Breakdown of Boltzmann-type models for the alignment of self-propelled rods

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dc.citation.articleNumber109266en_US
dc.citation.journalTitleMathematical Biosciencesen_US
dc.citation.volumeNumber376en_US
dc.contributor.authorMurphy, Patricken_US
dc.contributor.authorPerepelitsa, Mishaen_US
dc.contributor.authorTimofeyev, Ilyaen_US
dc.contributor.authorLieber-Kotz, Matanen_US
dc.contributor.authorIslas, Brandonen_US
dc.contributor.authorIgoshin, Oleg A.en_US
dc.contributor.orgCenter for Theoretical Biological Physicsen_US
dc.date.accessioned2024-09-10T19:29:02Zen_US
dc.date.available2024-09-10T19:29:02Zen_US
dc.date.issued2024en_US
dc.description.abstractStudies 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.en_US
dc.identifier.citationMurphy, P., Perepelitsa, M., Timofeyev, I., Lieber-Kotz, M., Islas, B., & Igoshin, O. A. (2024). Breakdown of Boltzmann-type models for the alignment of self-propelled rods. Mathematical Biosciences, 376, 109266. https://doi.org/10.1016/j.mbs.2024.109266en_US
dc.identifier.digital1-s2-0-S0025556424001263-mainen_US
dc.identifier.doihttps://doi.org/10.1016/j.mbs.2024.109266en_US
dc.identifier.urihttps://hdl.handle.net/1911/117858en_US
dc.language.isoengen_US
dc.publisherElsevieren_US
dc.rightsExcept where otherwise noted, this work is licensed under a Creative Commons Attribution (CC BY) license.  Permission to reuse, publish, or reproduce the work beyond the terms of the license or beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en_US
dc.titleBreakdown of Boltzmann-type models for the alignment of self-propelled rodsen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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