Free energy of a chemotactic model with nonlinear diffusion

Abstract The Patlak-Keller-Segel equation is a canonical model of chemotaxis to describe self-organized aggregation of organisms interacting with chemical signals. We investigate a variant of this model, assuming that the organisms exert effective pressure proportional to the number density. From th...

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Autores principales:	Seung Ki Baek, Beom Jun Kim
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/8ddd151f8afe46f4be547ac52713257f
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spelling	oai:doaj.org-article:8ddd151f8afe46f4be547ac52713257f2021-12-02T12:30:45ZFree energy of a chemotactic model with nonlinear diffusion10.1038/s41598-017-09369-w2045-2322https://doaj.org/article/8ddd151f8afe46f4be547ac52713257f2017-08-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-09369-whttps://doaj.org/toc/2045-2322Abstract The Patlak-Keller-Segel equation is a canonical model of chemotaxis to describe self-organized aggregation of organisms interacting with chemical signals. We investigate a variant of this model, assuming that the organisms exert effective pressure proportional to the number density. From the resulting set of partial differential equations, we derive a Lyapunov functional that can also be regarded as the free energy of this model, and minimize it with a Monte Carlo method to detect the condition for self-organized aggregation. Focusing on radially symmetric solutions on a two-dimensional disc, we find that the chemical interaction competes with diffusion so that aggregation occurs when the relative interaction strength exceeds a certain threshold. Based on the analysis of the free-energy landscape, we argue that the transition from a homogeneous state to aggregation is abrupt yet continuous.Seung Ki BaekBeom Jun KimNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-13 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Seung Ki Baek Beom Jun Kim Free energy of a chemotactic model with nonlinear diffusion
description	Abstract The Patlak-Keller-Segel equation is a canonical model of chemotaxis to describe self-organized aggregation of organisms interacting with chemical signals. We investigate a variant of this model, assuming that the organisms exert effective pressure proportional to the number density. From the resulting set of partial differential equations, we derive a Lyapunov functional that can also be regarded as the free energy of this model, and minimize it with a Monte Carlo method to detect the condition for self-organized aggregation. Focusing on radially symmetric solutions on a two-dimensional disc, we find that the chemical interaction competes with diffusion so that aggregation occurs when the relative interaction strength exceeds a certain threshold. Based on the analysis of the free-energy landscape, we argue that the transition from a homogeneous state to aggregation is abrupt yet continuous.
format	article
author	Seung Ki Baek Beom Jun Kim
author_facet	Seung Ki Baek Beom Jun Kim
author_sort	Seung Ki Baek
title	Free energy of a chemotactic model with nonlinear diffusion
title_short	Free energy of a chemotactic model with nonlinear diffusion
title_full	Free energy of a chemotactic model with nonlinear diffusion
title_fullStr	Free energy of a chemotactic model with nonlinear diffusion
title_full_unstemmed	Free energy of a chemotactic model with nonlinear diffusion
title_sort	free energy of a chemotactic model with nonlinear diffusion
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/8ddd151f8afe46f4be547ac52713257f
work_keys_str_mv	AT seungkibaek freeenergyofachemotacticmodelwithnonlineardiffusion AT beomjunkim freeenergyofachemotacticmodelwithnonlineardiffusion
_version_	1718394347731288064

Free energy of a chemotactic model with nonlinear diffusion

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