Importance of a finite speed of heat propagation in metals irradiated by femtosecond laser pulses

Activity spread and breathers induced by finite transmission speeds in two-dimensional neural fields

The work studies the spatiotemporal activity propagation in a two-dimensional spatial system involving a finite transmission speed. We derive a numerical scheme in detail to integrate the corresponding evolution equation and validate the derived algorithm by a study of a spatially periodic system. Finally, the work demonstrates numerically transmission delay-induced breathers subjected to anisotropic external input.

Generalization of the reaction-diffusion, Swift-Hohenberg, and Kuramoto-Sivashinsky equations and effects of finite propagation speeds

The work proposes and studies a model for one-dimensional spatially extended systems, which involve 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. Moreover, the Swift-Hohenberg equation is derived from a general energy functional. 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 unusual 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 nonhomogeneous material.