We study the support (i.e. the set of visited sites) of a t-step random walk on a two-dimensional square lattice in the large t limit. A broad class of global properties, M(t), of the support is considered, including for example the number, S(t), of its sites; the length of its boundary; the number of islands of unvisited sites that it encloses; the number of such islands of given shape, size, and orientation; and the number of occurrences in space of specific local patterns of visited and unvisited sites. On a finite lattice we determine the scaling functions that describe the averages, (M) over bar(t), on appropriate lattice size-dependent time scales. On an infinite lattice we first observe that the (M) over bar(t) all increase with t as similar to t/log(k), where k is an M-dependent positive integer. We then consider the class of random processes constituted by the fluctuations around average Delta M(t). We show that, to leading order as t gets large,these fluctuations are all proportional to a single universal random process, eta(t), normalized to <(eta(2))over bar>(t) = 1. For t --> infinity the probability law of eta(t) tends to that of Varadhan's renormalized local time of self-intersections. An implication is that in the long time limit all Delta M(t) are proportional to Delta S(t).

We investigate the random sequential adsorption of hard discs and hard aligned squares onto a plane, by a new series expansion method that we previously devised for a lattice. The method yields sequences of increasing lower bounds for the time-dependent covering fraction Theta(t). These bounds have non-trivial limit values for t --> infinity, i.e. for the saturated state. Hypercubes and an analytic continuation in the dimension D around D = 0 are also considered. Numerical results are given for the lowest orders in the series.

We present a new series-expansion method for the analysis of the covering fraction Theta in a random sequential adsorption process with nearest-neighbour exclusion on a lattice. It is the first method to yield sequences of increasing lower bounds and decreasing upper bounds on Theta . It is illustrated by numerical calculations for the hexagonal lattice.

It is shown that the quantum-mechanical spin-correlation function of the photon pairs emitted in atomic cascade experiments can be obtained by a limiting process from a local realistic theory which is symmetric between the analyzers.

It is shown that a necessary condition for objective local theories to be equivalent to quantum mechanics in correlation experiments in the existence of a dissymmetry between analyzers or, alternately, a space anisotropy. No supplementary assumption is made about detection probabilities when the variables of the local theory all lie in the plane of the analyzers. The proof extends to three-dimensional variables if one supposes the detection process to be free of instabilities.

A simple hidden-variable model of the Einstein-Podolsky-Rosen experiment with spin one-half particles and Stern-Gerlach magnets is considered. It is shown that a local dependence of the hidden-variable probability distribution on the vector potential of the magnets can, under certain conditions, lead to the same predictions as quantum mechanics.

Infinite momentum frame techniques are used to estimate the value of the chiral symmetry breaking parameter in the quark model of the pseudoscalar mesons.

Infinite momentum frame techniques are shown to imply the validity of the Schwinger formula for meson nonets and the Gell-Mann-Oakes-Renner value for the chiral symmetry breaking parameter. The nucleon σ-term problem is discussed.

The kinetics of high-energy particles produced along the boundary of the matter- antimatter emulsion of a symmetric universe during the radiative period is analyzed. It is shown that there exists a pressure discontinuity across the boundary which is of the Laplace--Kelvin form, thus implying the existence of a coalescence effect. The kinetics of thermal photons is also studied and hydrodynamical equations are derived for the radiation and plasma components. The anninilation rate at the boundary is computed and the rate of growth of the emulsion with time is derived by averaging over a large volume. The mean mass of galaxies is roughly estimated and found to be comparable with the observed value, which proved the efficiency of the coalescence process. No hydrodynamical instability or large scale turbulence occurs during the radiative period, and the effect of small scale turbulence is found to be negligible. Magnetic field effects have not been investigated although they may become impontant after recombination. The above results remain essentially valid whatever the initial mechanism for matter- antimatter separation. (auth) In chemistry division annual report, July 1971-June 1972. Content of /sup 236/U and /sup 237/Np in lunar samples was determined. Data from trace studies on lunar samplesmore » have been published elsewhere. Studies on the mineralogy of meteorites and lunar, the origin of organic matter in the early solar system, and archaeological problems are summarized. (JGB)« less

IT has been claimed recently1 that some redshifts can be explained by considering a new type of process in which the incident photon scatters inelastically on the 3K radiation to give four less energetic photons. The Lagrangian responsible for the interaction is taken as Λ(AμAμ)2 and the process is considered in the second order only to account for the necessary strong peaking of the cross-section (see Fig. 1). Here we describe the detailed calculation of this process.

The strong-interaction energy shift in the protonium atom is estimated and shown to be a possible test for the existence of a phase transition in the high-energy black-body radiation.

A new estimate of the temperature of the matter-antimatter phase transition in the black-body radiation is given using the theoretical nucleon-antinucleon phase-shifts computed in a previous work.

The OBE model for NN elastic scattering is improved by including inelasticity a phenomenological level in a pure S-matrix formulation. In this way it is possible to find the π and η poles at their physical masses. The corresponding phase-shifts are computed and shown to be remarkably independent of the inelasticiy parameters.

The method of Padé approximants is worked out numerically for the case of a Yukawa potential to find bound states and resonances. The calculation is performed to the sixth order of the perturbation series. An interesting result about the unitarity properties of non-diagonal approximants is proved. Some insight can be obtained in the way this method works in relativistic field theory, especially in connection with left-hand singularities.

If there are infinitely rising Regge trajectories, the asymptotic behaviour of the Regge-pole terms in thes- andt-channels cannot be compatible with each other in the whole (s, t) plane. Thus the background integral cannot be neglected asymptotically if crossing symmetry is to be valid. As a consequence of this, there does not remain any restriction either on the rate of increase of possible rising Regge trajectories except possibly a lower bound in √s or on the behaviour of the residue functions.

It is shown that the problems of daughter trajectories, conspiracy, and evasion, are closely related to the existence of fixed poles in angular momentum. If one has some reason to discard fixed poles, then daughters, conspirators or vanishing residues, occur. This is obtained by assuming the scattering amplitudebelow threshold to be given by a dispersion integral on the Regge behaviourabove threshold.