We measure momentum transferred from a single pulse of a standing wave of light to a sample of ultracold sodium atoms, and observe a sharp increase in the momentum transfer when the pulse duration exceeds a critical value ${\tau }_{\mathrm{cr}}$. A classical analysis of nonlinear resonances shows that resonance overlap occurs at ${\tau }_{\mathrm{cr}}$, and there is a transition to global classical chaos. These results are a direct experimental test of the “resonance overlap criteria” and illustrate that even the turning on and off of a simple spatially periodic interaction can lead to surprising and novel results.

A realistic model of a doped quantum well heterostructure exhibits a subharmonic signal in the presence of intense far-infrared radiation. Nonlinearity enters the model through the effective potential due to the density of electrons in the well. Dephasing and energy relaxation are introduced through a simple density matrix approach. The resultant dynamics show the period-doubling routes to chaos, in the form of strange attractors. All material parameters used are well within the present capabilities of present quantum well technology, and the driving field amplitudes and frequencies are easily obtainable with a free electron laser.

Feedback control of multidimensional, nonlinear single-input single-output systems is formulated in terms of an invariant hypersurface in the delayed state space of a system observable and a control parameter. The surface is created directly from the response of the system to random perturbations, providing a model-independent nonlinear control algorithm. The algorithm can be used to stabilize unstable states or to drive a system to any particular objective state in a minimum number of steps.

We propose an algorithm for control of spatiotemporal chaos in partial differential systems based on the idea of stabilization of unstable periodic patterns embedded in spatiotemporal chaotic states. This algorithm, using time- and space-dependent feedback, has been successfully demonstrated through our numerical analysis in controlling unstable roll patterns in a transversely extended three-level laser.

A numerical model for direct simulation of the surface of ideal fluid based on the expansion of the Hamiltonian of the surface up to terms of fourth order is developed. For the case of capillary wave we observe the formation of powerlike spectrum of spatial elevations close to one predicted by weak-turbulent theory $I_k\simeq k^{-19/4\mathrm{}}$, which previously was not confirmed either experimentally or numerically.

A single-mode nonlinear high-order perturbation theory is developed to describe the Richtmyer-Meshkov instability of an impulsively accelerated interface between an incompressible fluid and a constant supporting pressure. The nonlinear modification of Richtmyer's formula is presented and compared to experimental data with strong radiatively driven shocks. The theory allows a straightforward extension to more general cases of Richtmyer-Meshkov and Rayleigh-Taylor instabilities (multimode, more interfaces, three-dimensional flow, etc.).

A Rydberg atom placed in crossed static electric and magnetic fields is presented as a new testbed for phenomena not possible in two degrees of freedom. We compute the Arnol'd web for this system and explore the time scale and the physical consequences of diffusion along this web.

We describe a theory of four-wave mixing in the saturable absorber ${\mathrm{Cr}}^{4+}:\mathrm{Y}\mathrm{A}\mathrm{G}$ and compare with experiments performed at 1.064 μm wavelength. We show that the strong polarization dependence of the saturable absorption along orthogonal crystallographic axes leads to unique polarization properties for wave mixing in ${\mathrm{Cr}}^{4+}:\mathrm{Y}\mathrm{A}\mathrm{G}$. Also there are a range of conditions that lead to vector phase conjugation of the polarization state of a signal beam. Optimum reflectivity for vector phase conjugation occurs when the pump beams have either orthogonal circular polarizations or parallel linear polarizations at 45° to the crystallographic axes. The latter case is unique to this type of nonlinearity.

Fusion rules in turbulence specify the analytic structure of many-point correlation functisons of the turbulent field when a group of coordinates coalesce. We show that the existence of universal flux equilibrium in fully developed turbulent systems combined with a direct cascade induces universal fusion rules. In certain examples these fusion rules suffice to compute the multiscaling exponents exactly, and in other examples they give rise to an infinite number of scaling relations that constrain enormously the structure of the allowed theory.

We report a study of the dynamics of capillary rise of water in a column of glass beads. The water column height $h$ is measured over 5 decades in time, $1<t<\mathrm{}{10}^5\mathrm{s}$. We find that the early time data are well described by the classical Washburn equation for capillary tubes. At late times, however, the dynamics is governed by the randomness of the capillary forces on the air-water interface. Analyzing the data in terms of critical pinning, $\mathrm{dh}/\mathrm{dt}\propto ({P-P}_T{)}^{\beta }$, results in an anomalously large exponent $\beta$. We discuss the significance of this finding in light of recent theories for domain wall pinning in the random-field Ising model.

A Comment on the Letter by H. Alt et al., Phys. Rev. Lett. 74, 62 (1995).

A Reply to the Comment by A. Kudrolli and S. Sridhar.

The interpretation of delayed dynamical systems (DDS) in terms of a suitable spatiotemporal dynamics is put on a rigorous ground by deriving amplitude equations in the vicinity of a Hopf bifurcation. We show that comoving Lyapunov exponents can be defined and computed in a DDS. From the propagation of localized infinitesimal disturbances in DDS, we show the existence of convective type instabilities. Moreover, a widely studied class of DDS is mapped onto an evolution rule for a spatial system with drift and diffusion.

We study an isolated three-dimensional system composed of a slow one-freedom system of interest interacting with a soft-chaotic environment. We present numerical evidence that the averaged motion of the slow system is dissipative, though not exactly governed by the Langevin equation. An analytical reasoning is proposed to explain the results, circumventing the unsufficiency of the adiabatic hypothesis.

We investigate the properties of power spectra of a two-mode laser and predict that universal relations among the peaks of the power and noise spectra for different modes but the same frequency hold for deterministic and stochastic perturbations. These results are confirmed experimentally.

We report experiments showing of the attraction and novel fusion behavior of 3D bright spatial solitons, formed by modulation instability of an optical vortex in a saturable self-focusing medium.

Uniform shear flow is a prototype nonequilibrium state admitting detailed study at both the macroscopic and microscopic levels via theory and computer simulation. It is shown that the hydrodynamic equations for this state have a long wavelength instability. This result is obtained first from the Navier-Stokes equations and shown to apply at both low and high densities. Next, higher order rheological effects are included using a model kinetic theory. The results are compared favorably to those from Monte Carlo simulation.

For Kraichnan's problem of passive scalar advection by a velocity field delta correlated in time, the limit of large space dimensionality $d\gg 1$ is considered. Scaling exponents of the scalar field are analytically found to be ${\zeta }_{2n}=n{\zeta }_2-2\mathrm{}(2-{\zeta }_2)n(n-1\mathrm{})/d$, while those of the dissipation field are ${\mu }_n=-2\mathrm{}(2-{\zeta }_2)n(n-1\mathrm{})/d$ for orders $n\ll d$. The refined similarity hypothesis ${\zeta }_{2n}=n{\zeta }_2+{\mu }_n$ is thus established by a straightforward calculation for the case considered.

A new form of discontinuity for low Mach number compressible flow of an ideal gas in a channel is described. This “hybrid contact discontinuity” exhibits the expected jumps in temperature and density, but, surprisingly, also develops a discontinuity in the fluid velocity across the moving contact surface. In contrast to the standard contact discontinuity, the velocity of the contact surface is not equal to, but much slower than the gas velocity. The hybrid contact discontinuity results from the thermal interaction between the gas and the channel wall. This interaction can also stabilize the contact surface.

Recent advances in the theory of the quasiclassical approximation for systems that are chaotic in the classical limit are extended to the case of ray splitting, in particular, to the splitting of an incident ray into a reflected and refracted component at a sharp interface. An instructive example is presented and novel results are found. These include evidence for ray split and periodic orbits in the spectral correlations and a new type of “scarred” eigenstate based on combining nonisolated periodic orbits whose quasiclassical contributions have a nontrivial phase from total internal reflection.