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) equations for charge concentration and electric potential as a model of electro-diffusion. In the case at hand, the entire boundary is impermeable to ions and ...

This short note complements the recent paper of the authors [2]. We revisit the results on propagation of regularity and stability using Lp estimates for the gain and loss collision operators which had the exponent range misstated for the loss operator. We show here the correct range of exponents. We require a Lebesgue’s exponent α > 1 in the angular part of the collision kernel in order to obt...

Abstract: By adopting the upper half space realizations of the real, complex and quaternionic hyperbolic spaces and solving the corresponding stochastic differential equations, we can represent the Brownian motions on these classical families of the hyperbolic spaces as explicit Wiener functionals. Using the representations, we show that the almost sure convergence of the Brownian motions and t...

The Coulomb-gauge vector potential of a uniformly moving point charge is obtained by calculating the gauge function for the transformation between the Lorenz and Coulomb gauges. The expression obtained for the difference between the vector potentials in the two gauges is shown to satisfy a Poisson equation to which the inhomogeneous wave equation for this quantity can be reduced. The right-hand...

2014 We propose a model for describing electrostatic interactions in the aqueous core of a spherical reversed micelle. Some counterions are located at the surface of the aqueous core, the others are distributed inside the core following a Boltzmann law. The nonlinearized Poisson-Boltzmann equation is solved in spherical geometry; an asymptotic expansion of its solution is found near a logarithm...

In this paper, we have extended and completed our previous work, that was introducing a new method for finite differentiation. We show the applicability of the method for solving a wide variety of equations such as Poisson, Lap lace and Schrodinger. These equations are fundamental to the most semiconductor device simulators. In a section, we solve the Shordinger equation by this method in sever...

This paper presents an incompressible smoothed particle hydrodynamics (SPH) model to simulate wave propagation in a free surface flow. The Navier-Stokes equations are solved in a Lagrangian framework using a three-step fractional method. In the first step, a temporary velocity field is provided according to the relevant body forces. This velocity field is renewed in the second step to include t...

We prove that the periodic initial value problem for a modified Euler-Poisson equation is well-posed for initial data in Hs(Tm) when s > m/2 + 1. We also study the analytic regularity of this problem and prove a Cauchy-Kowalevski type theorem. After presenting a formal derivation of the equation on the semidirect product space Diff C∞(T) as a Hamiltonian equation, we concentrate on one space di...

In the remainder, we call such a variety a convex symplectic variety. A convex symplectic variety has been studied in [K-V], [Ka 1] and [G-K]. One of main difficulties we meet is the fact that tangent objects TX and T 1 Y are not finite dimensional, since Y may possibly have non-isolated singularities; hence the usual deformation theory does not work well. Instead, in [K-V], [G-K], they introdu...

In the remainder, we call such a variety a convex symplectic variety. A convex symplectic variety has been studied in [K-V], [Ka 1] and [G-K]. One of main difficulties we meet is the fact that tangent objects TX and T 1 Y are not finite dimensional, since Y may possibly have non-isolated singularities; hence the usual deformation theory does not work well. Instead, in [K-V], [G-K], they introdu...