Related papers: The Diffusion Equation on a Hypersphere
A quantum Markovian activated atom-surface diffusion model with interacting adsorbates is proposed for the intermediate scattering function, which is shown to be complex-valued and factorizable into a classical-like and a quantum-mechanical…
Almost nothing is known about the layer structure of solutions to strongly coupled systems of convection-diffusion equations in two dimensions. In some special cases we present first results.
Surface chemistry on interstellar dust grains is recognized as a central component in astrochemical models, representing a plausible formation route for many of the observed complex molecular species. However, key parameters governing…
In many applications, transport of particles can be described by the diffusion equation, or its convective-diffusion generalizations, in part of three-dimensional space. In particular, in surface deposition or in growth of aggregates or…
This article focuses on parabolic equations with rough diffusion coefficients which are ill-posed in the classical sense of distributions due to the presence of a singular forcing. Inspired by the philosophy of rough paths and regularity…
Molecular hydrogen is a fascinating candidate for quantum fluid showing bosonic and fermionic superfluidity. We have studied diffusion dynamics of thin films of H$_2$, HD and D$_2$ adsorbed on a glass substrate by measurements of…
A simple practical formula for the shear viscosity coefficient of Yukawa fluids is presented. This formula allows estimation of the shear viscosity in a very extended range of temperatures, from the melting point to $\simeq 100$ times the…
We formulate the dispersion equation for H modes of a circular waveguide with a perfectly conducting strip of zero thickness placed symmetrically in its diametral plane. The wave number of the lowest mode is calculated with high accuracy…
A description in terms of transition rates among cells is used to analyze self-diffusion of hard spheres in the fluid phase. Cell size is assumed much larger than the mean free path. Transition state theory is used to obtain an equation…
The aim of this paper is first to review the derivation of a model describing the propagation of an optical wave in a photorefractive medium and to present various mathematical results on this model: Cauchy problem, solitary waves.
The investigation of the diffusive transport of charged particles in a turbulent magnetic field remains a subject of considerable interest. Research has most frequently concentrated on determining the diffusion coefficient in the presence…
Within the framework of finite temperature field theory this paper discusses the shear viscosity of hot QED plasma through Kubo formula at one-loop skeleton diagram level with a finite chemical potential. The effective widths(damping rates)…
This paper considers the existence of local and global-in-time strong solutions to the advection-diffusion equation with variable coefficients on an evolving surface with a boundary. We apply both the maximal $L^p$-in-time regularity for…
We study a fractional diffusion problem in the divergence form in one space dimension. We define a notion of the viscosity solution. We prove existence of viscosity solutions to the fractional diffusion problem with the Dirichlet boundary…
The derivation of suitable analytical models is an important step for the design and analysis of molecular communication systems. However, many existing models have limited applicability in practical scenarios due to various simplifications…
In recent letter [Phys. Rev. Lett {\bf 105}, 150606 (2010)], the surface-mediated diffusion problem is theoretically discussed, and interesting results have been obtained. However, for more general cases, the ansatz of solutions of the…
We consider the effective surface motion of a particle that intermittently unbinds from a planar surface and performs bulk excursions. Based on a random walk approach we derive the diffusion equations for surface and bulk diffusion…
We present an exact calculation of the mean first-passage time to a target on the surface of a 2D or 3D spherical domain, for a molecule alternating phases of surface diffusion on the domain boundary and phases of bulk diffusion. We…
In this paper we propose a numerical method to solve a 2D advection-diffusion equation, in the highly oscillatory regime. We use an efficient and robust integrator which leads to an accurate approximation of the solution without any time…
In view of the usefulness and importance of the kinetic equation in certain physical problems, the authors derive the explicit solution of a fractional kinetic equation of general character, that unifies and extends earlier results.…