Scaling Dynamics of a Massive Piston in an Ideal Gas
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.
KeywordsElastic Collision BBGKY Hierarchy Suitable Initial Condition Cubical Domain Equal Mass Case
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