Genus Two Partition and Correlation Functions for Fermionic Vertex Operator Superalgebras I

We define the partition and $n$-point correlation functions for a vertex operator superalgebra on a genus two Riemann surface formed by sewing two tori together. For the free fermion vertex operator superalgebra we obtain a closed formula for the genus two continuous orbifold partition function in terms of an infinite dimensional determinant with entries arising from torus Szeg\"o kernels. We prove that the partition function is holomorphic in the sewing parameters on a given suitable domain and describe its modular properties. Using the bosonized formalism, a new genus two Jacobi product identity is described for the Riemann theta series. We compute and discuss the modular properties of the generating function for all $n$-point functions in terms of a genus two Szeg\"o kernel determinant. We also show that the Virasoro vector one point function satisfies a genus two Ward identity.Comment: A number of typos have been corrected, 39 pages. To appear in Commun. Math. Phy

TMI-2 core damage: a summary of present knowledge

Extensive fuel damage (oxidation and fragmentation) has occurred and the top approx. 1.5 m of the center portion of the TMI-2 core has relocated. The fuel fragmentation extends outward to slightly beyond one-half the core radius in the direction examined by the CCTV camera. While the radial extent of core fragmentation in other directions was not directly observed, control and spider drop data and in-core instrument data suggest that the core void is roughly symmetrical, although there are a few indications of severe fuel damage extending to the core periphery. The core material fragmented into a broad range of particle sizes, extending down to a few microns. APSR movement data, the observation of damaged fuel assemblies hanging unsupported from the bottom of the reactor upper plenum structure, and the observation of once-molten stainless steel immediately above the active core indicate high temperatures (up to at least 1720 K) extended to the very top of the core. The relative lack of damage to the underside of the plenum structure implies a sharp temperature demarcation at the core/plenum interface. Filter debris and leadscrew deposit analyses indicate extensive high temperature core materials interaction, melting of the Ag-In-Cd control material, and transport of particulate control material to the plenum and out of the vessel

Novae Ejecta as Colliding Shells

Following on our initial absorption-line analysis of fifteen novae spectra we present additional evidence for the existence of two distinct components of novae ejecta having different origins. As argued in Paper I one component is the rapidly expanding gas ejected from the outer layers of the white dwarf by the outburst. The second component is pre-existing outer, more slowly expanding circumbinary gas that represents ejecta from the secondary star or accretion disk. We present measurements of the emission-line widths that show them to be significantly narrower than the broad P Cygni profiles that immediately precede them. The emission profiles of novae in the nebular phase are distinctly rectangular, i.e., strongly suggestive of emission from a relatively thin, roughly spherical shell. We thus interpret novae spectral evolution in terms of the collision between the two components of ejecta, which converts the early absorption spectrum to an emission-line spectrum within weeks of the outburst. The narrow emission widths require the outer circumbinary gas to be much more massive than the white dwarf ejecta, thereby slowing the latter's expansion upon collision. The presence of a large reservoir of circumbinary gas at the time of outburst is suggestive that novae outbursts may sometime be triggered by collapse of gas onto the white dwarf, as occurs for dwarf novae, rather than steady mass transfer through the inner Lagrangian point.Comment: 12 pages, 3 figures; Revised manuscript; Accepted for publication in Astrophysics & Space Scienc

Low-temperature dynamical simulation of spin-boson systems

The dynamics of spin-boson systems at very low temperatures has been studied using a real-time path-integral simulation technique which combines a stochastic Monte Carlo sampling over the quantum fluctuations with an exact treatment of the quasiclassical degrees of freedoms. To a large degree, this special technique circumvents the dynamical sign problem and allows the dynamics to be studied directly up to long real times in a numerically exact manner. This method has been applied to two important problems: (1) crossover from nonadiabatic to adiabatic behavior in electron transfer reactions, (2) the zero-temperature dynamics in the antiferromagnetic Kondo region 1/2<K<1 where K is Kondo's parameter.Comment: Phys. Rev. B (in press), 28 pages, 6 figure

Stabilities of nanohydrated thymine radical cations: insights from multiphoton ionization experiments and ab initio calculations

Multi-photon ionization experiments have been carried out on thymine-water clusters in the gas phase. Metastable H2O loss from T+(H2O)n was observed at n ≥ 3 only. Ab initio quantum-chemical calculations of a large range of optimized T+(H2O)n conformers have been performed up to n = 4, enabling binding energies of water to be derived. These decrease smoothly with n, consistent with the general trend of increasing metastable H2O loss in the experimental data. The lowest-energy conformers of T+(H2O)3 and T+(H2O)4 feature intermolecular bonding via charge-dipole interactions, in contrast with the purely hydrogen-bonded neutrals. We found no evidence for a closed hydration shell at n = 4, also contrasting with studies of neutral clusters

Upper critical field for underdoped high-T_c superconductors. Pseudogap and stripe--phase

We investigate the upper critical field in a stripe--phase and in the presence of a phenomenological pseudogap. Our results indicate that the formation of stripes affects the Landau orbits and results in an enhancement of $H_{c2}$. On the other hand, phenomenologically introduced pseudogap leads to a reduction of the upper critical field. This effect is of particular importance when the magnitude of the gap is of the order of the superconducting transition temperature. We have found that a suppression of the upper critical field takes place also for the gap that originates from the charge--density waves.Comment: 7 pages, 5 figure

Atomic X-ray Spectroscopy of Accreting Black Holes

Current astrophysical research suggests that the most persistently luminous objects in the Universe are powered by the flow of matter through accretion disks onto black holes. Accretion disk systems are observed to emit copious radiation across the electromagnetic spectrum, each energy band providing access to rather distinct regimes of physical conditions and geometric scale. X-ray emission probes the innermost regions of the accretion disk, where relativistic effects prevail. While this has been known for decades, it also has been acknowledged that inferring physical conditions in the relativistic regime from the behavior of the X-ray continuum is problematic and not satisfactorily constraining. With the discovery in the 1990s of iron X-ray lines bearing signatures of relativistic distortion came the hope that such emission would more firmly constrain models of disk accretion near black holes, as well as provide observational criteria by which to test general relativity in the strong field limit. Here we provide an introduction to this phenomenon. While the presentation is intended to be primarily tutorial in nature, we aim also to acquaint the reader with trends in current research. To achieve these ends, we present the basic applications of general relativity that pertain to X-ray spectroscopic observations of black hole accretion disk systems, focusing on the Schwarzschild and Kerr solutions to the Einstein field equations. To this we add treatments of the fundamental concepts associated with the theoretical and modeling aspects of accretion disks, as well as relevant topics from observational and theoretical X-ray spectroscopy.Comment: 63 pages, 21 figures, Einstein Centennial Review Article, Canadian Journal of Physics, in pres

Dust Devil Populations and Statistics

The highly-skewed diameter and pressure drop distributions of dust devils on Earth and Mars are noted, and challenges of presenting and comparing different types of observations are discussed. The widely- held view that Martian dust devils are larger than Earth\u27s is critically-assessed: the question is confounded somewhat by different observation techniques, but some indication of a ~3x larger population on Mars is determined. The largest and most intense (in a relative pressure sense) devils recorded are on Mars, although the largest reported number density is on Earth. The difficulties of concepts used in the literature of \u27average\u27 diameter, pressure cross section, and area fraction are noted in the context of estimating population-integral effects such as dust lifting