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DY: Fachverband Dynamik und Statistische Physik
DY 44: Pattern Formation
DY 44.6: Talk
Thursday, March 19, 2015, 10:45–11:00, BH-N 333
Faraday Waves as dynamical system under time asymmetric periodic excitation — •Thomas John1,2, Dirk Pietschmann2, Ralf Stannarius2, and Christan Wagner1 — 1Universität des Saarlandes, 66123 Saarbrücken — 2Otto-von-Guericke-Universität Magdeburg, 39016 Magdeburg
The Faraday wave experiment is a paradigm for parametric excitable systems, in particular by periodic accelerations. We investigated the onset of the patter formation by periodic, however time asymmetric wave form shapes in excitation. In that case a new question arises: Does the threshold amplitude of the first instability changes - if the asymmetric periodic waveform is only reversed in time. Simple wave forms like sine or square waves are identical under time reversed transformation and can't lead to an influence of the stability of the system. We present our experimental and theoretical results for the Faraday system. The linear stability analysis derived from the Navier-Stokes equations will discussed for arbitrary periodic wave forms. In addition, a simpler analytical example system with parametric, periodic and time asymmetric driving is presented. In this example: if the shape of the excitation is exclusively time reversed (amplitude is the same) then the stability changes from unstable to stable and vice versa. The reduced complexity in the example system presents the mathematical properties more clear. Nevertheless, the linear stability analysis of the Faraday wave experiment shows a perfect agreement with our experimental obtained results. D. Pietschmann, R. Stannarius, C. Wagner and T. John, PRL 110, 094503 (2013).