Patterns, Nonlinear Dynamics and Applications - PANDA

Abstract:

Ever since D'Arcy Thomson and Turing there is much interest in explaining natural patterns in terms of underlying physico-chemical principles. Inspired by this line of thought in this talk I will present the essential features of a new mechanism for pattern formation based on the action of flow and diffusion which affects a local chemical reaction and consequently is being termed FDS (flow and diffusion distributed structures). FDS patterns appear in open flow reactors and have been very recently observed experimentally in chemical reactors. The FDS instability produces stationary space periodic waves as the flow rate of the species is sufficiently large. The celebrated Turing scenario is a particular and non-singular case of FDS, namely in the limit of no flow.

I shall review important properties of the FDS mechanism such as: robustness to parameter variations and the formation of waves with nontrivial phase differences between the maximum of the interacting species. In the second part I shall show how these essential features can be used to build up a mathematical model for periodic segmental patterns in early embryo of vertebrates. The formation of somites which are the precursors of the spinal column, vertebrae and various skeleton muscles can be described in the FDS framework.