Related papers: Integral boundary conditions in phase field models
We propose a model for the coupling of flow and transport equations with porous membrane-type conditions on part of the boundary. The governing equations consist of the incompressible Navier--Stokes equations coupled with an…
A cross-diffusion system describing ion transport through biological membranes or nanopores in a bounded domain with mixed Dirichlet-Neumann boundary conditions is analyzed. The ion concentrations solve strongly coupled diffusion equations…
Chalcogenide materials have received great attention in the last decade owing to their application in new memory systems. Recently, phase-change memories have, in fact, reached the early stages of production. In spite of the industrial…
Many ferroelectric solid solutions exhibit enhanced electro-mechanical properties at the morphotropic boundary separating two phases with different orientations of polarization. The mechanism of properties enhancement is associated with…
This paper develops a general approach to the derivation of the boundary conditions for hydrodynamic equations for charged and neutral plasma components. It includes both a well-known classical case for pure diffusion, and considers the…
We consider the numerical approximation of boundary conditions in radiative transfer problems by a perfectly matched layer approach. The main idea is to extend the computational domain by an absorbing layer and to use an appropriate…
We introduce a deep learning-based framework for weakly enforcing boundary conditions in the numerical approximation of partial differential equations. Building on existing physics-informed neural network and deep Ritz methods, we propose…
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…
A novel thermodynamically consistent diffuse interface model is derived for compressible electrolytes with phase transitions. The fluid mixtures may consist of N constituents with the phases liquid and vapor, where both phases may coexist.…
We present an efficient numerical method, inspired by transformation optics, for solving the Poisson equation in complex and arbitrarily shaped geometries. The approach operates by mapping the physical domain to a uniform computational…
We consider a general compressible MHD system, where the magnetic field propagates in a heterogeneous medium. Using suitable penalization in terms of the transport coefficients we perform several singular limits. As a result we obtain: 1. A…
The well-posedness for a system of partial differential equations and dynamic boundary conditions is discussed. This system is a sort of transmission problem between the dynamics in the bulk $\Omega $ and on the boundary $\Gamma$. The…
Numerical solution of the Poisson equation in metallic enclosures, open at one or more ends, is important in many practical situations such as High Power Microwave (HPM) or photo-cathode devices. It requires imposition of a suitable…
The model of homogeneous semicoherent interphase boundary describes the processes of absorption and thermoactivated migration of irradiation-produced inequilibrium point defects at a semicoherent boundary between a heterophase precipitate…
A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…
We prove well-posedness results for the solution to an initial and boundary-value problem for an Allen-Cahn type equation describing the phenomenon of phase transitions for a material contained in a bounded and regular domain. The dynamic…
We investigate the multi-order parameter phase field model of Steinbach and Pezzolla [I. Steinbach, F. Pezzolla, A generalized field method for multiphase transformations using interface fields, Physica D 134 (1999) 385-393] concerning its…
Interpolating scaling functions give a faithful representation of a localized charge distribution by its values on a grid. For such charge distributions, using a Fast Fourier method, we obtain highly accurate electrostatic potentials for…
Grain growth in polycrystals is one of the principal mechanisms that take place during heat treatment of metallic components. This work treats an aspect of the anisotropic grain growth problem. By applying the first principles of…
In this paper we perform, by means of Discontinuous Galerkin (DG) Finite Element Method (FEM) based numerical solvers for Boltzmann-Poisson (BP) semiclassical models of hot electronic transport in semiconductors, a numerical study of…