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Emergent Dynamics of a Thermodynamically Consistent Particle Model

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Abstract

We present a thermodynamically consistent particle (TCP) model motivated by the theory of multi-temperature mixture of fluids in the case of spatially homogeneous processes. The proposed model incorporates the Cucker-Smale (C-S) type flocking model as its isothermal approximation. However, it is more complex than the C-S model, because the mutual interactions are not only “mechanical” but are also affected by the “temperature effect” as individual particles may exhibit distinct internal energies. We develop a framework for asymptotic weak and strong flocking in the context of the proposed model.

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Authors and Affiliations

  1. Department of Mathematical Sciences and Research, Institute of Mathematics, Seoul National University, Seoul, 151-747, Korea

    Seung-Yeal Ha

  2. School of Mathematics, Korea Institute for Advanced Studies, Seoul, 130-722, South Korea

    Seung-Yeal Ha

  3. Department of Mathematics and Alma Mater Research, Center on Applied Mathematics AM2, University of Bologna, Bologna, Italy

    Tommaso Ruggeri

Authors
  1. Seung-Yeal Ha
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  2. Tommaso Ruggeri
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Correspondence to Tommaso Ruggeri.

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Communicated by C. Dafermos

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Ha, SY., Ruggeri, T. Emergent Dynamics of a Thermodynamically Consistent Particle Model. Arch Rational Mech Anal 223, 1397–1425 (2017). https://doi.org/10.1007/s00205-016-1062-3

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  • DOI: https://doi.org/10.1007/s00205-016-1062-3

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