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  • 1
    Electronic Resource
    Electronic Resource
    Fluctuations around the Boltzman equation (1981)
    Springer
    Journal of statistical physics 26 (1981), S. 285-305 
    Details
    ISSN: 1572-9613
    Keywords: Hard sphere gas ; Grad limit ; fluctuation theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract For a system of hard spheres we prove the convergence of the second moment of the fluctuation field in the low-density limit. This extends a previous result by van Beijeren, Lanford, Lebowitz and Spohn(1) to nonequilibrium states.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01013172
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  • 2
    Electronic Resource
    Electronic Resource
    Microscopic models of hydrodynamic behavior (1988)
    Springer
    Journal of statistical physics 51 (1988), S. 841-862 
    Details
    ISSN: 1572-9613
    Keywords: Stochastic particle systems ; hydrodynamic limit ; fluctuation theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We review recent developments in the rigorous derivation of hydrodynamic-type macroscopic equations from simple microscopic models: continuous time stochastic cellular automata. The deterministic evolution of hydrodynamic variables emerges as the “law of large numbers,” which holds with probability one in the limit in which the ratio of the microscopic to the macroscopic spatial and temporal scales go to zero. We also study fluctuations in the microscopic system about the solution of the macroscopic equations. These can lead, in cases where the latter exhibit instabilities, to complete divergence in behavior between the two at long macroscopic times. Examples include Burgers' equation with shocks and diffusion-reaction equations with traveling fronts.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01014887
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