Chaotic experimental systems are often investigated using delay coordinates. Estimated values of the correlation dimension in delay coordinate space typically increase with the number of delays and eventually reach a plateau (on which the dimension estimate is relatively constant) whose value is commonly taken as an estimate of the correlation dimension ${\mathit{D}}_2$ of the underlying chaotic attractor. We report a rigorous result which implies that, for long enough data sets, the plateau begins when the number of delay coordinates first exceeds ${\mathit{D}}_2$. Numerical experiments are presented. We also discuss how lack of sufficient data can produce results that seem to be inconsistent with the theoretical prediction.

We demonstrate the existence of an interference contribution to the average magnetoconductance, G¯(B), of ballistic cavities and use it to test the semiclassical theory of quantum billiards. G¯(B) is qualitatively different for chaotic and regular cavities (saturation versus linear increase) which is explained semiclassically by the differing classical distribution of areas. The magnitude of G¯(B) is poorly explained by the semiclassical theory of coherent backscattering (elastic enhancement factor); interference between trajectories which are not exactly time reversed must be included.

The cubic complex Ginzburg-Landau equation is often used to model oscillatory media. In 1D it has a one-parameter family of moving ‘‘hole’’ solutions acting as sources for traveling waves (Nozaki and Bekki). We find that this family is destroyed by arbitrarily small generic perturbations leaving only the stationary phase-slip solutions. Its stability as well as the border of spatiotemporal chaos depend crucially on the sign of the perturbation. For ‘‘stabilizing’’ perturbations one also finds oscillations of the holes. The scenario can be modeled by the Van der Pol oscillator.

We report the first direct measurement of coherent backscattering of scalar acoustic waves by disordered scattering medium. In two and three dimensions an excellent agreement between experimental data and the predictions of simple diffusion theory is found. These measurements have been done for the time dependent and independent cases.

We present experimental results on Rayleigh-Bénard convection in ${\mathrm{SF}}_6$ near the gas-liquid critical point. We measured the critical temperature difference for the onset of convection, Δ${\mathit{T}}_0$, as a function of the reduced average temperature τ=(T¯-${\mathit{T}}_{\mathit{c}}$)/${\mathit{T}}_{\mathit{c}}$ and found Δ${\mathit{T}}_0$=525×${\mathrm{\tau }}^{1.89}$, which is close to the expected power law behavior. The strong temperature dependence of the physical properties is used to scan the Prandtl number in a wide range. A new, many ‘‘target’’ pattern state, initiated by a defect instability, was observed.

In Bénard-Marangoni convection in a square vessel, of small aspect ratio, a sequence of bifurcations is observed as control parameters are slightly changed. Some of the emerging patterns are stationary and others are oscillatory in nature. The stationary patterns break the symmetry and the oscillatory ones can be classified in three kinds. We show that this dynamics can be explained assuming that the system is close to a Takens Bogdanov bifurcation.

Vortical flows in shallow water interact with long surface waves by virtue of the nonlinear terms of the fluid equations. Analytical formulas are derived that quantify the spontaneous generation of such waves by unsteady vorticity as well as the scattering of surface waves by vorticity. In the first Born approximation the radiated surface elevation is linearly related to the Fourier transform of the vorticity. The ‘‘dislocated’’ wave fronts that are analogous to the Aharonov-Bohm effect are obtained as a special case.

The Kramers-Kronig (KK) dispersion relation has been proved to hold between independently measured spectra of the phase shift φ(ω) and the modulus ‖χ${\mathrm{̃}}^{\mathrm{}\left(3\right)\mathrm{}}$/(ω)‖ of third-order electric susceptibility χ${\mathrm{̃}}^{\mathrm{}\left(3\right)\mathrm{}}$ (=‖χ${\mathrm{̃}}^{\mathrm{}\left(3\right)\mathrm{}}$‖${\mathit{e}}^{\mathit{i}\mathrm{\phi }}$) for the third-order harmonic generation in silicon-based polymer, poly(dihexylsilane) (PDHS) films, providing a direct experimental substantiation of the reciprocal KK relations in the nonlinear optical solids. The reciprocal dispersion relations have been also found to hold for the real and imaginary parts of χ${\mathrm{̃}}^{\mathrm{}\left(3\right)\mathrm{}}$ in PDHS films.

We have investigated the rise of a single large glass bead through a vibrated cylindrical column of smaller particles and found that vibration-induced size separation in this geometry arises from convective processes rather than from local rearrangements as had been proposed previously. A convection cycle, rising in the middle and dropping in a thin stream along the walls of the cell, is responsible for all particle movement. Particles larger than the width of the thin downward convection zone are carried to the top of the column and then trapped, resulting in size segregation. For a variety of accelerations the position of the rising particle can be scaled onto a single curve.

We prove the existence (as ħ→0) of the singular continuous (‘‘Cantor-like’’) spectrum for the Fermi-Ulam model on a torus for a certain phase-space domain and an irrational (diophantine) ratio of the minimum distance between the walls to the oscillation amplitude of the moving wall. Varied scenario of the stabilizing and destabilizing spectral transitions are observed in the limit of vanishing Planck’s constant, and their relation with the qualitative changes in the quasienergy eigenstates is brought out.

A new method of using an additional laser for electron-beam conditioning in free-electron lasers and synchrotrons is proposed. Theoretical analysis and calculations are presented, showing that the axial energy spread of electrons due to their betatron motion in undulators can be dramatically reduced by interacting with a quasi-${\mathrm{TEM}}_{10}$ mode Gaussian optical beam. It is required that the electrons be pre-bunched over half an optical cycle in advance.

The first observation of coherent backscattering (CB) in an optically anisotropic, homogeneous (liquid crystal) medium with long-range dielectric tensor fluctuations is reported. The results are compared with previous CB experiments in heterogeneous, centrosymmetric, isotropic scattering media and with theoretical predictions for isotropic, noncentrosymmetric media. Fundamental differences and analogies between these cases are observed and explained. Other liquid crystal phases of potential interest in the localization of electromagnetic modes are introduced briefly.

In a Langmuir monolayer of NBD-stearic acid, long rods (∼1 mm long, ∼20 μm wide) of a two-dimensional solid phase are obtained at the liquid-solid phase transition. A rod bent in the plane of the water under the effect of a bending stress breaks after a clearly defined delay. This delay is a function of the strain applied to the rod and of the temperature. For large deformations, a second mode of breaking appears and coexists with the previous one: A fraction of the rods break instantaneously while other break after a delay.

The energy spectral density of axial velocity components in a rotating Couette-Taylor system was obtained using a Fourier transform of axial velocity distributions. As this configuration has well defined spatial periodicity, strong peaks appear on the spectrum corresponding to Taylor vortex flow and wavy vortex flow modes and their harmonics. A continuous background shows an exponential decay with wave number, which supports the results of the numerical simulations. A variation in the decay rate at reduced Reynolds number shows a maximum at ${\mathit{R}}^{\mathrm{*}}$≊22. At this Reynolds number, an energy exchange between the first and second harmonics was observed.

We report an experimental study of the onset of convection in ethanol/water mixtures confined in a circular cell of radial aspect ratio of 11.6. The initial bifurcation was to radial traveling waves; however, the linear state typically gave way to a nonlinear one in which convection alternately focused along one cell diameter and then another roughly perpendicular to the first. After a number of cycles, this state frequently contracted radially to a localized pulse of traveling-wave convection very similar to those observed in 1D geometries. The pulses we observed either decayed back to pure conduction or grew to fill or nearly fill the cell.

We study the effect of fluctuations in the vicinity of an Eckhaus instability. Fluctuations smear out the stability limit into a region in which fluctuations and nonlinearities dominate the decay of unstable states. We also find an effective stability boundary that depends on the intensity of fluctuations. A numerical solution of the stochastic Swift-Hohenberg equation in one dimension is used to test these predictions and to study pattern selection when the initial unstable state lies within the fluctuation dominated region. The nonlinear relaxation is shown to exhibit a scaling form.

The hydrodynamic Maxwell equations of continuous media, valid for large amplitudes and small frequencies, are derived. As any hydrodynamic theory, these equations are universal, nonlinear, and irreversible. Consequences for dielectric liquids, ferrofluids, superconductors, and nematic liquid crystals are briefly outlined.

We report an interesting phenomenon of wavelength doubling bifurcations in the model of coupled (logistic) map lattices. The temporal and spatial periods of the observed patterns undergo successive period doubling bifurcations with decreasing coupling strength. The universality constants α and δ appear to be the same as in the case of period doubling route to chaos in the uncoupled logistic map. The analysis of the stability matrix shows that period doubling bifurcation occurs when an eigenvalue whose eigenvector has a structure with doubled spatial period exceeds unity.

The first experimental observation of limit-cycle power oscillations in a short-pulse free-electron laser is presented. These are due to a nonlinear modulation of the optical micropulse shape and phase by the electrons, which leads to the formation of a train of subpulses. Experimentally, the oscillations have been found to depend on the slippage distance and on the desynchronism between optical pulses and electron bunches, comparing well with theoretical predictions.

Scaling behavior in turbulence is studied on the basis of its relation to the wrinkling, or fractalization, of the graph of the velocity field in 3+3 dimensions. We propose a novel mechanism for deviations from the Kolmogorov exponents, which is realized if the fine structure of turbulence tends locally towards two dimensionality. It is argued that some of the popular fractal and multifractal models of intermittency in turbulence are not consistent with fluid mechanics, and miss some essential physics.