5,891 research outputs found
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, , containing no levels,
E_{\bt}(0,s), via Dyson's Coulomb Fluid approach. For the
Unitary-Laguerre Ensemble, we recover the exact spacing distribution found by
both Edelman and Forrester, while for , the leading terms of
, 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
Clumpy Ultracompact HII Regions I: Fully Supersonic Wind-blown Models
We propose that a significant fraction of the ultracompact HII regions found
in massive star-forming clouds are the result of the interaction of the wind
and ionizing radiation from a young massive star with the clumpy molecular
cloud gas in its neighbourhood. Distributed mass loading in the flow allows the
compact nebulae to be long-lived. In this paper, we discuss a particularly
simple case, in which the flow in the HII region is everywhere supersonic. The
line profiles predicted for this model are highly characteristic, for the case
of uniform mass loading. We discuss briefly other observational diagnostics of
these models.Comment: To appear in Monthly Notices of the Royal Astronomical Society. 5
pages LaTeX (uses mn.sty and epsf.sty macros) + 4 PS figures. Also available
via http://axp2.ast.man.ac.uk:8000/Preprints.htm
Mathematical modelling of curtain coating
We present a simple mathematical model for the fluid flow in the curtain coating process, exploiting the small aspect ratio, and examine the model in the large-Reynolds-number limit of industrial interest. We show that the fluid is in free fall except for a region close to the substrate, but find that the model can not describe the turning of the curtain onto the substrate. We find that the inclusion of a viscous bending moment close to the substrate allows the curtain to “turn the corner”
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
Flows along cometary tails in the Helix planetary nebula NGC 7293
Previous velocity images which reveal flows of ionized gas along the most
prominent cometary tail (from Knot 38) in the Helix planetary nebula are
compared with that taken at optical wavelengths with the Hubble Space Telescope
and with an image in the emission from molecular hydrogen. The flows from the
second most prominent tail from Knot 14 are also considered. The kinematics of
the tail from the more complex Knot 32, shown here for the first time, also
reveals an acceleration away from the central star. All of the tails are
explained as accelerating ionized flows of ablated material driven by the
previous, mildly supersonic, AGB wind from the central star. The longest tail
of ionized gas, even though formed by this mechanism in a very clumpy medium,
as revealed by the emission from molecular hydrogen, appears to be a coherent
outflowing feature.Comment: 8 pages, 4 figures, accepted for publication in MNRA
Fluctuation properties of strength functions associated with giant resonances
We performed fluctuation analysis by means of the local scaling dimension for
the strength function of the isoscalar (IS) and the isovector (IV) giant
quadrupole resonances (GQR) in Ca, where the strength functions are
obtained by the shell model calculation within up to the 2p2h configurations.
It is found that at small energy scale, fluctuation of the strength function
almost obeys the Gaussian orthogonal ensemble (GOE) random matrix theory limit.
On the other hand, we found a deviation from the GOE limit at the intermediate
energy scale about 1.7MeV for the IS and at 0.9MeV for the IV. The results
imply that different types of fluctuations coexist at different energy scales.
Detailed analysis strongly suggests that GOE fluctuation at small energy scale
is due to the complicated nature of 2p2h states and that fluctuation at the
intermediate energy scale is associated with the spreading width of the
Tamm-Dancoff 1p1h states.Comment: 14 pages including 13figure
Two-channel Kondo model as a generalized one-dimensional inverse square long-range Haldane-Shastry spin model
Majorana fermion representations of the algebra associated with spin, charge,
and flavor currents have been used to transform the two-channel Kondo
Hamiltonian. Using a path integral formulation, we derive a reduced effective
action with long-range impurity spin-spin interactions at different imaginary
times. In the semiclassical limit, it is equivalent to a one-dimensional
Heisenberg spin chain with two-spin, three-spin, etc. long-range interactions,
as a generalization of the inverse-square long-range Haldane-Shastry spin
model. In this representation the elementary excitations are "semions", and the
non-Fermi-liquid low-energy properties of the two-channel Kondo model are
recovered.Comment: 4 pages, no figure, to be published in J. Phys.: Condens. Matter,
200
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
Confinement, Turbulence and Diffraction Catastrophes
Many features of large N_c transition that occurs in the spectral density of
Wilson loops as a function of loop area (observed recently in numerical
simulations of Yang-Mills theory by Narayanan and Neuberger) can be captured by
a simple Burgers equation used to model turbulence. Spectral shock waves that
precede this asymptotic limit exhibit universal scaling with N_c, with indices
that can be related to Berry indices for diffraction catastrophes.Comment: Presented at PANIC 200
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