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- W4225897721 abstract "L'evy walks are a particular type of continuous-time random walks which results in a super-diffusive spreading of an initially localized packet. The original one-dimensional model has a simple schematization that is based on starting a new unidirectional motion event either in the positive or in the negative direction. We consider two-dimensional generalization of L'evy walks in the form of the so-called $XY$ model. It describes a particle moving with a constant velocity along one of the four basic directions and randomly switching between them when starting a new motion event. We address the ballistic regime and derive solutions for the asymptotic density profiles. The solutions have a form of first-order integrals which can be evaluated numerically. For specific values of parameters we derive an exact expression. The analytic results are in agreement with the results of finite-time numerical samplings." @default.
- W4225897721 created "2022-05-05" @default.
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- W4225897721 date "2021-12-22" @default.
- W4225897721 modified "2023-10-05" @default.
- W4225897721 title "Asymptotic densities of planar Lévy walks: A nonisotropic case" @default.
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- W4225897721 doi "https://doi.org/10.1103/physreve.104.064131" @default.
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