Memory Driven Pattern Formation
Abstract
The diffusion equation is extended by including spatial-temporal memory in such a manner that the conservation of the concentration is maintained. The additional memory term gives rise to the formation of non-trivial stationary solutions. The steady state pattern in an infinite domain is driven by a competition between conventional particle current and a feedback current. We give a general criteria for the existence of a non-trivial stationary state. The applicability of the model is tested in case of a strongly localized, time independent memory kernel. The resulting evolution equation is exactly solvable in arbitrary dimensions and the analytical solutions are compared with numerical simulations. When the memory term offers an spatially decaying behavior, we find also the exact stationary solution in form of a screened potential.
Cite
@article{arxiv.cond-mat/0406269,
title = {Memory Driven Pattern Formation},
author = {Steffen Trimper and Knud Zabrocki},
journal= {arXiv preprint arXiv:cond-mat/0406269},
year = {2009}
}
Comments
14 pages, 12 figures