Normalization of the covariant three-body bound state vertex function

The normalization condition for the relativistic three nucleon Bethe-Salpeter and Gross bound state vertex functions is derived, for the first time, directly from the three body wave equations. It is also shown that the relativistic normalization condition for the two body Gross bound state vertex function is identical to the requirement that the bound state charge be conserved, proving that charge is automatically conserved by this equation.Comment: 24 pages, 9 figures, published version, minor typos correcte

Analysis of a unidirectional composite containing broken fibers and matrix damage

An analytical solution is developed for the determination of the stresses and displacements in a unidirectional fiber-reinforced composite containing an arbitrary number of broken fibers as well as longitudinal yielding and splitting of the matrix. The solution is developed using a materials-modeling approach which is based on a shear-lag stress transfer mechanism. The equilibrium equation in the axial direction gives a pair of integral equations which are solved numerically. Excellent agreement is shown to exist between the solution and experimental results for notched unidirectional boron/aluminum laminates without splitting. For brittle matrix composites (i.e. epoxy) equally good results are indicated for both matrix yielding and splitting. For yielding without splitting the fracture strength depends on crack length while for large splitting it is crack length independent

Quark-Antiquark Bound States in the Relativistic Spectator Formalism

The quark-antiquark bound states are discussed using the relativistic spectator (Gross) equations. A relativistic covariant framework for analyzing confined bound states is developed. The relativistic linear potential developed in an earlier work is proven to give vanishing meson$\to$ $q+\bar{q}$ decay amplitudes, as required by confinement. The regularization of the singularities in the linear potential that are associated with nonzero energy transfers (i.e. $q^2=0,q^{\mu}\neq0$) is improved. Quark mass functions that build chiral symmetry into the theory and explain the connection between the current quark and constituent quark masses are introduced. The formalism is applied to the description of pions and kaons with reasonable results.Comment: 31 pages, 16 figure

Relativistic calculation of the triton binding energy and its implications

First results for the triton binding energy obtained from the relativistic spectator or Gross equation are reported. The Dirac structure of the nucleons is taken into account. Numerical results are presented for a family of realistic OBE models with off-shell scalar couplings. It is shown that these off-shell couplings improve both the fits to the two-body data and the predictions for the binding energy.Comment: 5 pages, RevTeX 3.0, 1 figure (uses epsfig.sty

Theory of ice premelting in porous media

Premelting describes the confluence of phenomena that are responsible for the stable existence of the liquid phase of matter in the solid region of its bulk phase diagram. Here we develop a theoretical description of the premelting of water ice contained in a porous matrix, made of a material with a melting temperature substantially larger than ice itself, to predict the amount of liquid water in the matrix at temperatures below its bulk freezing point. Our theory combines the interfacial premelting of ice in contact with the matrix, grain boundary melting in the ice, and impurity and curvature induced premelting, the latter occurring in regions which force the ice-liquid interface into a high curvature configuration. These regions are typically found at points where the matrix surface is concave, along contact lines of a grain boundary with the matrix, and in liquid veins. Both interfacial premelting and curvature induced premelting depend on the concentration of impurities in the liquid, which, due to the small segregation coefficient of impurities in ice are treated as homogeneously distributed in the premelted liquid. Our principal result is an equation for the fraction of liquid in the porous medium as a function of the undercooling, which embodies the combined effects of interfacial premelting, curvature induced premelting, and impurities. The result is analyzed in detail and applied to a range of experimentally relevant settings.Comment: 14 pages, 10 figures, accepted for publication in Physical Review

The String Calculation of QCD Wilson Loops on Arbitrary Surfaces

Compact string expressions are found for non-intersecting Wilson loops in SU(N) Yang-Mills theory on any surface (orientable or nonorientable) as a weighted sum over covers of the surface. All terms from the coupled chiral sectors of the 1/N expansion of the Wilson loop expectation values are included.Comment: 10 pages, LaTeX, no figure

Strings and Branes in Nonabelian Gauge Theory

It is an old speculation that SU(N) gauge theory can alternatively be formulated as a string theory. Recently this subject has been revived, in the wake of the discovery of D-branes. In particular, it has been argued that at least some conformally invariant cousins of the theory have such a string representation. This is a pedagogical introduction to these developments for non-string theorists. Some of the existing arguments are simplified.Comment: Reference adde

Calculating the Rest Tension for a Polymer of String Bits

We explore the application of approximation schemes from many body physics, including the Hartree-Fock method and random phase approximation (RPA), to the problem of analyzing the low energy excitations of a polymer chain made up of bosonic string bits. We accordingly obtain an expression for the rest tension $T_0$ of the bosonic relativistic string in terms of the parameters characterizing the microscopic string bit dynamics. We first derive an exact connection between the string tension and a certain correlation function of the many-body string bit system. This connection is made for an arbitrary interaction potential between string bits and relies on an exact dipole sum rule. We then review an earlier calculation by Goldstone of the low energy excitations of a polymer chain using RPA. We assess the accuracy of the RPA by calculating the first order corrections. For this purpose we specialize to the unique scale invariant potential, namely an attractive delta function potential in two (transverse) dimensions. We find that the corrections are large, and discuss a method for summing the large terms. The corrections to this improved RPA are roughly 15\%.Comment: 44 pages, phyzzx, psfig required, Univ. of Florida preprint, UFIFT-HEP-94

Multi-phonon scattering and Ti-induced hydrogen dynamics in sodium alanate

We use ab initio methods and neutron inelastic scattering (NIS) to study the structure, energetics, and dynamics of pure and Ti-doped sodium alanate (NaAlH_4), focusing on the possibility of substitutional Ti doping. The NIS spectrum is found to exhibit surprisingly strong and sharp two-phonon features. The calculations reveal that substitutional Ti doping is energetically possible. Ti prefers to substitute for Na and is a powerful hydrogen attractor that facilitates multiple Al--H bond breaking. Our results hint at new ways of improving the hydrogen dynamics and storage capacity of the alanates.Comment: 5 pages, with 4 postscript figures embedded. Uses REVTEX4 and graphicx macro