Related papers: Thin layer analysis of a non-local model for the d…
We provide a summary of the continuity properties of the boundary integral operator corresponding to the double layer potential associated to the fundamental solution of a {\em nonhomogeneous} second order elliptic differential operator…
We consider the Poisson-Boltzmann equation in a periodic cell, representative of a porous medium. It is a model for the electrostatic distribution of $N$ chemical species diluted in a liquid at rest, occupying the pore space with charged…
We consider divergence form elliptic equations $Lu:=\nabla\cdot(A\nabla u)=0$ in the half space $\mathbb{R}^{n+1}_+ :=\{(x,t)\in \mathbb{R}^n\times(0,\infty)\}$, whose coefficient matrix $A$ is complex elliptic, bounded and measurable. In…
We utilize the self-consistent field theory to explore the mechanical and electrical properties of charged surfaces immersed in polyelectrolyte solutions that could be potentially useful for electrochemical applications. Our research…
In the present work, we study an electrolyte solution confined between planar surfaces with nonopatterned charged domains, which has been connected to a bulk ionic reservoir. The system is investigated through an improved Monte Carlo (MC)…
We investigate the behavior, as a small parameter tends to zero, of a nonlocal Allen-Cahn equation. Given a rather general initial data, we perform a rigorous analysis of both the generation and the motion of interface, and obtain a new…
We study the potential and the charge distribution across the interface of a plasma and a dielectric wall. For this purpose, the charge bound to the wall is modelled as a quasi-stationary electron surface layer which satisfies Poisson's…
In this study, we examined the thickness of the electrical double layer (EDL) in ionic liquids using density functional theory (DFT) calculations and molecular dynamics (MD) simulations. We focused on the BF4- anion adsorption from…
We prove the validity of a regularizing property on the boundary of the double layer potential associated to the fundamental solution of a {\em nonhomogeneous} second order elliptic differential operator with constant coefficients in…
Exact solutions describing the nonlinear electrodynamics of a thin double layer foil are presented. These solutions correspond to a broad range of problems of interest for the interaction of high intensity laser pulses with overdense…
We derive and validate a quantitative analytical model of the near-field electrostatic effects in the vicinity (>=3\AA) of two-dimensional (2D) materials. In solving the Poisson equation of a near-planar point charge ansatz for the…
The problem of the one dimensional electro-diffusion of ions in a strong binary electrolyte is considered. In such a system the solute dissociates completely into two species of ions with unlike charges. The mathematical description…
We have found a (dense) basis for the N-representable, two-electron densities, in which all N-representable two-electron densities can be expanded, using positive coefficients. The inverse problem of finding a representative wavefunction,…
A flat elastic sheet may contain pointlike conical singularities that carry a metrical "charge" of Gaussian curvature. Adding such elementary defects to a sheet allows one to make many shapes, in a manner broadly analogous to the familiar…
The boundary double layer potential, or the Neumann-Poincare operator, is studied on the Sobolev space of order 1/2 along the boundary, coinciding with the space of charges giving rise to double layer potentials with finite energy in the…
We investigate the formation of a plasma boundary layer (sheath) by considering the Vlasov--Poisson system on a half-line with the completely absorbing boundary condition. In an earlier paper by the first two authors, the solvability of the…
We consider the nonlinear Poisson-Boltzmann equation in the context of electrostatic models for a biological macromolecule, embedded in a bounded domain containing a solution of an arbitrary number of ionic species which is not necessarily…
Motivated by lubrication problems, we consider a micropolar uid ow in a 2D domain with a rough and free boundary. We assume that the thickness and the roughness are both of order 0 < " << 1. We prove the existence and uniqueness of a…
The modification of the boundary condition for polyelectrolyte adsorption on charged surface with short-ranged interaction is investigated under two regimes. For weakly charged Gaussian polymer in which the short-ranged attraction…
Ionic behaviors, including ion distributions and hydration characteristics at solid-liquid interfaces, are important research interests in many important applications, such as electric double-layer capacitors and water lubrication. Here, we…