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Dispersion of particle systems in Brownian flows

Part of: Stochastic analysis Turbulence Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Craig L. Zirbel  and
Erhan Çinlar
Craig L. Zirbel*
Affiliation:
University of Massachusetts
Erhan Çinlar*
Affiliation:
Princeton University
*
* Postal address: Department of Mathematics and Statistics, Lederle GRC, Amherst, MA 01003-4515; USA.
** Postal address: Department of Civil Engineering and Operations Research, Engineering Quadrangle, Princeton, NJ 08544, USA.
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Abstract

We study the dispersion of a collection of particles carried by an isotropic Brownian flow in Of particular interest are the center of mass and the centered spatial second moments. Their asymptotic behavior depends strongly on the spatial dimension and the largest Lyapunov exponent of the flow. We use estimates for the pair separation process to give a fairly complete picture of this behavior as t → ∞. In particular, for incompressible flows in two dimensions, we show that the variance of the center of mass grows sublinearly, while dispersion relative to the center of mass grows linearly.

Keywords

STOCHASTIC FLOWSBROWNIAN FLOWSMASS TRANSPORT

MSC classification

Primary: 60H10: Stochastic ordinary differential equations
Secondary: 60G57: Random measures 76F05: Isotropic turbulence; homogeneous turbulence
Type
Stochastic Geometry amd Statistical Applications
Information
Advances in Applied Probability , Volume 28 , Issue 1 , March 1996 , pp. 53 - 74
Copyright
Copyright © Applied Probability Trust 1996 

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