Mathematics of collective dynamics and pattern formation in biological systems

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Guest Editors

Prof. Pierre Degond
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
Email: pdegond@imperial.ac.uk

Dr. Diane Peurichard
INRIA Paris, 2, rue Simone Iff, Paris Cedex 12 75589, France
Email: diane.a.peurichard@inria.fr

Dr. Nastassia Pouradier Duteil
Laboratoire Jacques-Louis Lions, Sorbonne University (Paris 6) 4, Place Jussieu, 75005 Paris, France
Email: nastassia.pouradierduteil@ljll.math.upmc.fr

Manuscript Topics

Collective motion refers to the emergent phenomenon observed in systems composed of a large number of independently moving units interacting locally via simple rules, leading to a global behavior. This self-organisation phenomenon often leads to the formation of spatio-temporal coherent structures known as patterns. Numerous examples of this phenomenon can be observed in biological systems at different scales, from the organization of cell fates to the coordination of animal groups. Because collective dynamics is so ubiquitous in biology, understanding the mechanisms leading to this behavior is of tremendous importance and has implications in multiple fields (tumour growth, morphogenesis, tissue engineering, etc).

Mathematical models can provide a powerful framework to understand these phenomena, test experimentally suggested conjectures, and make predictions about the behaviour of the studied system. The models lead to complex numerical and analytical problems, encouraging the development of new mathematical tools in areas as diverse as analysis of partial differential equations and of their long-term behavior, multiscale modeling, control theory, numerical analysis, etc. 

This special issue will collect articles dealing with the mathematical modeling and analysis of collective dynamics and pattern formation in biological systems, covering topics such as:

• Collective dynamics from the cell-scale to the population size (collective cell migration, flocking, etc.)
• Spatio-temporal pattern formation and self-organization (cell sorting, tumour growth, morphogenesis, etc.)
• Emergent networks (vascularization, neural systems, leaf venation, etc.)
• Mechanical regulation of collective dynamics (congestion, cluster formation, etc.)

Paper Submission
All manuscripts will be peer-reviewed before their acceptance for publication.
The deadline for manuscript submission is April 30, 2020.

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Marie Doumic, Sophie Hecht, Diane Peurichard
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Pierre Degond, Maxime Herda, Sepideh Mirrahimi
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Claudia Totzeck, Marie-Therese Wolfram
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Raimund Bürger, Paola Goatin, Daniel Inzunza, Luis Miguel Villada
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Jan Haskovec, Ioannis Markou
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