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Alignment of Self-propelled Rigid Bodies: From Particle Systems to Macroscopic Equations

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Stochastic Dynamics Out of Equilibrium (IHPStochDyn 2017)

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Abstract

The goal of these lecture notes is to present in a unified way various models for the dynamics of aligning self-propelled rigid bodies at different scales and the links between them. The models and methods are inspired from [17, 18], but, in addition, we introduce a new model and apply on it the same methods. While the new model has its own interest, our aim is also to emphasize the methods by demonstrating their adaptability and by presenting them in a unified and simplified way. Furthermore, from the various microscopic models we derive the same macroscopic model, which is a good indicator of its universality.

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Acknowledgments

P. Degond acknowledges support from the Royal Society and the Wolfson foundation through a Royal Society Wolfson Research Merit Award ref WM130048; the British “Engineering and Physical Research Council” under grants ref:

EP/M006883/1 and EP/P013651/1; the National Science Foundation under NSF Grant RNMS11-07444 (KI-Net). P. Degond is on leave from CNRS, Institut de Mathématiques de Toulouse, France.

A. Frouvelle acknowledges support from the EFI project ANR-17-CE40-0030 and the Kibord project ANR-13-BS01-0004 of the French National Research Agency (ANR), as well as from the project Défi S2C3 POSBIO of the interdisciplinary mission of CNRS, and the project SMS co-funded by CNRS and the Royal Society.

A. Trescases acknowledges support from the Kibord project ANR-13-BS01-0004 of the French National Research Agency (ANR).

Author information

Authors and Affiliations

  1. Department of Mathematics, Imperial College London, South Kensington Campus, London, SW7 2AZ, UK

    Pierre Degond & Sara Merino-Aceituno

  2. CEREMADE, CNRS, Université Paris-Dauphine, Université PSL, 75016, Paris, France

    Amic Frouvelle

  3. School of Mathematical and Physical Sciences, University of Sussex, Falmer, BN1 9RH, UK

    Sara Merino-Aceituno

  4. Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090, Wien, Austria

    Sara Merino-Aceituno

  5. IMT, UMR5219, Université de Toulouse, CNRS, 31400, Toulouse, France

    Ariane Trescases

Authors
  1. Pierre Degond
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  2. Amic Frouvelle
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  3. Sara Merino-Aceituno
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  4. Ariane Trescases
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Corresponding author

Correspondence to Pierre Degond .

Editor information

Editors and Affiliations

  1. Laboratoire de Probabilités, Statistiques et Modélisation (UMR 8001), Université Paris Diderot, Paris, France

    Giambattista Giacomin

  2. CEREMADE, CNRS UMR 7534, Université Paris Dauphine - PSL, Paris, France

    Stefano Olla

  3. CNRS UMR 8145, MAP5, Université Paris Descartes, Paris, France

    Ellen Saada

  4. Zentrum Mathematik, Technische Universität München, Garching, Bayern, Germany

    Herbert Spohn

  5. CERMICS, Ecole des Ponts, Marne-La-Vallée, France

    Gabriel Stoltz

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Degond, P., Frouvelle, A., Merino-Aceituno, S., Trescases, A. (2019). Alignment of Self-propelled Rigid Bodies: From Particle Systems to Macroscopic Equations. In: Giacomin, G., Olla, S., Saada, E., Spohn, H., Stoltz, G. (eds) Stochastic Dynamics Out of Equilibrium. IHPStochDyn 2017. Springer Proceedings in Mathematics & Statistics, vol 282. Springer, Cham. https://doi.org/10.1007/978-3-030-15096-9_2

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