This work deals with the propagation of granular-liquid waves over rigid beds, originated by the sudden removal of a sluice gate in a rectangular, inclined flume. In particular, we experimentally investigate the role of the initial volume ratio of granular material—monodispersed plastic cylinders—to water, the flume width, and the bed roughness on the time evolution of the granular front. Due to the presence of the interstitial liquid, we observed previously unreported types of collapse: (i) discontinuous flows, where the granular material stops after an initial spreading, and then flows again when the liquid, initially slower than the particles, reaches the front and remobilizes it; (ii) flows evolving into uniformly progressive waves at an angle of inclination of the flume well below the angle of repose of the dry granular material. We also noticed an unusual influence of the lateral confinement on the wave propagation. Indeed, the constant front velocity in the uniformly progressive state decreases when the channel width increases. We claim that the latter observation and the presence of discontinuous flows, strongly support the idea that only two-phase, stratified mathematical models can predict the behavior of unsteady, granular-liquid mixtures at high concentration, such as debris flows.

Two analytically tractable systems, Brownian particles in (i) moving harmonic oscillator or (ii) with a time-dependent natural frequency, obey a force fluctuation theorem similar to that proposed by Ponmurugan and Vemparala [Phys. Rev. E 84, 060101(R) (2011)]. Many of their results can be explained by using the former case as a model.

Analyzing real data on international trade covering the time interval 1950–2000, we show that in each year over the analyzed period the network is a typical representative of the ensemble of maximally random weighted networks, whose directed connections (bilateral trade volumes) are only characterized by the product of the trading countries' GDPs. It means that time evolution of this network may be considered as a continuous sequence of equilibrium states, i.e., a quasistatic process. This, in turn, allows one to apply the linear response theory to make (and also verify) simple predictions about the network. In particular, we show that bilateral trade fulfills a fluctuation-response theorem, which states that the average relative change in imports (exports) between two countries is a sum of the relative changes in their GDPs. Yearly changes in trade volumes prove that the theorem is valid.

In this paper we analyze stochastic synchronization of coupled chaotic maps over blinking networks composed of a pristine static network and stochastic on-off couplings between any pair of nodes. We focus on mean square linear stability of the synchronized state by analyzing the time evolution of the second moment of the variation transverse to the synchronization manifold. By projecting the variational equations on the eigenvectors of a higher order state matrix describing this variational dynamics, we establish a necessary and sufficient condition for stochastic synchronization based on the largest Lyapunov exponent of the map and the spectral radius of such matrix. This condition is further simplified by computing closed-form results for the spectral properties of the moments of the graph Laplacian associated to the intermittent coupling and using classical eigenvalue bounds. We illustrate the main results through simulations on synchronization of chaotic Henon maps.

The complementarity of the liquid and plasma descriptions of the classical one-component plasma is explored by studying wave number and frequency dependent dynamical quantities: the dynamical structure factor (DSF) and the dynamic local field correction (LFC). Accurate molecular dynamics (MD) simulations are used to validate and test models of the DSF and LFC. Our simulations, which span the entire fluid regime ($\Gamma =0.1–175$), show that the DSF is very well represented by a simple and well known memory function model of generalized hydrodynamics. On the other hand, the LFC, which we have computed using MD for the first time, is not well described by existing models.

Imaging techniques have been used to capture the temporal and spatial evolution of light emissions from collapsing bubble clouds at high static pressures. Emission events lasting up to 70 ns with peak diameters nearing 1 mm have been observed. Observations of the cloud evolution before and after emission events have been made. Photomultiplier tube monitoring has been employed in conjunction with imaging to study the temporal characteristics of light emission.

We propose a modularity optimization method, Mod-CSA, based on stochastic global optimization algorithm, conformational space annealing (CSA). Our method outperforms simulated annealing in terms of both efficiency and accuracy, finding higher modularity partitions with less computational resources required. The high modularity values found by our method are higher than, or equal to, the largest values previously reported. In addition, the method can be combined with other heuristic methods, and implemented in parallel fashion, allowing it to be applicable to large graphs with more than 10 000 nodes.

We show that the key transport states, insulating and conducting, of large regular networks of scatterers can be described generically by negative and zero Lyapunov exponents, respectively, of Möbius maps that relate the scattering matrix of systems with successive sizes. The conductive phase is represented by weakly chaotic attractors that have been linked with anomalous transport and ergodicity breaking. Our conclusions, verified for serial as well as parallel stub and ring structures, reveal that mesoscopic behavior results from a drastic reduction of degrees of freedom.

Numerical results for the directed polymer model in 1+4 dimensions in various types of disorder are presented. The results are obtained for a system size that is considerably larger than considered previously. For the extreme “strong” disorder case (min-max system), associated with the directed percolation model, the expected value of the meandering exponent, $\zeta =0.5$, is clearly revealed, with very weak finite size effects. For the “weak disorder” case, associated with the Kardar-Parisi-Zhang equation, finite size effects are stronger, but the value of $\zeta$ is clearly seen in the vicinity of 0.57. In systems with strong disorder it is expected that the system will cross over sharply from min-max behavior at short chains to weak disorder behavior at long chains. Our numerical results agree with that expectation. To complete the picture we obtain the energy fluctuation exponent $\omega$ for weak disorder, and we find that the value of $\omega$ is in the vicinity of 0.14. Thus, the meandering exponent and the energy fluctuation exponent obey the strong coupling scaling relation $2\xi -\omega =1$. Our results indicate that 1+4 is not the upper critical dimension in the weak disorder case, and thus 4+1 does not seem to be the upper critical dimension for the Kardar-Parisi-Zhang equation.

The nonequilibrium phase transition in driven two-dimensional Ising models with two different geometries is investigated using Monte Carlo methods as well as analytical calculations. The models show dissipation through fluctuation induced friction near the critical point. We first consider high driving velocities and demonstrate that both systems are in the same universality class and undergo a strongly anisotropic nonequilibrium phase transition, with anisotropy exponent $\theta =3$. Within a field theoretical ansatz the simulation results are confirmed. The crossover from Ising to mean field behavior in dependency of system size and driving velocity is analyzed using crossover scaling. It turns out that for all finite velocities the phase transition becomes strongly anisotropic in the thermodynamic limit.

We describe statistical properties of a single element in a nonlinear stochastic array with a finite number of elements with mean-field-like (global) coupling. Desai and Zwanzig [J. Stat. Phys. 19, 1 (1978)] made use of a self-consistent dynamic mean-field ansatz to derive, in the infinite-size limit, a nonlinear Fokker-Planck equation (NLFPE) for the single-particle distribution function. In this work we explore the reliability of this approximation to describe a finite system with a small number of elements. We carry out a numerical analysis of the NLFPE as well as numerical simulations of the full set of Langevin equations governing the dynamics of the coupled elements. We find that for parameter values such that the NLFPE has a single stationary solution, it provides a reliable asymptotic approximation to the time evolution and stationary properties of a finite system of even modest size. In contrast, for parameter values such that the NLFPE has two stable stationary coexisting solutions, the NLFPE leads to results that are greatly at variance with those obtained from the numerical simulations of the Langevin equations for small systems.

Recent progress in the study of dynamical phase transitions has been made with a large-deviation approach to study trajectories of stochastic jumps using a thermodynamic formalism. We study this method applied to an open quantum system consisting of a superconducting single-electron transistor, near the Josephson quasiparticle resonance, coupled to a resonator. We find that the dynamical behavior shown in rare trajectories can be rich even when the mean dynamical activity is small, and thus the formalism gives insights into the form of fluctuations. The structure of the dynamical phase diagram found from the quantum-jump trajectories of the resonator is studied, and we see that sharp transitions in the dynamical activity may be related to the appearance and disappearance of bistabilities in the state of the resonator as system parameters are changed. We also demonstrate that for a fast resonator, the trajectories of quasiparticles are similar to the resonator trajectories.

Nonequilibrium behavior and dynamic phase-transition properties of a kinetic Ising model under the influence of periodically oscillating random fields have been analyzed within the framework of effective-field theory based on a decoupling approximation. A dynamic equation of motion has been solved for a simple-cubic lattice ($q=6$) by utilizing a Glauber-type stochastic process. Amplitude of the sinusoidally oscillating magnetic field is randomly distributed on the lattice sites according to bimodal and trimodal distribution functions. For a bimodal type of amplitude distribution, it is found in the high-frequency regime that the dynamic phase diagrams of the system in the temperature versus field amplitude plane resemble the corresponding phase diagrams of the pure kinetic Ising model. Our numerical results indicate that for a bimodal distribution, both in the low- and high-frequency regimes, the dynamic phase diagrams always exhibit a coexistence region in which the stationary state (ferro or para) of the system is completely dependent on the initial conditions, whereas for a trimodal distribution, the coexistence region disappears depending on the values of the system parameters.

We consider an overdamped Brownian particle moving in a confining asymptotically logarithmic potential, which supports a normalized Boltzmann equilibrium density. We derive analytical expressions for the two-time correlation function and the fluctuations of the time-averaged position of the particle for large but finite times. We characterize the occurrence of aging and nonergodic behavior as a function of the depth of the potential, and we support our predictions with extensive Langevin simulations. While the Boltzmann measure is used to obtain stationary correlation functions, we show how the non-normalizable infinite covariant density is related to the superaging behavior.

The effect of temporal disorder on systems with up-down $Z_2$ symmetry is studied. In particular, we analyze two well-known families of phase transitions—the Ising and the generalized voter universality classes—and scrutinize the consequences of placing them under fluctuating global conditions. We observe that variability of the control parameter induces in both classes “temporal Griffiths phases” (TGPs). These recently uncovered phases are analogous to standard Griffiths phases appearing in systems with quenched spatial disorder, but where the roles of space and time are exchanged. TGPs are characterized by broad regions in parameter space in which (i) mean first-passage times scale algebraically with system size, and (ii) the system response (e.g., susceptibility) diverges. Our results confirm that TGPs are quite robust and ubiquitous in the presence of temporal disorder. Possible applications of our results to examples in ecology are discussed.

Transverse relaxation by dephasing in an inhomogeneous field is a general mechanism in physics, for example, in semiconductor physics, muon spectroscopy, or nuclear magnetic resonance. In magnetic resonance imaging the transverse relaxation provides information on the properties of several biological tissues. Since the dipole field is the most important part of the multipole expansion of the local inhomogeneous field, dephasing in a dipole field is highly important in relaxation theory. However, there have been no analytical solutions which describe the dephasing in a magnetic dipole field. In this work we give a complete analytical solution for the dephasing in a magnetic dipole field which is valid over the whole dynamic range.

We introduce a class of weighted graphs whose properties are meant to mimic the topological features of idiotypic networks, namely, the interaction networks involving the B core of the immune system. Each node is endowed with a bit string representing the idiotypic specificity of the corresponding B cell, and the proper distance between any couple of bit strings provides the coupling strength between the two nodes. We show that a biased distribution of the entries in bit strings can yield fringes in the (weighted) degree distribution, small-world features, and scaling laws, in agreement with experimental findings. We also investigate the role of aging, thought of as a progressive increase in the degree of bias in bit strings, and we show that it can possibly induce mild percolation phenomena, which are investigated too.

Electrostatic potential of a slowly moving ion in quantum plasmas is studied. This potential is composed of the Debye-Hückel potential and the wake potential. The near-field-wake potential is found. The binding energy levels of one-electron bound states of the ion are calculated by use of the Ritz variation method. The trial wave function contains three variational parameters. The presence of the wake field splits the binding energy levels. This effect is analogous to the Zeeman effect. The removal of the degeneracy of binding energy levels is influenced by the speed of ion and the number density of electrons. Compared with binding energy levels of a free ion, some binding energy levels of a moving ion in quantum plasmas are “pushed up.”

We study spectral properties and the dynamics after a quench of one-dimensional spinless fermions with short-range interactions and long-range random hopping. We show that a sufficiently fast decay of the hopping term promotes localization effects at finite temperature, which prevents thermalization even if the classical motion is chaotic. For slower decays, we find that thermalization does occur. However, within this model, the latter regime falls in an unexpected universality class, namely, observables exhibit a power-law (as opposed to an exponential) approach to their thermal expectation values.

We present a numerical study of random packings made of nonconvex grains. These particles are built by the agglomeration of overlapping spheres in order to control their sphericity $\phi$. The contact number $C$ is found to be much larger than the coordination number $Z$, providing a significant difference with convex grains. The packing properties are found to be highly dependent on the morphological parameters of the grains : packing fractions as low as 0.3 have been reached. More importantly, the way nonconvex grains develop multiple contacts, i.e., interlocking, is found to be a relevant effect in such packings. Interlocking provides more stability to loose packings.