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## List of Publications

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- Geschrieben von David A. Strehober
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### Feedback control of flow alignment in sheared liquid crystals

Based on a continuum theory, we investigate the manipulation of the non-equilibrium behavior of a sheared liquid crystal via closed-loop feedback control. Our goal is to stabilize a specific dynamical state, that is, the stationary "flow-alignment", under conditions where the uncontrolled system displays oscillatory director dynamics with in-plane symmetry. To this end we employ time-delayed feedback control (TDFC), where the equation of motion for the ith component, q_i(t), of the order parameter tensor is supplemented by a control term involving the difference q_i(t)-q_i(t-\tau). In this diagonal scheme, \tau is the delay time. We demonstrate that the TDFC method successfully stabilizes flow alignment for suitable values of the control strength, K, and \tau; these values are determined by solving an exact eigenvalue equation. Moreover, our results show that only small values of K are needed when the system is sheared from an isotropic equilibrium state, contrary to the case where the equilibrium state is nematic.

David A Strehober, Eckehard Schöll and Sabine H L Klapp. Feedback control of flow alignment in sheared liquid crystals.

*Phys. Rev. E*88:062509, Dezember 2013. URL, DOI BibTeX@article{PhysRevE.88.062509, title = "Feedback control of flow alignment in sheared liquid crystals", author = {Strehober, David A. and Sch\"oll, Eckehard and Klapp, Sabine H. L.}, journal = "Phys. Rev. E", volume = 88, issue = 6, pages = 062509, numpages = 10, year = 2013, month = "Dec", publisher = "American Physical Society", doi = "10.1103/PhysRevE.88.062509", url = "http://link.aps.org/doi/10.1103/PhysRevE.88.062509" }

### Oscillatory motion of sheared nanorods beyond the nematic phase

We study the role of the control parameter triggering nematic order (temperature or concentration) on the dynamical behavior of a system of nanorods under shear. Our study is based on a set of mesoscopic equations of motion for the components of the tensorial orientational order parameter. We investigating these equations via a systematic bifurcation analysis based on a numerical continuation technique, focusing on spatially homogeneous states. Exploring a wide range of parameters we find, unexpectedly, that states with oscillatory motion can exist even under conditions where the equilibrium system is isotropic. These oscillatory states are characterized by wagging motion of the paranematic director, and they occur if the tumbling parameter is sufficiently small. We also present full non-equilibrium phase diagrams, in the plane spanned by the concentration and the shear rate.

David A Strehober, Harald Engel and Sabine H L Klapp. Oscillatory motion of sheared nanorods beyond the nematic phase.

*Phys. Rev. E*88:012505, Juli 2013. URL, DOI BibTeX@article{PhysRevE.88.012505, title = "Oscillatory motion of sheared nanorods beyond the nematic phase", author = "Strehober, David A. and Engel, Harald and Klapp, Sabine H. L.", journal = "Phys. Rev. E", volume = 88, issue = 1, pages = 012505, numpages = 12, year = 2013, month = "Jul", doi = "10.1103/PhysRevE.88.012505", url = "http://link.aps.org/doi/10.1103/PhysRevE.88.012505", publisher = "American Physical Society" }

### Feedback control of flow alignment in a sheared liquid crystal

Nematic liquids under shear display a variety of dynamic states, reaching from stationary flow alignment of the nematic director over various types of periodic motion toward chaos. In the framework of a continuum theory, transitions between these states correspond to bifurcations in the parameter plane. In particular, a decrease of the (shape-dependent) coupling parameter λK at a fixed, high value of the shear rate γ̇ leads to a Hopf bifurcation, where flow alignment becomes unstable against oscillatory states. Here we show that within the oscillatory regime, flow alignment can be stabilized by employing time-delayed feedback control. Specifically, we explore a diagonal control scheme where the equation of motion for the ith dynamical variable qi(t) is supplemented by a control term involving the difference qi(t)−qi(t−τ). We also investigate the range of control strengths and delay times τ for which the control works.

David A Strehober, Eckehard Sch"oll and Sabine H L Klapp. Feedback control of flow alignment in a sheared liquid crystal.

*AIP Conference Proceedings*1493(1):552-558, 2012. URL, DOI BibTeX@article{Strehober2012, author = {David A. Strehober and Eckehard Sch\{"o}ll and Sabine H. L. Klapp}, editor = "Seenith Sivasundaram", collaboration = "", title = "Feedback control of flow alignment in a sheared liquid crystal", publisher = "AIP", year = 2012, journal = "AIP Conference Proceedings", volume = 1493, number = 1, pages = "552-558", keywords = "bifurcation; nematic liquid crystals", url = "http://link.aip.org/link/?APC/1493/552/1", doi = "10.1063/1.4765541" }