Related papers: Analysis of a diffusive effective mass model for n…
The Debye-Falkenhagen differential equation is commonly used as a mean-field macroscopic model for describing electrochemical ionic drift and diffusion in dilute binary electrolytes when subjected to a suddenly applied potential smaller…
We present the detailed analysis of the diffusive transport of spatially inhomogeneous fluid mixtures and the interplay between structural and dynamical properties varying on the atomic scale. The present treatment is based on different…
The flow of ions through permeable channels causes voltage drop in physiological nanodomains such as synapses, dendrites and dendritic spines, and other protrusions. How the voltage changes around channels in these nanodomains has remained…
We present a formal derivation of a drift-diffusion model for stationary electron transport in graphene, in presence of sharp potential profiles, such as barriers and steps. Assuming the electric potential to have steep variations within a…
The large-time asymptotics of the density matrix solving a drift-diffusion-Poisson model for the spin-polarized electron transport in semiconductors is proved. The equations are analyzed in a bounded domain with initial and Dirichlet…
We model the expansion of an interacting atomic Bose-Einstein condensate in a disordered lattice with a nonlinear diffusion equation normally used for a variety of classical systems. We find approximate solutions of the diffusion equation…
Density functional theory and density functional tight-binding are applied to model electron transport in copper nanowires of approximately 1 nm and 3 nm diameters with varying crystal orientation and surface termination. The copper…
We calculate exactly the velocity and diffusion constant of a microscopic stochastic model of $N$ evolving particles which can be described by a noisy traveling wave equation with a noise of order $N^{-1/2}$. Our model can be viewed as the…
The rates of electron scattering via phonons in the armchair single-wall carbon nanotubes were calculated by using the improved scattering theory within the tight-binding approximation. Therefore, the problem connected with the discrepancy…
We develop a drift-diffusion equation that describes electron spin polarization density in two-dimensional electron systems. In our approach, superpositions of spin-up and spin-down states are taken into account, what distinguishes our…
A model of a finite cylindrical ion channel through a phospholipid membrane of width $L$ separating two electrolyte reservoirs is studied. Analytical solution of the Poisson equation is obtained for an arbitrary distribution of ions inside…
This work derives the Navier--Stokes hydrodynamic equations for a model of a confined, quasi-two-dimensional, $s$-component mixture of inelastic, smooth, hard spheres. Using the inelastic version of the revised Enskog theory, macroscopic…
We introduce a model of a nonlinear double-barrier structure, to describe in a simple way the effects of electron-electron scattering while remaining analytically tractable. The model is based on a generalized effective-mass equation where…
A system of drift-diffusion equations with electric field under Dirichlet boundary conditions is analyzed. The system of strongly coupled parabolic equations for particle density and spin density vector describes the spin-polarized…
In this chapter, I will enter into the roots of entropically-driven transport with a focus on diffusio-osmotic transport in nanochannels. Diffusio-osmosis is a subtle surface transport, originating in entropic driving forces occuring within…
A brief review of the nanoscale free-electron model of metal nanowires is presented. This continuum description of metal nanostructures allows for a unified treatment of cohesive and conducting properties. Conductance channels act as…
There is great interest in the development of novel nanomachines that use charge, spin, or energy transport, to enable new sensors with unprecedented measurement capabilities. Electrical and thermal transport in these mesoscopic systems…
In this paper we present the complete derivation of the effective contour model for electrical discharges which appears as the asymptotic limit of the minimal streamer model for the propagation of electric discharges, when the electron…
The low-field electron mobility in rectangular silicon nanowire (SiNW) transistors was computed using a self-consistent Poisson-Schr\"{o}dinger-Monte Carlo solver. The behavior of the phonon-limited and surface-roughness-limited components…
We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. We demonstrate that the notion of weak localization is applicable to the strongly correlated…