Nonlinear Dynamics Group at Brandeis University

The overall goal of our research is to understand, design and control chemical systems that exhibit complex, nonlinear, dynamic behavior in time and space. This behavior includes periodic oscillation, chaos, wave propagation and pattern formation. Such systems may have important applications to, or provide insights into, related phenomena in biology, physics, mathematics, polymer and materials science. We employ a variety of techniques, both experimental and theoretical, in our work. 

Belousov-Zhabotinsky Reaction

The "Belousov-Zhabotinsky reac- tion" is a family of oscillating chemical reactions in which transition-metal ions or complexes catalyze the oxidation of a sub- strate by bromate in acidic, aqueous solution. In a stirred solution, nearly periodic oscil- lations occur in the concentrations of the oxidized and reduced forms of the catalyst. In a thin, unstirred layer of the reaction mixture, one can observe patterns in time and space. Studying this system has been a major focus of our research.

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Turing Patterns

Stationary patterns, e.g., the stripes or spots on the skins of animals, are ubiquitous in biology. Quite similar structures, however, can be found in non-living systems as well. Intricate patterns reminiscent of those on tropical fish can also emerge in homogeneous autocatalytic reaction-diffusion media when the difference between diffusion rates of certain chemical species is sufficiently large, just as it was predicted by the British mathematician, Alan Turing, in 1952. 

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Recent results in a joint project with the Fraden group provide experimental support for Turing's theory. Listen to a radio interview with professors Irving R. Esptein and Seth Fraden on the Radio Boston Channel (WBUR). 

Mechanistic and Design Studies of Chemical Oscillators

The first chemical oscillators, in- cluding the Belousov-Zhabotinsky reaction, were discovered acciden- tally. Our group pioneered the systematic design and mechanistic study of oscillating chemical reactions. We continue to develop new reactions with particularly desirable features, e.g., producing specific types of patterns or being photosensitive. We also carry out studies to elucidate the mechanisms of reactions displaying complex dynamical behavior.

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Patterns of Nanodroplets

Introducing microheterogeneity into reaction-diffusion media gives rise to a wealth of striking phenomena, many never before seen. In water-in-oil micro- emulsions, chemical species often diffuse at very different rates, which, combined with the complex, e.g., oscillatory, kinetics of the reactions between them, can create not only Turing patterns but also such exotic patterns as segmented spirals, jumping waves, inwardly moving spirals and target patterns, localized waves, etc.

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