We consider a system of rodlike molecules interacting with a model pair potential $\phi \left(\frac{r}{\sigma }\right)$, where $r$ is the center-of-mass distance and $\sigma$ is an angle-dependent range parameter. It is shown that if the pair correlation function $g$ scales as $g\left(\frac{r}{\sigma }\right)$, then the orientational degrees of freedom decouple from the translational ones to all orders in the density $n$. To lowest order in $n$, our free energy reduces to Onsager's virial-expansion result. The approximation transforms the system into a fluid of spheres interacting with a central potential $\phi \mathrm{}\left(y\right)\mathrm{}$ modulated by an angle-dependent excluded-volume term. The order parameter $Q$ is predicted to have a discontinuity $Q_c$ at the transition point, which is independent of $\phi \mathrm{}\left(y\right)\mathrm{}$ but which slowly increases with the axial ratio $k$ of the molecules. Calculations are done for the hard-rod fluid using the equation of state for the transformed hard-sphere fluid. A transition to an orientationally ordered state occurs at a critical value of the packing fraction ${\eta }_c$, which decreases with $k$. For $k\lesssim 3.5$, ${\eta }_c$ is so high that the system tends to crystallize before the ordered liquid state is reached. Using perturbation theory, calculations are done for a soft-rod fluid, where the transformed system of spheres interacts with a potential $\phi \mathrm{}\left(y\right)=\frac{\epsilon }{y^m}$. The transition temperature as a function of density and molecular shape is obtained, and it is shown that the order parameter obeys the scaling law $Q=Q\left(\eta {\left(\frac{\epsilon }{\mathrm{kt}}\right)}^{\frac{m}{3}}\right)$. For $m=12\mathrm{}$ this leads to good agreement with experiment and shows that most of the features of the transition can be explained with purely repulsive interactions.

We study the properties of subcritical Rayleigh-Bénard rolls induced by a triggering velocity applied to one side of a fluid layer maintained in controlled subcritical conditions. The induced rolls are spatially damped exponentially with increasing distance from the position of the triggering velocity. We point out a remarkable critical behavior of a characteristic penetration length $\xi (\xi ={\xi }_0{\epsilon }^{-\nu })$. The values of $\nu =0.50\mathrm{}\pm 0.02$ and ${\xi }_0=(0.38\mathrm{}\pm 0.01)d$ are in perfect agreement with those calculated according to the Landau-Hopf model.

A new statistical model [the quantum-statistical model (QSM)] was recently introduced by Kalitkin and Kuzmina for the calculation of thermodynamic properties of compressed matter. This paper examines the QSM and gives (i) a numerical QSM calculation of pressure and energy for aluminum and comparison to existing augmented-plane-wave data; (ii) display of separate kinetic, exchange, and quantum pressure terms; (iii) a study of electron density at the nucleus; (iv) a study of the effects of the Kirzhnitz-Weizsacker parameter controlling the gradient terms; (v) an analytic expansion for very high densities; and (vi) rigorous pressure theorems including a general version of the virial theorem which applies to an arbitrary microscopic volume. It is concluded that the QSM represents the most accurate and consistent theory of the Thomas-Fermi type.

Laser-irradiated targets filled with pure neon have been used to directly measure the peak density $\rho$ and $\rho R$ product (density X radius) using spectrally and spatially resolved neon x-ray line emission. In agreement with theoretical predictions for the explosive-pusher mode, we find peak densities in the range 0.25-0.5 g/${\mathrm{cm}}^3$ which are almost independent of laser power or fill pressure. In addition, $\rho R$ values increase from 2 × ${10}^{-4\mathrm{}}$ to 6 × ${10}^{-4\mathrm{}}$ g/${\mathrm{cm}}^2$ as the fill pressure increases from 2 to 56 atm. Using these methods for the density measurement as well as other experimental signatures (such as x-ray pinhole imaging, x-ray streak photography, and x-ray line emission from the glass microballoon), we systematically investigated the explosive-pusher mode of target dynamics for various fill pressures. These and similar methods may become crucial in diagnosing future higher-compression implosions.

In a previous paper (I) we carried out a model calculation for nematic liquid crystals which treats spatial correlations between molecules as for a classical isotropic liquid and orientational correlations in the meanfield approximation. Generalized Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) equations were derived for the density function and an orientationally averaged pair-correlation function. They were solved for a simple pairwise potential chosen to fit certain experimental data on $p$-azoxyanisole (PAA). A free-energy expression was obtained by identifying its Euler-Lagrange equation to the first BBGKY equation. In this paper we reformulated the molecular theory of nematic liquid crystals rigorously on the basis of a general probability distribution function $P_N(1,\dots ,N)$. It was shown that both the mean-field theory (MFT) and the above-stated orientation-averaged pair-correlation theory (OAPC) arise from applying low-order approximations to $P_N$. In the case of MFT, $P_N$ was approximated as a product of single-particle functions. In the case of OAPC, spatial correlations were introduced, but decoupling of spatial and orientational dependences were assumed. It is now clear how higher-order-approximation schemes can be systematically constructed. Furthermore, for each scheme chosen, the present formulation offers a uniquely consistent formula for the free energy. This places our previous work on a firm theoretical foundation. The theory in OAPC approximation was applied to model systems described by a more general pairwise potential than that employed in I. Potential parameters were chosen to mimic PAA and methoxybenzylidene butylaniline. For each substance we calculated the isotropic-nematic coexistence curve, temperature dependence of the order parameter, latent heat, and volume change at transition. The results were compared to experimental data.

We determine the optimal configuration for a class of heat engines with finite cycling times. The engines studied are those for which irreversible process occur through the coupling of the engine to the environment, while the working fluid in the engine is assumed to undergo reversible transformations. For the case in which the only irreversible process is heat conduction, we derive the optimal configuration of these engines for two different operating goals: maximum average power output and maximum efficiency. We suggest figures of merit based on these optimal configurations which may be more useful than those based on reversible processes.

In a previous paper we analyzed a class of irreversible cyclic heat engines to find their optimal operating configuration for specific performance goals. In that paper the thermodynamic variables of the working fluid were not treated as dynamical variables, instead the dynamics was replaced by an integral constraint. In this paper we reanalyze the same class of heat engines treating the thermodynamic variables of the working fluid as dynamical variables, and we obtain the optimal configuration of the engine when the performance goal is to maximize the average power output per cycle or, alternatively, to maximize the efficiency of the engine. To carry through this program it is necessary to use mathematical techniques from optimal-control theory. Since this subject is unfamiliar to most physicists and chemists, we briefly introduce some of the central ideas of the theory.

In this paper a microscopic theory for the nonequilibrium average of any dynamical variable, and of fluctuations in particular, is presented. The general theory is specialized to nonequilibrium stationary states (NESS) of simple fluids. It is found that the fluctuations around the NESS are qualitatively different from equilibrium fluctuations. There appears a coupling between the fluctuations and the macroscopic dissipative fluxes, linked to a breaking of time-reversal symmetry. The dynamic structure factor is analyzed in a heat-transporting NESS and is found to be ${S_{\overrightarrow{k}\omega }}^{=} {S_{\overrightarrow{k}\omega }}^{\mathrm{hom}}+i\xi (k,\omega )\overrightarrow{\mathrm{k}}·\overrightarrow{\nabla }\beta \mathit{\Phi }+\alpha (k,\omega )\overrightarrow{\mathrm{k}}·\overrightarrow{\nabla }\beta \mathit{\Phi }$, where the first term is the one predicted by local equilibrium theory and is even in $\overrightarrow{\mathrm{k}}$ and $\omega$, the second is even in $\omega$ and odd in $\overrightarrow{\mathrm{k}}$, and the third is odd in $\overrightarrow{\mathrm{k}}$ and in $\omega$. Possible light-scattering experiments for measuring the new effects are discussed.

The singlet distribution function (SDF) and the first two sum rules of the dynamic structure factor in lowdensity simple fluids are computed using the formalism developed in the first paper in this series. It is shown that the correlation-function expression for the SDF reduces to the Chapman-Enskog and Choh-Uhlenbeck forms in the low-density regime. The leading density dependence of the sum rules in nonequilibrium stationary states (NESS), with and without convection is given, and explicit forms for "Maxwell molecules" are computed. The results clearly show that local-equilibrium theories yield incomplete results for the sum rules in the small-wave-vector regime. The fact that time-reversal symmetry is broken in NESS yields the new result that the first sum rule is nonzero even in the absence of convection. Lastly, the validity of the separation of time-scale assumption used in the formal analysis is examined.

The detailed structure of correlation functions in nonequilibrium stationary states is analyzed. The theory is applied to time-correlation functions and static-correlation functions in simple dense fluids. We find that the breaking of time-reversal symmetry induces important changes that cannot be predicted from local-equilibrium theories. The spectrum of light scattered from argon at 235 K and 1 g/${\mathrm{cm}}^3$ subject to a temperature gradient of 0.5 K/cm is computed. We find a pronounced asymmetry in the Brillouin peaks. The static-correlation functions that are usually zero due to time-reversal symmetry are calculated and found to be nonzero and show the existence of a long-range order (1/r decay in physical space). The connection to phenomenology is discussed and a regressionlike hypothesis is shown to be consistent with the microscopic theory once the changes due to symmetry breaking are made.

We present solitary-wave solutions to a set of coupled nonlinear wave equations resulting from a model Lagrangian for a complex scalar (two-component) field in one space and one time dimension in the presence of fourfold phase anisotropy in the potential-energy density. We find two classes of solutions which correspond to 90° and 180° phase rotation, respectively. The 180° solution is found to bifurcate into two 90° solutions as the anisotropy magnitude is decreased past a special value. These results have application to commensurability-pinned one-dimensional charge-density-wave condensates and anisotropic ferromagnetic domain walls.

A generating functional for a classical system described by coordinates satisfying nonlinear equations of motion is constructed in terms of which any functional of the system's phase-space trajectory may be expressed. Statistical behavior of the system arising from either random initial conditions or random stirring forces may be handled simply within this theory. The analogy with Feynman's action-integral formalism of quantum theory provides an alternative approach to the operator methods recently developed by Martin, Siggia, and Rose. The connection with the earlier work of Onsager, Machlup, and Graham is also pointed out.

It is shown that a relativistic electron-positron plasma formed by the coalescence of two counterstreaming intense relativistic electron and positron beams can collapse into a very-small-diameter filament. The collapse is accompanied by the emission of intense coherent $\gamma$ radiation. The radius of the collapsed state is determined by the quantum-mechanical uncertainty principle. At its maximum contraction the electron-positron plasma can approach nuclear densities. The predicted effect may have many interesting applications, some of which are briefly mentioned. The generation of the intense beams seems to be possible with existing techniques.

In this Comment we report measurements of $K$-shell x-ray production cross section, $\frac{K\beta }{K\alpha }$ x-ray intensity ratios and $K\alpha$ and $K\beta$ x-ray energy shifts for ${}_{29}{}^{}{}_{}{}^{}\mathrm{Cu}$, ${}_{32}{}^{}{}_{}{}^{}\mathrm{Ge}$, ${}_{35}{}^{}{}_{}{}^{}\mathrm{Br}$, and ${}_{37}{}^{}{}_{}{}^{}\mathrm{Rb}$ for 4-38-MeV ${}_5{}^{10}{}_{}{}^{}\mathrm{B}$-ion bombardment. The dominant contribution to target $K$-shell ionization is believed to be direct Coulomb ionization. Electron-capture contributions to target $K$-shell ionization are expected to be ≤7%.

Integral and expansion techniques for Fourier transforming position-space wave functions containing interelectron coordinates are presented. Of the two techniques, the integral methods are the more powerful as exponential terms containing interelectron coordinates can be handled.

Nonrelativistic configuration-interaction calculations have been carried out with orbital basis specifically adapted for each one of the first seven even-parity ${}_{}{}^2{}_{}{}^{}P$ bound states of neutral Li. The results show that the lowest four ${}_{}{}^2{}_{}{}^{}P$ states have recently been observed by absorption spectroscopy from the $1s^{2}2p$ state. The calculated transition wavelengths (20.7452, 19.7613, 19.4728, and 19.4065±0.0005 nm agree well with the experimental ones (20.744, 19.762, 19.474, and 19.405±0.002 nm). Electric dipole transition probabilities to the $1s^{2}2p$, $3p$ and $4p$ states have also been calculated. The configurations for the two lowest ${}_{}{}^2{}_{}{}^{}P\mathrm{}\left(1\right)\mathrm{}$ and ${}_{}{}^2{}_{}{}^{}P\mathrm{}\left(2\right)\mathrm{}$ states are $1s2p^2$ and $\mathrm{}\left(1s2p\right)\mathrm{}{}_{}{}^3{}_{}{}^{}P3p$, respectively. The $\mathrm{}\left(1s2p\right)\mathrm{}{}_{}{}^3{}_{}{}^{}P\mathrm{np}$ and $\mathrm{}\left(1s2p\right)\mathrm{}{}_{}{}^1{}_{}{}^{}P{n}^{\prime }p$ series almost coincide at $n=4\mathrm{}$, $n^{\prime }=3\mathrm{}$, and as a consequence, the ${}_{}{}^2{}_{}{}^{}P\mathrm{}\left(3\right)\mathrm{}$ and ${}_{}{}^2{}_{}{}^{}P\mathrm{}\left(4\right)\mathrm{}$ levels are approximately described by $\mathrm{}\left(1s2p\right)\mathrm{}{}_{}{}^3{}_{}{}^{}P4p\pm \mathrm{}\left(1s2p\right)\mathrm{}{}_{}{}^1{}_{}{}^{}P3p$. This is the simplest known example of two-level series which mutually perturb each other.

The substate alignment has been determined through measurements of the linear polarization of the $1s-2p$ and $1s^2-1s3p$ x-ray transitions emitted by oxygen projectiles interacting with a thin helium target. For the initial $p$ states, the fractional population of substates with $m_l=0\mathrm{}$ (with respect to the beam axis) ranged from 58% to 74%. This high degree of alignment was relatively insensitive to the beam energy or mode of production of $p$ state by excitation or electron capture.

Absolute cross sections for electron capture into the $3s$, $3p$, and $3d$ states of hydrogen have been measured for 2.2-8.2-keV proton impact on CO, C${\mathrm{O}}_2$, and ${\mathrm{N}}_2$O. The relative magnitudes of the $3s$, $3p$, and $3d$ cross sections for CO are very similar to cross sections previously measured for elemental gases. The C${\mathrm{O}}_2$ and ${\mathrm{N}}_2$O cross sections have a very different relative distribution among the $3s$, $3p$, and $3d$ states compared to all other gases studied in this laboratory, with the $3p$ cross section being so small that only an estimate of the upper limit to the cross section was possible.