Bistability driven by white shot noise

We consider mean-first-passage times and transition rates in bistable systems driven by white shot noise. We obtain closed analytical expressions, asymptotic approximations, and numerical simulations in two cases of interest: (i) jumps sizes exponentially distributed and (ii) jumps of the same size.

Harmonic oscillators driven by colored noise: crossovers, resonances and spectra

We study second-order properties of linear oscillators driven by exponentially correlated noise. We focus our attention on dynamical exponents and crossovers and also on resonance phenomena that appear when the driving noise is dichotomous. We also obtain the power spectrum and show its different behaviors according to the color of the noise.

Bistability driven by dichotomous noise

We consider mean-first-passage times and transition rates in bistable systems driven by dichotomous colored noise. We carry out an asymptotic expansion for short correlation times ¿c of the colored noise and find results that differ from those reported earlier. In particular, to retain corrections to O(¿c) we find that it is necessary to retain up to four derivatives of the potential function. We compare our asymptotic results to existing ones and also to exact ones obtained from numerical integration.

Second-order processes driven by dichotomous noise

We study free second-order processes driven by dichotomous noise. We obtain an exact differential equation for the marginal density p(x,t) of the position. It is also found that both the velocity ¿(t) and the position X(t) are Gaussian random variables for large t.

Noise and dynamics of self-organized critical phenomena

Different microscopic models exhibiting self-organized criticality are studied numerically and analytically. Numerical simulations are performed to compute critical exponents, mainly the dynamical exponent, and to check universality classes. We find that various models lead to the same exponent, but this universality class is sensitive to disorder. From the dynamic microscopic rules we obtain continuum equations with different sources of noise, which we call internal and external. Different correlations of the noise give rise to different critical behavior. A model for external noise is proposed that makes the upper critical dimensionality equal to 4 and leads to the possible existence of a phase transition above d=4. Limitations of the approach of these models by a simple nonlinear equation are discussed.

Free inertial processes driven by Gaussian noise: Probability distributions, anomalous diffusion and fractal behavior

We study the motion of an unbound particle under the influence of a random force modeled as Gaussian colored noise with an arbitrary correlation function. We derive exact equations for the joint and marginal probability density functions and find the associated solutions. We analyze in detail anomalous diffusion behaviors along with the fractal structure of the trajectories of the particle and explore possible connections between dynamical exponents of the variance and the fractal dimension of the trajectories.

Mean first-passage times for systems driven by gamma and McFadden dichotomous noise

We consider mean first-passage times (MFPTs) for systems driven by non-Markov gamma and McFadden dichotomous noises. A simplified derivation is given of the underlying integral equations and the theory for ordinary renewal processes is extended to modified and equilibrium renewal processes. The exact results are compared with the MFPT for Markov dichotomous noise and with the results of Monte Carlo simulations.

Noise and periodic modulations in neural excitable medium

We have analyzed the interplay between noise and periodic modulations in a mean field model of a neural excitable medium. For this purpose, we have considered two types of modulations, namely, variations of the resistance and oscillations of the threshold. In both cases, stochastic resonance is present, irrespective of whether the system is monostable or bistable.

Mean first-passage times for systems driven by equilibrium persistent-periodic dichotomous noise

In a recent paper, [J. M. Porrà, J. Masoliver, and K. Lindenberg, Phys. Rev. E 48, 951 (1993)], we derived the equations for the mean first-passage time for systems driven by the coin-toss square wave, a particular type of dichotomous noisy signal, to reach either one of two boundaries. The coin-toss square wave, which we here call periodic-persistent dichotomous noise, is a random signal that can only change its value at specified time points, where it changes its value with probability q or retains its previous value with probability p=1-q. These time points occur periodically at time intervals t. Here we consider the stationary version of this signal, that is, equilibrium periodic-persistent noise. We show that the mean first-passage time for systems driven by this stationary noise does not show either the discontinuities or the oscillations found in the case of nonstationary noise. We also discuss the existence of discontinuities in the mean first-passage time for random one-dimensional stochastic maps.

Exact solution to the exit-time problem for an undamped free particle driven by Gaussian white noise

In a recent paper [Phys. Rev. Lett. 75, 189 (1995)] we have presented the exact analytical expression for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise out of a region (0,L) in space. In this paper we give a detailed account of the method employed and present results on asymptotic properties and averages of T(x,v).

Bistability driven by dichotomous noise: A comment

Two recently reported treatments [J. M. Porrà et al., Phys. Rev. A 44, 4866 (1991) and I. L¿Heureux and R. Kapral, J. Chem. Phys. 88, 7468 (1988)] of the problem of bistability driven by dichotomous colored noise with a small correlation time are brought into agreement with each other and with the exact numerical results of L¿Heureux and Kapral [J. Chem. Phys. 90, 2453 (1989)].

Guide Specification for Highway Construction Texturing Concrete Pavement for Reduced Tire/Pavement Noise using Diamond Grinding, March 1, 2011

This document provides language that can be used by an Owner-Agency to develop materials and construction specifications with the objective of reducing tire/pavement noise. While the practices described herein are largely prescriptive, they have been demonstrated to increase the likelihood of constructing a durable, quieter concrete surface.

Guide Specification for Highway Construction Texturing Concrete Pavement for Reduced Tire/Pavement Noise using Artificial Turf Drag, March 1, 2011

This document provides language that can be used by an Owner-Agency to develop materials and construction specifications with the objective of reducing tire/pavement noise. While the practices described herein are largely prescriptive, they have been demonstrated to increase the likelihood of constructing a durable, quieter concrete surface. Guidance is provided herein for texturing the concrete surface since texture geometry has a paramount effect on tire/pavement noise. Guidance for curing is also provided to improve strength and durability of the surface mortar, and thus to improve texture durability.

Guide Specification for Highway Construction Texturing Concrete Pavement for Reduced Tire/Pavement Noise using Longitudinal Tining, March 1, 2011

This document provides language that can be used by an Owner-Agency to develop materials and construction specifications with the objective of reducing tire/pavement noise. While the practices described herein are largely prescriptive, they have been demonstrated to increase the likelihood of constructing a durable, quieter concrete surface. Guidance is provided herein for texturing the concrete surface since texture geometry has a paramount effect on tire/pavement noise. Guidance for curing is also provided to improve strength and durability of the surface mortar, and thus to improve texture durability.

Do riverine barriers, history or introgression shape the genetic structuring of a common shrew (Sorex araneus) population?

The common shrew (Sorex araneus) is subdivided into numerous chromosome races. The Valais and Cordon chromosome races meet and hybridize at a mountain river in Les Houches (French Alps). Significant genetic structuring was recently reported among populations found on the Valais side of this hybrid zone. In this paper, a phylogenetic analysis and partial Mantel tests are used to investigate the patterns and causes of this structuring. A total of 185 shrews were trapped at 12 localities. All individuals were typed for nine microsatellite loci. Although several mountain rivers are found in the study area, riverine barriers do not have a significant influence on gene flow. Partial Mantel tests show that our result is caused by the influence of the hybrid zone with the Cordon race. The geographical patterns of this structuring are discussed in the context of the contact zone, which appears to extend up to a group of two rivers. The glacier they originate from is known to have cut the Arve valley as recently as 1818. The recent history of this glacier, its moraine and possibly rivers, may therefore be linked to the history of this hybrid zone.