Double Exchange Model in Triangular Lattice Studied by Truncated Polynomial Expansion Method

The low temperature properties of double exchange model in triangular lattice are investigated via truncated polynomial expansion method (TPEM), which reduces the computational complexity and enables parallel computation. We found that for the half-filling case a stable 120^◦spin configuration phase occurs owing to the frustration of triangular lattice and is further stabilized by antiferromagnetic (AF) superexchange interaction, while a transition between a stable ferromagnetic (FM) phase and a unique flux phase with small finite-size effect is induced by AF superexchange interaction for the quarter-filling case.     

Numerical Path Integral Approach to Quantum Dynamics and Stationary Quantum States

Applicability of Feynman path integral approach to numerical simulations of quantum dynamics of an electron in real time domain is examined. Coherent quantum dynamics is demonstrated with one dimensional test cases (quantum dot models) and performance of the Trotter kernel as compared with the exact kernels is tested. Also, a novel approach for finding the ground state and other stationary sates is presented. This is based on the incoherent propagation in real time. For both approaches the Monte Carlo grid and sampling are tested and compared with regular grids and sampling. We asses the numerical prerequisites for all of the above.     

A Three-Level Multi-Continua Upscaling Method for Flow Problems in Fractured Porous Media

Traditional two level upscaling techniques suffer from a high offline cost when the coarse grid size is much larger than the fine grid size one. Thus, multilevel methods are desirable for problems with complex heterogeneities and high contrast. In this paper, we propose a novel three-level upscaling method for flow problems in fractured porous media. Our method starts with a fine grid discretization for the system involving fractured porous media. In the next step, based on the fine grid model, we construct a nonlocal multi-continua upscaling (NLMC) method using an intermediate grid. The system resulting from NLMC gives solutions that have physical meaning. In order to enhance locality, the grid size of the intermediate grid needs to be relatively small, and this motivates using such an intermediate grid. However, the resulting NLMC upscaled system has a relatively large dimension. This motivates a further step of dimension reduction. In particular, we will apply the idea of the Generalized Multiscale Finite Element Method (GMsFEM) to the NLMC system to obtain a final reduced model. We present simulation results for a two-dimensional model problem with a large number of fractures using the proposed three-level method.     

Divergence-Free WENO Reconstruction-Based Finite Volume Scheme for Solving Ideal MHD Equations on Triangular Meshes

In this paper, we introduce a high-order accurate constrained transport type finite volume method to solve ideal magnetohydrodynamic equations on two-dimensional triangular meshes. A new divergence-free WENO-based reconstruction method is developed to maintain exactly divergence-free evolution of the numerical magnetic field. In this formulation, the normal component of the magnetic field at each face of a triangle is reconstructed uniquely and with the desired order of accuracy. Additionally, a new weighted flux interpolation approach is also developed to compute the z-component of the electric field at vertices of grid cells. We also present numerical examples to demonstrate the accuracy and robustness of the proposed scheme.     

A Wavelet-Adaptive Method for Multiscale Simulation of Turbulent Flows in Flying Insects

We present a wavelet-based adaptive method for computing 3D multiscale flows in complex, time-dependent geometries, implemented on massively parallel computers. While our focus is on simulations of flapping insects, it can be used for other flow problems. We model the incompressible fluid with an artificial compressibility approach in order to avoid solving elliptical problems. No-slip and in/outflow boundary conditions are imposed using volume penalization. The governing equations are discretized on a locally uniform Cartesian grid with centered finite differences, and integrated in time with a Runge–Kutta scheme, both of 4th order. The domain is partitioned into cubic blocks with different resolution and, for each block, biorthogonal interpolating wavelets are used as refinement indicators and prediction operators. Thresholding the wavelet coefficients allows to generate dynamically evolving grids, and an adaption strategy tracks the solution in both space and scale. Blocks are distributed among MPI processes and the grid topology is encoded using a tree-like data structure. Analyzing the different physical and numerical parameters allows us to balance their errors and thus ensures optimal convergence while minimizing computational effort. Different validation tests score accuracy and performance of our new open source code, WABBIT. Flow simulations of flapping insects demonstrate its applicability to complex, bio-inspired problems.     

Computation of Two-Phase Biomembranes with Phase Dependent Material Parameters Using Surface Finite Elements

The shapes of vesicles formed by lipid bilayers with phase separation are governed by a bending energy with phase dependent material parameters together with a line energy associated with the phase interfaces. We present a numerical method to approximate solutions to the Euler-Lagrange equations featuring triangulated surfaces, isoparametric quadratic surface finite elements and the phase field approach for the phase separation. Furthermore, the method involves an iterative solution scheme that is based on a relaxation dynamics coupling a geometric evolution equation for the membrane surface with a surface Allen-Cahn equation. Remeshing and grid adaptivity are discussed, and in various simulations the influence of several physical parameters is investigated.     

Multi-Mesh-Scale Approximation of Thin Geophysical Mass Flows on Complex Topographies

This paper is devoted to a multi-mesh-scale approach for describing the dynamic behaviors of thin geophysical mass flows on complex topographies. Because the topographic surfaces are generally non-trivially curved, we introduce an appropriate local coordinate system for describing the flow behaviors in an efficient way. The complex surfaces are supposed to be composed of a finite number of triangle elements. Due to the unequal orientation of the triangular elements, the distinct flux directions add to the complexity of solving the Riemann problems at the boundaries of the triangular elements. Hence, a vertex-centered cell system is introduced for computing the evolution of the physical quantities, where the cell boundaries lie within the triangles and the conventional Riemann solvers can be applied. Consequently, there are two mesh scales: the element scale for the local topographic mapping and the vertex-centered cell scale for the evolution of the physical quantities. The final scheme is completed by employing the HLL-approach for computing the numerical flux at the interfaces. Three numerical examples and one application to a large-scale landslide are conducted to examine the performance of the proposed approach as well as to illustrate its capability in describing the shallow flows on complex topographies.     

Contact double-contrast cholangiography.

Recently operative cholangiography has become an essential step in biliary surgery. However, an usual technique in which x-ray film is set beneath the patient has its limitation in visualization of fine changes. The author devised a new technique to resolve this problem. A triangular mammography film designed for good positioning is vaccum-packed, coupled with an intensifying screen of the same size, and then is sterilized in advance. Barium solution mixed with Gascon drop (a defoaming agent) is used as contrast material. The duodenum and head of the pancreas are mobilized. Usual cholangiography is performed at first, introducing angiographic media through a catheter placed into the catheter placed into the common duct via the cystic duct. After this study a triangle film pack is set beneath the second part of the duodenum. Two to three milliliters of barium, 1 to 2 ml of Gascon, and 15 ml of air are pushed in; thus a contact double-contrast cholangiogram is obtained. This technique promises clear demonstration of the distal bile duct without risk, and even fine mucosal plicae may be discernible in the film.     

Localized Exponential Time Differencing Method for Shallow Water Equations: Algorithms and Numerical Study

In this paper, we investigate the performance of the exponential time differencing (ETD) method applied to the rotating shallow water equations. Comparing with explicit time stepping of the same order accuracy in time, the ETD algorithms could reduce the computational time in many cases by allowing the use of large time step sizes while still maintaining numerical stability. To accelerate the ETD simulations, we propose a localized approach that synthesizes the ETD method and overlapping domain decomposition. By dividing the original problem into many subdomain problems of smaller sizes and solving them locally, the proposed approach could speed up the calculation of matrix exponential vector products. Several standard test cases for shallow water equations of one or multiple layers are considered. The results show great potential of the localized ETD method for high-performance computing because each subdomain problem can be naturally solved in parallel at every time step.     

Microsurgical Anatomy of the Cavernous Sinus: Measurements of the Triangles in and around It.

Objectives: Since the pioneering work of Parkinson, several studies have described the microsurgical anatomy and surgical procedures involving the cavernous sinus (CS). A proposed geometric construct has been adopted as nomenclature for the region by many neurosurgeons. However, authors differ in naming and describing some of these triangular spaces. The purpose of this study is to present the anatomy and measure the dimensions of the 10 triangles in and around this region. Materials and Methods: Eighteen CS of five cadaveric heads and four skull bases fixed in formalin were dissected using 3 x to 40 x magnification of the surgical microscope. The heads and skull bases were injected with colored silicone and the sides and area of the triangles were measured. Each cadaveric head was placed in a Sugita head-holder and a cranio-orbitozygomatic approach and a combined extra- and intradural approach were performed. The last step was the detachment of the brain from the skull base and measurement of the inferolateral paraclival and inferomedial paraclival triangles. Results: The measurements of the medial border, lateral border, and base of each triangle as well as the standard deviation and area are presented. The posteromedial middle fossa triangle was the largest and the clinoidal triangle the smallest. Conclusions: The normal anatomy of the CS triangle and its areas are important in the approach of the CS lesions because these spaces are natural corridors through which the lesions can be reached. The same concept must be used for the triangles around this space. Whenever these geometric spaces might be distorted by pathology or surgical maneuvers, the surgeon must have precise knowledge about their normal sizes.     

Multiscale Finite Element Methods for Flows on Rough Surfaces

In this paper, we present the Multiscale Finite Element Method (MsFEM) for problems on rough heterogeneous surfaces. We consider the diffusion equation on oscillatory surfaces. Our objective is to represent small-scale features of the solution via multiscale basis functions described on a coarse grid. This problem arises in many applications where processes occur on surfaces or thin layers. We present a unified multiscale finite element framework that entails the use of transformations that map the reference surface to the deformed surface. The main ingredients of MsFEM are (1) the construction of multiscale basis functions and (2) a global coupling of these basis functions. For the construction of multiscale basis functions, our approach uses the transformation of the reference surface to a deformed surface. On the deformed surface, multiscale basis functions are defined where reduced (1D) problems are solved along the edges of coarse-grid blocks to calculate nodal multiscale basis functions. Furthermore, these basis functions are transformed back to the reference configuration. We discuss the use of appropriate transformation operators that improve the accuracy of the method. The method has an optimal convergence if the transformed surface is smooth and the image of the coarse partition in the reference configuration forms a quasiuniform partition. In this paper, we consider such transformations based on harmonic coordinates (following H. Owhadi and L. Zhang [Comm. Pure and Applied Math., LX(2007), pp. 675–723]) and discuss gridding issues in the reference configuration. Numerical results are presented where we compare the MsFEM when two types of deformations are used for multiscale basis construction. The first deformation employs local information and the second deformation employs a global information. Our numerical results show that one can improve the accuracy of the simulations when a global information is used.     

Radiographic anatomic structure of the arthritic acetabulum and its influence on total hip arthroplasty

Acetabular bone structure is not the same in all patients and can be defined by the radiolucent triangle superior to the acetabulum. Of 132 hips, 81 had an isosceles triangular shape, which was named type A acetabulum. Forty-six hips had an extension of the triangle into the teardrop, which created a thickened medial wall and was named type B. Five hips had a right-angle triangle, which was found only with congenital disease of the hip and was named type C. The density of the superior acetabular bone in the triangle could be normally radiolucent (stage I), have vertical and transverse trabeculae throughout the triangle (stage II), or have the triangle filled with bone and cysts (stage III). The relationship between progressive radiolucent lines and acetabular type showed that type A3 (thin medial wall with dense triangle bone) had the highest incidence of progressive radiolucent lines (P < .05).     

Algebraic Multigrid Block Preconditioning for Multi-Group Radiation Diffusion Equations

The paper focuses on developing and studying efficient block preconditioners based on classical algebraic multigrid (AMG) for the large-scale sparse linear systems arising from the fully coupled and implicitly cell-centered finite volume discretization of multi-group radiation diffusion equations, whose coefficient matrices can be rearranged into the $(G+2)×(G+2)$ block form, where $G$ is the number of energy groups. The preconditioning techniques are the monolithic classical AMG method, physical-variable based coarsening two-level algorithm and two types of block Schur complement preconditioners. The classical AMG method is applied to solve the subsystems which originate in the last three block preconditioners. The coupling strength and diagonal dominance are further explored to improve performance. We take advantage of representative one- and twenty-group linear systems from capsule implosion simulations to test the robustness, efficiency, strong and weak parallel scaling properties of the proposed methods. Numerical results demonstrate that block preconditioners lead to mesh- and problem-independent convergence, outperform the frequently-used AMG preconditioner and scale well both algorithmically and in parallel.     

Performance of different optimal charging schemes in a solar charging station using dynamic programming

Electric Vehicles (EVs) are gradually replacing conventional vehicles as they are environmentally friendly and cause less pollution problems. Unregulated charging has severe impacts on the distribution grid and may incur EV owners higher charging costs. Therefore, controlled charging infrastructures to supply the charging needs of large numbers of EVs are of vital importance. In this article, an optimal control scenario is presented to formulate the charge scheduling problem of EVs in a solar charging station (CS). Two different objective functions are considered. The first objective function holds for minimizing the total charging cost of EVs. In this case, the benefits of Vehicle-to-Grid (V2G) are investigated by comparing the charging costs of EVs with and without this capability. The total EV charging costs and grid benefits are also investigated in the second objective function which holds for minimizing the extracted power from the grid. A modified version of Dynamic Programming is used to solve the large state-space model defined for the optimal control problem with extremely shorter computation time and minimal loss of optimality. Extensive simulations are done in two representative summer and winter climates to determine the role of solar energy in the CS performance. The results show that in the cost minimization algorithms, significant savings for EV owners and a smooth load shape for the grid are achieved. For the minimized power from the grid algorithm, a total near Photovoltaic (PV)-curve charging power is obtained to exploit the PV power as much as possible to minimize the impacts on the grid.     

Automated Parallel and Body-Fitted Mesh Generation in Finite Element Simulation of Macromolecular Systems

Mesh generation is a bottleneck for finite element simulations of biomolecules. A robust and efficient approach, based on the immersed boundary method proposed in [8], has been developed and implemented to generate large-scale mesh body-fitted to molecular shape for general parallel finite element simulations. The molecular Gaussian surface is adopted to represent the molecular surface, and is finally approximated by piecewise planes via the tool phgSurfaceCut in PHG [43], which is improved and can reliably handle complicated molecular surfaces, through mesh refinement steps. A coarse background mesh is imported first and then is distributed into each process using a mesh partitioning algorithm such as space filling curve [5] or METIS [22]. A bisection method is used for the mesh refinements according to the molecular PDB or PQR file which describes the biomolecular region. After mesh refinements, the mesh is optionally repartitioned and redistributed for load balancing. For finite element simulations, the modification of region mark and boundary types is done in parallel. Our parallel mesh generation method has been successfully applied to a sphere cavity model, a DNA fragment, a gramicidin A channel and a huge Dengue virus system. The results of numerical experiments show good parallel efficiency. Computations of electrostatic potential and solvation energy also validate the method. Moreover, the meshing process and adaptive finite element computation can be integrated as one PHG project to avoid the mesh importing and exporting costs, and improve the convenience of application as well.     

Analysis of 109 Japanese children's lip and nose shapes using 3-dimensional digitizer.

We assessed lip and nose shapes, which played an important role in performance evaluations, before and after cleft lip and nose surgery. We used a noncontact-type semiconductor laser 3-dimensional measurement system on normal Japanese children to obtain 3-dimensional images of noses and lips, which were accurate enough to measure facial shapes. We could rotate these images on the computer, therefore we measured the following points: the distance between the peaks of the Cupid's bow and the width of the labial fissure (frontal view), and the width of the nose and the nasal tip protrusion (basal view). Lip and nose shapes were evaluated for each gender. Additionally, nasolabial angles (NLA) were measured on the lateral views of faces. We classified the morphology of the philtral columns into four types; (1) triangular type, (2) parallel type, (3) concave type, and (4) flat type. We also classified nostril shapes into four types: (1) teardrop type, (2) heart shaped type, (3) round type, and (4) triangular type. We calculated the average of the 3-dimensional coordinate values for each landmark, and created standard facial models of normal Japanese children. Moreover, we invented a new morphological evaluation method before and after cleft lip and nose surgery, using the 3-dimensional data converting and editing software. The method was more feasible to evaluate the assessment cleft lip and nose surgery, by quantifying the surface areas of right and left nostrils and the surface areas of upper and lower vermilions, even now by measuring with the eyes and comparing them.     

Triangular configuration with headless compression screws in the fixation of transverse patellar fracture

A triangular configuration with three parallel cannulated screws is an established treatment for fixing transverse patellar fractures; however, the stability achieved with this approach is slightly lower than that attained with cannulated screws combined with anterior wiring. In the present study, triangular configurations were modified by partially or totally replacing the cannulated screws with headless compression screws (HCSs). Through finite element simulation involving a model of distal femoral, patellar, and proximal tibial fractures, the mechanical stability levels of the modified triangular configurations were compared with that of two cannulated screws combined with anterior wiring. Four triangular screw configurations were developed: three HCSs in a forward and backward triangular configuration, two deep cannulated screws along with one superficial HCS, and two superficial cannulated screws with one deep HCS. Also considered were two parallel cannulated screws (inserted superficially or deeply) combined with anterior wiring. The six approaches were all examined in full knee extension and 45° flexion under physiological loading. The highest stability was obtained with the three HCSs in a backward triangular configuration, as indicated by the least fragment displacement and the smallest fracture gap size. In extension and flexion, this size was smaller than that observed under the use of two deeply placed parallel cannulated screws with anterior wiring by 50.3% (1.53 vs. 0.76 mm) and 43.2% (1.48 vs. 0.84 mm), respectively. Thus, the use of three HCSs in a backward triangular configuration is recommended for the fixation of transverse patellar fractures, especially without the use of anterior wiring.     

Efficient Dynamic Floor Field Methods for Microscopic Pedestrian Crowd Simulations

Floor field methods are one of the most popular medium-scale navigation concepts in microscopic pedestrian simulators. Recently introduced dynamic floor field methods have significantly increased the realism of such simulations, i.e. agreement of spatio-temporal patterns of pedestrian densities in simulations with real world observations. These methods update floor fields continuously taking other pedestrians into account. This implies that computational times are mainly determined by the calculation of floor fields. In this work, we propose a new computational approach for the construction of dynamic floor fields. The approach is based on the one hand on adaptive grid concepts and on the other hand on a directed calculation of floor fields, i.e. the calculation is restricted to the domain of interest. Combining both techniques the computational complexity can be reduced by a factor of 10 as demonstrated by several realistic scenarios. Thus on-line simulations, a requirement of many applications, are possible for moderate realistic scenarios.     

外眦三角瓣组织旋转推进法外眦开大术的临床应用

目的:探讨外眦三角瓣组织旋转推进法外眦开大术的临床应用效果。方法:在外眦区设计三角形旋转皮瓣,充分游离三角皮瓣皮下组织,切断外眦韧带浅层,使外眦在无或微张力下旋转外移,将皮瓣下组织与眶骨骨膜固定,缝合表皮,达到开大外眦的目的。结果:7例因不同原因需行外眦开大的患者均取得满意效果,平均延长外眦睑裂3mm,且术后随访未见明显回退及瘢痕,无外眦粘连。结论:外眦三角瓣组织旋转推进法外眦开大术是一种设计简单,效果确切的外眦开大方法,值得临床推广应用。     

Random Batch Algorithms for Quantum Monte Carlo Simulations

Random batch algorithms are constructed for quantum Monte Carlo simulations. The main objective is to alleviate the computational cost associated with the calculations of two-body interactions, including the pairwise interactions in the potential energy, and the two-body terms in the Jastrow factor. In the framework of variational Monte Carlo methods, the random batch algorithm is constructed based on the over-damped Langevin dynamics, so that updating the position of each particle in an $N$-particle system only requires$\mathcal{O}(1)$ operations, thus for each time step the computational cost for $N$ particles is reduced from$\mathcal{O}(N^2)$ to$\mathcal{O}(N)$. For diffusion Monte Carlo methods, the random batch algorithm uses an energy decomposition to avoid the computation of the total energy in the branching step. The effectiveness of the random batch method is demonstrated using a system of liquid $^4$He atoms interacting with a graphite surface.