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Stages of Energy Transfer in the FPU Model
Discrete and Continuous Dynamical Systems, Expanded Volume for the Proceedings of the Fourth International Conference on Dynamical Systems and Differential Equations, 113(2003).

biellj@rpi.edu

JOSEPH A. BIELLO, PETER R. KRAMER, AND YURI V. LVOV

Department of Mathematical Sciences

Rensselaer Polytechnic Institute

301 Amos Eaton Hall

110 8th Street

Troy, NY 12180, USA

Abstract. The (alpha) version of the Fermi-Pasta-Ulam is revisited through direct numerical simulations and an application of weak turbulence theory. The energy spectrum, initialized with a large scale excitation, is traced through a series of distinct qualitative phases en route to eventual equipartition. Weak turbulence theory is applied in an attempt to provide an effective quantitative description of the evolution of the energy spectrum. Some scaling predictions are well-confirmed by the numerical simulations.

Introduction
Fermi-Pasta-Ulam Model
Numerical Simulation of Relaxation from Initial Large-Scale Excitation
Scaling Predictions
- Effect of strength of nonlinearity
- Effect of lattice size
Conclusion
Acknowledgements
Bibliography
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Next: Introduction

Dr Yuri V Lvov 2007-01-17

Stages of Energy Transfer in the FPU Model Discrete and Continuous Dynamical Systems, Expanded Volume for the Proceedings of the Fourth International Conference on Dynamical Systems and Differential Equations, 113(2003).

Stages of Energy Transfer in the FPU Model
Discrete and Continuous Dynamical Systems, Expanded Volume for the Proceedings of the Fourth International Conference on Dynamical Systems and Differential Equations, 113(2003).