Monte Carlo methods for linear and non-linear Poisson-Boltzmann equation

Monte Carlo Methods for the Linearized Poisson-Boltzmann Equation

We review efficient grid-free random walk methods for solving boundary value problems for the linearized Poisson-Boltzmann equation (LPBE). First we introduce the “Walk On Spheres” (WOS) algorithm [1] for the LPBE. Based on this WOS algorithm, another, related, Monte Carlo algorithm is presented. This modified Monte Carlo method reinterprets the weights used in the original WOS algorithm as sur...

Iterative methods for solving non linear Fokker-Planck equation

Monte Carlo Methods for Solving the Boltzmann Transport Equation

We review Monte Carlo methods for solving the Boltzmann equation for applications to small-scale transport processes, with particular emphasis on nanoscale heat transport as mediated by phonons. Our discussion reviews the numerical foundations of Monte Carlo algorithms, basic simulation methodology, as well as recent developments in the field. Examples of the latter include formulations for cal...

on the effect of linear & non-linear texts on students comprehension and recalling

چکیده ندارد.

Fast Boundary Element Method for the Linear Poisson-Boltzmann Equation

This article summarizes the development of a fast boundary element method for the linear Poisson-Boltzmann equation governing biomolecular electrostatics. Unlike previous fast boundary element implementations, the present treatment accommodates finite salt concentrations thus enabling the study of biomolecular electrostatics under realistic physiological conditions. This is achieved by using mu...