We investigate the ensemble and time averaged mean squared displacements for particle diffusion in a simple model for disordered media by assuming that the local diffusivity is both fluctuating in time and has a deterministic average growth or decay in time. In this study we compare computer simulations of the stochastic Langevin equation for this random diffusion process with analytical result...

A new spectral closure model of stably stratified turbulence is used to develop a K model suitable for applications to the atmospheric boundary layer. This K model utilizes vertical viscosity and diffusivity obtained from the spectral theory. In the equation, the Coriolis parameter-dependent formulation of the coefficient C1 suggested by Detering and Etling is generalized to include the depende...

Confinement of runaway electrons has been observed for the first time in a reversed field pinch during improved-confinement plasmas in the Madison Symmetric Torus. Energy-resolved hard-x-ray flux measurements have been used to determine the velocity dependence of the electron diffusion coefficient, utilizing computational solutions of the Fokker-Planck transport equation. With improved-confinem...

The phase separation between two immiscible liquids advected by a bidimensional velocity field is investigated numerically by solving the corresponding Cahn-Hilliard equation. We study how the spinodal decomposition process depends on the presence-or absence-of Lagrangian chaos. A fully chaotic flow, in particular, limits the growth of domains, and for unequal volume fractions of the liquids, a...

Exact solutions to the time-dependent diffusion equation are exhibited which correspond to the diffusion-limited growth of ellipsoidal precipitate particles with constant shape and dimensions proportional to the square root of the time. The asymmetry of the diffusion field in these solutions is consistent with the preservation of the particle's shape during growth even if the diffusivity is ani...

We study spreading of a nonmotile bacteria colony on a hard agar plate by using agent-based and continuum models. We show that the spreading dynamics depends on the initial nutrient concentration, the motility, and the inherent demographic noise. Population fluctuations are inherent in an agent-based model, whereas for the continuum model we model them by using a stochastic Langevin equation. W...

This letter demonstrates the potential for using diffuse ultrasound measurements to detect damage in concrete. Two different solutions to the diffusion equation, an infinite three-dimensional (3D) volume model that neglects geometric boundaries and a finite 3D cuboid model, are used for the required curve fitting procedure to determine the influence of geometric boundaries on the solution. The ...

The Advection-Diffusion Equation (ADE) is solved for a constant pollutant emission from a point-like source placed inside an unstable Atmospheric Boundary Layer (ABL). The solution is obtained adopting the novel analytical approach named Generalized Integral Laplace Transform Technique (GILTT). The concentration solution of the equation is expressed through an infinite series expansion. After s...

We consider solutions of the KPP equation with a time-dependent diffusivity of the form σ(t/T ). For an initial condition that is compactly supported, we show that when σ(s) is increasing in time the front position at time T is X(T ) = c∗T − ν̄T +O(log T ). That is, X(T ) lags behind the linear front by an amount that is algebraic in T , not by the Bramson correction (3/2) log T as in the unifor...