Berlin 2018 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 70: Poster: Flows, Patterns, Delay, Reaction Diffusion

DY 70.21: Poster

Donnerstag, 15. März 2018, 15:30–18:00, Poster A

Time-delayed feedback control of oscillatory states in sheared micellar systems — •Benjamin von Lospichl and Sabine H. L. Klapp — Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, 10623 Berlin

We investigate a rheological model for the shear stress [1], which is suitable to describe the dynamics of elongated micelles under shear. Within the model a link between a structural variable, namely the micellar length, and the mechanical variables (stress and shear rate) is made. Through this connection it is possible to find a great variety of dynamical states ranging from steady shear banding to spatio-temporal oscillatory and chaotic states. To explore the phase space of the model we employ concepts of linear stability analysis and solve the dynamical system numerically in space and time using a Crank-Nicolson algorithm. A key feature of this model is the appearance of a Hopf bifurcation separating a spatio-temporal oscillatory region from a homogeneous region. Motivated by experiments [2], we explore possibilities to manipulate the oscillatory states by applying time-delayed feedback control (TDFC) such that they become stationary. The TDFC is introduced via a Pyragas scheme [3].

• [1] S.M. Fielding and P.D. Olmsted, Phys. Rev. Lett. 92, 084502 (2004).
• [2] O. Lüthje et al., Phys. Rev. Lett. 86, 1745 (2001).
• [3] K. Pyragas, Phys. Lett. A 170, 421 (1992).