We present experimental evidence of the striking influence of small additions of high molecular weight polymers on stability and pattern selection in Couette-Taylor flow. Two novel oscillatory flow patterns were observed. One of them is essentially due to the fluid elasticity. The other results from inertial instability modified by the elasticity.

We present the first direct measurements of the scattered intensity from a nonequilibrium, temperature stressed liquid mixture (heating from above). The data have been obtained with an unconventional very low angle light scattering instrument. While at larger q the intensity diverges with a $q^{-4\mathrm{}}$ power law, we show for the first time that at smaller q the divergence is frustrated by gravity-induced effects. In spite of this, a staggering increase of more than 5 orders of magnitude above equilibrium scattering is reported.

A study is made of the scaling of the positive part (PP) and the negative part (NP) of velocity increments in turbulent pipe flow and in simulated homogeneous turbulence in a box. For moment orders above unity, the moments of NP are larger than those of PP for all separation distances, and the scaling exponents for PP are larger than those for NP. For moment orders below unity, the absolute value of the velocity increment and of NP, as well as PP, possess scaling exponents which vary linearly with the moment order q, though apparently greater than $q/3\mathrm{}$.

Using numerical simulations we show that the response to weak perturbations of a variable of Hamiltonian chaotic systems depends on the number of degrees of freedom: When this is small ( $\approx 2$) the response is not linear, in agreement with the well known objections to the Kubo linear response theory, while, for a larger number of degrees of freedom, the response becomes linear. This is due to the fact that increasing the number of degrees of freedom the shape of the distribution function, projected onto the subspace of the variable of interest, becomes fairly “regular.”

We discuss the effects of finite perturbations in fully developed turbulence by introducing a measure of the chaoticity degree associated to a given scale of the velocity field. This allows one to determine the predictability time for noninfinitesimal perturbations, generalizing the usual concept of maximum Lyapunov exponent. We also determine the scaling law for our indicator in the framework of the multifractal approach. We find that the scaling exponent is not sensitive to intermittency corrections, but is an invariant of the multifractal models. A numerical test of the results is performed in the shell model for the turbulent energy cascade.

Direct measurements of the velocity boundary layer in turbulent convection have been carried out using a novel light scattering technique. The experiment reveals that the velocity profile $v_h\left(z\right)$ as a function of the distance $z$ from the lower surface of a convection cell has an invariant form $v_h\left(z\right){=v}_{m}f(z/{\delta }_v)$ over varying Rayleigh numbers (Ra). It is found that the scaling velocity $v_m$, the viscous boundary layer thickness ${\delta }_v$, and the shear rate $\gamma$ all obey power laws of Ra, i.e., $v_m\sim {\mathrm{Ra}}^{0.5},{\delta }_v\sim {\mathrm{Ra}}^{-0.16\mathrm{}}$, and $\gamma \sim {\mathrm{Ra}}^{0.66}$.

The revised Enskog theory for a classical system of hard spheres provides a unified description of both fluid and crystal states over a wide range of densities and wavelengths. However, practical applications of this theory have been limited to fluid states near equilibrium. We propose here a simpler kinetic model that retains its essential physical and mathematical features, but which admits practical application to complex dynamical phenomena. This is illustrated by a calculation of the rheological properties of the fluid phase under shear flow. Good agreement is obtained in comparison with corresponding Monte Carlo simulation results.

Millimeter-radius liquid shells are acoustically levitated in an ultrasonic field. Capillary waves are observed on the shells. At low energies (minimal acoustic amplitude, thick shell) a resonance is observed between the symmetric and antisymmetric thin film oscillation modes. At high energies (high acoustic pressure, thin shell) the shell becomes fully covered with high-amplitude waves. Temporal spectra of scattered light from the shell in this regime exhibit a power-law decay indicative of turbulence.

The energy of, and the force exerted by, an electromagnetic field are only known if the medium is transparent, linear, and stationary. We present expressions that are valid in the presence of both dispersion and dissipation, for a moving system with nonlinear constitutive relations.

The maximal conserved phase gradient is introduced as an order parameter to characterize the transition from phase to defect turbulence in the complex Ginzburg-Landau equation. It has a finite value in the phase-turbulent regime and decreases to zero when the transition to defect turbulence is approached. Solutions with a nonzero phase gradient are studied via a Lyapunov analysis. The degree of “chaoticity” decreases for increasing values of the phase gradient and finally leads to stable traveling wave solutions. A modified Kuramoto-Sivashinsky equation for the phase dynamics is able to reproduce the main features of the stable waves and to explain their origin.

A recently developed approach to the quantum dynamical entropy for classical and infinite quantum dynamical systems involving von Neumann entropy for multitime correlation matrices is adapted to finite quantum systems and implemented numerically for a periodically kicked top. Significant quantitative differences between chaotic and regular regime are observed.

On working beyond the slowly varying envelope approximation, the instability of superfluorescent decay is investigated for the case in which the sample size is greater than or comparable to the resonant wavelength. The instability is associated with coupling between counterpropagating waves and can inhibit emission in the direction of the pump pulse. In particular, it is shown that tiny changes of the sample length can cause the forward emission to be switched off, suggesting that the optical analog of a directing antenna may be experimentally accessible.

We have experimentally determined the static structure factor $S\left(k\right)$ in low density argon gas for $1.0<k<\mathrm{}3.5{\mathrm{nm}}^{-1\mathrm{}}$, by means of the small-angle neutron scattering diffractometer PAXE at Laboratoire Léon Brillouin in Saclay. The experiment has been performed at three number densities between $1.51\times {10}^{27}$ and $2.30\times {10}^{27}{\mathrm{m}}^{-3\mathrm{}}$ along the $T=138.75\mathrm{K}$ isotherm. From the data the small-k dependence of the Fourier transform $c\left(k\right)$ of the direct correlation function $c\left(r\right)$ has been derived and the existence of the $|k{|}^3$ term in the behavior of $c\left(k\right)$ experimentally demonstrated. The experiment has allowed the first direct measurement of the coefficient $C_6$ of the London dispersion interaction in the pair potential of argon.

Current tests for nonlinearity compare a time series to the null hypothesis of a Gaussian linear stochastic process. For this restricted null assumption, random surrogates can be constructed which are constrained by the linear properties of the data. We propose a more general null hypothesis allowing for nonlinear rescalings of a Gaussian linear process. We show that such rescalings cannot be accounted for by a simple amplitude adjustment of the surrogates which leads to spurious detection of nonlinearity. An iterative algorithm is proposed to make appropriate surrogates which have the same autocorrelations as the data and the same probability distribution.

Multiple light scattering from thermal fluctuations is studied in single-domain nematic liquid crystals. These systems are uniaxial so that diffusion of light may be anticipated to be anisotropic and polarization to persist in the diffuse regime, in sharp contrast with what is known for light diffusion in isotropic media. Our study enables us to do the first quantitative predictions of light diffusion as a function of the scalar order parameter.

A magnetic fluid drop lying on a horizontal solid surface subjected to a vertical magnetic field $H_0$ peaks with a cone shape above a threshold value $H_c$. If $H_0$ is tilted, i.e., not parallel to the gravitational field, the shape becomes asymmetric. Using a tilted alternating magnetic field we observed the motion of the drop. We have measured this drift velocity, and we propose a simple two-level model to explain this new motion. Finally, we present another experiment with the same device concerning the free surface of a magnetic fluid: the so-called drifting instability.

The notion of geometrical resonance is introduced as a natural, fully nonlinear, generalization of the usual or frequency resonance. The geometrical resonance is shown to provide the mechanism underlying the so-called nonfeedback control of chaos by means of an almost adiabatic invariant associated with each geometrical resonance solution.

We introduce an approximation scheme for determining the evolution of spatially averaged quantities in large classes of extensively chaotic dynamical systems. The case of lattices of diffusively coupled logistic maps is presented. Results in two space dimensions show that the scheme succeeds in reproducing the nontrivial collective behavior observed in this system.

We report the first observation of self-trapping of a spatially incoherent optical beam in a nonlinear medium. Self-trapping occurs in both transverse dimensions, when diffraction is exactly balanced by photorefractive self-focusing.

We introduce a new procedure for the analysis of a chaotic time series with a “Lagrangian” variable of the system's trajectory. Using the density of points that the systems encounters as it evolves, we can extract all dynamically connected frequencies in a continuous time dynamical system. We apply this technique to simulated and experimental time series.