A hybrid approach for solving the nonlinear Poisson-Boltzmann equation (PBE) is presented. Under this approach, the electrostatic potential is separated into (1) a linear component satisfying the linear PBE and solved using a fast boundary element method and (2) a correction term accounting for nonlinear effects and optionally, the presence of an ion-exclusion layer. Because the correction pote...

In this paper an alternative model allowing the extension of the Debye-Hückel Theory (DHT) considering time dependence explicitly is presented. From the Electro-Quasistatic approach (EQS) introduced in earlier studies time dependent potentials are suitable to describe several phenomena especially conducting media as well as the behaviour of charged particles (ions) in electrolytes. This leads t...

K e y w o r d s Poisson-Boltzmann equation, Electrostatics in biology, Boundary conditions, Nonlinear partial differential equations, Finite-difference scheme. 1. I N T R O D U C T I O N Electrostatics is believed to play a pivotal role in regulating interactions between biological macromolecules, such as proteins and nucleic acids [1,2]. Specifically, the solvation contribution, that is the en...

The electrostatic interaction among molecules solvated in ionic solution is governed by the Poisson-Boltzmann equation (PBE). Here the hypersingular integral technique is used in a boundary element method (BEM) for the three-dimensional (3D) linear PBE to calculate the Maxwell stress tensor on the solvated molecular surface, and then the PB forces and torques can be obtained from the stress ten...

We present a robust and eecient numerical method for solution of the nonlinear Poisson-Boltzmann equation arising in molecular biophysics. The equation is discretized with the box method, and solution of the discrete equations is accomplished with a global inexact-Newton method, combined with linear multilevel techniques we have described in a previous paper. A detailed analysis of the resultin...

Poisson approximation using Stein’s method has been extensively studied in the literature. The main focus has been on bounding the total variation distance. This paper is a first attempt on moderate deviations in Poisson approximation for right-tail probabilities of sums of dependent indicators. We obtain results under certain general conditions for local dependence as well as for size-bias cou...

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Pulling back sets of functions in involution by Poisson mappings and adding Casimir functions during the process allows to construct completely integrable systems. Some examples are investigated in detail.

We study the Cauchy problem for the relativistic Boltzmann equation with near vacuum initial data. Unique global-in-time mild solutions are obtained uniformly in the speed of light parameter c ≥ 1. We furthermore prove that solutions to the relativistic Boltzmann equation converge to solutions of the Newtonian Boltzmann equation in the limit as c→∞ on arbitrary time intervals [0, T ], with conv...

The paper provides a survey of known results on geometric aspects related to Nambu-Poisson brackets.