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...

We consider an inhomogeneous linear Boltzmann equation, with an external confining potential. The collision operator is a simple relaxation toward a local Maxwellian, therefore without diffusion. We prove the exponential time decay toward the global Maxwellian, with an explicit rate of decay. The methods are based on hypoelliptic methods transposed here to get spectral information. They were in...

We determine the L p-L q-estimate of the linear equations of thermoelasticity for rhom-bic media in R 2. For this purpose we will transform the equations to an evolution equation showing that this equation has a unique solution with the help of the semigroup theory. In order to obtain the L p-L q-estimate, we will first apply the Fourier transformation to the evolution equation, thus determinin...

Continuum electrostatics methods have become increasingly popular due to their ability to provide approximate descriptions of solvation energies and forces without expensive sampling required by explicit solvent models. In particular, the Poisson-Boltzmann equation (PBE) provides electrostatic potentials, solvation energies, and forces by modeling the solvent as a featureless, dielectric materi...

Using atomic force microscopy (AFM) we investigated the interaction of amyloid beta (Aβ) peptide with chemically modified surfaces in order to better understand the mechanism of amyloid toxicity, which involves interaction of amyloid with cell membrane surfaces. We compared the structure and density of Aβ fibrils on positively and negatively charged as well as hydrophobic chemically-modified su...

We consider the numerical solution of the Poisson-Boltzmann equation (PBE), a three-dimensional second order nonlinear elliptic partial differential equation arising in biophysics. This problem has several interesting features impacting numerical algorithms, including discontinuous coefficients representing material interfaces, rapid nonlinearities, and three spatial dimensions. Similar equatio...

Abstract. In this article, we propose a model describing the transport of trapped particles in a surface potential. The potential confines particles close to the surface increasing the number of surface collisions. First, we consider the case of non charged particles. From a kinetic description, we rigorously derive a two dimensional Boltzmann equation. In the case of charged particles we intro...

A patch representation differing from the traditional treatments in the boundary element method (BEM) is presented, which we call the constant "node patch" method. Its application to solving the Poisson-Boltzmann equation (PBE) demonstrates considerable improvement in speed compared with the constant element and linear element methods. In addition, for the node-based BEMs, we propose an efficie...