This paper is intended to provide a stochastic approach involving the combined use of the Feynman-Kac formula and Monte Carlo method as a solution algorithm for estimating the timedependent effective diffusivity in a one-dimensional parabolic inverse problem. The inverse problem is purposed to design a mathematical model for the gas-diffusion process within the alveolar region of the human's lu...

A unique methodology due to the effect of stochastic heating is utilized study Moisture Diffusivity influence an elastic semiconductor medium under photo-thermoelasticity theory. Accurately, random processes are applied at boundary medium. The governing equations expressed in one-dimensional form (1D). conditions considered random; additional noise regarded as white noise. problem set up invest...

Long term moisture exposure has been shown to affect the mechanical performance of polymeric composite structures. This reduction in mechanical performance must be accommodated for during product design in order to ensure long term structure survival. In order to determine the longterm moisture effects on composite components, representative parts are commonly tested after having been exposed t...

We analyze the effective diffusivity of a passive scalar in a two-dimensional, steady, incompressible random flow that has mean zero and a stationary stream function. We show that in the limit of small diffusivity or large Peclet number, with convection dominating, there is substantial enhancement of the effective diffusivity. Our analysis is based on some new variational principles for convect...

In this work, a new model is described for the case of interference between thermal, plasma and elastic waves in non-local excited semiconductor medium. The governing equations have been put under influence moisture diffusion one dimension (1D) when thermal conductivity medium taken variable form. Linear transformations were used to describe dimensionless model. photo-thermoelasticity theory ac...

In this paper we establish conditions for the maximal, Pe, behavior of the effective diffusivity in time-periodic incompressible velocity fields for both the Pe oc and Pe 0 limits. Using ergodic theory, these conditions can be interpreted in terms of the Lagrangian time averages of the velocity. We reinterpret the maximal effective diffusivity conditions in terms of a Poincar6 map of the veloci...