We present experimental results which demonstrate for the first time that the onset of chaos in a nonlinear system can be either suppressed or induced by the application of a perturbation signal which is near resonant to a subharmonic of the fundamental system frequency. The technique represents a feedback independent method for stabilizing or destabilizing chaotic orbits. Shifts in the onset of chaos are demonstrated for perturbation signals which are near resonant to the period-2 orbit and the period-4 orbit of the experimental system.

Let $N\left(L\right)$ be the number of eigenvalues, in an interval of length $L$, of a matrix chosen at random from the Gaussian orthogonal, unitary, or symplectic ensembles of $N$ by $N$ matrices, in the limit $N\to \infty$. We prove that $\left[N\right(L)-〈N(L\left)〉\right]/\sqrt{\ln L}$ has a Gaussian distribution when $L\to \infty$. This theorem, which requires control of all the higher moments of the distribution, elucidates numerical and exact results on chaotic quantum systems and on the statistics of zeros of the Riemann zeta function.

We analyze a collapse mechanism of energy localization in nonlinear fiber arrays. The nonlinear fiber array is suggested as a device to amplify and compress optical pulses. Pulse propagation in one-dimensional fiber arrays has features of collapse (self-focusing) dynamics. Collapse-type compression leads to the localization of all energy initially dispersed in array into a few fibers. Numerical simulations demonstrate the robustness of the suggested compression mechanism.

The interfacial instability caused by viscosity stratification of a density-matched two-layer, rotating Couette flow is examined close to criticality. Weakly nonlinear analysis of the full governing equations indicates that the instability is supercritical, and measurements of amplitudes for steady, traveling periodic waves agree well with the theoretical predictions.

Superlong chaotic transients have been observed commonly in spatiotemporal chaotic dynamical systems. The phenomenology is that trajectories starting from random initial conditions behave chaotically for an extremely long time before settling into a final nonchaotic attractor. We demonstrate that supertransients are due to nonattracting chaotic saddles whose stable manifold measures have fractal dimensions that are arbitrarily close to the phase-space dimension. Numerical examples using coupled map lattices are given.

The direct simulation Monte Carlo method for the Boltzmann equation is modified by an additional displacement in the advection process and an enhanced collision rate in order to obtain the exact hard sphere equation of state at all densities. This leads to consistent thermodynamic and transport properties in the low density (Boltzmann) regime. At higher densities transport properties are comparable to the predictions of the Enskog model. The algorithm is faster than molecular dynamics at low and moderate densities and readily run on a parallel architecture.

We report the observation of maser emission from the $J=4,K=3\mathrm{}$ inversion transition of ammonia, ${}^{14}$N${\mathrm{H}}_3$, at temperatures from 10 to 27 K. The necessary population inversion is apparently created by selective collisional energy transfer as the ammonia is cooled in collisions with cold helium atoms in a cryogenic cell. Several other inversion transitions were also observed; however, only the (4,3) line was seen in emission. When the experiment was repeated using hydrogen molecules in place of helium, maser emission was not observed for any transition.

We introduce a new class of dynamical systems, analog generalizations of linear feedback shift registers, that can be designed with any number of degrees of freedom, generate optimal pseudorandom noise, and exhibit nonlinear dissipative entrainment which can be used to decode signals in communication and measurement applications.

A general approach for constructing chaotic synchronized dynamical systems is discussed that is based on a decomposition of given systems into active and passive parts. As a possible application we consider an improved encoding method where the information signal is injected into the dynamical system of the transmitter. Furthermore, we show how to design in a systematic way high-dimensional synchronized systems that may be used for efficient hyperchaotic encoding of information.

A spatial modulation of colloidal concentration of nanoscopic magnetic particles is written in a ferrofluid solution inside the fringes of a forced Rayleigh scattering device. The relaxation time of this transient grating is inversely proportional to the square of the characteristic wave vector and thus to the cooperative diffusion coefficient of particles. If an external magnetic field is applied in the plane of the fringes and perpendicularly to these ones, the experimental diffusion coefficient increases, due to local magnetic field gradients in the spatially inhomogeneous magnetic medium.

We report the first experimental demonstration of two-dimensional spatial solitary waves in second-order nonlinear optical material. When an intense optical beam is focused into a phase-matchable second-order nonlinear material, the fundamental and generated second-harmonic fields are mutually trapped as a result of the strong nonlinear coupling which counteracts both diffraction and beam walkoff.

We report experimental results for Rayleigh-Bénard convection of a fluid $\left({\mathrm{CO}}_2\right)$ in a cylindrical cell with radius-to-height ratio 40 and rotated about a vertical axis. Near the critical rotation frequency for the Küppers-Lortz instability and for small $\epsilon \equiv \Delta T/\Delta T_c-1\mathrm{}$, we measured the frequency ${\omega }_a$ and the correlation length $\xi$ of the pattern dynamics. They could be fit by power laws in $\epsilon$ only when exponent values much smaller than those predicted from amplitude equations were used. Alternately, the predicted exponents could be retained if the threshold were shifted to negative values of $\epsilon$, thus yielding finite ${\omega }_a$ and $\xi$ at onset.

The spatiotemporal behavior of a chain of diffusively coupled bistable oscillators is investigated. It is stated that there is spatial disorder and its evolutionary character is demonstrated.

Singularities induced by oscillating behavior are analyzed using the wavelet transform. We define two local exponents which allow us to characterize both the singularity strength (Hölder exponent) and the instantaneous frequency of the oscillations. Such oscillating singularities are shown to appear generically in local self-similar functions which are invariant under a nonhyperbolic mapping. We illustrate our results on both isolated singularities and nonisolated singularities appearing in fractal signals generated by nonhyperbolic iterative function systems.

We define an ideal optimal quantum measurement as that measurement on the apparatus for which the average algorithmic information in the measurement record is minimized. We apply the definition to a chaotic system subject to continuous (Markov) quantum nondemolition measurements. For optimized measurements the average information in the record is much closer to the von Neumann entropy than in the nonoptimized case, but increases more quickly in the chaotic region than in the regular region.

For the first time a three-dimensional (3D) chaotic billiard—the 3D Sinai billiard—was quantized, and high-precision spectra with thousands of eigenvalues were calculated. We present here a semiclassical and statistical analysis of the spectra, and point out some of the features which are genuine consequences of the three dimensionality of this chaotic billiard.

In quantum optics an ensemble of photons is treated as a Bose condensate which has a de Broglie wavelength given by ${\lambda }_0/N$ where ${\lambda }_0$ and $N$ are the wavelength and average number of constituent photons, respectively. We describe an interferometer which is capable of measuring this de Broglie wavelength. We show specifically that a coherent state input has a de Broglie coherence length proportional to $1/\sqrt{N}$. Finally we show that the interferometer is Heisenberg limited in sensitivity ( $\Delta {\phi }_{\min }=1\mathrm{}/N$) and thus forms a new class of interferometers operating at the fundamental quantum limit.

Parity breaking instabilities of spatially periodic patterns are considered. In homogeneous systems such instabilities produce steadily drifting patterns. Spatial inhomogeneities are shown to lead to pattern pinning. The transition from pinned patterns to drifting ones may be surprisingly complex. Examples are described containing infinite cascades of global bifurcations. The values of the bifurcation parameter at which these occur obey a simple scaling law. The predicted dynamics provide a qualitative understanding of recent experiments on binary fluid convection in an annulus.

A hydrodynamic instability has been observed in quasi-two-dimensional electrochemical deposition experiments in which the electrochemical cell is inclined with respect to the horizontal. Gravity-driven flows generated at both anode and cathode become unstable and form a pattern of fingers when the anode is uphill from the cathode. I report measurements of the onset wavelength and development of the pattern, and discuss ways in which the growth of the metal aggregate at the cathode interacts with the flow and its instability.

We discuss interactions of spatially localized solutions, which breathe in the modulus, for coupled quintic complex Ginzburg-Landau equations. The interaction behavior is much richer than and qualitatively different from that of the fixed-shape solutions reported previously. The outcome of a collision can depend on the initial conditions, and, in particular, sensitively on the initial conditions for chaotic solutions, even though parameter values are unchanged. The novelty of these interactions, as compared to those of the fixed-shape solutions and to those of solitons is emphasized.