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.

Recommended Practice for Accepting New Concrete Pavement Surfaces for Tire/Pavement Noise, March 2, 2011

This practice provides guidance and example specification language intended for use by Owner-Agencies in development of specific contract language when requiring the evaluation of tire/pavement noise for new concrete pavement surfaces. The overall sound intensity level is designated as the quality characteristic used for pay adjustment.

Effects of Pavement Surface Texture on Noise and Frictional Characteristics HR-281, February 1987

An experimental modification of the transverse groove surface texture of a section of an urban interstate highway was performed by the Iowa Department of Transportation. Transverse groove texturing i s a design feature required by the Federal Highway Administration t o reduce skidding under wet pavement conditions. Adjacent residents claimed the texturing was the cause of especially annoying tonal characteristics within the traffic noise. A research proposal to modify the existing texture pattern by surface grinding and to study the noise and friction effects was approved for funding by the Iowa Highway Research Board. Results i n the form of a comparison between traffic noise before modification and traffic noise immediately after and 15 months after modification indicate that the change in surface texture has lowered overall traffic noise levels by reducing a high frequency component of the traffic noise spectrum. Fraffic testing data show reduced capacity of the roadway to inhibit wet pavement skidding as a result of the surface modification.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

Coherence and anticoherence resonance tunned by noise

We present numerical evidence and a theoretical analysis of the appearance of anticoherence resonance induced by noise, not predicted in former analysis of coherence resonance. We have found that this phenomenon occurs for very small values of the intensity of the noise acting on an excitable system, and we claim that this is a universal signature of a nonmonotonous relaxational behavior near its oscillatory regime. Moreover, we demonstrate that this new phenomenon is totally compatible with the standard situation of coherence resonance appearing at intermediate values of noise intensity.

Excitability transitions and wave dynamics under spatiotemporal structured noise

We present an analytic and numerical study of the effects of external fluctuations in active media. Our analytical methodology transforms the initial stochastic partial differential equations into an effective set of deterministic reaction-diffusion equations. As a result we are able to explain and make quantitative predictions on the systematic and constructive effects of the noise, for example, target patterns created out of noise and traveling or spiral waves sustained by noise. Our study includes the case of realistic noises with temporal and spatial structures.

Suppression of scroll wave turbulence by noise

Rotating scroll waves are dynamical spatiotemporal structures characteristic of three-dimensional active media. It is well known that, under low excitability conditions, scroll waves develop an intrinsically unstable dynamical regime that leads to a highly disorganized pattern of wave propagation. Such a ¿turbulent¿ state bears some resemblance to fibrillation states in cardiac tissue. We show here that this unstable regime can be controlled by using a spatially distributed random forcing superimposed on a control parameter of the system. Our results are obtained from numerical simulations but an explicit analytical argument that rationalizes our observations is also presented.