We develop a theory describing the transition to a spatially homogeneous regime in a mixing flow with a chaotic in time reaction. The transverse Lyapunov exponent governing the stability of the homogeneous state can be represented as a combination of Lyapunov exponents for spatial mixing and temporal chaos. This representation, being exact for time-independent flows and equal Péclet numbers of different components, is demonstrated to work accurately for time-dependent flows and different Péclet numbers.

We study resonance patterns of a spiral-shaped dielectric microcavity with chaotic ray dynamics. Many resonance patterns of this microcavity, with refractive indices $n=2$ and 3, exhibit strong localization of simple geometric shape, and we call them quasiscarred resonances in the sense that there is, unlike conventional scarring, no underlying periodic orbits. It is shown that the formation of a quasiscarred pattern can be understood in terms of ray dynamical probability distributions and wave properties like uncertainty and interference.

We report experimental evidence of a global bifurcation on a highly turbulent von Kármán flow. The mean flow presents multiple solutions: the canonical symmetric solution becomes marginally unstable towards a flow which breaks the basic symmetry of the driving apparatus even at very large Reynolds numbers. The global bifurcation between these states is highly subcritical and the system thus keeps a memory of its history. The transition recalls low-dimension dynamical system transitions and exhibits very peculiar statistics. We discuss the role of turbulence in two ways: the multiplicity of hydrodynamical solutions and the effect of fluctuations on the nature of transitions.

The generation of attosecond pulses by superposition of high harmonics relies on their synchronization in the emission. Our experiments in the low-order, plateau, and cutoff regions of the spectrum reveal different regimes in the electron dynamics determining the synchronization quality. The shortest pulses are obtained by combining a spectral filtering of harmonics from the end of the plateau and the cutoff, and a far-field spatial filtering that selects a single electron quantum path contribution to the emission. This method applies to isolated pulses as well as pulse trains.

We show that modulational instability may arise even in the normal group-velocity dispersion regime of an optical fiber when the fiber loss (gain) varies depending on the wavelength. A simple analytical expression for the instability gain is obtained, which reveals that the odd-order terms of the loss dispersion are responsible for this phenomenon. The instability gain is measured experimentally in an optical-parametric-amplification configuration. Large parametric gain is induced in a non-phase-matched regime as we apply narrow band loss at the idler wavelength.

We subject a falling cloud of cold cesium atoms to periodic kicks from a sinusoidal potential created by a vertical standing wave of laser light. By controllably accelerating the potential, we show quantum accelerator mode dynamics to be highly sensitive to the effective gravitational acceleration when close to specific, resonant values. This quantum sensitivity to a control parameter is reminiscent of that associated with classical chaos and promises techniques for precision measurement.

We address the phenomenon of soliton self-bending in Kerr-type nonlocal nonlinear media with an imprinted transverse periodic modulation of the linear refractive index. We show that the imprinted optical lattice makes possible to control the mobility of soliton by varying the depth and the frequency of the linear refractive index modulation.

We present methods for detecting phase synchronization of two unidirectionally coupled, self-sustained noisy oscillators from a signal of the driven oscillator alone. One method detects soft phase locking; another hard phase locking. Both are applied to the problem of detecting phase synchronization in von Kármán vortex flow meters.

In the semiclassical limit of open ballistic quantum systems, we demonstrate the emergence of instantaneous decay modes guided by classical escape faster than the Ehrenfest time. The decay time of the associated quasibound states is smaller than the classical time of flight. The remaining long-lived quasibound states obey random-matrix statistics, renormalized in compliance with the recently proposed fractal Weyl law for open systems [W. T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. 91, 154101 (2003)]. We validate our theory numerically for a model system, the open kicked rotator.

We study the multiple scattering of short-wavelength ultrasound through the force networks in dry and wet glass bead packings under stress. Over long distance scales, the diffusion approximation is shown to describe adequately the transport of elastic waves dominated by shear waves. The recovered transport mean path reveals a short-range correlation of the force chains. Also we observe the drastic effect of wetting liquids on the energy dissipation in the granular medium. The relevance of these experimental findings for the seismological applications is discussed.

The influence of white noise on defect-mediated turbulence which is modeled by the complex Ginzburg-Landau equation is investigated. We show that the dynamics of defects in the noise-driven spatiotemporal chaos can be described by a simple statistical model. The noise enhances significantly the ability of the turbulent background to advocate new defects with a constant rate, and at the same time it increases the vanishing of defects in the system by introducing an additional annihilation rate that is proportional to the number of defects. A universal probability distribution function is derived for the number of defect pairs.

The coefficient of normal restitution in an oblique impact is theoretically studied. Using a two-dimensional lattice model for an elastic disk and an elastic wall, we demonstrate that the coefficient of normal restitution can exceed unity and has a peak against the incident angle in our simulation. We also explain this behavior based upon a phenomenological theory.

The lumped-mass method is applied to study the propagation of elastic waves in two-dimensional binary periodic systems, i.e., periodic soft rubber/epoxy and vacuum/epoxy composites, for which the conventional methods fail or converge very slowly. A comprehensive study is performed for the two-dimensional binary locally resonant phononic crystals, which are composed of periodic soft rubber cylinders immersed in epoxy host. Numerical simulations predict that subfrequency gaps also appear because of the high contrast of mass density and elastic constant of the soft rubber. The locally resonant mechanism in forming the subfrequency gaps is thoroughly analyzed by studying the two-dimensional model and its quasi-one-dimensional mechanical analog. The rule used to judge whether a resonant mode in the phononic crystals can result in a corresponding subfrequency gap or not is found.

We introduce a noninvasive, quantitative magnetic resonance imaging (MRI) wind-tunnel measurement in flowing gas ($>10\mathrm{m}{\mathrm{s}}^{-1}$) at high Reynolds numbers ($\mathrm{R}\mathrm{e}>{10}^5$). The method pertains to liquids and gases, is inherently three dimensional, and extends the range of Re to which MRI is applicable by orders of magnitude. There is potential for clear time savings over traditional pointwise techniques. The mean velocity and turbulent diffusivity of gas flowing past a bluff obstruction and a wing section at realistic stall speeds were measured. The MRI data are compared with computational fluid dynamics.

We present a theoretical and experimental study of multiple pulse formation in passively mode-locked lasers. Following a statistical-mechanics approach, the study yields a thermodynamic-like “phase diagram” with boundaries representing cascaded first order phase transitions. They correspond to abrupt creation or annihilation of pulses and a quantized rf power behavior, as system parameters (noise and/or pumping levels) are varied, in excellent accordance with the experiments. Remarkably, individual pulses carry an almost constant quantum of energy.

Nonlinear losses accompanying self-focusing substantially impact the dynamic balance of diffraction and nonlinearity, permitting the existence of localized and stationary solutions of the $2\mathrm{D}+1$ nonlinear Schrödinger equation, which are stable against radial collapse. These are featured by linear, conical tails that continually refill the nonlinear, central spot. An experiment shows that the discovered solution behaves as a strong attractor for the self-focusing dynamics in Kerr media.

We present new results for the time reversal of weakly nonlinear pulses traveling in a random dissipative environment. Also we describe a new theory for calculating the eddy viscosity for weakly nonlinear waves propagating over a random surface. The turbulent viscosity is calculated from first principles, namely, without imposing any stress-strain hypothesis. A viscous shallow water model is considered and its effective viscosity characterized. We also show that weakly nonlinear waves can still be time reversed under weak dissipation. Incoherently scattered signals are recompressed, both for time reversal in transmission as well as in reflection. Under the weakly nonlinear, weakly dissipative regime, dissipation only affects the refocused pulse profile regarding its amplitude, but its shape is not corrupted. Numerical experiments are presented.

The numerical simulation of two-dimensional decaying turbulence in a large but finite box presented in this Letter uncovered two physically different regimes of enstrophy decay. During the initial stage, the enstrophy $\Omega$, generated by a random Gaussian initial condition, decays as $\Omega (t)\propto t^{-\gamma }$ with $\gamma \approx 0.7–0.8$. After that, the flow undergoes a transition to a gas or fluid composed of distinct vortices. Simultaneously, the magnitude of the decay exponent crosses over to $\gamma \approx 0.4$. A theory predicting $N(t)\propto t^{-\xi }$ and the magnitudes of exponents $\gamma =2/5$ and $\xi =4/5$ is presented.

We predict a strong effective Kerr nonlinearity in hollow-core photonic crystal fibers filled with a Raman active gas which exceeds the intrinsic Kerr nonlinearity by 2 orders of magnitude. Two-color bright-bright and dark-bright solitons supported by this nonlinearity are found and the feasibility of their experimental observation is demonstrated.

We report an experimental and theoretical study on the optimization of $(2+1)\mathrm{D}$ self-written waveguide formation inside a photopolymerizable material. The accurate control of the refractive index value inside the bulk of the material during the polymerization process gives us the opportunity to define a virtual core and a virtual cladding for the system. The $V$ value which characterizes the guidance properties of a fiber can be applied to this propagation. The control of the $V$ value allows us to propagate single mode or multimode waveguides on a few centimeters. Numerical simulations of these waveguides based on a paraxial model including both photopolymerization and Kerr effect give very good agreement with our experimental results.