On quantization of singular varieties and applications to D-branes

We calculate the ring of differential operators on some singular affine varieties (intersecting stacks, a point on a singular curve or an orbifold). Our results support the proposed connection of the ring of differential operators with geometry of D-branes in (bosonic) string theory. In particular, the answer does know about the resolution of singularities in accordance with the string theory predictions.Comment: LaTeX2e, 17 pages, misprints correcte

Darboux Coordinates and Liouville-Arnold Integration in Loop Algebras

Darboux coordinates are constructed on rational coadjoint orbits of the positive frequency part \wt{\frak{g}}^+ of loop algebras. These are given by the values of the spectral parameters at the divisors corresponding to eigenvector line bundles over the associated spectral curves, defined within a given matrix representation. A Liouville generating function is obtained in completely separated form and shown, through the Liouville-Arnold integration method, to lead to the Abel map linearization of all Hamiltonian flows induced by the spectral invariants. Serre duality is used to define a natural symplectic structure on the space of line bundles of suitable degree over a permissible class of spectral curves, and this is shown to be equivalent to the Kostant-Kirillov symplectic structure on rational coadjoint orbits. The general construction is given for $\frak{g}=\frak{gl}(r)$ or $\frak{sl}(r)$, with reductions to orbits of subalgebras determined as invariant fixed point sets under involutive automorphisms. The case $\frak{g=sl}(2)$ is shown to reproduce the classical integration methods for finite dimensional systems defined on quadrics, as well as the quasi-periodic solutions of the cubically nonlinear Schr\"odinger equation. For $\frak{g=sl}(3)$, the method is applied to the computation of quasi-periodic solutions of the two component coupled nonlinear Schr\"odinger equation.Comment: 61 pg

An inverse model to determine the heat transfer coefficient and its evolution with time during solidification of light alloys

Infra-red probes linked to pyrometric chains and thermocouple arrays have been used to accurately determine both casting and die surface temperatures during the solidification of an aluminium A380 alloy and the magnesium alloy AZ91D. An inverse model was then used to accurately determine the heat flux densities and interfacial heat transfer coefficients and the rapid evolution of these values with time during high pressure die casting of these alloys

Stability and BPS branes

We define the concept of Pi-stability, a generalization of mu-stability of vector bundles, and argue that it characterizes N=1 supersymmetric brane configurations and BPS states in very general string theory compactifications with N=2 supersymmetry in four dimensions.Comment: harvmac, 18 p

First Measurements with NeXtRAD, a Polarimetric X/L Band Radar Network

NeXtRAD is a fully polarimetric, X/L Band radar network. It is a development of the older NetRAD system and builds on the experience gained with extensive deployments of NetRAD for sea clutter and target measurements. In this paper we will report on the first measurements with NeXtRAD, looking primarily at sea clutter and some targets, as well as early attempts at calibration using corner reflectors, and an assessment of the polarimetric response of the system. We also highlight innovations allowing for efficient data manipulation post measurement campaigns, as well as the plans for the coming years with this system

Probing the surfaces of core-shell and hollow nanoparticles by solvent relaxation NMR

Measurement of the spin-spin NMR relaxation time (or its inverse, the rate) of water molecules in aqueous nanoparticle dispersions has become a popular approach to probe of the nature and structure of the particle surface and any adsorbed species. Here, we report on the characterisation of aqueous dispersions of hollow amorphous nanoparticles, that have two liquid accessible surfaces (inner cavity surface and outer shell surface), plus the solid (silica) and core-shell (titania-silica) nanoparticle precursors from which the hollow particles have been prepared. In all cases, the observed water relaxation rates scale linearly with particle surface area, with the effect being more pronounced with increasing levels of titania present at the particle surface. Two distinct behaviours were observed for the hollow nanoparticles at very low volume fractions, which appear to merge with increasing surface area (particle concentration). Herewith, we further show the versatility of solvent NMR spectroscopy as a probe of surface character

Critical points and supersymmetric vacua, III: String/M models

A fundamental problem in contemporary string/M theory is to count the number of inequivalent vacua satisfying constraints in a string theory model. This article contains the first rigorous results on the number and distribution of supersymmetric vacua of type IIb string theories compactified on a Calabi-Yau 3-fold $X$ with flux. In particular, complete proofs of the counting formulas in Ashok-Douglas and Denef-Douglas are given, together with van der Corput style remainder estimates. We also give evidence that the number of vacua satisfying the tadpole constraint in regions of bounded curvature in moduli space is of exponential growth in $b_3(X)$.Comment: Final revision for publication in Commun. Math. Phys. Minor corrections and editorial change

Numerical solution to the hermitian Yang-Mills equation on the Fermat quintic

We develop an iterative method for finding solutions to the hermitian Yang-Mills equation on stable holomorphic vector bundles, following ideas recently developed by Donaldson. As illustrations, we construct numerically the hermitian Einstein metrics on the tangent bundle and a rank three vector bundle on P^2. In addition, we find a hermitian Yang-Mills connection on a stable rank three vector bundle on the Fermat quintic.Comment: 25 pages, 2 figure

The spectrum of BPS branes on a noncompact Calabi-Yau

We begin the study of the spectrum of BPS branes and its variation on lines of marginal stability on O_P^2(-3), a Calabi-Yau ALE space asymptotic to C^3/Z_3. We show how to get the complete spectrum near the large volume limit and near the orbifold point, and find a striking similarity between the descriptions of holomorphic bundles and BPS branes in these two limits. We use these results to develop a general picture of the spectrum. We also suggest a generalization of some of the ideas to the quintic Calabi-Yau.Comment: harvmac, 45 pp. (v2: added references