Related papers: Boundary integral formulation for interfacial crac…
The boundary integral method is extended to derive closed integro-differential equations applicable to computation of the shape and propagation speed of a steadily moving spot and to the analysis of dynamic instabilities in the sharp…
In this paper we apply the boundary elements method (BEM) and the dual reciprocity boundary elements method (DRBEM) for the numerical solution of two-dimensional time-fractional partial differential equations (TFPDEs). The fractional…
In this work, we initiate the study of the biharmonic heat equation in a spatial bounded domain subject to dynamic boundary conditions involving the bi-Laplace-Beltrami operator on the boundary. The boundary heat equation is coupled to the…
The two-dimensional transient problem that is studied concerns a semi-infinite crack in an isotropic solid comprising an infinite strip and a half-plane joined together and having the same elastic constants. The crack propagates along the…
The boundary element method (BEM) enables solving three-dimensional electromagnetic problems using a two-dimensional surface mesh, making it appealing for applications ranging from electrical interconnect analysis to the design of…
This paper tests a dielectric model for variation of hydration free energy with geometry of complex solutes in water. It works out some basic aspects of the theory of boundary integral methods for these problems. One aspect of the…
The immersed boundary method is a mathematical formulation and numerical method for solving fluid-structure interaction problems. For many biological problems, such as models that include the cell membrane, the immersed structure is a…
For the first time, a nonlinear interface problem on an unbounded domain with nonmonotone set-valued transmission conditions is analyzed. The investigated problem involves a nonlinear monotone partial differential equation in the interior…
The interactions between dislocations and interface/grain boundaries, including dislocation absorption, transmission, and reflection, have garnered significant attention from the research community for their impact on the mechanical…
Traditional ablation thermochemistry tables for atmospheric entry are derived from boundary-layer element diffusion assuming homogeneous and heterogeneous thermochemical equilibrium at the vehicle surface. Prior techniques for finite-rate…
Vacuum energy and other spectral functions of Laplace-type differential operators have been studied approximately by classical-path constructions and more fundamentally by boundary integral equations. As the first step in a program of…
We define a weight function in a bi-material strip containing a semi-infinite crack and an imperfect interface and analyse a problem of anti-plane shear. We then present an asymptotic algorithm which uses the weight function to evaluate the…
We derive sharp-interface models for one-dimensional brittle fracture via the inverse-deformation approach. Methods of Gamma-convergence are employed to obtain the singular limits of previously proposed models. The latter feature a local,…
Electrostatic forces play many important roles in molecular biology, but are hard to model due to the complicated interactions between biomolecules and the surrounding solvent, a fluid composed of water and dissolved ions. Continuum model…
Flexible boundary condition methods couple an isolated defect to a harmonically responding medium through the bulk lattice Green's function; in the case of an interface, interfacial lattice Green's functions. We present a method to compute…
The thermal boundary resistance of Si/Ge interfaces as been determined using approach-to-equilibrium molecular dynamics simulations. Assuming a reciprocal linear dependence of the thermal boundary resistance, a length-independent bulk…
We propose a boundary element method for the accurate solution of the cell-by-cell bidomain model of electrophysiology. The cell-by-cell model, also called Extracellular-Membrane-Intracellular (EMI) model, is a system of reaction-diffusion…
Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
The scattering and transmission of harmonic acoustic waves at a penetrable material are commonly modelled by a set of Helmholtz equations. This system of partial differential equations can be rewritten into boundary integral equations…