相关论文: High-order mixed finite elements for an energy-bas…
We are concerned with the mathematical modeling of the polarization process in ferroelectric media. We assume that this dissipative process is governed by two constitutive functions, which are the free energy function and the dissipation…
Flexoelectricity is characterised by the coupling of the gradient of the deformation and the electrical polarization in a dielectric material. A novel micromorphic approach is presented to accommodate the resulting higher-order gradient…
In biological and synthetic materials, many important processes involve charges that are present in a medium with spatially varying dielectric permittivity. To accurately understand the role of electrostatic interactions in such systems, it…
This letter addresses basic questions concerning ferroelectric order in positionally disordered dipolar materials. Three models distinguished by dipole vectors which have one, two or three components are studied by computer simulation.…
The modeling of coupled fluid transport and deformation in a porous medium is essential to predict the various geomechanical process such as CO2 sequestration, hydraulic fracturing, and so on. Current applications of interest, for instance,…
This paper focuses on the analysis of a free energy functional, that models a dilute suspension of magnetic nanoparticles in a two-dimensional nematic well. The {\it first part} of the article is devoted to the asymptotic analysis of global…
We review the phenomenology of coupled magnetic and electric order parameters for systems in which ferroelectric and incommensurate magnetic order occur simultaneously. We discuss the role that such materials might play in fabricating novel…
Metal-organic frameworks comprehend a wide class of hybrid organic-inorganic materials with general structure A$_m$BX$_n$, with $A$ and $X$ being organic molecules and B a metal cation. This often results in enhanced structural flexibility…
Density functional theory calculations have been performed for the structural, electronic, magnetic and ferroelectric properties of a mixed-valence Fe(II)-Fe(III) formate framework [NH$_2$(CH$_3$)$_2$][Fe$^{\rm III}$Fe$^{\rm II}$(HCOO)$_6$]…
A finite element discretization using a method of lines approached is proposed for approximately solving the Poisson-Nernst-Planck (PNP) equations. This discretization scheme enforces positivity of the computed solutions, corresponding to…
Modeling ferroelectric materials from first principles is one of the successes of density-functional theory, and the driver of much development effort, requiring an accurate description of the electronic processes and the thermodynamic…
In this paper, we develop a multiphysics finite element method for solving the quasi-static thermo-poroelasticity model with nonlinear permeability. The model involves multiple physical processes such as deformation, pressure, diffusion and…
This paper develops a comprehensive mathematical framework for energy-based modeling of physical systems, with particular emphasis on preserving fundamental structural properties throughout the modeling and discretization process. The…
This paper is concerned with modeling the polarization process in ferroelectric media. We develop a thermodynamically consistent model, based on phenomenological descriptions of free energy as well as switching and saturation conditions in…
In this work we study the solvability of the initial boundary value problems, which model a quasi-static nonlinear behavior of ferroelectric materials. Similar to the metal plasticity the energy functional of a ferroelectric material can be…
We present for static density functional theory and time-dependent density functional theory calculations an all-electron method which employs high-order hierarchical finite element bases. Our mesh generation scheme, in which structured…
Mixed finite element methods are considered for a ferrofluid flow model with magnetization paralleled to the magnetic field. The ferrofluid model is a coupled system of the Maxwell equations and the incompressible Navier-Stokes equations.…
We apply high-order mixed finite element discretization techniques and their associated preconditioned iterative solvers to the Variable Eddington Factor (VEF) equations in two spatial dimensions. The mixed finite element VEF…
The equations for phase transitions temperatures, order parameters and critical concentrations of components have been derived for mixed ferroelectrics. The electric dipoles randomly distributed over the system were considered as a random…
The basic continuum model for polar fluids is deceptively simple. The free energy integral consists of four terms: The coupling of polarization to an external field, the electrostatic energy of the induced electric field interacting with…