Table of contents

This review describes the evolution of stars during the period that starts just after formation in interstellar clouds and ends at the point of stabilization on the main sequence where nuclear reactions begin to provide the entire energy supply. During this pre-main-sequence phase the star shines at the expense of its gravitational potential energy. At the earlier stages this energy is released rapidly as the star experiences hydrodynamic collapse; later on the star contracts slowly through a series of states of quasihydrostatic equilibrium.

The initial-boundary-value problem that must be solved to obtain the structure of a star as a function of time is discussed. The equations have been solved numerically for a wide range of stellar masses during both the hydrostatic and hydrodynamic phases, under the assumption of spherical symmetry with neglect of rotational or magnetic effects. The character of these solutions is described, with particular attention given to the effect upon the results of the assumed initial conditions. Mass loss has been investigated in theoretical calculations; its short-term effects are undoubtedly important but observational evidence indicates that a star ejects a negligible fraction of its total mass during pre-main-sequence evolution.

The theoretical results are subject to a number of observational tests. The observations which are discussed include (i) the properties of T Tauri stars, (ii) the colour-magnitude diagrams of young clusters, (iii) the abundances of the rare light nuclei, particularly lithium, and (iv) the properties of the `infrared' stars. Calculations of evolution during the quasistatic contraction are found to be generally consistent with the observational results. However, information about stars in the hydrodynamic phase of evolution is difficult to obtain and is controversial. The observations of a number of objects which have been identified as protostars are reviewed.

Inclusion of the effects of rotation in calculations of pre-main-sequence evolution presents a difficult numerical problem, and relevant observational material is very scarce. Some recent progress has been made; in particular, numerical work has strengthened the hypothesis that close binary systems are formed by fission of a rapidly rotating single star. Rotation must be of dominant importance during the earliest phases of evolution just after star formation. Future work on this problem is essential to an understanding of the formation of the solar system.

This review was completed in January 1972.

This is a brief and elementary report on recent structural studies on nucleic acids, polysaccharides and proteins in a historical perspective. Molecular size, shape and conformation are considered in relation to function. Progress in the sequencing of amino acid residues in proteins and in the determination of the nucleotide sequences in the macromolecules of nucleic acids is mentioned. The total syntheses of some simple nucleic acids and proteins are described. The x ray crystallography is emphasized in the determination of the complete three-dimensional structure of globular proteins. Optical rotatory dispersion and circular dichroism are reviewed as useful methods in the study of conformational transitions in solution, and some previously unpublished work from our laboratory is mentioned. The significance of the structural aspects of the macromolecules in their biological roles is considered briefly.

This review was completed in December 1971.

A detailed description is given of certain results of domain structure theory which have been obtained recently and which have not, so far, been treated in monographs or reviews. A large part of the article consists of an analysis of the fundamentals of the theory; the properties of domain structures which are independent of those of the model are then considered in detail. Domain structures in uniaxial and cubic ferromagnets serve as practical examples; experimental results are given simply by way of illustration. Certain generally accepted ideas are shown to be mistaken and are criticized here. This criticism appears to be necessary because the ideas in question are widespread and are given in many text books.

Observational data accumulated over the past decade have considerably narrowed down the choice of proposals for grain models. Mixtures of particles composed of refractory species such as graphite, silicates, quartz and iron appear likely. Such particles may form in a wide range of astronomical situations, for example, cool stars, protostars and supernovae explosions. Dust grains are responsible for infrared radiation in galactic sources, and also play an important role in the synthesis of interstellar molecules.

This paper describes the application to three areas of physics of computer programs that carry out formal algebraic manipulation. The application areas discussed are celestial mechanics, general relativity and quantum electrodynamics. The paper describes typical problems from each of these disciplines which can be solved using algebraic manipulative systems and presents sample programs for the solution of these problems using several algebra systems. For each discipline a review of published work acknowledging the use of algebra programs is presented and the most advanced applications are discussed in detail. In particular the Lie transform, Petrov classification and Kahane's simplification procedure are reviewed from the standpoint of algebra programs.

A number of simple examples are used to introduce the reader to the capabilities of an algebra program and a brief review of the technical problems of algebraic manipulation is given. Further applications of such systems to mathematics, chemistry and engineering are briefly mentioned in the text and relevant work is referenced in the bibliography but the main emphasis is placed on applications in theoretical physics. However, the simple examples indicate, and the applications in the physical sciences confirm, that algebra systems are capable of exploitation over a much wider area than is covered in the present review.

This review was completed in December 1971.

We review various methods of deriving expressions for quantum-mechanical quantities in the limit when hslash is small (in comparison with the relevant classical action functions). To start with we treat one-dimensional problems and discuss the derivation of WKB connection formulae (and their reversibility), reflection coefficients, phase shifts, bound state criteria and resonance formulae, employing first the complex method in which the classical turning points are avoided, and secondly the method of comparison equations with the aid of which uniform approximations are derived, which are valid right through the turningpoint regions. The special problems associated with radial equations are also considered. Next we examine semiclassical potential scattering, both for its own sake and also as an example of the three-stage approximation method which must generally be employed when dealing with eigenfunction expansions under semiclassical conditions, when they converge very slowly. Finally, we discuss the derivation of semiclassical expressions for Green functions and energy level densities in very general cases, employing Feynman's path-integral technique and emphasizing the limitations of the results obtained. Throughout the article we stress the fact that all the expressions obtained involve quantities characterizing the families of orbits in the corresponding purely classical problems, while the analytic forms of the quantal expressions depend on the topological properties of these families.

This review was completed in February 1972.

This review is concerned with the observational data on pulsars, and the interpretations which can be made directly from them.

Introductory sections describe the discovery of the first pulsars, the search techniques now in use, the theory of neutron stars, and the relation between the Crab nebula pulsar and the nebula itself. A general description of the pulse observations, with a discussion of the accurate timing, leads to a detailed account of the radio observations, and particularly the pulse shapes and polarizations. Scintillation and Faraday rotation measurements are discussed, leading to a description of the ionized interstellar medium and the galactic magnetic field, and to the suggestion that pulsars have a high velocity relative to interstellar gas.

The descriptions of pulse shapes and polarizations are then related to various geometrical theories of the location of emitting regions on a rotating neutron star. The beaming mechanism and the emission mechanism are discussed in the light of these geometrical considerations.

Finally, the population of the pulsars within the galaxy is discussed in relation to the probable association between pulsars and the supernova remnants.

Comprehensive tables of positions, periods and other characteristics of all pulsars known in early 1972 are presented, with references.