Reentrant transition induced by multiplicative noise in the time-dependent Ginzburg-Landau model

Dynamic magnetic characteristics of the kinetic Ising model under the influence of randomness

In this paper, we propose to solve the issues of long-range or next-neighbor interactions by introducing randomness. This approach is applied to the square lattice Ising model. The Monte Carlo method with the Metropolis algorithm is utilized to calculate the critical temperature T_{C}^{*} under equilibrium thermodynamic phase transition conditions and to investigate the characterization of randomness in terms of magnetization. In order to further characterize the effect of this randomness on the magnetic system, clustering coefficients C_{p} are introduced. Furthermore, we investigate a number of dynamic magnetic behaviors, including dynamic hysteresis behaviors and metamagnetic anomalies. The results indicate that noise has the effect of destabilizing the system and promoting the dynamic phase transition. When the system is subjected to noise, the effect of this noise can be mitigated by the addition of a time-oscillating magnetic field. Finally, the evolution of anomalous metamagnetic fluctuations under the influence of white noise is examined. The relationship between the bias field corresponding to the peak of the curve h_{b}^{peak} and the noise parameter σ satisfies the exponential growth equation, which is consistent with other results.

Wave number selection in the presence of noise: Experimental results

In this study, we consider how the wave number selection in spherical Couette flow, in the transition to azimuthal waves after the first instability, occurs in the presence of noise. The outer sphere was held stationary, while the inner sphere rotational speed was increased linearly from a subcritical flow to a supercritical one. In a supercritical flow, one of two possible flow states, each with different azimuthal wave numbers, can appear depending upon the initial and final Reynolds numbers and the acceleration value. Noise perturbations were added by introducing small disturbances into the rotational speed signal. With an increasing noise amplitude, a change in the dominant wave number from m to m ± 1 was found to occur at the same initial and final Reynolds numbers and acceleration values. The flow velocity measurements were conducted by using laser Doppler anemometry. Using these results, the role of noise as well as the behaviour of the amplitudes of the competing modes in their stages of damping and growth were determined.

Discontinuous transitions in globally coupled potential systems with additive noise

An infinite array of globally coupled overdamped constituents moving in a double-well potential with nth order saturation term under the influence of additive Gaussian white noise is investigated. The system exhibits a continuous phase transition from a symmetric phase to a symmetry-broken phase. The qualitative behavior is independent on n. The critical point is calculated for strong and for weak noise; these limits are also bounds for the critical point. Introducing an additional nonlinearity, such that the potential can have up to three minima, leads to richer behavior. There the parameter space divides into three regions: a region with a symmetric phase, a region with a phase of broken symmetry and a region where both phases coexist. The region of coexistence collapses into one of the others via a discontinuous phase transition, whereas the transition between the symmetric phase and the phase of broken symmetry is continuous. The tricritical point where the three regions intersect can be calculated for strong and for weak noise. These limiting values form tight bounds on the tricritical point. In the region of coexistence simulations of finite systems are performed. One finds that the stationary distribution of finite but large systems differs qualitatively from the one of the infinite system. Hence the limits of stationarity and large system size do not commute.

Critical manifold of globally coupled overdamped anharmonic oscillators driven by additive Gaussian white noise

We consider an infinite array of globally coupled overdamped anharmonic oscillators subject to additive Gaussian white noise which is closely related to the mean field Φ(4)-Ginzburg-Landau model. We prove the existence of a well-behaved critical manifold in the parameter space which separates a symmetric phase from a symmetry broken phase. Given two of the system parameters, there is a unique critical value of the third. The proof exploits that the critical control parameter a(c) is bounded by its limit values for weak and strong noise. In these limits, the mechanism of symmetry breaking differs. For weak noise, the distribution is Gaussian and the symmetry is broken as the whole distribution is shifted in either the positive or the negative direction. For strong noise, there is a symmetric double-peak distribution and the symmetry is broken as the weights of the peaks become different. We derive an ordinary differential equation whose solution describes the critical manifold. Using a series ansatz to solve this differential equation, we determine the critical manifold for weak and strong noise and compare it to numerical results. We derive analytic expressions for the order parameter and the susceptibility close to the critical manifold.

Spatiotemporal bounded noises and transitions induced by them in solutions of the real Ginzburg-Landau model

In this work, we introduce two spatiotemporal colored bounded noises, based on the zero-dimensional Cai-Lin and Tsallis-Borland noises. Then we study and characterize the dependence of the defined stochastic processes on both a temporal correlation parameter τ and a spatial coupling parameter λ. In particular, we found that varying λ may induce a transition of the distribution of the noise from bimodality to unimodality. With the aim of investigating the role played by bounded noises in nonlinear dynamical systems, we analyze the behavior of the real Ginzburg-Landau time-varying model additively perturbed by such noises. The observed phase transition phenomenology is quite different from that observed when the perturbations are unbounded. In particular, we observed an inverse order-to-disorder transition and a reentrant transition, with dependence on the specific type of bounded noise.

Versatility of cooperative transcriptional activation: a thermodynamical modeling analysis for greater-than-additive and less-than-additive effects

We derive a statistical model of transcriptional activation using equilibrium thermodynamics of chemical reactions. We examine to what extent this statistical model predicts synergy effects of cooperative activation of gene expression. We determine parameter domains in which greater-than-additive and less-than-additive effects are predicted for cooperative regulation by two activators. We show that the statistical approach can be used to identify different causes of synergistic greater-than-additive effects: nonlinearities of the thermostatistical transcriptional machinery and three-body interactions between RNA polymerase and two activators. In particular, our model-based analysis suggests that at low transcription factor concentrations cooperative activation cannot yield synergistic greater-than-additive effects, i.e., DNA transcription can only exhibit less-than-additive effects. Accordingly, transcriptional activity turns from synergistic greater-than-additive responses at relatively high transcription factor concentrations into less-than-additive responses at relatively low concentrations. In addition, two types of re-entrant phenomena are predicted. First, our analysis predicts that under particular circumstances transcriptional activity will feature a sequence of less-than-additive, greater-than-additive, and eventually less-than-additive effects when for fixed activator concentrations the regulatory impact of activators on the binding of RNA polymerase to the promoter increases from weak, to moderate, to strong. Second, for appropriate promoter conditions when activator concentrations are increased then the aforementioned re-entrant sequence of less-than-additive, greater-than-additive, and less-than-additive effects is predicted as well. Finally, our model-based analysis suggests that even for weak activators that individually induce only negligible increases in promoter activity, promoter activity can exhibit greater-than-additive responses when transcription factors and RNA polymerase interact by means of three-body interactions. Overall, we show that versatility of transcriptional activation is brought about by nonlinearities of transcriptional response functions and interactions between transcription factors, RNA polymerase and DNA.

Front propagation sustained by additive noise

The effect of noise in a motionless front between a periodic spatial state and an homogeneous one is studied. Numerical simulations show that noise induces front propagation. From the subcritical Swift-Hohenberg equation with noise, we deduce an adequate equation for the envelope and the core of the front. The equation of the core of the front is characterized by an asymmetrical periodic potential plus additive noise. The conversion of random fluctuations into direct motion of the core of the front is responsible of the propagation. We obtain an analytical expression for the velocity of the front, which is in good agreement with numerical simulations.

Additive noise induces front propagation

The effect of additive noise on a static front that connects a stable homogeneous state with an also stable but spatially periodic state is studied. Numerical simulations show that noise induces front propagation. The conversion of random fluctuations into direct motion of the front's core is responsible of the propagation; noise prefers to create or remove a bump, because the necessary perturbations to nucleate or destroy a bump are different. From a prototype model with noise, we deduce an adequate equation for the front's core. An analytical expression for the front velocity is deduced, which is in good agreement with numerical simulations.

Noise-driven mechanism for pattern formation

We extend the mechanism for noise-induced phase transitions proposed by Ibañes et al. [Phys. Rev. Lett. 87, 020601 (2001)] to pattern formation phenomena. In contrast with known mechanisms for pure noise-induced pattern formation, this mechanism is not driven by a short-time instability amplified by collective effects. The phenomenon is analyzed by means of a modulated mean field approximation and numerical simulations.

Critical behavior of nonequilibrium phase transitions to magnetically ordered states

We describe nonequilibrium phase transitions in arrays of dynamical systems with cubic nonlinearity driven by multiplicative Gaussian white noise. Depending on the sign of the spatial coupling we observe transitions to ferromagnetic or antiferromagnetic ordered states. We discuss the phase diagram, the order of the transitions, and the critical behavior. For global coupling we show analytically that the critical exponent of the magnetization exhibits a transition from the value 1/2 to a nonuniversal behavior depending on the ratio of noise strength to the magnitude of the spatial coupling.

Analytical and numerical studies of noise-induced synchronization of chaotic systems

We study the effect that the injection of a common source of noise has on the trajectories of chaotic systems, addressing some contradictory results present in the literature. We present particular examples of one-dimensional maps and the Lorenz system, both in the chaotic region, and give numerical evidence showing that the addition of a common noise to different trajectories, which start from different initial conditions, leads eventually to their perfect synchronization. When synchronization occurs, the largest Lyapunov exponent becomes negative. For a simple map we are able to show this phenomenon analytically. Finally, we analyze the structural stability of the phenomenon. (c) 2001 American Institute of Physics.

Random Ginzburg-Landau model revisited: reentrant phase transitions

We analyze the phase diagram of the random Ginzburg-Landau model, where a quenched dichotomous noise affects the control parameter. We show that the system exhibits two types of counterintuitive reentrant second-order phase transitions. In the first case, increasing the coupling drives the system from a disordered to an ordered state and then back to a disordered state. In the second case, increasing the intensity of the quenched noise, the system goes from an ordered phase to a disordered phase and back to an ordered state. We discuss the general mechanism that produces these reentrant phase transitions, showing that it may appear in other physical systems, such as a modification of the spin-1 Blume-Capel model proposed to describe the critical behavior of helium mixtures in a random medium.

Multivariate Ornstein-Uhlenbeck processes with mean-field dependent coefficients: application to postural sway

We study the transient and stationary behavior of many-particle systems in terms of multivariate Ornstein-Uhlenbeck processes with friction and diffusion coefficients that depend nonlinearly on process mean fields. Mean-field approximations of this kind of system are derived in terms of Fokker-Planck equations. In such systems, multiple stationary solutions as well as bifurcations of stationary solutions may occur. In addition, strictly monotonically decreasing steady-state autocorrelation functions that decay faster than exponential functions are found, which are used to describe the erratic motion of the center of pressure during quiet standing.

Negative resistance and anomalous hysteresis in a collective molecular motor

A spatially extended model for a collective molecular motor is presented. The system is driven far from equilibrium by a quenched additive noise. As a result, it exhibits anomalous transport properties, namely, negative resistance and a clockwise hysteresis cycle. The phase diagram and the region of negative resistance are calculated using a Weiss mean field theory. Intuitive explanations of the anomalous transport properties as well as details of its energetics are given.

Nonequilibrium phase transitions induced by multiplicative noise: effects of self-correlation

A recently introduced lattice model, describing an extended system which exhibits a reentrant (symmetry-breaking, second-order) noise-induced nonequilibrium phase transition, is studied under the assumption that the multiplicative noise leading to the transition is colored. Within an effective Markovian approximation and a mean-field scheme it is found that when the self-correlation time tau of the noise is different from zero, the transition is also reentrant with respect to the spatial coupling D. In other words, at variance with what one expects for equilibrium phase transitions, a large enough value of D favors disorder. Moreover, except for a small region in the parameter subspace determined by the noise intensity sigma and D, an increase in tau usually prevents the formation of an ordered state. These effects are supported by numerical simulations.

Nonequilibrium first-order phase transition induced by additive noise

We show that a nonequilibrium first-order phase transition can be induced by additive noise. As a model system to study this phenomenon, we consider a nonlinear lattice of overdamped oscillators with both additive and multiplicative noise terms. Predictions from mean field theory are successfully confirmed by numerical simulations. A physical explanation for the mechanism of the transition is given.

Noise-induced phase separation: mean-field results

We present a study of a phase-separation process induced by the presence of spatially correlated multiplicative noise. We develop a mean-field approach suitable for conserved-order-parameter systems and use it to obtain the phase diagram of the model. Mean-field results are compared with numerical simulations of the complete model in two dimensions. Additionally, a comparison between the noise-driven dynamics of conserved and nonconserved systems is made at the level of the mean-field approximation.

Recent results on multiplicative noise

Recent developments in the analysis of Langevin equations with multiplicative noise (MN) are reported. In particular, we (i) present numerical simulations in three dimensions showing that the MN equation exhibits, like the Kardar-Parisi-Zhang (KPZ) equation, both a weak coupling fixed point and a strong coupling phase, supporting the proposed relation between MN and KPZ; (ii) present a dimensional and mean-field analysis of the MN equation to compute critical exponents; (iii) show that the phenomenon of the noise-induced ordering transition associated with the MN equation appears only in the Stratonovich representation and not in the Ito one; and (iv) report the presence of a first-order-like phase transition at zero spatial coupling, supporting the fact that this is the minimum model for noise-induced ordering transitions.