Noise induced stability in fluctuating, bistable potentials

Counterion Blockade in a Heterogeneously Charged Single-File Water Channel

The Possion-Nernst-Planck theories fail to describe the ionic transport in Angstrom channels, where conduction deviates from Ohm's law, which is attributed to the dehydration/self-energy barrier and dissociation of Bjerrum ion pairs in previous work. Here, we find that the cations can be strongly bound to the surface charge, which blocks the ionic transport in a single-file water channel, causing nonlinear current-voltage curves. The presence of free ions significantly increases the probability of bound ions being released, resulting in an ionic current. We find that ionic conduction gradually becomes Ohmic as the surface charge density increases, but the conduction amplitude decreases due to the increased friction from the bound ions. We rationalize the ionic transport using 1D Kramers' escape theory framework, which describes nonlinear ionic current and the impact of surface charge density on the I-V curves. Our results show that the strong Coulomb interaction between the counterion and surface charge may cause ionic blockade in Angstrom channels.

Enhancing Metastability by Dissipation and Driving in an Asymmetric Bistable Quantum System

The stabilizing effect of quantum fluctuations on the escape process and the relaxation dynamics from a quantum metastable state are investigated. Specifically, the quantum dynamics of a multilevel bistable system coupled to a bosonic Ohmic thermal bath in strong dissipation regime is analyzed. The study is performed by a non-perturbative method based on the real-time path integral approach of the Feynman-Vernon influence functional. We consider a strongly asymmetric double well potential with and without a monochromatic external driving, and with an out-of-equilibrium initial condition. In the absence of driving we observe a nonmonotonic behavior of the escape time from the metastable region, as a function both of the system-bath coupling coefficient and the temperature. This indicates a stabilizing effect of the quantum fluctuations. In the presence of driving our findings indicate that, as the coupling coefficient γ increases, the escape time, initially controlled by the external driving, shows resonant peaks and dips, becoming frequency-independent for higher γ values. Moreover, the escape time from the metastable state displays a nonmonotonic behavior as a function of the temperature, the frequency of the driving, and the thermal-bath coupling, which indicates the presence of a quantum noise enhanced stability phenomenon. Finally, we investigate the role of different spectral densities, both in sub-Ohmic and super-Ohmic dissipation regime and for different cutoff frequencies, on the relaxation dynamics from the quantum metastable state. The results obtained indicate that, in the crossover dynamical regime characterized by damped intrawell oscillations and incoherent tunneling, the spectral properties of the thermal bath influence non-trivially the short time behavior and the time scales of the relaxation dynamics from the metastable state.

Multiple current reversals and diffusion enhancement in a symmetrical periodic potential

Transport and diffusion of Brownian particles in a symmetrical periodic potential were investigated for both overdamped and underdamped cases, where the ratchet potential is driven by an external unbiased time periodic force and correlation between thermal and potential fluctuations. It is shown that the correlation between two noises breaks the symmetry of the potential to generate motion of the Brownian particles in particular direction, and the current can reverse its direction by changing the sign of the noise correlation. For the overdamped case, the systemic parameters only induce the directed current, and the noise correlation suppresses the diffusion of the overdamped Brownian particles. However for the underdamped case, the current reverses its direction multiple times with increasing the systemic parameters, i.e., the multiple current reversal is observed, and the noise negative correlation suppresses the diffusion of the underdamped Brownian particles, while the noise positive correlation enhances it.

Noise-induced stabilization in population dynamics

We investigate a model in which strong noise in a subpopulation creates a metastable state in an otherwise unstable two-population system. The induced metastable state is vortexlike, and its persistence time grows exponentially with the noise strength. A variety of distinct scaling relations are observed depending on the relative strength of the subpopulation noises.

Master equation approach to time-dependent escape rate over a periodically oscillating barrier

We propose a master equation approach to investigate the transition function and the escape dynamics of a general damping particle in a metastable potential. The transition function in the master equation is obtained analytically from the Langevin dynamics. We apply it to the oscillating barrier problem, in which the potential is structured by a harmonic potential smoothly linking with an inverse harmonic one, and thus both the barrier height and the curvature of potential change periodically with time. We use a Monte Carlo method to simulate the master equation and then calculate a time-dependent escape rate. This can decrease the coarse grain and save more computing time in comparison with the Langevin simulation. Our result has shown that there is a resonant activation phenomenon for the escape rate in the underdamped case.

Noise-induced enhancement of stability in a metastable system with damping

The mean first passage time of a Brownian particle from an initial unstable state in a metastable system with damping is investigated. The system is analyzed in the low to high damping regime, and the role played by the damping parameter is studied. We observe the noise enhanced stability effect for all the initial unstable states under study and for all values of the damping parameter γ investigated. The curves show a behavior of the mean first passage time vs γ very close to that observed for an overdamped particle in the presence of colored noise as a function of the correlation time.

Stability measures in metastable states with Gaussian colored noise

We present a study of the escape time from a metastable state of an overdamped Brownian particle in the presence of colored noise generated by Ornstein-Uhlenbeck process. We analyze the role of the correlation time on the enhancement of the mean first passage time through a potential barrier and on the behavior of the mean growth rate coefficient as a function of the noise intensity. We observe the noise-enhanced stability effect for all the initial unstable states used and for all values of the correlation time tau(c) investigated. We can distinguish two dynamical regimes characterized by weak and strong correlated noises, depending on the value of tau(c) with respect to the relaxation time of the system.

Thermally enhanced stability in fluctuating bistable potentials

Overdamped motion of Brownian particles in an asymmetric double-well potential driven by an additive nonequilibrium three-level noise and a thermal noise is considered. In the stationary regime, an exact formula for the mean occupancy of the metastable state is derived, and the phenomenon of enhancement of stability versus temperature is investigated. It is established that in a certain region of the system parameters the mean occupancy can be either multiply enhanced or suppressed by variations of temperature. We show that this effect is due to the involvement of different time scales in the problem. The necessary conditions for several different behaviors of the mean occupancy as a function of temperature are also discussed. The effect is more pronounced when the kurtosis of the three-level noise tends to -2 , i.e., in the case of dichotomous noise.

IL-8 release of HL-60 cells treated with electric currents of different wave forms

Human promyelocytic leukaemia HL-60 cells which have been differentiated by DMSO to granulocytes were used to investigate the effect of different waveforms on the release of interleukine-8 (IL-8). The cells were prestimulated with 100 pM fMLP and subsequently treated for 15 min with different electrical fields and currents. Three hours later the release of IL-8 into the medium was determined by ELISA. Varying the frequency of the sinusoidal electrical current between 0 and 20 Hz resulted in 2 maxima of IL-8 release at 5 and 13 Hz. Prestimulated cells were treated with sine-, triangular-, and rectangular-waveforms at 5 Hz in the current intensity range of 0-3 mA/cm(2). For the three waveforms tested, the IL-8 release was enhanced 1.5 fold. Treatment of the cells with capacitively coupled electric fields of 5 Hz using field strengths between 0 and 10 V(eff)/cm had no effect on the release of IL-8. In comparison to the positive results after sine wave exposure alone, an exposure with sine wave current to which noise had been superimposed had no effect on the HL-60 cells. From these investigations it can be concluded that for electrical current treatment of prestimulated HL-60 cells the release of IL-8 does not depend on the waveform if the waveform information is not destroyed by superimposed noise.

Thermal escape from a metastable state in periodically driven Josephson junctions

Resonant activation and noise-enhanced stability were observed in an underdamped real physical system, i.e., Josephson tunnel junctions. With a weak sinusoidal driving force applied, the thermal activated escape from a potential well underwent resonancelike behaviors as a function of the driving frequency. The resonances also crucially depended on the initial condition of the system. Numerical simulations showed good agreement with the experimental results.

Mean escape time in a system with stochastic volatility

We study the mean escape time in a market model with stochastic volatility. The process followed by the volatility is the Cox, Ingersoll, and Ross process which is widely used to model stock price fluctuations. The market model can be considered as a generalization of the Heston model, where the geometric Brownian motion is replaced by a random walk in the presence of a cubic nonlinearity. We investigate the statistical properties of the escape time of the returns, from a given interval, as a function of the three parameters of the model. We find that the noise can have a stabilizing effect on the system, as long as the global noise is not too high with respect to the effective potential barrier experienced by a fictitious Brownian particle. We compare the probability density function of the return escape times of the model with those obtained from real market data. We find that they fit very well.

Stochastic resonance for adhesion of membranes with active stickers

The behavior of two membranes that interact by active adhesion molecules or stickers is studied theoretically using mean-field theory and Monte Carlo simulations. The stickers are anchored in one of the membranes and undergo conformational transitions between on and off states. In their on states, the stickers can bind to ligands that are anchored in the other membrane. The transitions between the on and off states arise from the coupling of the stickers to some active, energy-releasing process, which keeps the system out of equilibrium. As one varies the transition rates of this active process, the membrane separation undergoes a stochastic resonance: this separation is maximal at intermediate rates of the sticker transitions and considerably smaller both at high and at low transition rates. This implies that the effective, fluctuation-induced repulsion between the membranes contains a rate-dependent contribution that arises from the switching of the active stickers.

Signatures of noise-enhanced stability in metastable states

The lifetime of a metastable state in the transient dynamics of an overdamped Brownian particle is analyzed, both in terms of the mean first passage time and by means of the mean growth rate coefficient. Both quantities feature nonmonotonic behaviors as a function of the noise intensity, and are independent signatures of the noise enhanced stability effect. They can therefore be alternatively used to evaluate and estimate the presence of this phenomenon, which characterizes metastability in nonlinear physical systems.

Asymmetric probability densities in symmetrically modulated bistable devices

A Brownian particle hopping in a symmetric double-well potential can be statistically confined into a single well by the simultaneous action of (a) two periodic input signals, one tilting the minima and the other one modulating the barrier height, and (b) an additive and a purely multiplicative random signal, generated by a unique source and thus preserving a certain degree of statistical correlation. The underlying gating mechanism is quite robust when compared, for instance, with biharmonic rocking. In view of technological implementation, asymmetric confinement through gating can be conveniently maximized by tuning the input signal parameters (correlation time, phase-time lag, amplitudes), thus revealing a resonant localization mechanism of general applicability.

Noise-enhanced stability in fluctuating metastable states

We derive general equations for the nonlinear relaxation time of Brownian diffusion in randomly switching potential with a sink. For piece-wise linear dichotomously fluctuating potential with metastable state, we obtain the exact average lifetime as a function of the potential parameters and the noise intensity. Our result is valid for arbitrary white noise intensity and for arbitrary fluctuation rate of the potential. We find noise enhanced stability phenomenon in the system investigated: The average lifetime of the metastable state is greater than the time obtained in the absence of additive white noise. We obtain the parameter region of the fluctuating potential where the effect can be observed. The system investigated also exhibits a maximum of the lifetime as a function of the fluctuation rate of the potential.

Propagating waves in one-dimensional discrete networks of coupled units

We investigate the behavior of discrete systems on a one-dimensional lattice composed of localized units interacting with each other through nonlocal, nonlinear reactive dynamics. In the presence of second-order and third-order steps coupling two or three neighboring sites, respectively, we observe, for appropriate initial conditions, the propagation of waves which subsist in the absence of mass transfer by diffusion. For the case of the third-order (bistable) model, a counterintuitive effect is also observed, whereby the homogeneously less stable state invades the more stable one under certain conditions. In the limit of a continuous space the dynamics of these networks is described by a generic evolution equation, from which some analytical predictions can be extracted. The relevance of this mode of information transmission in spatially extended systems of interest in physical chemistry and biology is discussed.

Noise-enhanced stability of periodically driven metastable states

We study the effect of noise-enhanced stability of periodically driven metastable states in a system described by piecewise linear potential. We find that the growing of the average escape time with the intensity of the noise is depending on the initial condition of the system. We analytically obtain the condition for the noise enhanced stability effect and verify it by numerical simulations.

Effective rate equations for the overdamped motion in fluctuating potentials

We discuss physical and mathematical aspects of the overdamped motion of a Brownian particle in fluctuating potentials. It is shown that such a system can be described quantitatively by fluctuating rates if the potential fluctuations are slow compared to relaxation within the minima of the potential, and if the position of the minima does not fluctuate. Effective rates can be calculated; they describe the long-time dynamics of the system. Furthermore, we show the existence of a stationary solution of the Fokker-Planck equation that describes the motion within the fluctuating potential under some general conditions. We also show that a stationary solution of the rate equations with fluctuating rates exists.