Related papers: Solution Poisson-Boltzmann equation: Application i…
We develop a mesoscopic approach to model the non-equilibrium behavior of membranes at the cellular scale. Relying on lattice Boltzmann methods, we develop a solution procedure to recover the Nernst-Planck equations and Gauss's law. A…
Electrochemical phenomena in biology often unfold in confined geometries where micrometer- to millimeter-scale domains coexist with nanometer-scale interfacial diffuse charge layers. We analyze a model lipid membrane-electrolyte system…
In electromagnetic statics, the standard procedure to determine the electric scalar potential or magnetic vector potential in a bounded space is to solve Poisson's equation subject to certain boundary conditions. On the other hand, as a…
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…
Membranes are present in all cells and tissues. Mathematical models of cells and tissues need a compact mathematical description of membranes with a resolution of about 1 nm. Membranes isolate cells because ions have difficulty penetrating…
In a continuum model of the solvation of charged molecules in an aqueous solvent, the classical Poisson-Boltzmann (PB) theory is generalized to include the solute point charges and the dielectric boundary that separates the high-dielectric…
The accurate determination of electron properties is fundamental to low-temperature plasma simulations, necessitating precise solutions to the spatially inhomogeneous electron Boltzmann equation (EBE). This work explores the use of…
In this paper we present a model based on dynamics of the electrons in the plasma using a simplified Boltzmann equation coupled with a Poisson equation. The motivation arose to simulate active plasma resonance spectroscopy which is used for…
We report here new electrical laws, derived from nonlinear electro-diffusion theory, about the effect of the local geometrical structure, such as curvature, on the electrical properties of a cell. We adopt the Poisson-Nernst-Planck (PNP)…
The linear Boltzmann equation for elastic and/or inelastic scattering is applied to derive the distribution function of a spatially homogeneous system of charged particles spreading in a host medium of two-level atoms and subjected to…
We numerically solve the non-linear Poisson-Boltzmann equation for two cylinders confined by two parallel charged plates. The repulsive electrical double layer component of the cylinder pair potential is substantially reduced by confinement…
Physics-informed neural networks (PINN) is a machine learning (ML)-based method to solve partial differential equations that has gained great popularity due to the fast development of ML libraries in the last few years. 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…
We present an extension to the Poisson-Boltzmann model where the dipolar features of solvent molecules are taken explicitly into account. The formulation is derived at mean-field level and can be extended to any order in a systematic…
Swollen stacks of finite-size disc-like Laponite clay platelets are investigated within a Wigner-Seitz cell model. Each cell is a cylinder containing a coaxial platelet at its centre, together with an overall charge-neutral distribution of…
Biological membranes are capacitors that can be charged by applying a field across the membrane. The charges on the capacitor exert a force on the membrane that leads to electrostriction, i.e. a thinning of the membrane. Since the force is…
Starting from the microscopic reduced Hartree-Fock equation, we derive the nanoscopic linearized Poisson-Boltzmann equation for the electrostatic potential associated with the electron density.
A method is described for embedding a deformable, elastic, membrane within a lattice Boltzmann fluid. The membrane is represented by a set of massless points which advect with the fluid and which impose forces on the fluid which are derived…
Simulating protein-membrane interactions is an important and dynamic area of research. A proper definition of electrostatic forces on membrane surfaces is necessary for developing electromechanical models of protein-membrane interactions.…
In this paper we study the hydrodynamic limit for a stochastic process describing the time evolution of the membrane potentials of a system of neurons with spatial dependency. We do not impose on the neurons mean-field type interactions.…