Asymptotic Level Spacing of the Laguerre Ensemble: A Coulomb Fluid Approach

We determine the asymptotic level spacing distribution for the Laguerre Ensemble in a single scaled interval, $(0,s)$, containing no levels, E_{\bt}(0,s), via Dyson's Coulomb Fluid approach. For the $\alpha=0$ Unitary-Laguerre Ensemble, we recover the exact spacing distribution found by both Edelman and Forrester, while for $\alpha\neq 0$, the leading terms of $E_{2}(0,s)$, found by Tracy and Widom, are reproduced without the use of the Bessel kernel and the associated Painlev\'e transcendent. In the same approximation, the next leading term, due to a ``finite temperature'' perturbation (\bt\neq 2), is found.Comment: 10pp, LaTe

The Formation of Broad Emission Line Regions in Supernova-QSO Wind Interactions

We show that a cooled region of shocked supernova ejecta forms in a type II supernova-QSO wind interaction, and has a density, an ionization parameter, and a column density compatible with those inferred for the high ionization component of the broad emission line regions in QSOs. The calculations are based on the assumption that the ejecta flow is described initially by a similarity solution investigated by Chevalier (1982) and Nadyozhin (1985) and is spherically symmetric. Heating and cooling appropriate for gas irradiated by a nearby powerful continuum source is included in our model, together with reasonable assumptions for the properties of the QSO wind. The model results are also in agreement with observational correlations and imply reasonable supernova rates.Comment: 13 pages, 7 figures, to be published in A&

The tails in the Helix Nebula NGC 7293

We have examined a stream-source model for the production of the cometary tails observed in the Helix Nebula NGC 7293 in which a transonic or moderately supersonic stream of ionized gas overruns a source of ionized gas. Hydrodynamic calculations reveal velocity structures which are in good agreement with the observational data on tail velocities and are consistent with observations of the nebular structure. The results also are indicative of a stellar atmosphere origin for the cometary globules. Tail remnants persist for timescales long enough for their identification with faint striations visible in the nebula gas to be plausible.Comment: 7 pages, 6 figures, accepted for publication in A&

Models relating the radio emission and ionised gas in Seyfert nuclei

Possible models are discussed in which the radio emitting components in Seyfert II nuclei can compress and accelerate the ambient nuclear medium to produce the characteristics of the narrow line region. A first order model, which considers only the expansion of the radio components, is briefly described. However, in many Seyfert nuclei it appears that the linear motion of the radio components is also important. This can result in shock heating of the ambient medium, and if the cooling time is long enough, can lead to a displacement between the radio component and the associated emission lines. This effect may be present in NGC 1068 and NGC 5929 and by considering ram pressure balance and the cooling length it is possible to estimate lobe velocities and ambient densities

High Resolution CO and H2 Molecular Line Imaging of a Cometary Globule in the Helix Nebula

We report high resolution imaging of a prominent cometary globule in the Helix nebula in the CO J=1-0 (2.6 mm) and H2 v=1-0 S(1) (2.12 micron) lines. The observations confirm that globules consist of dense condensations of molecular gas embedded in the ionized nebula. The head of the globule is seen as a peak in the CO emission with an extremely narrow line width (0.5 km/s) and is outlined by a limb-brightened surface of H2 emission facing the central star and lying within the photo-ionized halo. The emission from both molecular species extends into the tail region. The presence of this extended molecular emission provides new constraints on the structure of the tails, and on the origin and evolution of the globules.Comment: 12 pages, 3 figures. To appear in The Astrophysical Journal Letter

Energy level statistics for models of coupled single-mode Bose--Einstein condensates

We study the distribution of energy level spacings in two models describing coupled single-mode Bose-Einstein condensates. Both models have a fixed number of degrees of freedom, which is small compared to the number of interaction parameters, and is independent of the dimensionality of the Hilbert space. We find that the distribution follows a universal Poisson form independent of the choice of coupling parameters, which is indicative of the integrability of both models. These results complement those for integrable lattice models where the number of degrees of freedom increases with increasing dimensionality of the Hilbert space. Finally, we also show that for one model the inclusion of an additional interaction which breaks the integrability leads to a non-Poisson distribution.Comment: 5 pages, 4 figures, revte

Sickle cell, habitual dys-positions and fragile dispositions: young people with sickle cell at school

The experiences of young people living with a sickle cell disorder in schools in England are reported through a thematic analysis of forty interviews, using Bourdieu’s notions of field, capital and habitus. Young people with sickle cell are found to be habitually dys-positioned between the demands of the clinic for health maintenance through self-care and the field of the school, with its emphases on routines, consistent attendance and contextual demands for active and passive pupil behaviour. The tactics or dispositions that young people living with sickle cell can then employ, during strategy and struggle at school, are therefore fragile: they work only contingently, transiently or have the unintended consequences of displacing other valued social relations. The dispositions of the young people with sickle cell are framed by other social struggles: innovations in school procedures merely address aspects of sickle cell in isolation and are not consolidated into comprehensive policies; mothers inform, liaise, negotiate and advocate in support of a child with sickle cell but with limited success. Reactions of teachers and peers to sickle cell have the enduring potential to drain the somatic, cultural and social capital of young people living with sickle cell

The Probability of an Eigenvalue Number Fluctuation in an Interval of a Random Matrix Spectrum

We calculate the probability to find exactly $n$ eigenvalues in a spectral interval of a large random $N \times N$ matrix when this interval contains $s \ll N$ eigenvalues on average. The calculations exploit an analogy to the problem of finding a two-dimensional charge distribution on the interface of a semiconductor heterostructure under the influence of a split gate.Comment: 4 pages, postscrip

The evolution of mass loaded supernova remnants: II. Temperature dependent mass injection rates

We investigate the evolution of spherically symmetric supernova remnants in which mass loading takes place due to conductively driven evaporation of embedded clouds. Numerical simulations reveal significant differences between the evolution of conductively mass loaded and the ablatively mass loaded remnants studied in Paper I. A main difference is the way in which conductive mass loading is extinguished at fairly early times, once the interior temperature of the remnant falls below ~ 107 K. Thus, at late times remnants that ablatively mass load are dominated by loaded mass and thermal energy, while those that conductively mass load are dominated by swept-up mass and kinetic energy. Simple approximations to the remnant evolution, complementary to those in Paper I, are given

Impact of localization on Dyson's circular ensemble

A wide variety of complex physical systems described by unitary matrices have been shown numerically to satisfy level statistics predicted by Dyson's circular ensemble. We argue that the impact of localization in such systems is to provide certain restrictions on the eigenvalues. We consider a solvable model which takes into account such restrictions qualitatively and find that within the model a gap is created in the spectrum, and there is a transition from the universal Wigner distribution towards a Poisson distribution with increasing localization.Comment: To be published in J. Phys.