L Kramer

University of Bayreuth , Bayreuth, Bavaria, Germany

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Publications (139)411.51 Total impact

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    ABSTRACT: Hydrodynamic systems driven away from equilibrium by sufficiently strong external forcing can develop spatially periodic patterns. A popular and intensely studied example is the Rayleigh-Bénard (RB) convection instability in a fluid layer heated from below and cooled from above [1–4]. This system is isotropic in the plane of the layer. One needs then special precautions to prepare well-ordered patterns without defects, because a restoring force against weak bending and the resulting reorientation is lacking.
    07/2011: pages 291-301;
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    ABSTRACT: We study dynamics of domain walls in pattern forming systems that are externally forced by a moving space-periodic modulation close to 2:1 spatial resonance. The motion of the forcing induces nongradient dynamics, while the wave number mismatch breaks explicitly the chiral symmetry of the domain walls. The combination of both effects yields an imperfect nonequilibrium Ising-Bloch bifurcation, where all kinks (including the Ising-like one) drift. Kink velocities and interactions are studied within the generic amplitude equation. For nonzero mismatch, a transition to traveling bound kink-antikink pairs and chaotic wave trains occurs.
    Physical Review Letters 08/2007; 99(2):028302. · 7.73 Impact Factor
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    ABSTRACT: In homeotropically aligned nematics with negative dielectric anisotropy the electrohydrodynamic instability occurs above a bend Fréedericksz transition. In the presence of a magnetic field parallel to the liquid crystal slab, ordered roll patterns with a well-defined uniform wave vector id appear above the onset of convection. By rotating the cell around an axis perpendicular to the slab by a small angle α, one can manipulate the system into a state with wave vector = id + Δ, where Δ is roughly perpendicular to id. We have studied experimentally the motion of defects, which then move essentially perpendicular to the rolls. The direction as well as the magnitude of the velocity as a function of Δ agrees with predictions of the weakly nonlinear theory. In particular, we obtain evidence for the nonanalyticity for Δ → 0.
    EPL (Europhysics Letters) 01/2007; 57(6):824. · 2.26 Impact Factor
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    ABSTRACT: The response of pattern forming systems to external forcing either spatial or temporal has received much attention for several decades. The study of combined spatiotemporal forcing has only been introduced recently, in particular in the form of a spatially resonant traveling wave forcing R udiger et al., Phys. Rev. Lett. 90 2003 128301 . Since then, both a series of experiments, in the context of Turing patterns in reaction di usion systems, and the development of the corresponding generic theory, have unveiled a wealth of new and unexpected phenomena. In this article we review these phenomena, we provide a uni ed and comprehensive description of them, and extend the theoretical analysis to new situations. We formulate the generic amplitude equations for di erent orders of spatial resonance for 1d and 2d patterns stripes and hexagons . We identify and describe in detail the autonomous dynamical system which underlies the phenomenon of traveling stripe resonance. For 1d we focus on localized solutions kinks and pulses , their dynamics and their interaction for both 1 1 and 2 1 resonance. In particular we discuss the e ect of wave number mismatch inexact resonance combined with the non gradient dynamics induced by the motion of the forcing, resulting in nontrivial interactions and complex spatio temporal dynamics. Analytical results in the phase approximation are obtained, while numerical techniques are used to study the complete problem. We show that defect interaction is oscillatory with distance, allowing for the existence of locked chaotic wave trains. In 2d we discuss the modulational instabilities of striped patterns and focus mostly on the study of the generation of hexagons induced by travelling stripe forcing, in the case of 1 1 exact resonance. We examine in detail the complex bifurcation scenario beyond primary instabilities. We nally discuss the problem of traveling wave forcing in the context of a speci c system, the photosensitive CDIMA reaction, where most experiments have been carried out. We compare experiments and theoretical predictions and propose other experimental systems where the study could be extended. Finally we review related work by other authors and discuss possible further developments and open questions which hold the promise of new interesting findings
    Physics Reports 01/2007; · 22.93 Impact Factor
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    ABSTRACT: A systematic overview of various electric-field induced pattern forming instabilities in nematic liquid crystals is given. The standard hydrodynamic description of nematics predicts the occurrence of striped patterns (rolls) in various wavenumber ranges, which depend on the anisotropy of the dielectric permittivity and that of the electrical conductivity as well as on the initial director orientation (planar or homeotropic). We discuss in detail three basic configurations with emphasis on the characterization of the threshold voltage and the critical wavenumber of the resulting patterns. Some features of the weakly nonlinear behavior are also addressed. Experimental exploration of additional pattern types, not captured by the standard model of electroconvection, is also presented. The impact of flexoelectricity as a possible explanation of the nonstandard EC patterns is discussed.
    Physics Reports 01/2007; · 22.93 Impact Factor
  • Lorenz Kramer, Werner Pesch
    Macromolecular Systems: Microscopic Interactions and Macroscopic Properties: Final Report, 12/2006: pages 260 - 294; , ISBN: 9783527609284
  • A G Rossberg, L Kramer
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    ABSTRACT: After reviewing some of the recent progress achieved in electroconvection of planarly oriented nematics we present a weakly nonlinear theory for the homeotropically oriented case for materials with negative dielectric anisotropy. Then one first has a Freédericksz transition that spontaneously breaks the isotropy in the plane of the convection layer and subsequently the convective instability. As a result the Goldstone mode resulting from the broken isotropy couples to the amplitude of the patterning mode. The equations exhibit new types of spatio-temporal chaos at onset.
    Physica Scripta 12/2006; 1996(T67):121. · 1.03 Impact Factor
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    ABSTRACT: A wide range of interesting dynamical phenomena have been observed in nematic liquid crystals, that are induced by strong laser radiation. We review the latest theoretical advances in describing and understanding these complex phenomena.
    10/2006: pages 83-122;
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    ABSTRACT: The decay of stripe patterns in planarly aligned nematic liquid crystals has been studied experimentally and theoretically. The initial patterns have been generated by the electrohydrodynamic instability and a light diffraction technique has been used to monitor their decay. In our experiments different decay rates have been observed as a function of the pattern wave number. According to our theoretical analysis they belong to a spectrum of decay modes and are individually selected in dependence on the initial conditions. Additional insight has emerged from a refined physical optical description of the diffraction intensity. The results compare well with experiments, which include also controlled modifications of the initial conditions to assess different decay modes.
    Physical Review E 07/2006; 73(6 Pt 1):061705. · 2.31 Impact Factor
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    ABSTRACT: We have performed one-dimensional and two-dimensional experiments and simulations to study the formation of patterns in a system that grows continuously in one direction. Depending on the growth velocity, three basic spatial configurations can be obtained: stripes that are parallel, oblique, or perpendicular to the growth direction. The dependence of the wavelength on the growth velocity has also been observed. Our results illustrate the importance of these growth mechanisms in determining the final configuration of chemical and biological pattern-forming processes.
    Physical Review Letters 03/2006; 96(4):048304. · 7.73 Impact Factor
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    ABSTRACT: A systematic overview of various electric-field induced pattern forming instabilities in nematic liquid crystals is given. Particular emphasis is laid on the characterization of the threshold voltage and the critical wavenumber of the resulting patterns. The standard hydrodynamic description of nematics predicts the occurrence of striped patterns (rolls) in five different wavenumber ranges, which depend on the anisotropies of the dielectric permittivity and of the electrical conductivity as well as on the initial director orientation (planar or homeotropic). Experiments have revealed two additional pattern types which are not captured by the standard model of electroconvection and which still need a theoretical explanation.
    01/2006: pages 55-82;
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    ABSTRACT: We study the homogeneous and the spatially periodic instabilities in a nematic liquid crystal layer subjected to steady plane Couette or Poiseuille flow. The initial director orientation is perpendicular to the flow plane. Weak anchoring at the confining plates and the influence of the external electric and/or magnetic field are taken into account. Approximate expressions for the critical shear rate are presented and compared with semianalytical solutions in case of Couette flow and numerical solutions of the full set of nematodynamic equations for Poiseuille flow. In particular the dependence of the type of instability and the threshold on the azimuthal and the polar anchoring strength and external fields is analyzed.
    Physical Review E 12/2005; 72(5 Pt 1):051706. · 2.31 Impact Factor
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    G Demeter, D O Krimer, L Kramer
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    ABSTRACT: We investigate the director oscillations of a homeotropically aligned nematic liquid crystal that are generated by cw laser radiation incident at a slightly oblique angle. The full nematodynamic equations are solved numerically, and it is shown that the inclusion of backflow leads to a qualitative change of the theoretical bifurcation scenario at moderate to high intensities. Very good correspondence is achieved with recent observations. The route to chaos via a sequence of homoclinic gluing bifurcations, whose existence was suggested by simple models, but doubted by recent calculations and experiments, is shown to exist in a parameter region unexplored by experiments.
    Physical Review E 12/2005; 72(5 Pt 1):051712. · 2.31 Impact Factor
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    ABSTRACT: We consider instabilities, either homogeneous or periodic in space, which develop in a nematic liquid crystal layer under rectilinear oscillatory Couette flow for planar surface alignment of the director perpendicular to the flow plane. On the basis of a numerical and analytical linear stability analysis we determine the critical amplitude of the oscillatory flow, the wave number, and the symmetry of the destabilizing mode and present a comprehensive phase diagram of the flow instabilities. In particular it is found that by varying the frequency of the Couette flow the instability changes its temporal symmetry. This transition is shown to be related to the inertia effects of the nematic fluid, which become more important with increasing flow frequency. We also show that an electric field applied perpendicularly to the nematic layer can induce an exchange of instabilities with different spatial and temporal symmetries. The theoretical results are compared with experiments, when available.
    Physical Review E 10/2005; 72(3 Pt 1):031709. · 2.31 Impact Factor
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    A P Krekhov, L Kramer
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    ABSTRACT: We study theoretically the slow director precession and nonlinear waves observed in homeotropically oriented nematic liquid crystals subjected to circular or elliptical Couette and Poiseuille flow and an electric field. From a linear analysis of the nematodynamic equations it is found that in the presence of the flow the electric bend Fréedericksz transition is transformed into a Hopf-type bifurcation. In the framework of an approximate weakly nonlinear analysis we have calculated the coefficients of the modified complex Ginzburg-Landau equation, which slightly above onset describes nonlinear waves with strong nonlinear dispersion. We also derive the equation describing the precession and waves well above the Fréedericksz transition and for small flow amplitudes. Then the nonlinear waves are of diffusive nature. The results are compared with full numerical simulations and with experimental data.
    Physical Review E 10/2005; 72(3 Pt 1):031705. · 2.31 Impact Factor
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    E Brasselet, D O Krimer, L Kramer
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    ABSTRACT: We study theoretically the dynamical reorientation phenomena when a long-pitch cholesteric liquid-crystal film with homeotropic alignment is illuminated by a circularly polarized lightwave. In the present case, the natural cholesteric pitch is of the order of (or larger than) the film thickness. The helical cholesteric structure is thus frustrated by the boundary conditions without illumination. However, above a light intensity threshold reorientation occurs and the bifurcation scenario depends strongly on the natural cholesteric pitch. Recalling that a long-pitch cholesteric is achieved in practice by adding a small amount of chiral agents in a nematic liquid crystal, the observed dynamics can be viewed as the result of the competition between intrinsic and extrinsic unidimensional helical patterns. The intrinsic part consists of the helical deformations induced by the chirality of the dopant, whereas the extrinsic part is related to the chirality induced by the optical field through the non-uniform angular momentum transfer of light to a nematic. The all-optical analog in the case of a pure nematic (without chiral dopant), is also discussed.
    The European Physical Journal E 09/2005; 17(4):403-11. · 2.18 Impact Factor
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    ABSTRACT: We present a detailed bifurcation analysis of the nonlinear reorientation dynamics of a homeotropically aligned nematic liquid-crystal film excited by a circularly polarized beam at normal incidence with the light intensity as the control parameter. The secondary bifurcation above the optical Fréedericksz transition threshold is identified as a supercritical Hopf bifurcation leading to quasi-periodicity, and the subsequent discontinuous transition from quasi-periodicity to periodicity at higher intensity is identified as a homoclinic bifurcation. The bifurcation scenario is compared with the one obtained in the case of an ordinary light wave at small oblique incidence. Despite an analogous sequence of transitions, there are substantial differences. © 2005 Optical So-ciety of America OCIS codes: 190.0190, 160.3710.
    Journal of the Optical Society of America B 07/2005; 22(8). · 2.21 Impact Factor
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    ABSTRACT: We present a detailed bifurcation analysis of the nonlinear reorientation dynamics of a homeotropically aligned nematic liquid-crystal film excited by an elliptically polarized beam at normal incidence with the intensity and the polarization state of light as the control parameters. The asymmetry arising from the elliptical polarization of the excitation lightwave is shown to affect dramatically the dynamics, and various new dynamical behaviors are reported: (i) quasi-periodic rotations for almost circular polarization; (ii) a discontinuous transition, iden-tified as a homoclinic bifurcation, to a largely reoriented state over a large range of ellipticity values; (iii) os-cillations associated with large reorientation; and (iv) optical multistability between several distinct dynamical regimes.
    Journal of the Optical Society of America B 07/2005; 22(8). · 2.21 Impact Factor
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    ABSTRACT: Utilizing the Soret effect, we have employed a moderately focused laser beam (30 microm, 20 mW) to write spatial composition patterns into layers of the critical polymer blend poly(dimethyl siloxane)/poly(ethyl-methyl siloxane) (PDMS/PEMS, M(w)=16.4/22.8 kg/mol) both in the one- and in the two-phase region a few degrees above and below the critical temperature T(c)=37.7 degrees C. Because of the critical divergence of the Soret coefficient, moderate temperature gradients are sufficient to induce composition modulations of large amplitude. In the two-phase regime the spinodal demixing pattern can be locally manipulated in a controlled way. 2D simulations based on a modified Cahn-Hilliard equation are able to reproduce the essential spatial and temporal features observed in the experiments.
    Physical Review Letters 07/2005; 94(21):214501. · 7.73 Impact Factor
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    D O Krimer, G Demeter, L Kramer
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    ABSTRACT: We investigate the dynamical phenomena induced by a circularly polarized plane wave incident perpendicularly on a homeotropically aligned nematic layer. We study theoretically the influence of the velocity field (backflow effect) on the bifurcation scenario. Whereas backflow leads to substantial quantitative changes of secondary bifurcation thresholds, the overall bifurcation scenario remains unchanged. In the regime of uniform precession of the director with large reorientation, an unanticipated spatial oscillation of the flow field across the layer is found. Quantitative comparison with experimental large-aspect ratio systems is now possible.
    Physical Review E 06/2005; 71(5 Pt 1):051711. · 2.31 Impact Factor

Publication Stats

2k Citations
411.51 Total Impact Points

Institutions

  • 1984–2011
    • University of Bayreuth
      • • Institute of Physics
      • • Chair of Theoretical Physics I
      Bayreuth, Bavaria, Germany
  • 2007
    • Humboldt-Universität zu Berlin
      • Department of Physics
      Berlin, Land Berlin, Germany
  • 2006
    • Brandeis University
      • Department of Chemistry
      Waltham, MA, United States
  • 2005
    • Ufa Scientific Center of the Russian Academy of Science
      Oufa, Bashkortostan, Russia
    • Ecole normale supérieure de Lyon
      • UMR 5672 - Laboratoire de Physique
      Lyon, Rhone-Alpes, France
  • 1999–2005
    • Hungarian Academy of Sciences
      • • Institute for Particle and Nuclear Physics
      • • Institute for Solid State Physics and Optics
      Budapest, Budapest fovaros, Hungary
    • Kyoto University
      • Department of Physics II
      Kyoto, Kyoto-fu, Japan
  • 2004
    • University of Santiago de Compostela
      • Grupo de Física No Lineal
      Santiago de Compostela, Galicia, Spain
  • 1995
    • Bar Ilan University
      Gan, Tel Aviv, Israel
  • 1991–1993
    • Hebrew University of Jerusalem
      Yerushalayim, Jerusalem District, Israel
    • University of California, Santa Barbara
      • Department of Physics
      Santa Barbara, CA, United States
  • 1988
    • Cornell University
      Ithaca, New York, United States
  • 1973
    • Forschungszentrum Jülich
      Jülich, North Rhine-Westphalia, Germany