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Results for “Meanders”

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PubMed2004

Spiral wave drift in an electric field and scroll wave instabilities.

Here, I present the numerical computation of speed and direction of the drift of a spiral wave in an excitable medium in the presence of an electric field. The drift speed presents a strong variation close to the parameter value where the drift-speed component along the field direction from parallel becomes antiparallel. Using a simple phenomenological model and results from a numerical linear stability analysis of scroll waves, I show that this behavior can be attributed to a resonance of the meander modes with the translation modes of the spiral wave. Extending this phenomenological model to scroll waves also clarifies the link between the drift and long wavelength instabilities of scroll waves.

Journal Article↗

PubMed2004

Paradoxical nonlinear response of a Brownian particle.

We consider a Brownian particle in a "meandering" periodic potential when the ambient temperature is a periodically or stochastically varying function of time. Though far from equilibrium, the linear response of the particle to an external static force is exactly the same as in the equilibrium case, i.e., for constant temperature. Even more surprising is the nonlinear response: the particle slows down and then even starts to move in the direction opposite to the applied force.

Journal Article↗

PubMed2005

Observation of spiral pattern and spiral defect chaos in dielectric barrier discharge in argon/air at atmospheric pressure.

A rich variety of spiral patterns such as single-armed spiral, dipole spirals, target pattern, multiarmed spiral, and spiral defect chaos state have been observed in ac-driven atmospheric pressure gas discharge. The confined and free boundary conditions are defined by means of whether there is a sidewall in the discharge domain or not, respectively. In the free boundary condition, the spiral pattern arises when the stripe pattern undergoes core instability or notching instability. In the confined boundary condition, the spiral pattern is formed by sidewall forcing. The spiral drifts upward in the free boundary condition and meanders in the confined boundary condition. The topological charge of the spiral pattern can be changed when the spiral interacts with the dislocations. The spiral wavelength (average distance between two consecutive rolls) is a function of gas composition and decreases rapidly with increase of air concentration in discharge gas.

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PubMed2006

Dynamics of fluctuation-dominated phase ordering: hard-core passive sliders on a fluctuating surface.

We study the dynamics of a system of hard-core particles sliding downwards on a one-dimensional fluctuating interface, which in a special case can be mapped to the problem of a passive scalar advected by a Burgers fluid. Driven by the surface fluctuations, the particles show a tendency to cluster, but the hard-core interaction prevents collapse. We use numerical simulations to measure the autocorrelation function in steady state and in the aging regime, and space-time correlation functions in steady state. We have also calculated these quantities analytically in a related surface model. The steady-state autocorrelation is a scaling function of t/L(z), where L is the system size and z is the dynamic exponent. Starting from a finite intercept, the scaling function decays with a cusp, in the small argument limit. The finite value of the intercept indicates the existence of long-range order in the system. The space-time correlation, which is a function of r/L and t/L(z), is nonmonotonic in t for fixed r. The aging autocorrelation is a scaling function of t(1) and t(2) where t(1) is the waiting time and t(2) is the time difference. This scaling function decays as a power law for t(2)>>t(1); for t(1)>>t(2), it decays with a cusp as in steady state. To reconcile the occurrence of strong fluctuations in the steady state with the fact of an ordered state, we measured the distribution function of the length of the largest cluster. This shows that fluctuations never destroy ordering, but rather the system meanders from one ordered configuration to another on a relatively rapid time scale.

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PubMed2006

Dynamics of bound states of same-chirality spiral waves.

We describe the dynamics of bound states of same-chirality spirals in a generic numerical model of an excitable medium. For each bound state, we analyze its tip trajectory patterns and determine its characteristic frequencies. We report two previously unidentified bound states: for spiral pairs, a state that exhibits alternating cycles of small and large distances between collisions (A2); for triplets, the first example of a meandering bound state (M3). In parameter space, A2 lies in between the previously described oscillating pairs (O2) and master-slave pairs (MS). We present numerical evidence that the transition O2-->A2 occurs via a supercritical period-doubling bifurcation, while the transition A2-->MS occurs via a symmetry breaking secondary Hopf bifurcation. A classification of all regimes according to dynamical systems theory exposes the wealth of phenomena exhibited by multiarmed spiral waves.

Models, Theoretical↗

PubMed2006

Spiral turbulence developed through the formation of superimposed target waves in an oscillatory reaction-diffusion medium.

An approach leading to the development of spiral turbulence is reported here in an oscillatory reaction-diffusion medium, which is through the spontaneous formation of targetlike waves near the core of a spiral wave. The newly formed target wave emerges with its own characteristic frequency and propagates on top of the original spiral wave, which eventually leads to the breakup of the spiral at a location far from the spiral center. The radius of the surviving spiral segment decreases rapidly with the bifurcation control parameter. Calculation of power spectra suggests that the meandering of the spiral tip is responsible for the onset of the superimposed target and the phase desynchronization of the superimposed target waves.

Journal Article↗

PubMed2000

Two-step disordering of perpendicularly magnetized ultrathin films.

We have imaged the stripe domain structure of perpendicularly magnetized fcc ultrathin Fe films grown on Cu(100). The stripe phase has a strong local orientational order and sustains the two kinds of fluctuations predicted by Abanov et al. [Phys. Rev. B 51, 1023 (1995)]: meandering and dislocations. Before reaching the Curie temperature, the stripes transform into a new and so far unobserved domain structure, characterized by domains with predominantly square corners. We argue that this phase is the tetragonal liquid phase proposed by Abanov et al. to separate the stripe phase from the paramagnetic phase. This two-step disordering is reminiscent of a two-dimensional melting process.

Journal Article↗

PubMed2000

Critical points in heavy ion irradiated untwinned YBa(2)Cu3O(7-delta) crystals

The critical points in untwinned YBa(2)Cu(3)O(7-delta) crystals with dilute columnar defects are investigated. We find a convergence of a first order vortex melting line with an irreversibility line associated with the onset of the Bose glass critical regime at the lower critical point. In addition, we find that columnar defects raise the upper critical point, implying that vortex line meandering is a basic feature controlling its position.

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PubMed2000

Rotating spiral edge flames in von karman swirling flows

Experimental observations of rotating spiral flame edges formed during near-limit combustion of a downward-facing, polymethylmethacrylate disk spinning in quiescent air are reported. These flames exhibit similarities to patterns commonly found in quiescent excitable media. The tail rotates rigidly while the tip executes a compound, meandering motion sometimes observed in Belousov-Zhabotinskii reactions. A model assuming a rigid-body rotation with a constant speed of propagation relative to the swirling gas flow generated by the spinning disk predicts the observed spiral shapes well.

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PubMed2000

Preferential sputtering induced stress domains and mesoscopic phase separation on CaF2(111)

We report the formation of novel mesoscopic two-dimensional bubble structures coexisting with nanometer-scale, two monolayer high, meandering islands of characteristic separation approximately 11 nm on CaF2(111) surfaces exposed to glancing incidence ion beam irradiation (4 degrees, 4.5 keV Ar+). The island and bubble structures can be explained, respectively, by nanoscale stress domain related local self-ordering of a single calcium adlayer on phase-separated F- (fluorine ion) and F-center (color center) terminated mesoscopic domains.

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PubMed2001

Oscillatory driving of crystal surfaces: a route to controlled pattern formation.

We show that the oscillatory driving of crystal surfaces can induce pattern formation or smoothening. Depending on driving conditions, step bunching and meandering, mound formation, or surface smoothening may be seen in the presence of a kinetic asymmetry at the steps or kinks. We employ a step model to calculate the induced mass flux along misoriented surfaces, which accounts for surface dynamics and stability. Slope selection, surface metastability, and frequency-dependent surface stability are found. Quantitative predictions for pattern formation on metal surfaces in an electrolyte are provided.

Journal Article↗

PubMed2001

Continuum model for low temperature relaxation of crystal steps.

High and low temperature relaxation of crystal steps are described in a unified picture, using a continuum model based on a modified expression of the step-free energy. Results are in agreement with experiments and Monte Carlo simulations of step fluctuations and monolayer cluster diffusion and relaxation. In an extended model where mass exchange with neighboring terraces is allowed, step transparency and a low temperature regime for unstable step meandering are found.

Algorithms↗

PubMed2002

Adsorption phenomena in the transport of a colloidal particle through a nanochannel containing a partially wetting fluid.

Using molecular dynamics simulations, we study the motion of a closely fitting nanometer-size solid sphere in a fluid-filled cylindrical nanochannel at low Reynolds numbers. At early times, when the particle is close to the middle of the tube, its velocity is in agreement with continuum calculations, despite large thermal fluctuations. At later times, partially wetting fluids exhibit novel adsorption phenomena: the sphere meanders away from the center of the tube and adsorbs onto the wall, and subsequently either sticks to the wall and remains motionless on average, or separates slightly from the tube wall and then either slips parallel to the mean flow or executes an intermittent stick-slip motion.

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PubMed2003

Doppler effect of nonlinear waves and superspirals in oscillatory media.

Nonlinear waves emitted from a moving source are studied. A meandering spiral in a reaction-diffusion medium provides an example in which waves originate from a source exhibiting a back-and-forth movement in a radial direction. The periodic motion of the source induces a Doppler effect that causes a modulation in wavelength and amplitude of the waves ("superspiral"). Using direct simulations as well as numerical nonlinear analysis within the complex Ginzburg-Landau equation, we show that waves subject to a convective Eckhaus instability can exhibit monotonic growth or decay as well as saturation of these modulations depending on the perturbation frequency. Our findings elucidate recent experimental observations concerning superspirals and their decay to spatiotemporal chaos.

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PubMed2004

Global control of spiral wave dynamics in an excitable domain of circular and elliptical shape.

Experiments performed in a thin layer of the Belousov-Zhabotinsky solution subjected to a global feedback demonstrate the existence of the resonance attractor for meandering spiral waves within a domain of circular shape. In an elliptical domain, the resonance attractor can be destroyed due to a saddle-node bifurcation induced by a variation of the domain eccentricity. This conclusion explains the experimentally observed anchoring of spiral waves at certain points of an elliptical domain and is in good quantitative agreement with numerical data obtained for the Oregonator model.

Journal Article↗

PubMed2004

Quantized spiral tip motion in excitable systems with periodic heterogeneities.

Meandering spiral tips in homogeneous reaction-diffusion systems are characterized by two generically incommensurate radii and frequencies. Here, we create periodic perturbations in space to induce a transition to commensurate radii and frequencies that exhibit a devil's staircase. The plateaus of the staircase correspond to pinned or complex periodic orbits of the spiral tip.

Cell Physiological Phenomena↗

PubMed2004

Monitoring surface charge movement in single elongated semiconductor nanocrystals.

We demonstrate a universal correlation between the spectral linewidth and position of the excitonic transition in the spectral jitter observed from single elongated colloidal quantum dots. Breaking the symmetry of electron and hole confinement as well as of the spatial directions for surface charge diffusion enables us to microscopically track meandering surface charges, providing a novel probe of the particle's nanoenvironment. Spectral diffusion exhibits only a weak temperature dependence, which allows us to uncover the single particle homogeneous linewidth of 50 meV at room temperature.

Journal Article↗

PubMed2004

Peculiar effects of anisotropic diffusion on dynamics of vicinal surfaces.

We report on peculiar behaviors due to anisotropic terrace diffusion on step meandering on a vicinal surface. We find that anisotropy triggers tilted ripples. In addition, if the fast diffusion direction is perpendicular to the steps, the instability is moderate and coarsening is absent, while in the opposite case the instability is promoted, and interrupted coarsening may be observed. Strong enough anisotropy restabilizes the step for almost all step orientations. These findings point to the nontrivial effect of anisotropy and open promising lines of inquiries in the design of surface architectures.

Journal Article↗