Random Evolutions Are Driven by the Hyperparabolic Operators

Kolesnik, Alexander D.; Pinsky, Mark A.

doi:10.1007/s10955-011-0131-0

Cited by 32 publications

(30 citation statements)

References 12 publications

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“…We also obtain the characteristic function of the space-time fractional process and study some particular cases. We restrict ourselves to one-dimensional problems because of the inherent difficulties for generalizing persistence in dimensions greater than one [40][41][42][43] which, in turn, impedes obtaining higher-dimensional TEs from the persistent random walk formalism except in two dimensions [44,45] or asymptotically [46]. Higher dimensional FTE's will be the object of future work (see, nonetheless, the end of Sec.…”

Section: Introduction and General Scopementioning

confidence: 99%

Fractional telegrapher's equation from fractional persistent random walks

Masoliver

2016

Phys. Rev. E

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We generalize the telegrapher's equation to allow for anomalous transport. We derive the space-time fractional telegrapher's equation using the formalism of the persistent random walk in continuous time. We also obtain the characteristic function of the space-time fractional process and study some particular cases and asymptotic approximations. Similarly to the ordinary telegrapher's equation, the time-fractional equation also presents distinct behaviors for different time scales. Specifically, transitions between different subdiffusive regimes or from superdiffusion to subdiffusion are shown by the fractional equation as time progresses.

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Section: Introduction and General Scopementioning

confidence: 99%

Fractional telegrapher's equation from fractional persistent random walks

Masoliver

2016

Phys. Rev. E

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“…A recent study on multidimensional random motion shows that the evolutions are driven by hyperparabolic operators composed of the telegraph operator and their integer powers [8]. However, such a study is tied to the Markov assumption, or exponentially distributed interevents times.…”

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confidence: 99%

Isotropic Random Motion at Finite Speed with K-Erlang Distributed Direction Alternations

Pogorui

Rodríguez‐Dagnino

2011

J Stat Phys

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We study uniformly distributed direction of motion at finite speed where the direction alternations occur according to the renewal epochs of a K-Erlang pdf. At first sight, our generalizations of previous Markovian results appears to be a small step, however, it must be seen as an important non-Markovian case where we have found closed-form expressions for the pdf and the conditional characteristic function of this semi-Markov transport process. We present detailed calculations of a three-dimensional example for the 2-Erlang case, which is important not only from physical applications point of view but also to understand more general models. For instance, in principle the example of the 2-Erlang case can be extended to a K-Erlang case (K = 3, 4, . . .) but some of the mathematical expressions may be cumbersome.

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“…(28) in terms of the Fourier-Laplace transform of the densities h and H . To this end we need to specify the form of the waiting time density ψ(t).…”

Section: -4mentioning

confidence: 99%

“…The main reason lying in the difficulty of generalizing persistence in dimensions higher than one [22][23][24][25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional telegrapher's equation and its fractional generalization

Masoliver

2017

Phys. Rev. E

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We derive the three-dimensional telegrapher's equation out of a random walk model. The model is a threedimensional version of the multistate random walk where the number of different states form a continuum representing the spatial directions that the walker can take. We set the general equations and solve them for isotropic and uniform walks which finally allows us to obtain the telegrapher's equation in three dimensions. We generalize the isotropic model and the telegrapher's equation to include fractional anomalous transport in three dimensions.

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Random Evolutions Are Driven by the Hyperparabolic Operators

Cited by 32 publications

References 12 publications

Fractional telegrapher's equation from fractional persistent random walks

Fractional telegrapher's equation from fractional persistent random walks

Isotropic Random Motion at Finite Speed with K-Erlang Distributed Direction Alternations

Three-dimensional telegrapher's equation and its fractional generalization

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