Abstract
We study statistical properties of the process Y(t) of a passive advection by quenched random layered flows in situations when the inter-layer transfer is governed by a fractional Brownian motion X(t) with the Hurst index H ∈ (0,1). We show that the disorder-averaged mean-squared displacement of the passive advection grows in the large time t limit in proportion to , which defines a family of anomalous super-diffusions. We evaluate the disorder-averaged Wigner–Ville spectrum of the advection process Y(t) and demonstrate that it has a rather unusual power-law form with a characteristic exponent which exceed the value 2. Our results also suggest that sample-to-sample fluctuations of the spectrum can be very important.
Highlights
The power spectral density of a time-dependent stochastic processes Y(t) is a meaningful feature of its spectral content which describes how its power is distributed over frequency
We study statistical properties of the process Y(t) of a passive advection by quenched random layered flows in situations when the inter-layer transfer is governed by a fractional Brownian motion X(t) with the Hurst index H ä (0,1)
We show that the disorder-averaged mean-squared displacement of the passive advection grows in the large time t limit in proportion to t 2 - H, which defines a family of anomalous super-diffusions
Summary
Institut für Theoretische Physik, Universität Stuttgart, Pfaffenwaldring 57, D-70569 Stuttgart, Germany. Dipartimento di Fisica, Sapienza Università di Roma, P.le A. INFN, Sezione di Roma 1 and Nanotech-CNR, UOS di Roma, P.le A. Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), 4 Place Jussieu, F-75252 Paris. Poncelet (UMI CNRS 2615), Bolshoy Vlasyevskiy Pereulok 11, 119002 Moscow, Russia
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