Discreteness-induced Transition in Catalytic Reaction Networks

Drastic change in dynamics and statistics in a chemical reaction system, induced by smallness in the molecule number, is reported. Through stochastic simulations for random catalytic reaction networks, transition to a novel state is observed with the decrease in the total molecule number N, characterized by: i) large fluctuations in chemical concentrations as a result of intermittent switching over several states with extinction of some molecule species and ii) strong deviation of time averaged distribution of chemical concentrations from that expected in the continuum limit, i.e., $N \to \infty$. The origin of transition is explained by the deficiency of molecule leading to termination of some reactions. The critical number of molecules for the transition is obtained as a function of the number of molecules species M and that of reaction paths K, while total reaction rates, scaled properly, are shown to follow a universal form as a function of NK/M

Chromosomal Gains and Losses in Uveal Melanomas Detected by Comparative Genomic Hybridization

Eleven uveal melanomas were analyzed using comparative genomic hybridization (CGH). The most abundant genetic changes were loss of chromosome 3, overrepresentation of 6p, loss of 6q, and multiplication of 8q. The smallest overrepresented regions on 6p and 8q were 6pterp21 and 8q24qter, respectively. Several additional gains and losses of chromosome segments were repeatedly observed, the most frequent one being loss of 9p (three cases). Monosomy 3 appeared to be a marker for ciliary body involvement. CGH data were compared with the results of chromosome banding. Some alterations, e.g., gains of 6p and losses of 6q, were observed with higher frequencies after CGH, while others, e.g., 9p deletions, were detected only by CGH. The data suggest some similarities of cytogenetic alterations between cutaneous and uveal melanoma. In particular, the 9p deletions are of interest due to recent reports about the location of a putative tumor-suppressor gene for cutaneous malignant melanoma in this region

Emergence of stability in a stochastically driven pendulum: beyond the Kapitsa effect

We consider a prototypical nonlinear system which can be stabilized by multiplicative noise: an underdamped non-linear pendulum with a stochastically vibrating pivot. A numerical solution of the pertinent Fokker-Planck equation shows that the upper equilibrium point of the pendulum can become stable even when the noise is white, and the "Kapitsa pendulum" effect is not at work. The stabilization occurs in a strong-noise regime where WKB approximation does not hold.Comment: 4 pages, 7 figure

State selection in the noisy stabilized Kuramoto-Sivashinsky equation

In this work, we study the 1D stabilized Kuramoto Sivashinsky equation with additive uncorrelated stochastic noise. The Eckhaus stable band of the deterministic equation collapses to a narrow region near the center of the band. This is consistent with the behavior of the phase diffusion constants of these states. Some connections to the phenomenon of state selection in driven out of equilibrium systems are made.Comment: 8 pages, In version 3 we corrected minor/typo error

Steady-State L\'evy Flights in a Confined Domain

We derive the generalized Fokker-Planck equation associated with a Langevin equation driven by arbitrary additive white noise. We apply our result to study the distribution of symmetric and asymmetric L\'{e}vy flights in an infinitely deep potential well. The fractional Fokker-Planck equation for L\'{e}vy flights is derived and solved analytically in the steady state. It is shown that L\'{e}vy flights are distributed according to the beta distribution, whose probability density becomes singular at the boundaries of the well. The origin of the preferred concentration of flying objects near the boundaries in nonequilibrium systems is clarified.Comment: 10 pages, 1 figur

Arrival time distribution for a driven system containing quenched dichotomous disorder

We study the arrival time distribution of overdamped particles driven by a constant force in a piecewise linear random potential which generates the dichotomous random force. Our approach is based on the path integral representation of the probability density of the arrival time. We explicitly calculate the path integral for a special case of dichotomous disorder and use the corresponding characteristic function to derive prominent properties of the arrival time probability density. Specifically, we establish the scaling properties of the central moments, analyze the behavior of the probability density for short, long, and intermediate distances. In order to quantify the deviation of the arrival time distribution from a Gaussian shape, we evaluate the skewness and the kurtosis.Comment: 18 pages, 5 figure

Fluctuating epidemics on adaptive networks

A model for epidemics on an adaptive network is considered. Nodes follow an SIRS (susceptible-infective-recovered-susceptible) pattern. Connections are rewired to break links from non-infected nodes to infected nodes and are reformed to connect to other non-infected nodes, as the nodes that are not infected try to avoid the infection. Monte Carlo simulation and numerical solution of a mean field model are employed. The introduction of rewiring affects both the network structure and the epidemic dynamics. Degree distributions are altered, and the average distance from a node to the nearest infective increases. The rewiring leads to regions of bistability where either an endemic or a disease-free steady state can exist. Fluctuations around the endemic state and the lifetime of the endemic state are considered. The fluctuations are found to exhibit power law behavior.Comment: Submitted to Phys Rev

Three-photon states in nonlinear crystal superlattices

It has been a longstanding goal in quantum optics to realize controllable sources generating joint multiphoton states, particularly, photon triplet with arbitrary spectral characteristics. We demonstrate that such sources can be realized via cascaded parametric down-conversion (PDC) in superlattice structures of nonlinear and linear segments. We consider scheme that involves two parametric processes: $\omega_{0}\rightarrow\omega_{1}+\omega_{2}$, $\omega_{2}\rightarrow\omega_{1}+\omega_{1}$ under pulsed pump and investigate spontaneous creation of photon triplet as well as generation of high-intensity mode in intracavity three-photon splitting. We show preparation of Greenberger-Horne-Zeilinger polarization entangled states in cascaded type-II and type-I PDC in framework of consideration dual-grid structure that involves two periodically-poled crystals. We demonstrate the method of compensation of the dispersive effects in non-linear segments by appropriately chosen linear dispersive segments of superlattice for preparation heralded joint states of two polarized photons. In the case of intracavity three-photon splitting, we concentrate on investigation of photon-number distributions, third-order photon-number correlation function as well as the Wigner functions. These quantities are observed both for short interaction time intervals and in over transient regime, when dissipative effects are essential.Comment: 15 pages, 6 figure

Coexistence and critical behaviour in a lattice model of competing species

In the present paper we study a lattice model of two species competing for the same resources. Monte Carlo simulations for d=1, 2, and 3 show that when resources are easily available both species coexist. However, when the supply of resources is on an intermediate level, the species with slower metabolism becomes extinct. On the other hand, when resources are scarce it is the species with faster metabolism that becomes extinct. The range of coexistence of the two species increases with dimension. We suggest that our model might describe some aspects of the competition between normal and tumor cells. With such an interpretation, examples of tumor remission, recurrence and of different morphologies are presented. In the d=1 and d=2 models, we analyse the nature of phase transitions: they are either discontinuous or belong to the directed-percolation universality class, and in some cases they have an active subcritical phase. In the d=2 case, one of the transitions seems to be characterized by critical exponents different than directed-percolation ones, but this transition could be also weakly discontinuous. In the d=3 version, Monte Carlo simulations are in a good agreement with the solution of the mean-field approximation. This approximation predicts that oscillatory behaviour occurs in the present model, but only for d>2. For d>=2, a steady state depends on the initial configuration in some cases.Comment: 11 pages, 14 figure

Levy ratchets with dichotomic random flashing

Additive symmetric L\'evy noise can induce directed transport of overdamped particles in a static asymmetric potential. We study, numerically and analytically, the effect of an additional dichotomous random flashing in such L\'evy ratchet system. For this purpose we analyze and solve the corresponding fractional Fokker-Planck equations and we check the results with Langevin simulations. We study the behavior of the current as function of the stability index of the L\'evy noise, the noise intensity and the flashing parameters. We find that flashing allows both to enhance and diminish in a broad range the static L\'evy ratchet current, depending on the frequencies and asymmetry of the multiplicative dichotomous noise, and on the additive L\'evy noise parameters. Our results thus extend those for dichotomous flashing ratchets with Gaussian noise to the case of broadly distributed noises.Comment: 15 pages, 6 figure