The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

Electrostatic interactions between dielectric objects are complex and of a many-body nature,
owing to induced surface bound charge. We present a collection of techniques to simulate …

A three-dimensional numerical simulator based on Brownian dynamics (BD) for the study of
ion transport through membrane pores is presented. Published BD implementations suffer …

Numerous molecular processes, such as ion permeation through channel proteins, are
governed by relatively small changes in energetics. As a result, theoretical investigations of …

We present a robust integral equation method for the calculation of the electrostatic and
thermal properties of systems made of piecewise homogeneous, high contrast materials. By …

Boundary-element methods (BEMs) for solving integral equations numerically have been
used in many fields to compute the induced charges at dielectric boundaries. In this paper …

Particle-based simulation represents a powerful approach to modeling physical systems in
electronics, molecular biology, and chemical physics. Accounting for the interactions …

The importance of molecular electrostatic interactions in aqueous solution has motivated
extensive research into physical models and numerical methods for their estimation. The …

A variety of electrostatic phenomena, including the structure of electric double layers and the
aggregation of charged colloids and proteins, are affected by nonuniform electric permittivity …

The simplicity of dielectric continuum models has made them a standard tool in almost any
Quantum Chemistry (QC) package. Despite being intuitive from a physical point of view, the …