相关论文: Numerical Methods for Coupled Surface and Grain Bo…
Granular systems present surprisingly complicated dynamics. In particular, nonlinear interactions and energy dissipation play important roles in these dynamics. Usually, constant coefficients of restitution are introduced phenomenologically…
The geometric state of a flat boundary is frequently described using the so-called macroscopic parameters. They are a principal tool for dealing with interfaces at the continuous scale. The paper describes a new method for macroscopic…
Generalizations of tempered fractional Brownian from single index to two indices and variable index or tempered multifractional Brownian motion are studied. Tempered fractional Brownian motion and tempered multifractional Brownian motion…
A simple geometrical model is presented for the gravity-driven motion of a single particle on a rough inclined surface. Adopting a simple restitution law for the collisions between the particle and the surface, we arrive at a model in which…
The numerical analysis for the small amplitude motion of an elastic beam with internal damping is investigated in domain with moving ends. An efficient numerical method is constructed to solve this moving boundary problem. The stability and…
In this paper we consider scalar parabolic equations in a general non-smooth setting with emphasis on mixed interface and boundary conditions. In particular, we allow for dynamics and diffusion on a Lipschitz interface and on the boundary,…
We present two (a decoupled and a coupled) integral-equation-based methods for the Morse-Ingard equations subject to Neumann boundary conditions on the exterior domain. Both methods are based on second-kind integral equation (SKIE)…
Approximations of fractional Brownian motion using Poisson processes whose parameter sets have the same dimensions as the approximated processes have been studied in the literature. In this paper, a special approximation to the…
This paper presents a method for computing two-dimensional constant mean curvature surfaces. The method in question uses the variational aspect of the problem to implement an efficient algorithm. In principle it is a flow like method in…
Recently, Papadakis et al. proposed an efficient primal-dual algorithm for solving the dynamic optimal transport problem with quadratic ground cost and measures having densities with respect to the Lebesgue measure. It is based on the fluid…
We study the surface shape of two-dimensional piles using experiments and a continuum theory for surface flows of granular materials (the BCRE equations). We first obtain an analytical solution to the BCRE equations with a simple…
The original KWC-system is widely used in materials science. It was proposed in [Kobayashi et al, Physica D, 140, 141--150 (2000)] and is based on the phase field model of planar grain boundary motion. This model suffers from two key…
As a complementary tool to laboratory experiments, discrete numerical simulation, applied to granular materials, provides valuable information on the grain and contact scale microstructure, thereby enabling one to better understand the…
In molecular physics, it is often necessary to average over the orientation of molecules when calculating observables, in particular when modelling experiments in the liquid or gas phase. Evaluated in terms of Euler angles, this is closely…
The paper presents a two-dimensional geometrically nonlinear formulation of a beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which…
The existence of kinematic formulas for area measures with respect to any connected, closed subgroup of the orthogonal group acting transitively on the unit sphere is established. In particular, the kinematic operator for area measures is…
There are many numerical methods for solving partial different equations (PDEs) on manifolds such as classical implicit, finite difference, finite element, and isogeometric analysis methods which aim at improving the interoperability…
A simple analytical model of intergranular normal stresses is proposed for a general elastic polycrystalline material with arbitrary shaped and randomly oriented grains under uniform loading. The model provides algebraic expressions for the…
We propose a new model for the description of complex granular particles and their interaction in molecular dynamics simulations of granular material in two dimensions. The grains are composed of triangles which are connected by deformable…
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…