Monitoring Lévy-process crossovers

The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among different Lévy processes: in the first model we change gradually the order of the derivative in the Laplacian...

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Bibliographic Details
Published in:Communications in nonlinear science & numerical simulation 2021-01, Vol.92, p.105490, Article 105490
Main Authors: dos Santos, Maike A.F., Nobre, Fernando D., Curado, Evaldo M.F.
Format: Article
Language:English
Subjects:
Complex systems
Crossovers
Fractional calculus
Fractional dynamics
Laplace transforms
Lévy flights
Non-Gaussian distributions
Statistical analysis
Stochastic processes
Time dependence
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Summary:The crossover among two or more types of diffusive processes represents a vibrant theme in nonequilibrium statistical physics. In this work we propose two models to generate crossovers among different Lévy processes: in the first model we change gradually the order of the derivative in the Laplacian term of the diffusion equation, whereas in the second one we consider a combination of fractional-derivative diffusive terms characterized by coefficients that change in time. The proposals are illustrated by considering semi-analytical (i.e., analytical together with numerical) procedures to follow the time-dependent solutions. We find changes between two different regimes and it is shown that, far from the crossover regime, both models yield qualitatively similar results, although these changes may occur in different forms for the two models. The models introduced herein are expected to be useful for describing crossovers among distinct diffusive regimes that occur frequently in complex systems.
ISSN:1007-5704
1878-7274
DOI:10.1016/j.cnsns.2020.105490