Related papers: Beyond Poisson-Boltzmann: fluctuations and fluid s…

The Adaptive Poisson-Boltzmann Solver (APBS) software was developed to solve the equations of continuum electrostatics for large biomolecular assemblages that has provided impact in the study of a broad range of chemical, biological, and…

The Poisson-Boltzmann equation is widely used to model molecular electrostatics; however, it is usually solved in linearised form because the sinh nonlinearity is challenging, limiting its applicability in highly charged systems such as…

The Poisson-Boltzmann approach gives asymptotically exact counter-ion density profiles around charged objects in the weak-coupling limit of low valency and high temperature. In this paper we derive, using field-theoretic methods, a theory…

We study a hard sphere gas at equilibrium, and prove that in the low density limit, the fluctuations converge to a Gaussian process governed by the fluctuating Boltzmann equation. This result holds for arbitrarily long times. The method of…

A fundamental challenge in soft matter physics is to describe materials, such as the living cytoplasm and tissues, that are simultaneously active, chemically driven, and exhibit long-lasting memory of mechanical stresses. Here, we construct…

The theory of dark matter superfluidity has emerged as a compelling framework, in which the dynamics are governed by a non-relativistic $P(X)$ superfluid Lagrangian that naturally leads to Modified Newtonian Dynamics (MOND)-like behavior…

Simplest extensions of single particle dynamics in momentum conserving active fluid - that of an active suspension of two colloidal particles or a single particle confined by a wall - exhibit strong departures from Boltzmann behavior,…

We calculate ion distributions near a planar oil-water interface within non-linear Poisson-Boltzmann theory, taking into account the Born self-energy of the ions in the two media. For unequal self-energies of cations and anions, a…

Fluctuations arising in nonlinear dissipative systems (diode, transistors, chemical reaction, etc.) subject to an external drive (voltage, chemical potential, etc.) are well known to elude any simple characterization such as the…

The Vlasov-Poisson-Boltzmann system is often used to govern the motion of plasmas consisting of electrons and ions with disparate masses when collisions of charged particles are described by the two-component Boltzmann collision operator.…

We study in this work the important class of nonlocal Poisson Brackets (PB) which we call weakly nonlocal. They appeared recently in some investigations in the Soliton Theory. However there was no theory of such brackets except very special…

We perform a linearization of the Poisson-Boltzmann (PB) density functional for spherical Wigner-Seitz cells that yields Debye-H\"uckel-like equations agreeing asymptotically with the PB results in the weak-coupling (high-temperature)…

Combining analytical and numerical methods, we study within the framework of the homogeneous non-linear Boltzmann equation, a broad class of models relevant for the dynamics of dissipative fluids, including granular gases. We use the new…

At mesoscopic scales electrolyte solutions are modeled by the fluctuating generalized Poisson-Nernst-Planck (PNP) equations [J.-P. P\'eraud et al., Phys. Rev. F, 1(7):074103, 2016]. However, at length and time scales larger than the Debye…

A nonlinear Poisson--Boltzmann equation with transmission boundary conditions at the interface between two materials is investigated. The model describes the electrostatic potential generated by a vector of ion concentrations in a periodic…

We consider the compressible Navier-Stokes-Poisson equations in $\mathbb{R}^d$ ($d\geq2$), a classical model for barotropic compressible flows coupled with a self-consistent electrostatic potential. We show that the electrostatic coupling…

The Boltzmann equation is a nonlinear partial differential equation that plays a central role in statistical mechanics. From the mathematical point of view, the existence of global smooth solutions for arbitrary initial data is an…

Structure and thermodynamics in restricted primitive model electrolytes are examined using three recently developed versions of a linear form of the modified Poisson-Boltzmann equation. Analytical expressions for the osmotic coefficient and…

Thermal fluctuations play a central role in fluid dynamics at mesoscopic scales and must be incorporated into numerical schemes in a manner consistent with statistical mechanics. In this work, we develop a fluctuating lattice Boltzmann…

Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point…