588 research outputs found
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 or , with
reductions to orbits of subalgebras determined as invariant fixed point sets
under involutive automorphisms. The case 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 , 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 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 .Comment: Final revision for publication in Commun. Math. Phys. Minor
corrections and editorial change
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
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
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