such that the average mesh size (correlation length for local monomer concentration of the host) is ξ. If Rg≲ξ, the guest molecule only brushes against the host matrix and diffuses. On the other hand, if Rg≫ξ, a single guest molecule is partitioned among many meshes, resulting in its localization. In each occupied mesh, the partitioned portion of the guest under confinement can adopt numerous conformations with a confinement free energy. As a result, each occupied mesh functions as a free energy trap relative to its neighboring matrix domains that are inaccessible to the guest. Accounting for excluded volume interactions and ignoring correlations, the confinement free energy is proportional to M2/ξ3, where M≪N is the number of monomers inside a trap of volume ξ3 (42). The localization effect occurs within two boundary regions. One region corresponds to weaker confinement, Rg≲ξ, as mentioned above. At the other boundary region of transition into reptation, where the free energy traps cease to exist (M2/ξ3→0), we expect ξ to be so small that its corresponding three-dimensional mesh does not have enough space for the guest, namely, M→0. Let us define a length ℓc, comparable to that of only a small number of monomers, corresponding to this condition (vanishing confinement free energy). Furthermore, in the limit of very strong confinements with no free energy traps, the guest is confined inside an essentially one-dimensional tube of a diameter comparable to the entanglement length ℓe. The precise value of ℓc and its relation to ℓe are presently unknown. For brevity, we use ℓ in Fig. 1 to denote both ℓc and ℓe, and leave the detailed values of ℓc and ℓe and their relation to persistence length for future investigation (see Conclusions and Perspective). The movement of the guest molecule is dictated by the relative value of Rg to ξ, and the relative value of ξ to the length ℓ defined above. Different possible scenarios based on Rg/ξ and ξ/ℓ are portrayed in Fig. 1B.Open in a separate windowFig. 1.(A) Cartoon of a large charged macromolecule of radius of gyration Rg embedded in a hydrogel of mesh size ξ. (B) Sketch of the dependence of the diffusion coefficient D of the guest molecule on degree of confinement (which increases with a decrease in ξ). The four conventional regimes of polymer dynamics, namely, Zimm, Rouse, entropic barrier, and reptation, and their conditions of experimental relevance are denoted by 1, 2, 3, and 5, respectively. The corresponding scaling laws in these regimes connecting D and the degree of polymerization N of the polymer chain are given in Eq. 1. Regime 4 is the newly hypothesized nondiffusive (D≃0, as denoted by the red horizontal line) topologically frustrated state at intermediate confinements. Direct observation of this new dynamical state and measurement of the entropic barrier responsible for polymer localization are presented in Results. (C) Sketch of partitioning of a single chain into multiple deep entropic traps.Based on experiments during the past seven decades and buttressed by theories (43, 44), four regimes (1, 2, 3, and 5) have been widely recognized. These are described, respectively, by the Stokes–Einstein–Zimm, Rouse, entropic barrier, and reptation models. In all these regimes, the guest molecule undergoes diffusion. The dependence of the diffusion coefficient D on the degree of polymerization N of the polymer molecule is given by the scaling laws as (Fig. 1B)[1]where ν is the size exponent defined through Rg≈Nν, and A is a nonuniversal numerical factor denoting the local structure of the host medium (16). The above four regimes of polymer diffusion have been validated by a preponderance of experimental data in the past (17–20, 22–33).Furthermore, in a recent development, room temperature experiments on charged macromolecules (such as λ-DNA and sodium poly(styrene sulfonate)) embedded inside similarly charged hydrogels at intermediate confinements (Rg≫ξ≫ℓ, regime 4 in Fig. 1B) have revealed an apparent breakdown of even the phenomenon of diffusion, and the emergence of a new nondiffusive topologically frustrated dynamical state. When Rg≫ξ≫ℓ (regime 4 in Fig. 1B), each macromolecule is so large in comparison with the mesh size that it is partitioned among many meshes. Since ξ≫ℓ, each mesh is an entropic trap holding a significant portion of the macromolecule and allowing local Rouse–Zimm dynamics for that portion. Furthermore, that portion can move to a neighboring empty mesh only through an entropic barrier as in regime 3 (where a single entropic barrier is operative for the whole molecule). As a consequence, many sets of entropic barriers must be simultaneously negotiated for the center of mass of one molecule to diffuse. The free energy landscape for the situation in regime 4 is cartooned in Fig. 1C. Theoretical analysis (41) of the simultaneous crossing of multiple entropic barriers by a single chain shows that the net effective free energy barrier U arising only from conformational entropy isU≃kBT ln196ξ8ℓ8,[2]where kB is the Boltzmann constant, and T is the absolute temperature. Thus the barrier U can be enormous depending on ξ/ℓ. For example, for ξ/ℓ=50, U≃27kBT. Such large barriers result in extremely long times for a single chain to diffuse a distance comparable to its own size. As a result, the macromolecule is practically locked into an immobile state in regime 4. Therefore, in regime 4, the time evolution of the mean square displacement of the center of mass Rcm(t) of the guest molecule is hypothesized to be nondiffusive according to⟨Rcm(t)−Rcm(0)2⟩≈t0, (Rg≫ξ≫ℓ).[3]This additional dynamical state is included in Fig. 1B, where the red horizontal line denotes the nondiffusive regime 4.Although the above hypothesis of the emergence of a nondiffusive topologically frustrated long-lived metastable state at intermediate confinements is supported by dynamic light scattering experiments (41, 42), direct evidence for this phenomenon and quantification of the collective entropic barrier responsible for this effect are yet to be established. These are the primary goals of the present paper. Using a combination of theory and statistical analysis of thousands of trajectories of fluorescently labeled λ-DNA inside poly(acrylamide-coacrylate) hydrogels with more than 95% water content, we have measured the entropic barrier that results in the new topologically frustrated state, in addition to finding direct evidence for the immobility of λ-DNA at intermediate confinements.     

Enhanced microscopic dynamics in mucus gels under a mechanical load in the linear viscoelastic regime

Mucus is a biological gel covering the surface of several tissues and ensuring key biological functions, including as a protective barrier against dehydration, pathogen penetration, or gastric acids. Mucus biological functioning requires a finely tuned balance between solid-like and fluid-like mechanical response, ensured by reversible bonds between mucins, the glycoproteins that form the gel. In living organisms, mucus is subject to various kinds of mechanical stresses, e.g., due to osmosis, bacterial penetration, coughing, and gastric peristalsis. However, our knowledge of the effects of stress on mucus is still rudimentary and mostly limited to macroscopic rheological measurements, with no insight into the relevant microscopic mechanisms. Here, we run mechanical tests simultaneously to measurements of the microscopic dynamics of pig gastric mucus. Strikingly, we find that a modest shear stress, within the macroscopic rheological linear regime, dramatically enhances mucus reorganization at the microscopic level, as signaled by a transient acceleration of the microscopic dynamics, by up to 2 orders of magnitude. We rationalize these findings by proposing a simple, yet general, model for the dynamics of physical gels under strain and validate its assumptions through numerical simulations of spring networks. These results shed light on the rearrangement dynamics of mucus at the microscopic scale, with potential implications in phenomena ranging from mucus clearance to bacterial and drug penetration.

Mucus is a biogel ubiquitous across both vertebrates and invertebrates (1–3). The main mucus macromolecular components are a family of glycosylated proteins called mucins (4–6). Hydrophobic, hydrogen-bonding, and Ca2+-mediated (7) interactions between mucins are responsible for macromolecular associations determining the viscoelastic properties of mucus, which, in turn, control its biological functions (2, 5). Alteration of the viscoelastic properties compromises mucus functionality, resulting in severe diseases (8, 9).Mucus viscoelasticity stems from the reversible nature of the bonds between its constituents, which ensure solid-like behavior on short time scales while allowing flow on longer time scales. Rheological studies on mucus reporting the frequency dependence of the storage, G′, and loss, G″, components of the dynamic modulus reveal G′>G″, with G′ only weakly dependent on angular frequency ω on time scales of 0.1 to 100 s (8–10), a behavior typical of soft solids (11). Stress-relaxation tests probe viscoelasticity on longer time scales, up to thousands of seconds. They reveal a power law or logarithmic decay of the shear stress with time (12–14), indicative of a wide distribution of relaxation times, ascribed to the variety of macromolecular association mechanisms and the mucus complex, multiscale structure (7, 14, 15).Alongside conventional rheology, microrheology has gained momentum since it investigates the mechanical response of mucus on the length scales relevant to its biological functions, from a fraction of a micrometer up to ∼10 μm (7, 8, 16–19). Microrheology infers the viscoelastic moduli from the microscopic dynamics of tracer particles embedded in the sample (20), either due to spontaneous thermal fluctuations or externally driven, e.g., by a magnetic field. Mucus viscoelasticity as measured by microrheology is found to depend on the size of the tracer particles, the local environment they probe, and the length scale over which their motion is tracked (7, 8, 16, 17, 19, 21). Below ≈1 μm, microrheology data are dominated by the diffusion of the probe particles within the mucus pores, as inferred from the analysis of the localization of the tracers’ trajectories (7, 17), their dependence on probe size (8, 16, 21), and on the amplitude of the external drive in active microrheology (16). On larger length scales, microrheology reports the local viscoelasticity, which converges toward the macroscopic one above ≈10 μm, as revealed by the probe-size and drive-amplitude dependence of active microrheology (16).In vivo, mucus is submitted to stresses of various origin, involving strain on the microscopic scale, as in cilia beating in muco-ciliary clearance (22) and bacterial penetration (23, 24), up to macroscopic scales, e.g., during coughing and peristalsis (3, 25). Stresses due to the osmotic pressure exerted by the environment (26) or resulting from changes in hydration (27, 28) can modify the structure of mucus and, e.g., impair mucus clearance. By contrast, little is known on the impact of stress on the dynamics of mucus, in particular, at the microscopic level. Conventional rheology indicates that mucus is fluidized upon applying a large stress (29, 30), beyond the linear regime. This behavior is typical of soft solids (31–33); in concentrated nanoemulsions and colloidal suspensions and in colloidal gels, fluidization in the nonlinear regime has been shown to stem from enhanced microscopic dynamics (34–40). However, for mucus, we still lack knowledge of the effect of an applied stress on the microscopic dynamics.Here, we couple rheology and light and X-ray photon correlation methods to investigate the microscopic dynamics of pig gastric mucus under an applied shear stress. Surprisingly, we find that small stresses, well within the macroscopic linear viscoelastic regime, transiently enhance the mucus dynamics by up to 2 orders of magnitude. We propose a simple, yet general, model for the dynamics of physical gels under strain that rationalizes these findings.     

Thermodynamic controls on rates of iron oxide reduction by extracellular electron shuttles

Anaerobic microbial respiration in suboxic and anoxic environments often involves particulate ferric iron (oxyhydr-)oxides as terminal electron acceptors. To ensure efficient respiration, a widespread strategy among iron-reducing microorganisms is the use of extracellular electron shuttles (EES) that transfer two electrons from the microbial cell to the iron oxide surface. Yet, a fundamental understanding of how EES–oxide redox thermodynamics affect rates of iron oxide reduction remains elusive. Attempts to rationalize these rates for different EES, solution pH, and iron oxides on the basis of the underlying reaction free energy of the two-electron transfer were unsuccessful. Here, we demonstrate that broadly varying reduction rates determined in this work for different iron oxides and EES at varying solution chemistry as well as previously published data can be reconciled when these rates are instead related to the free energy of the less exergonic (or even endergonic) first of the two electron transfers from the fully, two-electron reduced EES to ferric iron oxide. We show how free energy relationships aid in identifying controls on microbial iron oxide reduction by EES, thereby advancing a more fundamental understanding of anaerobic respiration using iron oxides.

The use of iron oxides as terminal electron acceptors in anaerobic microbial respiration is central to biogeochemical element cycling and pollutant transformations in many suboxic and anoxic environments (1–6). To ensure efficient electron transfer to solid-phase ferric iron, Fe(III), at circumneutral pH, metal-reducing microorganisms from diverse phylae use dissolved extracellular electron shuttle (EES), including quinones (7–9), flavins (10–16), and phenazines (17–19), to transfer two electrons per EES molecule from the respiratory chain proteins in the outer membrane of the microbial cell to the iron oxide (17, 20, 21). The oxidized EES can diffuse back to the cell surface for rereduction, thereby completing the catalytic redox cycle involving the EES.The electron transfer from the reduced EES to Fe(III) is considered a key step in overall microbial Fe(III) respiration. Several lines of evidence suggest that the free energy of the electron transfer reaction, ΔrG, controls Fe(III) reduction rates (15, 17, 22, 23). For instance, microbial Fe(III) oxide reduction by dissolved model quinones as EES was accelerated only for quinones with standard two-electron reduction potentials, EH,1,20, that fell into a relatively narrow range of −180±80 mV at pH 7 (24). Furthermore, in abiotic experiments, Fe(III) reduction rates by EES decreased with increasing ΔrG that resulted from increasing either EH,1,20 of the EES (25, 26), the concentration of Fe(II) in the system (27), or solution pH (25, 26, 28). However, substantial efforts to relate Fe(III) reduction rates for different EES species, iron oxides, and pH to the EH,1,20 averaged over both electrons transferred from the EES to the iron oxides were only partially successful (25, 28). Reaction free energies of complex redox processes involving the transfer of multiple electrons can readily be calculated using differences in the reduction potentials averaged over all electrons transferred, and this approach is well established in biogeochemistry and microbial ecology. For kinetic considerations, however, the use of averaged reduction potentials is inappropriate.Herein, we posit that rates of Fe(III) reduction by EES instead relate to the ΔrG of the less exergonic first one-electron transfer from the two-electron reduced EES species to the iron oxide, following the general notion that reaction rates scale with reaction free energies (29). Our hypothesis is based on the fact that, at circumneutral to acidic pH and for many EES, the reduction potential of the first electron transferred to the fully oxidized EES to form the one-electron reduced intermediate semiquinone species, EH,1, is lower than the reduction potential of the second electron transferred to the semiquinone to form the fully two-electron reduced EES species, EH,2 [i.e., EH,1<EH,2 (30–33)]. This difference in one-electron reduction potentials implies that the two-electron reduced EES (i.e., the hydroquinone) is the weaker one-electron reductant for Fe(III) as compared to the semiquinone species. We therefore expect that rates of iron oxide reduction relate to the ΔrG of the first electron transferred from the hydroquinone to Fe(III). The ΔrG of this first electron transfer may even be endergonic provided that the two-electron transfer is exergonic.We verified our hypothesis in abiotic model systems by demonstrating that reduction rates of two geochemically important crystalline iron oxides, goethite and hematite, by two-electron reduced quinone- and flavin-based EES over a wide pH range, and therefore thermodynamic driving force for Fe(III) reduction, correlate with the ΔrG of the first electron transferred from the fully reduced EES to Fe(III). We further show that rates of goethite and hematite reduction by EES reported in the literature are in excellent agreement with our rate data when comparing rates on the basis of the thermodynamics of the less exergonic first of the two electron transfers.     

Low-Reynolds-number,biflagellated Quincke swimmers with multiple forms of motion

In the limit of zero Reynolds number (Re), swimmers propel themselves exploiting a series of nonreciprocal body motions. For an artificial swimmer, a proper selection of the power source is required to drive its motion, in cooperation with its geometric and mechanical properties. Although various external fields (magnetic, acoustic, optical, etc.) have been introduced, electric fields are rarely utilized to actuate such swimmers experimentally in unbounded space. Here we use uniform and static electric fields to demonstrate locomotion of a biflagellated sphere at low Re via Quincke rotation. These Quincke swimmers exhibit three different forms of motion, including a self-oscillatory state due to elastohydrodynamic–electrohydrodynamic interactions. Each form of motion follows a distinct trajectory in space. Our experiments and numerical results demonstrate a method to generate, and potentially control, the locomotion of artificial flagellated swimmers.

In a Newtonian fluid, locomotion of microswimmers requires nonreciprocal body motions (1–3). Bacteria or eukaryotic cells achieve this by beating or rotating their slender hair-like organelles, flagella (4, 5) or cilia (6), powered by molecular motors. Mimicking these organisms, artificial swimmers propelled by rotating helices (7, 8) or whipping filaments (9–12) have been fabricated. They are commonly driven by an external power source such as a magnetic field (7–9, 13, 14), sound (15), light (16, 17), and biological materials (12). However, there are very few electrically powered microswimmers (18–20), although electric fields have been exploited to drive other active systems (21–26) via a phenomenon called Quincke rotation (27).Quincke rotation originates from an electrohydrodynamic instability (28–30). Submerged in a liquid with permittivity εl and conductivity σl, a spherical particle with permittivity εs and electric conductivity σs is polarized under a uniform, steady electric field E→. When the particle is stationary, the induced dipole p→ due to the free charges is parallel or antiparallel to E→ (Fig. 1A): if the particle’s relaxation time τs=εs/σs is shorter than that of the ambient liquid, τl=εl/σl, p→ points in the same direction as E→; when τs>τl, p→ is opposite to E→, which generates an electric torque Γ→Q=p→×E→ that amplifies any angular perturbation. However, due to the resisting viscous torque Γ→μ, the system becomes unstable only when E=|E→| exceeds a threshold Ec. This instability causes the particle to rotate with a constant angular velocity ω:ω=1τEEc2−1,[1]where τ=εs+2εlσs+2σl is the relaxation time of the system (see SI Appendix, SI Text, or refs. 28, 29, 31 for derivation), and the rotational axis can be in any direction perpendicular to E→. During steady-state Quincke rotation, there is a constant angle between p→ and E→ (Fig. 1A), which results in a nonzero Γ→Q.Open in a separate windowFig. 1.Quincke rotation and the experimental setup. (A) Distribution of free charge and the corresponding dipole p→ on a sphere in a uniform, steady electric field E→. The sphere is (Left) stationary, (Middle) stationary, and (Right) rotating with a constant angular velocity ω. (B) A sketch of the biflagellated swimmer. Dashed lines show the roll axis (blue) and pitch axis (green). (C) A schematic illustration of the experimental setup.Recently, a flagellated swimmer in unbounded space driven by Quincke rotation has been proposed theoretically (32, 33). In light of the theory, we built a laboratory prototype, a biflagellated Quincke swimmer composed of a spherical particle and two attached elastic filaments, as shown in Fig. 1B, and systematically studied its behaviors at low Reynolds number (Re<0.3; Materials and Methods). Varying the electric field E→ and the angle between the two filaments, the Quincke swimmers exhibit three distinct forms of motion—two unidirectional rotations, which we call roll and pitch, and a self-oscillatory rotation, due to the balances between the electrical, elastic, and hydrodynamic torques, resulting in distinct trajectories in space. Surprisingly, it was recently reported (34) that spherical bacteria Magnetococcus marinus exhibit a similar pitch motion as our biflagellated artificial swimmers, which is rarely adopted by other microorganisms. Moreover, we found a threshold tail angle that separates the swimmers’ preferred forms of rotation, and within a small range close to this threshold angle, the three forms of motion coexist.     

Activation of indistinguishability-based quantum coherence for enhanced metrological applications with particle statistics imprint

Quantum coherence, an essential feature of quantum mechanics allowing quantum superposition of states, is a resource for quantum information processing. Coherence emerges in a fundamentally different way for nonidentical and identical particles. For the latter, a unique contribution exists linked to indistinguishability that cannot occur for nonidentical particles. Here we experimentally demonstrate this additional contribution to quantum coherence with an optical setup, showing that its amount directly depends on the degree of indistinguishability and exploiting it in a quantum phase discrimination protocol. Furthermore, the designed setup allows for simulating fermionic particles with photons, thus assessing the role of exchange statistics in coherence generation and utilization. Our experiment proves that independent indistinguishable particles can offer a controllable resource of coherence and entanglement for quantum-enhanced metrology.

A quantum system can reside in coherent superpositions of states, which have a role in the interpretation of quantum mechanics (1–4), lead to nonclassicality (5, 6), and imply the intrinsically probabilistic nature of predictions in the quantum realm (7, 8). Besides this fundamental role, quantum coherence is also at the basis of quantum algorithms (9–14) and, from a modern information-theoretic perspective, constitutes a paradigmatic basis-dependent quantum resource (15–17), providing a quantifiable advantage in certain quantum information protocols.For a single quantum particle, coherence manifests itself when the particle is found in a superposition of a reference basis, for instance, the computational basis of the Hilbert space. Formally, any quantum state whose density matrix contains nonzero diagonal elements when expressed in the reference basis is said to display quantum coherence (16). This is the definition of quantum coherence employed in our work. For multiparticle compound systems, the physics underlying the emergence of quantum coherence is richer and strictly connected to the nature of the particles, with fundamental differences for nonidentical and identical particles. A particularly intriguing observation is that the states of identical particle systems can manifest coherence even when no particle resides in superposition states, provided that the wave functions of the particles overlap (18–20). In general, a special contribution to quantum coherence arises thanks to the spatial indistinguishability of identical particles, which cannot exist for nonidentical (or distinguishable) particles (18). Recently, it has been found that the spatial indistinguishability of identical particles can be exploited for entanglement generation (21), applicable even for spacelike-separated quanta (22) and against preparation and dynamical noises (23–26). The presence of entanglement is a signature that the bipartite system as a whole carries coherence even when the individual particles do not, the amount of this coherence being dependent on the degree of indistinguishability. We name this specific contribution to quantumness of compound systems “indistinguishability-based coherence,” in contrast to the more familiar “single-particle superposition-based coherence.” Indistinguishability-based coherence qualifies in principle as an exploitable resource for quantum metrology (18). However, it requires sophisticated control techniques to be harnessed, especially in view of its nonlocal nature. Moreover, a crucial property of identical particles is the exchange statistics, while its experimental study requiring operating both bosons and fermions in the same setup is generally challenging.In the present work, we investigate the operational contribution of quantum coherence stemming from the spatial indistinguishability of identical particles. The main aim of our experiment is to prove that elementary states of two independent spatially indistinguishable particles can give rise to exploitable quantum coherence, with a measurable effect due to particle statistics. By utilizing our recently developed photonic architecture capable of tuning the indistinguishability of two uncorrelated photons (27), we observe the direct connection between the degree of indistinguishability and the amount of generated coherence and show that indistinguishability-based coherence can be concurrent with single-particle superposition-based coherence. In particular, we demonstrate its operational implications, namely, providing a quantifiable advantage in a phase discrimination task (28, 29), as depicted in Fig. 1. Furthermore, we design a setup capable of testing the impact of particle statistics in coherence production and phase discrimination for both bosons and fermions; this is accomplished by compensating for the exchange phase during state preparation, simulating fermionic states with photons, which leads to statistics-dependent efficiency of the quantum task.Open in a separate windowFig. 1.Illustration of the indistinguishability-activated phase discrimination task. A resource state ρin that contains coherence in a computational basis is generated from spatial indistinguishability. The state then enters a black box which implements a phase unitary U^k=eiG^ϕk,k∈{1,…,n} on ρin. The goal is to determine the ϕk actually applied through the output state ρout: indistinguishability-based coherence provides an operational advantage in this task.