We study the long-time behavior of decoupled continuous-time random walks characterized by superheavy-tailed distributions of waiting times and symmetric heavy-tailed distributions of jump lengths. Our main quantity of interest is the limiting probability density of the position of the walker multiplied by a scaling function of time. We show that the probability density of the scaled walker position converges in the long-time limit to a nondegenerate one only if the scaling function behaves in a certain way. This function as well as the limiting probability density are determined in explicit form. Also, we express the limiting probability density which has heavy tails in terms of the Fox $H$ function and find its behavior for small and large distances.

Vicious Brownian motion is a diffusion scaling limit of Fisher's vicious walk model, which is a system of Brownian particles in one dimension such that if two motions meet they kill each other. We consider the vicious Brownian motions conditioned never to collide with each other and call it noncolliding Brownian motion. This conditional diffusion process is equivalent to the eigenvalue process of the Hermitian-matrix-valued Brownian motion studied by Dyson [J. Math. Phys. 3, 1191 (1962)]. Recently, O’Connell [Ann. Probab. (to be published)] introduced a generalization of the noncolliding Brownian motion by using the eigenfunctions (the Whittaker functions) of the quantum Toda lattice in order to analyze a directed polymer model in 1 $+$ 1 dimensions. We consider a system of one-dimensional Brownian motions with a long-ranged killing term as a generalization of the vicious Brownian motion and construct the O’Connell process as a conditional process of the killing Brownian motions to survive forever.

We discuss stationary aspects of a set of driven lattice gases in which hard-core particles with spatial extent, covering more than one lattice site, diffuse and reconstruct in one dimension under nearest-neighbor interactions. As in the uncoupled case [M. Barma et al., J. Phys.: Condens. Matter 19, 065112 (2007)], the dynamics of the phase space breaks up into an exponentially large number of mutually disconnected sectors labeled by a nonlocal construct, the irreducible string. Depending on whether the particle couplings are taken attractive or repulsive, simulations in most of the studied sectors show that both steady state currents and pair correlations behave quite differently at low temperature regimes. For repulsive interactions an order-by-disorder transition is suggested.

We consider continuous-time random walks (CTRWs) in which the walkers have a finite probability to alter the waiting-time and/or step-length transport properties of their environment, resulting in possibly transient anomalous diffusion. We refer to these CTRWs as transmogrifying continuous-time random walks (TCTRWs) to emphasize that they change the form of the transport properties of their environment, and in a possibly strange way. The particular case in which the CTRW waiting-time density has a finite probability to be permanently altered at a given site, following a visitation by a walker, is considered in detail. Master equations for the probability density function of transmogrifying random walkers are derived, and results are compared with Monte Carlo simulations. An interesting finding is that TCTRWs can generate transient subdiffusion or transient superdiffusion without invoking truncated or tempered power law densities for either the waiting times or the step lengths. The transient subdiffusion or transient superdiffusion arises in TCTRWs with Gaussian step-length densities and exponential waiting-time densities when the altered average waiting time is greater than or less than, respectively, the original average waiting time.

By introducing a quantum entropy functional of the reduced density matrix, the principle of quantum maximum entropy is asserted as fundamental principle of quantum statistical mechanics. Accordingly, we develop a comprehensive theoretical formalism to construct rigorously a closed quantum hydrodynamic transport within a Wigner function approach. The theoretical formalism is formulated in both thermodynamic equilibrium and nonequilibrium conditions, and the quantum contributions are obtained by only assuming that the Lagrange multipliers can be expanded in powers of ${\hslash }^2.$ In particular, by using an arbitrary number of moments, we prove that (1) on a macroscopic scale all nonlocal effects, compatible with the uncertainty principle, are imputable to high-order spatial derivatives, both of the numerical density $n$ and of the effective temperature $T$; (2) the results available from the literature in the framework of both a quantum Boltzmann gas and a degenerate quantum Fermi gas are recovered as a particular case; (3) the statistics for the quantum Fermi and Bose gases at different levels of degeneracy are explicitly incorporated; (4) a set of relevant applications admitting exact analytical equations are explicitly given and discussed; (5) the quantum maximum entropy principle keeps full validity in the classical limit, when $\hslash \to 0$.

Game-theoretical models where the rules of the game and the interaction structure both coevolve with the game dynamics—multiadaptive games—capture very flexible situations where cooperation among selfish agents can emerge. In this work, we will discuss a multiadaptive model presented in a recent Letter [Phys. Rev. Lett. 106, 028702 (2011)] as well as generalizations of it. The model captures a nonequilibrium situation where social unrest increases the incentive to cooperate and, simultaneously, agents are partly free to influence with whom they interact. First, we investigate the details of how feedback from the behavior of agents determines the emergence of cooperation and hierarchical contact structures. We also study the stability of the system to different types of noise, and find that different regions of parameter space show very different response. Some types of noise can destroy an all-cooperator (C) state. If, on the other hand, hubs are stable, then so is the all-C state. Finally, we investigate the dependence of the ratio between the time scales of strategy updates and the evolution of the interaction structure. We find that a comparatively fast strategy dynamics is a prerequisite for the emergence of cooperation.

We report on the dynamics of a model frictional system submitted to minute external perturbations. The system consists of a chain of sliders connected through elastic springs that rest on an incline. By introducing cyclic expansions and contractions of the springs we observe a reptation of the chain. We account for the average reptation velocity theoretically. The velocity of small systems exhibits a series of plateaus as a function of the incline angle. Due to elastic effects, there exists a critical amplitude below which the reptation is expected to cease. However, rather than a full stop of the creep, we observe in numerical simulations a transition between a continuous-creep and an irregular-creep regime when the critical amplitude is approached. The latter transition is reminiscent of the transition between the continuous and the irregular compaction of granular matter submitted to periodic temperature changes.

Aerosil silica nanoparticles dispersed in a liquid crystal (LC) possess the interesting property of keeping memory of an electric- or magnetic-field-induced orientation. Two types of memory have been identified: thermally erasable memory arising from the pinning of defect lines versus a “permanent” memory where the orientation persists even after thermal cycling the samples up to the isotropic phase. To address the source of the latter type of memory, solid-state nuclear magnetic resonance spectroscopy and conventional x-ray diffraction (XRD) were first combined to characterize the LC orientational order as a function of multiple in-field temperature cycles. Microbeam XRD was then performed on aligned gels of different concentrations to gain knowledge of the structural properties at the origin of the memory effect. No detectable anisotropy of the gel or significant breaking of silica strands with heating ruled out the formation of an anisotropic silica network as the source of the permanent memory as previously proposed. Instead, support for a role of the surface memory effect, well known for planar substrates, in stabilizing the permanent memory was deduced from “training” of the composites, that is, optimizing the orientational order through the thermal in-field cycling. The ability to train the composites is inversely proportional to the strength of the random-field disorder. The portion of thermally erasable memory also decreases as the silica density increases. We propose that the permanent memory originates from the surface memory effect operating at points of intersection in the silica network. These areas, where the LC is strongly confined with conflicted surface interactions, are trained to achieve an optimized orientation and subsequently act as sites from which the LC orientational order regrows after zero-field thermal cycling up to the isotropic phase.

Tissue morphogenesis is controlled by the two-dimensional patterning of gene expression in epithelial layers, that determines cell fates. The mechanisms of pattern formation involve intracellular regulatory networks controlled by paracrine and autocrine signaling. We develop a general logical scheme to deduce the morphology of two-dimensional patterns in the field of two crossed morphogen gradients enriched by the action of autocrine signaling that may subdivide expression domains in nontrivial ways. A variety of persistent patterns, either stationary or oscillatory, are generated using the various interaction schemes, some of which have been generated by a special algorithm including random inputs and selected according to suitable criteria. We give the full classification of a variety of stationary and oscillatory expression patterns in the presence of a single autocrine signal based on logical arguments. These results are further confirmed by numerical computations based on reaction-diffusion equations for morphogens and ligands and the discrete (cell-level) description of intracellular dynamics. Model simulations also elucidate transient processes, in particular interaction schemes. Different internal schemes may lead to identical persistent patterns, although relaxation may proceed in distinct ways. As an illustration of the general method, we test a particular scheme suggested by genetic studies of dynamic gene expression patterns in the follicular epithelium of the Drosophila eggshell.

This work generalizes the recently introduced univariate multiscale entropy (MSE) analysis to the multivariate case. This is achieved by introducing multivariate sample entropy (MSampEn) in a rigorous way, in order to account for both within- and cross-channel dependencies in multiple data channels, and by evaluating it over multiple temporal scales. The multivariate MSE (MMSE) method is shown to provide an assessment of the underlying dynamical richness of multichannel observations, and more degrees of freedom in the analysis than standard MSE. The benefits of the proposed approach are illustrated by simulations on complexity analysis of multivariate stochastic processes and on real-world multichannel physiological and environmental data.

Crumpled paper has recently emerged as a model for disordered media. Here we use wave propagation to probe aluminum foils crumpled into balls made by hand or into cylinders obtained by confinement in a container. Surprisingly, the raw dispersion relations appear to differ from sample to sample. They correspond to bending waves that follow an effective path that is shorter than the distance between the input and output points. This can be interpreted in terms of two modes of propagation: slow bending waves and a fast mode whose possible origin is discussed. In addition, the effective paths behave differently in spheres and in cylinders. These results enable the characterization of the sample structure and point toward the geometric rigidity of the configurations.

We consider the Abelian sandpile model (ASM) on the square lattice with a single dissipative site (sink). Particles are added one by one per unit time at random sites and the resulting density of particles is calculated as a function of time. We observe different scenarios of evolution depending on the value of initial uniform density (height) $h_0$. During the first stage of the evolution, the density of particles increases linearly. Reaching a critical density ${\rho }_c\left(h_0\right)$, the system changes its behavior and relaxes exponentially to the stationary state of the ASM with density ${\rho }_s$. Considering initial heights $-1\le h_0\le 4$, we observe a dramatic decrease of the difference ${\rho }_c\left(h_0\right)-{\rho }_s$ when $h_0$ is zero or negative. In parallel with the ASM, we consider the conservative fixed energy sandpile (FES). The extensive Monte Carlo simulations show that the threshold density ${\rho }_{\mathrm{th}}\left(h_0\right)$ of the FES converges rapidly to ${\rho }_s$ for $h_0<1$.

Plants and animals of a given species tend to cluster within their habitats in accordance with a power function between their mean density and the variance. This relationship, Taylor's power law, has been variously explained by ecologists in terms of animal behavior, interspecies interactions, demographic effects, etc., all without consensus. Taylor's law also manifests within a wide range of other biological and physical processes, sometimes being referred to as fluctuation scaling and attributed to effects of the second law of thermodynamics. 1/$f$ noise refers to power spectra that have an approximately inverse dependence on frequency. Like Taylor's law these spectra manifest from a wide range of biological and physical processes, without general agreement as to cause. One contemporary paradigm for 1/$f$ noise has been based on the physics of self-organized criticality. We show here that Taylor's law (when derived from sequential data using the method of expanding bins) implies 1/$f$ noise, and that both phenomena can be explained by a central limit-like effect that establishes the class of Tweedie exponential dispersion models as foci for this convergence. These Tweedie models are probabilistic models characterized by closure under additive and reproductive convolution as well as under scale transformation, and consequently manifest a variance to mean power function. We provide examples of Taylor's law, 1/$f$ noise, and multifractality within the eigenvalue deviations of the Gaussian unitary and orthogonal ensembles, and show that these deviations conform to the Tweedie compound Poisson distribution. The Tweedie convergence theorem provides a unified mathematical explanation for the origin of Taylor's law and 1/$f$ noise applicable to a wide range of biological, physical, and mathematical processes, as well as to multifractality.

The significant enhancement of the creep of plasterboard by a humid environment is well known in the building industry. But despite its strong impact on the material durability, its origin remains unexplained. We present here experimental evidence that the creep of wet set plaster is driven by the dissolution kinetics of gypsum, its major component, in intercrystalline water layers. Linking this surface molecular behavior to a macroscopic mechanical property has been made possible by the establishment, using holographic interferometry, of an accurate method of convection-free dissolution measurement, and by the possibility of tuning the dissolution kinetics of the material by the use of additives. Although it is well known in geological contexts, this dissolution-creep correlation had not yet been observed outside this field. It enables one to propose pressure solution as the mechanism of the wet creep of set plaster and sheds light on the humid creep of polycrystalline mineral materials.

Modularity maximization is the most popular technique for the detection of community structure in graphs. The resolution limit of the method is supposedly solvable with the introduction of modified versions of the measure, with tunable resolution parameters. We show that multiresolution modularity suffers from two opposite coexisting problems: the tendency to merge small subgraphs, which dominates when the resolution is low; the tendency to split large subgraphs, which dominates when the resolution is high. In benchmark networks with heterogeneous distributions of cluster sizes, the simultaneous elimination of both biases is not possible and multiresolution modularity is not capable to recover the planted community structure, not even when it is pronounced and easily detectable by other methods, for any value of the resolution parameter. This holds for other multiresolution techniques and it is likely to be a general problem of methods based on global optimization.

Statistical and fractal properties of the spatial distribution of earthquakes in the central zone of Chile are studied. In particular, data are shown to behave according to the well-known Gutenberg-Richter law. The fractal structure is evident for epicenters, not for hypocenters. The multifractal spectrum is also determined, both for the spatial distribution of epicenters and hypocenters. For negative values of the index of multifractal measure $q$, the multifractal spectrum, which usually cannot be reliably found from data, is calculated from a generalized Cantor-set model, which fits the multifractal spectrum for $q>0$, a technique which has been previously applied for analysis of solar wind data.

We study numerically the behavior of one-dimensional arrays of aqueous droplets containing the oscillatory Belousov-Zhabotinsky reaction. Droplets are separated by an oil phase that allows coupling between neighboring droplets via two species: an inhibitor, Br${}_2$, and an activator, HBrO${}_2$. Excitatory coupling alone (through the activator) generates in-phase oscillations and/or “waves,” while inhibitory coupling alone (through Br${}_2$) gives rise to antiphase oscillations, Turing patterns, and their combinations. The simultaneous presence of excitatory and inhibitory coupling leads to a large number of new spatiotemporal patterns, including some that exhibit very complex behavior. Analysis of a simple model allows us to simulate patterns resembling those observed experimentally under similar conditions and to elucidate the contributions of droplet and gap sizes, activator and inhibitor partition coefficients, and malonic acid concentration to the coupling strengths.

We consider here a recent conjecture stating that correlation functions and tail probabilities of finite time Lyapunov exponents would have the same power law decay in weakly chaotic systems. We demonstrate that this conjecture fails for a generic class of maps of the Pomeau-Manneville type. We show further that, typically, the decay properties of such tail probabilities do not provide significant information on key aspects of weakly chaotic dynamics such as ergodicity and instability regimes. Our approaches are firmly based on rigorous results, particularly the Aaronson-Darling-Kac theorem, and are also confirmed by exhaustive numerical simulations.

We present a numerical study of the magnetic field generated by the Taylor-Green vortex. We show that periodic boundary conditions can be used to mimic realistic boundary conditions by prescribing the symmetries of the velocity and magnetic fields. This gives insight into some problems of central interest for dynamos: the possible effect of velocity fluctuations on the dynamo threshold, and the role of boundary conditions on the threshold and on the geometry of the magnetic field generated by dynamo action. In particular, we show that an axial dipolar dynamo similar to the one observed in a recent experiment can be obtained with an appropriate choice of the symmetries of the magnetic field. The nonlinear saturation is studied and a simple model explaining the magnetic Prandtl number dependence of the super- and subcritical nature of the dynamo transition is given.

We investigate the nature of propagation of electromagnetic waves (EMWs) in an antiferromagnetic medium with Dzyaloshinsky-Moriya (DM) interaction environment. The interplay of bilinear and DM exchange spin coupling with the magnetic field component of the EMW has been studied by solving Maxwell's equations coupled with a nonlinear spin equation for the magnetization of the medium. We made a nonuniform expansion of the magnetization and magnetic field along the direction of propagation of EMW, in the framework of reductive perturbation method, and the dynamics of the system is found to be governed by a generalized derivative nonlinear Schrödinger (DNLS) equation. We employ the Jacobi-elliptic function method to solve the DNLS equation, and the electromagnetic wave propagation in an antiferromagnetic medium is governed by the breatherlike spatially and temporally coherent localized modes under the influence of DM interaction parameter.