Table of contents

The intrinsic angular momentum of the cosmological substratum is able to prevent the appearance of the cosmological singularity in the Einstein-Cartan theory. Conditions for this to occur in Bianchi type I cosmologies are given, and several new cosmological models whose anisotropy diminishes with expansion are explicitly constructed.

A recent letter by Lesk (see abstr. A30330 of 1974) purporting to calculate the free energy of a hard-sphere gas is shown to be incorrect.

For n-electron systems with well defined total spin antisymmetric states are constructed by successively coupling the spins associated with each orbital. A second quantized scheme is used and the matrix elements of these states are expressed both for spin-independent and spin-dependent interactions in terms of recoupling coefficients of SU(2). The latter are evaluated to give very simple expressions. As a particular case a simple formula for the matrix elements of generators of U(N) for two-column partitions is obtained.

Some variational methods are considered in which the trial functions used are not required to satisfy prescribed boundary conditions. Applications of these methods are made to a two-body system interacting via a hard-core potential.

The author considers Maxwell's equations in a Schwarzschild space and determine the retarded solutions to order m²/r² of an electric dipole located at the centre of symmetry. The dipole moment p(t) is assumed to be variable in the interval t₁<or=t<or=t₂ and to have the constant values p₁ for t<t₁ and p₂ for t<t₂. It is found that for t to infinity the field tends asymptotically to the static field corresponding to a constant dipole p₂ even in the case p₂ not=p₁. This is due to the fact that the Newman-Penrose conservation laws are valid only in some region of the space-time adjacent to future null-infinity. The formulae for the wavetail (in the region u>t₂) to order m/r are discussed in some detail.

The dipole solution for Maxwell's equations in the Schwarzschild metric is found as a convergent series for r>2m. The validity of this representation by series is proved by a complete study of its convergence and differentiability.

The dimensional regularization technique is used to evaluate one-loop corrections to gravitational self-interaction. The applications of such a scheme contains certain ambiguities which are presented and discussed. Attempts to remove these ambiguities have not yet proved successful.

The classical Heisenberg model, with one lattice and three spin dimensions, has recently been solved for general anisotropy in terms of ellipsoidal wavefunctions. These functions are used here to obtain exact expressions for the pair correlation functions and susceptibility in the three spin directions. Explicit formulae, valid at high temperatures, are derived for these quantities on the basis of known series expansions for ellipsoidal functions and it is shown that these formulae reduce to known results in the partially anisotropic and isotropic cases.

For pt. I, see ibid, vol.8, no.3, 347 (1975). In the first of this pair of papers exact expressions were obtained for the pair correlation functions and susceptibilities of the classical Heisenberg model in terms of ellipsoidal wavefunctions. Here the author examines the low temperature behaviour of these quantities. This necessitates an asymptotic expression for the ellipsoidal functions. The derivation of such an expression follows the method of Langer and is to leading order only. This asymptotic form allows explicit calculation of the eigenvalues of the transfer matrix (to leading order) and hence a discussion of the low temperature behaviour of the correlation functions and susceptibilities.

The statistical, spatial and temporal coherence properties of electromagnetic radiation scattered into the far field by a deep random phase screen are investigated. It is shown that significant departures from Gaussian behaviour can occur even when the phase correlation length is much smaller than the dimensions of the scattering region-a situation in which the central limit theorem might be expected to apply. Formulae are derived relating these departures to elementary properties of the scattering structure, which may therefore be determined by measurement of the fluctuations in the scattered radiation. Application of the results to scattering from very rough surfaces is discussed.

For pt.I see ibid., vol.8, 369 (1975). The authors have studied experimentally the statistical, spatial coherence and temporal coherence properties of non-Gaussian fluctuations in light scattered by a thin layer of liquid crystal (MBBA) in its dynamic scattering state. The results are consistent with the deep phase-screen theory developed in the previous paper. With 20 V applied to the sample, experimental values of the parameters of the model are: mean square phase deviation phi ²=45.6+or-8.0 rad², phase correlation length xi =2.63+or-0.24 mu m and phase coherence time 2.2+or-0.2s. Indications are found that, while phase fluctuations in the emergent wave-front are probably dominant, amplitude fluctuations are not entirely negligible. It is argued, however, that the effects of amplitude fluctuations on the values of the above parameters are probably quite small. Taking a broader view, the results confirm that, in many scattering experiments, detailed information concerning the scattering process can be obtained from measurements in the non-Gaussian regime.

The theory for amplified spontaneous emission is formulated when reflections from the bounding medium are important. The theoretical predictions are compared to previously reported, but quantitatively unexplained, results for the beam divergence of the 3.39 mu m He-Ne system. Good agreement between theory and experiment is obtained.

De Genne's theory (1971) on the Brownian motion of a polymer chain in the presence of fixed obstacles is generalized so as to take into account the concentration of obstacles. The molecular weight dependences of the characteristic relaxation time and the self-diffusion constant of the chain are found to change continuously from de Gennes-type to Rouse's as the concentration of obstacles decreases.

We state and prove a theorem about the fact that B¹-type approximants have reciprocals with different boundary structure from their own.