Electric signals have been recently recorded at the Earth’s surface with amplitudes appreciably larger than those hitherto reported. Their entropy in natural time is smaller than that of a “uniform” distribution. The same holds for their entropy upon time reversal. Such a behavior, which is also found by numerical simulations in fractional Brownian motion time series and in an on-off intermittency model, stems from infinitely ranged long range temporal correlations and hence these signals are probably seismic electric signal activities (critical dynamics). This classification is strikingly confirmed since three strong nearby earthquakes occurred (which is an extremely unusual fact) after the original submission of the present paper. The entropy fluctuations are found to increase upon approaching bursting, which is reminiscent of the behavior identifying sudden cardiac death individuals when analyzing their electrocardiograms.

A theoretical study of energy and momentum accommodation coefficients and reduced force coefficients for molecular gases exchanging energy with surfaces has been carried out. The theoretical model uses classical mechanics for describing translational and rotational motions while internal molecular vibrational modes are treated quantum mechanically. Calculations for diatomic molecular gases are compared with recent measurements using hypersonic beams of ${\mathrm{N}}_2$ incident on ${\mathrm{SiO}}_2$ layers deposited on Kapton substrates. The theory gives good qualitative predictions of the behavior of the various accommodation coefficients as functions of the available experimentally controllable parameters such as incident translational energy, incident beam angle, molecular and surface masses, and surface temperature. Quantitative comparisons with measurements for energy and normal momentum accommodation indicate that these experiments can be used to obtain basic physical information about the molecule-surface interaction such as the physisorption potential well depth and the extent of surface roughness.

In liquids the decay of density fluctuations shows a slowing down at the structure factor maximum, which is well known as de Gennes narrowing. Molecular dynamics simulations of the liquid metal rubidium and mode coupling theory suggested that this process can be described by a two-step relaxation function. We have probed these predictions with inelastic neutron scattering using the spin-echo technique to measure the dynamics directly in the time domain. The dynamics of liquid rubidium was investigated near the melting point at times beyond the fast contribution. The resulting intermediate-scattering function is in remarkable agreement with predicted values from the mode coupling calculations.

The problem of coherent vortex and zonal jet formation in a system of oceanic or planetary nonlinear Rossby waves is considered from the point of view of the late time steady state achieved by free decay of a given initial state. Statistical equilibrium equations respecting all conservation laws are constructed for a broad class of models, generalizing those derived previously for two-dimensional inviscid Euler flow. Jetlike solutions are ubiquitous, with large coherent vortices existing only when there is a background flow whose velocity locally cancels the beta effect.

We study in detail the deformations of a liquid-liquid interface induced by the electromagnetic radiation pressure of a focused cw laser beam. Using a simple linear model of static equilibrium of the interface under the effect of radiation pressure, buoyancy, and Laplace pressure, we explain the observed hump height variations for any value of the optical Bond number ( is the capillary length and is the waist of the beam) in the regime of weak deformations and show that the deformations are independent of the direction of propagation of the laser. By increasing the beam power, we observe an instability of the interface leading to the formation of a long jet when the laser propagates from the more refringent phase to the less refringent one. We propose that the total internal reflection of the incident light on the highly deformed interface could be at the origin of this instability. Using a nonlinear model of static equilibrium of the interface taking account of the angular dependance of radiation pressure, we explain the measured beam power threshold of the instability , as well as the shape of the interface deformations observed at large waists just below the instability onset. According to this model, the instability should occur when the interface slope reaches the angle of total reflection, . We find experimentally that, just below the instability threshold, the maximum incidence angle along the interface, , is significantly smaller than and that our nonlinear model does not present any instability up to . Thus, although the proposed instability model correctly predicts the instability threshold , it fails to describe the actual instability mechanism. We finally discuss possible additional effects that could explain the instability.

We study the dynamics of the deformation of a soft liquid-liquid interface by the optical radiation pressure of a focused cw Gaussian laser beam. We measured the temporal evolution of both the hump height and the hump curvature by direct observation and by detecting the focusing effect of the hump acting as a lens. Extending the results of to the case of liquid-liquid interfaces and to the regime [, where is the beam waist and the capillary length], we show that, in the and ranges, the small-amplitude deformations are correctly described by a linear hydrodynamic theory predicting an overdamped dynamics. We also study the dynamics of the large-amplitude interface deformations at the onset of optohydrodynamic instability []. Using a simple, phenomenological model for the nonlinear evolution of the hump height, we interpret the observed interface dynamics at the instability onset as the signature of an imperfect subcritical instability.

Magnetic birefringence and dynamic light scattering measurements of orientational order parameter fluctuations at the isotropic-nematic phase transition of a bent-core liquid crystal reveal a pretransitional temperature dependence consistent with the standard Landau–deGennes mean field theory. However, as follows: the transition in the bent-core compound is more weakly first order $(T_{NI}-T^{*}\approx 0.4°\mathrm{C})$, the leading Landau coefficient is $\sim 30$ times lower, the viscosity associated with nematic order fluctuations is $\sim 10$ times higher, and the density change is $\sim 10$ times lower, than typically observed in calamitic (rod-shaped) liquid crystals. One consistent explanation for these anomalies is an optically isotropic phase composed of microscopic complexes or “clusters” of bent-core molecules.

We investigate particle transport in the honeycomb billiard which consists of connected channels placed on the edges of a honeycomb structure. The spreading of particles is superdiffusive due to the existence of ballistic trajectories which we term perfect paths. Simulations give a time exponent of 1.72 for the mean-square displacement and a starlike, i.e., anisotropic, particle distribution. We present an analytical treatment based on the formalism of continuous-time random walks and explain the anisotropic distribution under the assumption that the perfect paths follow the directions of the six lattice axes. Furthermore, we derive a relation between the time exponent and the exponent of the distribution function for trajectories close to a perfect path. In billiards with randomly distributed channels, conventional diffusion is always observed in the long-time limit, although for small disorder transient superdiffusional behavior exists. Our simulation results are again supported by an analytical analysis.

By using a perturbation approach, we investigate dynamic effects on nonlinear alternating current (ac) responses in electrorheological (ER) fluids under an ac or direct current electric field. We show that the dynamic effect due to a shear flow, which exerts a torque on ER particles and thus leads to the rotation of the particles about their centers, plays a significant role in the responses. Our results can be well interpreted in the dielectric dispersion spectral representation, and they offer a convenient method to determine the relaxation time and rotation velocity of ER particles by measuring the nonlinear ac responses.

The effect of interactions on dynamics of coupled motor proteins is investigated theoretically. A simple stochastic discrete model, which allows one to calculate explicitly the dynamic properties, is developed. It is shown that there are two dynamic regimes, depending on the interaction between the particles. For strong interactions the motor proteins move as one tight cluster, while for weak interactions there is no correlation in the motion of the proteins, and the particle separation increases steadily with time. The boundary between the two regimes is specified by a critical interaction that has a nonzero value only for the coupling of the asymmetric motor proteins, and it depends on the temperature and transition rates. At the critical interaction there is a change in slope for the mean velocities and a discontinuity in the dispersions of the motor proteins as a function of interactions.

We study theoretically the propagation of liquid surface waves over a bottom with one-dimensional (1D) periodic undulations. We find a general criterion for omnidirectional total reflection in such a system. Numerical simulations based on a transfer matrix method demonstrate unambiguously the existence of omnidirectional total reflection for liquid surface waves propagating over a bottom with 1D periodic undulations.

Stochastic dynamics is generated by a matrix of transition probabilities. Certain eigenvectors of this matrix provide observables, and when these are plotted in the appropriate multidimensional space the phases (in the sense of phase transitions) of the underlying system become manifest as extremal points. This geometrical construction, which we call an observable representation of state space, can allow hierarchical structure to be observed. It also provides a method for the calculation of the probability that an initial points ends in one or another asymptotic state.

We study centrality in urban street patterns of different world cities represented as networks in geographical space. The results indicate that a spatial analysis based on a set of four centrality indices allows an extended visualization and characterization of the city structure. A hierarchical clustering analysis based on the distributions of centrality has a certain capacity to distinguish different classes of cities. In particular, self-organized cities exhibit scale-free properties similar to those found in nonspatial networks, while planned cities do not.

We develop the general equation for the nonequilibrium reversible-irreversible coupling (GENERIC) framework of nonequilibrium thermodynamics for open systems. A clear distinction between bulk and boundary contributions to the Poisson and dissipative brackets employed to generate reversible and irreversible contributions to time evolution from energy and entropy allows us to formulate the bulk equations as well as the exchange and interaction with the environment directly. The full brackets keep all the structure and hence the predictive power of the original GENERIC for isolated systems. The straightforward procedure is illustrated for hydrodynamics of open systems. Boltzmann’s kinetic equation is discussed as a further example. In the Appendix, the thermodynamic treatment of surface excess variables at walls and their role in boundary conditions for the bulk variables is exemplified for a diffusion cell.

The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behavior into a central question of modern science. Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. Here we provide direct evidence that for five human activity patterns, such as email and letter based communications, web browsing, library visits and stock trading, the timing of individual human actions follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity. We show that the bursty nature of human behavior is a consequence of a decision based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, most tasks being rapidly executed, while a few experiencing very long waiting times. In contrast, priority blind execution is well approximated by uniform interevent statistics. We discuss two queuing models that capture human activity. The first model assumes that there are no limitations on the number of tasks an individual can hadle at any time, predicting that the waiting time of the individual tasks follow a heavy tailed distribution $P\left({\tau }_w\right)\sim {\tau }_w^{-\alpha }$ with $\alpha =3∕2$. The second model imposes limitations on the queue length, resulting in a heavy tailed waiting time distribution characterized by $\alpha =1$. We provide empirical evidence supporting the relevance of these two models to human activity patterns, showing that while emails, web browsing and library visitation display $\alpha =1$, the surface mail based communication belongs to the $\alpha =3∕2$ universality class. Finally, we discuss possible extension of the proposed queuing models and outline some future challenges in exploring the statistical mechanics of human dynamics.

We present a theorem that allows one to simplify the linear stability analysis of periodic and quasiperiodic nonlinear regimes in $N$-particle mechanical systems with different kinds of discrete symmetry. This theorem suggests a decomposition of the linearized system arising in the standard stability analysis into a number of subsystems whose dimensions can be considerably less than the dimension of the full system. As an example of such a simplification, we discuss the stability of bushes of modes (invariant manifolds) for the Fermi-Pasta-Ulam chains and prove another theorem about the maximal dimension of the above-mentioned subsystems.

We explore the effect of boundary curvature on the instability of reactive pulses in the catalytic oxidation of $\mathrm{CO}$ on microdesigned Pt catalysts. Using ring-shaped domains of various radii, we find that the pulses disappear (decollate from the inert boundary) at a turning point bifurcation, and we trace this boundary in both physical and geometrical parameter space. These computations corroborate experimental observations of pulse decollation.

We study Kuramoto oscillators, driven by one pacemaker, on $d$-dimensional regular topologies with nearest neighbor interactions. We derive the analytical expressions for the common frequency in the case of phase-locked motion and for the critical frequency of the pacemaker, placed at an arbitrary position in the lattice, so that above the critical frequency no phase-locked motion is possible. We show that the mere change in topology from an open chain to a ring induces synchronization for a certain range of pacemaker frequencies and couplings, while keeping the other parameters fixed. Moreover, we demonstrate numerically that the critical frequency of the pacemaker decreases as a power of the linear size of the lattice with an exponent equal to the dimension of the system. This leads in particular to the conclusion that for infinite-dimensional topologies the critical frequency for having entrainment decreases exponentially with increasing size of the system, or, more generally, with increasing depth of the network, that is, the average distance of the oscillators from the pacemaker.