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)].

Statistics of depth probed by cw measurement of photons in a turbid medium

Photon migration in a turbid medium has been modeled in many different ways. The motivation for such modeling is based on technology that can be used to probe potentially diagnostic optical properties of biological tissue. Surprisingly, one of the more effective models is also one of the simplest. It is based on statistical properties of a nearest-neighbor lattice random walk. Here we develop a theory allowing one to calculate the number of visits by a photon to a given depth, if it is eventually detected at an absorbing surface. This mimics cw measurements made on biological tissue and is directed towards characterizing the depth reached by photons injected at the surface. Our development of the theory uses formalism based on the theory of a continuous-time random walk (CTRW). Formally exact results are given in the Fourier-Laplace domain, which, in turn, are used to generate approximations for parameters of physical interest.

Mean first-passage time for system driven by the coin-toss square wave

We study the mean-first-passage-time problem for systems driven by the coin-toss square-wave signal. Exact analytic solutions are obtained for the driftless case. We also obtain approximate solutions for the potential case. The mean-first-passage time exhibits discontinuities and a remarkable nonsmooth oscillatory behavior which, to our knowledge, has not been observed for other kinds of driving noise.

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.

When telegrapher's equation furnishes a better approximation to transport equation than the difussion approximation

It has been suggested that a solution to the transport equation which includes anisotropic scattering can be approximated by the solution to a telegrapher's equation [A.J. Ishimaru, Appl. Opt. 28, 2210 (1989)]. We show that in one dimension the telegrapher's equation furnishes an exact solution to the transport equation. In two dimensions, we show that, since the solution can become negative, the telegrapher's equation will not furnish a usable approximation. A comparison between simulated data in three dimensions indicates that the solution to the telegrapher's equation is a good approximation to that of the full transport equation at the times at which the diffusion equation furnishes an equally good approximation.

Generalization of the persistent random walk to dimensions greater than 1

We propose a generalization of the persistent random walk for dimensions greater than 1. Based on a cubic lattice, the model is suitable for an arbitrary dimension d. We study the continuum limit and obtain the equation satisfied by the probability density function for the position of the random walker. An exact solution is obtained for the projected motion along an axis. This solution, which is written in terms of the free-space solution of the one-dimensional telegraphers equation, may open a new way to address the problem of light propagation through thin slabs.

Structural and magnetic characterization of the lithiated iron oxide LixFe3O4

The Rietveld profile‐analysis method is used to investigate the x‐ray diffraction pattern of lithiated Fe3O4. It is shown that, after exposure to air, pure magnetite coexists with a lithium‐inserted LixFe3O4 phase. The Mössbauer spectra at 300 and 4.2 K have been used to estimate the lithium content of the sample, the pure magnetite concentration, and the iron distribution over the available 16c and 16d sites of the spinel structure. Magnetization measurements from 4.2 to 120 K with an external magnetic field up to 150 kOe have been used to obtain the saturation magnetic moment, the magnetic anisotropy constants, and the susceptibility. It is concluded that a noncollinear spin structure should be present in Li0.5Fe3O4. These results indicate that there is no room‐temperature extrusion of iron even for x→2.0, but that on exposure to air LixFe3O4 samples with x>0.5 are oxidized at room temperature by delithiation.

En torno a los efectos de la edad en el aprendizaje escolar de una lengua extrangera

The purpose of this article is to treat a currently much debated issue, the effects of age on second language learning. To do so, we contrast data collected by our research team from over one thousand seven hundred young and adult learners with four popular beliefs or generalizations, which, while deeply rooted in this society, are not always corroborated by our data.Two of these generalizations about Second Language Acquisition (languages spoken in the social context) seem to be widely accepted: a) older children, adolescents and adults are quicker and more efficient at the first stages of learning than are younger learners; b) in a natural context children with an early start are more liable to attain higher levels of proficiency. However, in the context of Foreign Language Acquisition, the context in which we collect the data, this second generalization is difficult to verify due to the low number of instructional hours (a maximum of some 800 hours) and the lower levels of language exposure time provided. The design of our research project has allowed us to study differences observed with respect to the age of onset (ranging from 2 to 18+), but in this article we focus on students who began English instruction at the age of 8 (LOGSE Educational System) and those who began at the age of 11 (EGB). We have collected data from both groups after a period of 200 (Time 1) and 416 instructional hours (Time 2), and we are currently collecting data after a period of 726 instructional hours (Time 3). We have designed and administered a variety of tests: tests on English production and reception, both oral and written, and within both academic and communicative oriented approaches, on the learners' L1 (Spanish and Catalan), as well as a questionnaire eliciting personal and sociolinguistic information. The questions we address and the relevant empirical evidence are as follows: 1. "For young children, learning languages is a game. They enjoy it more than adults."Our data demonstrate that the situation is not quite so. Firstly, both at the levels of Primary and Secondary education (ranging from 70.5% in 11-year-olds to 89% in 14-year-olds) students have a positive attitude towards learning English. Secondly, there is a difference between the two groups with respect to the factors they cite as responsible for their motivation to learn English: the younger students cite intrinsic factors, such as the games they play, the methodology used and the teacher, whereas the older students cite extrinsic factors, such as the role of their knowledge of English in the achievement of their future professional goals. 2 ."Young children have more resources to learn languages." Here our data suggest just the opposite. The ability to employ learning strategies (actions or steps used) increases with age. Older learners' strategies are more varied and cognitively more complex. In contrast, younger learners depend more on their interlocutor and external resources and therefore have a lower level of autonomy in their learning. 3. "Young children don't talk much but understand a lot"This third generalization does seem to be confirmed, at least to a certain extent, by our data in relation to the analysis of differences due to the age factor and productive use of the target language. As seen above, the comparably slower progress of the younger learners is confirmed. Our analysis of interpersonal receptive abilities demonstrates as well the advantage of the older learners. Nevertheless, with respect to passive receptive activities (for example, simple recognition of words or sentences) no great differences are observed. Statistical analyses suggest that in this test, in contrast to the others analyzed, the dominance of the subjects' L1s (reflecting a cognitive capacity that grows with age) has no significant influence on the learning process. 4. "The sooner they begin, the better their results will be in written language"This is not either completely confirmed in our research. First of all, we perceive that certain compensatory strategies disappear only with age, but not with the number of instructional hours. Secondly, given an identical number of instructional hours, the older subjects obtain better results. With respect to our analysis of data from subjects of the same age (12 years old) but with a different number of instructional hours (200 and 416 respectively, as they began at the ages of 11 and 8), we observe that those who began earlier excel only in the area of lexical fluency. In conclusion, the superior rate of older learners appears to be due to their higher level of cognitive development, a factor which allows them to benefit more from formal or explicit instruction in the school context. Younger learners, however, do not benefit from the quantity and quality of linguistic exposure typical of a natural acquisition context in which they would be allowed to make use of implicit learning abilities. It seems clear, then, that the initiative in this country to begin foreign language instruction earlier will have positive effects only if it occurs in combination with either higher levels of exposure time to the foreign language, or, alternatively, with its use as the language of instruction in other areas of the curriculum.