On superdiffusive behavior of a passive tracer in a Poisson shot noise field |
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Authors: | Ernest Nieznaj |
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Institution: | 1. Department of Mathematics, Faculty of Electrical Engineering and Computer Science, Lublin University of Technology, Nadbystrzycka 38A, 20-618, Lublin, Poland
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Abstract: | In this paper, we investigate the trajectory of the passive tracer model governed by the ordinary differential equation $$ \frac{{\rm d} {\bf x} (t)}{{\rm d}t} = {\bf F} ({\bf x}(t)), \quad {\bf x}(0)= {\bf x}_{0}, $$ where F(x) is a zero mean, homogeneous, isotropic Poisson shot noise random field. We prove the superdiffusive character of the trajectories under certain conditions on the energy spectrum of the velocity field. |
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