An introductory review of the central ideas in the modern theory of dynamic critical phenomena is followed by a more detailed account of recent developments in the field. The concepts of the conventional theory, mode-coupling, scaling, universality, and the renormalization group are introduced and are illustrated in the context of a simple example—the phase separation of a symmetric binary fluid. The renormalization group is then developed in some detail, and applied to a variety of systems. The main dynamic universality classes are identified and characterized. It is found that the mode-coupling and renormalization group theories successfully explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions, but that a number of discrepancies exist with data at the superfluid transition of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$.

Research in integrated optics has two goals: One is to apply thin-film technology to the formation of optical devices and circuits. The other is the integration of a large number of optical devices on a small substrate, so forming an optical circuit reminiscent of the integrated circuit in microelectronics. The result is a new breed of optical devices in the form of miniature optical waveguides. They include lasers, modulators, switches, detectors, prisms, lenses, and polarizers, and many of them have efficiencies better than their bulk counterparts. Simple integrated optical circuits have also been constructed, and rapidly advancing semiconductor technology indicates that monolithic integrated optical circuits can readily be developed using GaAs-related compounds. In this paper, we review the state-of-the-art of integrated optics and explore new wave phenomena in optical circuits. The specific topics to be discussed are: light-wave couplers and $m$-line spectroscopy, refraction and reflection of light in thin films, normal modes of the uniform, the graded and the metal-clad waveguides, optics in tapered films, theory of corrugated waveguides, and more importantly, physics of various thin-film optical devices and the method of the circuit formation.

This is a short review of recent experimental and theoretical studies of phonon interactions in superfluid helium. Phonon-phonon scattering in helium is strongly influenced by the conservation laws and by the peculiarities of the phonon dispersion relation. Theory predicts that because of these factors the spontaneous decay rate varies dramatically with phonon energy, and experiments have confirmed this prediction. The conservation laws can also be used to show that phonon-phonon collisions are predominatly small-angle scattering. We discuss the influence of this special property of phonon collisions on the hydrodynamics of the phonon gas, and we consider the solutions of the hydrodynamic equations in several situations of experimental interest.

The processes leading to end loss of ions from a mirror machine are reviewed. These include breakdown of adiabaticity, scattering and energy drag by classical collisions, and scattering by unstable fluctuations. Described are the linear theory of those modes thought to be of significance in present and reactor-size plasmas, and those features known of their nonlinear saturation.

Prospect for the discovery of the charged and neutral intermediate vector bosons in high-energy nucleon—(anti)nucleon collisions are examined. Theoretical arguments for the existence of intermediate bosons are reviewed and the anticipated properties are enumerated. Detailed calculations based on the Drell-Yan model are presented for the production cross sections and for the distributions of decay products. On the basis of these computations the requirement r experimental detectors are assessed.

Recent work by K. G. Wilson, A. A. Migdal and others has led to a statistical mechanical treatment of systems of interaction quarks and strings. This work is summarized here. The major topics discussed include boson and fermion variables in statistical mechanics; descriptions of local and gauge symmetries; exact solutions of one-dimensional problems with nearest-neighbor interactions; exact solutions of two dimensional problems with plaquette interactions; Wilson's model of quarks and strings; asymptotic freedom and trapping for this model; the effect of a phase transition in this system; approximate recursion relations of the Migdal form. Finally, all this is put together to give a partial argument for the simultaneous existence of asymptotic freedom and trapping ${\mathrm{O}}_2$ in the quark-string case. Arguments are developed which distinguish this case from the superficially analogous example of quantum electrodynamics.

The theory of nuclear electron capture is reviewed in the light of current understanding of weak interactions. Experimental methods and results regarding capture probabilities, capture ratios, and $\frac{\mathrm{EC}}{{\beta }^{+}}$ ratios are summarized. Radiative electron capture is discussed, including both theory and experiment. Atomic wavefunction overlap and electron exchange effects are covered, as are atomic transitions that accompany nuclear electron capture. Tables are provided to assist the reader in determining quantities of interest for specific cases.

The measurements of the hyperfine structure of free, naturally occurring, alkali atoms are reviewed. The experimental methods are discussed, as are the relationships between hyperfine structure data and other atomic constants.

We review the possible contributions to the muon $g$-factor anomaly, ${\alpha }_{\mu }\equiv \frac{1}{2}(g_{\mu }-2)$ which are potentially significant for a comparison between theory and experiment at present. This includes purely quantum electrodynamic (QED) perturbation theory effects up to eighth order; hadronic effects at fourth and sixth order; and weak interaction effects. From these sources we get a total theoretical contribution ${\alpha }_{\mu }\left(\mathrm{theory}\right)=(1\mathrm{} 165 920.6\pm 12.9)\times {10}^{-9\mathrm{}}$, to be compared with the latest CERN experimental result (Bailey et al., 1975), ${\alpha }_{\mu }\left(\mathrm{experiment}\right)=1\mathrm{} 165 895\pm 27)\times {10}^{-9\mathrm{}}$.

The production of radioactive nuclei during the operation of a light-water reactor is traced, and their decay history is followed. The potential environmental impacts of this waste are calculated and shown to be comparable to those of other materials we produce. Assuming deep burial, it is shown that there are important time delays which prevent the waste from reaching the biosphere in the first few hundred years while its toxicity is decreasing by several orders of magnitude. In the long term, the most important pathway to man was found to be through groundwater into food and water supplies, with consequences calculated to be 0.4 fatalities in ${10}^6$ years from each year of all-nuclear power in U.S. Other pathways considered and found to be less important include meteorites, volcanism, release through ground water to airborne particulate, and human intrusion by drilling and mining for unspecified materials and for salt. For time scales longer than ${10}^6$ years, nuclear power is shown to reduce man's exposure to radiation by consuming uranium. A cost-benefit analysis is developed for surveillance of buried waste. It is shown that buried high-level waste is environmentally much less dangerous than uranium mill tailings.

Liquids exist in a relatively small part of the enormous range of temperatures and pressures existing in the universe. Nevertheless, they are of vital importance for physics and chemistry, for technology, and for life itself. A century of effort since the pioneering work of van der Waals has led to a fairly complete basic understanding of the static and dynamic physicochemical properties of liquids. Advances in statistical mechanics (the fundamental formulations of Gibbs and Boltzmann, integral equations and perturbation theories, computer simulations), in knowledge of intermolecular forces, and in experimental techniques; have all contributed to this. Thirty years ago the very existence of liquids seemed a little mysterious; today one can make fairly precise predictions of the solid-liquid-gas phase diagram and of the microscopic and macroscopic static and dynamic properties of liquids. This paper is a survey, with particular emphasis on equilibrium properties, of the theory which underlies that basic understanding, which is now at least comparable with our understanding of the physics of solids.

A general microscopic and macroscopic theory is developed for systems which are governed by a (linear) master equation. The theory is based on a network representation of the master equation, and the results are obtained mostly by application of some basic theorems of mathematical graph theory. In the microscopic part of the theory, the construction of a steady state solution of the master equation in terms of graph theoretical elements is described (Kirchhoff's theorem), and it is shown that the master equation satisfies a global asymptotic Liapunov stability criterion with respect to this state. The Glansdorff-Prigogine criterion turns out to be the differential version and thus a special case of the global criterion. In the macroscopic part of the theory, a general prescription is given describing macrostates of the systems arbitrarily far from equilibrium in the language of generalized forces and fluxes of nonlinear irreversible thermodynamics. As a particular result, Onsager's reciprocity relations for the phenomenological coefficients are obtained as coinciding with the reciprocity relations of a near-to-equilibrium network.

A fundamental paradox of classical physics is why matter, which is held together by Coulomb forces, does not collapse. The resolution is given here in three steps. First, the stability of atom is demonstrated, in the framework of nonrelativistic quantum mechanics. Next the Pauli principle, together with some facts about Thomas-Fermi theory, is shown, to account for the stability (i.e., saturation) of bulk matter. Thomas-Fermi theory is developed in some detail because, as is also pointed out, it is the asymptotically correct picture of heavy atoms and molecules (in the $Z\to \infty$ limit). Finally, a rigorous version of screening is introduced to account for thermodynamic stability.

Considerable progress has been made during the past five years toward a quantitative understanding of the formation and destruction processes for interstellar molecules. Two areas have been most successful—investigations of the formation process for molecular hydrogen on the surfaces of dust grains and studies of reactions involving positive ions in the gas. Laboratory measurements for ion-molecule reaction rates have provided strong support for the latter. Extensive studies at ultraviolet wavelengths from the Copernicus satellite make possible detailed comparisons between predictions and observations for ${\mathrm{H}}_2$ and other species in the diffuse interstellar gas. These confirm that a hydrogen atom is converted into an ${\mathrm{H}}_2$ molecule at approximately every collision with an interstellar dust grain. In the more dense interstellar gas, observations with radio telescopes provide vast data on complex molecules and have recently identified a number of reactive intermediate species—HC${\mathrm{O}}^{+}$, ${\mathrm{N}}_2$${\mathrm{H}}^{+}$, HNC, CCH—whose presence strongly supports the proposed reaction processes. The quite recent development of laboratory methods to measure the microwave frequencies of reactive molecules and molecular ions has been an essential contribution to these identifications. Observed fractionation of (deuterium/hydrogen) and possibly (carbon-13/carbon-12) in certain interstellar molecules provide additional challenges and information for studies of reactions. Although there is semiquantitative agreement between predictions and observed abundances for a wide range of small molecular species, the tests are sufficiently precise in only a few cases to reach reasonably definitive conclusions. To a large degree this is due to poor knowledge of the physical conditions in the gas where the molecules are located. Certain laboratory data are needed—especially, photodissociation cross sections and radiative lifetimes in the ultraviolet, as well as some charge-transfer and reaction rate coefficients under low temperature/density conditions. Information on surface reactions applicable to the astrophysical situation is also desirable. At present the chief problems for interstellar molecule reactions are understanding the formation of larger molecules (larger than triatomic), and the role of surface reactions on dust grains for molecules other than ${\mathrm{H}}_2$. A lengthy introduction to the interstellar medium is provided for the nonastronomer. The status of information on the basic surface and gas phase processes is reviewed. Finally, the reaction schemes which seem to be of most importance for the major species of small interstellar molecules are discussed and quantitatively compared with observations when possible. Reactions that produce isotope fractionation are treated in some detail.