We report the observation of synchronization of the chaotic intensity fluctuations of two Nd:YAG lasers when one or both the lasers are driven chaotic by periodic modulation of their pump beams.

General properties of nonlinear wave interactions in systems with periodic boundary conditions (so-called resonators) are studied. The wave field evolution in resonators displays striking, peculiar characteristics because only a small number of waves dominate the energy transfer processes. Indeed, the very fact of setting up boundary conditions is more important than the specific form of the nonlinear evolution equation. Results are presented for a number of wave fields whose evolution is governed by different nonlinear equations: planetary waves, gravity waves, capillary waves, and drift waves in plasmas.

A new kind of instability, induced by a uniform differential flow, is predicted. It affects dynamical systems of three or more variables that do not contain an unstable subsystem (activator). This is in contrast to the Turing instability and to the differential flow induced chemical instability which destabilize the homogeneous state of activator-inhibitor systems by releasing the inherent tendency of the activator to grow. A chemical example is given. Arguments are presented that interpret the mechanism of the instability as arising from a resonant excitation of a subsystem due to the differential flow.

The enhancement of acoustic caviation at a liquid-solid interface following laser-induced bubble formation is studied. The experiment results indicate that metastable ultramicroscopic bubbles formed on the solid surface cause a long-term ‘‘memory effect’’ on acoustic cavitation. By performing a double-pulse experiment using two excimer lasers, the temporal decay of this memory effect is determined for two different liquids on a chromium surface. An explanation of the observed decay mode by a diffusion model is presented.

We investigate the energy exchange between a Rydberg electron and the molecular core in the regime where the Born-Oppenheimer approximation is violated. The theory developed allows the possibility for a strong energy exchange even for high orbital momentum of the electron when quantum defects are small. We establish the existence of a classical chaos border and of a quantum delocalization border above which diffusive autoionization of the electron takes place. The relevance of theory for autoionization of doubly excited Rydberg atoms is also discussed.

A technique for empirically determining optimal coordinates for modeling a dynamical system is presented. The methodology may be viewed as a nonlinear extension of the Karhunen-Loève procedure and is implemented via an autoassociative neural network. Given a high-dimensional system of differential equations which model a dynamical system asymptotically residing on a stable attractor, the task of the network is to compute a reembedding of the attractor and the dynamics into an ambient space which reflects the intrinsic dimensionality of the problem. The method is demonstrated on the unforced Van der Pol oscillator, the forced Van der Pol, and the Kuramoto-Sivashinsky equation.

We demonstrate that some chaotic parameter subsets of a class of spatiotemporal chaotic systems modeled by globally coupled maps are riddled. That is, for every point in the chaotic parameter subset, there are parameter values arbitrarily nearby that lead to nonchaotic attractors. A consequence is an extremely sensitive parameter dependence characterized by a significant probability of error in numerical computation of asymptotic attractors, regardless of the precision with which parameters are specified.

Coherent behavior in ensembles of globally coupled maps is investigated in the limit of infinite number of elements. A self-consistent approach based on a nonlinear Frobenius-Perron equation is proposed for such systems, and a possibility of quasiperiodic and chaotic behavior of the mean field is demonstrated. For the study of finite ensembles a noisy nonlinear Frobenius-Perron equation is derived. Previous observations of violations of the law of large numbers are explained.

Synchronization of a pair of chaotic diode resonators has been experimentally achieved by applying a minute feedback signal to the amplitude of the drive voltage of a slave resonator. The signal is proportional to the voltage difference between the two resonators and is applied for a fraction of the driving cycle. This method is the synchronization analog of the occasional proportional feedback scheme developed by Hunt for controlling unstable periodic orbits in chaotic attractors.

Mean-field electrodynamics, including both α and β effects while accounting for the effects of small-scale magnetic fields, is derived for incompressible magnetohydrodynamics. The principal result is α=(${\mathrm{\alpha }}_0$+${\mathrm{\beta }}_0$R⋅∇×R)/(1+${\mathit{R}}^2$), β=${\mathrm{\beta }}_0$; where ${\mathrm{\alpha }}_0$,${\mathrm{\beta }}_0$ are conventional kinematic dynamo parameters, the reduction factor is proportional to the mean magnetic field R=${\mathit{R}}_{\mathit{m}}^{1/2}$B/(ρ${\mathit{V}}^2$${)}^{1/2}$, ${\mathit{R}}_{\mathit{m}}$ is the magnetic Reynolds number, and V is the characteristic turbulent velocity. This result follows from a generalization of the Zeldovich theorem to three dimensions, exploiting magnetic helicity balance.

We show that a pair of chaotic systems subjected to the same noise may undergo a transition at large enough noise amplitude and follow almost identical trajectories with complete insensitivity to initial conditions. An analytic argument is presented to show that a pair of generic systems in the same potential evolving to equilibrium through standard Langevin dynamics with the same noise collapse into the same trajectory at long times.

We present a new method that allows one to stabilize chaotic systems by applying proportional pulses to the system variables. The method does not require any previous knowledge of the system dynamics. Acting on the system variables may be most useful for chemical and biological systems, situations for which in some cases it may be difficult to find an accessible system parameter.

A video-feedback control experiment which successfully suppresses chaotic temporal fluctuations of thermal patterns on a catalytic wafer is reported. A Karhunen-Loeve scheme is used to identify the dominant spatial structures from video imaging and estimate the low-dimensional temporal dynamics. The projected dynamics shows that the spatiotemporal chaos is due to an intermittent chaotic attractor near a homoclinic orbit. The control strategy is then simply to stabilize the hyperbolic fixed point attached to the homoclinic orbit with a local modal feedback control.

The general properties of quantum transport fluctuations associated with classical chaotic diffusion are analyzed in the framework of chaotic scattering on a simple dynamical model exhibiting universal transmission fluctuations. Quasiclassical approximations for S-matrix correlations are found, and a connection between correlation width and average conductance is demonstrated on numerical data.

Ultrafast NMR imaging was used to clarify spatiotemporal structures of wavy Taylor-Couette flow. NMR images designed to give a radial velocity distribution in a cross-sectional plane containing the rotation axis were successively taken at 200 ms time intervals. Distributions of velocity power-spectral components were obtained by temporal Fourier transform of the sequential velocity images. The obtained spectral maps clearly visualized the spatial structures of the wavy components in the cross-sectional plane.

We report experimental investigation and theoretical interpretation of the formation of sprial waves in a nematic liquid crystal subjected to a rotating magnetic field and a high frequency electrical field.

Direct numerical simulations with up to ${1024}^2$ resolution are performed to study statistical properties of the inverse energy cascade in stationary homogeneous two-dimensional turbulence driven by small-scale Gaussian white-in-time noise. The energy spectra for the inverse energy cascade deviate strongly from the expected ${\mathit{k}}^{\mathrm{-}5/3}$ law and are close (somewhat flatter) to ${\mathit{k}}^{\mathrm{-}3}$. The reason for the deviation is traced to the emergence of strong vortices distributed over all scales. Statistical properties of the vortices are explored.

We present the first experimental evidence that near-resonant perturbations produce a destabilizing shift of a subcritical bifurcation. This is in direct contrast to supercritical bifurcations, where near-resonant perturbations always suppress the instability. Using a normal form analysis we derive a generic scaling law relating the magnitude of the destabilizing shift μ to the perturbation amplitude ɛ and detuning frequency δ. The predictions are in excellent agreement with our experiments. In the limit of very small δ the shift obeys a pure scaling law, μ∝(ɛ${)}^{2/3}$.

We consider a system in which a classical oscillator is interacting with a purely quantum mechanical oscillator, described by the Lagrangian L=1/2x${\mathrm{̇}}^2$+1/2A${\mathrm{̇}}^2$-1/2(${\mathit{m}}^2$+${\mathit{e}}^2$${\mathit{A}}^2$)${\mathit{x}}^2$, where A is a classical variable and x is a quantum operator. With 〈x(t)〉=0, the relevant variable for the quantum oscillator is 〈x(t)x(t)〉=G(t). The classical Hamiltonian dynamics governing the variables A(t),${\mathrm{\Pi }}_{\mathit{A}}$(t),G(t), and ${\mathrm{\Pi }}_{\mathit{G}}$(t) is chaotic so that the results of making measurements on the quantum system at later times are sensitive to initial conditions. This system arises as the zero momentum part of the problem of pair production of charged scalar particles by a strong external electric field.

We describe the application of path integrals to the problem of light propagation in turbid media. The photon propagation process is separated into an absorption dependent part and a part that depends only on scattering. We determine the nonabsorption photon path and nonabsorption probability distribution function, from which other measurable optical parameters can be obtained. As an example, we calculate the diffuse reflectance for a semi-infinite medium and obtain a new result which reduces to a previously derived expression in the approximate limiting case.