Critical Behaviour of a Fermionic Random Matrix Model at Large-N

We study the large-$N$ limit of adjoint fermion one-matrix models. We find one-cut solutions of the loop equations for the correlators of these models and show that they exhibit third order phase transitions associated with $m$-th order multi-critical points with string susceptibility exponents $\gamma_{\rm str}=-1/m$. We also find critical points which can be interpreted as points of first order phase transitions, and we discuss the implications of this critical behaviour for the topological expansion of these matrix models.Comment: 14 pages LaTeX; UBC/S-94/

Loop operators and S-duality from curves on Riemann surfaces

We study Wilson-'t Hooft loop operators in a class of N=2 superconformal field theories recently introduced by Gaiotto. In the case that the gauge group is a product of SU(2) groups, we classify all possible loop operators in terms of their electric and magnetic charges subject to the Dirac quantization condition. We then show that this precisely matches Dehn's classification of homotopy classes of non-self-intersecting curves on an associated Riemann surface--the same surface which characterizes the gauge theory. Our analysis provides an explicit prediction for the action of S-duality on loop operators in these theories which we check against the known duality transformation in several examples.Comment: 41 page

Lectures on the Asymptotic Expansion of a Hermitian Matrix Integral

In these lectures three different methods of computing the asymptotic expansion of a Hermitian matrix integral is presented. The first one is a combinatorial method using Feynman diagrams. This leads us to the generating function of the reciprocal of the order of the automorphism group of a tiling of a Riemann surface. The second method is based on the classical analysis of orthogonal polynomials. A rigorous asymptotic method is established, and a special case of the matrix integral is computed in terms of the Riemann $\zeta$-function. The third method is derived from a formula for the $\tau$-function solution to the KP equations. This method leads us to a new class of solutions of the KP equations that are \emph{transcendental}, in the sense that they cannot be obtained by the celebrated Krichever construction and its generalizations based on algebraic geometry of vector bundles on Riemann surfaces. In each case a mathematically rigorous way of dealing with asymptotic series in an infinite number of variables is established

The pervasive presence of oxygen in ZrC

Based on the recent interest in oxy-carbide materials in catalysis, we employ a thin film model concept to highlight that variation of key reaction parameters in the reactive magnetron sputtering of zirconium carbide films (sputtering power, template temperature or reactive plasma environment) under realistic preparation and application conditions often results in zirconium oxy-carbide films of varying stoichiometry. The composition of the films grown on silicon wafers and in vacuo - cleaved NaCl (001) single crystal facets was confirmed by depth profiling X-ray photoelectron spectroscopy and electron microscopy analysis. A correlation between methane-to-argon ratio, excess carbon and template temperature with elemental composition emphasizes the exclusive presence of oxygen-containing zirconium carbides. To generalize the approach, we also show that embedding of highly ordered Cu particles with uniform sizes in zirconium oxy-carbide matrices yields well-defined metal / oxy-carbide interfaces. As the presence of an oxy-carbide and its reactivity has been inextricably linked to enhanced activity and selectivity in a variety of processes, including hydrogenation, oxidation or reduction reactions, our model thin film approach provides the necessary well-defined catalysts to derive mechanistic details and to study the decomposition/re-carburization cycles of oxy-carbides. We have exemplified the concept for zirconium oxy-carbide, but deliberate extension to similar systems is easily possible

Topological closed-string interpretation of Chern-Simons theory

The exact free energy of SU($N$) Chern-Simons theory at level $k$ is expanded in powers of $(N+k)^{-2}.$ This expansion keeps rank-level duality manifest, and simplifies as $k$ becomes large, keeping $N$ fixed (or vice versa)---this is the weak-coupling (strong-coupling) limit. With the standard normalization, the free energy on the three-sphere in this limit is shown to be the generating function of the Euler characteristics of the moduli spaces of surfaces of genus $g,$ providing a string interpretation for the perturbative expansion. A similar expansion is found for the three-torus, with differences that shed light on contributions from different spacetime topologies in string theory.Comment: 6 pages, iassns-hep-93-30 (title change, omitted refs. added, two sign errors corrected, no significant change

Puncture Self-Healing Polymers for Aerospace Applications

Space exploration launch costs on the order of $10K per pound provide ample incentive to seek innovative, cost-effective ways to reduce structural mass without sacrificing safety and reliability. Damage-tolerant structural systems can provide a route to avoiding weight penalty while enhancing vehicle safety and reliability. Self-healing polymers capable of spontaneous puncture repair show great promise to mitigate potentially catastrophic damage from events such as micrometeoroid penetration. Effective self-repair requires these materials to heal instantaneously following projectile penetration while retaining structural integrity. Poly(ethylene-co-methacrylic acid) (EMMA), also known as Surlyn is an ionomer-based copolymer that undergoes puncture reversal (self-healing) following high impact puncture at high velocities. However EMMA is not a structural engineering polymer, and will not meet the demands of aerospace applications requiring self-healing engineering materials. Current efforts to identify candidate self-healing polymer materials for structural engineering systems are reported. Rheology, high speed thermography, and high speed video for self-healing semi-crystalline and amorphous polymers will be reported

Matrix models as solvable glass models

We present a family of solvable models of interacting particles in high dimensionalities without quenched disorder. We show that the models have a glassy regime with aging effects. The interaction is controlled by a parameter $p$. For $p=2$ we obtain matrix models and for $p>2$ `tensor' models. We concentrate on the cases $p=2$ which we study analytically and numerically.Comment: 10 pages + 2 figures, Univ.Roma I, 1038/94, ROM2F/94/2

Anti-Kaon Induced Reactions on the Nucleon

Using a previously established effective Lagrangian model we describe anti-kaon induced reactions on the nucleon. The dominantly contributing channels in the cm-energy region from threshold up to 1.72 GeV are included (K N, \pi \Sigma, \pi \Lambda). We solve the Bethe-Salpeter equation in an unitary $K$-matrix approximation.Comment: 21 pages, 13 figures, minor typos corrected, accepted for publication in Phys. Rev.

Extension of geodesic algebras to continuous genus

Using the Penner--Fock parameterization for Teichmuller spaces of Riemann surfaces with holes, we construct the string-like free-field representation of the Poisson and quantum algebras of geodesic functions in the continuous-genus limit. The mapping class group acts naturally in the obtained representation.Comment: 16 pages, submitted to Lett.Math.Phy