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.

Absorbing boundary conditions for inertial processos

A recent paper by J. Heinrichs [Phys. Rev. E 48, 2397 (1993)] presents analytic expressions for the first-passage times and the survival probability for a particle moving in a field of random correlated forces. We believe that the analysis there is flawed due to an improper use of boundary conditions. We compare that result, in the white noise limit, with the known exact expression of the mean exit time.

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.

Solutions of the telegrapher's equation in the presence of traps

Several problems in the theory of photon migration in a turbid medium suggest the utility of calculating solutions of the telegrapher¿s equation in the presence of traps. This paper contains two such solutions for the one-dimensional problem, the first being for a semi-infinite line terminated by a trap, and the second being for a finite line terminated by two traps. Because solutions to the telegrapher¿s equation represent an interpolation between wavelike and diffusive phenomena, they will exhibit discontinuities even in the presence of traps.

Properties of resonant activation phenomena

The phenomenon of resonant activation of a Brownian particle over a fluctuating barrier is revisited. We discuss the important distinctions between barriers that can fluctuate among up and down configurations, and barriers that are always up but that can fluctuate among different heights. A resonance as a function of the barrier fluctuation rate is found in both cases, but the nature and physical description of these resonances is quite distinct. The nature of the resonances, the physical basis for the resonant behavior, and the importance of boundary conditions are discussed in some detail. We obtain analytic expressions for the escape time over the barrier that explicitly capture the minima as a function of the barrier fluctuation rate, and show that our analytic results are in excellent agreement with numerical results.

Continued fraction solution for the radiative transfer equation in three dimensions

Starting from the radiative transfer equation, we obtain an analytical solution for both the free propagator along one of the axes and an arbitrary phase function in the Fourier-Laplace domain. We also find the effective absorption parameter, which turns out to be very different from the one provided by the diffusion approximation. We finally present an analytical approximation procedure and obtain a differential equation that accurately reproduces the transport process. We test our approximations by means of simulations that use the Henyey-Greenstein phase function with very satisfactory results.

Solution to telegrapher's equation in the presence of reflecting and partly reflecting broundaries

We show that the reflecting boundary condition for a one-dimensional telegraphers equation is the same as that for the diffusion equation, in contrast to what is found for the absorbing boundary condition. The radiation boundary condition is found to have a quite complicated form. We also obtain exact solutions of the telegraphers equation in the presence of these boundaries.

First-passage-time statistics for diffusion processes with an external random force

We present exact equations and expressions for the first-passage-time statistics of dynamical systems that are a combination of a diffusion process and a random external force modeled as dichotomous Markov noise. We prove that the mean first passage time for this system does not show any resonantlike behavior.

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.

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.

Reply to "Comment on 'Solutions of the telegrapher's equation in the presence of traps'"

This reply adds a number of details to remarks by Foong and Kanno [preceding Comment, Phys. Rev. A 46, 5296 (1992)] on our paper [Phys. Rev. A 45, 2222 (1992)] regarding the discontinuities observed in the curves generated in that paper.

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)].