Search results for " Statistical"
showing 10 items of 1649 documents
Stability measures in metastable states with Gaussian colored noise
2009
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 noise respectively, depending on the value of $\tau_c$ with respect to …
Lifetime of metastable states and suppression of noise in interdisciplinary physical models
2008
Transient properties of different physical systems with metastable states perturbed by external white noise have been investigated. Two noise-induced phenomena, namely the noise enhanced stability and the resonant activation, are theoretically predicted in a piece-wise linear fluctuating potential with a metastable state. The enhancement of the lifetime of metastable states due to the noise, and the suppression of noise through resonant activation phenomenon will be reviewed in models of interdisciplinary physics: (i) dynamics of an overdamped Josephson junction; (ii) transient regime of the noisy FitzHugh-Nagumo model; (iii) population dynamics.
Noise-enhanced stability of periodically driven metastable states
2000
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.
Noise Enhanced Stability
2004
The noise can stabilize a fluctuating or a periodically driven metastable state in such a way that the system remains in this state for a longer time than in the absence of white noise. This is the noise enhanced stability phenomenon, observed experimentally and numerically in different physical systems. After shortly reviewing all the physical systems where the phenomenon was observed, the theoretical approaches used to explain the effect are presented. Specifically the conditions to observe the effect: (a) in systems with periodical driving force, and (b) in random dichotomous driving force, are discussed. In case (b) we review the analytical results concerning the mean first passage time…
Exact Results for Spectra of Overdamped Brownian Motion in Fixed and Randomly Switching Potentials
2004
The exact formulae for spectra of equilibrium diffusion in a fixed bistable piecewise linear potential and in a randomly flipping monostable potential are derived. Our results are valid for arbitrary intensity of driving white Gaussian noise and arbitrary parameters of potential profiles. We find: (i) an exponentially rapid narrowing of the spectrum with increasing height of the potential barrier, for fixed bistable potential; (ii) a nonlinear phenomenon, which manifests in the narrowing of the spectrum with increasing mean rate of flippings, and (iii) a nonmonotonic behaviour of the spectrum at zero frequency, as a function of the mean rate of switchings, for randomly switching potential. …
Nonlinear response functions in an exponential trap model
2014
The nonlinear response to an oscillating field is calculated for a kinetic trap model with an exponential density of states and the results are compared to those for the model with a Gaussian density of states. The calculations are limited to the high temperature phase of the model. It is found that the results are qualitatively different only in a temperature range near the glass transition temperature $T_0$ of the exponential model. While for the Gaussian model the choice of the dynamical variable that couples to the field has no impact on the shape of the linear response, this is different for the exponential model. Here, it is found that also the relaxation time strongly depends on the …
First-order interface localization-delocalization transition in thin Ising films using Wang-Landau sampling
2004
Using extensive Monte Carlo simulations, we study the interface localization- delocalization transition of a thin Ising film with antisymmetric competing walls for a set of parameters where the transition is strongly first-order. This is achieved by estimating the density of states (DOS) of the model by means of Wang-Landau sampling (WLS) in the space of energy, using both, single-spin-flip as well as N-fold way updates. From the DOS we calculate canonical averages related to the configurational energy, like the internal energy, the specific heat, as well as the free energy and the entropy. By sampling microcanonical averages during simulations we also compute thermodynamic quantities relat…
Cross Correlations in Scaling Analyses of Phase Transitions
2008
Thermal or finite-size scaling analyses of importance sampling Monte Carlo time series in the vicinity of phase transition points often combine different estimates for the same quantity, such as a critical exponent, with the intent to reduce statistical fluctuations. We point out that the origin of such estimates in the same time series results in often pronounced cross-correlations which are usually ignored even in high-precision studies, generically leading to significant underestimation of statistical fluctuations. We suggest to use a simple extension of the conventional analysis taking correlation effects into account, which leads to improved estimators with often substantially reduced …
Signatures of noise-enhanced stability in metastable state
2005
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 non monotonic 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.
Ornstein-Zernike equation and Percus-Yevick theory for molecular crystals
2004
We derive the Ornstein-Zernike equation for molecular crystals of axially symmetric particles and apply the Percus-Yevick approximation to this system. The one-particle orientational distribution function has a nontrivial dependence on the orientation and is needed as an input. Despite some differences, the Ornstein-Zernike equation for molecular crystals has a similar structure as for liquids. We solve both equations for hard ellipsoids on a sc lattice. Compared to molecular liquids, the tensorial orientational correlators exhibit less structure. However, depending on the lengths a and b of the rotation axis and the perpendicular axes of the ellipsoids, different behavior is found. For obl…