Fractional telegrapher's equation from fractional persistent random walks

Masoliver, Jaume

doi:10.1103/physreve.93.052107

Cited by 39 publications

(62 citation statements)

References 60 publications

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“…We proceed as we did in the one-dimensional case [50] and first obtain a fractional generalization of the homogeneous and isotropic walk of the previous section.…”

Section: The Fractional Isotropic Walkmentioning

confidence: 99%

“…(41). In order to propose a fractional generalization of the isotropic walk we reproduce the steps of the derivation of the fractional persistent random walk that we did in one dimension [50]. Thus looking at Eq.…”

Section: The Fractional Isotropic Walkmentioning

confidence: 99%

“…Let us stress that this is simply a conjecture because the approximation given by Eq. (49) might have depended on ω as well [50]. Substituting Eqs.…”

Section: The Fractional Isotropic Walkmentioning

confidence: 99%

“…In a recent work [50] we have presented a derivation of the fractional telegrapher's equation (FTE) in one dimension which is based on a fractional generalization of the persistent random walk on the line. We also have shown there that a simple and direct three-dimensional generalization of the one-dimensional persistent random walk leads to inconsistent results.…”

Section: Introductionmentioning

confidence: 99%

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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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“…We proceed as we did in the one-dimensional case [50] and first obtain a fractional generalization of the homogeneous and isotropic walk of the previous section.…”

Section: The Fractional Isotropic Walkmentioning

confidence: 99%

Section: The Fractional Isotropic Walkmentioning

confidence: 99%

“…Let us stress that this is simply a conjecture because the approximation given by Eq. (49) might have depended on ω as well [50]. Substituting Eqs.…”

Section: The Fractional Isotropic Walkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Three-dimensional telegrapher's equation and its fractional generalization

Masoliver

2017

Phys. Rev. E

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“…1 2 -order. Masoliver generalize the telegrapher´s equation from the formalism of the persistent random walk in continuous time [21]. Khamzin, Popov, and Nigmatullin [22], have done the fractal correction for the ion conductivity transport theory.…”

Section: Introductionmentioning

confidence: 99%

Continued-Fraction Expansion of Transport Coefficients with Fractional Calculus

et al. 2016

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Abstract:The main objective of this paper is to generalize the Extended Irreversible Thermodynamics in order to include the anomalous transport in systems in non-equilibrium conditions. Considering the generalized entropy, the corresponding flux and entropy production, and using the time fractional derivative, we have derived a space-time generalized telegrapher's equation with a fractional nested hierarchy which can be used in separate developments for the mass transport, for the heat conduction and for the flux of ions. We have obtained a new formalism which includes the contribution of fast of higher-order fluxes in the mesoscopic and inhomogeneous media. The results take the form of continued fraction expansions. The balance equations are used in a scheme of continued fractions, and they appear as a closure condition. In this way the transport equation and its corresponding wave number-frequency relation are obtained, both of them in the mathematical structure of the continued fraction scheme. Numerical examples are included to show the dispersive nature of the solutions, and the generalized fractional transport equation in the same mathematical form, which can be applied to the mass transport, the heat conduction and the flux of ions.

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Untangling cell tracks: Quantifying cell migration by time lapse image data analysis

et al. 2017

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Automated microscopy has given researchers access to great amounts of live cell imaging data from in vitro and in vivo experiments. Much focus has been put on extracting cell tracks from such data using a plethora of segmentation and tracking algorithms, but further analysis is normally required to draw biologically relevant conclusions. Such relevant conclusions may be whether the migration is directed or not, whether the population has homogeneous or heterogeneous migration patterns. This review focuses on the analysis of cell migration data that are extracted from time lapse images. We discuss a range of measures and models used to analyze cell tracks independent of the biological system or the way the tracks were obtained. For single-cell migration, we focus on measures and models giving examples of biological systems where they have been applied, for example, migration of bacteria, fibroblasts, and immune cells. For collective migration, we describe the model systems wound healing, neural crest migration, and Drosophila gastrulation and discuss methods for cell migration within these systems. We also discuss the role of the extracellular matrix and subsequent differences between track analysis in vitro and in vivo. Besides methods and measures, we are putting special focus on the need for openly available data and code, as well as a lack of common vocabulary in cell track analysis. © 2017 International Society for Advancement of Cytometry.

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Fractional telegrapher's equation from fractional persistent random walks

Cited by 39 publications

References 60 publications

Three-dimensional telegrapher's equation and its fractional generalization

Three-dimensional telegrapher's equation and its fractional generalization

Continued-Fraction Expansion of Transport Coefficients with Fractional Calculus

Untangling cell tracks: Quantifying cell migration by time lapse image data analysis

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