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This article is cited in 28 scientific papers (total in 28 papers)
Dynamics of a massive piston in an ideal gas
N. I. Chernova, J. L. Lebowitzb, Ya. G. Sinaic a University of Alabama at Birmingham
b Rutgers, The State University of New Jersey
c Princeton University, Department of Mathematics
Abstract:
This survey is a study of a dynamical system consisting of a massive piston in a cubic container of large size $L$ filled with an ideal gas. The piston has mass $M\sim L^2$ and undergoes elastic collisions with $N\sim L^3$ non-interacting gas particles of mass $m=1$. It is found that under suitable initial conditions there is a scaling regime with time and space scaled by $L$ in which the motion of the piston and the one-particle distribution of the gas satisfy autonomous coupled equations (hydrodynamic equations) such that in the limit $L\to\infty$ the mechanical trajectory of the piston converges in probability to the solution of the hydrodynamic equations for a certain period of time. There is also a heuristic discussion of the dynamics of the system on longer intervals of time.
Received: 16.05.2002
Citation:
N. I. Chernov, J. L. Lebowitz, Ya. G. Sinai, “Dynamics of a massive piston in an ideal gas”, Uspekhi Mat. Nauk, 57:6(348) (2002), 3–86; Russian Math. Surveys, 57:6 (2002), 1045–1125
Linking options:
https://www.mathnet.ru/eng/rm572https://doi.org/10.1070/RM2002v057n06ABEH000572 https://www.mathnet.ru/eng/rm/v57/i6/p3
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Abstract page: | 1035 | Russian version PDF: | 429 | English version PDF: | 40 | References: | 109 | First page: | 5 |
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