Noise-induced Nonequilibrium Phase Transition Research Articles

Stochastic model of domain kinetics in biological membranes

A stochastic storage model based on the behavior of macroscopic variables of the system is used to describe the kinetics of raft-like domains in biological membranes. For a simple output model, we examine the features of the system behavior corresponding to the noise-induced nonequilibrium phase transitions. Characteristics of the behavior of the statistical system are obtained: an explicit form of the stationary distribution of the number of domains; ratios for the phase transition points; the expression for the first two moments of the random domain concentration, and the expression for the lifetime of membrane domains in the stationary state.

Steady state characteristics in FHN neural system driven by correlated non-Gaussian noise and Gaussian noise

Recently, the dynamics problems of nonlinear systems driven by noises have attracted considerable attention. The researches indicate that the noise plays a determinative role in system evolution. This irregular random interference does not always play a negative role in the macro order. Sometimes it can play a positive role. The various effects of noise are found in physics, biology, chemistry and other fields, such as noise-induced non-equilibrium phase transition, noise-enhanced system stability, stochastic resonance, etc. Especially, in the field of biology, the effects of noise on life process are significant. At present, a large number of researchers have studied the kinetic properties of the neuron system subjected to noises. However, these studies focus on the Gaussian noise, while the researches about non-Gaussian noise are less. In fact, it is found that all the noise sources among neuronal systems, physical systems and biological systems tend to non-Gaussian distribution. So it is reasonable to consider the effects of the non-Gaussian noise on systems, and it is closer to the actual process. Therefore, it has some practical significance to study the FHN system driven by the non-Gaussian noise and analyze the kinetic properties of this system. In this work, we study the stationary probability distribution (SPD) in FitzHugh-Nagumo (FHN) neural system driven by correlated multiplicative non-Gaussian noise and additive Gaussian white noise. Using the path integral approach and the unified colored approximation, the analytical expression of the stationary probability distribution is first derived, and then the change regulations of the SPD with the strength and relevance between multiplicative noise and additive noise are analyzed. After that, the simulation results show that the intensity of multiplicative noise, the intensity of additive noise, the correlation time of the non-Gaussian noise and the cross-correlation strength between noises can induce non-equilibrium phase transition. This means that the effect of the non-Gaussian noise intensity on SPD is the same as that of the Gaussian noise intensity. However, the non-Gaussian noise deviation parameter cannot induce non-equilibrium phase transition. Moreover, we also find that the increases of the multiplicative noise intensity and the cross-correlation strength between noises are conducive to the conversion of the exciting state into the resting state. And with the additive noise intensity and the correlation time increasing, the conversion of the resting state into the exciting state becomes obvious. Meanwhile, the increase of non-Gaussian noise deviation parameter increases the probability of staying in the resting state.

Noise-Induced Phase Transition: Zero-Dimensional Brownian Particles Varying between Ergodicity and Nonergodicity

We study in phase space a zero-dimensional system of Brownian particles which move in a periodic potential and subject to an internal time derivative Ornstein–Uhlenbeck noise. To resolve the Fokker–Planck equation in such a case, we propose an approximate analytical method. The theoretical predictions exhibit a second order noise-induced nonequilibrium phase transition, which is confirmed by numerical simulation results. The phase transition brings the system from an ergodicity to a nonergodicity phase as the potential barrier height decreases.

The Role of Noise-Induced Nonequilibrium Phase Transitions in the Structurization of Hydrodynamic Turbulence

The aim of this paper is to develop a continual theory of developed structurized turbulence in shear flows in a compressible fluid modeled by a superposition of two mutually penetrating continuums, where the first continuum refers to the averaged field of turbulent motion, and the second, to the turbulent spacetime chaos associated with the fine-grained fluctuation motion. Incorporating into the thermohydrodynamic description of the subsystem of turbulent chaos a set of internal stochastic coordinates q k (like the locally averaged rate of turbulent energy dissipation), which characterize the structure and temporal evolution of the vorticity of the pulsational hydrodynamic field, has made it possible to use methods of statistical nonequilibrium thermodynamics to derive stochastic differential equations for these parameters and the corresponding Fokker-Planck-Kolmogorov equations for the probability density of transition. In accordance with the modified Kolmogorov similarity theory, positive fluctuating parameters q k are believed to obey the lognormal distribution in the stationary state of chaos. The Gaussian white noise with zero memory, which provides an idealized description of the real noise of vortex chaos with a very short but still finite memory, is used to model the force effect of the noise of chaos (whose fluctuations are due to the cumulative effect of numerous factors determining the state of the turbulized medium). A general concept of the birth of coherent structures in the thermodynamically open subsystem of turbulent chaos is formulated, which attributes the formation of such structures to the phenomenon of nonequilibrium phase transitions induced by the multiplicative noise of chaos during an increase of supercriticality. The interrelation between such transitions and the process of self-organization—the development of ordered “multimolecular” formations with lower symmetry as compared to that of the initial state—is discussed. The ultimate aim of this study is to refine a number of representative hydrodynamic models of natural space environments, including the formation of galaxies and galactic clusters; the birth of stars from the diffuse medium of gas and dust clouds; the formation of accretion disks and subsequent accumulation of planetary systems, and the formation of gaseous envelopes (atmospheres) of planets; variously scaled flows in the atmospheres and in the circumplanetary plasma, etc. The study continues the stochastically thermodynamic approach to the synergetic description of structurized turbulence in astrogeophysical systems that the author has been developing in a series of previous papers (Kolesnichenko, 2002, 2003, 2004).

Recombination instability and double S-switching in p-Ge(Au)

We report on the experimental investigation of p-Ge(Au) samples and compare the results qualitatively to a one-dimensional theoretical model describing the recombination instability of current in gold-compensated germanium in a two-parameter (voltage-emission) space. Experiments showed the existence of three regimes of the system functioning in the parametric space. The second S-switching region was found on the current-voltage characteristic, which is probably related to a noise-induced nonequilibrium phase transition.

Disordering effects of colour in a system of coupled Brownian motors: phase diagram and anomalous to normal hysteresis transition

A system of periodically coupled nonlinear phase oscillators—submitted to both additive and multiplicative white noises—has been recently shown to exhibit ratchetlike transport, negative zero-bias conductance, and anomalous hysteresis. These features stem from the asymmetry of the stationary probability distribution function, arising through a noise-induced non-equilibrium phase transition which is re-entrant as a function of the multiplicative noise intensity. Using an explicit mean-field approximation we analyse the effect of the multiplicative noises being coloured, finding a contraction of the ordered phase (and a re-entrance as a function of the coupling) on one hand, and a shift of the transition from anomalous to normal hysteresis inside this phase on the other.

Transition from anomalous to normal hysteresis in a system of coupled Brownian motors: a mean-field approach.

We address a recently introduced model describing a system of periodically coupled nonlinear phase oscillators submitted to multiplicative white noises, wherein a ratchetlike transport mechanism arises through a symmetry-breaking noise-induced nonequilibrium phase transition. Numerical simulations of this system reveal amazing novel features such as negative zero-bias conductance and anomalous hysteresis, explained by performing a strong-coupling analysis in the thermodynamic limit. Using an explicit mean-field approximation, we explore the whole ordered phase finding a transition from anomalous to normal hysteresis inside this phase, estimating its locus, and identifying (within this scheme) a mechanism whereby it takes place.

Dynamics and scaling of noise-induced domain growth

The domain growth processes originating from noise-induced nonequilibrium phase transitions are analyzed, both for non-conserved and conserved dynamics. The existence of a dynamical scaling regime is established in the two cases, and the corresponding growth laws are determined. The resulting universal dynamical scaling scenarios are those of Allen-Cahn and Lifshitz-Slyozov, respectively. Additionally, the effect of noise sources on the behaviour of the pair correlation function at short distances is studied.

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.

TURBULENCE AND COHERENT STRUCTURES IN SUBSONIC SUBMERGED JETS: CONTROL OF THE TURBULENCE

The onset of turbulence and formation of large-scale patterns (coherent structures) in subsonic submerged jets are considered from the standpoint of noise-induced nonequilibrium phase transitions of the second kind. It is shown by the example of noise-induced oscillations of a pendulum with a randomly vibrating suspension axis that such a transition can be controlled by an additional harmonic action. The known possibility of notable suppression or intensification of turbulence in jets and free shear layers by means of a slight acoustic action at one or another frequency can be attributable to such control.

Disordering Effects of Color in Nonequilibrium Phase Transitions Induced by Multiplicative Noise

The model introduced by Van den Broeck, Parrondo and Toral [Phys. Rev. Lett.73, 3395 (1994)] -- leading to a second-order-like noise-induced nonequilibrium phase transition which shows reentrance as a function of the (multiplicative) noise intensity $\sigma$-- is investigated beyond the white-noise assumption. Through a Markovian approximation and within a mean-field treatment it is found that -- in striking contrast with the usual behavior for equilibrium phase transitions -- for noise self-correlation time $\tau>0$, the stable phase for (diffusive) spatial coupling $D\to\infty$ is always the disordered one. Another surprising result is that a large noise "memory" also tends to destroy order. These results are supported by numerical simulations.

Comment on “Noise-Induced Nonequilibrium Phase Transition”

Comment on “Noise-Induced Nonequilibrium Phase Transition”

A theory of dislocation cell formation based on stochastic dislocation dynamics

A stochastic effective medium theory is developed that accounts for the geometrically necessary fluctuations of the local stress and strain rate resulting from dynamic dislocation interactions. The concept is applied to the formation of dislocation cells in multiple slip. Starting from a Langevin-type evolution equation for the total dislocation density ϱ, a corresponding Fokker-Planck equation for the probability distribution p s( ϱ) is derived. Cell formation is related to a noise-induced non-equilibrium phase transition associated with a qualitative change of p s( ϱ). The cell size is found to be in inverse proportion to the flow stress (principle of similitude). Critical conditions for, and the role of cross slip in, cell formation are discussed.

Comment on "Noise-induced nonequilibrium phase transition"

A Comment on the Letter by C. Van den Broeck, J. M. R. Parrondo, and R. Toral, Phys. Rev. Lett. 73, 3395 (1994). The authors of the Letter offer a Reply.

Noise-induced nonequilibrium phase transition.

We report on a simple model of a spatially distributed system which, subject to multiplicative noise, white in space and time, can undergo a nonequilibrium phase transition to a symmetry-breaking state, while no such transition exists in the absence of the noise term. The transition possesses features similar to those observed at second order equilibrium phase transitions: divergence of the correlation length and of the susceptibility, critical slowing down, and scaling properties. Furthermore, the transition is found to be reentrant: The ordered state appears at a critical value of the noise intensity but disappears again at a higher value of the noise strength.

NOISE-INDUCED NONEQUILIBRIUM PHASE TRANSITIONS IN THE COLORED LOSS-NOISE DYE-LASER MODEL

A single-mode colored loss-noise dye-laser model is treated by means of a new version of approximate effective Markovian equation for all values of noise intensity and correlation time. The steady-state probability density is derived and various scenarios of possible noise-induced nonequilibrium phase transitions are considered. The proposed method of investigation is proved to be valid for other physical systems driven by the multiplicative colored noise.