We investigate the collapse of an axisymmetric cavity or bubble inside a fluid of small viscosity, like water. Any effects of the gas inside the cavity as well as of the fluid viscosity are neglected. Using a slender-body description, we compute the local scaling exponent $\alpha =d\ln h_0/d\ln t^{\prime }$ of the minimum radius $h_0$ of the cavity, where $t^{\prime }$ is the time from collapse. The exponent $\alpha$ very slowly approaches a universal value according to $\alpha =1/2+1/[4\sqrt{-\ln (t^{\prime })}]$. Thus, as observed in a number of recent experiments, the scaling can easily be interpreted as evidence of a single nontrivial scaling exponent. Our predictions are confirmed by numerical simulations.

The relative entropy between the joint probability distribution of backward and forward sequences is used to quantify time asymmetry (or irreversibility) for stationary time series. The parallel with the thermodynamic theory of nonequilibrium steady states allows us to link the degree of asymmetry in the time signal with the distance from equilibrium and the lack of detailed balance among its states. We study the statistics of time asymmetry in terms of the fluctuation theorem, showing that this type of relationship derives from simple general symmetries valid for any stationary time series.

We report white-light generation and intense linear scattering from magnetic dipoles established by the time-varying magnetic flux of an incident light field in a dielectric medium. Large magnetic response is very unexpected at optical frequencies, and should lead to the discovery of new magneto-optical phenomena and the realization of low-loss homogeneous optical media with negative refractive indices.

Torsional oscillations, temporal variations in the differential rotation in rotating systems, are a well-established phenomenon in the fluid regions of convective stars and planets. We show for the first time that nonlinear torsional oscillations can be generated and maintained by convective instabilities in rotating systems.

In turbulent Taylor-Couette flow, the injection of bubbles reduces the overall drag. On the other hand, rough walls enhance the overall drag. In this work, we inject bubbles into turbulent Taylor-Couette flow with rough walls (with a Reynolds number up to $4\times {10}^5$), finding an enhancement of the dimensionless drag as compared to the case without bubbles. The dimensional drag is unchanged. As in the rough-wall case no smooth boundary layers can develop, the results demonstrate that bubbly drag reduction is a pure boundary layer effect.

Spatial distributions of heavy particles suspended in an incompressible isotropic and homogeneous turbulent flow are investigated by means of high resolution direct numerical simulations. In the dissipative range, it is shown that particles form fractal clusters with properties independent of the Reynolds number. Clustering is there optimal when the particle response time is of the order of the Kolmogorov time scale ${\tau }_{\eta }$. In the inertial range, the particle distribution is no longer scale invariant. It is, however, shown that deviations from uniformity depend on a rescaled contraction rate, which is different from the local Stokes number given by dimensional analysis. Particle distribution is characterized by voids spanning all scales of the turbulent flow; their signature in the coarse-grained mass probability distribution is an algebraic behavior at small densities.

We show that surface electromagnetic waves (SEMWs) propagating along two-dimensional (2D) interfaces separating different metamaterials can behave analogously to 3D electromagnetic waves in either usual or left-handed media, depending on the permeabilities and/or permittivities of the two materials forming the interface. We derive the conditions when SEMWs carry energy opposite to the phase velocity. In analogy to three-dimensional (3D) left-handed media, we derive both an anomalous Cherenkov emission and a reversed Doppler effect. We also predict a negative refraction at the boundary between two different interfaces, which can be useful for perfect 2D lensing.

We characterize the spatiotemporal evolution of a photosensitive Belousov-Zhabotinsky medium that is made up of coupled oscillatory cells with randomly distributed frequencies. The medium evolves from an initial state of multiple wave sources to a synchronized state governed by a single wave source. The synchronization occurs via a competition between the sources, which arises when the oscillators are not identical but have slightly different natural frequencies. The evolution of each cell is monitored to demonstrate frequency and phase synchronization of the inhomogeneous cellular medium, and a simple kinematic description for the advance of the phase-diffusion wave is presented.

Novel soliton solutions for the nonautonomous nonlinear Schrödinger equation models with linear and harmonic oscillator potentials substantially extend the concept of classical solitons and generalize it to the plethora of nonautonomous solitons that interact elastically and generally move with varying amplitudes, speeds, and spectra adapted both to the external potentials and to the dispersion and nonlinearity variations. The nonautonomous soliton concept can be applied to different physical systems, from hydrodynamics and plasma physics to nonlinear optics and matter waves, and offer many opportunities for further scientific studies.

Using reciprocity, we investigate the breaking of time-reversal ($T$) symmetry due to a ferrite embedded in a flat microwave billiard. Transmission spectra of isolated single resonances are not sensitive to $T$ violation, whereas those of pairs of nearly degenerate resonances do depend on the direction of time. For their theoretical description a scattering matrix model from nuclear physics is used. The $T$-violating matrix elements of the effective Hamiltonian for the microwave billiard with the embedded ferrite are determined experimentally as functions of the magnetization of the ferrite.

We introduce a new class of excitable systems with two-dimensional fast dynamics that includes inertia. A novel transition from excitability to relaxation oscillations is discovered where the usual Hopf bifurcation is followed by a cascade of period doubled and chaotic small excitable attractors and, as they grow, by a new type of canard explosion where a small chaotic background erratically but deterministically triggers excitable spikes. This scenario is also found in a model for a nonlinear Fabry-Perot cavity with one pendular mirror.

An experimental study of the morphological evolution of thermal plumes in turbulent thermal convection is presented. Individual sheetlike plumes are extracted and their area, circumference, and “heat content” are found to all exhibit log-normal distributions. As the sheetlike plumes move across the plate they collide and convolute into spiraling swirls. These swirls then spiral away from the plates to become mushroomlike plumes which are accompanied by strong vertical vorticity. The measured profiles of plume numbers and of vertical vorticity quantify the morphological transition of sheetlike plumes to mushroomlike ones and the mixing and merging or clustering of mushroomlike plumes. The fluctuating vorticity is found to have the same exponential distribution and scaling behavior as the fluctuating temperature.

We present experimental data of the frequency-resolved optical gating measurements of light pulses revealing interference features which correspond to sub-Planck structures in phase space. For superpositions of pulses, a small, sub-Fourier shift in the carrier frequency leads to a state orthogonal to the initial one, although in the representation of standard time-frequency distributions these states seem to have a nonvanishing overlap.

An experimental search for nuclear fusion inside imploding bubbles of degassed deuterated acetone at $0°\mathrm{C}$ driven by a 15 atm sound field and seeded with a neutron generator reveals an upper bound that is a factor of 10 000 less than the signal reported by Taleyarkhan et al. The strength of our upper bound is limited by the weakness of sonoluminescence, which we ascribe to the relatively high vapor pressure of acetone.

Liquid propane nanobridges were found through molecular dynamics simulations to exhibit in vacuum a symmetric break-up profile shaped as two cones joined in their apexes. With a surrounding gas of sufficiently high pressure, a long-thread profile develops with an asymmetric shape. The emergence of a long-thread profile, discussed previously for macroscopic fluid structures, originates from the curvature-dependent evaporation-condensation processes of the nanobridge in a surrounding gas. A modified stochastic hydrodynamic description captures the crossover between these universal break-up regimes.

Experimental results obtained over more than a century have shown that laminar flow in a circular pipe becomes naturally turbulent at a critical Reynolds number of $\mathrm{Re}\approx 2000$. In this Letter a theoretical explanation, based on the minimum energy of an axisymmetric deviation (from the developed pipe flow profile), is suggested for this critical value. It is shown that for $\mathrm{Re}>1840$ the minimum energy of the deviation, associated with the central part of the pipe, becomes a global minimum for triggering secondary instabilities. For $\mathrm{Re}<1840$ the global minimum energy deviation is located next to the pipe wall. Previous experimental observations support this explanation.

We describe a transition from fully synchronous periodic oscillations to partially synchronous quasiperiodic dynamics in ensembles of identical oscillators with all-to-all coupling that nonlinearly depends on the generalized order parameters. We present an analytically solvable model that predicts a regime where the mean field does not entrain individual oscillators, but has a frequency incommensurate to theirs. The self-organized onset of quasiperiodicity is illustrated with Landau-Stuart oscillators and a Josephson junction array with a nonlinear coupling.

Using Lie group theory and canonical transformations, we construct explicit solutions of nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities. We present the general theory, use it to show that localized nonlinearities can support bound states with an arbitrary number solitons, and discuss other applications of interest to the field of nonlinear matter waves.

The evolution of the distance $r(t)$ between a pair of passive tracer particles in rough compressible velocity fields is studied. The scaling behavior depends on the stickiness of the particles. Sticky particles start aggregating in moderately compressible flows, which can be realized on the free-slip surface of a turbulent fluid; nonsticky particles can aggregate only in less common strongly compressible flows (even then, the aggregation rate remains lower). Aggregation gives rise to an anomalous scaling law for the mean-square-distance growth rate, slower than Richardson’s law. These findings help understand the results of recent experiments.

We consider a superstatistical model for a Lagrangian tracer particle in a high-Reynolds-number turbulent flow. The analytical model predictions are in excellent agreement with recent experimental data for flow between counter-rotating disks. In particular, the predicted Lagrangian scaling exponents ${\zeta }_j$ agree well with the measured exponents reported in H. Xu et al. [Phys. Rev. Lett. 96, 114503 (2006)]. The model also correctly predicts the shape of acceleration probability densities, correlation functions, statistical dependencies between components, and explains the fact that enstrophy lags behind dissipation.