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The Poisson-Fermi model is an extension of the classical Poisson-Boltzmann model to include the steric and correlation effects of ions and water treated as nonuniform spheres in aqueous solutions. Poisson-Boltzmann electrostatic…

Computational Physics · Physics 2018-07-04 Jen-Hao Chen , Ren-Chuen Chen , Jinn-Liang Liu

We describe a three-stage procedure to analyze the dependence of Poisson Boltzmann calculations on the shape, size and geometry of the boundary between solute and solvent. Our study is carried out within the boundary element formalism, but…

Biological Physics · Physics 2007-11-27 P. Kar , Y. Wei , U. H. E. Hansmann , S. Hoefinger

The Poisson-Nernst-Planck equations with generalized Frumkin-Butler-Volmer boundary conditions (PNP-FBV) describe ion transport with Faradaic reactions and have applications in a wide variety of fields. Using an adaptive time-stepper based…

Numerical Analysis · Mathematics 2020-06-24 M. C. Pugh , D. Yan , F. P. Dawson

In the framework of a multiscale modeling approach, we present a systematic study of a bipolar rectifying nanopore using a continuum and a particle simulation method. The common ground in the two methods is the application of the…

The Poisson-Boltzmann equation offers an efficient way to study electrostatics in molecular settings. Its numerical solution with the boundary element method is widely used, as the complicated molecular surface is accurately represented by…

Numerical Analysis · Mathematics 2021-08-25 Stefan D. Search , Christopher D. Cooper , Elwin van't Wout

We present an extension of the Poisson-Boltzmann model in which the solute of interest is immersed in an assembly of self-orienting Langevin water dipoles, anions, cations, and hydrophobic molecules, all of variable densities. Interactions…

Biological Physics · Physics 2021-04-08 Patrice Koehl , Marc Delarue , Henri Orland

For multispecies ions, we study boundary layer solutions of charge conserving Poisson-Boltzmann (CCPB) equations [50] (with a small parameter \k{o}) over a finite one-dimensional (1D) spatial domain, subjected to Robin type boundary…

Analysis of PDEs · Mathematics 2015-04-28 Chiun-Chang Lee , Hijin Lee , YunKyong Hyon , Tai-Chia Lin , Chun Liu

This paper is devoted to the homogenization (or upscaling) of a system of partial differential equations describing the non-ideal transport of a N-component electrolyte in a dilute Newtonian solvent through a rigid porous medium. Realistic…

Analysis of PDEs · Mathematics 2014-10-14 Gregoire Allaire , Robert Brizzi , Jean-Francois Dufreche , Andro Mikelic , Andrey Piatnitski

In this paper, we consider a class of systems of nonlinear equations, which arise in discretized mixed formulations of problems in solid mechanics by $hp$-finite elements. We introduce a semismooth Newton solver for this specific class and…

Numerical Analysis · Mathematics 2025-11-24 Patrick Bammer , Lothar Banz , Miriam Schönauer , Andreas Schröder

When ions are crowded, the effect of steric repulsion between ions becomes significant and the conventional Poisson--Boltzmann (PB) equation (without steric effect) should be modified. For this purpose, we study the asymptotic limit of…

Analysis of PDEs · Mathematics 2022-05-26 Jhih-Hong Lyu , Tai-Chia Lin

A coarse-grained computational procedure based on the Finite Element Method is proposed to calculate the normal modes and mechanical response of proteins and their supramolecular assemblies. Motivated by the elastic network model, proteins…

Biomolecules · Quantitative Biology 2007-05-23 Mark Bathe

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…

Analysis of PDEs · Mathematics 2022-04-26 José A. Iglesias , Svetoslav Nakov

We developed a multiscale approach (MultiSCAAL) that integrates the potential of mean force (PMF) obtained from all-atomistic molecular dynamics simulations with a knowledge-based energy function for coarse-grained molecular simulations in…

Biological Physics · Physics 2010-05-10 Antonios Samiotakis , Dirar Homouz , Margaret S. Cheung

We prove the existence and uniqueness of the complexified Nonlinear Poisson-Boltzmann Equation (nPBE) in a bounded domain in $\mathbb{R}^3$. The nPBE is a model equation in nonlinear electrostatics. The standard convex optimization argument…

Analysis of PDEs · Mathematics 2021-06-11 Brian Choi , Jie Xu , Trevor Norton , Mark Kon , Julio E. Castrillon-Candas

Finite difference method and pseudo-spectral method have been widely used in the numerical relativity to solve the Einstein equations. As the third major category method to solve partial differential equations, finite element method is much…

General Relativity and Quantum Cosmology · Physics 2018-05-29 Zhoujian Cao , Pei Fu , Li-Wei Ji , Yinhua Xia

When ions are crowded, the effect of steric repulsion between ions (which can produce oscillations in charge density profiles) becomes significant and the conventional Poisson-Boltzmann (PB) equation should be modified. Several modified PB…

Analysis of PDEs · Mathematics 2024-03-21 Jhih-Hong Lyu , Tai-Chia Lin

In this paper we have derived explicitly computable bounds on the error in energy norms for the fully nonlinear Poisson-Boltzmann equation. Together with the computable bounds, we have also obtained efficient error indicators which can…

Numerical Analysis · Mathematics 2018-05-30 Johannes Kraus , Svetoslav Nakov , Sergey Repin

In the post-Moore era, the need for efficient solutions to non-deterministic polynomial-time (NP) problems is becoming more pressing. In this context, the Ising model implemented by the probabilistic computing systems with probabilistic…

Applied Physics · Physics 2025-02-28 Chao Fang , Yihan He , Xiao Gong , Gengchiau Liang

We propose a field-theoretical approach based on the thermodynamic perturbation theory and within it derive a grand thermodynamic potential of the inhomogeneous ionic fluid as a functional of electrostatic potential for an arbitrary…

Soft Condensed Matter · Physics 2022-05-25 Yu. A. Budkov , A. L. Kolesnikov

The Poisson-Boltzmann (PB) equation provides a mean-field theory of electrolyte solutions at interfaces and in confinement, describing how ions reorganize close to charged surfaces to form the so-called electrical double layer (EDL), with…

Soft Condensed Matter · Physics 2024-09-10 Cecilia Herrero , Laurent Joly