Summary

Proceedings of the 2013 International Symposium on Nonlinear Theory and its Applications

2013

Session Number:B3L-C

Session:

Number:314

Network analysis of transport phenomena in flow fields

Naoya Fujiwara,  

pp.314-317

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.2.314

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Summary:
We construct a network from the transport data of particles driven by a flow field and analyze this network using the analytical tools developed in the network science. The aim of this study is to clarify the property which has not been clarified in conventional analytical methods of fluid dynamics. The targets are specification of the important spatial regions, relaxation process to steady state, impact of perturbation, etc. In this paper, we outline the construction method of the network and apply it to a model of the Lagrangian turbulence. We show that the betweenness centrality computed from the network of the transition probability between subregions of the system takes a high value in the boundary region of the roll. This result suggests that those regions are important regions in the sense that they are the bottlenecks of the network. This method has a lot of potential applicability to the local climate analysis, control of transport, etc. Our method serves a new picture to the transport phenomena in turbulent flows.

References:

[1] D. J. Watts and S. H. Strogatz. Collective dynamics of 'small-world' networks. Nature (London), 393:440, 1998.

[2] Albert Laszlo Barabási and Reka Albert. Emergenge of scaling in random networs. Science, 286:509-512, 1999.

[3] Réka Albert and Albert-László Barabási. Statistical mechanics of complex networks. Rev. Mod. Phys., 74:47-97, Jan 2002.

[4] Alex Arenas, Albert Díaz-Guilera, Jurgen Kurths, Yamir Moreno, and Changsong Zhou. Synchronization in complex networks. Physics Reports, 469(3):93-153, 2008.

[5] N. Fujiwara and J. Kurths. Spectral universality of phase synchronization in non-identical oscillator networks. Eur. Phys. J. B, 69(1):45-49, may 2009.

[6] A. Barrat, M. Barthlemy, and A. Vespignani. Dynamical processes on complex networks. Cambridge University Press, 2008.

[7] Naoya Fujiwara, Jürgen Kurths, and Albert Díaz-Guilera. Synchronization in networks of mobile oscillators. Phys. Rev. E, 83(2):025101(R), Feb 2011.

[8] Naoya Fujiwara, Jurgen Kurths, and Albert Díaz-Guilera. Spectral analysis of synchronization in mobile networks. AIP Conference Proceedings, 1389(1):1015-1018, 2011.

[9] I. Hanski. Metapopulation ecology. Oxford University Press Oxford, UK, 1999.

[10] K. Yamasaki, A. Gozolchiani, and S. Havlin. Climate networks around the globe are significantly affected by el niño. Phys. Rev. Lett., 100:228501, Jun 2008.

[11] J. F. Donges, Y. Zou, N. Marwan, and J. Kurths. The backbone of the climate network. EPL (Europhysics Letters), 87(4):48007, 2009.

[12] J. N. UNDERWOOD, L. D. SMITH, M. J. H. VAN OPPEN, and J. P. GILMOUR. Multiple scales of genetic connectivity in a brooding coral on isolated reefs following catastrophic bleaching. Molecular Ecology, 16(4):771-784, 2007.

[13] Soyoka Muko and Yoh Iwasa. Long-term effect of coral transplantation: Restoration goals and the choice of species. Journal of Theoretical Biology, 280(1):127-138, 2011.

[14] Katsuya Ouchi, Nobuyuki Mori, Takehiko Horita, and Hazime Mori. Advective diffusion of particles in rayleigh-bénard convection. Progress of Theoretical Physics, 85(4):687-691, 1991.