Diffusion of Power in Randomly Perturbed Hamiltonian Partial Differential Equations

Details Diffusion of Power in Randomly Perturbed Hamiltonian Partial Differential Equations Diffusion of Power in Randomly Perturbed Hamiltonian Partial Differential Equations

2003-11-11

arxiv.org/abs/nlin/0311020v1

Nonlinear Sciences

Adaptation and Self-Organizing Systems

51 pages LaTex

Scientific paper

We study the evolution of the energy (mode-power) distribution for a class of randomly perturbed Hamiltonian partial differential equations and derive {\it master equations} for the dynamics of the expected power in the discrete modes. In the case where the unperturbed dynamics has only discrete frequencies (finitely or infinitely many) the mode-power distribution is governed by an equation of discrete diffusion type for times of order $\cO(\ve^{-2})$. Here $\ve$ denotes the size of the random perturbation. If the unperturbed system has discrete and continuous spectrum the mode-power distribution is governed by an equation of discrete diffusion-damping type for times of order $\cO(\ve^{-2})$. The methods involve an extension of the authors' work on deterministic periodic and almost periodic perturbations, and yield new results which complement results of others, derived by probabilistic methods.

Affiliated with

Also associated with

No associations

Rating

Diffusion of Power in Randomly Perturbed Hamiltonian Partial Differential Equations 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 Diffusion of Power in Randomly Perturbed Hamiltonian Partial Differential Equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Diffusion of Power in Randomly Perturbed Hamiltonian Partial Differential Equations will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-337557