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Andrea Gabrielli |
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SMC INFM-CNR |
Abstract
We introduce a new method to study and classify the solutions of Langevin equation with multiplicative noise around the singularity where the noise vanishes. In particular we develop this method to study the dynamics of the two-point statistics of the Kraichnan ensemble which describes the transport of a passive pollutant by a stochastic turbulent flow characterized by scale invariant structure functions. The fundamental equation of this problem consists in the Fokker-Planck equation for the two-point correlation function of the density of particles performing spatially correlated Brownian motions with scale invariant correlations. This problem is equivalent to the stochastic motion of an effective particle driven by a generic multiplicative noise