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Biaxial model of the surface anchoring of bent-core smectic liquid crystals.

In synclinically tilted smectic phases, bent-core liquid crystal molecules aligned with the director in the plane of a cell boundary will, in general, have their molecular (bow) planes parallel to the boundary, normal to it, or at a well-defined intermediate orientation. A model describing the interaction of such bent-core (banana-shaped) molecules with planar surfaces that distinguishes energetically between molecules lying flat on the surface and those oriented edge on is given by a biaxial modification of the uniaxial surface anchoring expression used for chiral smectics of rod-shaped molecules. When combined with a field-induced straightening of the smectic layers, the model provides a mechanism for the transition from an analog to a bistable director response observed electro-optically in the ferroelectric banana-shaped material (R,S)-MHOBOW.

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Barrier crossing of a semiflexible ring polymer.

Motivated by the dynamics of a membrane in response to an external force, we study the thermally activated crossing of a semiflexible ring polymer over a potential barrier. For the bistable potential of Kramers type smoothly varying over a long length scale, we calculate the crossing rate using the multidimensional Kramers' rate theory and the functional integral method. We find that, due to its conformational fluctuation, the rate for a flexible ring is much larger than that for a stiff ring. For a sufficiently long chain length or a sufficiently weak bending modulus, the ring undergoes a compact-stretch transition. The stretched conformation of the chain results in a decrease of the activation energy and so the further increase of the rate. This result implies that the soft matter conformational flexibility and adaptability facilitate the barrier crossing.

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Noise-induced phase synchronization enhanced by dichotomic noise.

We study the nonlinear response of a stochastic bistable system driven by both a weak periodic signal and a dichotomic noise in terms of stochastic phase synchronization. We show that the effect of noise-induced phase synchronization can be significantly enhanced by the addition of a dichotomic noise.

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Robust stochastic resonance: signal detection and adaptation in impulsive noise.

Stochastic resonance (SR) occurs when noise improves a system performance measure such as a spectral signal-to-noise ratio or a cross-correlation measure. All SR studies have assumed that the forcing noise has finite variance. Most have further assumed that the noise is Gaussian. We show that SR still occurs for the more general case of impulsive or infinite-variance noise. The SR effect fades as the noise grows more impulsive. We study this fading effect on the family of symmetric alpha-stable bell curves that includes the Gaussian bell curve as a special case. These bell curves have thicker tails as the parameter alpha falls from 2 (the Gaussian case) to 1 (the Cauchy case) to even lower values. Thicker tails create more frequent and more violent noise impulses. The main feedback and feedforward models in the SR literature show this fading SR effect for periodic forcing signals when we plot either the signal-to-noise ratio or a signal correlation measure against the dispersion of the alpha-stable noise. Linear regression shows that an exponential law gamma(opt)(alpha)=cA(alpha) describes this relation between the impulsive index alpha and the SR-optimal noise dispersion gamma(opt). The results show that SR is robust against noise "outliers." So SR may be more widespread in nature than previously believed. Such robustness also favors the use of SR in engineering systems. We further show that an adaptive system can learn the optimal noise dispersion for two standard SR models (the quartic bistable model and the FitzHugh-Nagumo neuron model) for the signal-to-noise ratio performance measure. This also favors practical applications of SR and suggests that evolution may have tuned the noise-sensitive parameters of biological systems.

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Quantum decay rates for driven barrier potentials in the strong friction limit.

Quantum decay rates for barrier potentials driven by external stochastic and periodic forces in the strong damping regime are studied. Based on the quantum Smoluchowski equation derived recently by Ankerhold, Pechukas, and Grabert [Phys. Rev. Lett. 87, 086802 (2001)] explicit analytical and numerical results are presented for the case of the resonant activation phenomenon in a bistable potential and the escape from a metastable well with oscillating barrier, respectively. The significant impact of quantum fluctuations is revealed.

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Stochastic resonance of small-world networks.

Stochastic resonance (SR) of a coupled array of bistable oscillators with small-world connectivity is numerically studied. At certain coupling strength, it is found that both temporal SR and spatial synchronization of the oscillators can be considerably improved by increasing the order of randomness of the network due to the long-range couplings. Moreover, our results show that a small fraction of long-range couplings is sufficient to obtain great improvement in SR and synchronization.

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Birhythmicity induced by perturbing an oscillating electrochemical system.

We describe the generation of new limit cycles in electrochemical systems under the influence of external periodic perturbations. For certain specific parameters of a nonharmonic forcing function, two coexisting periodic orbits can be generated from a single limit cycle observed in the unperturbed dynamics. This inception of birhythmicity (bistability) is observed in both simulations and actual experiments involving potentiostatic electrodissolution of copper in an acetate buffer.

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Oscillatory systems driven by noise: frequency and phase synchronization.

The phenomenon of effective phase synchronization in stochastic oscillatory systems can be quantified by an average frequency and a phase diffusion coefficient. A different approach to compute the noise-averaged frequency is put forward. The method is based on a threshold crossing rate pioneered by Rice. After the introduction of the Rice frequency for noisy systems we compare this quantifier with those obtained in the context of other phase concepts, such as the natural and the Hilbert phase, respectively. It is demonstrated that the average Rice frequency R typically supersedes the Hilbert frequency H, i.e. R > or = H. We investigate next the Rice frequency for the harmonic and the damped, bistable Kramers oscillator, both without and with external periodic driving. Exact and approximative analytic results are corroborated by numerical simulation results. Our results complement and extend previous findings for the case of noise-driven inertial systems.

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Drifting pattern domains in a reaction-diffusion system with nonlocal coupling.

Drifting pattern domains (DPDs), i.e., moving localized patches of traveling waves embedded in a stationary (Turing) pattern background and vice versa, are observed in simulations of a reaction-diffusion model with nonlocal coupling. Within this model, a region of bistability between Turing patterns and traveling waves arises from a codimension-2 Turing-wave bifurcation (TWB). DPDs are found within that region in a substantial distance from the TWB. We investigated the dynamics of single interfaces between Turing and wave patterns. It is found that DPDs exist due to a locking of the interface velocities, which is imposed by the absence of space-time defects near these interfaces.

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Slow excitation supports propagation of slow pulses in networks of excitatory and inhibitory populations.

We study the propagation of traveling solitary pulses in one-dimensional networks of excitatory and inhibitory neurons. Each neuron is represented by the integrate-and-fire model, and is allowed to fire only one spike. Two types of propagating pulses are observed. During fast pulses, inhibitory neurons fire a short time before or after the excitatory neurons. During slow pulses, inhibitory cells fire well before neighboring excitatory cells, and potentials of excitatory cells become negative and then positive before they fire. There is a bistable parameter regime in which both fast and slow pulses can propagate. Fast pulses can propagate at low levels of inhibition, are affected by fast excitation but are almost unaffected by slow excitation, and are easily elicited by stimulating groups of neurons. In contrast, slow pulses can propagate at intermediate levels of inhibition, and are difficult to evoke. They can propagate without slow excitation, but slow excitation makes their propagation substantially more robust. Fast pulses can propagate in a wider parameter regime if inhibition decays slowly with time, whereas slow pulses can propagate in a wider parameter regime if the passive time constant of inhibitory cells is large. Strong inhibitory-to-inhibitory conductance eliminates the slow pulses and converts the fast traveling pulses into irregular pulses, in which the inhibitory neurons segregate into two groups that have different firing delays with respect to their neighboring excitatory cells. In general, the velocity of the fast pulse increases with the axonal conductance velocity c, but there are cases in which it decreases with c. We suggest that the fast and slow pulses observed in our model correspond to the fast and slow propagating activity observed in experiments on neocortical slices.

Biophysical Phenomena↗

Tunable front interaction and localization of periodically forced waves.

In systems that exhibit a bistability between nonlinear traveling waves and the basic state, pairs of fronts connecting these two states can form localized wave pulses whose stability depends on the interaction between the fronts. We investigate wave pulses within the framework of coupled Ginzburg-Landau equations describing the traveling-wave amplitudes. We find that the introduction of resonant temporal forcing results in a tunable mechanism for stabilizing such wave pulses. In contrast to other localization mechanisms the temporal forcing can achieve localization by a repulsive as well as by an attractive interaction between the fronts. Systems for which the results are expected to be relevant include binary-mixture convection and electroconvection in nematic liquid crystals.

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Localized vegetation patches: a self-organized response to resource scarcity.

We show that spatial self-organization allows vegetation to survive greater resource limitation. Isolated vegetation patches observed in nutrient-poor territories of South America and West Africa are interpreted as localized structures arising from the bistability between the bare state and the patchy vegetation state.

Africa, Western↗

Vibrational resonance in a noise-induced structure.

We report on the effect of vibrational resonance in a spatially extended system of coupled noisy oscillators under the action of two periodic forces, a low-frequency one (signal) and a high-frequency one (carrier). Vibrational resonance manifests itself in the fact that for optimally selected values of high-frequency force amplitude, the response of the system to a low-frequency signal is optimal. This phenomenon is a synthesis of two effects, a noise-induced phase transition leading to bistability, and a conventional vibrational resonance, resulting in the optimization of signal processing. Numerical simulations, which demonstrate this effect for an extended system, can be understood by means of a zero-dimensional "effective" model. The behavior of this "effective" model is also confirmed by an experimental realization of an electronic circuit.

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Memory driven Ginzburg-Landau model.

The time evolution of a bistable Ginzburg-Landau model (GL) with a non-Markovian memory term of strength lambda is studied. Due to the nonlinear feedback coupling, the two branches of the stationary solution are not only controlled by the sign of the initial condition P(0), but also by the strength and the sign of lambda. Whereas in case of a positive lambda the stationary solution is ever reduced through the memory, it may be increasing for lambda<0. In that case the system is also able to switch over between both branches of the stationary solution. Such an ability is exclusively achieved for a negative lambda within an interval -u<lambda<lambda(c), where lambda(c) is a critical memory strength and u is the strength of the conventional nonlinear term within the GL. The complete phase diagram is presented in the P(0)-lambda plane analytically and numerically.

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Effect of asymmetry on stochastic resonance and stochastic resonance induced by multiplicative noise and by mean-field coupling.

In the paper, we investigate the effect of asymmetry of the potential on stochastic resonance (SR) for a model with an asymmetric bistable potential and driven by additive noise, the signal-to-noise ratio (SNR) for a model with a monostable potential and driven by additive and multiplicative noises, and the SNR for a mean-field coupled model with infinite globally coupling oscillators driven by additive noises. It is shown that for the first model,the asymmetry of the potential can weaken the phenomenon of SR; for the second and third models, a SR induced by multiplicative noise and a different one caused by mean-field coupling are found.

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Symmetries of the Doi kinetic theory for nematic polymers of arbitrary aspect ratio: at rest and in linear flows.

The Doi theory has successfully modeled the monodomain shear flow problem for rigid, rodlike nematic polymers. Numerical simulations of the Smoluchowski equation for the orientational probability distribution function (PDF) predict monodomain attractors in regions of nematic concentration N and shear rate gamma. Theoretical work has focused on approximate constructions of PDF solutions in linear flow regimes. Here we develop a collection of simple observations, expressed by symmetries of the Smoluchowski equation, which imply global properties that all PDF solutions must obey. The well-known orientational degeneracy of quiescent nematics is a continuous O(3) symmetry. In simple shear, a discrete reflection symmetry survives that is evident in recent numerical simulations and implies bistability of out-of-plane attractors; and rodlike and discotic nematic liquids of reciprocal aspect ratio respond identically up to a fixed rotation of the PDF. Finally, we show the orientational effects due to varying molecular aspect ratio in any linear flow are equivalent to varying the straining component of the flow field.

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Self-replication of a pulse in excitable reaction-diffusion systems.

We investigate self-replication of a pulse in Bonhoffer-van der Pol type reaction-diffusion systems in one dimension. The interface dynamics of front and back of a pulse developed for a bistable system is extended to a monostable case, which is useful to clarify the mechanism of the self-replication. We shall show that the threshold parameter for excitability plays the central role for self-replication. The present theory can be applied not only to a symmetric pulse, but also to a propagating asymmetric pulse.

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