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At least 415 records · Page 23Linked to original sources
PubMed2000

Analytical results for random walk persistence

In this paper, we present a detailed calculation of the persistence exponent straight theta for a nearly Markovian Gaussian process X(t), a problem initially introduced elsewhere in [Phys. Rev. Lett. 77, 1420 (1996)], describing the probability that the walker never crosses the origin. Resummed perturbative and nonperturbative expressions for straight theta are derived, which suggest a connection with the result of the alternative independent interval approximation. The perturbation theory is extended to the calculation of straight theta for non-Gaussian processes, by making a strong connection between the problem of persistence and the calculation of the energy eigenfunctions of a quantum mechanical problem. Finally, we give perturbative and nonperturbative expressions for the persistence exponent straight theta(X0), describing the probability that the process remains larger than X(0)sqrt[ ].

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PubMed2000

Levy scaling in random walks with fluctuating variance

Truncated Levy flights with correlated fluctuations of the variance (heteroskedasticity) are considered. A stylized model is introduced, in which the variance fluctuates between two possible values following a Markov chain process. Analogously to conventional truncated Levy flights with fixed variance, the central part of the probability distribution function of the increments at short time scales is found to be close to a Levy distribution. What makes these processes interesting is the fact that the crossover to the Gaussian regime may occur for times considerably larger than for uncorrelated (or no) variance fluctuations. Processes of this type may find direct application in the modeling of some economic time series, in which Levy scaling and heteroskedasticity are known to coexist.

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PubMed2004

Free surface Hele-Shaw flows around an obstacle: A random walk simulation.

This paper presents computer simulations of pressure driven viscous flows that creep in two dimensions (Hele-Shaw cells). We model the time and spatial evolution of free liquid-gas interfaces perturbed by solid obstacles of various configurations such as wedges, steps, and ellipses. Our goal is to study short- and long-scale obstacle effects on the interface shape and velocity. Specific focus is given to the dynamics of a triple (gas-liquid-solid) contact line, which determines local wetting of obstacles. As a principal contribution, we derive a functional relationship between the contact line velocity and the obstacle geometry.

Journal Article↗
PubMed2004

Comment on "Diffusion of epicenters of earthquake aftershocks, Omori's law, and generalized continuous-time random walk models".

Modeling of earthquake sequences using an epidemic-type aftershock sequence model by Phys. Rev. E 66, 061104 (2002)] has led these authors to conclude that previous analyses of apparent earthquake diffusions were flawed. We show here that diffusion analyses based on spatiotemporal correlation measures for earthquake populations are an appropriate method for capturing the space-time coupling present in earthquake triggering processes.

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