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arXiv2013

Introduction to eXtended Finite Element (XFEM) Method

In the present study the software CrackComput, based on the Xfem and Xcrack libraries has been used for three problems- to experiment on the convergence properties of the method applied to elasto-statics crack problems, comparison of stress intensity factors to simplified analytical results and study of the Brazilian fracture test. All the problems are treated in two dimensions under plane strain assumption and the material is supposed elastic and isotropic. For the first example, comparison for different parameter-enrichment type and radius, degree of polynomial has been performed. Second example convergence of SIF with the L/h ratio has been performed and compared with the analytical solution. Third example is the study of snapback phenomenon.

physics.comp-ph↗

arXiv2013

Extreme Loading of Aircraft Fan Blade

The response of an aircraft fan blade manufactured by composites under the action of static and impact load has been studied in this report. The modeling and analysis of the geometry has been done using CASTEM 2007 version. For the quasi static analysis, the pressure has been incrementally applied until it satisfies the failure criteria. The deformed configuration, strain, Von-Mises stress, and the deflection of the blade have been studied. The response of the system e.g. deformation time history due to the impact of the projectile has been studied where the Newmark method for the dynamic problem has been implemented.

physics.comp-ph↗

arXiv2013

Numerical Solution of Advection-Diffusion Equation Using Preconditionar as Incomplete LU Decomposition and the BiCGSTAB Aceleration Method

In the present study, an advection-diffusion problem has been considered for the numerical solution. The continuum equation is discretized using both upwind and centered scheme. The linear system is solved using the ILU preconditioned BiCGSTAB method. Both Dirichlet and Neumann boundary condition has been considered. The obtained results have been compared for different cases.

physics.comp-ph↗

arXiv2013

Local dynamics of a randomly pinned crack front: A numerical study

We investigate numerically the dynamics of crack propagation along a weak plane using a model consisting of fibers connecting a soft and a hard clamp. This bottom-up model has previously been shown to contain the competition of two crack propagation mechanisms: coalescence of damage with the front on small scales and pinned elastic line motion on large scales. We investigate the dynamical scaling properties of the model, both on small and large scale. The model results compare favorable with experimental results.

cond-mat.dis-nn↗

arXiv2013

Simulated annealing: in mathematical global optimization computation, hybrid with local or global search, and practical applications in crystallography and molecular modelling

Simulated annealing (SA) was inspired from annealing in metallurgy, a technique involving heating and controlled cooling of a material to increase the size of its crystals and reduce their defects, both are attributes of the material that depend on its thermodynamic free energy. In this Paper, firstly we will study SA in details on its practical implementation. Then, hybrid pure SA with local (or global) search optimization methods allows us to be able to design several effective and efficient global search optimization methods. In order to keep the original sense of SA, we clarify our understandings of SA in crystallography and molecular modeling field through the studies of prion amyloid fibrils.

math.OC↗

arXiv2013

Accurate lubrication corrections for spherical and non-spherical particles in discretized fluid simulations

Discretized fluid solvers coupled to a Newtonian dynamics method are a popular tool to study suspension flow. As any simulation technique with finite resolution, the lattice Boltzmann method, when coupled to discrete particles using the momentum exchange method, resolves the diverging lubrication interactions between surfaces near contact only insufficiently. For spheres, it is common practice to account for surface-normal lubrication forces by means of an explicit correction term. A method that additionally covers all further singular interactions for spheres is present in the literature as well as a link-based approach that allows for more general shapes but does not capture non-normal interactions correctly. In this paper, lattice-independent lubrication corrections for aspherical particles are outlined, taking into account all leading divergent interaction terms. An efficient implementation for arbitrary spheroids is presented and compared to purely normal and link-based models. Good consistency with Stokesian dynamics simulations of spheres is found. The non-normal interactions affect the viscosity of suspensions of spheres at volume fractions Φ>= 0.3 but already at Φ>= 0.2 for spheroids. Regarding shear-induced diffusion of spheres, a distinct effect is found at 0.1 <= Φ<= 0.5 and even increasing the resolution of the radius to 8 lattice units is no substitute for an accurate modeling of non-normal interactions.

cond-mat.soft↗

arXiv2013

Modeling the interaction of an arbitrary light field with a diffraction grating by the Monte Carlo method

A high-accuracy solution of the diffraction problem has become necessary for the treatment of certain special questions of statistical physics. This article reports the creation of a computer program that serves as an instrumental method of calculating the parameters of diffraction phenomena when complex optical systems are being theoretically investigated. The program solves the diffraction problem by a rigorous method based on Maxwell"s equations under specified boundary conditions. An arbitrary for instance, diffuse configuration of the initial light field is allowed. Reflective gratings with a linear or crossed sinusoidal profile of the surface micro relief are considered as the diffraction optical elements. The characteristics of the self-consistent total light field can be calculated when several diffraction elements are present in the system.

physics.optics↗

arXiv2013

Universal Lattice Basis

We report on the utility of using Shannons Sampling theorem to solve Quantum Mechanical systems. We show that by extending the logic of Shannons interpolation theorem we can define a Universal Lattice Basis, which has superior interpolating properties compared to traditional methods. This basis is orthonormal, semi-local, has a Euclidean norm, and a simple analytic expression for the derivatives. Additionally, we can define a bounded domain for which band-limited functions, such as Gaussians, show quadratic convergence in the representation error in respect to the sampling frequency. This theory also extends to the periodic domain and we illustrate the simple analytic forms of the periodic semi-local basis and derivatives. Additionally, we show that this periodic basis is equivalent to the space defined by the Fast Fourier Transform. This novel basis has great utility in solving quantum mechanical problems for which the wave functions are known to be naturally band-limited. Several numerical examples in single and multi-dimensions are given to show the convergence and equivalence of the periodic and bounded domains for compact states.

physics.comp-ph↗

arXiv2013

Optimizing the performance of Lattice Gauge Theory simulations with Streaming SIMD extensions

Two factors, which affect simulation quality are the amount of computing power and implementation. The Streaming SIMD (single instruction multiple data) extensions (SSE) present a technique for influencing both by exploiting the processor's parallel functionalism. In this paper, we show how SSE improves performance of lattice gauge theory simulations. We identified two significant trends through an analysis of data from various runs. The speed-ups were higher for single precision than double precision floating point numbers. Notably, though the use of SSE significantly improved simulation time, it did not deliver the theoretical maximum. There are a number of reasons for this: architectural constraints imposed by the FSB speed, the spatial and temporal patterns of data retrieval, ratio of computational to non-computational instructions, and the need to interleave miscellaneous instructions with computational instructions. We present a model for analyzing the SSE performance, which could help factor in the bottlenecks or weaknesses in the implementation, the computing architecture, and the mapping of software to the computing substrate while evaluating the improvement in efficiency. The model or framework would be useful in evaluating the use of other computational frameworks, and in predicting the benefits that can be derived from future hardware or architectural improvements.

cs.CE↗

arXiv2013

Implementation of PDE models of cardiac dynamics on GPUs using OpenCL

Graphical processing units (GPUs) promise to revolutionize scientific computing in the near future. Already, they allow almost real-time integration of simplified numerical models of cardiac tissue dynamics. However, the integration methods that have been developed so far are typically of low order and use single precision arithmetics. In this work, we describe numerical implementation of double precision integrators required by, e.g., matrix-free Newton-Krylov solvers and compare several higher order, fully explicit numerical methods using finite-difference discretization of a range of models of two-dimensional cardiac tissue.

nlin.CD↗

arXiv2013

Multiscale modeling of solar cells with interface phenomena

We describe a mathematical model for heterojunctions in semiconductors which can be used, e.g., for modeling higher efficiency solar cells. The continuum model involves well-known drift-diffusion equations posed away from the interface. These are coupled with interface conditions with a nonhomogeneous jump for the potential, and Robin-like interface conditions for carrier transport. The interface conditions arise from approximating the interface region by a lower-dimensional manifold. The data for the interface conditions are calculated by a Density Functional Theory (DFT) model over a few atomic layers comprising the interface region. We propose a domain decomposition method (DDM) approach to decouple the continuum model on subdomains which is implemented in every step of the Gummel iteration. We show results for CIGS/CdS, Si/ZnS, and Si/GaAs heterojunctions.

physics.comp-ph↗

arXiv2013

Characteristics of scalar dispersion in turbulent-channel flow

The dispersion of a passive scalar by wall turbulence, in the limit of infinite Peclet number, is analyzed using frozen velocity fields from the DNS by our group. The Lagrangian trajectories of fluid particles in those fields are integrated and used to compute the first and second-order moments of the distribution of fluid-particle displacements. It is shown that the largest scales in the flow dominate turbulent diffusion, and the computed dispersions are in good agreement with measurements in the atmospheric boundary layer. This agreement can be understood noting that the life times of the large strucutures are much longer than the time scale of the transition from linear to Gaussian particle spreading in the cross-stream plane. Numerical experiments performed computing the Lagrangian trajectories in reference frames moving at different velocities suggest that this transition is controlled by the difference between the mean streamwise velocity and the phase speed of the large-scale structures of the cross-stream velocities. In the streamwise direction, the effect of the mean shear dominates and produces elongated scalar patches, with dispersion exponents which are different from the transverse ones.

physics.flu-dyn↗

arXiv2013

Mechanical control of heat conductivity in microscopic models of dielectrics

We discuss a possibility to control a heat conductivity in simple one-dimensional models of dielectrics by means of external mechanical loads. To illustrate such possibilities we consider first a well-studied chain with degenerate double-well potential of the interparticle interaction. Contrary to previous studies, we consider varying length of the chain with fixed number of particles. Number of possible energetically degenerate ground states strongly depends on the overall length of the chain, or, in other terms, on average length of the link between neighboring particles. These degenerate states correspond to mechanical equilibrium, therefore one can say that the transition between them mimics to some extent a process of plastic deformation. We demonstrate that such modification of the chain length can lead to quite profound (almost five-fold) reduction of the heat conduction coefficient. Even more profound effect is revealed for a model with single-well non-convex potential. It is demonstrated that in certain range of constant external forcing this model becomes "effectively"\ double-well, and has a multitude of possible states of equilibrium for the same value of the external load. Thus, the heat conduction coefficient can be reduced by two orders of magnitude. We suggest a mechanical model of a chain with periodic double-well potential, which allows control over the heat conduction. The models considered may be useful for description of heat transport in biological macromolecules and for control of the heat transport in microsystems.

cond-mat.mes-hall↗

arXiv2013

Discretization of Time-Dependent Quantum Systems: Real-Time Propagation of The Evolution Operator

We discuss time dependent quantum systems on bounded domains. Our work may be viewed as a framework for several models, including linear iterations involved in time dependent density functional theory (TDDFT), the Hartree-Fock model, or other quantum models. A key aspect of the analysis of the algorithms is the use of time-ordered evolution operators, which allow for both a well-posed problem and its approximation. The approximation theorems obtained for the time-ordered evolution operators complement those in the current literature. We discuss the available theory at the outset, and proceed to apply the theory systematically in later sections via approximations and a global existence theorem for a nonlinear system, obtained via a fixed point theorem for the evolution operator. Our work is consistent with first-principle real time propagation of electronic states, aimed at finding the electronic responses of quantum molecular systems and nanostructures. We present two full 3D quantum atomistic simulations using the finite element method for discretizing the real-space, and the FEAST eigenvalue algorithm for solving the evolution operator at each time step. These numerical experiments are representative of the theoretical results.

math.DS↗

arXiv2014

Iterative methods for obtaining solvation structures on a solid plate: The methods for Surface Force Apparatus and Atomic Force Microscopy in Liquids

We propose iterative methods for obtaining solvation structures on a solid plate which use force distributions measured by surface force apparatus (SFA) and atomic force microscopy (AFM) as input data. Two model systems are considered here. In the model system for SFA, the same two solid plates are immersed in a solvent, and a probe tip and a solid plate are immersed in a solvent in the model system for AFM. Advantages of the iterative methods are as follows: The iterative method for SFA can obtain the solvation structure, for example, in a Lennard-Jones liquid; The iterative method for AFM can obtain the solvation structure without an input datum of solvation structure around the probe tip.

physics.comp-ph↗

arXiv2013

Simple free-surface detection in two and three-dimensional SPH solver

A simple free-surface particle detection method for two and three-dimensional SPH simulation has been implemented. The method uses sphere representation for the SPH particle. The fluid domain is covered by overlapping spheres. A sphere whose surface is not fully covered considered as boundary. To test particle boundary status, we used a sum of normalized relative position vectors from neighbouring particles to the test particle. By checking the existence of un- covered sphere surface by this vector sum, boundary status of the test particle can be determined. This boundary detection method can be easily embedded in the SPH solver algorithm.

physics.flu-dyn↗

arXiv2013

On Metropolis Integrators for Molecular Dynamics

This paper invites the reader to experiment with an easy-to-use MATLAB implementation of Metropolis integrators for Molecular Dynamics (MD) simulation. These integrators are analysis-based, in the sense that they can rigorously simulate dynamics along an infinitely long MD trajectory. Among explicit integrators for MD, they seem to be the only ones that satisfy the fundamental requirement of stability. The schemes can handle stiff or hard-core potentials, and are straightforward to set up, apply and extend to new situations. Potential pitfalls in high dimension are discussed, and tricks for mitigation are given.

physics.comp-ph↗

arXiv2014

Comparison of polynomial approximations to speed up planewave-based quantum Monte Carlo calculations

The computational cost of quantum Monte Carlo (QMC) calculations of realistic periodic systems depends strongly on the method of storing and evaluating the many-particle wave function. Previous work [A. J. Williamson et al., Phys. Rev. Lett. 87, 246406 (2001); D. Alfè and M. J. Gillan, Phys. Rev. B 70, 161101 (2004)] has demonstrated the reduction of the O(N^3) cost of evaluating the Slater determinant with planewaves to O(N^2) using localized basis functions. We compare four polynomial approximations as basis functions -- interpolating Lagrange polynomials, interpolating piecewise-polynomial-form (pp-) splines, and basis-form (B-) splines (interpolating and smoothing). All these basis functions provide a similar speedup relative to the planewave basis. The pp-splines have eight times the memory requirement of the other methods. To test the accuracy of the basis functions, we apply them to the ground state structures of Si, Al, and MgO. The polynomial approximations differ in accuracy most strongly for MgO and smoothing B-splines most closely reproduce the planewave value for of the variational Monte Carlo energy. Using separate approximations for the Laplacian of the orbitals increases the accuracy sufficiently to justify the increased memory requirement, making smoothing B-splines, with separate approximation for the Laplacian, the preferred choice for approximating planewave-represented orbitals in QMC calculations.

physics.comp-ph↗