Motivated by recent experiments on intensity correlations of the waves transmitted through disordered media, we demonstrate that the speckle pattern from disordered photonic crystal with incomplete band gap represents a sensitive tool for determination of the stop-band width. We establish the quantitative relation between this width and the angular anisotropy of the intensity correlation function.

Recent experiments involving femtosecond pulses in water displayed long-distance propagation analogous to that reported in air. We verify this phenomenon numerically and show that the propagation is dynamic as opposed to self-guided. Furthermore, we demonstrate that the propagation can be interpreted as being due to dynamic nonlinear X waves whose robustness and role in long-distance propagation follows from the interplay between nonlinearity and chromatic dispersion.

The breakup of a drop of inviscid fluid into two smaller drops is determined by a competition between surface and inertial forces. This process forms a thin filament of fluid with a connecting neck that shrinks to zero diameter at a finite time singularity. We present measurements of the electrical resistance of a liquid bridge of mercury as it undergoes pinch off. The electrical measurements allow us to probe the region of the singularity down to nanosecond times and nanometer lengths. Near pinch off, the resistance of the liquid bridge diverges as $t^{-2/3}$, as expected for inviscid flow.

We consider the flow being a superposition of random waves and describe the evolution of the spectrum of the passive scalar in the leading (fourth) order with respect to the wave amplitudes. We find that wave turbulence can produce an exponential growth of the passive scalar fluctuations when either both solenoidal and potential components are present in the flow or there are potential waves with the same frequencies but different wave numbers.

Wave functions of pseudointegrable plane polygonal billiards are investigated. It is demonstrated that they have clear structures (superscars) related with families of classical periodic orbits which do not disappear at large energy.

We elucidate the mechanism of drag reduction by polymers in turbulent wall-bounded flows: while momentum is produced at a fixed rate by the forcing, polymer stretching results in the suppression of momentum flux to the wall. On the basis of the equations of fluid mechanics we develop the phenomenology of the “maximum drag reduction asymptote” which is the maximum drag reduction attained by polymers. Based on Newtonian information only we demonstrate the existence of drag reduction, and with one experimental parameter we reach agreement with the experimental measurements.

We describe analytically the nonlinear dynamics of the incommensurate surface layer (“self-modulated” system) with a spatially periodical structure. In the framework of the Frenkel-Kontorova model the nonlinear excitations of the periodic soliton lattice, such as moving additional kinks and gap solitons, are investigated.

The macroscopic flow properties of pure He II are probed in the limit of zero temperature using an oscillating grid. As the oscillation amplitude passes a first critical threshold, the resonant frequency starts decreasing but the flow remains nondissipative. Beyond a second critical amplitude, the flow undergoes a transition to turbulence and becomes dissipative. Nonlinearity and hysteresis observed between the thresholds are attributed to a boundary layer of quantized vortices.

Interacting surface waves, parametrically excited by two commensurate frequencies, yield a number of nonlinear states. Near the system’s bicritical point, a state, highly disordered in space and time, results from competition between nonlinear states. Experimentally, this disordered state can be rapidly stabilized to a variety of nonlinear states via open-loop control with a small-amplitude third frequency excitation, whose temporal symmetry governs the temporal and the spatial symmetry of the selected nonlinear state. This technique also excites rapid switching between nonlinear states.

The noise-induced escape process from a nonhyperbolic chaotic attractor is of physical and fundamental importance. We address this problem by uncovering the general mechanism of escape in the relevant low noise limit using the Hamiltonian theory of large fluctuations and by establishing the crucial role of the primary homoclinic tangency closest to the basin boundary in the dynamical process. In order to demonstrate that, we provide an unambiguous solution of the variational equations from the Hamiltonian theory. Our results are substantiated with the help of physical and dynamical paradigms, such as the Hénon and the Ikeda maps. It is further pointed out that our findings should be valid for driven flow systems and for experimental data.

A global bifurcation of the blue sky catastrophe type has been found in a small Prandtl number binary mixture contained in a laterally heated cavity. The system has been studied numerically applying the tools of bifurcation theory. The catastrophe corresponds to the destruction of an orbit which, for a large range of Rayleigh numbers, is the only stable solution. This orbit is born in a global saddle-loop bifurcation and becomes chaotic in a period-doubling cascade just before its disappearance at the blue sky catastrophe.

We develop a continuum theory of self-assembly and pattern formation in metallic microparticles immersed in a poorly conducting liquid in a dc electric field. The theory is formulated in terms of conservation laws for the densities of immobile particles (precipitate) and bouncing particles (gas) coupled to the Navier-Stokes equation for the liquid. This theory successfully reproduced the correct topology of the phase diagram and primary patterns observed in the experiment [Sapozhnikov et al., Phys. Rev. Lett. 90, 114301 (2003)]: static crystals, honeycombs, dynamic pulsating rings, and rotating multipetal vortices.

A quantitative relationship is found between the multifractal properties of the asymptotic mass distribution in a random dissipative system and the long-time fluctuations of the local stretching rates of the dynamics. It captures analytically the fine aspects of the strongly intermittent clustering of dynamical trajectories. Applied to a simple compressible hydrodynamical model with known stretching-rate statistics, the relation produces a nontrivial spectrum of multifractal dimensions that is confirmed numerically.

We report the spontaneous emergence of a doubly periodic train of sedimented knolls in a dense suspension. These solidified knolls rise out of, and coexist alongside, a sea of freely flowing liquid in a slowly rotating horizontal bottle. We apply a variable viscosity model that permits simultaneous analysis of fluidlike and solidlike behaviors that are ubiquitous in a variety of sedimenting flows. The model generates qualitative agreement with experiments, and produces new insights into mechanisms by which sedimented structures form.

We predict the existence of random phase solitons in nonlinear periodic lattices. These solitons exist when the nonlinear response time is much longer than the characteristic time of random phase fluctuations. The intensity profiles, power spectra, and statistical (coherence) properties of these stationary waves conform to the periodicity of the lattice. The general phenomenon of such solitons is analyzed in the context of nonlinear photonic lattices.

We investigate the nonlinear propagation of two forward propagating modes coupled by a resonant traveling-wave grating, which is photoinduced by illuminating an optical fiber with a beat signal. This interaction, representative of systems whose dispersion relation $K=K(\Omega )$ exhibits a gap in momentum $K$, shows evidence of localization mediated by resonance solitons. The signature of a still (in the grating frame) soliton is grating-induced cancellation of modal group-velocity mismatch.

We extend the theory of diffusing-wave spectroscopy using a random-walk approach and a numerical solution of the radiative transfer equation. The theory is not restricted to the diffusive regime and allows one to describe the crossover between the single-scattering and the diffusive regimes, which has been observed experimentally. It also predicts a lower bound of the scattered-field correlation time at long paths. This extended theory should have broad experimental applications in the field of imaging through biological tissues.

Strain in sheared dense granular material is often localized in a narrow region called the shear band. Recent experiments in a modified Couette cell provided localized shear flow in the bulk away from the confining walls. The nontrivial shape of the shear band was measured as the function of the cell geometry. First, we present a geometric argument for narrow shear bands that connects the function of their surface position with the shape in the bulk. Assuming a simple dissipation mechanism, we show that the principle of minimum dissipation of energy provides a good description of the shape function. Furthermore, we discuss the possibility and behavior of shear bands that are detached from the free surface and are entirely covered in the bulk.

We report that essentially isolated microcavity lasers may interact in the most complicated manner and drive each other chaotic. As the optical isolation between these lasers reaches presently practically attainable limits, instead of approaching independent operation, the lasers exhibit mutually induced chaotic oscillations. The chaos arises from an intricate coupling of the nonlinearities associated with coupled optical resonators and those evolving from the population dynamics in the active region. The investigation is performed using a composite-cavity theory and a class-$B$ description of the gain medium. Bifurcation analysis identifies the source of instabilities and determines their robustness.

Self-similar propagation of ultrashort, parabolic pulses in a laser resonator is observed theoretically and experimentally. This constitutes a new type of pulse shaping in mode-locked lasers: in contrast to the well-known static (solitonlike) and breathing (dispersion-managed soliton) pulse evolutions, asymptotic solutions to the nonlinear wave equation that governs pulse propagation in most of the laser cavity are observed. Stable self-similar pulses exist with energies much greater than can be tolerated in solitonlike pulse shaping, and this has implications for practical lasers.