Stretched exponential relaxation for growing interfaces in quenched disordered media

Growing interfaces in quenched disordered media

We present the microscopic equation of growing interface with quenched noise for the Tang and Leschhorn model [Phys. Rev. A 45, R8309 (1992)]. The evolution equations for the mean heigth and the roughness are reached in a simple way. Also, an equation for the interface activity density (i.e. interface density of free sites) as function of time is obtained. The microscopic equation allows us to ...

Microscopic Equation for Growing Interfaces in Quenched Disordered Media

We present the microscopic equation of growing interface with quenched noise for the Tang and Leschhorn model [L. H. Tang and H. Leschhorn, Phys. Rev. A 45, R8309 (1992)]. The evolution equation for the height, the mean height, and the roughness are reached in a simple way. An equation for the interface activity density (or free sites density) as function of time is obtained. The microscopic eq...

A Review of Growing Interfaces in Quenched Disordered Media

We make a review of the two principal models that allows to explain the imbibition of fluid in porous media. These models, that belong to the directed percolation depinning (DPD) universality class, where introduced simultaneously by the Tang and Leschhorn [Phys. Rev A 45, R8309 (1992)] and Buldyrev et al. [Phys. Rev. A 45, R8313 (1992)] and reviewed by Braunstein et al. [J. Phys. A 32, 1801 (1...

Stretched exponential relaxation and ac universality in disordered dielectrics

Stretched Exponential Relaxation

2 Stretched exponential relaxation in glassy systems 2 2.1 Mathematical properties of the stretched exponential . . . . . . . . . . . . . . . . 3 2.1.1 τ distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.2 Behavior near zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.3 Properties of G(k)/G(τ) . . . . . . . . . . . . . . . . . . . . ....