PMID: 11909024Mar 23, 2002Paper

Velocity correlations, diffusion, and stochasticity in a one-dimensional system

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
V BalakrishnanC Van Den Broeck

Abstract

We consider the motion of a test particle in a one-dimensional system of equal-mass point particles. The test particle plays the role of a microscopic "piston" that separates two hard-point gases with different concentrations and arbitrary initial velocity distributions. In the homogeneous case when the gases on either side of the piston are in the same macroscopic state, we compute and analyze the stationary velocity autocorrelation function C(t). Explicit expressions are obtained for certain typical velocity distributions, serving to elucidate in particular the asymptotic behavior of C(t). It is shown that the occurrence of a nonvanishing probability mass at zero velocity is necessary for the occurrence of a long-time tail in C(t). The conditions under which this is a t(-3) tail are determined. Turning to the inhomogeneous system with different macroscopic states on either side of the piston, we determine its effective diffusion coefficient from the asymptotic behavior of the variance of its position, as well as the leading behavior of the other moments about the mean. Finally, we present an interpretation of the effective noise arising from the dynamics of the two gases, and thence that of the stochastic process to which the...Continue Reading

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Citations

Feb 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A Taloni, F Marchesoni
Mar 16, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Benoit Palmieri, David Ronis
Aug 7, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ioana Bena, Satya N Majumdar
Aug 8, 2009·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Kazuo AokiGuido Cavallaro
Sep 28, 2017·Physical Review Letters·Marko MedenjakTomaž Prosen
Sep 19, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Alessandro TaloniAdrián Huerta
Dec 31, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·V Balakrishnan, C Van den Broeck
Oct 10, 2006·Physical Review Letters·Fabio Marchesoni, Alessandro Taloni

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