Sound-velocity and attenuation measurements are reported for the smectic liquid crystal $p$-butoxybenzylidene-$p^{\prime }$-octylaniline. At the smectic-$A$ smectic-$B$ transition temperature $T_{\mathrm{AB}}$, $v$ and $\alpha$ change rapidly, with a peak in $\alpha$ occurring below $T_{\mathrm{AB}}$. A very small anomaly is also visible 2 to 2.5 degrees above $T_{\mathrm{AB}}$. The data at $T_{\mathrm{AB}}$ are analyzed in terms of dislocation-mediated melting theories by assuming that the transition occurs at a crossover between two- and three-dimensional behavior. The low-frequency velocity change of $\frac{\Delta v}{v}=0.047\mathrm{}$ within the planes agrees well with the predicted value of 0.040.

We have measured fluctuations in the dc electrical conductivity of isobutyric acid-water mixtures near the critical temperature $T_c$. Power spectra $S_V\mathrm{}\left(f\right)\mathrm{}$ were measured in the frequency range $0.04\le f\le 100$ Hz and temperature range $1\lesssim T-T_c\lesssim 1000$ mK. Near $T_c$ the spectra cannot be characterized by a simple power law. Rather $S_V\mathrm{}\left(f\right)\mathrm{}$ has a shoulder, which is theoretically expected to occur near a frequency $f_o=\frac{D}{{\xi }^2}$, where $D$ is the composition diffusivity and $\xi$ is the correlation length. The measurements are only in qualitative agreement with our calculations. Far from $T_c$, $S_V$ is proportional to $\frac{1}{f^{\psi }}$ with $\psi =0.95\mathrm{}\pm 0.1$. This $\frac{1}{f}$ noise is presumably not associated with critical thermodynamic fluctuations.

Using a microscope, we have studied the formation and growth of nuclei in a supercooled binary liquid mixture of 2,6-lutidine and water close to the critical point. The results have been compared with a recent theoretical prediction by Langer and Schwartz. Although the observed growth is in good agreement with the diffusion model they used, their predicted nucleation rates remain untested. Our most important finding is the clear experimental evidence of the effect of critical slowing down on the phase-separation process in the nucleation regime. These observations thus account for the anomalously large supercoolings reported in liquids and binary mixtures near the critical point.

Optical ray retracing in stimulated Brillouin backscatter from laser-produced plasmas is studied numerically, using a 2-D propagation code (BOUNCE). This code treats steady-state behavior in the strong damping limit, and includes self-focusing effects. Ray retracing phenomena are grouped into two limiting cases. In the "whole-beam" limit, the pump field at the lens has a broad spatial profile that can be focused to a long narrow waist within the plasma. This geometry selectively amplifies only those initial noise components that are propagating back along the axis, where the net gain is highest. The simulations show that such effects exhibit a pronounced threshold due to self-focusing, and disappear when the focal width becomes comparable to the length of the gain medium. In the opposite limit, where the pump radiation at the lens is dominated by small-scale transverse structure, the backscatter can reproduce this structure in detail (i.e., exhibit wavefront reversal) when the far field of the pump produces an interference pattern in the plasma. The plasma then behaves as an active volume hologram as it amplifies the backward-propagating random noise fields. If the target is moved far out of focus so that the pump components can no longer interfere, the ray retracing disappears, and the actual backscatter profile depends upon the noise structure. Wavefront reversal is found to be influenced by several other factors, including focal spot size, spatial gain narrowing, gain inhomogeneity, and self-focusing. The simulations show that it is most pronounced when the spatial profiles of the pump and the backscatter are wide in comparison to the transverse wavelengths of the interference structure, and the $\frac{1}{e}$ gain length (especially in the last one or two $e$ foldings) is large in comparison to the optical diffraction lengths. It is enhanced significantly if the plasma has a monotonically decreasing gain coefficient away from the target. In the strong-damping limit, where the nonlinear phase change/cm is comparable to the gain coefficient, filamentation can be important near the target; however, its effect on small-scale ray retracing is usually minimal, provided that the above conditions are satisfied. If the focal spot decreases below a critical width, however, whole-beam self-focusing takes over and quickly destroys the small-scale retrace.

In this paper we establish the connection between the energetic instability encountered in stochastic oscillators with fluctuating frequencies and the parametric instability of deterministic oscillators with time-dependent frequencies.

General theoretical relationships consistent with experiments are obtained for isotropic homogeneous incompressible-fluid turbulence governed by the Navier-Stokes flow equation. A key quantity that structures the turbulence is the "broadness" $B$ of the probability measure over velocity fields. Both the decay law and the longitudinal correlation function for small $r$ appear as simple functions of this quasiconstant parameter $B$.

We show that a one-dimensional Coulomb system on a circle has a phase transition of the molecular-field-type if one allows only for an alternating sequence of charges.

As a sequel to our previous discussion of a hydrodynamic model for the condensation of a near-critical fluid, we describe the dynamics of a diffuse planar liquid-vapor interface. We show that inclusion of the thermal mode and its coupling to the density mode is essential in deriving the dispersion relation for capillary waves, and the isothermal approach based either on hydrodynamic or mean-field kinetic theory must lead to a nonphysical description of excitations of the diffuse interface. The problem of the rate of growth of a critical liquid droplet in a supersaturated vapor is reconsidered, and a corrected expression for this rate is shown to have the expected scaling behavior.

A detailed theoretical model of the collisional and radiative couplings within the aluminum $K$ shell is described which has been used to self-consistently calculate the functional dependence of the excitation state of the $K$ shell and its emission spectrum on ambient plasma conditions for a wide range of $K$-shell opacities. Both line and continuum couplings are included in the model over a range of photon energies from 442 eV to 6.13 keV. The approach of the interior of the aluminum plasma to local thermodynamic equilibrium has been investigated for millimeter sized plasmas where the $K$-shell couplings are photodominated and the plasma interior must come into radiative equilibrium. The approach of the $K$-series emission spectrum, which includes satellite and intercombination lines of the heliumlike resonance line, to the blackbody curve is computed. Temperature variations of the power output in continuum and line radiation are also computed and discussed. Finally, a set of calculations that relate to the ability of an external source of x radiation to selectively photopump the $3p$ state and maintain an inversion between $2p-3d$ levels within the heliumlike ionization stage is described. Two important effects are seen. One, the opacity of the heliumlike $L\alpha$ line plays an important role in determining the ability of the external radiation to invert levels within the plasma interior, and two, the inversion saturates with increasing pump strengths as the heliumlike ground-state population is depleted by the pump.

Electron beams of tW/${\mathrm{cm}}^2$ (∼0.4 MeV) which are split into filaments are produced by an inductive generator which transfers field energy to beam particles in 1-10-ns pulses. Target-damage analysis reveals the composite internal structure of each filament as a sequence of concentric circles with a discontinuous pattern. The nonuniform distribution of collectively accelerated positive ions within a filament contributes to resolve the filament structure which propagates at a speed $\sim \frac{3c}{4}$ and can cross unaffected a ${10}^3$-G magnetic field.

We consider a lattice gas for which particles possessing magnetic moments can interact via magnetic long-range Kac potential and short-range intermolecular potential. From the exact equation of state of the lattice gas and the magnetization we construct and discuss phase diagrams in one and two dimensions. The appearance of any of the possible phases—nonmagnetic gas, nonmagnetic liquid, or magnetic liquid—is shown to depend crucially on the value of the parameter $R$, the ratio of the short-range (nonmagnetic) to long-range (magnetic) interaction strengths.

A theory is presented to study the depolarized light scattered by dense rare-gas fluids. This theory is based on the Zwanzig-Mori theory of Brownian motion; the transport matrix is estimated by a lattice-gas model. Two modes are theoretically predicted, a dissipative mode due to the translational diffusion of rare-gas atoms and an oscillatory mode associated with their oscillations around a given site in the fluid. The resulting profile has a Lorentzian shape at low frequencies and non-Lorentzian wings at high frequencies. The electron-overlap effect modifies the integrated intensity of the scattered light but has only a minor influence on its spectral density.

Measurements of orientational order parameters which express different aspects of relative order of the individual segments of the hydrocarbon chain are reported, some for the first time, in the lamellar $L_a$ region of the potassium palmitate-water system. The order parameters are time averages of spherical harmonic functions which are measured directly from deuterium spectral splittings. From these measurements it is found that the order of each hydrocarbon segment relative to that at the alpha position deviates strongly from cylindrical symmetry. This asymmetry is found to increase in a linear fashion proceeding from the head group toward the terminal end of the chain. The order of each segment relative to the alpha position reflects the noncylindrical time average conformation of the hydrocarbon chain. These measurements were made in the high temperature, phase I, of this lamellar system. In this phase the order of the molecular long axis was found to be anisotropic reflecting a biased rather than a free rotation about the molecular long axis as normally assumed in nuclear magnetic resonance studies of ordered lipids. A model is introduced for the other $L_a$ phases in this system which involves a change in axis about which the molecule rotates.

A quantitative definition is given to the accuracy of the computation of the partial densities of the ionization states in a steady-state plasma when there is an inaccuracy in the rate coefficients used in the rate equation. It is found that the partial density of the most abundant ion species is almost independent of the exact form of the rate coefficients, but large errors may occur for the rare species. The effect of the variation of the total ion density on the partial densities is also calculated. For low-ion densities the partial ionization-state densities grow proportionally to the change of the total density, but at high densities there is an alteration of the charge-state distribution as well.

The effect of a shear flow on the critical behavior of a binary fluid (cyclohexane-aniline) has been investigated by light-scattering techniques. Turbidity and scattered-light-intensity measurements have been made, and the influence of all the independent parameters of the phenomenon were considered, i.e., temperature $T$, shear rate $S$, transfer wave vector $\left|\overrightarrow{\mathrm{q}}\right|$, and its projection $q_X$ along the flow direction $X$. The data support the Onuki-Kawasaki (OK) description, namely, (i) an effect exists only in the region $S\tau >1\mathrm{}$, with $\tau$ the lifetime of concentration fluctuation. (ii) The critical temperature $T_c$ is lowered by the shear, so that $T_c=T_c\mathrm{}\left(S\right)=T_c\mathrm{}\left(0\right)-T_0{S}^{{\sigma }_0}$, with ${\sigma }_0=\frac{1}{3\nu }$ and $\nu =0.630\mathrm{}$ the standard exponent of the correlation length in fluids. We find experimentally $T_0=(1.8\mathrm{}\pm 0.2)\times {10}^{-4\mathrm{}}$ and ${\sigma }_0=0.53\mathrm{}\pm 0.03$, to be compared with the OK values 1.28 × ${10}^{-4\mathrm{}}$ and 0.529. (iii) The susceptibility ${\chi }_{\overrightarrow{\mathrm{q}}}$ shows an anisotropy versus $X$, and follows a mean-field behavior versus temperature. The OK dependence $\chi _{\overrightarrow{q}}^{}{}_{}{}^{-1\mathrm{}}\mathrm{v}\simeq A{S}^{{\sigma }_1}{[T-T_c\mathrm{}(S\left)\right]}^{\gamma }+B{S}^{{\sigma }_2}{q}_X^{\omega }+q^2$ fits the data well, with ${\sigma }_1\simeq 0.14\pm 0.05 [\mathrm{OK}:\frac{(2\mathrm{}\nu -1)}{3\nu }=0.137]$, $\gamma \simeq 1.00\pm 0.06 (\mathrm{OK}:\gamma =1)$, $\omega \simeq 0.40\pm 0.05 (\mathrm{OK}:\frac{2}{5})$, except for ${\sigma }_2$, whose experimental value ${\sigma }_2\simeq 1\pm 0.15$ is about twice the OK value 8/15. Discrepancies of about a factor 2 are also found for the amplitudes $A$ and $B$.

A moment method is used to obtain exact solutions of the nonlinear Boltzmann equation for the relaxation to equilibrium of a spatially uniform gas of Maxwell-model molecules. The results contradict a recent conjecture of Krook and Wu concerning similarity solutions. Unless the initial conditions are very special, long-time relaxation follows linear modes corresponding to solutions of the linearized Boltzmann equation, rather than similarity solutions. Application of the moment method to other collision models gives approximate rather than exact results, but shows that there is coupling between the linear relaxation modes, which are independent for the Maxwell model. At long times all moments, therefore, decay together along the lowest linear mode. Numerical calculations for rigid spheres illustrate this behavior.

Cross sections for $2s-2p$ excitation of one-electron ions scattering from ${\mathrm{He}}^{2+}$ and ${\mathrm{He}}^0$ are evaluated in the planewave Born approximation. The total cross section diverges logarithmically as the $2s-2p$ binding energy difference $\Delta E$ goes to zero for excitation by ${\mathrm{He}}^{2+}$ due to contributions from small momentum transfers. In contrast for ${\mathrm{He}}^0$ as $\Delta E$ goes to zero the total cross section is finite since the small-momentum-transfer contribution is damped corresponding to screening of the nucleus by the helium electrons at large distances. Calculations are presented for $2s-2p$ excitation of F and Si scattering from ${\mathrm{He}}^{2+}$ and ${\mathrm{He}}^0$ at velocities of several MeV/amu. For F and Si there is about an order of magnitude difference between scattering from ${\mathrm{He}}^{2+}$ and from ${\mathrm{He}}^0$, suggesting that electron screening is important here. However, our results are not in consistent agreement with recent observations.

The Lyman-$\alpha$ polarization fractions resulting from $e^{-}-\mathrm{H}\mathrm{}\left(1s\right)\mathrm{}$ collision are calculated within the conventional Glauber and modified Glauber methods, in which the Glauber exchange effects are no longer neglected. It is found that in the conventional Glauber case, the inclusion of exchange effect completely changes the shape of the theoretical result curve at energies below 30 eV in comparison to the one obtained in the previous calculation without exchange and, furthermore, worsens somewhat the agreement with experimental data at energies between 30 and 60 eV. The new theoretical values obtained with the modified Glauber method with exchange are found to improve significantly the agreement with experimental data at intermediate scattering energies. However, the modified method still fails to account for experimental data below 30 eV, as expected.

A magnetic dipole line in the ground configuration of Ti XVIII has been identified and the accuracy of previous measurements of Ti XIV, XV, and XVII lines has been significantly improved.

The structure recently observed by Vogler in the dissociation spectrum of the ${\mathrm{H}}_3$ molecule is attributed to the predissociation of the $2s{}_{}{}^2{}_{}{}^{}A_1^{}{}_{}{}^{\prime }$ electronic state of ${\mathrm{H}}_3$ to H atoms and various vibration-rotation levels of the ground electronic state of ${\mathrm{H}}_2$. The process ${\mathrm{H}}_3(2s{}_{}{}^2{}_{}{}^{}A_1^{}{}_{}{}^{\prime },v=0)\to {\mathrm{H}}_2(X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{},v=J=0)+\mathrm{H}\left(1s{}_{}{}^2{}_{}{}^{}S\right)$ is found to be exothermic by 5.52 eV.