Application of Weak Turbulence Theory to FPU Model

Details Application of Weak Turbulence Theory to FPU Model Application of Weak Turbulence Theory to FPU Model

2002-10-07

arxiv.org/abs/nlin/0210007v1

Nonlinear Sciences

Chaotic Dynamics

10 pages, to appear "Proceedings of the Fourth International Converence on Dynamical Systems and Differential Equations"

Scientific paper

The foundations of weak turbulence theory is explored through its application to the (alpha) Fermi-Pasta-Ulam (FPU) model, a simple weakly nonlinear dispersive system. A direct application of the standard kinetic equations would miss interesting dynamics of the energy transfer process starting from a large-scale excitation. This failure is traced to an enforcement of the exact resonance condition, whereas mathematically the resonance should be broadened due to the energy transfer happening on large but finite time scales. By allowing for the broadened resonance, a modified three-wave kinetic equation is derived for the FPU model. This kinetic equation produces some correct scaling predictions about the statistical dynamics of the FPU model, but does not model accurately the detailed evolution of the energy spectrum. The reason for the failure seems not to be one of the previously clarified reasons for breakdown in the weak turbulence theory.

Affiliated with

Also associated with

No associations

Rating

Application of Weak Turbulence Theory to FPU Model does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Application of Weak Turbulence Theory to FPU Model, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Application of Weak Turbulence Theory to FPU Model will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-440158