2006/10/31 by Axel Hutt · 1 citation
Physics and Astronomy · #cond-mat.other #cond-mat.dis-nn
paper · pdf · doi:10.1103/physreve.75.026214
20 pages, 6 figures
arxiv created 2007/01/27 · arxiv updated 2015/06/25
The work proposes and studies a one-dimensional model, which involves nonlocal interactions and finite propagation speed. It shows that the general reaction-diffusion equation, the Swift-Hohenberg equation and the general Kuramoto-Sivashinsky equation represent special cases of the proposed model for limited spatial interaction ranges and for infinite propagation speeds. After a detailed validity study on the generalization conditions, the three equations are extended to involve finite propagation speeds. Moreover linear stability studies of the extended equations reveal critical propagation speeds and novel types of instabilities in all three equations. In addition, an extended diffusion equation is derived and studied in some detail with respect to finite propagation speeds. The extended model allows for the explanation of recent experimental results on non-Fourier heat conduction in non-homogeneous material.