A Hamilton-Jacobi formulation of the Lyapunov spectrum and Kolmogorov-Sinai (KS) entropy is developed. It is numerically efficient and reveals a close relation between the KS invariant and the classical action. This formulation is extended to the quantum domain using the Madelung-Bohm orbits associated with the Schroedinger equation. The resulting quantum KS invariant for a given orbit equals the mean decay rate of the probability density along the orbit, while its ensemble average measures the mean growth rate of configuration-space information for the quantum system.

We report the failure of the semiclassical eigenfunction hypothesis if regular classical transport coexists with chaotic dynamics. All eigenstates, instead of being restricted to either a regular island or the chaotic sea, ignore these classical phase-space structures. We argue that this is true even in the semiclassical limit for extended systems with transporting regular islands such as the standard map with accelerator modes.

A mechanism responsible for the directed transport of symmetrically coupled lattices in a symmetric periodic potential is proposed. Under the action of an external wave that breaks the spatiotemporal symmetry and introduces inhomogeneities of the lattice, a net unidirectional current can be observed, originating from a collaboration of the lattice (periodic potential and mutual interactions) and the wave (amplitude, frequency, and phase shifts). Mode-locking induced resonant steps are observed and predicted. The directed transport can be optimized and furthermore controlled by suitably adjusting the parameters of the system.

We study the long-time evolution of deep-water ocean surface waves in order to better understand the behavior of the nonlinear interaction processes that need to be accurately predicted in numerical models of wind-generated ocean surface waves. Of particular interest are those nonlinear interactions which are predicted by weak turbulence theory to result in a wave energy spectrum of the form of $|\mathbf{k}{|}^{-2.5}$. We numerically implement the primitive Euler equations for surface waves and demonstrate agreement between weak turbulence theory and the numerical results.

Velocity differences in the direct enstrophy cascade of two-dimensional turbulence are correlated with the underlying flow topology. The statistics of the transverse and longitudinal velocity differences are found to be governed by different structures. The wings of the transverse distribution are dominated by strong vortex centers, whereas the tails of the longitudinal differences are dominated by saddles. Viewed in the framework of earlier theoretical work, this result suggests that the transfer of enstrophy to smaller scales is accomplished in regions of the flow dominated by saddles.

It is shown, both theoretically and experimentally, that during laser pulse filamentation in air an intense ultrashort third-harmonic pulse is generated forming a two-colored filament. The third-harmonic pulse maintains both its peak intensity and energy over distances much longer than the characteristic coherence length. We argue that this is due to a nonlinear phase-locking mechanism between the two pulses in the filament and is independent of the initial material wave-vector mismatch. A rich spatiotemporal propagation dynamics of the third-harmonic pulse is predicted. Potential applications of this phenomenon to other parametric processes are discussed.

We formulate the theory describing the evolution and interactions between optical spatial solitons that propagate in opposite directions. We show that coherent collisions between counterpropagating solitons give rise to a new focusing mechanism resulting from the interference between the beams, and that interactions between such solitons are insensitive to the relative phase between the beams.

A nonlinear chain driven by one end may propagate energy in the forbidden band gap by means of nonlinear modes. For harmonic driving at a given frequency, the process occurs at a threshold amplitude by sudden large energy flow that we call nonlinear supratransmission. The bifurcation of energy transmission is demonstrated numerically and experimentally on the chain of coupled pendula (sine-Gordon and nonlinear Klein-Gordon equations) and sustained by an extremely simple theory.

Temperature measurements have been performed in the vertical access pit of an underground quarry. During autumn, air avalanches induce an initial thermal feedback and a stationary mixing state characterized by spatially coherent broad-band fluctuations with a standard deviation of about $0.2°\mathrm{C}$, linearly increasing with the inside-minus-outside temperature difference. Phase changes of water are shown to contribute to the onset condition, the feedback, and the stationary mixing state. This experiment may give insight on turbulent thermal and compositional convection with nonadiabatic boundaries.

We establish the existence of a duality transformation for generic models of interacting fermions with two-body interactions. The eigenstates at weak and strong interaction $U$ possess similar statistical properties when expressed in the $U=0$ and $U=\infty$ eigenstates bases, respectively. This implies the existence of a duality point $U_d$ where the eigenstates have the same spreading in both bases. $U_d$ is surrounded by an interval of finite width which is characterized by a non-Lorentzian spreading of the strength function in both bases. Scaling arguments predict the survival of this intermediate regime as the number of particles is increased.

The proposed universality of small scale turbulence is investigated for a set of measurements in a cryogenic free jet with a variation of the Reynolds number (Re) from $8500$ to ${10}^6$ ($\max R_{\lambda }\approx 1200$). The traditional analysis of the statistics of velocity increments by means of structure functions or probability density functions is replaced by a new method which is based on the theory of Markov processes. It gives access to a more complete characterization by means of joint probabilities of finding velocity increments at several scales. Based on this more comprehensive method, our results are very far from a possible universal state, even for $R_{\lambda }$ above 1000.

In recent years, time-reversal (TR) mirrors have been developed that create TR waves for ultrasonic transient fields propagating through complex media. A TR wave back propagates and refocuses exactly at its initial source. However, because of diffraction, even if the source is pointlike the wave refocuses on a spot size that cannot be smaller than half a wavelength. Here, by using a TR interpretation of this limit, we show that this latter limitation can be overcome if the source is replaced by its TR image. This new device acts as an acoustic sink that absorbs the TR wave. Here we report the first experimental result obtained with an acoustic sink where a focal spot size of less than 1/14th of one wavelength is recorded.

The Kolmogorov-Batchelor-Kraichnan (KBK) theory of two-dimensional turbulence is generalized for turbulence on the surface of a rotating sphere. The energy spectrum develops considerable anisotropy; a steep $-5$ slope emerges in the zonal direction, while in all others the classical KBK scaling prevails. This flow regime in robust steady state is reproduced in simulations with linear drag. The conditions favorable for this regime may be common for giant planets’ atmospheric circulations; the same steep spectra are found in their observed zonal velocity profiles and utilized to explain their basic characteristics.

In Newtonian and relativistic hydrodynamics the Riemann problem determines the evolution of a fluid which is initially characterized by two states having different rest-mass density, pressure, and velocity. When the fluid is allowed to relax, one of three possible wave patterns is produced, corresponding to the propagation in opposite directions of two nonlinear hydrodynamical waves. New effects emerge in a relativistic Riemann problem when velocities tangential to the initial discontinuity are present. A smooth transition from one wave pattern to another can be produced by varying the initial tangential velocities while maintaining the initial states unmodified. These special relativistic effects are produced by the Lorentz factors and do not have a Newtonian counterpart.

We study sandpile models with stochastic toppling rules and having sticky grains so that with a nonzero probability no toppling occurs, even if the local height of pile exceeds the threshold value. Dissipation is introduced by adding a small probability of particle loss at each toppling. Generically for the models with a preferred direction, the avalanche exponents are those of critical directed percolation clusters. For undirected models, avalanche exponents are those of directed percolation clusters in one higher dimension.

Single-axis acoustic levitation of the heaviest solid (iridium, $\rho =22.6\mathrm{g}\mathrm{c}{\mathrm{m}}^{\mathrm{-}\mathrm{3}}$) and liquid (mercury, $\rho =13.6\mathrm{g}\mathrm{c}{\mathrm{m}}^{\mathrm{-}\mathrm{3}}$ on the Earth is achieved by greatly enhancing both the levitation force and stability through optimizing the geometric parameters of the levitator. The acoustically levitated Pb-Sn eutectic alloy melt ($\rho =8.5\mathrm{g}\mathrm{c}{\mathrm{m}}^{\mathrm{-}\mathrm{3}}$) is highly undercooled by up to 38 K, which results in a microstructural transition of “lamellae—broken lamellae—dendrites.” The drastic enhancement of levitation capability indicates a broader application range of single-axis acoustic levitation.

We have repeated the experiment of Taleyarkhan et al. [Science 295, 1868 (2002)] in an attempt to detect the emission of neutrons from $d\mathrm{\text{−}}d$ fusion during bubble collapse in deuterated acetone. Using the same cavitation apparatus, a more sophisticated data acquisition system, and a larger scintillator detector, we find no evidence for 2.5-MeV neutron emission correlated with sonoluminescence form collapsing bubbles. Any neutron emission that might occur is at least 4 orders of magnitude too small to explain the tritium production reported in Taleyarkhan et al. as being due to $d\mathrm{\text{−}}d$ fusion. We show that proper allowance for random coincidence rates in such experiments requires the simultaneous measurement of the count rates in the individual detectors.

We have studied spontaneous imbibition fronts generated by capillary rise between two roughened glass plates, the separation $d$ of which varied between 10 and $50\mu \mathrm{m}$. Perfect agreement with Washburn’s law was obtained. We have determined the roughness exponent $\chi$ of the fronts, and found $\chi =0.81\pm 0.01$ for small length scales. Above a certain crossover length $\xi$, it reached $\chi =0.58\pm 0.04$, as predicted by the quenched noise Kardar-Parisi-Zhang equation. The crossover length is found to scale with the plate separation as $\sqrt{d}$, as predicted by recent models which properly include nonlocal dynamics effects on the front. We believe this to be the first clear identification of crossover from nonlocal to local dynamics.

Poiseuille flow between parallel plates alters the shapes and velocities of chemical reaction fronts. In the narrow-gap limit, the cubic reaction-diffusion-advection equation predicts a front-velocity correction equal to the gap-averaged fluid velocity $ϵ$. In the singular wide-gap limit, the correction equals the midgap fluid velocity $3ϵ/2$ when the flow is in the direction of propagation of the reaction front, and equals zero for adverse flow of any amplitude for which the front has a midgap cusp. Stationary fronts are possible only for adverse flow and finite gaps. Experiments are suggested.

Small quantities of a long chain molecule or polymer affect two-dimensional turbulence in unexpected ways. Their presence inhibits the transfers of energy to large scales causing their suppression in the energy density spectrum. This also leads to the change of the spectral properties of a passive scalar which turns out to be highly sensitive to the presence of energy transfers.