Comptes Rendus
no. 19-20
Partial Differential Equations
Mathematical and numerical modeling of wave propagation in fractal trees
[Modélisation mathématique et numérique de la propagation dʼondes dans des arbres fractals]

Présenté par : the Editorial Board

Patrick Joly1 ; Adrien Semin2
1 POEMS, UMR 7231, CNRS-ENSTA-INRIA, INRIA, domaine de Voluceau, 78153 Le Chesnay cedex, France
2 Applied Mathematics, University of Crete and IACM/FORTH, 71409 Heraklion, Greece
Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1047-1051.

Nous proposons et analysons un modèle mathématique pour la propagation dʼondes dans des arbres infinis qui sont auto-similaires à lʼinfini. Lʼaccent est mis sur la construction et lʼapproximation de conditions aux limites transparentes.

We propose and analyze a mathematical model for wave propagation in infinite trees with self-similar structure at infinity. The emphasis is put on the construction and approximation of transparent boundary conditions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.09.008
Patrick Joly 1 ; Adrien Semin 2

1 POEMS, UMR 7231, CNRS-ENSTA-INRIA, INRIA, domaine de Voluceau, 78153 Le Chesnay cedex, France
2 Applied Mathematics, University of Crete and IACM/FORTH, 71409 Heraklion, Greece 
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     title = {Mathematical and numerical modeling of wave propagation in fractal trees},
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     language = {en},
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Patrick Joly; Adrien Semin. Mathematical and numerical modeling of wave propagation in fractal trees. Comptes Rendus. Mathématique, Volume 349 (2011) no. 19-20, pp. 1047-1051. doi : 10.1016/j.crma.2011.09.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.09.008/

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[2] P. Joly; A. Semin Construction and analysis of improved Kirchoff conditions for acoustic wave propagation in a junction of thin slots, ESAIM Proc., Volume 25 (2008), pp. 44-67

[3] P. Kuchment Graph models for waves in thin structures, Waves Random Media, Volume 12 (2002) no. 4, p. R1-R24

[4] B. Maury; D. Salort; C. Vannier Trace theorems for trees, application for the human lung, Netw. Heterog. Media, Volume 4 (2009) no. 3, pp. 469-500

[5] E.R. Wiebel Morphometry of the Human Lung, Springer Verlag/Academic Press, Berlin/New York, 1963

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