We study 2D and 3D localized oscillating patterns in a simple model system exhibiting nonlinear Faraday resonance. The corresponding amplitude equation is shown to have exact soliton solutions which are found to be always unstable in 3D. On the contrary, the 2D solitons are shown to be stable in a certain parameter range; hence the damping and parametric driving are capable of suppressing the nonlinear blowup and dispersive decay of solitons in two dimensions. The negative feedback loop occurs via the enslaving of the soliton’s phase, coupled to the driver, to its amplitude and width.

A novel theory for the ordering of many interacting modes in lasers is presented. By exactly solving a Fokker-Planck equation for the distribution of waveforms in the laser in steady state, equivalence of the system to a canonical ensemble is established, where the role of temperature is taken by amplifier noise. Passive mode locking is obtained as a phase transition of the first kind and threshold is calculated, employing mean field theory backed up by a numerical study. For zero noise, compliance with the existing noiseless theory is shown.

We propose a theory for axial segregation of suspensions of non-neutrally buoyant particles in a rotating cylinder. The cylinder is oriented in the horizontal plane, so that any axial forces must arise from interparticle interactions. We show that the hydrodynamic interaction between pairs of particles produces a relative motion in the axial direction, independent of the gravitational force. If the particles are denser than the suspending fluid, differential centrifuging between particles at different radial positions leads to an attractive interaction, inducing a rapid growth of axial density perturbations. We suggest that this mechanism can explain the origin of band formation in rotating suspensions of non-neutrally buoyant particles.

An analytical theory of low frequency electromagnetic waves in metallic photonic crystals with a small volume fraction of a metal is presented. The evidence for such waves has been obtained recently by experiments and computations. The cutoff frequency of these waves, ${\omega }_0$, is studied. An analytical expression for the permittivity $ϵ$ is obtained and shown to be negative below ${\omega }_0$. If the crystal is embedded into a medium with a negative $\mu$, there are no propagating modes at any frequency. Thus, such a compound system is not a left-handed material (LHM). The recent experimental results on the LHM are discussed.

We have studied the dynamics of avalanching wet granular media in a rotating drum apparatus. Quantitative measurements of the flow velocity and the granular flux during avalanches allow us to characterize novel avalanche types unique to wet media. We also explore the details of viscoplastic flow (observed at the highest liquid contents) in which there are lasting contacts during flow, leading to coherence across the entire sample. This coherence leads to a velocity-independent flow depth at high rotation rates and novel robust pattern formation in the granular surface.

We study the breakup of a liquid jet a few nanometers in diameter, based on a stochastic differential equation derived recently by Moseler and Landman [Science 289, 1165 (2000)]. In agreement with their simulations, we confirm that noise qualitatively changes the characteristics of breakup, leading to symmetric profiles. Using the path integral description, we find a self-similar profile that describes the most probable breakup mode. As illustrated by a simple physical argument, noise is the driving force behind pinching, speeding up the breakup to make surface tension irrelevant.

Classical Rayleigh theory predicts an instability of a surface charged liquid sphere, when the Coulomb energy $E_C$ exceeds twice the surface energy $E_S$. Previously, electrified liquid droplets have been found to disintegrate at a fissility $X=E_C/2E_S$ well below one, however. We determine the stability of charged droplets in an electrodynamic levitator by observing the amplitude and phase of their quadrupolar shape oscillations as a function of the fissility. With this novel approach, which does not rely on an independent determination of the charge and surface tension of the droplets, we are able to confirm for the first time the Rayleigh limit of stability at $X=1$ for micrometer sized droplets of ethylene glycol.

We observed complicated emission patterns consisting of different transverse modes and associated intensity pulsations at beat frequencies between pairs of transverse eigenmodes in a solid-state thin-slice Fabry-Perot laser with asymmetric end-pumping. The dependence of transverse patterns and pulsation frequencies on pump power has been demonstrated. The interference among nonorthogonal transverse eigenmodes, which are formed in a deformed Fabry-Perot microcavity possessing an asymmetric, gradient refractive-index potential for optical waves, is proposed for explaining observed instabilities. Intensity modulations have been remarkably reproduced by numerical simulations of model equations.

A theory for stabilization of quantum resonances by a mechanism similar to one leading to classical resonances in nonlinear systems is presented. It explains recent surprising experimental results, obtained for cold cesium atoms when driven in the presence of gravity, and leads to further predictions. The theory makes use of invariance properties of the system allowing for separation into independent kicked rotor problems. The analysis relies on a fictitious classical limit where the small parameter is not Planck’s constant, but rather the detuning from the frequency that is resonant in the absence of gravity.

It has been claimed that quasistatic granular materials, as well as nanoscale materials, exhibit departures from elasticity even at small loadings. It is demonstrated, using 2D and 3D models with interparticle harmonic interactions, that such departures are expected at small scales [below $\mathcal{O}(100)$ particle diameters], at which continuum elasticity is invalid, and vanish at large scales. The models exhibit force chains on small scales, and force and stress distributions which agree with experimental findings. Effects of anisotropy, disorder, and boundary conditions are discussed as well.

Using a fiber-based four-channel correlation scheme to investigate spatial and temporal correlations, we show that observations of period-doubling phenomena in single bubble sonoluminescence are primarily a result of spontaneously breaking the spherical symmetry in the bubble collapse and, at most, may show up as secondary effects in the flash-to-flash spatially integrated light output.

We exploit the approximate (broken) symmetries of time translation, time reversal, and Hamiltonian structure to obtain general scaling laws governing the process of pattern formation in weakly damped Faraday waves. Using explicit parameter symmetries we determine, for the case of two-frequency forcing, how the strength of observed three-wave interactions depends on the frequency ratio and on the relative phase of the two driving terms. These symmetry-based predictions are verified for numerically calculated coefficients, and help explain the results of recent experiments.

The role of forcing on the dynamics of a vertically shaken granular monolayer is investigated. Using a flat plate, surprising negative velocity correlations are measured. A mechanism for this anticorrelation is proposed with support from both experimental results and molecular dynamics simulations. Using a rough plate, velocity correlations are positive, and the velocity distribution evolves from a Gaussian at very low densities to a broader distribution at high densities. These results are interpreted as a balance between stochastic forcing, interparticle collisions, and friction with the plate.

We show experimentally that the two-component multimode spatial optical vector soliton, i.e., a two-hump self-guided laser beam, exhibits in Kerr media a sharp space-inversion symmetry-breaking instability. The experiment is performed in a ${\mathrm{C}\mathrm{S}}_2$ planar waveguide using the orthogonal circular polarization states of light as the two components of the vector soliton.

Feshbach’s projector technique is employed to quantize the electromagnetic field in optical resonators with an arbitrary number of escape channels. We find spectrally overlapping resonator modes coupled due to the damping and noise inflicted by the external radiation field. For wave chaotic resonators the mode dynamics is determined by a non-Hermitean random matrix. Upon including an amplifying medium, our dynamics of open-resonator modes may serve as a starting point for a quantum theory of random lasing.

We present a new theoretical approach aimed to describe the dynamical properties of avalanches. Starting from simple microscopic considerations, we propose an analytical derivation accounting for the avalanche growth as a function of time. The solution resembles very closely recent experimental observations. We show in particular that the two observed regimes of growth proceed from a singularity in the rear front velocity as a function of the slope.

We consider shell models that display an inverse energy cascade similar to two-dimensional turbulence (together with a direct cascade of an enstrophylike invariant). Previous attempts to construct such models ended negatively, stating that shell models give rise to a “quasiequilibrium” situation with equipartition of the energy among the shells. We show analytically that the quasiequilibrium state predicts its own disappearance upon changing the model parameters in favor of the establishment of an inverse cascade regime with Kolmogorov scaling. The latter regime is found where predicted, offering a useful model to study inverse cascades.

Control of spatio-temporal chaos by the time-delay autosynchronization method is improved by several orders of magnitude. Unstable time periodic patterns are efficiently stabilized if one employs filters and couplings which originate from the Floquet eigenvalue problem of the unstable orbit. We illustrate our scheme by an application to a globally coupled reaction-diffusion model which describes charge transport in semiconductor devices.

Recent molecular dynamics simulations of water transport through the interior channel of a carbon nanotube in contact with an aqueous reservoir showed that conduction occurred in bursts with collective water motion. A continuous-time random-walk model is used to describe concerted transport through channels densely filled with molecules in a single-file arrangement, as also found in zeolites, as well as ion channels and aquaporins in biological membranes. Theoretical predictions for different collective properties of the single-file transport agree with the simulation results.

Strong resonant transmission of microwave radiation through a very narrow (much less than the radiation wavelength) metallic slit is recorded. The results show that a set of resonant self-coupled surface plasmons are excited within the small gap, giving a Fabry-Pérot-like behavior in accord with analytical results published earlier [Y. Takakura, Phys. Rev. Lett. 86, 5601 (2001)]. The metallic slit, formed by two thick metal plates spaced apart by tens of microns, is inserted in a wavelength-sized aperture. On resonance the transmissivity through the metal slit is more than 2 orders of magnitude greater than the radiation impinging on the slit area.