Towards the Evaluation of the Relevant Degrees of Freedom in Nonlinear Partial Differential Equations

Details Towards the Evaluation of the Relevant Degrees of Freedom in Nonlinear Partial Differential Equations Towards the Evaluation of the Relevant Degrees of Freedom in Nonlinear Partial Differential Equations

2001-06-08

arxiv.org/abs/cond-mat/0106156v2

Physics

Condensed Matter

Statistical Mechanics

49 pages, 23 ps figures. Accepted for publication in Journal of Statistical Physics

Scientific paper

We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical method providing the fundamental concepts of a numerical algorithm applicable to various dynamical systems. We examine dynamical scaling characteristics in the short-time and the long-time evolution regime providing only a reduced number of degrees of freedom to the evolution process.

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