We study the zero temperature dynamics in an Ising chain in the presence of a dynamically induced field that favors locally the “ $-$” phase compared to the “ $+$” phase. At late times, while the “ $+$” domains coarsen as $t^{1/2}$, the “ $-$” domains coarsen as $t^{1/2}\log \left(t\right)$. Hence, at late times, the magnetization decays slowly as $m\left(t\right)=-1+\mathrm{const}/\log \left(t\right)$. We establish this behavior both analytically within an independent interval approximation and numerically. Our model can be viewed as a simple model for granular compaction, where the system decays into a fully compact state (with all spins “ $-$”) in a slow logarithmic manner as seen in recent experiments on granular systems.

The asymptotic decay of passive scalar fields is solved analytically for the Kraichnan model, where the velocity has a short correlation time. At long times, two universality classes are found, both characterized by a distribution of the scalar—generally non-Gaussian—with global self-similar evolution in time. Analogous behavior is found numerically with a more realistic flow resulting from an inverse energy cascade.

Direct numerical simulations of chevrons, blinking states, and repeated transients in binary fluid mixtures with a negative separation ratio heated from below are described. The calculations are performed in two-dimensional containers for experimental parameter values and boundary conditions. Quantitative agreement with the experiments of Kolodner [Phys. Rev. E 47, 1038 (1993)] is obtained, and the origin of the blinking and repeated transient states is elucidated.

We show analytically and numerically that, under certain conditions, coherent localized structures can be generated and sustained from an incoherent source in quadratic nonlinear media. This phenomenon, which relies on the convection between the waves interacting in the medium, leads to the formation of a novel type of three-wave parametric soliton composed of both coherent and incoherent fields.

The phase separation between two immiscible liquids advected by a bidimensional velocity field is investigated numerically by solving the corresponding Cahn-Hilliard equation. We study how the spinodal decomposition process depends on the presence—or absence—of Lagrangian chaos. A fully chaotic flow, in particular, limits the growth of domains, and for unequal volume fractions of the liquids, a characteristic exponential distribution of droplet sizes is obtained. The limiting domain size results from a balance between chaotic mixing and spinodal decomposition, measured in terms of Lyapunov exponent and diffusivity constant, respectively.

We study the dynamics of holes and defects in the 1D complex Ginzburg-Landau equation in ordered and chaotic cases. Ordered hole-defect dynamics occurs when an unstable hole invades a plane wave state and periodically nucleates defects from which new holes are born. The results of a detailed numerical study of these periodic states are incorporated into a simple analytic description of isolated “edge” holes. Extending this description, we obtain a minimal model for general hole-defect dynamics. We show that interactions between the holes and a self-disordered background are essential for the occurrence of spatiotemporal chaos in hole-defect states.

General results concerning maintenance or enhancement of chaos are presented for dissipative systems subjected to two harmonic perturbations (one chaos inducing and the other chaos enhancing). The connection with previous results on chaos suppression is also discussed in a general setting. It is demonstrated that, in general, a second harmonic perturbation can reliably play an enhancer or inhibitor role by solely adjusting its initial phase. Numerical results indicate that general theoretical findings concerning periodic chaos-inducing perturbations also work for aperiodic chaos-inducing perturbations, and in arrays of identical chaotic coupled oscillators.

Extensive coherent control over quantum chaotic diffusion using the kicked rotor model is demonstrated and its origin in deviations from random matrix theory is identified. Further, the extent of control in the presence of external decoherence is established. The results are relevant to both areas of quantum chaos and coherent control.

We demonstrate that unstable periodic orbits embedded in the experimental chaotic attractor determined by the Taylor-Couette flow can be stabilized with a time-delay autosynchronization algorithm. The optimal parameters of the feedback and their dependence on the control parameter are shown as experimental results.

A novel approach is suggested for detecting the presence or absence of synchronization between two or three interacting processes with different time scales in univariate data. It is based on an angle-of-return-time map. A model is derived to describe analytically the behavior of angles for a periodic oscillator under weak periodic and quasiperiodic forcing. An explicit connection is demonstrated between the return angle and the phase of the external periodic forcing. The technique is tested on simulated nonstationary data and applied to human heart rate variability data.

We demonstrate that the shift of the stop-band position with increasing oblique angle in periodic structures results in a wide transverse exponential field distribution corresponding to strong angular confinement of the radiation. The beam expansion follows an effective diffusive equation depending only upon the spectral mode width. In the presence of gain, the beam cross section is limited only by the size of the gain area. As an example of an active periodic photonic medium, we calculate and measure laser emission from a dye-doped cholesteric liquid crystal film.

We investigate experimentally granular piles exhibiting steady surface flow. Below the surface flow, it has been believed that a “frozen” bulk region exists, but our results show no such frozen bulk. We report here that even the particles in layers deep in the bulk exhibit very slow flow and that such motion can be detected at an arbitrary depth. The mean velocity of the creep motion decays exponentially with depth, and the characteristic decay length is approximately equal to the particle size and is independent of the flow rate. It is expected that the creep motion we have seen is observable in all sheared granular systems.

A statistical method for calculating equilibrium solutions of the shallow water equations, a model of essentially 2D fluid flow with a free surface, is described. The model contains a competing acoustic turbulent direct energy cascade, and a 2D turbulent inverse energy cascade. It is shown, nonetheless that, just as in the corresponding theory of the inviscid Euler equation, the infinite number of conserved quantities constrains the flow sufficiently to produce nontrivial large-scale vortex structures which are solutions to a set of explicitly derived coupled nonlinear partial differential equations.

Transport by normal diffusion can be decomposed into hydrodynamic modes which relax exponentially toward the equilibrium state. In chaotic systems with 2 degrees of freedom, the fine scale structures of these modes are singular and fractal, characterized by a Hausdorff dimension given in terms of Ruelle's topological pressure. For long-wavelength modes, we relate the Hausdorff dimension to the diffusion coefficient and the Lyapunov exponent. This relationship is tested numerically on two Lorentz gases, one with hard repulsive forces, the other with attractive, Yukawa forces. The agreement with theory is excellent.

Dynamic behavior of coupled chaotic oscillators is investigated. A transition from high-dimensional hyperchaos to a generalized periodic splay state is found for extremely weak coupling. Chaotic nature of a single oscillator and mutual resonant interactions are regarded to be responsible for this self-organized ordering. The functional phase distribution of the generalized splay state, which is essentially different from the equal-phase-separation distribution of the conventional splay states, can be well predicted by analyzing a single periodically forced oscillator.

One of the central paradigms for classical and quantum chaos in conservative systems is the two-dimensional billiard in which particles are confined to a closed region in the plane, undergoing elastic collisions with the walls and free motion in between. We report the first realization of billiards using ultracold atoms bouncing off beams of light. These beams create the desired spatial pattern, forming an “optical billiard.” We find excellent agreement between theory and our experimental demonstration of chaotic and stable motion in optical billiards, establishing a new testing ground for classical and quantum chaos.

We report on experimental observations of chaotic and regular motion of ultracold atoms confined by a billiard-shaped optical dipole potential induced by a rapidly scanning laser beam. To investigate the dynamics of the atoms confined by such an “atom-optics” billiard we measure the decay of the number of trapped atoms through a hole on the boundary. A fast and purely exponential decay, the clear signature of chaotic motion, is found for a stadium billiard, but not for a circular or an elliptical billiard, in agreement with theory. We also investigated the effects of decoherence, velocity spread, and gravity on regular and chaotic motion.

We have performed enhanced backscattering experiments in a high gain random laser, under circumstances where a stationary theory predicts the laser intensity to diverge. Above the laser threshold the observed backscatter cone changes only gradually, not showing any signs of the divergence. We present measurements and theory—generalized laser equations with a diffusive transport term for pump and laser light—to explain the observed behavior. The population dynamics prevent an indefinite growth of the intensity. Time dependence is essential for a theory of random lasers above the laser threshold.

We demonstrate that 2D photonic crystals can possess optical trirefringence in which there are six field orientations for which linear incident light is not perturbed on reflection or transmission. Such a property is rigorously forbidden in homogeneous nonmagnetic dielectrics which can possess only optical birefringence. We experimentally demonstrate this phenomena in silicon-based mesostructures formed from photonic crystal waveguides embedded in a Fabry-Perot cavity. Multirefringence is controlled by the presence of submicron dielectric patterning and is well explained by an exact scattering matrix theory.

The scattering of high-frequency sound wave, under geometrical acoustic approximation, by three stationary vortices in two dimensions is investigated. For a sufficiently high Mach number of the vortex flow, the scattering of sound rays becomes irregular, displaying a new example of chaotic scattering for a time-reversal breaking system. The fractal dimension, as well as the unstable and stable manifolds of the scattering dynamics, is presented.