Celso Grebogi Institute for Complex Systems and Mathematical Biology King's College, University of Aberdeen FRACTAL SKELETONS: T

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Celso Grebogi Institute for Complex Systems and Mathematical Biology King's College, University of Aberdeen FRACTAL SKELETONS: THE UNIVERSALITY IN DEATH BY STARVATION Nature is permeated by phenomena in which active processes, such as chemical reactions and biological interactions, take place in environmental flows. They include the dynamics of growing populations of plankton in the oceans and the evolving distribution of ozone in the polar stratosphere. I will show that if the dynamics of active particles in flows is chaotic, then necessarily the concentration of particles have the observed fractal filamentary structures. These structures, in turn, are the skeletons and the dynamic catalysts of active processes, yielding an unusual singularly enhanced productivity. I will argue that this singular productivity could be the hydrodynamic explanation for the plankton paradox, in which an extremely large number of species are able to coexist, negating the competitive exclusion principle that asserts the survival of only the most perfectly adapted to each limiting resource. By including finite-size effects, I will define a stochastic description supported on the natural measure of the attractor to show that the death kinetics assume a universal behaviour exhibiting a 1/t decay law in the population, which becomes distributed on a subset characterised by the correlation dimension of the chaotic flow. Chaotic Advection in Blood Flow: Fractal Filaments in Stenoses and Aneurysms, A. Schelin, G. Karolyi, N. Booth, A. Moura, and C. Grebogi, Phys. Rev. E (2009) Chemical and biological activity in open flows: A dynamical system approach, T. TÈl, A. Moura, C. Grebogi and G. K·rolyi, Phys. Reports 413, pages 91-196 (2005) Advective Coalescence in Chaotic Flows, T. Nishikawa, Z. Toroczkai, and C. Grebogi, Phys. Rev. Lett. 87, 038301 (2001) Finite-size effects on active chaotic advection, T. Nishikawa, Z. Toroczkai, T. Tel, and C. Grebogi, Phys. Rev. E 66, 046213 (2002).

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Chaotic Advection, Diffusion, and Reactions in Open Flows Tamás Tél, György Károlyi, Áron Péntek, István Scheuring, Zoltán Toroczkai, Celso Grebogi, and James Kadtke
Chaotic advection, diffusion, and reactions in open flows Tamás Tél, György Károlyi, Áron Péntek, István Scheuring, Zoltán Toroczkai, Celso Grebogi, and James Kadtke Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science 10, 89 (2000); doi: 10.1063/1.166478 View online: http://dx.doi.org/10.1063/1.166478 View Table of Contents: http://scitation.aip.org/content/aip/journal/chaos/10/1?ver=pdfcov Published by the AIP Publishing This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 128.173.125.76 On: Mon, 24 Mar 2014 14:44:01 CHAOS VOLUME 10, NUMBER 1 MARCH 2000 Chaotic advection, diffusion, and reactions in open flows Tama´sTe´l Institute for Theoretical Physics, Eo¨tvo¨s University, P.O. Box 32, H-1518 Budapest, Hungary Gyo¨rgy Ka´rolyi Department of Civil Engineering Mechanics, Technical University of Budapest, Muëgyetem rpk. 3, H-1521 Budapest, Hungary A´ ron Peńtek Marine Physical Laboratory, Scripps Institution of Oceanography, University of California at San Diego, La Jolla, California 92093-0238 Istvań Scheuring Department of Plant Taxonomy and Ecology, Research Group of Ecology and Theoretical Biology, Eo¨tvo¨s University, Ludovika te´r 2, H-1083 Budapest, Hungary Zoltań Toroczkai Department of Physics, University of Maryland, College Park, Maryland 20742-4111 and Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061-0435 Celso Grebogi Institute for Plasma Research, University of Maryland, College Park, Maryland 20742 James Kadtke Marine Physical Laboratory, Scripps Institution of Oceanography, University of California at San Diego, La Jolla, California 92093-0238 ͑Received 30 July 1999; accepted for publication 8 November 1999͒ We review and generalize recent results on advection of particles in open time-periodic hydrodynamical flows.
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Data Based Identification and Prediction of Nonlinear and Complex Dynamical Systems
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