Recent experiments [R. A. Gray et al., Phys. Rev. Lett. 87, 168104 (2001)] have revealed striking standing wave patterns in cardiac muscle. In excitable media, such as cardiac tissue where colliding waves annihilate, standing wave patterns result from a fully nonlinear mechanism. We present a possible physical mechanism explaining these patterns. The phenomenon does not depend on the precise excitable model chosen. Analogies are drawn with weak links in superconductors, and phase-slip solutions in the Ginzburg-Landau equations.

A new phenomenon of self-induced hysteresis has been observed in the interaction of bulk acoustic waves with a cracked solid. It consists in a hysteretic behavior of material nonlinearity as a function of the incident pump wave amplitude. Hysteresis manifests itself in the self-action of the monochromatic pump wave and in the excitation of its superharmonics and of its subharmonics. The proposed theoretical models attribute the phenomenon to hysteresis in transition of the acoustically forced oscillation of cracks from a nonclapping regime to a regime of clapping contacts.

Elliptic instability in fluids is discussed in the context of the Lagrangian-averaged Navier-Stokes-alpha (LANS-$\alpha$) turbulence model. This model preserves the Craik-Criminale (CC) family of solutions consisting of a columnar eddy and a Kelvin wave. The LANS-$\alpha$ model is shown to preserve elliptic instability. However, the model shifts the critical stability angle. This shift increases (decreases) the maximum growth rate for long (short) waves. It also introduces a band of stable CC solutions for short waves.

We introduce the concept of a hybrid 2D–3D photonic band gap (PBG) heterostructure which enables both complete control of spontaneous emission of light from atoms and planar light-wave propagation in engineered wavelength-scale microcircuits. Using three-dimensional (3D) light localization, this heterostructure enables flow of light without diffraction through micron-scale air waveguide networks. Achieved by intercalating two-dimensional photonic crystal layers containing engineered defects into a 3D PBG material, this provides a general and versatile solution to the problem of “leaky modes” and diffractive losses in integrated optics.

Stable two- and three-dimensional spatiotemporal solitons (STSs) in second-harmonic-generating media are found in the case of normal dispersion at the second-harmonic (SH). This result, surprising from the theoretical viewpoint, opens the way for experimental realization of STSs. An analytical estimate for the existence of STSs is derived, and full results, including a complete stability diagram, are obtained in numerical form. STSs withstand not only the normal SH dispersion, but also finite walk-off between the harmonics, and readily self-trap from a Gaussian pulse launched at the fundamental frequency.

A broad class of exact self-similar solutions to the nonlinear Schrödinger equation (NLSE) with distributed dispersion, nonlinearity, and gain or loss has been found. Appropriate solitary wave solutions applying to propagation in optical fibers and optical fiber amplifiers with these distributed parameters have also been studied. These solutions exist for physically realistic dispersion and nonlinearity profiles in a fiber with anomalous group velocity dispersion. They correspond either to compressing or spreading solitary pulses which maintain a linear chirp or to chirped oscillatory solutions. The stability of these solutions has been confirmed by numerical simulations of the NLSE.

We have observed slow light propagation with a group velocity as low as $57.5\pm 0.5\mathrm{m}/\mathrm{s}$ at room temperature in a ruby crystal. A quantum coherence effect, coherent population oscillations, produces a very narrow spectral “hole” in the homogeneously broadened absorption profile of ruby. The resulting rapid spectral variation of the refractive index leads to a large value of the group index. We observe slow light propagation both for Gaussian-shaped light pulses and for amplitude modulated optical beams in a system that is much simpler than those previously used for generating slow light.

Broadband noise on supercontinuum spectra generated in microstructure fiber is shown to lead to amplitude fluctuations as large as 50% for certain input laser pulse parameters. We study this noise using both experimental measurements and numerical simulations with a generalized stochastic nonlinear Schrödinger equation, finding good quantitative agreement over a range of input-pulse energies and chirp values. This noise is shown to arise from nonlinear amplification of two quantum noise inputs: the input-pulse shot noise and the spontaneous Raman scattering down the fiber.

This paper proposes a new volume function for calculation of the entropy of planar granular assemblies. This function is extracted from the antisymmetric part of a new geometric tensor and is rigorously additive when summed over grains. It leads to the identification of a conveniently small phase space. The utility of the volume function is demonstrated on several case studies, for which we calculate explicitly the mean volume and the volume fluctuations.

Experimental results are presented on the segregation of a mixture of spheres with two different sizes, rolling on a circularly vibrating table. Beyond a critical density of particles a demixing occurs leading to a clustering of the larger ones. A monodisperse layer of spheres shows a liquid-solid-like phase transition at a slightly lower critical density. These critical particle densities are both found to be independent of the driving frequency, but decrease with increasing vibration amplitude.

We show that granular media, consisting of metallic microparticles immersed in a poorly conducting liquid in a strong dc electric field, self-assemble into a rich variety of novel phases. These phases include static precipitates: honeycombs and Wigner crystals; and novel dynamic condensates: toroidal vortices and pulsating rings. The observed structures are explained by the interplay between charged granular gas and electrohydrodynamic convective flows in the liquid.

We show that self-pulsating vertical-cavity surface-emitting lasers can exhibit vectorial chaos, i.e., chaos in both intensity and polarization. The achievable synchronization degree of two such lasers is high when using a continuous control scheme and unidirectional coupling. We propose a novel encryption scheme, where the phase of the vectorial field is modulated. Therefore, the total intensity of these lasers remains synchronized while the intensities in the polarization modes (de)synchronize following the phase modulation at a ps time scale. This technique allows for transmission of secure data at high bit rates that are not limited by the relaxation oscillation frequency.

Bloch-like surface waves associated with a quasiperiodic structure are observed in a classic wave propagation experiment which consists of pulse propagation with a shallow fluid covering a quasiperiodically drilled bottom. We show that a transversal pulse propagates as a plane wave with quasiperiodic modulation, displaying the characteristic undulatory propagation in this quasiperiodic system and reinforcing the idea that analogous concepts to Bloch functions can be applied to quasicrystals under certain circumstances.

The production rate of polymer fibers by extrusion is usually limited by the appearance of a series of instabilities (“melt fracture”) that lead to unwanted undulations of the surface. We present both qualitative and quantitative experimental evidence that—in addition to previously known polymer-specific scenarios—there is an intrinsic route towards melt fracture type phenomena: a nonlinear (“subcritical”) instability of viscoelastic Poiseuille flow.

We present a new description of nonequilibrium square patterns as a harmonically coupled crystal lattice. In a vertically oscillating granular layer, different transverse normal modes of the granular square-lattice pattern are observed for different driving frequencies ($f_d$) and accelerations. The amplitude of a mode can be further excited by either frequency modulation of $f_d$ or reduction of friction between the grains and the plate. When the mode amplitude becomes large, the lattice melts (disorders), in accord with the Lindemann criterion for melting in two dimensions.

We present experimental data on the direct enstrophy cascade in decaying two-dimensional turbulence. Velocity and vorticity fields are obtained using particle tracking velocimetry. From those fields we directly compute the enstrophy and energy flux by using a filtering technique inspired by large-eddy simulations. This allows considerable insight into the physical processes of turbulence when compared with structure-function or spectral analysis. The direct cascade of enstrophy is weakly forward, with almost as much backscatter as down-scale enstrophy transfer, whereas the inverse energy cascade is strongly upscale with a modest amount of backscatter.

We investigate aging behavior in a simple dynamical system: a nonlinear map which generates subdiffusion deterministically. Asymptotic behaviors of the diffusion process are described using aging continuous time random walks. We show how these processes are described by an aging diffusion equation which is of fractional order. Our work demonstrates that aging behavior can be found in deterministic low dimensional dynamical systems.

Based on the approach suggested by Tarantola, and Gauthier et al., we show that the alternate use of the step (linear) function basis and the block function (quasi-$\delta$ function) basis can give accurate full waveform inversion results for the layered acoustic systems, starting from a uniform background. Our method is robust against additive white noise (up to $20\%$ of the signal) and can resolve layers that are comparable to or smaller than a wavelength in thickness. The physical reason for the success of our approach is illustrated through a simple example.

We address the experimentally observed non-Gaussian fluctuations for the energy injected into a closed turbulent flow at fixed Reynolds number. We propose that the power fluctuations mirror the internal kinetic energy fluctuations. Using a stochastic cascade model, we construct the excess kinetic energy as the sum over the energy transfers at different levels of the cascade. We find an asymmetric distribution that strongly resembles the experimental data. The asymmetry is an explicit consequence of intermittency and the global measure is dominated by small scale events correlated over the entire system. Our calculation is consistent with the statistical analogy recently made between a confined turbulent flow and a critical system of finite size.

We report a study of transient ultrasonic waves inside a reverberant cavity containing moving scatterers. We show that the elastic mean free path and the dynamics of the scatterers govern the evolution of the autocorrelation of acoustic wave field. A parallel is established between these results and a closely related technique, diffusing acoustic wave spectroscopy. Excellent agreement is found between experiment and theory for a moving stainless steel ball in a water tank, thereby elucidating the underlying physics, and a potential application, fish monitoring inside aquariums, is demonstrated.