Dresden 2003 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 21: Brownian motion
DY 21.5: Vortrag
Dienstag, 25. März 2003, 11:00–11:15, G\"OR/229
Mode selection in a spatial extended pattern forming system at noise excitation — •Thomas John1,2, Ralf Stannarius2, and Ulrich Behn1 — 1Institut für Theoretische Physik, Universität Leipzig — 2Institut für Experimentelle Physik I, Universität Leipzig
Electroconvection in liquid crystals is well suited for studies of mode selection in dissipative systems. Control parameters are the applied voltage U and frequency f. Under periodic excitation, a spatially periodic modulation of the director occurs above a critical voltage Uc(f), it approaches a saturation value. A low frequency conduction regime and a high frequency dielectric regime can be distinguished. In the first, cell dimensions determine the constant critical wave number kc; in the latter, the critical wave number kc(f) is diffusively selected. We determine the wave numbers of the patters experimentally by laser diffraction.
A spatially periodic pattern appears also, when the driving is non-periodic (here stochastic with a Dichotomous Markov Process, DMP). However, the amplitude strongly fluctuates. With increasing voltage, the rate of bursts (intervals with high amplitudes) increases. Depending upon a mean jump rate α in the excitation, again, the two regimes can distinguished. In the fist regime, kc≈ const, but in the dielectric regime, the system selects different wave numbers k(f,t) in individual bursts. The stochastic system cannot be described by a single mode ansatz. In numerical simulations based on linearized electro-hydrodynamic equations, we calculate growth rates for all possible wave numbers. The results are in agreement with the experimental data.
[1] Th. John, et al. Phys. Rev. E, 65 046229 (2002).