A quantitative understanding of non-equilibrium systems is fundamentally lacking. Such systems include the weather, plasmas, industrial chemical reactors, surface reactions, and living organisms. Each of these diverse examples falls into the class known as reaction-diffusion systems, in which the competition between transport and reaction gives rise to the complex dynamics which dominates them. Our lab conducts experiments and numerical simulations to investigate open questions in non-equilibrium dynamics and statistical mechanics focused on pattern forming systems, i.e. systems which order themselves.
An equilibrium-state is determined by the universal physics of a system at equilibrium, and quantitative measures of these macroscopic states were the foundation upon which thermodynamics and statistical mechanics were built. Developing a theory of non-equilibrium statistical mechanics and thermodynamics requires, among other things, a quantitative understanding of pattern formation, the measurable macroscopic states of systems out of equilibrium, i.e. the non-equilibrium analogue of an equilibrium phase or state.
Because of their simplicity, fluid and liquid crystal systems are the "Hydrogen atom" of non-equilibrium extended systems, allowing well-controlled and precise measurements of pattern formation and non-equilibrium "phase" transitions. Reaction-diffusion systems complement these studies, adding new insights about the broad class of systems governed by transport coupled with interactions, transformations or change. In addition, comparing and contrasting results from reaction-diffusion systems to those from fluid systems tests the universality of pattern formation and non-equilibrium transitions.
We are interested in contributing new insights to the field of non-equilibrium thermodynamics and nonlinear dynamics through the systematic study of different reaction-diffusion systems. In addition, we apply and test current understanding to novel chemical and biological systems. Current experimental research projects in my lab include: (1) investigations of resonant pattern formation in a periodically forced Belouzov-Zhabotinsky system, (2) studies of transition phenomena (e.g. extinction, localization) of bacterial populations living under inhomogeneous growth conditions, and (3) examination of neuron-glia network dynamics.