Preliminary Results of Micropetrographic Investigation of Enigmatic Volcanic Ash Material in the Upper Cretaceous Austin Chalk of Central and South Texas

Bureau of Economic Geolog

Improving lattice perturbation theory

Lepage and Mackenzie have shown that tadpole renormalization and systematic improvement of lattice perturbation theory can lead to much improved numerical results in lattice gauge theory. It is shown that lattice perturbation theory using the Cayley parametrization of unitary matrices gives a simple analytical approach to tadpole renormalization, and that the Cayley parametrization gives lattice gauge potentials gauge transformations close to the continuum form. For example, at the lowest order in perturbation theory, for SU(3) lattice gauge theory, at $\beta=6,$ the `tadpole renormalized' coupling $\tilde g^2 = {4\over 3} g^2,$ to be compared to the non-perturbative numerical value $\tilde g^2 = 1.7 g^2.$Comment: Plain TeX, 8 page

New Integrable Systems from Unitary Matrix Models

We show that the one dimensional unitary matrix model with potential of the form $a U + b U^2 + h.c.$ is integrable. By reduction to the dynamics of the eigenvalues, we establish the integrability of a system of particles in one space dimension in an external potential of the form $a \cos (x+\alpha ) + b \cos ( 2x +\beta )$ and interacting through two-body potentials of the inverse sine square type. This system constitutes a generalization of the Sutherland model in the presence of external potentials. The positive-definite matrix model, obtained by analytic continuation, is also integrable, which leads to the integrability of a system of particles in hyperbolic potentials interacting through two-body potentials of the inverse hypebolic sine square type.Comment: 13 page

Revisiting Mississippian Barnett Shale: Lithological and Geochemical Control on Varied Reservoir Heterogeneity and Fluid Saturation from Late Oil to Dry Gas Window, Fort Worth Basin, Texas

Bureau of Economic Geolog

New exact solutions for the discrete fourth Painlev\'e equation

In this paper we derive a number of exact solutions of the discrete equation x_{n+1}x_{n-1}+x_n(x_{n+1}+x_{n-1})= {-2z_nx_n^3+(\eta-3\delta^{-2}-z_n^2)x_n^2+\mu^2\over (x_n+z_n+\gamma)(x_n+z_n-\gamma)},\eqno(1) where $z_n=n\delta$ and $\eta$, $\delta$, $\mu$ and $\gamma$ are constants. In an appropriate limit (1) reduces to the fourth \p\ (PIV) equation {\d^2w\over\d z^2} = {1\over2w}\left({\d w\over\d z}\right)^2+\tfr32w^3 + 4zw^2 + 2(z^2-\alpha)w +{\beta\over w},\eqno(2) where $\alpha$ and $\beta$ are constants and (1) is commonly referred to as the discretised fourth Painlev\'e equation. A suitable factorisation of (1) facilitates the identification of a number of solutions which take the form of ratios of two polynomials in the variable $z_n$. Limits of these solutions yield rational solutions of PIV (2). It is also known that there exist exact solutions of PIV (2) that are expressible in terms of the complementary error function and in this article we show that a discrete analogue of this function can be obtained by analysis of (1).Comment: Tex file 14 page

A Matrix Integral Solution to [P,Q]=P and Matrix Laplace Transforms

In this paper we solve the following problems: (i) find two differential operators P and Q satisfying [P,Q]=P, where P flows according to the KP hierarchy \partial P/\partial t_n = [(P^{n/p})_+,P], with p := \ord P\ge 2; (ii) find a matrix integral representation for the associated \t au-function. First we construct an infinite dimensional space {\cal W}=\Span_\BC \{\psi_0(z),\psi_1(z),... \} of functions of z\in\BC invariant under the action of two operators, multiplication by z^p and A_c:= z \partial/\partial z - z + c. This requirement is satisfied, for arbitrary p, if \psi_0 is a certain function generalizing the classical H\"ankel function (for p=2); our representation of the generalized H\"ankel function as a double Laplace transform of a simple function, which was unknown even for the p=2 case, enables us to represent the \tau-function associated with the KP time evolution of the space \cal W as a ``double matrix Laplace transform'' in two different ways. One representation involves an integration over the space of matrices whose spectrum belongs to a wedge-shaped contour \gamma := \gamma^+ + \gamma^- \subset\BC defined by \gamma^\pm=\BR_+\E^{\pm\pi\I/p}. The new integrals above relate to the matrix Laplace transforms, in contrast with the matrix Fourier transforms, which generalize the Kontsevich integrals and solve the operator equation [P,Q]=1.Comment: 27 pages, LaTeX, 1 figure in PostScrip

Strong coupling expansion of chiral models

A general precedure is outlined for an algorithmic implementation of the strong coupling expansion of lattice chiral models on arbitrary lattices. A symbolic character expansion in terms of connected values of group integrals on skeleton diagrams may be obtained by a fully computerized approach.Comment: 2 pages, PostScript file, contribution to conference LATTICE '9

K-Theory and S-Duality: Starting Over from Square 3

Recently Maldacena, Moore, and Seiberg (MMS) have proposed a physical interpretation of the Atiyah-Hirzebruch spectral sequence, which roughly computes the K-homology groups that classify D-branes. We note that in IIB string theory, this approach can be generalized to include NS charged objects and conjecture an S-duality covariant, nonlinear extension of the spectral sequence. We then compute the contribution of the MMS double-instanton configuration to the derivation d_5. We conclude with an M-theoretic generalization reminiscent of 11-dimensional E_8 gauge theory.Comment: 27 pages, 3 figure

Stability of Schottky and Ohmic Au Nanocatalysts to ZnO Nanowires

Manufacturable nanodevices must now be the predominant goal of nanotechnological research to ensure the enhanced properties of nanomaterials can be fully exploited and fulfill the promise that fundamental science has exposed. Here, we test the electrical stability of Au nanocatalyst-ZnO nanowire contacts to determine the limits of the electrical transport properties and the metal-semiconductor interfaces. While the transport properties of as-grown Au nanocatalyst contacts to ZnO nanowires have been well-defined, the stability of the interfaces over lengthy time periods and the electrical limits of the ohmic or Schottky function have not been studied. In this work, we use a recently developed iterative analytical process that directly correlates multiprobe transport measurements with subsequent aberration-corrected scanning transmission electron microscopy to study the electrical, structural, and chemical properties when the nanowires are pushed to their electrical limits and show structural changes occur at the metal-nanowire interface or at the nanowire midshaft. The ohmic contacts exhibit enhanced quantum-mechanical edge-tunneling transport behavior because of additional native semiconductor material at the contact edge due to a strong metal-support interaction. The low-resistance nature of the ohmic contacts leads to catastrophic breakdown at the middle of the nanowire span where the maximum heating effect occurs. Schottky-type Au-nanowire contacts are observed when the nanowires are in the as-grown pristine state and display entirely different breakdown characteristics. The higher-resistance rectifying I-V behavior degrades as the current is increased which leads to a permanent weakening of the rectifying effect and atomic-scale structural changes at the edge of the Au interface where the tunneling current is concentrated. Furthermore, to study modified nanowires such as might be used in devices the nanoscale tunneling path at the interface edge of the ohmic nanowire contacts is removed with a simple etch treatment and the nanowires show similar I-V characteristics during breakdown as the Schottky pristine contacts. Breakdown is shown to occur either at the nanowire midshaft or at the Au contact depending on the initial conductivity of the Au contact interface. These results demonstrate the Au-nanowire structures are capable of withstanding long periods of electrical stress and are stable at high current densities ensuring they are ideal components for nanowire-device designs while providing the flexibility of choosing the electrical transport properties which other Au-nanowire systems cannot presently deliver

Covariant Harmonic Supergraphity for N = 2 Super Yang--Mills Theories

We review the background field method for general N = 2 super Yang-Mills theories formulated in the N = 2 harmonic superspace. The covariant harmonic supergraph technique is then applied to rigorously prove the N=2 non-renormalization theorem as well as to compute the holomorphic low-energy action for the N = 2 SU(2) pure super Yang-Mills theory and the leading non-holomorphic low-energy correction for N = 4 SU(2) super Yang-Mills theory.Comment: 17 pages, LAMUPHYS LaTeX, no figures; based on talks given by I. Buchbinder and S. Kuzenko at the International Seminar ``Supersymmetries and Quantum Symmetries'', July 1997, Dubna; to be published in the proceeding