bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the Connection Between the Spectral Difference Method and the Discontinuous Galerkin Method
Authors: May Georg 
Published: July 2016

AbstractIn this short note we present a derivation of the Spectral Difference Scheme from a Discontinuous Galerkin (DG) discretization of a nonlinear conservation law. This allows interpretation of the Spectral Difference Scheme as a particular discretization under the quadrature-free nodal DG paradigm. Moreover, it enables identification of the key differences between the Spectral Difference Scheme and standard nodal DG schemes.
Hydrodynamic Interaction of Elastic Capsules in Bounded Shear Flow
Authors: Le D. V. , Tan Zhijun 
Published: July 2016

AbstractThis paper presents a modified Loop’s subdivision algorithm for studying the deformation of a single capsule, the hydrodynamic interaction between two capsules and the hydrodynamic diffusion of a suspension of capsules in bounded shear flow. A subdivision thin-shell model is employed to compute the forces generated on the surface of the elastic capsule during deformation. The capsule surface is approximated using the modified Loop’s subdivision scheme which guarantees bounded curvature and C1 continuity everywhere on the limit surface. The present numerical technique has been validated by studying the deformation of a spherical capsule in shear flow. Computations are also performed for a biconcave capsule over a wide range of shear rates and viscosity ratios to investigate its dynamics. In addition, the hydrodynamic interaction between two elastic capsules in bounded shear flow is studied. Depending on the wall separation distance, the trajectory-bifurcation points that separate reversing and crossing motions for both spherical and biconcave capsules can be found. Compared to the spherical capsules, the biconcave capsules exhibit additional types of interaction such as rotation and head-on collision. The head-on collision results in a large trajectory shift which contribute to the hydrodynamic diffusion of a suspension. A suspension of a large number of biconcave capsules in shear flow is also simulated to show the ability of the modified scheme in running a large-scale simulation over a long period of time.
Numerical Approximation of a Compressible Multiphase System
Authors: Abgrall Remi , Kumar Harish 
Published: July 2016

AbstractThe numerical simulation of non conservative system is a difficult challenge for two reasons at least. The first one is that it is not possible to derive jump relations directly from conservation principles, so that in general, if the model description is non ambiguous for smooth solutions, this is no longer the case for discontinuous solutions. From the numerical view point, this leads to the following situation: if a scheme is stable, its limit for mesh convergence will depend on its dissipative structure. This is well known since at least [1]. In this paper we are interested in the “dual” problem: given a system in non conservative form and consistent jump relations, how can we construct a numerical scheme that will, for mesh convergence, provide limit solutions that are the exact solution of the problem. In order to investigate this problem, we consider a multiphase flow model for which jump relations are known. Our scheme is an hybridation of Glimm scheme and Roe scheme.
Finite Volume Hermite WENO Schemes for Solving the Hamilton-Jacobi Equation
Authors: Zhu Jun , Qiu Jianxian 
Published: July 2016

AbstractIn this paper, we present a new type of Hermite weighted essentially non-oscillatory (HWENO) schemes for solving the Hamilton-Jacobi equations on the finite volume framework. The cell averages of the function and its first one (in one dimension) or two (in two dimensions) derivative values are together evolved via time approaching and used in the reconstructions. And the major advantages of the new HWENO schemes are their compactness in the spacial field, purely on the finite volume framework and only one set of small stencils is used for different type of the polynomial reconstructions. Extensive numerical tests are performed to illustrate the capability of the methodologies.
Thin Layer Models for Electromagnetism
Authors: Duruflé Marc , Péron Victor , Poignard Clair 
Published: July 2016

AbstractWe present a review on the accuracy of asymptotic models for the scattering problem of electromagnetic waves in domains with thin layer. These models appear as first order approximations of the electromagnetic field. They are obtained thanks to a multiscale expansion of the exact solution with respect to the thickness of the thin layer, that makes possible to replace the thin layer by approximate conditions. We present the advantages and the drawbacks of several approximations together with numerical validations and simulations. The main motivation of this work concerns the computation of electromagnetic field in biological cells. The main difficulty to compute the local electric field lies in the thinness of the membrane and in the high contrast between the electrical conductivities of the cytoplasm and of the membrane, which provides a specific behavior of the electromagnetic field at low frequencies.
On the Choice of Design Points for Least Square Polynomial Approximations with Application to Uncertainty Quantification
Authors: Gao Zhen , Zhou Tao 
Published: July 2016

AbstractIn this work, we concern with the numerical comparison between different kinds of design points in least square (LS) approach on polynomial spaces. Such a topic is motivated by uncertainty quantification (UQ). Three kinds of design points are considered, which are the Sparse Grid (SG) points, the Monte Carlo (MC) points and the Quasi Monte Carlo (QMC) points. We focus on three aspects during the comparison: (i) the convergence properties; (ii) the stability, i.e. the properties of the resulting condition number of the design matrix; (iii) the robustness when numerical noises are present in function values. Several classical high dimensional functions together with a random ODE model are tested. It is shown numerically that (i) neither the MC sampling nor the QMC sampling introduce the low convergence rate, namely, the approach achieves high order convergence rate for all cases provided that the underlying functions admit certain regularity and enough design points are used; (ii)The use of SG points admits better convergence properties only for very low dimensional problems (say d ≤ 2); (iii)The QMC points, being deterministic, seem to be a good choice for higher dimensional problems not only for better convergence properties but also in the stability point of view.
A Modified Gas-Kinetic Scheme for Turbulent Flow
Authors: Righi Marcello 
Published: July 2016

AbstractThe implementation of a turbulent gas-kinetic scheme into a finite-volume RANS solver is put forward, with two turbulent quantities, kinetic energy and dissipation, supplied by an allied turbulence model. This paper shows a number of numerical simulations of flow cases including an interaction between a shock wave and a turbulent boundary layer, where the shock-turbulent boundary layer is captured in a much more convincing way than it normally is by conventional schemes based on the Navier-Stokes equations. In the gas-kinetic scheme, the modeling of turbulence is part of the numerical scheme, which adjusts as a function of the ratio of resolved to unresolved scales of motion. In so doing, the turbulent stress tensor is not constrained into a linear relation with the strain rate. Instead it is modeled on the basis of the analogy between particles and eddies, without any assumptions on the type of turbulence or flow class. Conventional schemes lack multiscale mechanisms: the ratio of unresolved to resolved scales – very much like a degree of rarefaction – is not taken into account even if it may grow to non-negligible values in flow regions such as shocklayers. It is precisely in these flow regions, that the turbulent gas-kinetic scheme seems to provide more accurate predictions than conventional schemes.
Immersed Finite Element Method for Interface Problems with Algebraic Multigrid Solver
Authors: Feng Wenqiang , He Xiaoming , Lin Yanping , Zhang Xu 
Published: July 2016

AbstractThis article is to discuss the bilinear and linear immersed finite element (IFE) solutions generated from the algebraic multigrid solver for both stationary and moving interface problems. For the numerical methods based on finite difference formulation and a structured mesh independent of the interface, the stiffness matrix of the linear system is usually not symmetric positive-definite, which demands extra efforts to design efficient multigrid methods. On the other hand, the stiffness matrix arising from the IFE methods are naturally symmetric positive-definite. Hence the IFE-AMG algorithm is proposed to solve the linear systems of the bilinear and linear IFE methods for both stationary and moving interface problems. The numerical examples demonstrate the features of the proposed algorithms, including the optimal convergence in both L2and semi-H1norms of the IFE-AMG solutions, the high efficiency with proper choice of the components and parameters of AMG, the influence of the tolerance and the smoother type of AMG on the convergence of the IFE solutions for the interface problems, and the relationship between the cost and the moving interface location.
Image Charge Method for Reaction Fields in a Hybrid Ion-Channel Model
Authors: Xu Zhenli , Cai Wei , Cheng Xiaolin 
Published: July 2016

AbstractA multiple-image method is proposed to approximate the reaction-field potential of a source charge inside a finite length cylinder due to the electric polarization of the surrounding membrane and bulk water. When applied to a hybrid ion-channel model, this method allows a fast and accurate treatment of the electrostatic interactions of protein with membrane and solvent. To treat the channel/membrane interface boundary conditions of the electric potential, an optimization approach is used to derive image charges by fitting the reaction-field potential expressed in terms of cylindric harmonics. Meanwhile, additional image charges are introduced to satisfy the boundary conditions at the planar membrane interfaces. In the end, we convert the electrostatic interaction problem in a complex inhomogeneous system of ion channel/membrane/water into one in a homogeneous free space embedded with discrete charges (the source charge and image charges). The accuracy of this method is then validated numerically in calculating the solvation self-energy of a point charge.
An Efficient Numerical Model for Immiscible Two-Phase Flow in Fractured Karst Reservoirs
Authors: Huang Zhao-Qin , Yao Jun , Wang Yue-Ying 
Published: July 2016

AbstractNumerical simulation of two-phase flow in fractured karst reservoirs is still a challenging issue. The triple-porosity model is the major approach up to now. However, the triple-continuum assumption in this model is unacceptable for many cases. In the present work, an efficient numerical model has been developed for immiscible two-phase flow in fractured karst reservoirs based on the idea of equivalent continuum representation. First, based on the discrete fracture-vug model and homogenization theory, the effective absolute permeability tensors for each grid blocks are calculated. And then an analytical procedure to obtain a pseudo relative permeability curves for a grid block containing fractures and cavities has been successfully implemented. Next, a full-tensor simulator has been designed based on a hybrid numerical method (combining mixed finite element method and finite volume method). A simple fracture system has been used to demonstrate the validity of our method. At last, we have used the fracture and cavity statistics data from TAHE outcrops in west China, effective permeability values and other parameters from our code, and an equivalent continuum simulator to calculate the water flooding profiles for more realistic systems.
In Silico Investigation of pH-Dependence of Prolactin and Human Growth Hormone Binding to Human Prolactin Receptor
Authors: Wang Lin , Witham Shawn , Zhang Zhe , Li Lin , Hodsdon Michael , Alexov Emil 
Published: July 2016

AbstractExperimental data shows that the binding of human prolactin (hPRL) to human prolactin receptor (hPRLr-ECD) is strongly pH-dependent, while the binding of the same receptor to human growth hormone (hGH) is pH-independent. Here we carryin silicoanalysis of the molecular effects causing such a difference and reveal the role of individual amino acids. It is shown that the computational modeling correctly predicts experimentally determined pKa’s of histidine residues in an unbound state in the majority of the cases and the pH-dependence of the binding free energy. Structural analysis carried in conjunction with calculated pH-dependence of the binding revealed that the main reason for pH-dependence of the binding of hPRL-hPRLr-ECD is a number of salt-bridges across the interface of the complex, while no salt-bridges are formed in the hGH-hPRlr-ECD. Specifically, most of the salt-bridges involve histidine residues and this is the reason for the pH-dependence across a physiological range of pH. The analysis not only revealed the molecular mechanism of the pH-dependence of the hPRL-hPRLr-ECD, but also provided critical insight into the underlying physic-chemical mechanism.
An Implicit Algorithm of Solving Nonlinear Filtering Problems
Authors: Bao Feng , Cao Yanzhao , Han Xiaoying 
Published: July 2016

AbstractNonlinear filter problems arise in many applications such as communications and signal processing. Commonly used numerical simulation methods include Kalman filter method, particle filter method, etc. In this paper a novel numerical algorithm is constructed based on samples of the current state obtained by solving the state equation implicitly. Numerical experiments demonstrate that our algorithm is more accurate than the Kalman filter and more stable than the particle filter.
A Runge Kutta Discontinuous Galerkin Method for Lagrangian Compressible Euler Equations in Two-Dimensions
Authors: Li Zhenzhen , Yu Xijun , Zhu Jiang , Jia Zupeng 
Published: July 2016

AbstractThis paper presents a new Lagrangian type scheme for solving the Euler equations of compressible gas dynamics. In this new scheme the system of equations is discretized by Runge-Kutta Discontinuous Galerkin (RKDG) method, and the mesh moves with the fluid flow. The scheme is conservative for the mass, momentum and total energy and maintains second-order accuracy. The scheme avoids solving the geometrical part and has free parameters. Results of some numerical tests are presented to demonstrate the accuracy and the non-oscillatory property of the scheme.
Examining Electrostatic Influences on Base-Flipping: A Comparison of TIP3P and GB Solvent Models
Authors: Brice Allyn R. , Dominy Brian N. 
Published: July 2016

AbstractRecently, it was demonstrated that implicit solvent models were capable of generating stable B-form DNA structures. Specifically, generalized Born (GB) implicit solvent models have improved regarding the solvation of conformational sampling of DNA [1,2]. Here, we examine the performance of the GBSW and GBMV models in CHARMM for characterizing base flipping free energy profiles of undamaged and damaged DNA bases. Umbrella sampling of the base flipping process was performed for the bases cytosine, uracil and xanthine. The umbrella sampling simulations were carried-out with both explicit (TIP3P) and implicit (GB) solvent in order to establish the impact of the solvent model on base flipping. Overall, base flipping potential of mean force (PMF) profiles generated with GB solvent resulted in a greater free energy difference of flipping than profiles generated with TIP3P. One of the significant differences between implicit and explicit solvent models is the approximation of solute-solvent interactions in implicit solvent models. We calculated electrostatic interaction energies between explicit water molecules and the base targeted for flipping. These interaction energies were calculated over the base flipping reaction coordinate to illustrate the stabilizing effect of the explicit water molecules on the flipped-out state. It is known that nucleic base pair hydrogen bonds also influenced the free energy of flipping since these favorable interactions must be broken in order for a base to flip-out of the helix. The Watson-Crick base pair hydrogen bond fractions were calculated over the umbrella sampling simulation windows in order to determine the effect of base pair interactions on the base flipping free energy. It is shown that interaction energies between the flipping base and explicit water molecules are responsible for the lower base flipping free energy difference in the explicit solvent PMF profiles.
Shape Recovery of Elastic Capsules from Shear Flow Induced Deformation
Authors: Gounley John , Peng Yan 
Published: July 2016

AbstractRed blood cells undergo substantial shape changes in vivo. Modeled as a viscoelastic capsule, their deformation and equilibrium behavior has been extensively studied. We consider how 2D capsules recover their shape, after having been deformed to ‘equilibrium’ behavior by shear flow. The fluid-structure interaction is modeled using the multiple-relaxation time lattice Boltzmann (LBM) and immersed boundary (IBM) methods. Characterizing the capsule’s shape recovery with the Taylor deformation parameter, we find that a single exponential decay model suffices to describe the recovery of a circular capsule. However, for biconcave capsules whose equilibrium behaviors are tank-treading and tumbling, we posit a two-part recovery, modeled with a pair of exponential decay functions. We consider how these two recovery modes depend on the capsule’s shear elasticity, membrane viscosity, and bending stiffness, along with the ratio of the viscosity of the fluid inside the capsule to the ambient fluid viscosity. We find that the initial recovery mode for a tank-treading biconcave capsule is dominated by shear elasticity and membrane viscosity. On the other hand, the latter recovery mode for both tumbling and tank-treading capsules, depends clearly on shear elasticity, bending stiffness, and the viscosity ratio.
Numerical Optimization of a Walk-on-Spheres Solver for the Linear Poisson-Boltzmann Equation
Authors: Mackoy Travis , Harris Robert C. , Johnson Jesse , Mascagni Michael , Fenley Marcia O. 
Published: July 2016

AbstractStochastic walk-on-spheres (WOS) algorithms for solving the linearized Poisson-Boltzmann equation (LPBE) provide several attractive features not available in traditional deterministic solvers: Gaussian error bars can be computed easily, the algorithm is readily parallelized and requires minimal memory and multiple solvent environments can be accounted for by reweighting trajectories. However, previously-reported computational times of these Monte Carlo methods were not competitive with existing deterministic numerical methods. The present paper demonstrates a series of numerical optimizations that collectively make the computational time of these Monte Carlo LPBE solvers competitive with deterministic methods. The optimization techniques used are to ensure that each atom’s contribution to the variance of the electrostatic solvation free energy is the same, to optimize the bias-generating parameters in the algorithm and to use an epsilon-approximate rather than exact nearest-neighbor search when determining the size of the next step in the Brownian motion when outside the molecule.
Adaptive Bayesian Inference for Discontinuous Inverse Problems, Application to Hyperbolic Conservation Laws
Authors: Birolleau Alexandre , Poëtte Gaël , Lucor Didier 
Published: July 2016

AbstractVarious works from the literature aimed at accelerating Bayesian inference in inverse problems. Stochastic spectral methods have been recently proposed as surrogate approximations of the forward uncertainty propagation model over the support of the prior distribution. These representations are efficient because they allow affordable simulation of a large number of samples from the posterior distribution. Unfortunately, they do not perform well when the forward model exhibits strong nonlinear behavior with respect to its input.In this work, we first relate the fast (exponential) L2-convergence of the forward approximation to the fast (exponential) convergence (in terms of Kullback-Leibler divergence) of the approximate posterior. In particular, we prove that in case the prior distribution isuniform, the posterior is at least twice as fast as the convergence rate of the forwardmodel in those norms. The Bayesian inference strategy is developed in the framework of a stochastic spectral projectionmethod. The predicted convergence rates are then demonstrated for simple nonlinear inverse problems of varying smoothness.We then propose an efficient numerical approach for the Bayesian solution of inverse problems presenting strongly nonlinear or discontinuous systemresponses. This comes with the improvement of the forward model that isadaptivelyapproximated by an iterative generalized Polynomial Chaos-based representation. The numerical approximations and predicted convergence rates of the former approach are compared to the new iterative numericalmethod for nonlinear time-dependent test cases of varying dimension and complexity, which are relevant regarding our hydrodynamics motivations and therefore regarding hyperbolic conservation laws and the apparition of discontinuities in finite time.
On Time-Splitting Pseudospectral Discretization for Nonlinear Klein-Gordon Equation in Nonrelativistic Limit Regime
Authors: Dong Xuanchun , Xu Zhiguo , Zhao Xiaofei 
Published: July 2016

AbstractIn this work, we are concerned with a time-splitting Fourier pseudospectral (TSFP) discretization for the Klein-Gordon (KG) equation, involving a dimensionless parameterɛ ∊(0,1]. In the nonrelativistic limit regime, the smallɛproduces high oscillations in exact solutions with wavelength of(ɛ2) in time. The key idea behind the TSFP is to apply a time-splitting integrator to an equivalent first-order system in time, with both the nonlinear and linear subproblems exactly integrable in time and, respectively, Fourier frequency spaces. The method is fully explicit and time reversible. Moreover, we establish rigorously the optimal error bounds of a second-order TSFP for fixedɛ=(1), thanks to an observation that the scheme coincides with a type of trigonometric integrator. As the second task, numerical studies are carried out, with special efforts made to applying the TSFP in the nonrelativistic limit regime, which are geared towards understanding its temporal resolution capacity and meshing strategy for(ɛ2)-oscillatory solutions when 0 <ɛ« 1. It suggests that the method has uniform spectral accuracy in space, and an asymptotic(ɛ−2Δt2) temporal discretization error bound (Δtrefers to time step). On the other hand, the temporal error bounds for most trigonometric integrators, such as the well-established Gautschi-type integrator in, are(ɛ−4Δt2). Thus, our method offers much better approximations than the Gautschi-type integrator in the highly oscillatory regime. These results, either rigorous or numerical, are valid for a splitting scheme applied to the classical relativistic NLS reformulation as well.