We show that the power emitted from phase-locked soliton oscillators can exceed the upper limit given by the theory for superradiance from phase-locked point oscillators. As an experimentally relevant example, we consider two magnetically coupled long Josephson junctions, operated in single-fluxon modes. Analytical results indicate that the coupling between the two oscillators enables the phase-locked modes to localize in space thereby creating the possibility of an enhancement of the power level beyond the point-oscillator limit. Good agreement is found between analytical results and numerical simulations, and with recently published experimental data.

We propose a model system based on the Euler equations with integral constraints to describe high-Reynolds-number Navier-Stokes turbulence. This system is Galilean invariant. It is demonstrated computationally that the system, under appropriate constraints, evolves to a quasiequilibrium state which reproduces accurately both low- and high-order statistical measures of turbulence observed in laboratory experiments and direct numerical simulations. A large-eddy simulation model based on the constrained Euler system is formulated and computationally validated. The theoretical interest of the proposed system in the context of nonequilibrium statistical mechanics is briefly discussed.

The deformed Gaussian orthogonal ensemble introduced earlier is developed here for large dimensional matrices. Both the spacing and eigenvector distributions are studied and compared to other ones suggested for the chaos-order transition problem. The concept of a universal lower entropy with respect to the Gaussian orthogonal ensemble entropy is proved very useful.

We report for the first time quantum calculations for the so-called bouncer model, the classical analog of which is well known to manifest a chaotic behavior. Three versions of our model are fully tractable quantum mechanically and are potentially a rich source of data for establishing properties of a quantum system of which the classical mechanics can be chaotic. Among the results presented here, consequences of the varying bandwidth of infinite-dimensional transition matrices on the use of the correspondence between classical chaos and non-Poissonian quasienergy statistics are discussed.

Accumulated photon-echo experiments in pumped Er-doped fibers are reported. The echoes were observed to decrease and disappear as the fiber was pumped to transparency, and then to increase again as the system was inverted. Coherent saturation between the pulses unbalanced the initially identical excitation pulses. We describe a simple frequency domain model that explains all the observed features.

We develop a large-N method for the problem of homogeneous turbulence. The spherical (N→∞) limit yields Kraichnan’s direct interaction approximation equations. Implications for real turbulence (N=1) are discussed. In particular, we argue that the renormalization-group results obtained by setting the expansion parameter y=4 are incorrect, and that the Kolmogorov exponent ζ has a nontrivial dependence on N, with ζ(N→∞)=3/2. This value is remarkably close to the experimental result ζ≃5/3, which must therefore result from higher-order corrections in powers of 1/N.

We provide a sum rule for the length spectrum of pseudointegrable systems in terms of the quantal energies. Further, we derive an expression for the form factor and infer the dependence of spectral fluctuations on the geometry of the system. Our analysis allows us to explain various numerical results obtained in recent years.

A beam propagating in a planar waveguide exhibits the characteristics of both a fundamental soliton (little change in waist of a 5-μm beam; diffraction is compensated by self-focusing nonlinear refraction) and a second-order soliton (10-μm beam focuses to 3 μm with side peaks). These one-dimensional spatial solitons are quite stable; bifurcations of transverse solitary waves are not seen, in sharp contrast with the case for two transverse dimensions. Plasma-theory planar-wave beam-propagation computations agree well with the data and resemble Kerr-medium solitons quite closely.

A Ka-band gyrotron backward-wave oscillator (gyro-BWO) experiment has been performed to investigate the phase control, fast tunability, and power capability. Efficient injection locking was accomplished by novel circuit arrangements. Maximum power of 113 kW at ∼19% efficiency was achieved, showing favorable scaling to still higher powers. Stable voltage tuning bandwidth of 5% at 67 kW peak power was also observed. The measured performance has demonstrated a strong potential of the gyro-BWO for new applications requiring high-power tunable millimeter-wave sources.

It is shown that a resonant interaction between a laser beam, a standing light wave, and a relativistic electron beam can be built up in a Lorentz frame different from that of the laboratory. The conditions for which external electromagnetic radiation with wavelength shorter than that of the laser pump field can be amplified via an electron-scattering process of the Kapitsa-Dirac type are then determined. The linear gain of this device is estimated and the possibility of building an ‘‘optical-wiggler’’ free-electron laser working from the IR to the VUV range is investigated.

We present experimental results of harmonic generation using a 1-ps ${10}^{15\mathrm{-}}$W/${\mathrm{cm}}^2$ Nd-glass laser. We see up to the 29th harmonic in Xe, 57th in Ar, and at least up to the 135th harmonic in Ne (160 eV), being then limited by our monochromator’s resolution. The conversion efficiencies in Xe, Ar, Ne, and He are compared and different ways of optimizing the number of photons by defocusing the laser beam or increasing the density are discussed.

We have experimentally verified the prediction that a homogeneous steady state of an activator-inhibitor system can be destabilized by a differential flow of the key species, rather than by their differential diffusivity for Turing instability. Traveling waves are generated by a flow of Belousov-Zhabotinsky reactants through a tube containing ferroin immobilized on a cation exchanger. Without flow the system resides in a homogeneous steady state. This mechanism of spatiotemporal pattern formation avoids the restrictions of the Turing instability on the diffusion coefficients and can thus be expected to operate in a larger class of chemical, physical, and biological systems.

A discrete model of random transport is analyzed both numerically and theoretically. Non-Gaussian fluctuations are always realized when a finite portion is transported at a time. Gaussian and power-law fluctuations appear in extreme limits.

The understand the role of nonlinear dispersion in pattern formation, we introduce and study Korteweg–de Vries–like equations wtih nonlinear dispersion: ${\mathit{u}}_{\mathit{t}}$+(${\mathit{u}}^{\mathit{m}}$${)}_{\mathit{x}}$+(${\mathit{u}}^{\mathit{n}}$${)}_{\mathit{x}\mathit{x}\mathit{x}}$=0, m,n>1. The solitary wave solutions of these equations have remarkable properties: They collide elastically, but unlike the Korteweg–de Vries (m=2, n=1) solitons, they have compact support. When two ‘‘compactons’’ collide, the interaction site is marked by the birth of low-amplitude compacton-anticompacton pairs. These equations seem to have only a finite number of local conservation laws. Nevertheless, the behavior and the stability of these compactons is very similar to that observed in completely integrable systems.

The quantum density of states of the Hénon-Heiles Hamiltonian exhibits prominent low-frequency beats as a function of energy. We interpret the beats in terms of interferences of the three simplest isolated classical periodic orbits by a calculation of their amplitudes in the Gutzwiller trace formula. We show that periodic orbit theory can reproduce classically the main characteristics of the quantum beats. Both stable and unstable orbits contribute substantially in generating these long-range correlations, which coexist with the short-range fluctuations giving nearest-neighbor spacings distributions typical for chaos. With a Fourier analysis our conclusions confirm the quantum spectrum.

The signature of chaos in the spectral autocorrelation function and in its Fourier transform, the survival probability, is shown to be in good agreement with the predictions of random matrix theory. An expression is proposed for the survival probability of an experimentally prepared nonstationary state when the dynamics are intermediate between chaotic and regular. Its validity is tested through the study of a model Hamiltonian . Two parameters can be extracted from the above observable, one which characterizes the level statistics and one which characterizes the distribution of transition intensities.

Stochastic resonance is a phenomenon seen in multistable systems where the addition of noise to the system can amplify small periodic signals. We show in an experiment with a circuit that many of the concepts used to describe crises may also be used to describe stochastic resonance. We speculate that stochastic resonance may be an example of a crisis. This would allow the use of dynamical concepts to describe a process that is usually considered statistically.

A quantitative measure of determinism in a recurrent time series is developed. Specifically, scalar time series data are used to form a vector series in reconstructed phase space. A statistic is then developed to measure the observed ‘‘continuity’’ of the vector series. The statistic is used as a measure of determinism. Several examples are included to demonstrate the effectiveness of the method.

Laser-induced fluorescence imaging of a shock-accelerated thin gas layer, produced by a planar ${\mathrm{SF}}_6$ jet in air, shows multiple flow evolutions. Richtmyer-Meshkov instability causes spatially periodic perturbations initially imposed on the jet to develop into one of three distinct flow patterns, indicating nonlinear instability growth. Slight differences in the vorticity distribution deposited on the air-${\mathrm{SF}}_6$ interfaces by the shock interaction produce a bifurcated flow, observed as mushroom-shaped or sinuous-shaped interfacial patterns.

We consider the unfolded spectra of disordered systems with the topology of a ring, in the presence of an Aharonov-Bohm flux. We study the flux dependence of a single energy level. We find that the correlator of the derivatives at two different fluxes has a universal functional form, and propose that the result is valid for all systems with Wigner-Dyson statistics.