The stochastic piston problem.
We obtain analytical solutions for the perturbed shock paths induced by time-varying random motions of a piston moving inside an adiabatic tube of constant area. The variance of the shock location grows quadratically with time for early times and switches to linear growth for longer times. The analytical results are confirmed by stochastic numerical simulations, and deviations for large random piston motions are established.
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Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA.
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Karniadakis
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