We study the problem of homogenization for inertial particles moving in a time dependent random velocity field and subject to molecular diffusion. We show that, under appropriate assumptions on the velocity field, the large–scale, long–time behavior of the inertial particles is governed by an effective diffusion equation for the position variable alone. This is achieved by the use of a formal m...

We propose a nonlinear partial differential equation (PDE) for regularizing a tensor which contains the first derivative information of an image such as strength of edges and a direction of the gradient of the image. Unlike a typical diffusivity matrix which consists of derivatives of a tensor data, we propose a diffusivity matrix which consists of the tensor data itself, i.e., derivatives of a...

An exact solution to the barotropic potential vorticity equation is used to examine the properties of barotropic vortices under arbitrary nth-order hyper-diffusivity. Analytical expressions are derived for an eddy’s lifetime, meridional drift, decay in size, and energy, as functions of the Coriolis parameter, order and magnitude of diffusivity, and the eddy’s size, shape and strength. These exp...

Preserving scalar boundedness is an important prerequisite to performing large-eddy simulations of turbulent reacting flows. A number of popular combustion models use a conserved-scalar, mixture-fraction to parameterize reactions that, by definition, is bound between zero and one. To avoid unphysical clipping, the numerical scheme solving the conserved-scalar transport equation must preserve th...

A single particle model for homopolymerization of ethylene in the presence hydrogen is used to predict impact induced condensing agents on evolution concentration profiles growing particle, rate homopolymerization, and molecular weight distribution. The formulation based random-pore polymer flow associated with a kinetic using method moments describe chain length. Sanchez–Lacombe equation state...

We consider the active Brownian particle (ABP) model for a two-dimensional microswimmer with fixed speed, whose direction of swimming changes according to process. The probability density swimmer evolves Fokker-Planck equation defined on configuration space, structure depends swimmer's shape, center rotation and domain swimming. enforce zero flux at boundaries space. derive reduced in an infini...

The ultrafast spatial and temporal dynamics of excited carriers are important to understanding the response of materials to laser pulses. Here we use scanning ultrafast electron microscopy to image the dynamics of electrons and holes in silicon after excitation with a short laser pulse. We find that the carriers exhibit a diffusive dynamics at times shorter than 200 ps, with a transient diffusi...

This work is concerned with the construction of a lattice-Boltzmann (LB) model for ideal miscible fluids. In this particular case, the collision term in the LB equation can be modelled by only considering mutual and cross collisions between, respectively, particles of the same and of different kinds. A non-linear LB model with three distinct relaxation times intended to be used in problems with...

A simplified mathematical model is proposed to provide an analytic solution for the transient behavior of a Langmuirian zeolite membrane subjected to a step increase in sorbate pressure at the upstream surface at time zero. The concentration profiles derived from the simplified model agree with those calculated by numerical solution of the governing partial differential equation. The model is u...

Flux-dominated solar dynamo models, which have demonstrated to be quite successful in reproducing most of the observed features of the large scale solar magnetic cycle, generally produce an inappropriate latitudinal distribution of the toroidal magnetic fields, showing fields of large magnitude in polar regions where the radial shear has a maximum amplitude. Employing a kinematic solar dynamo m...