In this work, we study the critical behavior of a one-dimensional model that mimics the propagation of an epidemic process mediated by a density of diffusive individuals which can infect a static population upon contact. We simulate the above model on linear chains to determine the critical density of the diffusive population, above which the system achieves a statistically stationary active state, as a function of two relevant parameters related to the average lifetimes of the diffusive and nondiffusive populations. A finite-size scaling analysis is employed to determine the order parameter and correlation length critical exponents. For high-recovery rates, the critical exponents are compatible with the usual directed percolation universality class. However, in the opposite regime of low-recovery rates, the diffusion is a relevant mechanism responsible for the propagation of the disease and the absorbing state phase transition is governed by a distinct set of critical exponents.

We have studied diffusion in a quasi-two-dimensional granular gas composed of plastic balls confined in a vertically vibrating thin box. The horizontal motion of the balls in the box is found to follow the Langevin equation with the top and bottom of the box acting on the balls with a viscous drag like that in a fluid. Surprisingly, we find that both the granular temperature and the diffusion constant increase with the number of balls $\left(N\right)$ in the box for small $N$. The unusual diffusion can be explained by a two-state model, in which a ball is in contact with two effective temperature baths due to collisions with the top or bottom of the box and collisions with other balls.

Influence of reactive defects on size distribution of one-dimensional islands is studied by means of kinetic Monte Carlo simulations in combination with an analytical approach. Two different models are examined: a model with anisotropically diffusing atoms irreversibly aggregating to islands, and a reversible model close to thermal equilibrium which allows atom detachment from islands during the growth. The models can be used to simulate island growth of group III metals deposited on the $\text{Si}\left(100\right)2\times 1$ surface at room temperature: Al, Ga (irreversible model), and In (equilibrium model). We demonstrate that concentration of the reactive defects 0.0025 per site may change the island size distribution from monomodal to monotonically decreasing in the case of the irreversible model. At concentration $\ge 0.005$ defects per site, a difference between results of the studied models is suppressed by the influence of the defects and similar island size distributions are obtained.

The Pitman-Yor, or Chinese restaurant process, is a stochastic process that generates distributions following a power law with exponents lower than 2, as found in numerous physical, biological, technological, and social systems. We discuss its rich behavior with the tools and viewpoint of statistical mechanics. We show that this process invariably gives rise to a condensation, i.e., a distribution dominated by a finite number of classes. We also evaluate thoroughly the finite-size effects, finding that the lack of stationary state and self-averaging of the process creates realization-dependent cutoffs and behavior of the distributions with no equivalent in other statistical mechanical models.

Friedel oscillations of electron densities near step edges have an analog in microwave billiards. A random plane-wave model, normally only appropriate for the eigenfunctions of a purely chaotic system, can be applied and is tested for non-purely-chaotic dynamical systems with measurements on pseudointegrable and mixed dynamics geometries. It is found that the oscillations in the pseudointegrable microwave cavity match the random plane-wave modeling. Separating the chaotic from the regular states for the mixed system requires incorporating an appropriate phase-space projection into the modeling in multiple ways for good agreement with experiment.

We present several observations into spiral turbulence in a Taylor-Couette geometry gained through a three-dimensional direct numerical simulation. Conditionally averaged flow statistics show the persistence of an azimuthal gradient of the mean flow across both the turbulent and laminar spirals, and distinct distribution features of the turbulent intensity. The data provide a physical picture qualitatively different from the existing model of spiral turbulence. Certain aspects of the spiral pattern are observed to bear similarities to the stationary laminar-turbulent pattern in plane Couette flow.

Refraction and deflection of shear zones in layered granular materials were studied experimentally and numerically. We show that (i) according to a recent theoretical prediction [T. Unger, Phys. Rev. Lett. 98, 018301 (2007)] shear zones refract in layered systems in analogy with light refraction, (ii) zone refraction obeys Snell’s law known from geometric optics, and (iii) under natural pressure conditions (i.e., in the presence of gravity) the zone can also be deflected by the interface, so that the deformation of the high friction material is avoided.

Monocular deprivation experiments can be used to distinguish between different ideas concerning properties of cortical synaptic plasticity. Monocular deprivation by lid suture causes a rapid disconnection of the deprived eye connected to cortical neurons whereas total inactivation of the deprived eye produces much less of an ocular dominance shift. In order to understand these results one needs to know how lid suture and retinal inactivation affect neurons in the lateral geniculate nucleus (LGN) that provide the cortical input. Recent experimental results by Linden et al. showed that monocular lid suture and monocular inactivation do not change the mean firing rates of LGN neurons but that lid suture reduces correlations between adjacent neurons whereas monocular inactivation leads to correlated firing. These, somewhat surprising, results contradict assumptions that have been made to explain the outcomes of different monocular deprivation protocols. Based on these experimental results we modify our assumptions about inputs to cortex during different deprivation protocols and show their implications when combined with different cortical plasticity rules. Using theoretical analysis, random matrix theory and simulations we show that high levels of correlations reduce the ocular dominance shift in learning rules that depend on homosynaptic depression (i.e., Bienenstock-Cooper-Munro type rules), consistent with experimental results, but have the opposite effect in rules that depend on heterosynaptic depression (i.e., Hebbian/principal component analysis type rules).

This Brief Report presents the hierarchical reaction-diffusion partial differential equations (PDE) system, which reproduces a mean-square displacement and a density relaxation process corresponding to the anomalous diffusion on a small-world network. These results are confirmed by the comparison with the known direct numerical simulations.

We propose an efficient and fast bit-multiplexed encryption scheme exploiting hyperchaotic regimes of a single nonlinear oscillator with multiple time-delay feedback loops. Each data stream is encrypted by digitally modulating the values of the various time delays and decrypted using chaos synchronization and cross-correlation measurements. We have numerically applied our approach to an optoelectronic chaotic oscillator based on standard semiconductor lasers subjected to multiple feedbacks and have demonstrated successful data transmission and recovery between multiple users at several Gbits/s on a single communication channel.

A scale-similarity model for Lagrangian two-point, two-time velocity correlations (LVCs) in isotropic turbulence is developed from the Kolmogorov similarity hypothesis. It is a second approximation to the isocontours of LVCs, while the Smith-Hay model is only a first approximation. This model expresses the LVC by its space correlation and a dispersion velocity. We derive the analytical expression for the dispersion velocity from the Navier-Stokes equations using the quasinormality assumption. The dispersion velocity is dependent on enstrophy spectra and shown to be smaller than the sweeping velocity for the Eulerian velocity correlation. Therefore, the Lagrangian decorrelation process is slower than the Eulerian decorrelation process. The data from direct numerical simulation of isotropic turbulence support the scale-similarity model: the LVCs for different space separations collapse into a universal form when plotted against the separation axis defined by the model.

We investigate simple three-dimensionally crossed wires carrying electric currents which generate chaotic magnetic-field lines (CMFLs). As such wire systems, cross-ring and perturbed parallel-ring wires are studied, since topologically equivalent configurations to these systems can often be found in contemporary electric and integrated circuits. For realistic fundamental wire configurations, the conditions for wire dimensions (size) and current values to generate CMFLs are numerically explored under the presence of the weak but inevitable geomagnetic field. As a result, it is concluded that CMFLs can exist everywhere; i.e., they are ubiquitous in the modern technological world.

An approach to the kinetics of barrier formation of supercritical gas bubbles in a strongly supersaturated liquid solution is presented. A common assumption of uniform reduction of a dissolved gas supersaturation in a liquid solution via stationary diffusion to nucleating gas bubbles is shown to be not applicable to the case of high gas supersaturations. The approach recognizes that the diffusion growth of supercritical bubbles at high gas supersaturation is essentially nonstationary. Nonstationary growth of an individual gas bubble is described by a self-similar solution of the diffusion equation which predicts a renormalized growth rate and thin highly nonuniform diffusion layer around the bubble. The depletion of a dissolved gas due to intake of gas molecules by the bubble occurs only within this thin layer. An integral equation for the total volume of an ensemble of supercritical gas bubbles within a liquid solution is derived. This equation describes the effect of excluding a total volume of the depleted diffusion layers around the growing bubbles nucleated at all previous moments of time until nucleation of new bubbles ceases due to elimination of the nondepleted volume of the solution. An analytical solution of this equation is found. The swelling of the liquid solution, the number of gas bubbles nucleated, the distribution function of bubbles in their sizes, and the mean radius of the bubbles are determined in their dependence on time.

We provide a simple interpretation of non-Gaussian nature of the light scattering-intensity fluctuations from an aging colloidal suspension of Laponite using the multiplicative cascade model, Markovian method, and volatility correlations. The cascade model and Markovian method enable us to reproduce most of recent empirical findings: long-range volatility correlations and non-Gaussian statistics of intensity fluctuations. We provide evidence that the intensity increments $\Delta x\left(\tau \right)=I\left(t+\tau \right)-I\left(t\right)$, upon different delay time scales $\tau$, can be described as a Markovian process evolving in $\tau$. Thus, the $\tau$ dependence of the probability density function $p\left(\Delta x,\tau \right)$ on the delay time scale $\tau$ can be described by a Fokker-Planck equation. We also demonstrate how drift and diffusion coefficients in the Fokker-Planck equation can be estimated directly from the data.

Motivated by a series of experiments that revealed a temperature dependence of the dynamic scaling regime of growing surfaces, we investigate theoretically how a nonequilibrium growth process reacts to a sudden change of system parameters. We discuss quenches between correlated regimes through exact expressions derived from the stochastic Edwards-Wilkinson equation with a variable diffusion constant. Our study reveals that a sudden change of the diffusion constant leads to remarkable changes in the surface roughness. Different dynamic regimes, characterized by a power-law or by an exponential relaxation, are identified, and a dynamic phase diagram is constructed. We conclude that growth processes provide one of the rare instances where quenches between correlated regimes yield a power-law relaxation.

We study the electroencephalogram (EEG) of 30 closed-eye awake subjects with a technique of analysis recently proposed to detect punctual events signaling rapid transitions between different metastable states. After single-EEG-channel event detection, we study global properties of events simultaneously occurring among two or more electrodes termed coincidences. We convert the coincidences into a diffusion process with three distinct rules that can yield the same $\mu$ only in the case where the coincidences are driven by a renewal process. We establish that the time interval between two consecutive renewal events driving the coincidences has a waiting-time distribution with inverse power-law index $\mu \approx 2$ corresponding to ideal $1/f$ noise. We argue that this discovery, shared by all subjects of our study, supports the conviction that $1/f$ noise is an optimal communication channel for complex networks as in art or language and may therefore be the channel through which the brain influences complex processes and is influenced by them.

The unexpected features of the two-stream instability in electrostatic quantum plasmas are interpreted in terms of the coupling of approximate fast and slow waves. This is accomplished through the factorization of the dispersion relation into different sectors having positive or negative energy. Therefore, the concept of negative and positive energy waves is useful not only for classical, but for quantum plasmas as well. We discuss the limitations of the quantum two-stream model in view of the weak coupling assumption.

We analyze the method for calculation of properties of nonrelativistic quantum systems based on exact diagonalization of space-discretized short-time evolution operators. In this paper we present a detailed analysis of the errors associated with space discretization. Approaches using direct diagonalization of real-space discretized Hamiltonians lead to polynomial errors in discretization spacing $\Delta$. Here we show that the method based on the diagonalization of the short-time evolution operators leads to substantially smaller discretization errors, vanishing exponentially with $1/{\Delta }^2$. As a result, the presented calculation scheme is particularly well suited for numerical studies of few-body quantum systems. The analytically derived discretization errors estimates are numerically shown to hold for several models. In the follow up paper [I. Vidanović, A. Bogojević, A. Balaž, and A. Belić, Phys. Rev. E 80, 066706 (2009)] we present and analyze substantial improvements that result from the merger of this approach with the recently introduced effective-action scheme for high-precision calculation of short-time propagation.

In this paper, building on a previous analysis [I. Vidanović, A. Bogojević, and A. Belić, preceding paper, Phys. Rev. E 80, 066705 (2009)] of exact diagonalization of the space-discretized evolution operator for the study of properties of nonrelativistic quantum systems, we present a substantial improvement to this method. We apply recently introduced effective action approach for obtaining short-time expansion of the propagator up to very high orders to calculate matrix elements of space-discretized evolution operator. This improves by many orders of magnitude previously used approximations for discretized matrix elements and allows us to numerically obtain large numbers of accurate energy eigenvalues and eigenstates using numerical diagonalization. We illustrate this approach on several one- and two-dimensional models. The quality of numerically calculated higher-order eigenstates is assessed by comparison with semiclassical cumulative density of states.