Path Laplacian operators and superdiffusive processes on graphs. II. Two-dimensional lattice

Ernesto Estrada; Ehsan Mejeed Hameed; Matthias Langer; Aleksandra Puchalska

doi:10.1016/j.laa.2018.06.026

Path Laplacian operators and superdiffusive processes on graphs. II. Two-dimensional lattice

Ernesto Estrada, Ehsan Mejeed Hameed, Matthias Langer, Aleksandra Puchalska

Mathematics And Statistics

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Abstract

In this paper we consider a generalized diffusion equation on a square lattice corresponding to Mellin transforms of the k-path Laplacian. In particular, we prove that superdiffusion occurs when the parameter s in the Mellin transform is in the interval (2,4) and that normal diffusion prevails when s > 4.

Original language	English
Pages (from-to)	373-397
Number of pages	25
Journal	Linear Algebra and its Applications
Volume	555
Early online date	27 Jun 2018
DOIs	https://doi.org/10.1016/j.laa.2018.06.026
Publication status	Published - 15 Oct 2018

Keywords

k-path Laplacian
anomalous diffusion
square lattice

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10.1016/j.laa.2018.06.026

Estrada-etal-LAA2018-Path-Laplacian-operators-and-superdiffusive-processesAccepted author manuscript, 1.71 MBLicence: CC BY-NC-ND 4.0

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abstract = "In this paper we consider a generalized diffusion equation on a square lattice corresponding to Mellin transforms of the k-path Laplacian. In particular, we prove that superdiffusion occurs when the parameter s in the Mellin transform is in the interval (2,4) and that normal diffusion prevails when s > 4. ",

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AU - Estrada, Ernesto

AU - Hameed, Ehsan Mejeed

AU - Langer, Matthias

AU - Puchalska, Aleksandra

PY - 2018/10/15

Y1 - 2018/10/15

N2 - In this paper we consider a generalized diffusion equation on a square lattice corresponding to Mellin transforms of the k-path Laplacian. In particular, we prove that superdiffusion occurs when the parameter s in the Mellin transform is in the interval (2,4) and that normal diffusion prevails when s > 4.

AB - In this paper we consider a generalized diffusion equation on a square lattice corresponding to Mellin transforms of the k-path Laplacian. In particular, we prove that superdiffusion occurs when the parameter s in the Mellin transform is in the interval (2,4) and that normal diffusion prevails when s > 4.

KW - k-path Laplacian

KW - anomalous diffusion

KW - square lattice

UR - https://www.sciencedirect.com/journal/linear-algebra-and-its-applications

U2 - 10.1016/j.laa.2018.06.026

DO - 10.1016/j.laa.2018.06.026

M3 - Article

SN - 0024-3795

VL - 555

SP - 373

EP - 397

JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

Path Laplacian operators and superdiffusive processes on graphs. II. Two-dimensional lattice

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