In high-temperature magnetically confined plasmas, the individual Zeeman components of electric and magnetic dipole transitions in multiply charged atomic ions are usually not spectroscopically resolvable on account of the dominance of the Doppler broadening due to the thermal motion of the radiating ions. However, it is possible to measure the shift of the blended circularly polarized components from the position of the unshifted line. In the weak-magnetic-field regime, this average shift is linearly proportional to the magnetic field strength and to a Zeeman-splitting parameter. Simple expressions for this parameter have been derived which involve only the g factors for the upper and lower levels and their total electronic-angular-momentum quantum numbers. These expressions are valid for both electric and magnetic dipole transitions. With use of relativistic multiconfiguration wave functions, the Zeeman-splitting parameters have been evaluated for magnetic dipole transitions between the fine-structure levels of the ground-state configuration in carbonlike ions with even values of the nuclear charge from Z=22 to Z=30. A discussion is presented on the feasibility of determining local magnetic fields in magnetically confined plasmas from the analysis of the Zeeman splitting and polarization of the magnetic dipole radiation emitted by multiply charged atomic ions. In particular, it may be possible to determine the poloidal magnetic field in a tokamak plasma by observing the circularly polarized radiation emitted in a direction perpendicular to the precisely known toroidal field. It may also be possible to employ Zeeman-splitting and polarization measurements to determine the magnetic field distributions which are known to be associated with regions of solar activity, e.g., solar flares.

Radiative energy transport in hot dense matter has been investigated in the sub-keV region. In a medium-Z element (aluminum), ionization burn-through has been observed. Burn-through speed is estimated to be 6×${10}^5$ g/${\mathrm{cm}}^2$ sec or more at an x-ray intensity of 7.4×${10}^{12}$ W/${\mathrm{cm}}^2$. At a high Z (gold), the spectral structure of transmitted x rays indicates the formation of an x-ray heat conduction band via absorption resonance. Penetration depth (ρ ΔR) of radiative energy transport in Au is found to be 3–4 times larger than that in aluminum.

The technique of molecular-dynamics simulation—in which the equations of motion of a system of interacting particles are solved numerically to yield the temporal evolution of the system—is used in a study of the flow of a two-dimensional fluid past a circular obstacle. The flow is observed to develop with time, passing through a series of well-defined patterns that bear a striking similarity with flow patterns observed experimentally in liquid and gas flow; the patterns include stationary eddies, periodic shedding of vortices, and a vortex street characterized by a Strouhal number close to the experimental value. Very large systems—by current molecular-dynamics standards—need to be used in order to accommodate the obstacle and the region occupied by the structured wake, and the present work includes the largest such simulations carried out to date. Though more extensive work is called for, the results suggest that continuum hydrodynamics is applicable down to much shorter length scales than hitherto believed, and that the molecular-dynamics approach can thus be used to study certain kinds of hydrodynamic instabilities.

A series of molecular-dynamics simulations of binary-fluid mixtures composed of softly repelling spheres have been made as part of an investigation of the glass-forming properties of mixtures. These mixtures are simple prototypes of glass-forming systems, as both randomness and frustration are intrinsic to them. The randomness is inherent in the fluid and frustration is due to the large, local rearrangement of atoms required for the formation of a crystal from a fluid or glassy configuration. The equation of state, pair and triplet correlation functions, single-particle velocity time autocorrelation functions, and some measures of local glassy order have been determined for a range of compositions, X, and effective reduced densities, ${\mathrm{\Gamma }}_{\mathrm{eff}}$=(${\mathrm{n}}^{\mathrm{*}}$/${\mathrm{T}}^{\mathrm{*}1/4}$)(${\mathrm{\sigma }}_{\mathrm{eff}}$/${\mathrm{\sigma }}_{11}$${)}^3$ where ${\sigma }_{\mathrm{eff}}$ is the one-fluid van der Waals equivalent diameter. In addition, attention has been focused on the relaxation of some anisotropic correlation functions characterizing the local environment. Attempts have been made to analyze some of these quantities using plausible phenomenological models. The changes in these quantities which occur as the fluid is supercooled and finally forms a glass are examined and the possible implication of these findings for certain dynamical theories of the glass transition are discussed. Calculations have also been performed to determine compositional conditions necessary for a supercooled liquid to crystallize and the relevance of this to recent experiments is discussed.

Two line ratios, the forbidden line at 845.5 Å (2s${}^2$2p ${}^2$$P_{1/2}$–2s${}^2$2p ${}^2$$P_{3/2}$) to the allowed line at 135.7 Å (2s${}^2$2p ${}^2$$P_{1/2}$–2s2$p^2$ ${}^2$$D_{3/2}$) in Fe xxii and the forbidden line at 592.1 Å (2s${}^2$2$p^4$ ${}^3$$P_2$–2s${}^2$2$p^4$ ${}^1$$D_2$) to the forbidden line at 1118.2 Å (2s${}^2$2$p^4$ ${}^3$$P_2$–2$s^2$2$p^4$ ${\mathrm{}}^3$$P_1$) in Fe xix, have been measured as ion-temperature-sensitive line ratios during rf heating in the Princeton Large Torus. The results indicate that deuteron collisions in plasmas of high deuteron temperature have a noticeable effect on the intensity of the forbidden lines. Measured relative intensities are compared with values from level-population calculations, which include deuteron collisional excitation between the levels of the ground configuration. The agreement between the observed and calculated ratios is within 30%. A method for deuteron (or proton) temperature measurement in tokamak plasmas is discussed.

The recent analysis of the fluctuating Navier-Stokes equations with a random force with a $k^{\mathrm{-}y}$ spectrum by Yakhot and Orszag [Phys. Rev. Lett. 57, 1722 (1986)] is repeated using field-theoretical renormalization techniques. A dimensional expansion around the full equilibrium state in two spatial dimensions is performed to one-loop order. The results differ from those of Yakhot and Orszag in a number of ways. A nontrivial fixed point is found which is the natural extension of that presented by Forster, Stephen, and Nelson [Phys. Rev. A 16, 732 (1977)], and various correlation functions in crossover form are presented. The application of the model to turbulence, i.e., in cases where the Kolmogorov (5/3 law is obtained, is analyzed in detail. Unlike the work of Yakhot and Orszag, a choice of the random force correlation exponent (y=-1.5851 in three dimensions) is found which gives the Kolmorov (5/3 law at high wave vectors.

Equilibrium properties of the tiling model, recently introduced by Stillinger and Weber as a means of studying glass phenomena, are investigated. In the two-dimensional model, a square lattice is covered by tiles of all sizes. The tiles represent domains of well-packed particles and the boundaries between the domains have a positive mismatch energy proportional to the length of the wall. The existence of the thermodynamic limit for this model is proved. It is shown how to obtain bounds for the free energy and the transition temperature from the free energy of semi-infinite strips. A transfer-matrix method is developed for calculating the thermodynamic properties of such semi-infinite strips. The best bound obtained is λ/$k_B$$T_c$≥0.2459 from a 9×∞ strip, where λ is the basic energy parameter in the problem. By extrapolation, the transition temperature is estimated as λ/$k_B$$T_c$=0.270 02. By direct counting of states for finite squares, the infinite-temperature entropy is obtained by extrapolation as $s_{\infty }$=0.314. A connection between the tiling model and electrical networks is discussed in Appendix A.

We study, within a WKB approximation, the evolution of time-dependent deformations of the needle crystal solution of the two-dimensional symmetric model of solidification. We find that perturbations with fixed small frequencies are initially amplified as they propagate from near the tip down the dendrite but ultimately decay. Localized wave packets behave rather differently; the packet continues to grow exponentially as it moves to arbitrarily large distances from the tip. The relevance of these results to sidebranching of dendrites is discussed.

The time-dependent behavior of sidebranching deformations in the three-dimensional symmetric model of dendritic solidification is studied within a WKB approximation. Localized wave packets generated by pulses in the neighborhood of the tip are found to grow in amplitude and to spread and stretch as they move down the sides of the dendrite. This behavior is shown to imply that noise in the solidifying medium is selectively amplified in such a way as to produce a fluctuating train of sidebranches in qualitative agreement with experimental observations. A rough estimate indicates that purely thermal noise is probably not quite strong enough to fit the data.

We begin with a one-dimensional discrete microscopic model for the ripple phase which is based on the packing competition between molecular head groups and hydrocarbon chains in the bilayer. This model leads to three distinct phases: (1) uniformly tilted chains, as in the low-temperature phase $L_{\beta \mathcal{’}}$; (2) uniform chain spacing with zero tilt, which we associate with the high-temperature phase $L_{\alpha }$; (3) long-wavelength periodic density modulation like the $P_{\beta \mathcal{’}}$ phase. The minimum-energy configuration in the modulated regime is composed of pinched regions of closely spaced chains separated by gaps. In the continuum limit, the bulk free energy of the pinched regions is described by a frustrated ${\phi }^4$ theory, and the gaps give rise to a defect term. The frustration may be thought of in two ways. It produces spontaneous splay of the hydrocarbon chains in the bulk, and it makes a negative contribution to the energy associated with the defect. Viewing the frustration the second way, we find that the modulated phase is preferred when the total energy of the defect becomes sufficiently negative.

An overdamped chain of balls connected by ideal springs in a sinusoidal potential is examined and the response to periodic forcing is discussed from the viewpoint of dynamical systems theory. Discrete multivariate mappings are derived from the coupled differential equations that describe the motion, and the behavior of these mappings is discussed.

A mean-field theory of a class of isotropic, spatially frustrated lattice-model Hamiltonians is constructed. Some general features of the mean-field equations are examined. Analytical techniques for determining the paramagnetic phase boundary and the low-temperature phases in the vicinity of this boundary are discussed. Finally, a numerical approach which has proved to be helpful in solving the mean-field equations is outlined.

We consider one-dimensional diffusion with an absorbing boundary in the context of a model that retains the essential ‘‘missing’’ boundary condition feature that complicates the solution of the Fokker-Planck equation for this problem. The model solution is obtained and some of its features are briefly discussed but our primary purpose is to demonstrate a limiting process that transforms the solution of a related diffusion problem to that for the absorbing-boundary problem. This approach, which we refer to as the absorbing-boundary limit, consists of obtaining the solution for the infinite-space case with the physical space -∞<x<∞ characterized by separate friction coefficients for x≶0. The solution obtained will be a function of these two quantities, ${\beta }_1$ for x>0 and ${\beta }_2$ for x<0, and in the limit ${\beta }_2$→0 describes a process for which the Brownian particle diffuses to x=-∞ when it crosses the origin and does not return to x>0. The solution for x>0 is thus identical to that for the case where the origin is an absorbing ‘‘boundary.’’ This limiting process provides a new method for obtaining a solution to the Fokker-Planck equation with an absorbing-boundary condition and may lead to a result that is in closed form and more transparent than the eigenfunction expansions recently obtained by other means.

We have studied the scaling and shadowing properties of two-dimensional off-lattice ballistic aggregation on a seed. The computer simulations show that the limiting semivertical cone angle is about 15.5°. The density as a function of distance from the seed tends to a constant value showing a basic two-dimensional nature of the aggregates and has a correction with a metadimension of about 0.56. The density as a function of angle near the edges of the cone is found to obey a scaling relation similar to the on-lattice case. The probabilities for the fingers of different lengths which shadow the particle near the edge are determined in the computer experiment and also determined analytically.

A derivation of a general relationship between the frequency- and wave-number-dependent longitudinal quadratic response functions and the three-point dynamical structure function (the Fourier transform of the equilibrium three-point density-density correlations) is presented. This relationship is the full quadratic equivalent, valid for quantum systems of arbitrary degeneracy, of the customary (linear) fluctuation-dissipation theorem. The high-temperature limit reproduces earlier classical results, while its zero-temperature limit is characterized by a piecewise analytic behavior in the (${\omega }_1$${\omega }_2$) plane, generated by the respective dominance of the differently ordered triplets of density operators. There are two main versions of the theorem. In the first the completely symmetrized combination of the three-point functions is expressed in terms on a ‘‘triangle-symmetrized’’ [in the (kω) space] combination of the response functions. In the second ‘‘inverted’’ form, each of the six differently ordered three-point functions is expressed in terms of combinations of response functions, where the triangle symmetry is broken.

We report the results of elastic and quasielastic light scattering measurements on dilute aggregates of colloidal silica. The elastic scattering measurements indicate a fractal dimension of 2.05±0.06, in agreement with previous results, but the quasielastic measurements demonstrate several novel characteristics. First, it is found that the linewidth Γ scales as a fractional power, Γ∼$q^{2.7}$, of the momentum transfer q. Second, the inverse average relaxation time, defined as the integral of the field autocorrelation function, does not scale with the same power of q as the linewidth, implying that the autocorrelation functions cannot be scaled by a single nondimensioned time. Third, ‘‘stretched’’ exponential behavior is found for the long-time behavior of the autocorrelation function. These observations are interpreted in terms of a power-law polydisperse ensemble of aggregate clusters, with a number distribution of the form N(m)∼$m^{\mathrm{-}\tau }$, where τ=1.9–2. Finally, the kinetics of growth are studied and the average radius is found to grow exponentially with time. These results are shown to be consistent, in part, with the predictions of the Smoluchowski equation and with simulations of aggregation.

A method to construct relevant Hilbert subspaces for unbounded operators is developed. The thermodynamical properties of systems described by density matrices built up out of such operators are studied. Edge effects that arise as a consequence of projections onto finite Hilbert subspaces are also carefully analyzed.

A connected-moments expansion (CMX) is constructed for the overlap between the approximate and the exact (but unknown) wave function of the ground state. The CMX series provides approximations to the overlap that do not require the knowledge of the exact energy of either the ground or the first excited state. Moreover, the obtained approximate overlaps have a correct size extensivity. A numerical example is given, demonstrating the performance of the new method.

A new method is presented by which the quantum-mechanical free energy can be approximated quite effectively. This approximation is easy to handle and compares favorably with a recent proposal by Feynman and Kleinert. An extension to a many-particle system is discussed.

A general expression for the critical coupling (in terms of the particle masses which constitute the three-particle system) is derived at which isosceles symmetry breaks down. Application of the ideas to the muon-mesic molecules as well as to the positronium and hydrogenic negative ions is considered.