H. Riecke - Profile on Academia.edu (original) (raw)

Papers by H. Riecke

Physica D: Nonlinear Phenomena, 2002

Weakly nonlinear hexagon convection patterns coupled to mean flow are investigated within the fra... more Weakly nonlinear hexagon convection patterns coupled to mean flow are investigated within the framework of coupled Ginzburg-Landau equations. The equations are in particular relevant for non-Boussinesq Rayleigh-Bénard convection at low Prandtl numbers. The mean flow is found to (1) affect only one of the two longwave phase modes of the hexagons and (2) suppress the mixing between the two phase modes. As a consequence, for small Prandtl numbers the transverse and the longitudinal phase instability occur in sufficiently distinct parameter regimes that they can be studied separately. Through the formation of penta-hepta defects, they lead to different types of transient disordered states. The results for the dynamics of the penta-hepta defects shed light on the persistence of grain boundaries in such disordered states.

Wellenlaengeneinschraenkung in quasi-eindimensionalen strukturbildenden Systemen

With 264 refs.SIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinforma... more With 264 refs.SIGLECopy held by FIZ Karlsruhe; available from UB/TIB Hannover / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Wellenlaengeneinschraenkung in quasi-eindimensionalen strukturbildenden Systemen

Action Editor: C. Linster

Pattern orthogonalization via channel decorrelation

Modeling and Computation Modeling and Computation in Science and Engineering - 346

Motivated by the rich variety of complex patterns observed on the surface of fluid layers that ar... more Motivated by the rich variety of complex patterns observed on the surface of fluid layers that are vibrated at multiple frequencies, we investigate the effect of such resonant forcing on systems undergoing a Hopf bifurcation to spatially homogeneous oscillations. We use an extension of the complex Ginzburg-Landau equation that systematically captures weak forcing functions with a spectrum consisting of frequencies close to the 1:1-, the 1:2-, and the 1:3-resonance. By slowly modulating the amplitude of the 1:2-forcing component we render the bifurcation to subharmonic patterns supercritical despite the quadratic interaction introduced by the 1:3-forcing. Our weakly nonlinear analysis shows that quite generally the forcing function can be tuned such that resonant triad interactions with weakly damped modes stabilize subharmonic patterns comprised of four or five Fourier modes, which are similar to quasi-patterns with 4-fold and 5-fold rotational symmetry, respectively. Using direct s...

SIAM Journal on Applied Dynamical Systems, 2004

Motivated by the rich variety of complex periodic and quasi-periodic patterns found in systems su... more Motivated by the rich variety of complex periodic and quasi-periodic patterns found in systems such as two-frequency forced Faraday waves, we study the interaction of two spatially periodic modes that are nearly resonant. Within the framework of two coupled one-dimensional Ginzburg-Landau equations we investigate analytically the stability of the periodic solutions to general perturbations, including perturbations that do not respect the periodicity of the pattern, and which may lead to quasi-periodic solutions. We study the impact of the deviation from exact resonance on the destabilizing modes and on the final states. In regimes in which the mode interaction leads to traveling waves our numerical simulations reveal localized waves in which the wavenumbers are resonant and which drift through a steady background pattern that has an off-resonant wavenumber ratio.

Physical Review Letters, 2000

Using coupled Ginzburg-Landau equations, the dynamics of hexagonal patterns with broken chiral sy... more Using coupled Ginzburg-Landau equations, the dynamics of hexagonal patterns with broken chiral symmetry are investigated, as they appear in rotating non-Boussinesq or surface-tension-driven convection. We find that close to the secondary Hopf bifurcation to oscillating hexagons the dynamics are well described by a single complex Ginzburg-Landau equation (CGLE) coupled to the phases of the hexagonal pattern. At the bandcenter these equations reduce to the usual CGLE and the system exhibits defect chaos. Away from the bandcenter a transition to a frozen vortex state is found.

Physica D: Nonlinear Phenomena, 2001

Quasipatterns have been found in dissipative systems ranging from Faraday waves in vertically vib... more Quasipatterns have been found in dissipative systems ranging from Faraday waves in vertically vibrated fluid layers to nonlinear optics. We describe the dynamics of octagonal, decagonal and dodecagonal quasipatterns by means of coupled Ginzburg-Landau equations and study their stability to sideband perturbations analytically using long-wave equations as well as by direct numerical simulation. Of particular interest is the influence of the phason modes, which are associated with the quasiperiodicity, on the stability of the patterns. In the dodecagonal case, in contrast to the octagonal and the decagonal case, the phase modes and the phason modes decouple and there are parameter regimes in which the quasipattern first becomes unstable with respect to phason modes rather than phase modes. We also discuss the different types of defects that can arise in each kind of quasipattern as well as their dynamics and interactions. Particularly interesting is the decagonal quasipattern, which allows two different types of defects. Their mutual interaction can be extremely weak even at small distances.

Physica D: Nonlinear Phenomena, 2000

Three coupled Ginzburg-Landau equations for hexagonal patterns with broken chiral symmetry are in... more Three coupled Ginzburg-Landau equations for hexagonal patterns with broken chiral symmetry are investigated. They are relevant for the dynamics close to onset of rotating non-Boussinesq or surface-tension-driven convection. Steady and oscillatory, long-and short-wave instabilities of the hexagons are found. For the long-wave behavior coupled phase equations are derived. Numerical simulations of the Ginzburg-Landau equations indicate bistability between spatio-temporally chaotic patterns and stable steady hexagons. The chaotic state can, however, not be described properly with the Ginzburg-Landau equations.

Instabilities and Spatio-Temporal Chaos of Hexagonal Convection Patterns in the Presence of Rotation

The stability of Marangoni roll convection in a liquid-gas system with deformable interface is st... more The stability of Marangoni roll convection in a liquid-gas system with deformable interface is studied in the case when there is a nonlinear interaction between two modes of Marangoni instability: long-scale surface deformations and short-scale convection. Within the framework of a model derived in [1], it is shown that the nonlinear interaction between the two modes substantially changes the width of the band of stable wave numbers of the short-scale convection pattern as well as the type of the instability limiting the band. Depending on the parameters of the system, the instability can be either longor short-wave, either monotonic or oscillatory. The stability boundaries strongly differ from the standard ones and sometimes exclude the band center. The long-wave limit of the side-band instability is studied in detail within the framework of the phase approximation. It is shown

Wie findet der Taylor-Wirbel seine Größe?: Selektion und Phasendiffusion in Strukturen fern vom Gleichgewicht

Physik Journal, 1992

ABSTRACT

Suppression of Spatio-temporal Chaos through Anisotropy in Rotating Convection

We study the stability of patterns arising in rotating convection in weakly anisotropic systems u... more We study the stability of patterns arising in rotating convection in weakly anisotropic systems using a modified Swift-Hohenberg equation. The anisotropy, either an endogenous characteristic of the system, or induced by external forcing, can stabilize periodic rolls in the Küppers-Lortz chaotic regime. In the particular case of rotating convection with time-modulated rotation where recently, in experiment (Guenter Ahlers, et al.),

Rotating convection in an anisotropic system (vol 65, art no 046219, 2002)

Journal of neurophysiology, Jan 15, 2014

In many forms of retinal degeneration, photoreceptors die but inner retinal circuits remain intac... more In many forms of retinal degeneration, photoreceptors die but inner retinal circuits remain intact. In the rd1 mouse, an established model for blinding retinal diseases, spontaneous activity in the coupled network of AII amacrine and ON cone bipolar cells leads to rhythmic bursting of ganglion cells. Since such activity could impair retinal and/or cortical responses to restored photoreceptor function, understanding its nature is important for developing treatments of retinal pathologies. Here we analyzed a compartmental model of the wild-type mouse AII amacrine cell to predict that the cell's intrinsic membrane properties, specifically, interacting fast Na and slow, M-type K conductances, would allow its membrane potential to oscillate when light-evoked excitatory synaptic inputs were withdrawn following photoreceptor degeneration. We tested and confirmed this hypothesis experimentally by recording from AIIs in a slice preparation of rd1 retina. Additionally, recordings from gan...

Physical Review E, 2014

A feature common to many models of vegetation pattern formation in semi-arid ecosystems is a sequ... more A feature common to many models of vegetation pattern formation in semi-arid ecosystems is a sequence of qualitatively different patterned states, "gaps → labyrinth → spots", that occurs as a parameter representing precipitation decreases. We explore the robustness of this "standard" sequence in the generic setting of a bifurcation problem on a hexagonal lattice, as well as in a particular reaction-diffusion model for vegetation pattern formation. Specifically, we consider a degeneracy of the bifurcation equations that creates a small bubble in parameter space in which stable small-amplitude patterned states may exist near two Turing bifurcations. Pattern transitions between these bifurcation points can then be analyzed in a weakly nonlinear framework. We find that a number of transition scenarios besides the standard sequence are generically possible, which calls into question the reliability of any particular pattern or sequence as a precursor to vegetation collapse. Additionally, we find that clues to the robustness of the standard sequence lie in the nonlinear details of a particular model.

Physics Letters A, 1989

Communicated by D.D. Hoim Recent experiments in circular geometry have studied the dynamics produ... more Communicated by D.D. Hoim Recent experiments in circular geometry have studied the dynamics produced by two parametrically excited surface waves. There is a natural theoretical context for experiments ofthis type,the mode interaction between two period-doublingbifurcations in the presence of0(2) symmetry. We formulate this interaction as a map in four dimensions, andclassify the primary, secondary, and tertiary bifurcations. We find that the observed amplitude oscillations can arise as a tertiary Hopfbifurcation from a mixed mode pattern provided exactly oneof the primary instabilities is subcritical.

Physical Review E, 1999

The motion of a thin layer of granular material on a plate undergoing sinusoidal vibrations is co... more The motion of a thin layer of granular material on a plate undergoing sinusoidal vibrations is considered. We develop equations of motion for the local thickness and the horizontal velocity of the layer. The driving comes from the violent impact of the grains on the plate. A linear stability theory reveals that the waves are excited nonresonantly, in contrast to the usual Faraday waves in liquids. Together with the experimentally observed continuum scaling, the model suggests a close connection between the neutral curve and the dispersion relation of the waves, which agrees quite well with experiments. For strong hysteresis we find localized oscillon solutions. ͓S1063-651X͑99͒10404-5͔

Physica D: Nonlinear Phenomena, 2002

Wellenlaengeneinschraenkung in quasi-eindimensionalen strukturbildenden Systemen

Action Editor: C. Linster

Pattern orthogonalization via channel decorrelation

Modeling and Computation Modeling and Computation in Science and Engineering - 346

SIAM Journal on Applied Dynamical Systems, 2004

Physical Review Letters, 2000

Physica D: Nonlinear Phenomena, 2001

Physica D: Nonlinear Phenomena, 2000

Instabilities and Spatio-Temporal Chaos of Hexagonal Convection Patterns in the Presence of Rotation

Wie findet der Taylor-Wirbel seine Größe?: Selektion und Phasendiffusion in Strukturen fern vom Gleichgewicht

Physik Journal, 1992

ABSTRACT

Suppression of Spatio-temporal Chaos through Anisotropy in Rotating Convection

Rotating convection in an anisotropic system (vol 65, art no 046219, 2002)

Journal of neurophysiology, Jan 15, 2014

Physical Review E, 2014

Physics Letters A, 1989

Physical Review E, 1999