Related papers: Long Range Electron Transfer Reactions: An Analyti…
In this work the explicit solution of the electronic plasma diffusion with radiation reaction force, under the action of an exponential decay external electric field is given. The electron dynamics is described by a classical generalized…
We present an extension of the work of D'Amato and Pastawski on electron transport in a one-dimensional conductor modeled by the tight binding lattice Hamiltonian and in which inelastic scattering is incorporated by connecting each site of…
We calculate the linear response conductance of electrons in a Luttinger liquid with arbitrary interaction g_2, and subject to a potential barrier of arbitrary strength, as a function of temperature. We first map the Hamiltonian in the…
We present a general phase-space kinetic model for charged particle transport through combined localised and delocalised states, capable of describing scattering collisions, trapping, detrapping and losses. The model is described by a…
We solve a weakly singular integral equation by Laplace transformation over a finite interval of R. The equation is transformed into a Cauchy integral equation, whose resolution amounts to solving two Fredholm integral equations of the…
We present a method which uses density functional theory (DFT) to treat transport through a single molecule connected to two conducting leads for the weak and intermediate coupling. This case is not accessible to standard non-equilibrium…
In this paper we present a mathematical model for the electrochemical deposition aimed at the production of inverse opals. The real system consists of an arrangement of sub micrometer spheres, through which the species in an electrolytic…
We study the long-time asymptotics of prototypical non-linear diffusion equations. Specifically, we consider the case of a non-degenerate diffusivity function that is a (non-negative) polynomial of the dependent variable of the problem. We…
We propose a boundary integral formulation for the dynamic problem of electromagnetic scattering and transmission by homogeneous dielectric obstacles. In the spirit of Costabel and Stephan, we use the transmission conditions to reduce the…
Using a Green's function formalism we derive analytical expressions for the electronic transmittance through a benzene ring. To motivate the approach we first solve the resonant level system and then extend the method to the benzene case.…
We reexamine several issues related to the physics of scaling in electron scattering from nuclei. A basic model is presented in which an assumed form for the momentum distribution having both long- and short-range contributions is…
Electrons accelerated by solar flares and observed as type III solar radio bursts are not only a crucial diagnostic tool for understanding electron transport in the inner heliosphere but also a possible early indication of potentially…
The narrow escape problem consists of deriving the asymptotic expansion of the solution of a drift-diffusion equation with the Dirichlet boundary condition on a small absorbing part of the boundary and the Neumann boundary condition on the…
The response of a model micro-electrochemical system to a time-dependent applied voltage is analyzed. The article begins with a fresh historical review including electrochemistry, colloidal science, and microfluidics. The model problem…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
This paper reports a mass transfer model of a reactant flowing in a large aspect ratio microfluidic chip made of a channel with electrodes on the side walls. A semi-analytical solution to the two-dimensional Fickian diffusion of a reactant…
We present exact analytical solutions for charge transfer reactions between two arbitrarily charged hard dielectric spheres. These solutions, and the corresponding exact ones for sphere-sphere interaction energies, include sums that…
In this note, we study the phase transitions arising in a modified Smoluchowski equation on the sphere with dipolar potential. This equation models the competition between alignment and diffusion, and the modification consists in taking the…
Starting from the recently proposed dynamical exchange-correlation field framework, the equation of motion of the diagonal part of the many-electron Green function is derived, from which the spectral function can be obtained. The resulting…
A system of interacting Brownian particles subject to short-range repulsive potentials is considered. A continuum description in the form of a nonlinear diffusion equation is derived systematically in the dilute limit using the method of…