Publication Date
10-1-2024
Document Type
Article
Publication Title
Mathematical Biosciences
Volume
376
DOI
10.1016/j.mbs.2024.109266
Abstract
Studies in the collective motility of organisms use a range of analytical approaches to formulate continuous kinetic models of collective dynamics from rules or equations describing agent interactions. However, the derivation of these kinetic models often relies on Boltzmann's “molecular chaos” hypothesis, which assumes that correlations between individuals are short-lived. While this assumption is often the simplest way to derive tractable models, it is often not valid in practice due to the high levels of cooperation and self-organization present in biological systems. In this work, we illustrated this point by considering a general Boltzmann-type kinetic model for the alignment of self-propelled rods where rod reorientation occurs upon binary collisions. We examine the accuracy of the kinetic model by comparing numerical solutions of the continuous equations to an agent-based model that implements the underlying rules governing microscopic alignment. Even for the simplest case considered, our comparison demonstrates that the kinetic model fails to replicate the discrete dynamics due to the formation of rod clusters that violate statistical independence. Additionally, we show that introducing noise to limit cluster formation helps improve the agreement between the analytical model and agent simulations but does not restore the agreement completely. These results highlight the need to both develop and disseminate improved moment-closure methods for modeling biological and active matter systems.
Funding Number
1903270
Funding Sponsor
Rice University
Keywords
Agent-based model, Boltzmann equation, Cluster formation, Kinetic models, Self-propelled rods, Statistical independence
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 License.
Department
Mathematics and Statistics
Recommended Citation
Patrick Murphy, Misha Perepelitsa, Ilya Timofeyev, Matan Lieber-Kotz, Brandon Islas, and Oleg A. Igoshin. "Breakdown of Boltzmann-type models for the alignment of self-propelled rods" Mathematical Biosciences (2024). https://doi.org/10.1016/j.mbs.2024.109266
