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10.9.26 11:30 s.t. - Seminarroom 25.32 O2.51
Kabir Ramola: „Fisher waves, phase separation and pattern formation in the active stepping stone model”
Tata Institute of Fundamental Research, Hyderabad, India
Genetic drift plays a crucial role in evolution by enhancing diversity within ecosystems. On the other hand active self-propulsion can drive systems into phase separated regions promoting homogeneity within a spatial region. To analyze the intricate effects produced by such competing processes, we introduce a minimal model for a proliferating active population, where run-and-tumble migration is combined with a stochastic birth-death process. Beginning with the microscopic dynamics of the particles, we derive the corresponding hydrodynamic equations and validate them through numerical simulations. We demonstrate that the inclusion of activity leads to the emergence of novel morphological patterns, which are sensitive to the specific rules governing migration. Furthermore, we show that activity significantly alters the characteristics of Fisher invasion waves, increasing their propagation speed. However, beyond a threshold, excessive activity disrupts the wave-like nature of the invasion process. We also extend our study to two dimensions and analyze the instabilities that lead to pattern formation in such systems.
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