This paper studies the innovation diffusion problemwith the affection of urbanization, proposing a dynamical innovation diffusion model with fuzzy coefficient, and uses the shifting rate of people from rural areas stepping into urban areas to show the process of urbanization. The numerical simulation shows the diffusion process for telephones in China with Genetic Algorithms and this model is e...

The apparent diffusion coefficient (ADC) obtained by helium-3 magnetic resonance imaging over several seconds is thought to reflect diffusion impairment due to both intra- and interacinar structure. In this study, numerical simulations of intra-acinar gas mixing and effective diffusion were performed in a multiple-branch-point model of the human acinus. Using a previously described method, we c...

The stochastic dynamics of an active particle undergoing a constant speed and additionally driven by an overall fluctuating torque is investigated. The random torque forces are expressed by a stochastic differential equation for the angular dynamics of the particle determining the orientation of motion. In addition to a constant torque, the particle is supplemented by random torques, which are ...

The effective diffusion coefficient D, for porous media composed of identical obstacles of radius A in which the diffusing particles have finite radius PR (fl>O) is determined by an efficient Brownian motion simulation technique. This is accomplished by first computing D, for diffusion of “point” Brownian particles in a certain system of interpenetrable spherical obstacles and then employing an...

This article is on the simultaneous diffusion approximation and homogenization of the linear Boltzmann equation when both the mean free path ε and the heterogeneity length scale η vanish. No periodicity assumption is made on the scattering coefficient of the background material. There is an assumption made on the heterogeneity length scale η that it scales as ε for β ∈ (0,∞). In one space dimen...

Abstract. This paper presents one-dimensional (1-D) and two-dimensional (2-D) in-space mathematical models for amperometric biosensors with an outer perforated membrane. The biosensor action was modelled by reaction-diffusion equations with a nonlinear term representing the Michaelis-Menten kinetics of an enzymatic reaction. The conditions at which the 1-D model can be applied to simulate the b...

In chromatography, electrophoresis and sedimentation, an irreversible zone or boundary spreading is often observed which is greater than that attributable to ordinary molecular diffusion and to dispersion caused by flow in porous media. The additional spreading can often be identified with kinetic processes such as adsorption, partition, and chemical interconversion. The existence of this kinet...