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TMF, 1999, Volume 121, Number 1, Pages 110–116 (Mi tmf800)  

This article is cited in 21 scientific papers (total in 21 papers)

Dynamics of a heavy particle surrounded by a finite number of light particles

Ya. G. Sinaiab

a L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
b Princeton University, Department of Mathematics

Abstract: We consider a dynamic system consisting of a heavy particle of mass $M$ and surrounding light particles moving independently with elastic reflections in the segment $[0,1]$. At a given total energy value independent of $M$, we find the dynamics of the heavy particle with respect to the slow time $t/\sqrt M$.


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English version:
Theoretical and Mathematical Physics, 1999, 121:1, 1351–1357

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Received: 30.06.1999

Citation: Ya. G. Sinai, “Dynamics of a heavy particle surrounded by a finite number of light particles”, TMF, 121:1 (1999), 110–116; Theoret. and Math. Phys., 121:1 (1999), 1351–1357

Citation in format AMSBIB
\by Ya.~G.~Sinai
\paper Dynamics of a heavy particle surrounded by a finite number of light particles
\jour TMF
\yr 1999
\vol 121
\issue 1
\pages 110--116
\jour Theoret. and Math. Phys.
\yr 1999
\vol 121
\issue 1
\pages 1351--1357

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    This publication is cited in the following articles:
    1. Lebowitz, J, “Dynamics of an adiabatic piston”, Doklady Mathematics, 62:3 (2000), 398  zmath  isi
    2. Piasecki, J, “A model of Brownian motion in an inhomogeneous environment”, Journal of Physics-Condensed Matter, 14:40 (2002), 9265  crossref  adsnasa  isi  scopus
    3. Barre, J, “Out-of-equilibrium states as statistical equilibria of an effective dynamics in a system with long-range interactions”, Physical Review Letters, 89:11 (2002), 110601  crossref  adsnasa  isi  scopus  scopus  scopus
    4. Gruber, C, “Deterministic motion of the controversial piston in the thermodynamic limit”, Journal of Statistical Physics, 108:3–4 (2002), 669  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    5. Dauxois T., Latoro V., Rapisarda A., Ruffo S., Torcini A., “The Hamiltonian Mean Field model: From dynamics to statistical mechanics and back”, Dynamics and Thermodynamics of Systems With Long-Range Interactions, Lecture Notes in Physics, 602, 2002, 458–487  crossref  mathscinet  adsnasa  isi
    6. Neishtadt, AI, “Adiabatic piston as a dynamical system”, Journal of Statistical Physics, 116:1–4 (2004), 815  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    7. Mansour, MM, “Hydrodynamic relaxation of the adiabatic piston”, Europhysics Letters, 69:4 (2005), 510  crossref  mathscinet  adsnasa  isi  scopus  scopus  scopus
    8. Wright, P, “A simple piston problem in one dimension”, Nonlinearity, 19:10 (2006), 2365  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    9. Gorelyshev, IV, “On the adiabatic perturbation theory for systems with impacts”, Pmm Journal of Applied Mathematics and Mechanics, 70:1 (2006), 4  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    10. Mansour, MM, “Hydrodynamic description of the adiabatic piston”, Physical Review E, 73:1 (2006), 016121  crossref  adsnasa  isi  scopus  scopus  scopus
    11. Hurtado, PI, “Simplest piston problem. I. Elastic collisions”, Physical Review E, 73:1 (2006), 016136  crossref  adsnasa  isi  scopus  scopus  scopus
    12. Hurtado, PI, “Simplest piston problem. II. Inelastic collisions”, Physical Review E, 73:1 (2006), 016137  crossref  adsnasa  isi  scopus  scopus  scopus
    13. Van den Broeck, C, “CARNOT EFFICIENCY REVISITED”, Special Volume in Memory of Ilya Prigogine, 135, 2007, 189  crossref  isi
    14. Wright, P, “The periodic oscillation of an adiabatic piston in two or three dimensions”, Communications in Mathematical Physics, 275:2 (2007), 553  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    15. Balint, P, “On the zero mass limit of tagged particle diffusion in the 1-d Rayleigh-gas”, Journal of Statistical Physics, 127:4 (2007), 657  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    16. Caglioti, E, “Long time behavior of particle systems in the mean field limit”, Communications in Mathematical Sciences, 5 (2007), 11  crossref  mathscinet  isi
    17. Uranagase, M, “Piston dynamics from a microcanonical ensemble”, Physical Review E, 75:1 (2007), 011110  crossref  adsnasa  isi  scopus  scopus  scopus
    18. A. V. Kargovsky, L. S. Bulushova, O. A. Chichigina, “Theorem on energy distribution over degrees of freedom for a quasistable symmetric anharmonic oscillator”, Theoret. and Math. Phys., 167:2 (2011), 636–644  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    19. Gorelyshev I., “On the dynamics in the one-dimensional piston problem”, Nonlinearity, 24:8 (2011), 2119–2142  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus  scopus
    20. Ee J.-H., Lee J., “Magic Mass Ratios of Complete Energy-Momentum Transfer in One-Dimensional Elastic Three-Body Collisions”, Am. J. Phys., 83:2 (2015), 110–120  crossref  adsnasa  isi  scopus  scopus  scopus
    21. Gay-Balmaz F., Yoshimura H., “Dirac Structures in Nonequilibrium Thermodynamics”, J. Math. Phys., 59:1 (2018), 012701  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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