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• W1991312535 abstract "We show that the longitudinal position $x(t)$ of a particle in a $(d+1)$-dimensional layered random velocity field (the Matheron-de Marsily model) can be identified as a fractional Brownian motion (fBm) characterized by a variable Hurst exponent $H(d)=1-d/4$ for $d<2$ and $H(d)=1/2$ for $d>2$. The fBm becomes marginal at $d=2$. Moreover, using the known first-passage properties of fBm we prove analytically that the disorder averaged persistence (the probability of no zero crossing of the process $x(t)$ upto time $t$) has a power law decay for large $t$ with an exponent $theta=d/4$ for $d<2$ and $theta=1/2$ for $dgeq 2$ (with logarithmic correction at $d=2$), results that were earlier derived by Redner based on heuristic arguments and supported by numerical simulations (S. Redner, Phys. Rev. E {bf 56}, 4967 (1997))." @default.
• W1991312535 created "2016-06-24" @default.
• W1991312535 creator A5047748977 @default.
• W1991312535 date "2003-11-03" @default.
• W1991312535 modified "2023-10-16" @default.
• W1991312535 title "Persistence of a particle in the Matheron–de Marsily velocity field" @default.
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• W1991312535 doi "https://doi.org/10.1103/physreve.68.050101" @default.
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