21,011 research outputs found
The Surface Region of Superfluid He as a Dilute Bose-Condensed Gas
In the low-density surface region of superfluid He, the atoms are far
apart and collisions can be ignored. The only effect of the interactions is
from the long-range attractive Hartree potential produced by the distant
high-density bulk liquid. As a result, at , all the atoms occupy the same
single-particle state in the low-density tail. Striking numerical evidence for
this 100\% surface BEC was given by Pandharipande and coworkers in 1988. We
derive a generalized Gross-Pitaevskii equation for the inhomogeneous condensate
wave function in the low-density region valid at all temperatures.
The overall amplitude of is fixed by the bulk liquid, which ensures
that it vanishes everywhere at the bulk transition temperature.Comment: 6 pages, paper submitted to Low Temperature Conference (LT21),
Prague, Aug., 1996; to appear in proceeding
Small and Large Time Stability of the Time taken for a L\'evy Process to Cross Curved Boundaries
This paper is concerned with the small time behaviour of a L\'{e}vy process
. In particular, we investigate the {\it stabilities} of the times,
\Tstarb(r) and \Tbarb(r), at which , started with , first leaves
the space-time regions (one-sided exit),
or (two-sided exit), , as
r\dto 0. Thus essentially we determine whether or not these passage times
behave like deterministic functions in the sense of different modes of
convergence; specifically convergence in probability, almost surely and in
. In many instances these are seen to be equivalent to relative stability
of the process itself. The analogous large time problem is also discussed
Stability of the Exit Time for L\'evy Processes
This paper is concerned with the behaviour of a L\'{e}vy process when it
crosses over a positive level, , starting from 0, both as becomes large
and as becomes small. Our main focus is on the time, , it takes the
process to transit above the level, and in particular, on the {\it stability}
of this passage time; thus, essentially, whether or not behaves
linearly as u\dto 0 or . We also consider conditional stability
of when the process drifts to , a.s. This provides
information relevant to quantities associated with the ruin of an insurance
risk process, which we analyse under a Cram\'er condition
Design study of test models of maneuvering aircraft configurations for the National Transonic Facility (NTF)
The feasibility of designing advanced technology, highly maneuverable, fighter aircraft models to achieve full scale Reynolds number in the National Transonic Facility (NTF) is examined. Each of the selected configurations are tested for aeroelastic effects through the use of force and pressure data. A review of materials and material processes is also included
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Asymptotic Distributions of the Overshoot and Undershoots for the L\'evy Insurance Risk Process in the Cram\'er and Convolution Equivalent Cases
Recent models of the insurance risk process use a L\'evy process to
generalise the traditional Cram\'er-Lundberg compound Poisson model. This paper
is concerned with the behaviour of the distributions of the overshoot and
undershoots of a high level, for a L\'{e}vy process which drifts to
and satisfies a Cram\'er or a convolution equivalent condition. We derive these
asymptotics under minimal conditions in the Cram\'er case, and compare them
with known results for the convolution equivalent case, drawing attention to
the striking and unexpected fact that they become identical when certain
parameters tend to equality.
Thus, at least regarding these quantities, the "medium-heavy" tailed
convolution equivalent model segues into the "light-tailed" Cram\'er model in a
natural way. This suggests a usefully expanded flexibility for modelling the
insurance risk process. We illustrate this relationship by comparing the
asymptotic distributions obtained for the overshoot and undershoots, assuming
the L\'evy process belongs to the "GTSC" class
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