States supported by chaotic open quantum systems fall into two categories: a majority showing instantaneous ballistic decay, and a set of quantum resonances of classically vanishing support in phase space. We present a theory describing these structures within a unified semiclassical framework. Emphasis is put on the quantum diffraction mechanism which introduces an element of probability and is crucial for the formation of resonances. Our main result is boundary conditions on the semiclassical propagation along system trajectories. Depending on whether the trajectory propagation time is shorter or longer than the Ehrenfest time, these conditions describe deterministic escape, or probabilistic quantum decay.

We apply the Empirical Mode Decomposition method to extract intrinsic modes in the fluctuations of the spectra of random matrices. The hierarchy of the modes follows a power law with an exponent that changes smoothly in the whole range of the transition from the Gaussian orthogonal to the Gaussian diagonal ensemble. This property of scale invariance represents a new quantification of quantum chaos in systems that are characterized by the statistics of Random Matrix Theory.

Molecular dynamics (MD) simulation is used to study slip at the fluid-solid boundary in an unsteady flow based on the Stokes’ second problem. An increase in slip is observed in comparison to the steady flow for shear rates below the critical shear rate of the corresponding steady flow. This increased slip is attributed to fluid inertial forces not represented in a steady flow. An unsteady mathematical model for slip is established, which estimates the increment in slip at the boundary. The model shows that slip is also dependent on acceleration in addition to the shear rate of fluid at the wall. By writing acceleration in terms of shear rate, it is shown that slip at the wall in unsteady flows is governed by the gradient of shear rate and shear rate of the fluid. Nondimensionalizing the model gives a time dependent yet universal curve, independent of wall-fluid properties, which can be used to find the slip boundary condition at the fluid-solid interface based on the information of shear rate, gradient of shear rate of the fluid, and the instant of time during the cycle. A governing nondimensional number, defined as the ratio of phase speed to speed of sound, is identified to help in explaining the mechanism responsible for the transition of slip boundary condition from finite to a perfect slip and determining when this would occur. Phase lag in fluid velocity relative to wall is observed. The lag increases with decreasing time period of wall oscillation and increasing wall hydrophobicity. The phenomenon of hysteresis is seen when looking into the variation of slip velocity as a function of wall velocity and slip velocity as a function of fluid shear rate. The cause for hysteresis is attributed to the unsteady inertial forces of the fluid. The rate of heat generated by viscous shear is compared for an unsteady Stokes’ second problem and simple Couette flow and is shown to be higher for the unsteady flow.

Motivated by the classical picture of heat flow, we construct a stationary temperature gradient in a relativistic microscopic transport model. Employing the relativistic Navier-Stokes ansatz, we extract the heat conductivity $\kappa$ for a massless Boltzmann gas using only binary collisions with isotropic cross sections. We compare the numerical results to analytical expressions from different theories and discuss the final results. The directly extracted value for the heat conductivity can be referred to as a literature reference within the numerical uncertainties.

Dynamical processes exhibiting non-Poissonian kinetics with nonexponential waiting times are frequently encountered in nature. Examples are biochemical processes like gene transcription which are known to involve multiple intermediate steps. However, often a second process, obeying Poissonian statistics, affects the first one simultaneously, such as the degradation of mRNA in the above example. The aim of the present article is to provide a concise treatment of such random systems which are affected by regular and non-Poissonian kinetics at the same time. We derive the governing master equation and provide a controlled approximation scheme for this equation. The simplest approximation leads to generalized reaction rate equations. For a simple model of gene transcription we solve the resulting equation and show how the time evolution is influenced significantly by the type of waiting time distribution assumed for the non-Poissonian process.

This is the first paper of a series devoted to the micro-mechanical modeling of clayey soils, by means of discrete element simulations. We specifically focus here on the effect of the platy shape of particles by reducing the interactions between particles to mechanical contact forces (i.e., neither electrostatic repulsion nor van der Waals forces are taken into account). The particles are three-dimensional square plates, approximated as spheropolyhedra. Several samples composed of particles of different levels of platyness (related to the ratio of length to thickness) were numerically prepared and sheared up to large deformations. We analyzed the shear strength, packing fraction, orientation of the particles, connectivity, fabric of the interactions network, and interaction forces as functions of the platyness. We find that both the mechanical behavior and microstructure are strongly dependent on the degree of platyness. The principal underlying phenomenon is the alignment of particle faces along a particular direction. This ordering phenomenon, which emerges even for shapes that deviate only slightly from that of a sphere, enhances the ability of the packing to develop an anisotropic structure leading to large shear strength, especially as a consequence of the fabric and mobilization of friction forces. Moreover, the connectivity of the packings and their packing fraction also evolve with the platyness. In particular, the packing fraction evolves in a nonmonotonic fashion, as observed in other granular materials composed of elongated or angular particles.

We present a study of the DNA translocation of the bacteriophage $\varphi 29$ packaging molecular motor. From the available experimental information we present a model system based on a stochastic flashing potential, which reproduces the experimental observations such as detailed trajectories, steps and substeps, spatial correlation, and velocity. Moreover, the model allows the evaluation of the power and efficiency of this motor. We have found that the maximum power regime does not correspond with that of the maximum efficiency. This information can stimulate further experiments.

We study the influence of motion on the emergence of synchronization in a metapopulation of random walkers moving on a heterogeneous network and subject to Kuramoto interactions at the network nodes. We discover a mechanism of transition to macroscopic dynamical order induced by the walkers’ motion. Furthermore, we observe two different microscopic paths to synchronization: depending on the rule of the motion, either low-degree nodes or the hubs drive the whole system towards synchronization. We provide analytical arguments to understand these results.

The recursive removal of leaves (dead end vertices) and their neighbors from an undirected network results, when this pruning algorithm stops, in a so-called core of the network. This specific subgraph should be distinguished from $k$-cores, which are principally different subgraphs in networks. If the vertex mean degree of a network is sufficiently large, the core is a giant cluster containing a finite fraction of vertices. We find that generalization of this pruning algorithm to directed networks provides a significantly more complex picture of cores. By implementing a rate equation approach to this pruning procedure for directed uncorrelated networks, we identify a set of cores progressively embedded into each other in a network and describe their birth points and structure.

It is well known that solutions to the Fourier-Galerkin truncation of the inviscid Burgers equation (and other hyperbolic conservation laws) do not converge to the physically relevant entropy solution after the formation of the first shock. This loss of convergence was recently studied in detail [Ray et al., Phys. Rev. E 84, 016301 (2011)] and traced back to the appearance of a spatially localized resonance phenomenon perturbing the solution. In this work we propose a way to remove this resonance by filtering a wavelet representation of the Galerkin-truncated equations. A method previously developed with a complex-valued wavelet frame is applied and expanded to embrace the use of real-valued orthogonal wavelet bases, which we show to yield satisfactory results only under the condition of adding a safety zone in wavelet space. We also apply the complex-valued wavelet based method to the two-dimensional Euler equation problem, showing that it is able to filter the resonances in this case as well.

We investigate the dynamics of solitons of the cubic nonlinear Schrödinger equation with an external time-independent force of the form $f\left(x\right)=r\exp (-iKx)$. Here the solitons travel with an oscillating velocity and all other characteristics of the solitons (amplitude, width, momentum, and phase) also oscillate. This behavior was predicted by a collective variable theory and confirmed by simulations. However, the reason for these oscillations remains unclear. Moreover, the spectrum of the oscillations exhibits a second strong peak, in addition to the intrinsic soliton peak. We show that the additional frequency belongs to a certain extended linear mode (which we refer to as a phonon for short) close to the lower band edge of the phonon continuum. Initially the soliton is at rest. When it starts to move it is deformed, begins to oscillate, and excites the above phonon mode such that the total momentum in a certain moving frame is conserved. In this frame the phonon does not move. However, not only does the soliton move in the homogeneous, time-periodic field of the phonon, but it also oscillates.

Prompted by recent findings [Teboul, Saiddine, and Nunzi, Phys. Rev. Lett. 103, 265701 (2009); Orsi et al., Phys. Rev. E 82, 031804 (2010)] that the isomerization of few azobenzene molecules dispersed in a glass former greatly enhances the dynamic heterogeneity (DH) of the medium, we raise the issue as to whether the isomerization process gives rise to additional DHs or whether instead it stimulates the mechanisms at the origin of the thermal DHs, accelerating them in time. To this end, molecular dynamics simulations are made to study the much insightful four-point susceptibility, dynamic facilitation, and Van Hove correlation functions both when the isomerization is activated and when it is artificially switched off. Our results do not rule out any of the two scenarios as a possible cause for the enhancement of DHs upon switching on the isomerization process, but clearly show that the second one is by far the dominant mechanism in the dynamics of the supercooled liquid.

The scaling of transient times to zero-lag synchronization in networks composed of excitable units is shown to be governed by three features of the graph representing the network: the longest path between pairs of neurons (diameter), the largest loop (circumference) and the loop with the maximal average out degree. The upper bound of transient times can vary between $O\left(1\right)$ and $O\left(N^2\right)$, where $N$ is the size of the network, and its scaling can be predicted in many scenarios from finite time accumulated information of the transient. Results challenge the assumption that functionality of neural networks might depend solely upon the synchronized repeated activation such as zero-lag synchronization.

In this study, a multifractal formalism based on the empirical mode decomposition is proposed. Scaling exponents are estimated from statistical moments computed over a discrete set of multiresolution parameters, namely, the dominant amplitude coefficients, which are selected among the local maxima observed across the set of envelopes of the intrinsic mode functions. Analyses of synthetic fractal and multifractal processes demonstrate that the proposed technique is capable of overcoming the negative moment divergence problem, and is competitive with other multifractal formalisms.

Terahertz (THz) radiation via the two-color laser scheme is investigated theoretically and numerically when the second laser is at different harmonic orders of the main laser. It is found that THz radiation can be generated only when the second laser is an even harmonic and the THz field strength does not show a simple scaling with the two laser amplitudes, suggesting that this is different from normal optical rectification or frequency mixing processes. The THz strength generally tends to decrease with increase of the even harmonic order. The strength is also sensitive to the carrier envelope (CE) phases of both the laser pulses even if their durations are quite long. With different CE phases, the strength can be proportional to either the sine or cosine of the relative phase displacement of the two lasers. For a given gas target except hydrogen, it increases with the laser amplitude between several saturation plateaus, each corresponding to a different ionization level. For a given main laser intensity, there is an optimized intensity of the second laser for the strongest THz radiation.

We study the role of delay in phase synchronization and phenomena responsible for cluster formation in delayed coupled maps on various networks. Using numerical simulations, we demonstrate that the presence of delay may change the mechanism of the unit to unit interaction. At weak coupling values, the same parity delays are associated with the same phenomenon of cluster formation and exhibit similar dynamical evolution. Intermediate coupling values yield rich delay-induced driven cluster patterns. A Lyapunov function analysis sheds light on the robustness of the driven clusters observed for delayed bipartite networks. Our results reveal that delay may lead to a completely different relation, between dynamical and structural clusters, than that observed for the undelayed case.

We show that microseismic events—earthquakes with small magnitudes—can be fruitfully used to gain insight into the properties of the fracture network of large-scale porous media, such as oil, gas, and geothermal reservoirs. As an example, we analyze extensive data for the Geysers geothermal field in northeast California. Injection of cold water into the reservoir to produce steam leads to microseismic events. It is demonstrated that the analysis can also lead to insight into whether the fractures are of tectonic type or induced by injection of cold water. To demonstrate this we estimate, using the catalogue of the microseismic events, the fractal dimension $D_f$ of the spatial distribution of hypocenters of the events in three seismic clusters associated with the injection of cold water into the field, as well as the $b$ values in the Gutenberg-Richter frequency-magnitude distribution. The fractal dimensions are all in a narrow range centered around $D_f\simeq 2.57\pm 0.06$, comparable to the measured fractal dimension of fracture sets in the greywacke reservoir rock. For most cases the $b$ values are about $b\simeq 1.3\pm 0.1$, consistent with the Aki relation, $D_f=2b$. Both $D_f$ and $b$ are significantly higher than those commonly observed for regional tectonic seismicity or aftershock sequences for which $D_f\approx 2$ and $b\approx 1$ are typical. Our results do not imply that no tectonic triggering exists in the reservoir, but rather that the overpressure allows the activation of less favorably oriented fractures that produce an increase in both $b$ and $D_f$. The estimate $D_f\approx 2$ for tectonic seismicity has been interpreted as indicating that most tectonic events occur on the subset of near-vertical faults—because they have lower normal stress—or that they occur on the backbone of the fracture and fault network, the multiply connected part of the network that enables finite shear strain. Our results lend support to the latter. The results that the entire fracture network, and not just its backbone, is active at the Geysers indicate that the seismicity is not a result of the triggered release of tectonic stress, but is induced by the release of local stress concentrations, driven by thermal contraction that is not constrained by friction. The possible implication for hydraulic fracturing—so-called fracking—is also briefly discussed.

We study diffusion processes of local fluctuations of heat, energy, momentum, and mass in three paradigmatic one-dimensional systems. For each system, diffusion processes of four physical quantities are simulated and the cross correlations between them are investigated. We find that, in all three systems, diffusion processes of energy and mass can be perfectly expressed as a linear combination of those of heat and momentum, suggesting that diffusion processes of heat and momentum may represent the heat mode and the sound mode in the hydrodynamic theory. In addition, the dynamic structure factor, which describes the diffusion behavior of local mass density fluctuations, is in general insufficient for probing diffusion processes of other quantities because in some cases there is no correlation between them. We also find that the diffusion behavior of heat can be qualitatively different from that of energy, and, as a result, previous studies trying to relate heat conduction to energy diffusion should be revisited.

The transverse-field Ising models with random exchange interactions in finite dimensions are investigated by means of a real-space renormalization-group method. The scheme yields the exact values of the critical point and critical exponent $\nu$ in one dimension and some previous results in the case of random ferromagnetic interactions are reproduced in two and three dimensions. We apply the scheme to spin glasses in transverse fields in two and three dimensions, which have not been analyzed very extensively. The phase diagrams and the critical exponent $\nu$ are obtained and evidence for the existence of an infinite-randomness fixed point in these models is found.