K-orbit closures on G/B as universal degeneracy loci for flagged vector bundles with symmetric or skew-symmetric bilinear form

We use equivariant localization and divided difference operators to determine formulas for the torus-equivariant fundamental cohomology classes of $K$-orbit closures on the flag variety $G/B$, where G = GL(n,\C), and where $K$ is one of the symmetric subgroups O(n,\C) or Sp(n,\C). We realize these orbit closures as universal degeneracy loci for a vector bundle over a variety equipped with a single flag of subbundles and a nondegenerate symmetric or skew-symmetric bilinear form taking values in the trivial bundle. We describe how our equivariant formulas can be interpreted as giving formulas for the classes of such loci in terms of the Chern classes of the various bundles.Comment: Minor revisions and corrections suggested by referees. Final version, to appear in Transformation Group

Full load testing in the platform module prior to tow-out: A case history of subsynchronous instability

An electric motor driven centrifugal compressor to supply gas for further compression and reinjection on a petroleum production platform in the North Sea was examined. The compressor design, raised concerns about susceptibility to subsynchronous instability. Log decrement, aerodynamic features, and the experience of other compressors with similar ratios of operating to critical speed ratio versus gas density led to the decision to full load test. Mixed hydrocarbon gas was chosen for the test to meet discharge temperature restrictions. The module was used as the test site. Subsynchronous vibrations made the compressor inoperable above approximately one-half the rated discharge pressure of 14500 kPa. Modifications, which includes shortening the bearing span, change of leakage inlet flow direction on the back to back labyrinth, and removal of the vaned diffusers on all stages were made simultaneously. The compressor is operating with satisfactory vibration levels

Particle-wave duality: a dichotomy between symmetry and asymmetry

Symmetry plays a central role in many areas of modern physics. Here we show that it also underpins the dual particle and wave nature of quantum systems. We begin by noting that a classical point particle breaks translational symmetry whereas a wave with uniform amplitude does not. This provides a basis for associating particle nature with asymmetry and wave nature with symmetry. We derive expressions for the maximum amount of classical information we can have about the symmetry and asymmetry of a quantum system with respect to an arbitrary group. We find that the sum of the information about the symmetry (wave nature) and the asymmetry (particle nature) is bounded by log(D) where D is the dimension of the Hilbert space. The combination of multiple systems is shown to exhibit greater symmetry and thus more wavelike character. In particular, a class of entangled systems is shown to be capable of exhibiting wave-like symmetry as a whole while exhibiting particle-like asymmetry internally. We also show that superdense coding can be viewed as being essentially an interference phenomenon involving wave-like symmetry with respect to the group of Pauli operators.Comment: 20 pages, 3 figure

Schur Q-functions and degeneracy locus formulas for morphisms with symmetries

We give closed-form formulas for the fundamental classes of degeneracy loci associated with vector bundle maps given locally by (not necessary square) matrices which are symmetric (resp. skew-symmetric) w.r.t. the main diagonal. Our description uses essentially Schur Q-polynomials of a bundle, and is based on a certain push-forward formula for these polynomials in a Grassmann bundle.Comment: 22 pages, AMSTEX, misprints corrected, exposition improved. to appear in the Proceedings of Intersection Theory Conference in Bologna, "Progress in Mathematics", Birkhause

The free energy in a class of quantum spin systems and interchange processes

We study a class of quantum spin systems in the mean-field setting of the complete graph. For spin $S=\tfrac12$ the model is the Heisenberg ferromagnet, for general spin $S\in\tfrac12\mathbb{N}$ it has a probabilistic representation as a cycle-weighted interchange process. We determine the free energy and the critical temperature (recovering results by T\'oth and by Penrose when $S=\tfrac12$). The critical temperature is shown to coincide (as a function of $S$) with that of the $q=2S+1$ state classical Potts model, and the phase transition is discontinuous when $S\geq1$.Comment: 22 page

Character Formulae and Partition Functions in Higher Dimensional Conformal Field Theory

A discussion of character formulae for positive energy unitary irreducible representations of the the conformal group is given, employing Verma modules and Weyl group reflections. Product formulae for various conformal group representations are found. These include generalisations of those found by Flato and Fronsdal for SO(3,2). In even dimensions the products for free representations split into two types depending on whether the dimension is divisible by four or not.Comment: 43 pages, uses harvmac,version 2 2 references added, minor typos correcte

Stringy K-theory and the Chern character

For a finite group G acting on a smooth projective variety X, we construct two new G-equivariant rings: first the stringy K-theory of X, and second the stringy cohomology of X. For a smooth Deligne-Mumford stack Y we also construct a new ring called the full orbifold K-theory of Y. For a global quotient Y=[X/G], the ring of G-invariants of the stringy K-theory of X is a subalgebra of the full orbifold K-theory of the the stack Y and is linearly isomorphic to the ``orbifold K-theory'' of Adem-Ruan (and hence Atiyah-Segal), but carries a different, ``quantum,'' product, which respects the natural group grading. We prove there is a ring isomorphism, the stringy Chern character, from stringy K-theory to stringy cohomology, and a ring homomorphism from full orbifold K-theory to Chen-Ruan orbifold cohomology. These Chern characters satisfy Grothendieck-Riemann-Roch for etale maps. We prove that stringy cohomology is isomorphic to Fantechi and Goettsche's construction. Since our constructions do not use complex curves, stable maps, admissible covers, or moduli spaces, our results simplify the definitions of Fantechi-Goettsche's ring, of Chen-Ruan's orbifold cohomology, and of Abramovich-Graber-Vistoli's orbifold Chow. We conclude by showing that a K-theoretic version of Ruan's Hyper-Kaehler Resolution Conjecture holds for symmetric products. Our results hold both in the algebro-geometric category and in the topological category for equivariant almost complex manifolds.Comment: Exposition improved and additional details provided. To appear in Inventiones Mathematica

Moduli Spaces of Lumps on Real Projective Space

Harmonic maps that minimize the Dirichlet energy in their homotopy classes are known as lumps. Lump solutions on real projective space are explicitly given by rational maps subject to a certain symmetry requirement. This has consequences for the behaviour of lumps and their symmetries. An interesting feature is that the moduli space of charge three lumps is a D2-symmetric 7-dimensional manifold of cohomogeneity one. In this paper, we discuss the charge three moduli spaces of lumps from two perspectives: discrete symmetries of lumps and the Riemann-Hurwitz formula. We then calculate the metric and find explicit formula for various geometric quantities. We also discuss the implications for lump decay

HAT-P-65b and HAT-P-66b: Two Transiting Inflated Hot Jupiters and Observational Evidence for the Reinflation of Close-In Giant Planets

We present the discovery of the transiting exoplanets HAT-P-65b and HAT-P-66b, with orbital periods of 2.6055 and 2.9721 days, masses of 0.527 ± 0.083 M_J and 0.783 ± 0.057 M_J, and inflated radii of 1.89 ± 0.13 R_J and 1.59^(+0.16)_(-0.10) R_J, respectively. They orbit moderately bright (v = 13.145 ± 0.029 and v = 12.993 ± 0.052) stars of mass 1.212 ± 0.050 M⊙ and 1.255^(+0.107)_(-0.054) M⊙. The stars are at the main-sequence turnoff. While it is well known that the radii of close-in giant planets are correlated with their equilibrium temperatures, whether or not the radii of planets increase in time as their hosts evolve and become more luminous is an open question. Looking at the broader sample of well-characterized close-in transiting giant planets, we find that there is a statistically significant correlation between planetary radii and the fractional ages of their host stars, with a false-alarm probability of only 0.0041%. We find that the correlation between the radii of planets and the fractional ages of their hosts is fully explained by the known correlation between planetary radii and their present-day equilibrium temperatures; however, if the zero-age main-sequence equilibrium temperature is used in place of the present-day equilibrium temperature, then a correlation with age must also be included to explain the planetary radii. This suggests that, after contracting during the pre-main-sequence, close-in giant planets are reinflated over time due to the increasing level of irradiation received from their host stars. Prior theoretical work indicates that such a dynamic response to irradiation requires a significant fraction of the incident energy to be deposited deep within the planetary interiors