The phase-ordering properties of lattices of band-chaotic maps coupled diffusively with some coupling strength $g$ are studied in order to determine the limit value $g_{\mathrm{e}}$ beyond which multistability disappears and nontrivial collective behavior is observed. The persistence of equivalent discrete spin variables and the characteristic length of the patterns observed scale algebraically with time during phase ordering. The associated exponents vary continuously with $g$ but remain proportional to each other, with a ratio close to that of the time-dependent Ginzburg-Landau equation. The corresponding individual values seem to be recovered in the space-continuous limit.

Symbolic dynamics play a central role in the description of the evolution of nonlinear systems. Yet there are few methods for determining symbolic dynamics of chaotic data. One difficulty is that the data contains random fluctuations associated with the experimental process. Using data obtained from a magnetoelastic ribbon experiment we show how a topological approach that allows for experimental error and bounded noise can be used to obtain a description of the dynamics in terms of subshift dynamics on a finite set of symbols.

We investigated a single mode semiconductor laser system pumped near threshold and subject to optical feedback from a short distance. We found both experimentally and numerically that as the feedback strength is increased the laser undergoes a cascade of bifurcations as one external cavity mode becomes unstable and the next one with higher intensity becomes stable only to be destabilized and replaced by the next stable external cavity mode. In the stable regions the laser operates in the so-called maximum gain mode and the unstable regions exhibit chaos which evolves into low-frequency fluctuations characterized by intensity dropouts.

A hierarchy of exact analytic solitary-wave solutions for $N$ coupled nonlinear Schrödinger equations for which the nonlinear coupling parameters can change continuously and cover many regions is presented. Besides their potentially many practical applications to optical communication and multispecies Bose-Einstein condensates for couplings outside the special integrable cases, these analytically solvable cases for special initial conditions supplement and provide important links to and among the integrable cases.

Granular materials exhibit several regimes of behavior: plastic, inertial, fluidized, and entrained flow, but not all materials can pass through all of these states. Our concern is with the criteria that determine the transition from one regime to another and with the boundaries to the various flow regimes that these criteria define. Experimentally we have focused on fine, cohesive powders, where the interparticle cohesive force dominates over gravitational force and where entrained air can cause moving powder to become fluidized.

Instabilities (breakup) of spiral waves in two dimensions and their one-dimensional analogs—wave trains triggered by a specific boundary condition—leading to spatiotemporally chaotic dynamics are investigated in a simple activator-inhibitor model. These instabilities always require an absolute instability of the emitted wave trains and coincide with the Eckhaus instability for the excitable case, while for oscillatory conditions the well-known convective variant of the Eckhaus instability is found. The different cases correspond to different spiral breakup phenomenologies.

A Comment on the Letter by Joel Koplik and Jayanth R. Banavar, Phys. Rev. Lett. 80, 6125 (1998). The authors of the Letter offer a Reply.

A Reply to the Comment by Venkat Ganesan and Howard Brenner.

The Fermi-Pasta-Ulam model with the time-dependent nonlinear term is used to explore the relation between the thermodynamic entropy change due to irreversible processes and the change of information loss as a chaotic dynamical system. We define a novel quantity called the “excess information loss” and conjecture a quantitative relation between the thermodynamic entropy increase and this new quantity, purely defined by dynamical system theory.

In the framework of recently introduced frustrated lattice gas models, we study the out-of-equilibrium dynamical processes during the compaction in granular media. We find irreversible-reversible cycles in agreement with recent experimental observations, along which we can individuate an equivalent “glass transition,” ${\Gamma }_g$. In analogy with the phenomenology of glassy systems we find aging effects during the compaction process. In particular, we find that the two-time density correlation function $C\left({t,t}^{\prime }\right)$ asymptotically scales as a function of the single variable $\ln \left(t^{\prime }\right)/\ln \left(t\right)$.

Using a novel, overdamped, oscillator flown aboard the space shuttle, we measured the viscosity of xenon near the liquid-vapor critical point in the frequency range $2\mathrm{Hz}\le f\le 12\mathrm{Hz}$. The measured viscosity divergence is characterized by the exponent $z_{\eta }=0.0690\mathrm{}\pm 0.0006$, in agreement with the value $z_{\eta }=0.067\mathrm{}\pm 0.002$ calculated from a two-loop perturbation expansion. Viscoelastic behavior was evident when $t=\left({T-T}_c\right){/T}_c<{10}^{-5\mathrm{}}$ and dominant when $t<\mathrm{}{10}^{-6\mathrm{}}$, further from $T_c$ than predicted. Viscoelastic behavior scales as $\mathrm{Af}\tau$ where $\tau$ is the fluctuation decay time. The measured value of $A$ is $2.0\pm 0.3$ times the result of a one-loop calculation. (Uncertainties stated are one standard uncertainty.)

We measure the joint distribution of the energy transmission coefficient ${\varepsilon }_{\mathrm{ab}}$ and the single channel delay time ${\tau }_{\mathrm{ab}}$ for microwave radiation propagating through a random medium in the limit of zero pulse bandwidth. For fixed ${\varepsilon }_{\mathrm{ab}}$ the distribution of ${\tau }_{\mathrm{ab}}$ is Gaussian with variance inversely proportional to ${\varepsilon }_{\mathrm{ab}}$. In contradistinction to ${\tau }_{\mathrm{ab}}$, the dynamic matrix element ${\varepsilon }_{\mathrm{ab}}{\tau }_{\mathrm{ab}}$ has substantial long-range correlation with frequency shift. We present a new dynamic theory for a Gaussian process, which is in excellent agreement with experiment.

We study the long-wavelength limit for an arbitrary photonic crystal (PC) of 2D periodicity. Light propagation is not restricted to the plane of periodicity. We proved that 2D PC's are uniaxial or biaxial and derived compact, explicit formulas for the effective (“principal”) dielectric constants; these are plotted for silicon-air composites. This could facilitate the custom design of optical components for diverse spectral regions and applications. Our method of “homogenization” is not limited to optical properties, but is also valid for electrostatics, magnetostatics, dc conductivity, thermal conductivity, etc. Thus our results are applicable to inhomogeneous media where exact, explicit formulas are scarce. Our numerical method yields results with unprecedented accuracy, even for very large dielectric contrasts and filling fractions.

An exact analytical solution describing the evolution of nonlinear optical envelope pulses in an optical fiber is obtained. The propagation of the pulse is modeled by a higher order nonlinear Schrödinger equation containing third order and nonlinear dispersive terms. This solution includes pulses that are symmetric solitary waves, asymmetric solitary waves, and asymmetric structures that develop into an optical shock.

We study the propagation of an elastic excitation through a magnetorheological slurry made of hydrogen-reduced iron particles suspended in glycerine. Two different low-frequency longitudinal modes are observed, the second of them appearing as soon as a magnetic field is applied to the fluid. The first mode travels through glycerine channels within the suspension, whereas the second one propagates through the fibrillated structure formed by the iron particles. This second mode is very strong in amplitude and travels at lower speeds, depending on the magnetic field intensity.

We present an experimental study of a topological excitation, interface, in a vertically vibrated layer of granular material. We show that these interfaces, which separate regions of granular material oscillating with opposite phases, can be shifted and controlled by a very small amount of additional subharmonic driving mixed with the harmonic driving signal. The speed and the direction of the interface motion depends sensitively on the phase and the amplitude of the subharmonic driving.

The results of the first realistic computer simulation of diffusion of charged species in heterogeneous media with a quenched distribution of charge centers are reported. They indicate that the charge centers create deep traps that capture the mobile particles and slow down their motion for a long time. However, the mobile particles eventually escape the traps. Their motion between the traps is diffusive. These results explain several sets of hitherto unexplained experimental data and resolve a long-standing controversy regarding the nature of transport of charged particles in a heterogeneous charged medium.

We elucidate the connection between the Kolmogorov-Sinai entropy rate $\kappa$ and the time evolution of the physical or statistical entropy $S$. For a large family of chaotic conservative dynamical systems including the simplest ones, the evolution of $S\left(t\right)$ for far-from-equilibrium processes includes a stage during which $S$ is a simple linear function of time whose slope is $\kappa$. We present numerical confirmation of this connection for a number of chaotic symplectic maps, ranging from the simplest two-dimensional ones to a four-dimensional and strongly nonlinear map.

We show that quantum effects modify the decay rate of Poincaré recurrences $P\left(t\right)$ in classical chaotic systems with hierarchical structure of phase space. The exponent $p$ of the algebraic decay $P\left(t\right)\propto 1/t^p$ is shown to have the universal value $p=1\mathrm{}$ due to tunneling and localization effects. Experimental evidence of such decay should be observable in mesoscopic systems and cold atoms.