We introduce the concept of soliton clusters—multisoliton bound states in a homogeneous bulk optical medium—and reveal a key physical mechanism for their stabilization associated with a staircaselike phase distribution that induces a net angular momentum and leads to cluster rotation. The ringlike soliton clusters provide a nontrivial generalization of the concepts of two-soliton spiraling, optical vortex solitons, and necklace-type optical beams.

We introduce a sandpile model where, at each unstable site, all grains are transferred randomly to downstream neighbors. The model is local and conservative, but not Abelian. This does not appear to change the universality class for the avalanches in the self-organized critical state. It does, however, introduce long-range spatial correlations within the metastable states. For the transverse direction $d_{\perp }>0\mathrm{}$, we find a fractal network of occupied sites, whose density vanishes as a power law with distance into the sandpile.

We demonstrate the existence of phase synchronization of two chaotic rotators. Contrary to phase synchronization of chaotic oscillators, here the Lyapunov exponents corresponding to both phases remain positive even in the synchronous regime. Such frequency locked dynamics with different ratios of frequencies are studied for driven continuous-time rotators and for discrete circle maps. We show that this transition to phase synchronization occurs via a crisis transition to a band-structured attractor.

The sensitivity of a wave field’s evolution to small perturbations is of fundamental interest. For chaotic systems, there are two distinct regimes of either exponential or Gaussian overlap decay in time. We develop a semiclassical approach for understanding both regimes and give a simple expression for the crossover time between the regimes. The wave field’s evolution is considerably more stable than the exponential instability of chaotic trajectories seems to suggest. The resolution of this paradox lies in the collective behavior of the appropriate set of trajectories. Results are given for the standard map.

Anomalous correlation functions of the temperature field in two-dimensional turbulent convection are shown to be universal with respect to the choice of external sources. Moreover, they are equal to the anomalous correlations of the concentration field of a passive tracer advected by the convective flow itself. The statistics of velocity differences is found to be universal, self-similar, and close to Gaussian. These results point to the conclusion that temperature intermittency in two-dimensional turbulent convection may be traced back to the existence of statistically preserved structures, as it is in passive scalar turbulence.

This Letter introduces a control strategy for taming the wake turbulence behind a cylinder. An angular momentum injection scheme is proposed to synchronize the vertical velocity field. We show that the base suction, wake formation length, absolute instability, and the Kármán vortex street are effectively controlled by the angular momentum injection. A control equation is designed to implement the injection. The Navier-Stokes equations, along with the control equation, are solved. The occurrence of a new recirculation free zone is identified.

A novel approach is suggested for the statistical description of quantum systems of interacting particles. We show that the occupation numbers for single-particle states can be represented as a convolution of a classical analog of the eigenstate, with the quantum occupation number for noninteracting particles. The latter takes into account the wave function symmetry and depends on the unperturbed energy spectrum only. As a result, the distribution of occupation numbers $n_s$ can be found even for a large number of interacting particles. Using the model of interacting spins, we demonstrate that this approach gives a correct description of $n_s$ even in deep quantum regions with few single-particle orbitals.

We propose a minimal model for aeolian sand dunes. It combines an analytical description of the turbulent wind velocity field above the dune with a continuum saltation model that allows for saturation transients in the sand flux. The model provides a qualitative understanding of important features of real dunes, such as their longitudinal shape and aspect ratio, the formation of a slip face, the breaking of scale invariance, and the existence of a minimum dune size.

We report quantitative measurements of both wave number selection and defect motion in nonequilibrium hexagonal patterns. A novel optical technique (“thermal laser writing”) is used to imprint initial patterns with selected characteristics in a Bénard-Marangoni convection experiment. Initial patterns of ideal hexagons are imposed to determine the band of stable pattern wave numbers while initial patterns containing an isolated penta-hepta defect are imprinted to study defect propagation directions and velocities. The experimental results are compared to recent theoretical predictions.

A nonlinear integral-differential equation describing the cellular front of an overdriven detonation is obtained by an analysis carried out in the neighborhood of the instability threshold. The analysis reveals both an unusual mean streaming motion, resulting from the rotational part of the oscillatory flow, and pressure bursts generated by the crossover of cusps representative of Mach stems propagating on the detonation front. A numerical study of the nonlinear equation exhibits the “diamond” patterns observed in experiments. An overall physical understanding is provided.

We identify a set of quantum graphs with unique and precisely defined spectral properties called regular quantum graphs. Although chaotic in their classical limit with positive topological entropy, regular quantum graphs are explicitly solvable. The proof is constructive: we present exact, convergent periodic orbit expansions for individual energy levels, thus obtaining an analytical solution for the spectrum of regular quantum graphs that is complete, explicit, and exact.

It is shown that direct interaction approximation closure solutions for passive scalar and dispersed inertial particles in compressible turbulent flows result in the phenomena, proposed by Elperin et al. [Phys. Rev. E 58, 3113 (1998)], of turbulent thermal diffusion and turbulent barodiffusion. A more rigorous analysis of Lagrangian history direct interaction approximation for the dispersed phase in the kinetic approach framework is used to accurately quantify the phenomena.

An original geometry for parametric fluorescence is proposed and analyzed theoretically, in which counterpropagating twin photons are emitted in a thin waveguide. In this original down-conversion process, a dramatic decrease of the spectral signal bandwidth at degeneracy is expected, as compared to usual parametric fluorescence processes. The possibility of using the counterpropagating twin photons for quantum cryptography is emphasized. It is shown that the realization of a fibered semiconductor source of Einstein-Podolsky-Rosen photons is possible by this method.

We have used an NMR technique to measure the short-time, three-dimensional displacement of grains in a system of mustard seeds vibrated vertically at $15g$. The technique averages over a time interval in which the grains move ballistically, giving a direct measurement of the granular temperature profile. The dense, lower portion of the sample is well described by a recent hydrodynamic theory for inelastic hard spheres. Near the free upper surface the mean free path is longer than the particle diameter and the hydrodynamic description fails.

We report experimental results on the defect turbulent state of undulation chaos in inclined layer convection of a fluid with Prandtl number $\approx 1$. By measuring defect density and undulation wave number, we find that the onset of undulation chaos coincides with the theoretically predicted onset for stable, stationary undulations. At stronger driving, we observe a competition between ordered undulations and undulation chaos, suggesting bistability between a fixed-point attractor and spatiotemporal chaos. In the defect turbulent regime, we measured the defect creation, annihilation, entering, leaving, and rates. We derive a universal probability distribution function which agrees with the experimental findings.

We study the influence of noise in the dynamics of a laser with optical feedback. For appropriate choices of the feedback parameters, several attractors coexist, and large enough noise induces jumps among the attractors. Based on the residence times probability density, it is shown that with increasing noise the dynamics of attractor jumping exhibits a resonant behavior, which is due to the interplay of noise and delayed feedback. It is also shown that this type of resonance is not specific to the model equations used, since it also occurs in other delay differential equations.

We demonstrate for the first time that the temporal response of a random medium can be obtained from optical intensity fluctuations. Our method uses third-order intensity correlations of measured speckle patterns from a multiple scattering random medium as a function of optical frequency. In particular, our experimental results for the temporal response extracted from third-order intensity correlations are in good agreement with the predictions of a diffusion model. Our results are valid for waves in random media where the scattered field is described by circular complex Gaussian statistics.

Low-divergence, high-brightness harmonic emission has been generated by using a fundamental beam with a truncated Bessel intensity profile. Such a beam is directly obtained by using the hollow-fiber compression technique, which indeed allows one to optimize both temporal and spatial characteristics of the high-order harmonic generation process. This is particularly important for the applications of radiation, where extreme temporal resolution and high brightness are required.

We report observation of lasing in the scarred modes in an asymmetrically deformed microcavity made of liquid jet. The observed scarred modes correspond to morphology-dependent resonance of radial mode order 3 with their $Q$ values in the range of ${10}^6$. Emission directionality is also observed, corresponding to a hexagonal unstable periodic orbit.

The generation of dark solitons in Bose-Einstein condensates with phase imprinting is studied by mapping it into the classic problem of a damped driven pendulum. We provide a simple but powerful scheme, designing the phase imprint for various desired outcomes of soliton generation. For a given phase step, we derive a formula for the number of dark solitons traveling in each direction, and examine the physics behind the generation of counterpropagating dark solitons.