Coexisting Pulses in a Model for Binary-Mixture Convection

We address the striking coexistence of localized waves (`pulses') of different lengths which was observed in recent experiments and full numerical simulations of binary-mixture convection. Using a set of extended Ginzburg-Landau equations, we show that this multiplicity finds a natural explanation in terms of the competition of two distinct, physical localization mechanisms; one arises from dispersion and the other from a concentration mode. This competition is absent in the standard Ginzburg-Landau equation. It may also be relevant in other waves coupled to a large-scale field.Comment: 5 pages revtex with 4 postscript figures (everything uuencoded

Instabilities and Spatio-temporal Chaos of Long-wave Hexagon Patterns in Rotating Marangoni Convection

We consider surface-tension driven convection in a rotating fluid layer. For nearly insulating boundary conditions we derive a long-wave equation for the convection planform. Using a Galerkin method and direct numerical simulations we study the stability of the steady hexagonal patterns with respect to general side-band instabilities. In the presence of rotation steady and oscillatory instabilities are identified. One of them leads to stable, homogeneously oscillating hexagons. For sufficiently large rotation rates the stability balloon closes, rendering all steady hexagons unstable and leading to spatio-temporal chaos.Comment: 26 pages, 9 jpeg figures. Postscript file with all figures included available at http://www.esam.northwestern.edu/~riecke/lit/lit.html Movies available at http://www.esam.northwestern.edu/~riecke/research/Marangoni/marangoni.htm

Phase Diffusion in Localized Spatio-Temporal Amplitude Chaos

We present numerical simulations of coupled Ginzburg-Landau equations describing parametrically excited waves which reveal persistent dynamics due to the occurrence of phase slips in sequential pairs, with the second phase slip quickly following and negating the first. Of particular interest are solutions where these double phase slips occur irregularly in space and time within a spatially localized region. An effective phase diffusion equation utilizing the long term phase conservation of the solution explains the localization of this new form of amplitude chaos.Comment: 4 pages incl. 5 figures uucompresse

Parametric Forcing of Waves with Non-Monotonic Dispersion Relation: Domain Structures in Ferrofluids?

Surface waves on ferrofluids exposed to a dc-magnetic field exhibit a non-monotonic dispersion relation. The effect of a parametric driving on such waves is studied within suitable coupled Ginzburg-Landau equations. Due to the non-monotonicity the neutral curve for the excitation of standing waves can have up to three minima. The stability of the waves with respect to long-wave perturbations is determined $via$ a phase-diffusion equation. It shows that the band of stable wave numbers can split up into two or three sub-bands. The resulting competition between the wave numbers corresponding to the respective sub-bands leads quite naturally to patterns consisting of multiple domains of standing waves which differ in their wave number. The coarsening dynamics of such domain structures is addressed.Comment: 23 pages, 6 postscript figures, composed using RevTeX. Submitted to PR

Attractive Interaction Between Pulses in a Model for Binary-Mixture Convection

Recent experiments on convection in binary mixtures have shown that the interaction between localized waves (pulses) can be repulsive as well as {\it attractive} and depends strongly on the relative {\it orientation} of the pulses. It is demonstrated that the concentration mode, which is characteristic of the extended Ginzburg-Landau equations introduced recently, allows a natural understanding of that result. Within the standard complex Ginzburg-Landau equation this would not be possible.Comment: 7 pages revtex with 3 postscript figures (uuencoded

Reicht optischer Fluß wirklich nicht zum Heimfinden?

Die Literatur legt nahe, daß selbst für einfache Orientierungs- und Heimfindeaufgaben die durch optischen Fluß gegebene Information unzureichend ist und vestibuläre und kinästhetische Reize benötigt werden. Um diese Behauptung zu testen, führten wir Dreiecksvervollständigungsexperimente in einer virtuellen Umgebung durch, die als einzige Informationsquelle optischen Fluß anbot. Die simulierte Eigenbewegung wurden visuell auf einer halbzylindrischen 180° Projektionsleinwand (7m Durchmesser) dargeboten und über Maus-Tasten gesteuert. Damit die Versuchspersonen zur Navigation nur Pfadintegration und keine Landmarkeninformation verwenden konnten, bestand die simulierte Welt lediglich aus einer 3D Punktewolke. Diese enthielt keinerlei hilfreiche Orientierungspunkte (Landmarken), vermittelte jedoch ein überzeugendes Gefühl von Eigenbewegung (Vektion). In Exp 1 sollten die Versuchspersonen Drehungen um bestimmte Winkel ausführen sowie Distanzen reproduzieren, wobei die Geschwindigkeiten randomisiert wurden. Exp 2 3 waren Dreiecksvervollständigungsexperimente: Versuchspersonen folgten zwei Schenkeln eines Dreiecks und sollten dann selbstständig zum nicht markierten Ausgangspunkt zurückfinden. In Exp 2 wurden fünf verschiedene gleichschenklige Dreiecke für Links- und Rechtsdrehungen verwendet, in Exp 3 hingegen 60 verschiedene Dreiecke mit randomisierten Schenkellängen und Winkeln. Unabhängig von der Bewegungsgeschwindigkeit konnten untrainierte Versuchspersonen in Exp 1 Drehungen und Distanzen mit nur geringfügigem systematischen Fehler ausführen. Wir fanden in Exp 2 3 generell eine lineare Korrelation zwischen ausgeführten und korrekten Werten für die Meßgrößen Drehwinkel und zurückgelegte Distanz. Für die weitere Analyse verwendeten wir deshalb für beide Meßgrößen die Steigungen der Regressionsgeraden (“Kompressionsrate”) und die Abweichungen vom korrekten Wert (signed error). Exp 2 zeigte keine signifikanten Fehler (d.h. generelle Über- oder Unterschätzung) für Drehungen oder Distanzen. Distanzantworten waren stark in Richtung Mittelwert verschoben (Kompressionsrate 0.58), Winkelantworten jedoch kaum (0.91). Für randomisierte Dreiecksgeometrien in Exp 3 reduzierte sich diese Tendenz zu mittleren Antworten für Distanzen (0.86), verstärkte sich jedoch für Drehungen (0.77). In ähnlichen Experimenten zur Dreiecksvervollständigung unter Beschränkung auf visuelle Information (Virtual Reality: Péruch et al., Perc. ‘97; Duchon et al., Psychonomics ‘99) und auf propriozeptive Reize (blindes gehen: Loomis et al., JEP ‘93) zeigte sich eine starke Tendenz zu mittleren Drehwinkeln (Kompressionsrate < 0.5), die wir nicht fanden. Die Tendenz, bei reinen Drehaufgaben in visuellen virtuellen Umgebungen nicht weit genug zu drehen (Péruch ‘97; Bakker, Presence ‘99) konnte ebenfalls nicht beobachtet werden (Exp 1). Pfadintegration aufgrund optischen Flusses erwies sich in unseren Experimenten als ausreichend und verläßlich für Orientierungs- und Heimfindeaufgaben. Vestibuläre und kinästhetische Information waren hierfür nicht erforderlich

Stability and dynamics of spatio-temporal structures

The main goal of the project supported in this grant is to contribute to the understanding of localized spatial and spatio-temporal structures far from thermodynamic equilibrium. Here we report on our progress in the study of two classes of systems. (1) We have started to investigate localized wave-pulses in binary-mixture convection. This work is based on our recently derived extension of the conventionally used complex Ginzburg-Landau equations. We are considering three regimes: Dispersion-less supercritical waves; strongly dispersive subcritical waves; and localized waves as bound states of fronts between dispersionless subcritical waves and the motionless conductive state. (2) We have completed our investigation of steady domain structures in which domains of structures with different wave numbers alternate, separated by domain walls. In particular, we have studied their regimes of existence and stability within the framework of a Ginzburg-Landau equation and have compared it to previous results. Those were based on a long-wavelength approximation, which misses certain aspects which turn out to be important for the stability of the domain structures in realistic situations. In addition, we give a description of our work on resonantly forced waves in two-dimensional anisotropic systems

Modulation of Localized States in Electroconvection

We report on the effects of temporal modulation of the driving force on a particular class of localized states, known as worms, that have been observed in electroconvection in nematic liquid crystals. The worms consist of the superposition of traveling waves and have been observed to have unique, small widths, but to vary in length. The transition from the pure conduction state to worms occurs via a backward bifurcation. A possible explanation of the formation of the worms has been given in terms of coupled amplitude equations. Because the worms consist of the superposition of traveling waves, temporal modulation of the control parameter is a useful probe of the dynamics of the system. We observe that temporal modulation increases the average length of the worms and stabilizes worms below the transition point in the absence of modulation.Comment: 4 pages, 4 figure

Measuring Vection in a Large Screen Virtual Environment

This paper describes the use of a large screen virtual environment to induce the perception of translational and rotational self-motion. We explore two aspects of this problem. Our first study investigates how the level of visual immersion (seeing a reference frame) affects subjective measures of vection. For visual patterns consistent with translation, self-reported subjective measures of self-motion were increased when the floor and ceiling were visible outside of the projection area. When the visual patterns indicated rotation, the strength of the subjective experience of circular vection was unaffected by whether or not the floor and ceiling were visible. We also found that circular vection induced by the large screen display was reported subjectively more compelling than translational vection. The second study we present describes a novel way in which to measure the effects of displays intended to produce a sense of vection. It is known that people unintentionally drift forward if asked to run in place while blindfolded and that adaptations involving perceived linear self-motion can change the rate of drift. We showed for the first time that there is a lateral drift following perceived rotational self-motion and we added to the empirical data associated with the drift effect for translational self-motion by exploring the condition in which the only self-motion cues are visual