We consider the wide class of systems modeled by an integrable approximation to the 3 degrees of freedom elastic pendulum with $1:1:2$ resonance, or the swing-spring. This approximation has monodromy which prohibits the existence of global action-angle variables and complicates the dynamics. We study the quantum swing-spring formed by bending and symmetric stretching vibrations of the ${\mathrm{C}\mathrm{O}}_2$ molecule. We uncover quantum monodromy of ${\mathrm{C}\mathrm{O}}_2$ as a nontrivial codimension 2 defect of the three dimensional energy-momentum lattice of its quantum states.

The interaction of ultrashort laser pulses with opaque droplets in the atmosphere is examined numerically. Intense filaments resulting from the balance between self-focusing and ionization of air molecules are shown to be robust against obscurants sized up to $2/3$ of the filament diameter. $(3D+1)$-dimensional numerical simulations confirm recent experimental data [F. Courvoisier et al., Appl. Phys. Lett. 83, 213 (2003)]. The filament is rapidly rebuilt with minimal loss of energy over a few cm after the interaction region. The replenishment of the pulse mainly proceeds from the nonlinear attractor responsible for the formation of a spatial soliton modeling the filament core.

We present a combined experimental and theoretical study of phonon focusing phenomena in a pass band above the complete band gap in a 3D phononic crystal. Wave propagation was found to depend dramatically on both frequency and incident direction. This propagation anisotropy leads to very large negative refraction, which can be used to focus a diverging ultrasonic beam into a narrow focal spot with a large focal depth. The experimental field patterns are well explained using a Fourier imaging technique, based on the 3D equifrequency surfaces calculated from multiple scattering theory.

We show that different ways of extracting time scales from time-dependent velocity structure functions lead to different dynamic-multiscaling exponents in fluid turbulence. These exponents are related to equal-time multiscaling exponents by different classes of bridge relations, which we derive. We check this explicitly by detailed numerical simulations of the Gledzer-Ohkitani-Yamada shell model for fluid turbulence. Our results can be generalized to any system in which both equal-time and time-dependent structure functions show multiscaling.

We report interesting results of light scattering in periodic $\beta$-aligned carbon nanotubes (CNTs). Observations of spatial symmetric scattering as a consequence of strong interference agree well with analysis of periodic hexagonal lattices of the CNTs. We found that the scattering is maximally enhanced at a particular angle where the backward incident and scattered directions are exactly superposed for both $s$ and $p$ polarization. The experimental results are explained using a mechanism of electromagnetically induced excitation of surface plasmon polaritons which result in enhanced backscattering effect in CNTs.

We sketch the semiclassical core of a proof of the so-called Bohigas-Giannoni-Schmit conjecture: A dynamical system with full classical chaos has a quantum energy spectrum with universal fluctuations on the scale of the mean level spacing. We show how in the semiclassical limit all system specific properties fade away, leaving only ergodicity, hyperbolicity, and combinatorics as agents determining the contributions of pairs of classical periodic orbits to the quantum spectral form factor. The small-time form factor is thus reproduced semiclassically. Bridges between classical orbits and (the nonlinear sigma model of) quantum field theory are built by revealing the contributing orbit pairs as topologically equivalent to Feynman diagrams.

We report on an experimental observation of repetitively nanosecond spatial solitons in a saturable absorber $Q$-switched microchip laser. The formation of high-peak-power spatial localized structures is achieved by controlling the self-focusing effect in a nearly hemispherical resonator. Our experimental results not only show qualitative agreement with theoretical predictions but also give quantitative criteria for the self-focusing nonlinearity. In addition, we also observe the coexistence of amplitude and phase solitons.

The effects of a quenched chaotic signal on the overdamped motion of a driven particle on a periodic, asymmetric potential are studied. It is shown that the chaotic signal can induce “drift” motion, the phenomenon of “resonance,” and “diffusion” motion. The possible applications to experiments on nanoscale surfaces and particle separation are discussed.

We present experimental observations of two-dimensional macroscopic Coulomb crystals of charged water droplets created on the surface of a thin layer of mineral oil that covers a volume of deionized water. The crystallization process is triggered by an electrohydrodynamic instability of the oil-water interface induced in the system by the simultaneous application of a corona discharge and a dc voltage bias. The experimental scale sizes of the observed crystals agree well with quantitative theoretical estimates of the interfacial instability. Our experiment also provides a novel and simple method for creating long-lived ordered patterns that can serve as excellent systems for basic studies of strongly coupled matter with potentially interesting applications.

The chaotic low energy region of the Fermi-Ulam simplified accelerator model is characterized by the use of scaling analysis. It is shown that the average velocity and the roughness (variance of the average velocity) obey scaling functions with the same characteristic exponents. The formalism is widely applicable, including to billiards and to other chaotic systems.

A theory of enstrophy decay in two-dimensional turbulence, accurately accounting for the role of the large-scale coherent structures, is presented. It is shown that in the limit $\mathrm{R}\mathrm{e}\to \infty$ the total enstrophy in the system obeys a universal asymptotic relation: $\Omega \propto t^{-2/3}$.

We demonstrate a low-loss, optical four port resonant coupler (add-drop geometry), using ultrahigh $Q$ ($>{10}^8$) toroidal microcavities. Different regimes of operation are investigated by variation of coupling between resonator and fiber taper waveguides. As a result, waveguide-to-waveguide power transfer efficiency of 93% (0.3 dB loss) and nonresonant insertion loss of 0.02% ($<0.001\mathrm{dB}$) for narrow bandwidth (57 MHz) four port couplers are achieved in this work. The combination of low-loss, fiber compatibility, and wafer-scale design would be suitable for a variety of applications ranging from quantum optics to photonic networks.

The critical relations for statistical properties on saddle-node bifurcations are shown to display undulating fine structure, in addition to their known smooth dependence on the control parameter. A piecewise linear map with the type-I intermittency is studied and a log-periodic dependence is numerically obtained for the average time between laminar events, the Lyapunov exponent, and attractor moments. The origin of the oscillations is built in the natural probabilistic measure of the map and can be traced back to the existence of logarithmically distributed discrete values of the control parameter giving Markov partition. Reinjection and noise effect dependences are discussed and indications are given on how the oscillations are potentially applicable to complement predictions made with the usual critical exponents, taken from data in critical phenomena.

Oscillatory solution branches of the hydrodynamic field equations describing convection in the form of a standing wave (SW) in binary fluid mixtures heated from below are determined completely for several negative Soret coefficients $\psi$. Galerkin as well as finite-difference simulations were used. They were augmented by simple control methods to obtain also unstable SW states. For sufficiently negative $\psi$, unstable SWs bifurcate subcritically out of the quiescent conductive state. They become stable via a saddle-node bifurcation when lateral phase pinning is exerted. Eventually their invariance under timeshift by half a period combined with reflection at midheight of the fluid layer gets broken. Thereafter, they terminate by undergoing a period-doubling cascade into chaos.

We have observed a natural periodic pattern occurring in partially melted snow lying on the ground under certain atmospheric conditions. We explain this phenomenon quantitatively by considering heat flow through this layer coexisting in two phases (snow and water). Our model equations exhibit a range of patterns depending on the average density of snow. Strikingly similar patterns have been observed by Plass and co-workers in monolayer depositions of Pb on heated PbCu substrates. We argue that the physics of the two phenomena, differing in length scales by 7 orders of magnitude, is similar.

We suggest that the dynamics of stable viscous invasion fronts in porous media depends on the volume capacitance of the media. At high volume capacitance, our network simulations provide numerical evidence of a scaling relation between the front width and its velocity. In the low volume capacitance regime, we derive a new effective scaling supported by network simulations and that is in agreement with previous experiments on imbibition in paper and collections of glass beads.

Spatial structures as a result of a modulational instability are studied in a nonlinear cavity with a photonic crystal. The interaction of the modulated refractive index with the nonlinearity inhibits the instability via the creation of a photonic band gap. A novel mechanism of light localization due to defects and pattern inhibition is also described.

Large populations of globally coupled identical maps subjected to independent additive noise are shown to undergo qualitative changes as the features of the stochastic process are varied. We show that, for strong coupling, the collective dynamics can be described in terms of a few effective macroscopic degrees of freedom, whose deterministic equations of motion are systematically derived through an order parameter expansion.

The propagation of intense 200 fs pulses in water reveals light filaments not sustained by static balance between Kerr-induced self-focusing and plasma-induced defocusing. Numerical calculations outline the occurrence of a possible scenario where filaments appear because of spontaneous reshaping of the Gaussian input beam into a conical wave, driven by the requirement of maximum localization, maximum stationarity, and minimum nonlinear losses.

We study energy transport in a one-dimensional model of elastically colliding particles with alternate masses $m$ and $M$. In order to prevent total momentum conservation, we confine particles with mass $M$ inside a cell of finite size. We provide convincing numerical evidence for the validity of Fourier law of heat conduction in spite of the lack of exponential dynamical instability. Comparison with previous results on similar models shows the relevance of the role played by total momentum conservation.