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PubMed2000

Macroscopic effects of the perturbation of the particle velocity distribution in a trigger wave

Departure from the equilibrium particle velocity distribution induced by a chemical reaction is studied in an inhomogeneous chemical bistable system in which a trigger wave can propagate. These nonequilibrium effects influence the speed and shape of the trigger wave propagating between the two stable stationary states. In contrast to the Fisher front, the discretization of the variables and the internal fluctuations do not sensitively modify the macroscopic properties of the trigger wave. Analytical results deduced from the Boltzmann equation agree well with microscopic simulations using Bird's method. Both approaches lead to large relative corrections to the front speed, in particular for parameter values close to that corresponding to a stationary interface between the two stable states.

Journal Article↗
PubMed2000

Shear-induced structural transitions in newtonian non-newtonian two-phase flow

We show the existence under shear flow of steady states in a two-phase region of a brine-surfactant system in which lyotropic dilute lamellar (non-Newtonian) and sponge (Newtonian) phases are coexisting. At high shear rates and low sponge phase-volume fractions, we report on the existence of a dynamic transition corresponding to the formation of a colloidal crystal of multilamellar vesicles (or "onions") immersed in the sponge matrix. As the sponge phase-volume fraction increases, this transition exhibits a hysteresis loop leading to a structural bistability of the two-phase flow. Contrary to single phase lamellar systems where it is always 100%, the onion volume fraction can be monitored continuously from 0 to 100 %.

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PubMed2000

Long-range interaction and nonlinear localized modes in photonic crystal waveguides

We develop the theory of nonlinear localized modes (intrinsic localized modes or discrete breathers) in two-dimensional (2D) photonic crystal waveguides. We consider different geometries of the waveguides created by an array of nonlinear dielectric rods embedded into an otherwise perfect linear 2D photonic crystal, and demonstrate that the effective interaction in such waveguides is nonlocal, being described by a nonlinear lattice model with long-range coupling and nonlocal nonlinearity. We reveal the existence of different types of nonlinear guided mode that are also localized in the waveguide direction, and describe their unique properties, including bistability.

Journal Article↗
PubMed2000

Nonlinear stochastic resonance: the saga of anomalous output-input gain

We reconsider stochastic resonance (SR) for an overdamped bistable dynamics driven by a harmonic force and Gaussian noise from the viewpoint of the gain behavior, i.e., the signal-to-noise ratio (SNR) at the output divided by that at the input. The primary issue addressed in this work is whether a gain exceeding unity can occur for this archetypal SR model, for subthreshold signals that are beyond the regime of validity of linear response theory: in contrast to nondynamical threshold systems, we find that the nonlinear gain in this conventional SR system exceeds unity only for suprathreshold signals, where SR for the spectral amplification and/or the SNR no longer occurs. Moreover, the gain assumes, at weak to moderate noise strengths, rather small (minimal) values for near-threshold signal amplitudes. The SNR gain generically exhibits a distinctive nonmonotonic behavior versus both the signal amplitude at fixed noise intensity and the noise intensity at fixed signal amplitude. We also test the validity of linear response theory; this approximation is strongly violated for weak noise. At strong noise, however, its validity regime extends well into the large driving regime above threshold. The prominent role of physically realistic noise color is studied for exponentially correlated Gaussian noise of constant intensity scaling and also for constant variance scaling; the latter produces a characteristic, resonancelike gain behavior. The gain for this typical SR setup is further contrasted with the gain behavior for a "soft" potential model.

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PubMed2000

Efficient dynamic importance sampling of rare events in one dimension.

Exploiting stochastic path-integral theory, we obtain by simulation substantial gains in efficiency for the computation of reaction rates in one-dimensional, bistable, overdamped stochastic systems. Using a well-defined measure of efficiency, we compare implementations of "dynamic importance sampling" (DIMS) methods to unbiased simulation. The best DIMS algorithms are shown to increase efficiency by factors of approximately 20 for a 5k(B)T barrier height and 300 for 9k(B)T, compared to unbiased simulation. The gains result from close emulation of natural (unbiased), instantonlike crossing events with artificially decreased waiting times between events that are corrected for in rate calculations. The artificial crossing events are generated using the closed-form solution to the most probable crossing event described by the Onsager-Machlup action. While the best biasing methods require the second derivative of the potential (resulting from the "Jacobian" term in the action, which is discussed at length), algorithms employing solely the first derivative do nearly as well. We discuss the importance of one-dimensional models to larger systems, and suggest extensions to higher-dimensional systems.

Algorithms↗
PubMed2001

Coil-to-stretch transition, kink formation, and efficient barrier crossing of a flexible chain.

We study the thermally activated barrier crossing of a linear, flexible chain (polymer) under the Kramers bistable potential using the multidimensional barrier crossing theory and the functional integral method. We find that above a critical chain length or below a critical chain spring constant the chain at the barrier top undergoes coil-to-stretch transition, resulting in the formation of a kink. The emergence of the kink mode renormalizes the activation energy to a smaller value so as to facilitate the barrier crossing. In addition to this, the larger fluctuation of the polymer in the unstable region of the potential (compared to that in the confining well) further reduces the free energy barrier, and greatly enhances the crossing rate of a flexible chain. We calculate analytically the crossing rates and confirm the results by numerical simulations. The polymer in barrier crossing thus reveals its conformational flexibility and adjustment to external forces as characteristic features of soft matter dynamics.

Journal Article↗
PubMed2001

Global dynamics and stochastic resonance of the forced FitzHugh-Nagumo neuron model.

We have analyzed the responses of an excitable FitzHugh-Nagumo neuron model to a weak periodic signal with and without noise. In contrast to previous studies which have dealt with stochastic resonance in the excitable model when the model with periodic input has only one stable attractor, we have focused our attention on the relationship between the global dynamics of the forced excitable neuron model and stochastic resonance. Our results show that for some parameters the forced FitzHugh-Nagumo neuron model has two attractors: the small-amplitude subthreshold periodic oscillation and the large-amplitude suprathreshold periodic oscillation. Random transitions between these two periodic oscillations are the essential mechanism underlying stochastic resonance in this model. Differences of such stochastic resonance to that in a classical bistable system and the excitable system are discussed. We also report that the state of the basin of attraction has a significant effect on the stability of neuronal firings, in the sense that the fractal basin boundary of the system enhances the noise-induced transitions.

Action Potentials↗
PubMed2001

Noise-assisted transmission of binary information: theory and experiment.

We study the response of a bistable vertical cavity surface emitting laser to an aperiodic binary signal, by adding a variable amount of noise. The resulting behavior is an example of aperiodic stochastic resonance, and in this work we give a detailed comparison between analytical and numerical results and accurate experimental measurements. We characterize the phenomenon by using different appropriate indicators, which also allow us to quantify the binary information transmission. We show that the quality of the transmission is enhanced by a suitable amount of noise, and we give a physical picture of the phenomenon.

Journal Article↗
PubMed2001

Analysis of front interaction and control in stationary patterns of reaction-diffusion systems.

We have analyzed the stability of one-dimensional patterns in one- or two-variable reaction-diffusion systems, by analyzing the interaction between adjacent fronts and between fronts and the boundaries in bounded systems. We have used model reduction to a presentation that follows the front positions while using approximate expressions for front velocities, in order to study various control modes in such systems. These results were corroborated by a few numerical experiments. A stationary single front or a pattern with n fronts is typically unstable due to the interaction between fronts. The two simplest control modes, global control and point-sensor control (pinning), will arrest a front in a single-variable problem since both control modes, in fact, respond to the front position. In a two-variable system incorporating a localized inhibitor, in the domain of bistable kinetics, global control may stabilize a single front only in short systems while point-sensor control can arrest such a front in any system size. Neither of these control modes can stabilize an n-front pattern, in either one- or two-variable systems, and that task calls for a distributed actuator. A single space-dependent actuator that is spatially qualitatively similar to the patterned setpoint, and which responds to the sum of deviations in front positions, may stabilize a pattern that approximates the desired state. The deviation between the two may be sufficiently small to render the obtained state satisfactory. An extension of these results to diffusion-convection-reaction systems are outlined.

Journal Article↗
PubMed2001

First-order Fréedericksz transition in the presence of light-driven feedback in nematic liquid crystals.

We show that feedback, which introduces a dependence of the electric field on the liquid-crystal director, renders the Fréedericksz transition first order. Experimentally, the feedback is introduced as a light loop in a liquid-crystal light valve. Theoretically, we include the feedback term into the Frank free energy and we derive an amplitude equation that is valid close to the transition. The theoretical description is in qualitative agreement with the experimental observations. Depending on the values of the feedback parameters, both theory and experiment exhibit bistability, propagation of fronts, and a Maxwell point.

Journal Article↗
PubMed2001

Analytical and numerical investigation of escape rate for a noise driven bath.

We consider a system-reservoir model where the reservoir is modulated by an external noise. Both the internal noise of the reservoir and the external noise are stationary, Gaussian, and are characterized by arbitrary decaying correlation functions. Based on a relation between the dissipation of the system and the response function of the reservoir driven by external noise, we numerically examine the model using a full bistable potential to show that one can recover the turn-over features of the usual Kramers' dynamics when the external noise modulates the reservoir rather than the system directly. We derive the generalized Kramers' rate for this nonequilibrium open system. The theoretical results are verified by numerical simulation.

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PubMed2001

Thermal resonance in signal transmission.

We use temperature tuning to control signal propagation in simple one-dimensional arrays of masses connected by hard anharmonic springs and with no local potentials. In our numerical model a sustained signal is applied at one site of a chain immersed in a thermal environment and the signal-to-noise ratio is measured at each oscillator. We show that raising the temperature can lead to enhanced signal propagation along the chain, resulting in thermal resonance effects akin to the resonance observed in arrays of bistable systems.

Journal Article↗
PubMed2001

Bifurcations and global stability of synchronized stationary states in the Kuramoto model for oscillator populations.

Bistability between synchronized stationary states is shown to occur in large populations of nonlinearly coupled random oscillators (Kuramoto model), governed by trimodal natural frequency distributions. Numerical simulations and a numerical investigation of bifurcating states provide evidence of global stability of such states, subject to unimodal, bimodal, and trimodal frequency distributions. All this may be important in the framework of large superconducting Josephson junctions arrays, as well as of neural networks.

Journal Article↗
PubMed2001

Continuum description of avalanches in granular media.

We develop a continuum description of partially fluidized granular flows. Our theory is based on the hydrodynamic equation for the flow coupled with the order parameter equation, which describes the transition between flowing and static components of the granular system. This theory captures important phenomenology recently observed in experiments with granular flows on rough inclined planes [A. Daerr and S. Douady, Nature (London) 399, 241 (1999)]: layer bistability, and transition from triangular avalanches propagating downhill at small inclination angles to balloon-shaped avalanches also propagating uphill for larger angles.

Journal Article↗
PubMed2001

Efficient transition path sampling for nonequilibrium stochastic dynamics.

The transition path sampling methodology is adapted to the efficient sampling of large fluctuations in nonequilibrium systems evolving according to Langevin's equations of motion. This technique is used to simulate the behavior of the bistable Maier-Stein system at noise intensities much lower than those previously possible.

Journal Article↗
PubMed2001

Spatiotemporal dynamics near a supercritical Turing-Hopf bifurcation in a two-dimensional reaction-diffusion system.

Pattern formation in semiconductor heterostructures is studied on the basis of a spatially two-dimensional model of reaction-diffusion type. In particular, we investigate the neighborhood of a codimension-two Turing-Hopf instability by analytical methods. Amplitude equations are derived which predict the absence of mixed modes but extended ranges of bistability between homogeneous oscillatory states and hexagonal Turing patterns. Our results are confirmed by numerical simulations. The features are not confined to a neighborhood of the bifurcation point so that the conclusions of the weakly nonlinear analysis explain the observations in large portions of the parameter space at least qualitatively

Journal Article↗
PubMed2001

Stochastic resonant memory storage device.

We show that an extended system operating in the regime of stochastic resonance can act as a short-term memory device. The system under study is a ring of overdamped bistable oscillators coupled directionally, being each also subject to an external source of Gaussian white noise (the noise sources are independent). A single oscillator is driven by an external periodic force, assumed to act only over the time that the signal takes to traverse the whole ring. A traveling wave is then found to be transmitted several times along the ring with a small damping, provided that the driven oscillator operates in a regime close to stochastic resonance. If noise is suppressed from any oscillator of the chain, the traveling wave is immediately damped. The ring is thus found to act as a short-term memory device in which the stored information (one bit, corresponding to the presence or absence of the external driving) is sustained by noise during a characteristic time T(mem).

Journal Article↗
PubMed2001

Experimental observation of stochastic resonance in a linear electronic array.

We report the experimental observation of array-enhanced stochastic resonance, spatiotemporal synchronization, and noise-enhanced propagation in a simple coupled linear array of bistable electronic triggers. In addition, we highlight an analogy between charge density wave (CDW) like conductivity and spatiotemporal synchronization in stochastic resonances, several aspects of which are supported by the experimental evidence presented here. This may prove to be important in the understanding of nonlinear conductivity in CDW solids.

Journal Article↗