活动阶梯模型中的行波、相分离与图案形成
Traveling waves, phase separation and pattern formation in the active stepping stone model
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中文总结 AI 辅助
本文提出活动阶梯模型，结合游动-翻滚迁移与出生-死亡过程，推导流体动力学方程，发现活动导致新图案、加速入侵波，但过度活动破坏波状性，并分析二维图案形成的不稳定性。
中文摘要 AI 辅助
选择优势导致物种在生态系统中的增殖。另一方面，自推进可能导致个体的动态聚集。为了分析这些竞争过程所产生的复杂效应，我们引入了一个用于增殖活动群体的最小模型，其中游动-翻滚迁移与随机出生-死亡过程相结合。从粒子的微观动力学出发，我们推导了相应的流体动力学方程，并通过数值模拟对其进行了验证。我们证明，活动的引入导致了新型形态图案的出现，这些图案对控制迁移的具体规则敏感。此外，我们表明活动显著改变了入侵波的特征，增加了其传播速度。然而，超过阈值后，过度活动会破坏入侵过程的波状性质。我们还将研究扩展到二维，并分析了导致此类系统中图案形成的不稳定性。
英文摘要
Selective advantage leads to the proliferation of a species into an ecosystem. On the other hand, self-propulsion can lead to dynamic clustering of individuals. 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 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.
发表机构
- Tata Institute of Fundamental Research（塔塔基础研究所）
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