Pattern formation in dissipative systems: A particle approach

Experimental investigations of self-organizing processes in physical, chemical, physico-chemical and biological systems lead to numerous examples of localized patterns embedded in a more or less homogeneous background. Starting from fundamental one- and two-component reaction-diffusion equations, which represent a large share of the models used in the above mentioned fields, this work reports on recent advances made concerning a systematic approach to particle-level descriptions. Basic results are concerned with the existence and shape of the particles and their ability to move as an intrinsic property. More advanced topics deal with particle-particle interactions including mere repulsion and attraction as well as spatially varying types of forces with alternating signs, which appear as a generic effect in a broad parameter range close to the famous Turing bifurcation. This leads to scattering phenomena and bound multi-particle states resembling molecules of various shapes, which are able to move as stable superstructures.