Berlin 2005 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 34: Poster

DY 34.3: Poster

Montag, 7. März 2005, 15:30–18:00, Poster TU D

Calculating the degrees of freedom governing dynamical systems — •Sebastian Getfert¹, Javier Rodriguez-Laguna², and Andreas Degenhard¹ — ¹Fakultät für Physik, Universität Bielefeld, Postfach 100131, 33501 Bielefeld — ²Instituto de Fisica Teorica, UAM-CSIC, Madrid, Spain

The numerical analysis of dynamical systems that are described by evolutionary partial differential equations (PDEs) is inevitably connected with field discretization. Therefore, efficient computations are often difficult due to the high number of degrees of freedom involved.

For equilibrium phenomena Real Space Renormalization Group Methods were successfully developed to reduce the number of degrees of freedom. Here we investigate the use of such methods for dynamical systems [1]. Our approach is based on the construction of a reduction operator that projects the system to a subspace including only a restricted subset of all the degrees of freedom. The reduction operator concept explicitly allows for selecting the relevant degrees of freedom, i.e. those that dominate the time evolution of the system under consideration. As the final result we obtain a reduced description for the evolution of the PDE, thereby increasing the computational efficiency.

[1] Degenhard A., Rodriguez-Laguna J., J. Stat. Phys. 106, 1093 (2002)