Pattern Formation in Non-equilibrium Systems: Self-organization and Stochasticity

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0101793LevineThis award supports theoretical and computational research on pattern formation with applications to physical, chemical, and biological problems. The focus of the research includes pattern nucleation, self-organized flocking states, and stochasticity in interface dynamics. The PI aims to apply a combined numerical and analytical approach to the problem of pattern nucleation. Pattern nucleation refers to the creation of patterns by fluctuation effects in systems exhibiting multistability. The research effort will include applications. Of immediate interest is the spontaneous creation of intracellular calcium waves by stochastic channel openings. Flocking behavior occurs in interacting multiparticle systems away from any simple equilibrium state. Self-organized structures arising from flocking have been found in a wide range of diverse systems from microorganism colonies to human pedestrian traffic. Continuum equations will be devised for these processes with an aim to better understand allowed parameter ranges and instability mechanisms. Results from model calculations will be compared to real-world data obtained in part through collaboration with leading experts in the fields of animal flocking, traffic patterns, and amoeba aggregation. The PI will also continue his studies of how stochasticity influences interface dynamics. Efforts will focus on extending two possibilities, pulse backfiring in excitable systems and noise-induced diffusive instabilities. The PI aims to find an analytic approach and to find necessary and sufficient conditions for the occurrence of these anomalous noise effects. A new effort is planned on an application to noise effects during infection spreading. This award also supports education through research results that are incorporated into a course on pattern formation and through the preparation of a textbook on pattern formation.%%%This award supports theoretical and computational research on the physics of non-equilibrium processes, especially in the emergence of spatial patterns in extended systems. The research will in part, capitalize on tremendous advances in the field over the past decade to make critical and nontrivial predictions regarding the behavior of a wide variety of complex systems. The work will focus on how fluctuations influence the formation of patterns in systems with coexisting dynamical states, on understanding the self-organizing properties of interacting self-propelled particles, and on better characterizing the conditions under which noise-sensitive interfaces occur.Results of this work will provide a foundation for a wide range of specific applications to physical, chemical, and biological systems. The PI will focus on the spontaneous creation of intracellular calcium waves by stochastic channel openings, animal flocking, traffic patterns, amoeba aggregation, and infection spreading. This award also supports education through research results that are incorporated into a course on pattern formation and through the preparation of a textbook on pattern formation.***