Geodesic
Gaussian random waves in elastic medium
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 3, pp. 349-356.

Voir la notice de l'article provenant de la source Math-Net.Ru

Similar to Berry conjecture for quantum chaos we consider elastic analogue which incorporates longitudinal and transverse random waves. Based on that we derive the intensity correlation function of elastic displacement field. Comparison to numerics in a quarter Bunimovich stadium demonstrates a good agreement. We also consider nodal points (NPs) $u=0$, $v=0$ of the in-plane random vectorial displacement field $\mathbf u=(u,v)$. We derive the mean density and correlation function of NPs. Consequently, we derive the distribution of the nearest distances between NPs.
Keywords: Gaussian random waves, wave chaos
Mots-clés : billiard, nodal points. 
@article{JSFU_2010_3_3_a8,
     author = {Dmitry N. Maksimov and Almas F. Sadreev},
     title = {Gaussian random waves in elastic medium},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {349--356},
     publisher = {mathdoc},
     volume = {3},
     number = {3},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2010_3_3_a8/}
}
TY  - JOUR
AU  - Dmitry N. Maksimov
AU  - Almas F. Sadreev
TI  - Gaussian random waves in elastic medium
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2010
SP  - 349
EP  - 356
VL  - 3
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2010_3_3_a8/
LA  - en
ID  - JSFU_2010_3_3_a8
ER  - 
%0 Journal Article
%A Dmitry N. Maksimov
%A Almas F. Sadreev
%T Gaussian random waves in elastic medium
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2010
%P 349-356
%V 3
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2010_3_3_a8/
%G en
%F JSFU_2010_3_3_a8
Dmitry N. Maksimov; Almas F. Sadreev. Gaussian random waves in elastic medium. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 3 (2010) no. 3, pp. 349-356. http://geodesic.mathdoc.fr/item/JSFU_2010_3_3_a8/

[1] H.-J. Stöckmann, Quantum Chaos: An Introduction, Cambridge University Press, Cambridge, UK, 1999 | MR | Zbl

[2] G. Tanner, N. Søndergaard, J. Phys. A Math. Theor., 40 (2007), R443 | DOI | MR | Zbl

[3] R. L. Weaver, J. Acoust. Soc. Am., 85 (1989), 1005 | DOI

[4] C. Ellegaard, T. Guhr, K. Lindemann, J. Nygård, M. Oxborrow, Phys. Rev. Lett., 77 (1996), 4918 | DOI

[5] O. Legrand, C. Schmitt, D. Sornette, Europhys. Lett., 18 (1992), 101 | DOI

[6] K. Schaadt, A. Kudrolli, Phys. Rev. E, 60 (1999), R3479 | DOI

[7] P. Bertelsen, C. Ellegaard, E. Hugues, Eur. Phys. J. B, 15 (2000), 87 | DOI

[8] A. Andersen, C. Ellegaard, A. D. Jackson, K. Schaadt, Phys. Rev. E, 63 (2001), 066204 | DOI

[9] K. Schaadt, T. Guhr, C. Ellegaard, M. Oxborrow, Phys. Rev. E, 68 (2003), 036205 | DOI

[10] L. D. Landau, E. M. Lifshitz, Theory of Elasticity, Pergamon, Oxford, 1959 | MR

[11] R. L. Weaver, J. Acoust. Soc. Am., 71 (1982), 1608 | DOI

[12] A. Akolzin, R. L. Weaver, Phys. Rev. E, 70 (2004), 46212 | DOI

[13] M. V. Berry, M. R. Dennis, Proc. R. Soc. Lond. A, 456 (2000), 2059 ; 457 (2001), 2251 | DOI | MR | Zbl | DOI | Zbl

[14] A. I. Saichev, K.-F. Berggren, A. F. Sadreev, Phys. Rev. E, 64 (2001), 036222 | DOI

[15] B. A. Dubrovin, A. T. Fomenko, S. P. Novikov, Modern geometry-methods and applications. Part II: The geometry and topology of manifolds, Graduate Texts in Mathematics, 104, Springer-Verlag, New York–Berlin–Heidelberg–Tokyo, 1985 | MR | Zbl

[16] M. R. Dennis, J. Phys. A Math. Gen., 36 (2003), 6611 | DOI | MR | Zbl

[17] J. R. Eggert, Phys. Rev. B, 29 (1984), 6664 | DOI

[18] D. N. Maksimov, A. F. Sadreev, JETP Lett., 86 (2007), 670

[19] D. N. Maksimov, A. F. Sadreev, Phys. Rev. E, 77 (2008), 056204 | DOI | MR