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The asymptotic behavior of a class of stochastic reaction-diffusion-advection equations in the plane is studied. We show that as the divergence-free advection term becomes larger and larger, the solutions of such equations converge to the…
The resonant state expansion (RSE), a rigorous perturbative method in electrodynamics, is applied to two-dimensional open optical systems. The analytically solvable homogeneous dielectric cylinder is used as unperturbed system, and its…
We study the thermal conductivity of amorphous solids by constructing a continuum model whose degrees of freedom are propagating vibrational modes (phonons) and extended Volterra dislocation line defects with their own vibrational degrees…
We study linear time dispersive and dissipative systems. Very often such systems are not conservative and the standard spectral theory can not be applied. We develop a mathematically consistent framework allowing (i) to constructively…
We study the problem of lateral diffusion on a static, quasi-planar surface generated by a stationary, ergodic random field possessing rapid small-scale spatial fluctuations. The aim is to study the effective behaviour of a particle…
The advection-diffusion and wave equations are the fundamental equations governing any physical law and therefore arise in many areas of physics and astrophysics. For complex problems and geometries, only numerical simulations can give…
Diffusive shock acceleration (DSA) by relativistic shocks is thought to generate the $dN/dE\propto E^{-p}$ spectra of charged particles in various astronomical relativistic flows. We show that for test particles in one dimension (1D),…
Among the dipole models of deep inelastic scattering at small values of the Bjorken variable $x$, one has been recently proposed which relates the virtual photon-proton cross section to the dipole-proton forward scattering amplitude in…
Dense suspensions often exhibit a dramatic response to large external deformation. The recent body of work has related this behavior to transition from an unconstrained lubricated to a constrained frictional state. Here, we use numerical…
We derive formulas for Whispering Gallery Mode resonances and bending losses in infinite cylindrical dielectric shells and sets of concentric cylindrical shells. The formulas also apply to spherical shells and to sections of bent…
We construct a pseudospectral method for the solution of time-dependent, non-linear partial differential equations on a three-dimensional spherical shell. The problem we address is the treatment of tensor fields on the sphere. As a test…
We investigate the fluctuating incompressible Navier--Stokes equation driven by spatially correlated thermal noise characterized by a single length scale. This formulation is constructed to preserve thermal equilibrium through the…
We present the exact analytical equation of diffusion-mobility for two-dimensional (2D) Schr\"odinger type transport systems, from molecules to materials. The density of electronic states in such Schr\"odinger systems pertains to the 2D…
We present an explicit method for simulating stochastic differential equations (SDEs) that have variable diffusion coefficients and satisfy the detailed balance condition with respect to a known equilibrium density. In Tupper and Yang…
We investigate the influence of quantum fluctuations upon dipolar Bose gases by means of the Bogoliubov-de Gennes theory. Thereby, we make use of the local density approximation to evaluate the dipolar exchange interaction between the…
Anomalous diffusion and L\'evy flights, which are characterized by the occurrence of random discrete jumps of all scales, have been observed in a plethora of natural and engineered systems, ranging from the motion of molecules to climate…
Two drift-diffusion models for the quantum transport of electrons in graphene, which account for the spin degree of freedom, are derived from a spinorial Wigner equation with relaxation-time or mass- and spin-conserving matrix collision…
In this paper, the hybrid sparse/diffuse (HSD) channel model in frequency domain is proposed. Based on the structural analysis on the resolvable paths and diffuse scattering statistics in the channel, the Hybrid Atomic-Least-Squares (HALS)…
In this paper we introduce a new PDE model in frequency space for the inertial energy cascade that reproduces the classical scaling laws of Kolmogorov's theory of turbulence. Our point of view is based upon studying the energy flux through…
We have extended the radiation diffusion model of Hammer and Rosen to diverging spherical and cylindrical geometries. The effect of curvilinear geometry on the supersonic, expanding wavefront increases as the internal radius of a spherical…