Since the discovery of superconductivity above 30 K by Bednorz and Müller in the La copper oxide system, the critical temperature has been raised to 90 K in Y${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ and to 110 and 125 K in Bi-based and Tl-based copper oxides, respectively. In the two years since this Nobel-prize-winning discovery, a large number of electronic structure calculations have been carried out as a first step in understanding the electronic properties of these materials. In this paper these calculations (mostly of the density-functional type) are gathered and reviewed, and their results are compared with the relevant experimental data. The picture that emerges is one in which the important electronic states are dominated by the copper $d$ and oxygen $p$ orbitals, with strong hybridization between them. Photon, electron, and positron spectroscopies provide important information about the electronic states, and comparison with electronic structure calculations indicates that, while many features can be interpreted in terms of existing calculations, self-energy corrections ("correlations") are important for a more detailed understanding. The antiferromagnetism that occurs in some regions of the phase diagram poses a particularly challenging problem for any detailed theory. The study of structural stability, lattice dynamics, and electron-phonon coupling in the copper oxides is also discussed. Finally, a brief review is given of the attempts so far to identify interaction constants appropriate for a model Hamiltonian treatment of many-body interactions in these materials.

The blue phases of cholesteric liquid crystals are liquids that exhibit orientational order characterized by crystallographic space-group symmetries. We present here a pedagogical introduction to the current understanding of the equilibrium structure of these phases accompanied by a general overview of major experimental results. Using the Ginzburg-Landau free energy appropriate to the system, we first discuss in detail the character and stability of the usual helical phase of cholesterics, showing that for certain parameter ranges the helical phase is unstable to the appearance of one or more blue phases. The two principal models for the blue phases are two limiting cases of the Ginzburg-Landau theory. We explore each limit and conclude with some general considerations of defects in both models and an exact minimization of the free energy in a curved three-dimensional space.

Diffusion in silicon of elements from columns III and V of the Periodic Table is reviewed in theory and experiment. The emphasis is on the interactions of these substitutional dopants with point defects (vacancies and interstitials) as part of their diffusion mechanisms. The goal of this paper is to unify available experimental observations within the framework of a set of physical models that can be utilized in computer simulations to predict diffusion processes in silicon. The authors assess the present state of experimental data for basic parameters such as point-defect diffusivities and equilibrium concentrations and address a number of questions regarding the mechanisms of dopant diffusion. They offer illustrative examples of ways that diffusion may be modeled in one and two dimensions by solving continuity equations for point defects and dopants. Outstanding questions and inadequacies in existing formulations are identified by comparing computer simulations with experimental results. A summary of the progress made in this field in recent years and of directions future research may take is presented.

Large computing machines have been built from relays, vacuum tubes, and transistors. Strenuous efforts to develop computing technology based on other devices have failed. The relay, vacuum tube, and transistor are three-terminal devices, and the essential physical factors that account for their success are described and used to discuss the reasons for the failure of other devices.

Optical excitation function measurements for electron-atom and electron-ion collisions are reviewed. Sources of experimental error are discussed and, for cases in which adequate documentation is provided, publications are reviewed for accuracy of experimental method. The effects of polarization of the emitted radiation and methods of normalization are considered. The reliability of specific reported data is discussed based on these considerations, on the results of consistency checks, and, where possible, on comparison with other measurements. Data sources for 50 atoms and 20 atomic ions are identified. Comparative plots are presented for cases in which enough data are available: H, $\mathrm{He}(n{}_{}{}^1{}_{}{}^{}S, n{}_{}{}^1{}_{}{}^{}P, n{}_{}{}^1{}_{}{}^{}D, 4{}_{}{}^3{}_{}{}^{}S, 3{}_{}{}^3{}_{}{}^{}P)$, ${\mathrm{He}}^{+}$, Ne, ${\mathrm{Ne}}^{+}$, Ar, ${\mathrm{Ar}}^{+}$, Xe, Li, Na, K, Mg, ${\mathrm{Mg}}^{+}$, Ca, Sr, ${\mathrm{Sr}}^{+}$, Cu, ${\mathrm{Zn}}^{+}$, Cd, Hg, and Mn.

The density distribution arising at the nonlinear stage of gravitational instability is similar to intermittency phenomena in acoustic turbulence. Initially small-amplitude density fluctuations of Gaussian type transform into thin dense pancakes, filaments, and compact clumps of matter. It is perhaps surprising that the motion of self-gravitating matter in the expanding universe is like that of noninteracting matter moving by inertia. A similar process is the distribution of light reflected or refracted from rippled water. The similarity of gravitational instability to acoustic turbulence is highlighted by the fact that late nonlinear stages of density perturbation growth can be described by the Burgers equation, which is well known in the theory of turbulence. The phenomena discussed in this article are closely related to the problem of the formation of large-scale structure of the universe, which is also discussed.

The Riemann problem for fluid flow of real materials is examined. An arbitrary equation of state is allowed, subject only to the physical requirements of thermodynamics. The properties of the isentropes and the shock Hugoniot loci that follow from conditions imposed on the equation of state are reviewed systematically. Important properties of these wave curves are determined by three dimensionless variables characterizing the equation of state: the adiabatic exponent $\gamma$, the Grüneisen coefficient $\Gamma$, and the fundamental derivative $\mathcal{G}$. Standard assumptions on these variables break down near phase transitions. The result is an anomalous wave structure: either shock waves split into multiple waves, or composite waves form. Additional questions related to shock stability and nonuniqueness of the solution of the Riemann problem are discussed.

The concept of transmission of heat by waves is reviewed and interpreted. The notion of an effective thermal conductivity, an effective heat capacity, and relaxation functions for heat and energy is introduced along lines used recently to describe the elastic response of viscous liquids. An annotated bibliography of the literature on heat waves, from the beginning until now, gives a complete or nearly complete survey of the history of this subject.

The authors present a simplified model of helium synthesis in the early universe. The purpose of the model is to explain clearly the physical ideas relevant to the cosmological helium synthesis in a manner that does not overlay these ideas with complex computer calculations. The model closely follows the standard calculation, except that it neglects the small effect of Fermi-Dirac statistics for the leptons. The temperature difference between photons and neutrinos during the period in which neutrons and protons interconvert is also neglected. These approximations permit the expression of neutron-proton conversion rates in a closed form, which agrees to 10% accuracy or better with the exact rates. Using these analytic expressions for the rates, the authors reduce the calculation of the neutron-proton ratio as a function of temperature to a simple numerical integral. They also estimate the effect of neutron decay on the helium abundance. Their result for this quantity agrees well with precise computer calculations. Their semianalytic formulas are used to determine how the predicted helium abundance varies with such parameters as the neutron lifetime, the baryon-to-photon ratio, the number of neutrino species, and a possible electron-neutrino chemical potential.

Empirical evidence for the existence of pair fluctuations in rapidly rotating nuclei in connection with the pair gap is reviewed. The quantities considered are single-particle energies (routhians) and alignments. While the cranked shell model in the presence of static pair correlations provides an accurate description of data at rotational frequencies below the critical frequency corresponding to the collapse of the static pair gap, conspicuous discrepancies are found in the region of and above the pairing phase transition. In particular, a group of excitations is observed displaying lower excitation energies and smaller alignments than those predicted by the cranked shell model. Such excitations can be characterized as behaving as if the correlations induced by the presence of a pairing condensate were not totally obliterated after the "phase transition." A theoretical model, based on the renormalization of the single-particle motion mixed by the coupling to pairing vibrations, is quite successful in explaining the overall trend of the data at rotational frequencies larger than the critical frequency. Smaller alignments and excitation energies are correlated with configurations displaying particle coupling schemes which profit most from fluctuations of the pair gap about its zero equilibrium value. While this model reproduces many of the experimental features, it still overpredicts the alignments by 2-3 units of $\hslash$ in the crossing region. Thus other degrees of freedom (both static and dynamic), e.g., deformations, also must play a role at large rotational frequencies.

Astronomical observations indicate that the cosmological constant is many orders of magnitude smaller than estimated in modern theories of elementary particles. After a brief review of the history of this problem, five different approaches to its solution are described.

This paper is devoted to recent progress made towards the understanding of closed bosonic and fermionic string perturbation theory, formulated in a Lorentz-covariant way on Euclidean space-time. Special emphasis is put on the fundamental role of Riemann surfaces and supersurfaces. The differential and complex geometry of their moduli space is developed as needed. New results for the superstring presented here include the supergeometric construction of amplitudes, their chiral and superholomorphic splitting and a global formulation of supermoduli space and amplitudes.

The adiabatic quantum transport in multiply connected systems is examined. The systems considered have several holes, usually three or more, threaded by independent flux tubes, the transport properties of which are described by matrix-valued functions of the fluxes. The main theme is the differential-geometric interpretation of Kubo's formulas as curvatures. Because of this interpretation, and because flux space can be identified with the multitorus, the adiabatic conductances have topological significance, related to the first Chern character. In particular, they have quantized averages. The authors describe various classes of quantum Hamiltonians that describe multiply connected systems and investigate their basic properties. They concentrate on models that reduce to the study of finite-dimensional matrices. In particular, the reduction of the "free-electron" Schrödinger operator, on a network of thin wires, to a matrix problem is described in detail. The authors define "loop currents" and investigate their properties and their dependence on the choice of flux tubes. They introduce a method of topological classification of networks according to their transport. This leads to the analysis of level crossings and to the association of "charges" with crossing points. Networks made with three equilateral triangles are investigated and classified, both numerically and analytically. Many of these networks turn out to have nontrivial topological transport properties for both the free-electron and the tight-binding models. The authors conclude with some open problems and questions.

After a period of initial confusion, we now seem to understand in some detail why a star like Sanduleak -69° 202 gave rise to a supernova like 1987A. The detection of the neutrino burst produced at core collapse has confirmed basic ideas of Type-II supernova causality and energetics (without being able to distinguish prompt from delayed shock ejection). Constraints on the nature of the neutrinos themselves confirm or extend laboratory limits on, and conventional theory for, rest mass, magnetic moment, etc. The unusual early light curve and spectra turn out to be a natural result of core collapse when the star was compact and blue, after passing through a red, extended phase (confirmed by evidence for mixing and mass loss characteristic of red supergiants). Synthesis of about $0.07M_{\odot }$ of ${\mathrm{Ni}}^{56}$ (as was previously suspected in SNII's with exponentially tailed light curves) has been revealed by a similar light curve and by an infrared line, gamma rays, and hard x rays, all widely believed to reflect the presence and decay of ${\mathrm{Ni}}^{56}$ to ${\mathrm{Co}}^{56}$ to ${\mathrm{Fe}}^{56}$. A number of puzzles remain concerning unexpected variable soft-x-ray emission, a possible speckle companion, and evidence for extensive mixing, fragmentation, and filamentation. Most of the lessons still to be learned from 1987A probably pertain to the detailed (three-dimensional) structure and composition of evolved massive stars rather than to the basic physics of Type-II supernovae.

In many materials with a highly anisotropic band structure, electron-phonon interactions lead to a novel type of ground state called the charge-density wave. The condensate is pinned to the underlying lattice by impurities and by boundary effects, but can, even for small electric fields, carry current in a fashion originally envisioned by Fröhlich. This review discusses some of the underlying theories and the main experimental observations on this new collective transport phenomenon. The frequency- and electric-field-dependent conductivity, current oscillations, electric-field-dependent transport coefficients and elastic properties, together with nuclear-magnetic-resonance experiments, provide clear evidence for a translational motion of the condensate. Various theories, involving classical and quantum-mechanical concepts, are able to account for a broad variety of experimental findings, which were also made in the presence of combined dc and ac fields.

The screening effects in fluid phases of charged particles give rise to a variety of exact sum rules for their correlation functions. Some of them have been known for a long time, while others have been derived more recently—in particular, for nonuniform fluids. A presentation of these sum rules for static and time-displaced, classical or quantum-mechanical correlations is given from a unifying viewpoint: they appear as consistency relations imposed by the long range of the Coulomb force in the equilibrium or dynamical equations. The cluster properties and the fluctuations of electrical quantities are also discussed.

The authors report detailed experiments and comparison with first-principle theoretical calculation of the diffraction of cold neutrons ($\lambda \approx 2$ nm) at single- and double-slit assemblies of dimensions in the 20-100 μm range. Their experimental results show all predicted features of the diffraction patterns in great detail. Particularly, their double-slit diffraction experiment is its most precise realization hitherto for matter waves.

Self-localized nonlinear excitations (solitons, polarons, and bipolarons) are fundamental and inherent features of quasi-one-dimensional conducting polymers. Their signatures are evident in many aspects of the physical and chemical properties of this growing class of novel materials. As a result, these polymers represent an opportunity for exploring the novel phenomena associated with topological solitons and their linear confinement which results from weakly lifting the ground-state degeneracy. The authors review the theoretical models that have been developed to describe the physics of polyacetylene and related conducting polymers and summarize the relevant experimental results obtained for these materials. An attempt is made to assess the validity of the soliton model of polyacetylene and its generalization to related systems in which the ground-state degeneracy has been lifted.