Related papers: Accurate boundary-integral formulations for the ca…
In this paper we propose a nonlinear elasticity model of macromolecular conformational change (deformation) induced by electrostatic forces generated by an implicit solvation model. The Poisson-Boltzmann equation for the electrostatic…
The properties of ionic solutions between charged surfaces are often studied within the Poisson-Boltzmann framework, by finding the electrostatic potential profile. For example, the osmotic pressure between two charged planar surfaces can…
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…
A surface integral representation of Maxwell's equations allows the efficient electromagnetic (EM) modeling of three-dimensional structures with a two-dimensional discretization, via the boundary element method (BEM). However, existing BEM…
Wereportonanewmultiscalemethodapproachforthestudyofsystemswith wide separation of short-range forces acting on short time scales and long-range forces acting on much slower scales. We consider the case of the Poisson-Boltzmann equation that…
Electrokinetic phenomena in nanopore sensors and microfluidic devices require accurate simulation of coupled fluid-electrostatic interactions in geometrically complex domains with irregular boundaries and adaptive mesh refinement. We…
We present the theory and implementation of a Poisson-Boltzmann implicit solvation model for electrolyte solutions. This model can be combined with arbitrary electronic structure methods that provide an accurate charge density of the…
The paper presents a two-dimensional geometrically nonlinear formulation of a beam element that can accommodate arbitrarily large rotations of cross sections. The formulation is based on the integrated form of equilibrium equations, which…
We present a novel numerical method that allows the calculation of nonlinear force-free magnetostatic solutions above a boundary surface on which only the distribution of the normal magnetic field component is given. The method relies on…
We develop a systematic approach to calculating the electrostatic force between point charges in an arbitrary geometry with arbitrary boundary conditions. When the boundary is present, the simple expression for the force acting on a charge…
This paper is concerned with the derivation of computable and guaranteed upper and lower bounds of the difference between the exact and the approximate solution of a boundary value problem for static Maxwell equations. Our analysis is based…
Understanding the behavior of biomolecules such as proteins requires understanding the critical influence of the surrounding fluid (solvent) environment--water with mobile salt ions such as sodium. Unfortunately, for many studies, fully…
Modeling the chemical, electric, and thermal transport as well as phase transitions and the accompanying mesoscale microstructure evolution within a material in an electronic device setting involves the solution of partial differential…
The Poisson-Boltzmann equation (PBE) models the electrostatic interactions of charged bodies such as molecules and proteins in an electrolyte solvent. The PBE is a challenging equation to solve numerically due to the presence of…
We develop a computational method for modeling electrostatic interactions of arbitrarily-shaped, polarizable objects on colloidal length scales, including colloids/nanoparticles, polymers, and surfactants, dispersed in explicit ion…
We derive the equations of nonlinear magnetoelastostatics using several variational formulations involving the mechanical deformation and an independent field representing the magnetic component. An equivalence is also discussed, modulo…
We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be…
Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective…
This paper presents a re-formulation of the boundary integral method (BIM) for the Debye-Huckel model of molecular and colloidal electrostatics that removes the mathematical singularities that have been accepted as an intrinsic part of the…
A numerical method is developed to efficiently calculate the stress (and displacement) field in finite 2D rectangular media. The solution is expanded on a function basis with elements that satisfy the Navier-Cauchy equation. The obtained…