Seminars of the Focus Area Complex Systems

Prof. Dr. C. Beta, Prof. Dr. K. Dethloff, Prof. Dr. R. Engbert, Prof. Dr. M. Holschneider, Prof. Dr. W. Huisinga, Prof. Dr. Ralf Metzler, Prof. Dr. A. Pikovsky, Prof. Dr. S. Reich, Prof. Dr. M. Rosenblum, Prof. Dr. G. Rüdiger, Prof. Dr. T. Scheffer, Prof. Dr. F. Scherbaum, Prof. Dr. J. Selbig, Prof. Dr. F. Spahn


Speaker: Yuli Starosvetsky, Faculty of Mechanical Engineering, Technion - Israel Institute of Technology, Haifa, Israel

Title: Resonant energy transport and channeling in the essentially nonlinear systems * Colloquium on Complex and Biological Systems

Time: Fri, Dec 5, 2014, 10:15am

Place: bldg 28, room 0.108

System under consideration comprises three weakly coupled, non-linear oscillators and oscillatory chains subjected to initial excitation. In the present study we show that providing initial impulse to the first oscillator and varying the parameter of coupling one observes the formation of various patterns of energy transport and localization. Thus, for sufficiently low strength of coupling the total system energy gets localized on the first oscillator. Slightly increasing the value of coupling above the first threshold, one observes the formation of complete energy exchanges between the first two oscillators when the response recorded on the third oscillator is negligibly small. Further increasing the value of coupling above the second transition threshold leads to the formation of the recurrent energy transport among all the three, coupled oscillators. The later regime is manifested by the beating like motion where energy gets transferred from one oscillator to another in a somewhat complex irregular fashion.
In the framework of the present work we study analytically the mechanism of transitions from energy localization to energy transport. To this end we devise a special analytical approach based on the recently developed concept of the limiting phase trajectories and non-smooth transformations. The derived analytical approximation is further extended to the system of three weakly coupled chains where the transport of localized excitations is considered. It is worthwhile emphasizing that the first and the second criteria can be hardly obtained by the conventional bifurcation analysis of stationary regimes, which provides the very crude, unsatisfactory predictions.

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Udo Schwarz, Zentrum für Dynamik komplexer Systeme,
Universität Potsdam, Campus Golm Karl-Liebknecht-Str. 24, 14476 Potsdam, building 28, room 2.107
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DFG SFB 1294

DFG Sonderforschungsbereich 1294 Data assimilation

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DFG Schwerpunktprogramm 1488 Planetmag

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