We have investigated the electromagnetic properties of a 3D wire mesh in a geometry resembling covalently bonded diamond. The frequency and wave vector dispersion show forbidden bands at those frequencies ${\nu }_0$, corresponding to the lattice spacing, just as dielectric photonic crystals do. But they have a new forbidden band which commences at zero frequency and extends, in our geometry, to $\sim \frac{1}{2}{\nu }_0$, acting as a type of plasma cutoff frequency. Wire mesh photonic crystals appear to support a longitudinal plane wave, as well as two transverse plane waves. We identify an important new regime for microwave photonic crystals, an effective medium limit, in which electromagnetic waves penetrate deeply into the wire mesh through the aid of an impurity band.

We study the dielectric response of impurity two-level atoms in a photonic band gap (PBG) to an applied laser field. In this system, the atoms may exchange energy coherently by resonance dipole-dipole interaction (RDDI) which is assumed to be strong compared to the spontaneous emission rate. When the applied Rabi frequency exceeds the RDDI energy scale, nonlinear saturation of the absorptive part of the susceptibility occurs while the real part of the nonlinear susceptibility remains large. This suggests that doped PBG materials may act as nearly lossless, but highly nonlinear dielectrics.

Numerical integration of Maxwell's equations for propagation of a femtosecond pulse in a medium with linear Lorentz response and a Kerr nonlinearity shows shock formation on the underlying carrier wave prior to the envelope shock. The carrier shock is characterized by the appearance of a strong third harmonic pulse, whereas the envelope shock appears later as spectral broadening and modulation of the fundamental and higher harmonic spectral features.

Inspired by the discovery of Oddershede et al. [Phys. Rev. Lett. 71, 3107 (1993)] concerning the dimensionality dependence of mass distributions after shock fragmentation, we have performed further experiments using thick plates of dry clay. We observe mass distributions with composite power laws, i.e., different exponents for fragments larger and smaller than the plate thickness. This implies that the dominant exponent for any given fragment mass corresponds to the dimensionality of the original object on the length scale of the fragment considered. We study two profoundly different models, both of which agree qualitatively with the observed features. Thus the measured mass distribution tells little about the mechanisms of the fragmentation process.

Invariant sets embedded in a chaotic attractor can generate time averages that differ from the average generated by typical orbits on the attractor. Motivated by two different topics (namely, controlling chaos and riddled basins of attraction), we consider the question of which invariant set yields the largest (optimal) value of an average of a given smooth function of the system state. We present numerical evidence and analysis which indicate that the optimal average is typically achieved by a low period unstable periodic orbit embedded in the chaotic attractor.

In a random matrix model, the transition from arbitrary to chaotic correlations is analytically evaluated for the case of broken time-reversal invariance. The use of the supersymmetry method allows for a nonperturbative calculation. As an application, the transition from Poisson regularity to chaos is worked out. The result is a double integral which is exact for the entire transition.

We analyze the evolution of $(1+1)$ dimensional dark stripe beams in bulk media with a photorefractive nonlinear response. These beams, including solitary wave solutions, are shown to be unstable with respect to symmetry breaking and formation of structure along the initially homogeneous coordinate. Experimental results show the complete sequence of events starting from self-focusing of the stripe, its bending due to the snake instability, and subsequent decay into a set of optical vortices.

We have observed spontaneous atomic spin polarization of a Cs vapor undergoing rapid spin exchange in a cell when illuminated with plane-polarized 894 nm ( $D$1) light. The spin polarization shows marked hysteresis in switching between two stable orientations, fully aligned parallel or antiparallel to an external magnetic field, as the circular polarization of the pump light is varied about zero. We show that our observations agree with theoretical expectations and point out possible applications of spontaneous polarization.

It has been conjectured that essential features of fast kinematic magnetic dynamos in the presence of small magnetic diffusivity can be extracted from the ideal (i.e., diffusionless) kinematic dynamo equation. In particular, predictions concerning the cancellation exponent, the dynamo growth rate, and the growth of moments of the magnetic field in the nonideal case can be made based on the ideal dynamics. This paper presents the first confirmation of these predictions by numerical computations on a spatially smooth chaotic flow at very high magnetic Reynolds number.

A Comment on the Letter by Olivier J. F. Martin, Christian Girard, and Alain Dereux, Phys. Rev. Lett. 74, 526 (1995). The authors of the Letter offer a Reply.

A Reply to the Comment by N. Garcia and M. Nieto-Vesperinas.

A simplified nonlinear dynamo model is constructed that allows the transition from the kinematic to the dynamic regime to be studied in detail. We apply this construction to a chaotic flow recently studied in the context of fast dynamo action. It is found that the structure of the magnetic field in the two regimes is markedly different. Furthermore, the saturation of the exponential growth of the magnetic field is achieved by a drastic suppression of the chaotic properties of the flow.

Cellular flames stabilized on a porous plug burner at low pressure form ordered patterns consisting of concentric rings of cells. In certain regions of the parameter space of propane-air mixtures, ordered patterns appear intermittently. In these states, patterns of concentric rings persist for varying lengths of time, abruptly dissolve into highly irregular structures with no discernible ring pattern, and then reappear as ordered patterns with the same or slightly different numbers of cells. Experimental evidence and theoretical arguments show that these intermittently ordered states correspond to a network of heteroclinic connections among unstable equilibria.

We present the new effect of phase synchronization of weakly coupled self-sustained chaotic oscillators. To characterize this phenomenon, we use the analytic signal approach based on the Hilbert transform and partial Poincaré maps. For coupled Rössler attractors, in the synchronous regime the phases are locked, while the amplitudes vary chaotically and are practically uncorrelated. Coupling a chaotic oscillator with a hyperchaotic one, we observe another new type of synchronization, where the frequencies are entrained, while the phase difference is unbounded. A relation between the phase synchronization and the properties of the Lyapunov spectrum is studied.

We consider coupled map lattices of the type $x_i(n+1\mathrm{})=(1-\epsilon )f\left(x_i\right(n\left)\right)+\left(\epsilon /2\right)\left[f\right(x_{i-1\mathrm{}}\left(n\right))+f(x_{i+1\mathrm{}}\left(n\right)\left)\right]$, where for concreteness we take $f\left(x\right)=1-\left(\mu /4\right)|1-2x{|}^p$, with $p>\mathrm{}1\mathrm{}$. We show that near $\epsilon =0\mathrm{}$ (no coupling) and $\mu =4\mathrm{}$ the envelope of the largest Lyapunov exponent of the full system obeys the scaling law $\overline{\Lambda }={\Lambda }_0-[a\epsilon +b(4-\mu ){]}^{1/p}$. We further argue that this law is universal in that it is independent of the details of $f\left(x\right)$ insofar as $f\left(x\right)$ has a single critical point $x_c$ in the interval $[0,1]$ and its lowest order power expansion about $x_c$ has the form $|{x-x}_c{|}^p$. The dependence of $\overline{\Lambda }$ on the size of the lattice as well as on the range of the coupling is also discussed.

An ab initio theoretical expression for the $N$-body Lyapunov exponent of a dilute gas is derived. It shows the Lyapunov exponent to be a function of the time integral of the correlation function for the second derivative of the interparticle potential (approximately a power $\frac{1}{3}$ law). This establishes a link between the Lyapunov exponent and the transport coefficients. We compare the theory with numerical simulations of a one component plasma.

Necessary and sufficient conditions for the occurrence of generalized synchronization of unidirectionally coupled dynamical systems are given in terms of asymptotic stability. The relation between generalized synchronization, predictability, and equivalence of dynamical systems is discussed. All theoretical results are illustrated by analytical and numerical examples. In particular, the existence of generalized synchronization in the case of parameter mismatch between coupled systems leads to a new interpretation of recent experimental results. Furthermore, the possible application of generalized synchronization for attractor reconstruction in nonlinear time series analysis is discussed.

Semiconductor light emission is analyzed as a paradigm of a nonequilibrium quantum mechanical many-body problem. The medium excitations and the quantized light field inside and outside a semiconductor slab are treated consistently. Splitting the photon density of states into a medium and a vacuum induced contribution the arbitrarily strong semiconductor emission is described as spontaneous emission into the vacuum induced part. With increasing gain narrowing peaks of growing intensity evolve for each propagation direction, whereas under laser conditions one propagation direction is favored by the cavity.

Surface wave experiments confirm predictions of a threshold amplitude for droplet ejection. Droplet ejection and spray originate from highly focused surface singularities in the simplest states. The threshold is found to be dependent on forcing frequency and surface tension in accordance with a simple scaling theory presented here. Linear stability analysis indicates that the dynamics of the ejections at low frequency are low dimensional. Observations confirm this, and show periodic ejections as the simplest observed state. Ejecting states at higher frequency appear turbulent in nature.

In turbulent flows the nth order structure functions $S_n\left(R\right)$ scale like $R^{{\zeta }_n}$ when $R$ is in the “inertial range.” Extended self-similarity refers to the substantial increase in the range of power law behavior of the $S_n\left(R\right)$ when they are plotted as a function of $S_2\left(R\right)$ or $S_3\left(R\right)$. Here we demonstrate this phenomenon analytically in the context of the “multiscaling” turbulent advection of a passive scalar. This model gives rise to a series of differential equations for the structure functions $S_n\left(R\right)$ which can be solved and shown to exhibit extended self-similarity. The phenomenon is understood by comparing the equations for $S_n\left(R\right)$ to those for $S_n\left(S_2\right)$.