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)].

pH Sensitive surfactants from lysine: assessment of their cytotoxicity and environmental behavior

The toxicity and environmental behavior of new pH-sensitive surfactants from lysine are presented. Three different chemical structures are studied: surfactants with one amino acid and one alkyl chain, surfactants with two amino acids on the polar head and one alkyl chain, and gemini surfactants. The pH sensitivity of these compounds can be tuned by modifying their chemical structures. Cytotoxicity has been evaluated using erythrocytes and fibroblast cells. The toxic effects against these cells depend on the hydrophobicity of the molecules as well as their cationic charge density. The effect of hydrophobicity and cationic charge density on toxicity is different for each type of cells. For erythrocytes, the toxicity increases as hydrophobicity and charge density increases. Nevertheless, for fibroblasts cationic charge density affects cytotoxicity in the opposite way: the higher charge density, the lower the toxicity. The effect of the pH on hemolysis has been evaluated in detail. The aquatic toxicity was established using Daphnia magna. All surfactants yielded EC50 values considerably higher than that reported for cationic surfactants based on quaternary ammonium groups. Finally, their biodegradability was evaluated using the CO2 headspace test (ISO 14593). These lysine derivatives showed high levels of biodegradation under aerobic conditions and can be classified as"readily biodegradable compounds".

Antibiotic resistance genes in the bacteriophage DNA fraction of environmental samples

Antibiotic resistance is an increasing global problem resulting from the pressure of antibiotic usage, greater mobility of the population, and industrialization. Many antibiotic resistance genes are believed to have originated in microorganisms in the environment, and to have been transferred to other bacteria through mobile genetic elements. Among others, ß-lactam antibiotics show clinical efficacy and low toxicity, and they are thus widely used as antimicrobials. Resistance to ß-lactam antibiotics is conferred by ß-lactamase genes and penicillin-binding proteins, which are chromosomal- or plasmid-encoded, although there is little information available on the contribution of other mobile genetic elements, such as phages. This study is focused on three genes that confer resistance to ß-lactam antibiotics, namely two ß-lactamase genes (blaTEM and blaCTX-M9) and one encoding a penicillin-binding protein (mecA) in bacteriophage DNA isolated from environmental water samples. The three genes were quantified in the DNA isolated from bacteriophages collected from 30 urban sewage and river water samples, using quantitative PCR amplification. All three genes were detected in the DNA of phages from all the samples tested, in some cases reaching 104 gene copies (GC) of blaTEM or 102 GC of blaCTX-M and mecA. These values are consistent with the amount of fecal pollution in the sample, except for mecA, which showed a higher number of copies in river water samples than in urban sewage. The bla genes from phage DNA were transferred by electroporation to sensitive host bacteria, which became resistant to ampicillin. blaTEM and blaCTX were detected in the DNA of the resistant clones after transfection. This study indicates that phages are reservoirs of resistance genes in the environment.

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.

Noise-enhanced excitability in bistable activator-inhibitor media

We show that external fluctuations induce excitable behavior in a bistable spatially extended system with activator-inhibitor dynamics of the FitzHugh-Nagumo type. This can be understood as a mechanism for sustained signal propagation in bistable media. The phase diagram of the stochastic system is analytically obtained and numerically verified. For small-noise intensities, front propagation becomes unstable, and excitable pulses arise as the only possible spatiotemporal behavior of the system. For large-noise intensities, on the other hand, the system enters an effective regime of oscillatory behavior, where it exhibits spontaneous nucleation of pulses and synchronized firing.