Abstract
We study the dynamical system consisting of N non-interacting point particles of mass m, in a cubical domain Ω L of sides L, separated into two regions by an idealized movable wall: a massive particle (piston), of cross-sectional area L 2 and mass M L ~ L 2. The piston is constrained to move along the x-axis and undergoes elastic collisions with the gas particles. We find that, under suitable initial conditions, there is, in the limit L → ∞, 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.
The research of JLL was supported by NSF Grant NSF DMR-9813268, and AFOSR Grant F49620-98-1-0207. The work of JP was supported by KBN (Committee for Scientific Research, Poland) Grant 2 P03B 127 16. JP also acknowledges the hospitality at the Department of Mathematics of the Princeton University. The research of YaS was supported by NSF Grant DMS-9706794, and RFFI Grant 99-01-00314. We thank C. Gruber for many useful comments.
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Lebowitz, J.L., Piasecki, J., Sinai, Y. (2000). Scaling Dynamics of a Massive Piston in an Ideal Gas. In: Szász, D. (eds) Hard Ball Systems and the Lorentz Gas. Encyclopaedia of Mathematical Sciences, vol 101. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04062-1_9
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DOI: https://doi.org/10.1007/978-3-662-04062-1_9
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