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Cross-Diffusion and pattern formation in reaction diffusion systems


We propose to study spatiotemporal patterns that occur in chemically reacting systems as a result of cross-diffusion, the phenomenon whereby gradients in the concentration of one species affect the diffusion of another species. Patterns that arise by this mechanism appear to constitute a new class of self-organized structures that lies between thermodynamically stable structures like micelles or membranes and patterns like Turing structures or standing waves that exist only far from equilibrium. Our initial theoretical studies indicate that patterns induced by cross-diffusion can arise in quite simple reactions without the need for an activator-inhibitor couple. The predicted characteristic sizes of these patterns - tens to hundreds of nanometers with diffusion-controlled reactions - suggest their potential application in nanotechnology. We shall first reexamine patterns in such systems as the Belousov-Zhabotinsky reaction in AOT microemulsions and lipid membranes, the chlorite-iodide-malonic acid reaction and the ferrocyanide-iodate-sulfite reaction. Next, we shall apply numerical and analytic techniques to simple model systems with appropriate cross-diffusion coefficients to establish both the concentration dependence of cross-diffusion coefficients and the range of pattern formation to be expected. We will also make needed modifications to the Taylor dispersion method for measuring cross-diffusion coefficients in multi-component systems and apply this approach to systems containing both unreactive and reactive species. Combining the results obtained from these three approaches, we will carry out experiments to find novel patterns induced by cross-diffusion, i.e., we will tune cross-diffusion fluxes to generate patterns.

Field of science

  • /engineering and technology/nanotechnology

Call for proposal

See other projects for this call

Funding Scheme

MC-IOF - International Outgoing Fellowships (IOF)


Via Banchi Di Sotto 55
53100 Siena
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 154 013,61
Administrative Contact
Silvano Focardi (Prof.)