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DY: Fachverband Dynamik und Statistische Physik

DY 18: Pattern Formation, Delay and Nonlinear Stochastic Systems

DY 18.2: Talk

Tuesday, March 19, 2024, 10:00–10:15, BH-N 128

Influence of physical interactions on spatiotemporal patterns — •Chengjie Luo, Lucas Menou, and David Zwicker — Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany

Complex spatiotemporal patterns are often modeled by reaction-diffusion equations, which combine complex reactions between constituents with ideal diffusion. Such descriptions neglect physical interactions between constituents, which might affect resulting patterns. To overcome this, we investigate the influence of physical interactions on two representative chemical reactions: the Hill-Langmuir equation, generating static Turing patterns for ideal diffusion, and cyclic dominant reactions, like the seminal rock-paper-scissors (rps) game, yielding dynamic spiral waves. In the Hill-Langmuir system, we find that weak repulsion substantially lowers the required differential diffusivity and reaction nonlinearity for Turing pattern formation, while strong interactions induce phase separation. For cyclic-dominant reactions, we discover that weak interactions change the length- and time scales of spiral waves. In contrast, strong repulsive interactions typically generate oscillating lattices, and strong attraction leads to an interplay of phase separation and chemical oscillations. Despite the distinct nature of the two chemical reactions, physical interactions play a crucial role in pattern formation in both cases. We thus suggest that physical interactions are crucial for forming spatiotemporal patterns in nature, so they should be incorporated when modeling realistic systems.

Keywords: spatiotemporal patterns; reaction-diffusion equations; Turing pattern; spiral waves; rock-paper-scissors game