We consider the heat equation with a multiplicative Gaussian potential in dimensions d ≥ 3. We show that the renormalized solution converges to the solution of a deterministic diffusion equation with an effective diffusivity. We also prove that the renormalized large scale random fluctuations are described by the Edwards-Wilkinson model, that is, the stochastic heat equation (SHE) with additive...

Polycrystalline alumina developed by the Japan Fine Ceramics Center (JFCC) has been studied as a candidate thermal diffusivity reference material. It was experimentally confirmed that the alumina developed by the JFCC is homogeneous and stable enough to be used as a reference material. The thermal diffusivities of two specimens of different thicknesses (2 and 3 mm) were measured by the laser fl...

Please cite this article in press as: Oldroyd HJ et http://dx.doi.org/10.1016/j.advwatres.2012.06.0 Thermal diffusivity of snow is an important thermodynamic property associated with key hydrological phenomena such as snow melt and heat and water vapor exchange with the atmosphere. Direct determination of snow thermal diffusivity requires coupled point measurements of thermal conductivity and d...

The spreading and diffusion of two-dimensional vortices subject to weak external random strain fields is examined. The response to such a field of given angular frequency depends on the profile of the vortex and can be calculated numerically. An effective diffusivity can be determined as a function of radius and may be used to evolve the profile over a long time scale, using a diffusion equatio...

We consider the Cauchy problem for the nonlinear degenerate equation in R div(A∇u) + u(b · ∇u)− ∂tu = f(·, u), where A ≥ 0 is a constant symmetric matrix and ker(A) is generated by b. We prove the existence of a local viscosity solution u and we study the interior regularity of u in the framework of Hörmander type operators.

Distinguishing productive zones of a drilled oil well plays a very important role for petroleum engineers to decide where to perforate to produce oil. Conventionally, net pay zones are determined by applying a set of cut-offs on perophysical logs. As a result, the conventional method finds productive intervals crisply. In this investigation, a net index value is proposed, then; diffusivity equa...

The motion of a one-spike solution to a simplified form of the Gierer-Meinhardt activatorinhibitor model is studied in both a one-dimensional and a two-dimensional domain. The pinning effect on the spike motion associated with the presence of spatially varying coefficients in the differential operator, referred to as precursor gradients, is studied in detail. In the one-dimensional case, we der...

We study the velocity of travelling waves of a reaction-diffusion system coupling a standard reaction-diffusion equation in a strip with a one-dimensional diffusion equation on a line. We show that it grows like the square root of the diffusivity on the line. This generalises a result of Berestycki, Roquejoffre and Rossi in the context of Fisher-KPP propagation where the question could be reduc...

A data reduction method based on numerical solutions of the heat conduction equation has been developed for obtaining thermal diffusivity values from thermal flash measurements. Using the new method, the computed evolution in temperature is fitted to the measured temperature evolution instead of using the t1/2 point alone, as is done in many other analyzes. The numerical solutions used are base...

This study makes the first attempt to use the 2/3-order fractional Laplacian modeling of Kolmogorov -5/3 scaling of fully developed turbulence and enhanced diffusing movements of random turbulent particles. A combined effect of inertial interactions induced diffusivity and the molecular Brownian diffusivity is considered the bi-fractal mechanism behind multifractal scaling of moderate Reynolds ...