Related papers: The Anisotropic Interface Continuum Solvation Mode…
The ab-initio computational treatment of electrochemical systems requires an appropriate treatment of the solid/liquid interfaces. A fully quantum mechanical treatment of the interface is computationally demanding due to the large number of…
We present a local formulation for 2D Discrete Exterior Calculus (DEC) similar to that of the Finite Element Method (FEM), which allows a natural treatment of material heterogeneity (element by element). It also allows us to deduce, in a…
In this article, we analyse a stabilised equal-order finite element approximation for the Stokes equations on anisotropic meshes. In particular, we allow arbitrary anisotropies in a sub-domain, for example along the boundary of the domain,…
We propose a new nonconforming \(P_1\) finite element method for elliptic interface problems. The method is constructed on a locally anisotropic mixed mesh, which is generated by fitting the interface through a simple connection of…
An Integral Equation (IE) based field solver to compute the scattered fields from spatially dispersive metasurfaces is proposed and numerically confirmed using various examples involving physical unit cells. The work is a continuation of…
Within a dipolar Poisson-Boltzmann theory including electrostatic correlations, we consider the effect of explicit solvent structure on solvent and ion partition confined to charged nanopores. We develop a relaxation scheme for the solution…
A new finite element method (FEM) using meshes that do not necessarily align with the interface is developed for two- and three-dimensional anisotropic elliptic interface problems with nonhomogeneous jump conditions. The degrees of freedom…
An Integral Equation (IE) based electromagnetic field solver using metasurface susceptibility tensors is proposed and validated using variety of numerical examples in 2D. The proposed method solves for fields generated by the metasurface…
In this paper we develop a methodology for the mesoscale simulation of strong electrolytes. The methodology is an extension of the Fluctuating Immersed Boundary (FIB) approach that treats a solute as discrete Lagrangian particles that…
The interface stresses at of the solid-melt interface are, in general, anisotropic. The anisotropy in the interfacial stress can be evaluated using molecular dynamics (MD) and phase field crystal (PFC) models. In this paper, we report our…
This work presents an open-source interface that couples the viscoplastic self-consistent (VPSC) model capable of simulating anisotropic creep and irradiation growth in polycrystalline materials with the finite element solver Code_Aster.…
We present a diffuse-interface model for the solid-state dewetting problem with anisotropic surface energies in ${\mathbb R}^d$ for $d\in\{2,3\}$. The introduced model consists of the anisotropic Cahn--Hilliard equation, with either a…
Reliable first-principles calculations of electrochemical processes require accurate prediction of the interfacial capacitance, a challenge for current computationally-efficient continuum solvation methodologies. We develop a model for the…
Recently, a nonlinear Poisson equation has been introduced to model nonlinear and nonlocal hyperpolarization effects in electrostatic solute-solvent interaction for biomolecular solvation analysis. Due to a strong nonlinearity associated…
Tasker type III polar terminations of ionic crystals carry a net surface charge as well as a dipole moment and are fundamentally unstable. In contact with electrolytes, such polar surfaces can be stabilized by adsorption of counter ions…
We extend the simplex-in-cell (SIC) technique recently introduced in the context of collisionless dark matter fluids (Abel et al. 2012; Hahn et al. 2012) to the case of collisionless plasmas. The six-dimensional phase space distribution…
In this thesis, the electrostatic interaction between two chemically identical colloids, both carrying constant surface potential is studied in the limit of short inter-particle separation at the interface of two immiscible fluids. Using an…
A common approach for generating an anisotropic mesh is the M-uniform mesh approach where an adaptive mesh is generated as a uniform one in the metric specified by a given tensor M. A key component is the determination of an appropriate…
Continuum electrolyte models represent a practical tool to account for the presence of the diffuse layer at electrochemical interfaces. However, despite the increasing popularity of these in the field of materials science it remains unclear…
In multi-phase fluid flow, fluid-structure interaction, and other applications, partial differential equations (PDEs) often arise with discontinuous coefficients and singular sources (e.g., Dirac delta functions). These complexities arise…