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DY: Dynamik und Statistische Physik

DY 46: Poster

DY 46.99: Poster

Donnerstag, 30. März 2006, 16:00–18:00, P1

Time-Delayed Feedback Control of Stochastic Growth Equations — •Michael Block and Eckehard Schöll — Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin

Various growth phenoma in general, and especially crystal growth, can be described by continuous stochastic differential equations. Utilizing a forward-backward Euler algorithm we solve various growth equations in 1+1 and 2+1 dimensions. The focus is on the exponents describing the time-evolution of a surface: the growth exponent, the roughness exponent and the dynamic exponent, where only two of those are independent. We apply two different time-delayed feedback control methods to the stochastic growth equations with the aim of controlling the surface roughness. Different coupling schemes of the control force are investigated and compared. In particular, we propose a digital control scheme and a differential control scheme, where the difference between the desired growth exponent and the actual local growth exponent enters into the control force in a digital or differential way, respectively. These schemes are applied to the Kardar-Parisi-Zhang equation and the so called MBE (Molecular Beam Epitaxy) equation. It is shown that the growth exponent β, and thus the temporal evolution of the rms surface roughness, can be adjusted within certain ranges. Limitations of those control schemes are investigated in detail.