An impact oscillator is shown to exhibit complex dynamics. Its resonance response contains regions where, after an infinite cascade of period-doubling bifurcations, chaotic motion typical of a strange attractor is observed. The regions are bounded on both sides by subharmonic resonances. Quantitative agreements are obtained with the Feigenbaum scenario of chaos. This novel feature of a substantial marine technology program may be of general cross-disciplinary interest to mathematicians and physicists.

A new pulsing electrohydrodynamic instability has been noticed in a compensated cholesteric mixture, as a "host" in which a cumylphenol azo compound was introduced as a "guest." The liquid-crystal sample was placed in a steady dc electric field. Observations of the microstructural aspects and measurements of the transmitted light were simultaneously performed. Pulsing instabilities of 0.02-0.05 Hz were revealed. Upon an increase of the electric field under constant temperature the frequency of the instabilities increased.

We carry out a systematic adiabatic elimination of the atomic degrees of freedom from the quantum-mechanical master equation for the single-mode laser. We represent the reduced density operator of the field mode by various quasiprobabilities and construct the respective equations of motion. The generators of infinitesimal time translations are obtained as series in powers of two parameters, the smallness of which defines the adiabatic limit. Our "adiabatic" expansion treats that part of the atom-field interaction as a zeroth-order effect which describes the action of the field on the atoms, while the reaction of the atoms is treated perturbatively. The adiabatic equilibrium thus assigned to the atomic variables at all times is a conditional one, contingent on the current state of the field mode. As a result, saturation effects in the atoms are fully accounted for in low orders of our expansion. In second order, especially, we obtain a Fokker-Planck equation for the Wigner function of the field mode which is valid for arbitrary pump strengths below, near, and above threshold. We compare our results with those of previous theories.

The problem of calculating transition probabilities in two-level systems is studied in the limit where the detuning is large compared to the inverse duration of the interaction. Coupling potentials whose Fourier transforms $\tilde{V}\left(\omega \right)$ are of the form $f\left(\omega \right)e^{-\left(\right|b\omega \mathrm{}\left|\right)\mathrm{}}$ for large frequencies give rise to solutions which may be classified into families according to the form of $f\left(\omega \right)$. Within each family transition probabilities may be calculated from formulas that differ only in the numerical value of a scaling parameter. In cases where the coupling function has a pole in the complex time plane, the families are identified with the order of this singularity. In particular, for poles of first order, a connection with the Rosen-Zener solution can be made. The analysis is performed via high-order perturbation expansions which are shown to always converge for two-level systems driven by coupling potentials of finite pulse area.

A fully quantized many-particle theory of the standard free-electron laser in the small-signal, cold-beam regime is presented. The approach is based on an evaluation of the time-evolution operator in the interaction picture to first order in the quantum-mechanical recoil. For algebraic convenience we use the moving (Bambini-Renieri) frame, in which resonance occurs for zero electron momentum. Though we neglect space-charge effects, genuine many-particle contributions still show up, because the radiation emitted by one electron can be amplified by another electron. Our main results are gross features of the amplification, such as gain and spread, are virtually without many-particle effects. These effects are mainly important in the case of spontaneous emission. For a sufficiently high current, the buildup of the laser field from vacuum is enhanced by amplified spontaneous emission. Incoherence of the spontaneous radiation from several electrons induces deviations from Poisson statistics even if gain is neglected. For a dilute electron beam, spontaneous radiation is slightly antibunched for negative gain. Squeezing is obtained for positive gain independent of the number of electrons. However, owing to some idealizations used in the model, it is uncertain whether this applies to a physically realizable situation.

The propagation of a Gaussian electromagnetic (optical) pulse with center frequency $\overline{\omega }$ (laser) through a spatially dispersive exciton-polariton medium is investigated by a combination of analytical and numerical methods. The analysis used extends previous work by Garrett and McCumber to the multiwave coupled exciton-polariton case. With the assumption of normal incidence on a semi-infinite medium, laser frequencies very close to exciton resonance and far from resonance are studied. Numerical results are obtained for power spectrum $P(z,\omega )$ and amplitude profile $f(z,t)\mathrm{}$ for parameters suitable to $\mathrm{CdS} 1S A$ exciton (a fairly typical semiconductor). For pulses with $\Gamma \tau \gg 1$ or $\Gamma \tau \sim 1$ the pulse remains essentially Gaussian, and its peak propagates with velocity close to the classical group velocity $v_{\mathrm{gj}}=\left(\frac{d{\omega }_j}{d{k}_r}\right)$, where $j$ is the polariton branch index and $k_r$ is the real part of the propagation wave number. The power spectrum shows a crossover from lower to upper branch as the laser frequency is varied through resonance. Some comparison with experiments on CuCl, GaAs, CdSe, and CdS semiconductors is also given.

A simple definition of random close packing of hard spheres is presented, and the consequences of this definition are explored. According to this definition, random close packing occurs at the minimum packing fraction $\eta$ for which the median nearest-neighbor radius equals the diameter of the spheres. Using the radial distribution function at more dilute concentrations to estimate median nearest-neighbor radii, lower bounds on the critical packing fraction ${\eta }_{\mathrm{RCP}}$ are obtained and the value of ${\eta }_{\mathrm{RCP}}$ is estimated by extrapolation. Random close packing is predicted to occur for ${\eta }_{\mathrm{RCP}}=0.64\mathrm{}\pm 0.02$ in three dimensions and ${\eta }_{\mathrm{RCP}}=0.82\mathrm{}\pm 0.02$ in two dimensions. Both of these predictions are shown to be consistent with the available experimental data.

We discuss the linearized hydrodynamic equations for the incommensurate phases of smectic-$E$ liquid crystals and of the mercury chain compound ${\mathrm{Hg}}_{3-\delta }\mathrm{As}{\mathrm{F}}_6$. In particular, we clarify the nature of the spontaneously broken continuous symmetries and point out their consequences for the number of hydrodynamic variables and thus for the number of propagating and diffusive normal modes. In addition, contact is made with a microscopic description by deriving Kubo relations for the transport parameters involved. A discussion of the crossover between propagating and diffusive modes due to finite interactions between the chains and the host lattice of ${\mathrm{Hg}}_{3-\delta }\mathrm{As}{\mathrm{F}}_6$ is also included.

Accurate measurements of the time dependence of the order-parameter fluctuations in the binary liquid mixture 3-methylpentane and nitroethane very close to the critical temperature are reported. The experiments were performed by cross correlating the scattered light received by two different photomultiplier tubes to eliminate distortions of the observed correlation function due to afterpulsing. The measurements reveal the presence of small but noticeable deviations from exponential decay of the critical concentration fluctuations. The observed phenomenon can be attributed to the effect of a frequency-dependent critical viscosity as predicted by Ferrell and co-workers.

Extensive measurements were made of light scattering intensity, quasielastic spectral width, and shear viscosity of the binary-liquid system $n-\mathrm{hexane}$ and nitrobenzene in the critical region. The measurements cover both the critical isochore and some other isochores in the temperature range $T=1\mathrm{} \mathrm{mK} \mathrm{to} 30 \mathrm{K}$ around the consolute temperature. The scattering experiments were made at five different angles covering a range of wave-vector transfer $q$ from 3.5×${10}^4$ to 28.2×${10}^4$ ${\mathrm{cm}}^{-1\mathrm{}}$ with values of the scaling variable $q\xi$ ($\xi$ is the correlation length) spanning from 0.006 to 51. The data on viscosity and linewidth are analyzed in the light of recent theoretical predictions taking into account the background effects on the transport coefficients. The agreement between theory and the experiments is very good in the whole range of $q\xi$ when the background effect is included.

The three-dimensional flow of the Lorenz model on its strange attractor is approximated by a two-dimensional flow with a branch curve with the use of the approximation of the Lorenz attractor by invariant two-dimensional manifolds obtained in earlier work. The Poincaré map on the branch curve and the associated invariant measure are determined. The probability density generated by the flow on the invariant manifolds in the steady state is related to and computed from the invariant measure on the branch curve. In a second part of this paper it is shown how the same probability density arises in the Lorenz model subject to stochastic forcing as a self-consistent approximation for the case of very small but finite noise intensity. The distribution transverse to the attractor is determined in the same approximation.

The van Hove scattering function $S(q,\omega )$ has been measured at 12 state conditions along the 297-K isotherm of krypton gas between 6 and 14×${10}^{27}$ atoms/${\mathrm{m}}^3$ and for the magnitude of the scattering vectors ($\overrightarrow{\mathrm{q}}$) between 0.4 and 3.3 ${\mathrm{\AA }}^{-1\mathrm{}}$. Integration of the data gives the static structure factors which have a major peak at $q\simeq 1.8$ ${\mathrm{\AA }}^{-1\mathrm{}}$. These data are compared to Monte Carlo calculations with the use of the pair potential for krypton, and differences due to many-body forces are observed. Then the $S(q,\omega )$ functions are compared to hardsphere molecular-dynamics simulations and the predictions of the kinetic theory of gases. Data are presented as a function of $q$ for fixed $\omega$, and for low momentum transfer ($q\le 1.8$ ${\mathrm{\AA }}^{-1\mathrm{}}$) significant differences are observed, while for higher momentum transfer the hard-sphere results are in reasonable agreement with the data. Diffraction maxima are observed for energy transfers up to 3 meV with the peak position moving to higher $q$ as $\omega$ is increased.

The conventional thermodynamic fluctuation theory, originated by Einstein in 1907, fails at volumes less than the correlation volume because it does not include the effects of local correlations. In this paper, a new thermodynamic fluctuation theory is developed in which an attempt is made to include local correlations by considering successive fluctuations in a sequence of systems of decreasing volume. The mathematics used is a path-integral formalism developed recently primarily for application in irreversible thermodynamics. An important result of the new theory is that it predicts the correlation length in terms of purely thermodynamic quantities, confirming a conjecture made earlier by the author on the basis of a Riemannian geometric model of thermodynamics. There is also a possibility that this new theory works at volumes less than the correlation volume and, hence, that it provides a thermodynamic theory of critical fluctuations. Unfortunately, due to mathematical difficulties, this interesting possibility is not put to a direct test in this paper.

We have experimentally and theoretically investigated the polarized and depolarized double-scattered intensity in the critical system methanol-cyclohexane in the temperature range $0.003<T-T_c<1\mathrm{}$°C. We have used a scattering geometry typical of spectroscopic studies, in which the single-scattering volume is illuminated by a narrow, cylindrically symmetric beam, viewed through small circular pinholes by a detector at a 90° scattering angle. We have investigated the multiple-scattering effects for aperture sizes ranging from 5×${10}^{-3\mathrm{}}$ to 5×${10}^{-4\mathrm{}}$ rad, where coherence effects become important. Our results for the total polarized and depolarized intensity are well described by double-scattering theory with $\gamma =1.26\mathrm{}$, ${\xi }_0=2.6\mathrm{}$ Å, and $\nu =0.60\mathrm{}$. At our closest approach to $T_c$, we find that the contribution of polarized double scattering to the total scattered intensity is ≅40%. At this temperature the effects of attenuation on the incident and scattered light become important. We have observed the effects of triple- and higher-order scattering events as an additional attenuation of the singly and doubly scattered light, and we have employed this observation to estimate the intensity of these higher-order scattering events.

Predictions are obtained for light-scattering spectra for disparate-mass gas mixtures at wave numbers such that species temperature separation produces strong deviations from hydrodynamic predictions. Recent light-scattering experiments in xenon-helium mixtures by Letamendia show good qualitative agreement with the present approximate predictions, thus providing the first experimental confirmation of the existence of a two-temperature regime in disparate-mass neutral gases. Physical reasons are suggested for the strong disagreement between two-temperature and hydrodynamic spectral predictions in the two-temperature regime.

Bond-orientational order in materials that form three-dimensional uniaxial solids is investigated. New phases are found that scatter light strongly, like nematics, but with a quantitatively different anisotropy of scattering. X-ray scattering from these phases would also exhibit novel anisotropy. This type of order may occur at higher temperatures in materials that form "stacked hexatic" phases at lower temperatures, and will occur whenever a hexagonal crystal melts via dislocation unbinding.

The dynamics of envelope solitons accompanied by density depressions (cavitons) is analyzed with the use of the driven Zakharov equations for inhomogeneous plasmas; damping effects are included. The acceleration in a spatially inhomogeneous plasma is found to be dominated by ion inertia, in contrast to the corresponding (adiabatic) Schrödinger predictions. The maximum speed is the ion-sound velocity. The dynamic-plasma response hinders the center of the wave packet from obeying a Newtonian force equation with the inhomogeneity acting as a force. Damping terms in the high-frequency equation introduce a new acceleration mechanism which is investigated explicitly. We analyze these effects on the basis of a moment method which starts from conservation laws. Finally, the complete set of equations, in the presence of a driver, is solved numerically. Energy transfer and relaxation oscillations are investigated.

Thermal fluctuations in nematic liquid crystals about a noneqilibrium stationary state due to an external temperature gradient are investigated. The influence of the nonequilibrium situation on the light-scattering spectrum is discussed. The equilibrium Lorentzian due to transverse director fluctuations does not change height, but is slightly shifted and changes its shape into an asymmetric one due to the applied temperature gradient. The anisotropy arising from the various possible directions of temperature gradient, director, and wave vector has a pronounced effect on the nonequilibrium contributions to the light-scattering spectrum.

In a recent paper Pathak and Gadre have established lower bounds for the first gradient-expansion corrections to the kinetic- and exchange-energy terms of the Thomas-Fermi-Dirac model of an atom. In the present report, with the use of the Na atom as an example, the bounds are calculated with the recent electron (number) densities of Wang and Parr, Csavinszky, and Wang, who considered statistical energy-density functionals for atoms with shell structure.

A modification in the procedure for calculating level shifts of atoms described by Sharma and Bowtell [Can. J. Phys. 51, 1637 (1973)] is proposed which, while retaining the extreme simplicity of the procedure, improves its accuracy substantially. Attention is drawn to certain curious and puzzling features associated with the procedure which require further investigation.