Dynamics of the mixmaster-type vacuum universe with geometryR×S 3×S 3×S 3

A model of a spatially homogeneous and anisotropic, vacuum universe with geometryR×S ³×S ³×S ³ is studied using a hamiltonian formalism. The formalism is developed by first deriving the hamiltonian for aD-dimensional, mixmaster-type, vacuum universe. The model evolves from an initial Kasner-like state to a final Kasner-like state upon irreversible collapse. The collapse is predicted to be inevitable based on qualitative analysis and numerical calculations verify this behavior. A lower bound of 0.286 is found for the ratio of the contraction rate of the universe long after a Kasner phase transition to the contraction rate long before the transition. Seven of the seventeen theoretically possible qualitatively different compactification schemes are found numerically and tabulated. A subset of all the constraint satisfying initial conditions which leads to three isotropically expanding dimensions and six contracting dimensions is found.     

Some properties of the (ψψ)2 model in two dimensions

We show that the two-dimensional $\text{(}\text{ψ}\text{ψ)}{}^2$ model is, for N = 3, equivalent to the supersymmetric sine-Gordon equation, and for N = 4, equivalent to two decoupled sine-Gordon systems. In addition, we argue that the kinks of this model are isospinors, and we construct some of the higher conservation laws that are responsible for the exact solubility of this system.     

Current algebra theorems for the U(1) “Goldstone boson”

The U(1) problem is reconsidered from the point of view of the $\text{1}\text{N}$ expansion. It is argued that various heuristic ideas about the η′ are valid from this point of view. Current algebra theorems, similar to soft π theorems, are derived for the η′. They are valid to lowest order in $\text{1}\text{N}$.     

Quantization of Newton's constant in certain supergravity theories

We show that the nonlinear sigma model can be coupled to supergravity only if Newton's constant is an integral multiple of 1/F_π².     

Anomalous cross section for photon-photon scattering in gauge theories

We consider the deep inelastic structure functions of the photon in an asymptotically free gauge theory. In contrast to the case of a hadronic target, we find that the shortdistance analysis determines the shape and magnitude and not merely the Q² dependence of the structure functions. The structure functions of the free quark theory are renormalized by finite, calculable factors. For example, at x = 0.1, we find that F₂ will, at large Q², exceed the free quark result by a factor 1.751, while for x = 0.5, F₂ is suppressed asymptotically, relative to the free quark theory, by a factor 0.964, and at x = 0.8, by a factor 0.611.     

Gravitational anomalies

It is shown that in certain parity-violating theories in 4k+2 dimensions, general covariance is spoiled by anomalies at the one-loop level. This occurs when Weyl fermions of $\text{spin}\text{-}\text{1}\text{2}\text{or}\text{-3}\text{2}$ or self-dual antisymmetric tensor fields are coupled to gravity. (For Dirac fermions there is no trouble.) The conditions for anomaly cancellation between fields of different spin is investigated. In six dimensions this occurs in certain theories with a fairly elaborate field content. In ten dimensions there is a unique theory with anomaly cancellation between fields of different spin. It is the chiral n = 2 supergravity theory, which is the low-energy limit of one of the superstring theories. Beyond ten dimensions there is no way to cancel anomalies between fields of different spin.     

Accuracy of the multipole expansion applied to a sphere in a creeping flow parallel to a wall

An example system is studied to discuss precision of the multipoleexpansion, applied to determine forces exerted on particlesby a viscous low-Reynolds-number fluid flow. A single spherein an ambient flow (pure shear, quadratic, and modulated shear)parallel to a close plane wall is considered. Forces and torquesexerted by the ambient flow on a motionless sphere are evaluated.Their precision is determined and related to a multipole orderof the truncation. Similar analysis is performed for a movingsphere with no ambient flow and for a freely moving sphere.Relative motion of the sphere with respect to the wall givesrise to strong lubrication interactions. It is analysed howthese interactions affect accuracy of the pure multipole expansion,and what are the smallest distances where it becomes insufficient.An alternative precise method is applied, in which lubricationexpressions are subtracted from the hydrodynamic forces andtorques, and the residue is evaluated as a fast-convergent seriesof inverse powers of the distance between the sphere centreand the wall. The accuracy of this procedure is carefully analysed.     

The polymer mat: arrested rebound of a compressed polymer layer

Compression of an adsorbed polymer layer distorts its relaxed structure. Surface force measurements from different laboratories show that the return to this relaxed structure after the compression is released can require tens of minutes and that the recovery time can grow rapidly with molecular weight. We argue that the arrested state of the free layer before relaxation can be described as a Guiselin brush structure (O. Guiselin, Europhys. Lett. 17, 225 (1992)), in which the monomer density falls off only weakly with distance from the surface. This brush structure predicts an exponential falloff of the force at large distance with a decay length that varies as the initial compression distance to the 6/5 power. This exponential falloff is consistent with surface force measurements. We propose a relaxation mechanism that accounts for the increase in relaxation time with chain length.     

Kinematically-complete study of pion production by the reaction 1H(p, π+p)n at 800 MeV

The differential cross section d⁵σ/dp₁dΩ₁dΩ₂ has been measured in a kinematically-complete study of the reaction ¹H(p, π⁺p)n at 800 MeV, for several pairs of coplanar angles. The spectra at all observed angle pairs are dominated by the formation of the δ⁺⁺ isobar, with a tendency of forward peaking in the pion angular distribution.