H. Riecke | Northwestern University (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.

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

Pattern orthogonalization via channel decorrelation

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

Physical Review Letters, 2000

Physica D: Nonlinear Phenomena, 2001

Physica D: Nonlinear Phenomena, 2000

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

Physik Journal, 1992

ABSTRACT

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.),

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