The Poisson-Boltzmann equation is a partial differential equation that describes the electrostatic behavior of molecules in ionic solutions. Significant efforts have been devoted to accurate and efficient computation for solving this equation. In this paper, we developed a boundary element framework based on the linear time fast multipole method for solving the linearized PoissonBoltzmann equat...

We present a derivation of generalized Poisson-Boltzmann equations starting from classical theories of binary fluid mixtures, employing an approach based on the Legendre transform as recently applied to the case of local descriptions of the fluid free energy. Under specific symmetry assumptions, and in the linearized regime, the Poisson-Boltzmann equation reduces to a phenomenological equation ...

Electrostatics plays a fundamental role in virtually all processes involving biomolecules in solution. The Poisson-Boltzmann equation constitutes one of the most fundamental approaches to treat electrostatic effects in solution. The theoretical basis of the Poisson-Boltzmann equation is reviewed and a wide range of applications is presented, including the computation of the electrostatic potent...

The Poisson Boltzmann equation is a model that describes electrostatic interactions between molecules in ionic solutions. As the mathematical base for the Gouy Chapman double layer (interfacial) theory, it was first proposed by Gouy in 1910 and then complemented by Chapman in 1913. The equation is extraordinarily important in the fields of molecular dynamics and biophysics, because it can be us...

By identifying a norm capturing the effect of forcing governed by Poisson equation, we give detailed spectrum analysis on linearized Vlasov–Poisson–Boltzmann system around global Maxwellian. It is shown that electric field self-consistent equation plays key role in so structure genuinely different from well-known one Boltzmann equation. Based this, optimal time decay rates solutions to equilibr...

Abstract. The size-modified Poisson-Boltzmann equation (SMPBE) has been developed to consider ionic size effects in the calculation of electrostatic potential energy, but its numerical solution for a biomolecule remains a challenging research issue. To address this challenge, in this paper, we propose a solution decomposition formula and then develop an effective minimization protocol for solvi...

This paper analyzes various schemes for the Euler-Poisson-Boltzmann (EPB) model of plasma physics. This model consists of the pressureless gas dynamics equations coupled with the Poisson equation and where the Boltzmann relation relates the potential to the electron density. If the quasi-neutral assumption is made, the Poisson equation is replaced by the constraint of zero local charge and the ...