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...

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 ...

We are concerned with the study of the diffusion and homogenization approximation of the Boltzmann-Poisson system in presence of a spatially oscillating electrostatic potential. By analyzing the relative entropy, we prove uniform energy estimate for well prepared boundary data. An averaging lemma and two scale convergence techniques are used to prove rigorously the convergence of the scaled Bol...

We consider the flow of a dilute gas around a macroscopic heavy object. The state of the gas is described by an extended Boltzmann equation where the interactions between the gas molecules and the object are taken into account in computing the rate of change of the distribution function of the gas. We then show that the extended Boltzmann is equivalent to the usual Boltzmann equation, supplemen...

Effective Poisson-Nernst-Planck (PNP) equations are derived for macroscopic ion transport in charged porous media. Homogenization analysis is performed for a two-component periodic composite consisting of a dilute electrolyte continuum (described by standard PNP equations) and a continuous dielectric matrix, which is impermeable to the ions and carries a given surface charge. Three new features...

The double bracket dissipation approach is applied to the Vlasov kinetic equation. The Vlasov equation is then transformed by a Poisson map to moment dynamics, leading to a nonlocal form of Darcy’s law. Next, kinetic equations for particles with anisotropic interaction are considered and also cast into the double bracket dissipation form. The moment dynamics for these double bracket kinetic equ...

Measurements of shear Alfvén waves are used to test the predictions of a variety of different electron collision operators, including several Krook collision operators as well as a Lorentz collision operator. New expressions for the collisional warm-plasma dielectric tensor resulting from the use of the fully-magnetized collisional Boltzmann equation are presented here. Theoretical predictions ...

We investigate numerical solution schemes for the semiconductor Boltzmann transport equation using an expansion of the distribution function in spherical harmonics. A complexity analysis shows that traditional implementations using higher-order expansions suffer from huge memory requirements, especially for twoand three-dimensional devices. To overcome these complexity limitations, a compressed...

The coalgebra approach to the construction of classical integrable systems from Poisson coalgebras is reviewed, and the essential role played by symplectic realizations in this framework is emphasized. Many examples of Hamiltonians with either undeformed or q-deformed coalgebra symmetry are given, and their Liouville superintegrability is discussed. Among them, (quasi-maximally) superintegrable...