Agent-Based Simulation of the Two-Dimensional Patlak-Keller-Segel Model

Abstract

The Patlak-Keller-Segel equation describes the chemotactic interactions of small organisms in the continuum limit, and a singular peak appears through spontaneous aggregation when the total mass of the organisms exceeds a critical value. To deal with this singular behavior numerically, we propose an agent-based simulation method in which both the organisms and the chemicals are represented as particles. Our numerical estimates for the threshold behavior are consistent with the analytic predictions.

arXiv comment6 pages, 2 figures (to appear in J. Korean Phys. Soc.)

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