On the physical interpretation of fractional diffusion

Enrique Nadal; Emmanuelle Abisset-Chavanne; Elias Cueto; Francisco Chinesta

doi:10.1016/j.crme.2018.04.004

Model reduction, data-based and advanced discretization in computational mechanics

On the physical interpretation of fractional diffusion

Enrique Nadal ¹ ; Emmanuelle Abisset-Chavanne ²; Elias Cueto ³; Francisco Chinesta ⁴

¹ Research Centre on Mechanical Engineering (CIIM), Universitat Politècnica de València, Camino de Vera s/n, 46071 Valencia, Spain
² High Performance Computing Institute & ESI GROUP Chair, École centrale de Nantes, 1, rue de la Noë, BP 92101, 44321 Nantes cedex 3, France
³ I3A, University of Zaragoza, Maria de Luna s/n, 50018 Zaragoza, Spain
⁴ PIMM Laboratory & ESI GROUP Chair, ENSAM ParisTech, 151, boulevard de l'Hôpital, 75013 Paris, France

Comptes Rendus. Mécanique, Model reduction, data-based and advanced discretization in computational mechanics / Réduction de modèles, données et techniques de discrétisation avancées en mécanique numérique, Volume 346 (2018) no. 7, pp. 581-589.

Abstract

Even if the diffusion equation has been widely used in physics and engineering, and its physical content is well understood, some variants of it escape fully physical understanding. In particular, anormal diffusion appears in the so-called fractional diffusion equation, whose main particularity is its non-local behavior, whose physical interpretation represents the main part of the present work.

Received: 2017-08-26
Accepted: 2018-01-21
Published online: 2018-04-23

DOI: 10.1016/j.crme.2018.04.004

Keywords: Fractional calculus, Anomalous diffusion, Non-local models

Author's affiliations:

Enrique Nadal ¹; Emmanuelle Abisset-Chavanne ²; Elias Cueto ³; Francisco Chinesta ⁴

¹ Research Centre on Mechanical Engineering (CIIM), Universitat Politècnica de València, Camino de Vera s/n, 46071 Valencia, Spain
² High Performance Computing Institute & ESI GROUP Chair, École centrale de Nantes, 1, rue de la Noë, BP 92101, 44321 Nantes cedex 3, France
³ I3A, University of Zaragoza, Maria de Luna s/n, 50018 Zaragoza, Spain
⁴ PIMM Laboratory & ESI GROUP Chair, ENSAM ParisTech, 151, boulevard de l'Hôpital, 75013 Paris, France

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     author = {Enrique Nadal and Emmanuelle Abisset-Chavanne and Elias Cueto and Francisco Chinesta},
     title = {On the physical interpretation of fractional diffusion},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {581--589},
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     number = {7},
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     doi = {10.1016/j.crme.2018.04.004},
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Enrique Nadal; Emmanuelle Abisset-Chavanne; Elias Cueto; Francisco Chinesta. On the physical interpretation of fractional diffusion. Comptes Rendus. Mécanique, Model reduction, data-based and advanced discretization in computational mechanics / Réduction de modèles, données et techniques de discrétisation avancées en mécanique numérique, Volume 346 (2018) no. 7, pp. 581-589. doi : 10.1016/j.crme.2018.04.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.04.004/

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