The complete set of resonance parameters for 950 resonances of a superconducting microwave cavity connected to three antennas has been measured. This cavity simulates the quantum mechanics of a particle in a Bunimovich stadium. The partial widths are found to follow a Porter-Thomas distribution. The Fourier transforms of the $S$-matrix autocorrelation functions decay algebraically (nonexponentially) in time. These results agree perfectly with the predictions of random-matrix theory. They constitute one of the most stringent tests ever of this expected connection between chaotic dynamics and randommatrix theory.

We characterize the complexity in dynamical systems with a random perturbation by considering the rate $K$ of divergence of nearby orbits evolving under two different noise realizations. We discuss the meaning of $K$ in the context of the information theory and its physical relevance for the analysis of experimental data. Our definition of complexity becomes crucial for strongly intermittent systems where $K$ is very different from the Lyapunov exponent. This behavior is illustrated by some numerical computations.

The Lyapunov exponents of a chaotic system quantify the exponential divergence of initially nearby trajectories. For Hamiltonian systems the exponents are related to the eigenvalues of a symplectic matrix. We make use of this fact to develop a new method for the calculation of Lyapunov exponents of such systems. Our approach avoids the renormalization and reorthogonalization of usual techniques. It is also easily extendible to damped systems. We apply our method to two examples of physical interest: a model system that describes the beam halo in charged particle beams and the driven van der Pol oscillator.

Studies of slider-block systems, used for decades to model the interactions between geological fault segments, have been mostly theoretical due to the difficulty in producing well-controlled mechanical systems which mimic these models' dynamics. We present here an experimental study of the dynamics of two elastically coupled slider blocks, using an electronic circuit with highly nonlinear load-unload elements. Unlike earlier computer simulations, a nominally symmetric circuit exhibits several alternating periodic and chaotic solutions as a function of the coupling parameter, emphasizing the importance of experimental studies in understanding this model.

It is first shown from the modulation instability of the conserved Zakharov equations that regular soliton patterns with a periodic sequence in space and time, and spatiotemporal chaos with irregular localized patterns, are formed in the different regions of the unstable wave numbers. The route from quasiperiodic to the coexistence of quasiperiodic and subharmonic, then from quasiperiodic and subharmonic to subharmonic, and furthermore to spatiotemporal chaos evolving from regular spatial patterns, is found. The formation mechanism of irregularly localized patterns is also revealed.

The dynamics of passive Brownian tracer particles in steady two-dimensional potential flows between sources and sinks is investigated. The first-passage probability $p\left(t\right)\mathrm{}$ exhibits power-law decay with a velocity-dependent exponent in radial flow and an order-dependent exponent in multipolar flows. For the latter, there also occur diffusive "echo" shoulders and exponential decays associated with stagnation points in the flow. For spatially extended dipole sinks, the spatial distribution of the collected tracer is independent of the overall magnitude of the flow field.

We present direct experimental and numerical evidence for riddled basins of attraction for the synchronous chaotic state in a system of coupled chaotic oscillator circuits. Both experiment and computation show scaling typical of basin riddling.

A stable, high efficiency, high power oscillation was performed in a gyrotron with beam energy recovery. By the application of an electron retarding potential, efficiency was enhanced from 30% to 50% at an output power of 610 kW (110 GHz). Numerical analysis indicates that the electrostatically trapped electrons are reaccelerated in the cavity due to electron cyclotron resonance and are swept out to the collector or electron gun. This mechanism avoids electron accumulation in the gyrotron even with the high retarding potential.

We present a method for constructing lattice tridiagonal Hamiltonians having a preassigned multifractal measure as local spectrum. Using this construction we investigate how the fractal structure of the spectrum affects the motion of wave packets. We find that the quantum evolution is intermittent: The moments of particle's position on the lattice are characterized by a nontrivial scaling function, even when the spectrum is a one-scale, balanced Cantor set. Numerical data show that the minimum scaling exponent is always larger than the information dimension of the spectral measure, and qualitatively follows the behavior of this quantity, as the spectral measure is varied.

Population inversion leads to the phenomena of superluminality, in which wave packets can propagate dispersionlessly near dc faster than $c$, and parelectricity, in which the dc susceptibility is negative, implying the levitation of a charge above a parelectric medium. Also, charges placed in a cavity surrounded by a parelectric medium form stable configurations, in seeming violation of Earnshaw's theorem. Einstein causality is not violated.

Berry's phase of the Lorentz group has been measured in a system of connected nonlinear electronic oscillators. Each oscillator was driven so that it was in the vicinity of a period-doubling bifurcation where the response to a small perturbation transforms similarly to a Lorentz boost of a spinor. By connecting the output of one oscillator to the input of the next, it was possible to make a closed loop on a hyperboloid (the invariant surface of the Lorentz group), the enclosed area of which is Berry's phase. Good agreement between theory and experiment is found.

Recent observations indicate that the shape of a fluid interface undergoes repeated instabilities arbitrarily close to breakoff. We interpret this behavior as the result of successive instabilities of the similarity solution of Eggers. [Phys. Rev. Lett. 71, 3458 (1993)]. We show that the similarity solution is unstable to finite amplitude perturbations, with critical amplitude going to zero at the singularity. Thermal fluctuations in the fluid can trigger the instabilities.

We report on a simple model of a spatially distributed system which, subject to multiplicative noise, white in space and time, can undergo a nonequilibrium phase transition to a symmetry-breaking state, while no such transition exists in the absence of the noise term. The transition possesses features similar to those observed at second order equilibrium phase transitions: divergence of the correlation length and of the susceptibility, critical slowing down, and scaling properties. Furthermore, the transition is found to be reentrant: The ordered state appears at a critical value of the noise intensity but disappears again at a higher value of the noise strength.

The probability density distributions (PDD) of the velocity differences $\Delta u\left(r\right)=u\left(x\right)-u(x+r)\mathrm{}$ for separations $r$ within the inertial range are studied in a large wind tunnel and in the atmospheric surface layer at $R_{\lambda }\approx \mathrm{}(2.0-12.7)\mathrm{}\times {10}^3$. For large velocity differences, the PDD behave as $P\left(\Delta u\right)\propto \exp \mathrm{}[-b(r\left)\right|\frac{\Delta u}{{\sigma }_{\Delta u}}\mathrm{}\left|\right]\mathrm{}$. The logarithmic decrement $b\left(r\right)\mathrm{}$ is found to scale as $b\left(r\right)=\alpha r^{\beta }$. The value of $\alpha$ is found to be 0.51 ± 0.02 for the negative ($\Delta u<\mathrm{}0\mathrm{}$) tails of the PDD and 0.58 ± 0.02 for the positive ($\Delta u>\mathrm{}0\mathrm{}$) tails. In both cases, $\beta =0.17\mathrm{}\pm 0.01$.

Steady-state dark (bright) planar spatial solitons are predicted for photorefractive materials when the diffraction of an optical beam is exactly compensated by nonlinear self-defocusing (focusing), due to the screening field set up around a dark notch (or a bright beam) in a photorefractive material to which an external field is applied. These screening solitons appear in steady state and differ from previously observed spatial solitons in their properties and physical origin.

We have studied plasma waveguiding in soft x-ray laser experiments. A curved-slab target was used in order to compensate for x-ray refraction in a gradient-density plasma. In addition to significant increase in the x-ray laser intensity in single-pass amplification, a small beam divergence of less than 1 mrad has been stably generated in double-pass amplification with the curved target. The angular intensity distribution of the double-passed beam indicates that the x-ray laser has been amplified in a plasma waveguide.

It is shown that complete and precise first arrival time tomography data are not capable of uniquely reconstructing certain realistic velocity distributions. The nonuniqueness is demonstrated by different velocity distributions that share identical first arrival time data. In these examples, the combined Fresnel zone for all source and receiver combinations do not cover the entire imaging region and leave there uncovered regions we call white holes.

The Taylor-Reynolds and Reynolds number (${\mathrm{Re}}_{\lambda }$ and Re) dependence of the dimensionless energy dissipation rate $c_{\epsilon }=\frac{\epsilon L}{u_{1,\mathrm{rms}}^3}$ is derived for statistically stationary isotropic turbulence, employing the results of a variable range mean field theory. Here $\epsilon$ is the energy dissipation rate, $L$ the (fixed) outer length scale, and $u_{1,\mathrm{rms}}$ a rms velocity component. Results for $c_{\epsilon }\left({\mathrm{Re}}_{\lambda }\right)$ and also for ${\mathrm{Re}}_{\lambda }\left(\mathrm{Re}\right)$ are in good agreement with experiment. Using the Re dependence of $c_{\epsilon }$ we account for the time dependence of the mean vorticity $\omega \mathrm{}\left(t\right)\mathrm{}$ for decaying isotropic turbulence. The lifetime of decaying turbulence, depending on the initial ${\mathrm{Re}}_{\lambda ,0\mathrm{}}$ is predicted to saturate at $\frac{0.18L^2}{\nu }\propto {\mathrm{Re}}_{\lambda ,0\mathrm{}}^2$ ($\nu$ the viscosity) for large ${\mathrm{Re}}_{\lambda ,0\mathrm{}}$.

Using an axisymmetric jet with helium at low temperature we have studied the velocity intermittency on a large range of Taylor scale based Reynolds number $R_{\lambda }$. The results show, for the first time, evidence for a transition between two types of turbulence in a jet. Above the transition ($R_{\lambda }>180\mathrm{}$) a clear separation occurs between small and large scales. In the intermediate range, the existence of a Reynolds dependent scaling law is confirmed. It illustrates the way in which viscosity can have some influence up close to the integral scale in developed turbulent flows.

Using a new experimental geometry, we have proved for the first time that the generation of spatial subharmonic gratings in photorefractive crystals is not dependent on optical nonlinearity. We present results which confirm that the subharmonic gratings result from a parametric excitation of ultra low-frequency eigenmodes of a crystal by a time modulated fundamental grating.