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Relativistic Mixture of Gases and Relativistic Cucker-Smale Model

In: Classical and Relativistic Rational Extended Thermodynamics of Gases

Author

Listed:
  • Tommaso Ruggeri

    (University of Bologna, Department of Mathematics and Research Center on Applied Mathematics)

  • Masaru Sugiyama

    (Nagoya Institute of Technology)

Abstract

We present in this chapter a relativistic model of a mixture of Euler gases with multi-temperature. We explicitly determine the production terms resulting from the interchange of energy-momentum between the components by using the entropy principle. We use the analogy between the homogeneous case of a mixture of gases and the thermo-mechanical Cucker-Smale (TCS) flocking model in a classical setting to derive a relativistic counterpart of the TCS model. Moreover, we employ a theory of principal subsystem to derive the relativistic Cucker-Smale (CS) model. Then we provide a sufficient framework leading to the exponential flocking in terms of communication weights. We also show that the relativistic CS model reduces to the classical CS model when the speed of light tends to infinity in any finite-time interval.

Suggested Citation

  • Tommaso Ruggeri & Masaru Sugiyama, 2021. "Relativistic Mixture of Gases and Relativistic Cucker-Smale Model," Springer Books, in: Classical and Relativistic Rational Extended Thermodynamics of Gases, chapter 0, pages 607-616, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-59144-1_32
    DOI: 10.1007/978-3-030-59144-1_32
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