# Dresden 2006 – wissenschaftliches Programm

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# SYSS: Structure Formation and Self-Organization in non-equilibrium Systems

## SYSS 1: Structure Formation and Self-Organization in non-equilibrium Systems I

### SYSS 1.12: Vortrag

### Donnerstag, 30. März 2006, 12:30–12:45, BAR Sch\"o

**Coherent structures in nonequilibrium wave dynamics** — •Benno Rumpf^{1}, Guenter Radons^{1}, Alan Newell^{2}, and Laura Biven^{3} — ^{1}Physics Institute, TU Chemnitz, 09107 Chemnitz, Germany — ^{2}Mathematics Department, University of Arizona, Tucson, Arizona, USA — ^{3}Max-Planck-Institut fuer Physik komplexer Systeme, 01187 Dresden, Germany

Turbulence of dispersive nonlinear waves transfers energy from a long spatial scale, where a driving force is applied, to a short viscous scale. In many physical systems, the wave amplitude is almost everywhere small, while strongly nonlinear structures with high amplitudes emerge intermittently. Our study of these coherent structures in nonequilibrium systems is based on a simple statistical analysis of a wide class of Hamiltonian wave equations. The formation of coherent structures depends critically on the thermodynamic parameters of the low-amplitude waves, and on the frequency of coherent structures.

[1] B.Rumpf, L.Biven, Weak turbulence in the Majda-McLaughlin-Tabak equation: Fluxes in wavenumber and in amplitude space, Physica D 204, 188-203, (2005)

[2] B.Rumpf, A.C.Newell, Intermittency as a consequence of turbulent transport in nonlinear systems, Phys.Rev.E 69, 026306, (2004)

[3] B.Rumpf, Intermittent movement of localized excitations of a nonlinear lattice, Phys.Rev.E 70, 016609 (2004)

[4] B.Rumpf, Simple statistical explanation for the localization of energy in nonlinear lattices with two conserved quantities, Phys.Rev.E 69, 016618 (2004)