The existence of a novel inwards propagating wave motion is demonstrated in a limit-cycle medium both for the FitzHugh-Nagumo and for modified Chernyak-Starobin-Cohen reaction-diffusion systems. The waves (pulses) are seen to be moving “backwards,” that is, towards the point where the triggering pulse was initiated, instead of the regular propagation away from the origin. The feasibility of the phenomenon and some of its features are analyzed.

We analyze the existence and stability of nonlinear localized waves in a periodic medium described by the Kronig-Penney model with a nonlinear defect. We demonstrate the existence of a novel type of stable nonlinear band-gap localized state, and also reveal a generic physical mechanism of the oscillatory wave instabilities associated with the band-gap resonances.

The Bethe ansatz method and an iterative procedure based on detailed balance are used to obtain exact results for an asymmetric avalanche process on a ring. The average velocity of particle flow, $v$, is derived as a function of the toppling probabilities and the density of particles, $\rho$. As $\rho$ increases, the system shows a transition from intermittent to continuous flow, and $v$ diverges at a critical point ${\rho }_c$ with exponent $\alpha$. The exact phase diagram of the transition is obtained and $\alpha$ is found to depend on the toppling rules.

We utilize two-dimensional discrete element computer simulations to investigate the equilibrium position of an impurity in a vibrofluidized bed of otherwise homogeneous particles. The steady state equilibrium height of the impurity increases with increasing vibration velocity amplitude and decreases with the impurity to the surrounding particle density ratio. A simple model whereby the impurity weight is balanced by a “buoyant” force due to the surrounding particle impacts makes a good prediction of the impurity position.

We present detailed observations of the quantum delta-kicked rotor in the vicinity of a quantum resonance. Our experiment consists of an ensemble of cold cesium atoms subject to a pulsed off-resonant standing wave of light. We measure the mean energy and show clearly that at the quantum resonance it is a local maximum. We also examine the effect of noise on the system and find that the greatest sensitivity to this occurs at the resonances. This makes these regions ideal for examining quantum-classical correspondence. A picture based on diffraction is developed which allows the experiments to be readily understood.

When solving heat-conduction problems with periodic temperature perturbations, the thermal conductivity is assumed to remain frequency independent. We, however, show by using the molecular dynamics technique and the fluctuation-dissipation theorem a decrease of the effective thermal conductivity of 2 orders of magnitude when the excitation frequency approaches or exceeds the reverse of the phonon mean relaxation time. Most of the dielectric and semiconductor materials have to be considered as strongly insulating in those conditions. The comparison between molecular-dynamics simulations performed in Si crystals and theoretical predictions reveals a clear agreement.

We study the focusing of noncircular shock waves in a perfect gas. We construct an explicit self-similar solution by combining three convergent plane waves with regular shock reflections between them. We then show, with a numerical Riemann solver, that there are initial conditions with smooth shocks whose intermediate asymptotic stage is described by the exact solution. Unlike the focusing of circular shocks, our self-similar shocks have bounded energy density.

We measure the Kerr-nonlinear index of refraction of a three-level $\Lambda$-type atomic system inside an optical ring cavity. The Kerr nonlinearity is modified and greatly enhanced near atomic resonant conditions for both probe and coupling beams. The Kerr nonlinear coefficient $n_2$ changes sign when the coupling beam frequency detuning switches sign, which can lead to interesting applications in optical devices such as all-optical switches.

We consider the collective dynamics in an ensemble of globally coupled chaotic maps. The transition to the coherent state with a macroscopic mean field is analyzed in the framework of the linear response theory. The linear response function for the chaotic system is obtained using the perturbation approach to the Frobenius-Perron operator. The transition point is defined from this function by virtue of the self-excitation condition for the feedback loop. Analytical results for the coupled Bernoulli maps are confirmed by the numerics.

Dynamical tunneling between symmetry related invariant tori is studied in the near-integrable regime. Using the kicked Harper model as an illustration, we show that the exponential decay of the wave functions in the classically forbidden region is modified due to coupling processes that are mediated by classical resonances. This mechanism leads to a substantial deviation of the splitting between quasidegenerate eigenvalues from the purely exponential decrease with $1/ħ$ obtained for the integrable system. A simple semiclassical framework, which takes into account the effect of the resonance substructure on the invariant tori, allows one to quantitatively reproduce the behavior of the eigenvalue splittings.

We report the scaling properties of temperature in turbulent convection in water. In the central region of the convection cell, we find that the peak frequency of the temperature dissipation spectra may be identified as the “Bolgiano frequency,” with respect to which the temperature power spectra are universal functions; and that the usual inertial range is taken up entirely by the buoyancy subrange, so that a “high frequency” scaling subrange emerges only through an extended-self-similarity-type analysis. Moreover, the buoyancy subrange assumes the value of $2/5$ predicted for the Bolgiano-Obukhov scaling only in the central region of the cell; in the mixing zone the exponent for the high frequency scaling exponent has a value of $2/3$.

We report direct measurements of hydrodynamic drainage forces, which show clear evidence of boundary slip in a Newtonian liquid. The degree of boundary slip is found to be a function of the liquid viscosity and the shear rate, as characterized by the slip length, and is up to $\sim 20\mathrm{nm}$. This has implications for confined biological systems, the permeability of microporous media, and for the lubrication of nanomachines, and will be important in the microcontrol of liquid flow. We also show that current theories of slip do not adequately describe the experimental data.

Because of the small momentum of photons, very intense fields are generally required to bend a liquid interface with the optical radiation pressure. We explore this issue in a near-critical phase-separated liquid mixture to vary continuously the meniscus softness by tuning the temperature. Low power continuous laser waves become sufficient to induce huge stationary bulges. Using the beam size to build an “optical” Bond number, $\mathrm{Bo}$, we investigate the crossover from low to large $\mathrm{Bo}$. The whole set of data collapses onto a single master curve which illustrates the universality of the phenomenon.

Many studies have shown that nonintegrable systems with modulational instabilities constrained by more than one conservation law exhibit universal long time behavior involving large coherent structures in a sea of small fluctuations. We show how this behavior can be explained in detail by simple thermodynamic arguments.

Under intense optical excitation, the polarizability of transparent optical materials has a significant third order, nonlinear contribution. This manifests itself in a wide variety of effects, which, under certain conditions, are collectively referred to as white light continuum generation. We report on a new approach that isolates, for the first time, some of these effects.

We study the influence of external noise on the relaxation to an invariant probability measure for two types of nonhyperbolic chaotic attractors, a spiral (or coherent) and a noncoherent one. We find that for the coherent attractor the rate of mixing changes under the influence of noise, although the largest Lyapunov exponent remains almost unchanged. A mechanism of the noise influence on mixing is presented which is associated with the dynamics of the instantaneous phase of chaotic trajectories. This also explains why the noncoherent regime is robust against the presence of external noise.

This Letter presents a wavelet technique for extracting coherent vortices from three-dimensional turbulent flows, which is applied to a homogeneous isotropic turbulent flow at resolution ${N=256\mathrm{}}^3$. The coherent flow is reconstructed from only $3\%N$ wavelet coefficients that retain the vortex tubes, and $98.9\%$ of the energy with the same $k^{-5/3\mathrm{}}$ spectrum as the total flow. In contrast, the remaining $97\%N$ wavelet coefficients correspond to the incoherent flow which is structureless, decorrelated, and whose effect can therefore be modeled statistically.

The influence of chemical reactions on the hydrodynamical fingering instability is analyzed for miscible systems in porous media. Using a realistic reaction scheme, it is shown that the stability of chemical fronts towards density fingering crucially depends on the width and the speed of the front which are functions of chemical parameters. The major difference between the pure and chemically driven fingering is that, in the presence of chemical reactions, the dispersion curves do not vary in time which has important practical experimental consequences. Good agreement with recent experimental data is found.

An analytic model of the ultrasonic modulation of multiply scattered coherent light in scattering media is developed based on two mechanisms: the ultrasonic modulation of the index of refraction and the ultrasonic modulation of the displacements of Rayleigh scatterers. In water solutions, for example, the first mechanism is slightly less important than the second mechanism when the scattering mean free path is less than a critical fraction (0.0890) of the acoustic wavelength, and it becomes increasingly more important beyond this point. This model agrees well with an independent Monte Carlo model.

We observed simultaneous focusing in both space and time for light pulses propagating in a planar waveguide. In particular, 60 fs pulses with a width of $170\mu \mathrm{m}$ were injected into a planar glass waveguide in the anomalous dispersion regime. Output pulses as short as 30 fs and as narrow as $20\mu \mathrm{m}$ were measured. The results suggest that multiphoton absorption and intrapulse stimulated Raman scattering arrest the spatiotemporal contraction. The results were compared to the pulse evolution in zero and normal dispersion regimes and were shown to be significantly different. All of the experimental results were reproduced by a numerical model.