Effect of Non Gaussian Noises on the Stochastic Resonance-Like Phenomenon in Gated Traps

We exploit a simple one-dimensional trapping model introduced before, prompted by the problem of ion current across a biological membrane. The voltage-sensitive channels are open or closed depending on the value taken by an external potential that has two contributions: a deterministic periodic and a stochastic one. Here we assume that the noise source is colored and non Gaussian, with a $q$-dependent probability distribution (where $q$ is a parameter indicating the departure from Gaussianity). We analyze the behavior of the oscillation amplitude as a function of both $q$ and the noise correlation time. The main result is that in addition to the resonant-like maximum as a function of the noise intensity, there is a new resonant maximum as a function of the parameter $q$.Comment: Communication to LAWNP01, Proceedings to be published in Physica D, RevTex, 8 pgs, 5 figure

Trapping Dynamics with Gated Traps: Stochastic Resonance-Like Phenomenon

We present a simple one-dimensional trapping model prompted by the problem of ion current across biological membranes. The trap is modeled mimicking the ionic channel membrane behaviour. Such voltage-sensitive channels are open or closed depending on the value taken by a potential. Here we have assumed that the external potential has two contributions: a determinist periodic and a stochastic one. Our model shows a resonant-like maximum when we plot the amplitude of the oscillations in the absorption current vs. noise intensity. The model was solved both numerically and using an analytic approximation and was found to be in good accord with numerical simulations.Comment: RevTex, 5 pgs, 3 figure

Persistence in One-dimensional Ising Models with Parallel Dynamics

We study persistence in one-dimensional ferromagnetic and anti-ferromagnetic nearest-neighbor Ising models with parallel dynamics. The probability P(t) that a given spin has not flipped up to time t, when the system evolves from an initial random configuration, decays as P(t) \sim 1/t^theta_p with theta_p \simeq 0.75 numerically. A mapping to the dynamics of two decoupled A+A \to 0 models yields theta_p = 3/4 exactly. A finite size scaling analysis clarifies the nature of dynamical scaling in the distribution of persistent sites obtained under this dynamics.Comment: 5 pages Latex file, 3 postscript figures, to appear in Phys Rev.

Stochastic Aggregation: Rate Equations Approach

We investigate a class of stochastic aggregation processes involving two types of clusters: active and passive. The mass distribution is obtained analytically for several aggregation rates. When the aggregation rate is constant, we find that the mass distribution of passive clusters decays algebraically. Furthermore, the entire range of acceptable decay exponents is possible. For aggregation rates proportional to the cluster masses, we find that gelation is suppressed. In this case, the tail of the mass distribution decays exponentially for large masses, and as a power law over an intermediate size range.Comment: 7 page

Exact Solution of a Drop-push Model for Percolation

Motivated by a computer science algorithm known as `linear probing with hashing' we study a new type of percolation model whose basic features include a sequential `dropping' of particles on a substrate followed by their transport via a `pushing' mechanism. Our exact solution in one dimension shows that, unlike the ordinary random percolation model, the drop-push model has nontrivial spatial correlations generated by the dynamics itself. The critical exponents in the drop-push model are also different from that of the ordinary percolation. The relevance of our results to computer science is pointed out.Comment: 4 pages revtex, 2 eps figure

Kinetics of stochastically-gated diffusion-limited reactions and geometry of random walk trajectories

In this paper we study the kinetics of diffusion-limited, pseudo-first-order A + B -> B reactions in situations in which the particles' intrinsic reactivities vary randomly in time. That is, we suppose that the particles are bearing "gates" which interchange randomly and independently of each other between two states - an active state, when the reaction may take place, and a blocked state, when the reaction is completly inhibited. We consider four different models, such that the A particle can be either mobile or immobile, gated or ungated, as well as ungated or gated B particles can be fixed at random positions or move randomly. All models are formulated on a $d$-dimensional regular lattice and we suppose that the mobile species perform independent, homogeneous, discrete-time lattice random walks. The model involving a single, immobile, ungated target A and a concentration of mobile, gated B particles is solved exactly. For the remaining three models we determine exactly, in form of rigorous lower and upper bounds, the large-N asymptotical behavior of the A particle survival probability. We also realize that for all four models studied here such a probalibity can be interpreted as the moment generating function of some functionals of random walk trajectories, such as, e.g., the number of self-intersections, the number of sites visited exactly a given number of times, "residence time" on a random array of lattice sites and etc. Our results thus apply to the asymptotical behavior of the corresponding generating functions which has not been known as yet.Comment: Latex, 45 pages, 5 ps-figures, submitted to PR

Borderline Aggregation Kinetics in ``Dry'' and ``Wet'' Environments

We investigate the kinetics of constant-kernel aggregation which is augmented by either: (a) evaporation of monomers from finite-mass clusters, or (b) continuous cluster growth -- \ie, condensation. The rate equations for these two processes are analyzed using both exact and asymptotic methods. In aggregation-evaporation, if the evaporation is mass conserving, \ie, the monomers which evaporate remain in the system and continue to be reactive, the competition between evaporation and aggregation leads to several asymptotic outcomes. For weak evaporation, the kinetics is similar to that of aggregation with no evaporation, while equilibrium is quickly reached in the opposite case. At a critical evaporation rate, the cluster mass distribution decays as $k^{-5/2}$, where $k$ is the mass, while the typical cluster mass grows with time as $t^{2/3}$. In aggregation-condensation, we consider the process with a growth rate for clusters of mass $k$, $L_k$, which is: (i) independent of $k$, (ii) proportional to $k$, and (iii) proportional to $k^\mu$, with $0<\mu<1$. In the first case, the mass distribution attains a conventional scaling form, but with the typical cluster mass growing as $t\ln t$. When $L_k\propto k$, the typical mass grows exponentially in time, while the mass distribution again scales. In the intermediate case of $L_k\propto k^\mu$, scaling generally applies, with the typical mass growing as $t^{1/(1-\mu)}$. We also give an exact solution for the linear growth model, $L_k\propto k$, in one dimension.Comment: plain TeX, 17 pages, no figures, macro file prepende

On the universality of a class of annihilation-coagulation models

A class of $d$-dimensional reaction-diffusion models interpolating continuously between the diffusion-coagulation and the diffusion-annihilation models is introduced. Exact relations among the observables of different models are established. For the one-dimensional case, it is shown how correlations in the initial state can lead to non-universal amplitudes for time-dependent particles density.Comment: 18 pages with no figures. Latex file using REVTE

Growth Kinetics in Systems with Local Symmetry

The phase transition kinetics of Ising gauge models are investigated. Despite the absence of a local order parameter, relevant topological excitations that control the ordering kinetics can be identified. Dynamical scaling holds in the approach to equilibrium, and the growth of typical length scale is characteristic of a new universality class with $L(t)\sim \left(t/\ln t\right)^{1/2}$. We suggest that the asymptotic kinetics of the 2D Ising gauge model is dual to that of the 2D annihilating random walks, a process also known as the diffusion-reaction $A+A\to \hbox{inert}$.Comment: 10 pages in Tex, 2 Postscript figures appended, NSF-ITP-93-4

Multiparticle Reactions with Spatial Anisotropy

We study the effect of anisotropic diffusion on the one-dimensional annihilation reaction kA->inert with partial reaction probabilities when hard-core particles meet in groups of k nearest neighbors. Based on scaling arguments, mean field approaches and random walk considerations we argue that the spatial anisotropy introduces no appreciable changes as compared to the isotropic case. Our conjectures are supported by numerical simulations for slow reaction rates, for k=2 and 4.Comment: nine pages, plain Te