I adapted a model recently introduced in the context of seismic phenomena to study creep rupture of materials. It consists of linear elastic fibers that interact in an equal load sharing scheme, complemented with a local viscoelastic relaxation mechanism. The model correctly describes the three stages of the creep process; namely, an initial Andrade regime of creep relaxation, an intermediate regime of rather constant creep rate, and a tertiary regime of accelerated creep toward final failure of the sample. In the tertiary regime, creep rate follows the experimentally observed creep rate over time-to-failure dependence. The time of minimum strain rate is systematically observed to be about 60%–65 % of the time to failure, in accordance with experimental observations. In addition, burst size statistics of breaking events display a $-3/2$ power law for events close to the time of failure and a steeper decay for the all-time distribution. Statistics of interevent times shows a tendency of the events to cluster temporarily. This behavior should be observable in acoustic emission experiments.

Many natural and technological applications generate time-ordered sequences of networks, defined over a fixed set of nodes; for example, time-stamped information about “who phoned who” or “who came into contact with who” arise naturally in studies of communication and the spread of disease. Concepts and algorithms for static networks do not immediately carry through to this dynamic setting. For example, suppose A and B interact in the morning, and then B and C interact in the afternoon. Information, or disease, may then pass from A to C, but not vice versa. This subtlety is lost if we simply summarize using the daily aggregate network given by the chain A-B-C. However, using a natural definition of a walk on an evolving network, we show that classic centrality measures from the static setting can be extended in a computationally convenient manner. In particular, communicability indices can be computed to summarize the ability of each node to broadcast and receive information. The computations involve basic operations in linear algebra, and the asymmetry caused by time’s arrow is captured naturally through the noncommutativity of matrix-matrix multiplication. Illustrative examples are given for both synthetic and real-world communication data sets. We also discuss the use of the new centrality measures for real-time monitoring and prediction.

We propose a modified time lag random matrix theory in order to study time-lag cross correlations in multiple time series. We apply the method to 48 world indices, one for each of 48 different countries. We find long-range power-law cross correlations in the absolute values of returns that quantify risk, and find that they decay much more slowly than cross correlations between the returns. The magnitude of the cross correlations constitutes “bad news” for international investment managers who may believe that risk is reduced by diversifying across countries. We find that when a market shock is transmitted around the world, the risk decays very slowly. We explain these time-lag cross correlations by introducing a global factor model (GFM) in which all index returns fluctuate in response to a single global factor. For each pair of individual time series of returns, the cross correlations between returns (or magnitudes) can be modeled with the autocorrelations of the global factor returns (or magnitudes). We estimate the global factor using principal component analysis, which minimizes the variance of the residuals after removing the global trend. Using random matrix theory, a significant fraction of the world index cross correlations can be explained by the global factor, which supports the utility of the GFM. We demonstrate applications of the GFM in forecasting risks at the world level, and in finding uncorrelated individual indices. We find ten indices that are practically uncorrelated with the global factor and with the remainder of the world indices, which is relevant information for world managers in reducing their portfolio risk. Finally, we argue that this general method can be applied to a wide range of phenomena in which time series are measured, ranging from seismology and physiology to atmospheric geophysics.

Once controlled for the trend, the distribution of personal income appears to be double Pareto, a distribution that obeys the power law exactly in both the upper and the lower tails. I propose a model of income dynamics with a stationary distribution that is consistent with this fact. Using US male wage data for 1970–1993, I estimate the power law exponent in two ways—(i) from each cross section, assuming that the distribution has converged to the stationary distribution, and (ii) from a panel directly estimating the parameters of the income dynamics model—and obtain the same value of 8.4.

This paper proposes a deterministic complex network model, which is inspired by the natural ripple-spreading phenomenon. The motivations and main advantages of the model are the following: (i) The establishment of many real-world networks is a dynamic process, where it is often observed that the influence of a few local events spreads out through nodes, and then largely determines the final network topology. Obviously, this dynamic process involves many spatial and temporal factors. By simulating the natural ripple-spreading process, this paper reports a very natural way to set up a spatial and temporal model for such complex networks. (ii) Existing relevant network models are all stochastic models, i.e., with a given input, they cannot output a unique topology. Differently, the proposed ripple-spreading model can uniquely determine the final network topology, and at the same time, the stochastic feature of complex networks is captured by randomly initializing ripple-spreading related parameters. (iii) The proposed model can use an easily manageable number of ripple-spreading related parameters to precisely describe a network topology, which is more memory efficient when compared with traditional adjacency matrix or similar memory-expensive data structures. (iv) The ripple-spreading model has a very good potential for both extensions and applications.

We study the thermalization of the classical Klein-Gordon equation under a $u^4$ interaction. We numerically show that even in the presence of strong nonlinearities, the local thermodynamic equilibrium state exhibits a weakly nonlinear behavior in a renormalized wave basis. The renormalized basis is defined locally in time by a linear transformation and the requirement of vanishing wave-wave correlations. We show that the renormalized waves oscillate around one frequency, and that the frequency dispersion relation undergoes a nonlinear shift proportional to the mean square field. In addition, the renormalized waves exhibit a Planck-like spectrum. Namely, there is equipartition of energy in the low-frequency modes described by a Boltzmann distribution, followed by a linear exponential decay in the high-frequency modes.

We have performed an experiment to demonstrate the approximate time reversal of a “chaotic” time evolution of atomic de Broglie waves. We use ultracold atoms from a Bose-Einstein condensate in a quantum $\delta$-kicked rotor experiment, and show that an initial state can be approximately re-created even after a period of “chaotic” evolution (a number of kicks). As this mechanism only works for a very narrow range of momenta, the net effect is a narrowing of the momentum distribution after the kick sequence.

We verify numerically the phenomenon of logical stochastic resonance in a polarization bistable laser. Namely, we show that when one presents two weak binary inputs to the laser system, the response mirrors a logical or(nor) output. The reliability of the logic operation is dependent on the noise intensity. As one increases the noise, the probability of the output reflecting the desired or(nor) operation increases to nearly unity and then decreases. We also demonstrate that changing the bias morphs the output into another logic operation, and(nand), whose probability displays analogous behavior. Furthermore, we highlight the possibility of processing two logic gates in parallel in our laser system by exploiting two coupled orthogonal polarizations that can be detected simultaneously. This suggests that the computational power of the optical system may be enhanced by this additional potential for parallel processing.

We investigate analytically and numerically the conditions for the Turing instability to occur in a one-dimensional chain of nonlinear oscillators coupled nonlocally, in such a way that the coupling strength decreases with the spatial distance as a power law. A range parameter makes it possible to cover the two limiting cases of local (nearest-neighbor) and global (all-to-all) couplings. We consider an example from a nonlinear autocatalytic reaction-diffusion model.

Inspired by recent laboratory observations, we propose a mechanical model for eccentrically weighted motors coupled through a vibrating plate. The equations are found to generalize those of Kuramoto to frequency- and position-dependent coupling. The behavior of the model, as determined analytically for no disorder and numerically for systems with and without quenched disorder, shows the key features observed in the laboratory, including hysteresis, bistability, and a spectral gap. The model exhibits stimulated emission and discontinuous lasinglike transitions.

The transient electron temperature in a weakly ionized femtosecond-laser-produced air plasma filament was determined from optical absorption and diffraction experiments. The electron temperature and plasma density decay on similar time scales of a few hundred picoseconds. Comparison with plasma theory reveals the importance of inelastic collisions that lead to energy transfer to vibrational degrees of freedom of air molecules during the plasma cooling.

By using three tunable wavelengths on different cones of laser beams on the National Ignition Facility, numerical simulations show that the energy transfer between beams can be tuned to redistribute the energy within the cones of beams most prone to backscatter instabilities. These radiative hydrodynamics and laser-plasma interaction simulations have been tested against large-scale hohlraum experiments with two tunable wavelengths and reproduce the hohlraum energetics and symmetry. Using a third wavelength provides a greater level of control of the laser energy distribution and coupling in the hohlraum, and could significantly reduce stimulated Raman scattering losses and increase the hohlraum radiation drive while maintaining a good implosion symmetry.

We study the interaction of highly nonlinear solitary waves propagating in granular crystals with an adjacent linear elastic medium. We investigate the effects of interface dynamics on the reflection of incident waves and on the formation of primary and secondary reflected waves. Experimental tests are performed to correlate the linear medium geometry, materials, and mass with the formation and propagation of reflected waves. We compare the experimental results with theoretical analysis based on the long-wavelength approximation and with numerical predictions obtained from discrete particle models. Experimental results are found to be in agreement with theoretical analysis and numerical simulations. This preliminary study establishes the foundation for utilizing reflected solitary waves as novel information carriers in nondestructive evaluation of elastic material systems.

We propose an approach to derive the thermal lattice Boltzmann method that is based on the Taylor expansion in variables of temperature as well as velocity and a direct calculation upon the Gaussian quadrature based hypothesis. This enables us to overcome the isothermal limitation and the low-order accuracy simultaneously. A systematic framework is explained for constructing numerically stable lattice Boltzmann models. The stability of this one-dimensional lattice Boltzmann model is demonstrated with a shock tube simulation.

This work analyzes numerically the role played by the asymmetry of a piecewise linear potential, in the presence of both a Gaussian white noise and a dichotomous noise, on the resonant activation phenomenon. The features of the asymmetry of the potential barrier arise by investigating the stochastic transitions far behind the potential maximum, from the initial well to the bottom of the adjacent potential well. Because of the asymmetry of the potential profile together with the random external force uniform in space, we find, for the different asymmetries: (1) an inversion of the curves of the mean first passage time in the resonant region of the correlation time $\tau$ of the dichotomous noise, for low thermal noise intensities; (2) a maximum of the mean velocity of the Brownian particle as a function of $\tau$; and (3) an inversion of the curves of the mean velocity and a very weak current reversal in the miniratchet system obtained with the asymmetrical potential profiles investigated. An inversion of the mean first passage time curves is also observed by varying the amplitude of the dichotomous noise, behavior confirmed by recent experiments.

The long-time dynamics and pattern formation in semidilute suspensions of colloidal spheres in a viscous electrolyte under a uniform electric field are investigated using numerical simulations. The rapid chain formation that occurs in the field direction as a result of dipolar interactions is found to be followed by a slow coarsening process by which chains coalesce into hexagonal sheets and eventually rearrange to form mesoscale cellular structures, in qualitative agreement with recent experiments. The morphology and characteristic wavelength of the patterns that emerge at steady state are shown to depend on the suspension’s volume fraction, electrode spacing, and field strength, suggesting additional ways of controlling effective suspension properties in practical applications.

We propose a mechanism to grow a large superlattice of phase domains from a continuum homogenous binary film by sequential activation of self-assembly. Self-assembly was initiated in a small mobile region (where atoms could diffuse) to form a seed pattern, and then the mobile region was shifted gradually. This process led to a long-range ordered superlattice regardless whether the seed was perfect or not, since the pattern quickly improved to a perfect superlattice along with the sequential activation. At a bistable state the scanning velocity controlled the type of superlattice. Further exploration led to an intriguing finding that we call the self-activation of self-assembly, a domino effect where the self-assembly in a small region causes a long-range interaction that destabilizes its homogeneous neighbor and triggers the propagation of self-assembly to the entire system.

A capsule is a liquid drop enclosed by a solid, deformable membrane. To analyze the deformation of a capsule accurately, both the fluid mechanics of the internal and external fluids and the solid mechanics of the membrane must be solved precisely. Recently, many researchers have used discrete spring network models to express the membrane mechanics of capsules and biological cells. However, it is unclear whether such modeling is sufficiently accurate to solve for capsule deformation. This study examines the correlations between the mechanical properties of the discrete spring network model and continuum constitutive laws. We first compare uniaxial and isotropic deformations of a two-dimensional (2D) sheet, both analytically and numerically. The 2D sheet is discretized with four kinds of mesh to analyze the effect of the spring network configuration. We derive the relationships between the spring constant and continuum properties, such as the Young modulus, Poisson ratio, area dilation modulus, and shear modulus. It is found that the mechanical properties of spring networks are strongly dependent on the mesh configuration. We then calculate the deformation of a capsule under inflation and in a simple shear flow in the Stokes flow regime, using various membrane models. To achieve high accuracy in the flow calculation, a boundary-element method is used. Comparing the results between the different membrane models, we find that it is hard to express the area incompressibility observed in biological membranes using a simple spring network model.

Anomalous diffusion, observed in many biological processes, is a generalized description of a wide variety of processes, all obeying the same law of mean-square displacement. Identifying the basic mechanisms of these observations is important for deducing the nature of the biophysical systems measured. We implement a previously suggested method for distinguishing between fractional Langevin dynamics, fractional Brownian motion, and continuous time random walk based on the ergodic nature of the data. We apply the method together with the recently suggested $P$-variation test and the displacement correlation to the lately measured dynamics of telomeres in the nucleus of mammalian cells and find strong evidence that the telomeres motion obeys fractional dynamics. The ergodic dynamics are observed experimentally to fit fractional Brownian or Langevin dynamics.