78 research outputs found
Spectral gap of the Erlang A model in the Halfin-Whitt regime
We consider a hybrid diffusion process that is a combination of two Ornstein-Uhlenbeck processes with different restraining forces. This process serves as the heavy-traffic approximation to the Markovian many-server queue with abandonments in the critical Halfin-Whitt regime. We obtain an expression for the Laplace transform of the time-dependent probability distribution, from which the spectral gap is explicitly characterized. The spectral gap gives the exponential rate of convergence to equilibrium. We further give various asymptotic results for the spectral gap, in the limits of small and large abandonment effects. It turns out that convergence to equilibrium becomes extremely slow for overloaded systems with small abandonment effects
Buoyancy driven rotating boundary currents
The structure of boundary currents formed from intermediately dense water
introduced into a rotating, stably stratified, two-layer environment is
investigated in a series of laboratory experiments, performed for Froude
numbers ranging from 0.01 to 1. The thickness and streamwise velocity profiles
in quasi-steady currents are measured using a pH activated tracer (thymol blue)
and found to compare favorably to simplified analytic solutions and numerical
models. Currents flowing along sloping boundaries in a stratified background
exhibit robust stability at all experimental Froude numbers. Such stability is
in sharp contrast to the unequivocal instability of such currents flowing
against vertical boundaries, or of currents flowing along slopes in a uniform
background. The presence of a variety of wave mechanisms in the ambient medium
might account for the slower and wider observed structures and the stability of
the currents, by effecting the damping of disturbances through wave radiation.Comment: 9 pages with 2 figures to appear in Ann NYAS "Long range effects in
physics and astrophysics
Supergravity Higgs Inflation and Shift Symmetry in Electroweak Theory
We present a model of inflation in a supergravity framework in the Einstein
frame where the Higgs field of the next to minimal supersymmetric standard
model (NMSSM) plays the role of the inflaton. Previous attempts which assumed
non-minimal coupling to gravity failed due to a tachyonic instability of the
singlet field during inflation. A canonical K\"{a}hler potential with
\textit{minimal coupling} to gravity can resolve the tachyonic instability but
runs into the -problem. We suggest a model which is free of the
-problem due to an additional coupling in the K\"{a}hler potential which
is allowed by the Standard Model gauge group. This induces directions in the
potential which we call K-flat. For a certain value of the new coupling in the
(N)MSSM, the K\"{a}hler potential is special, because it can be associated with
a certain shift symmetry for the Higgs doublets, a generalization of the shift
symmetry for singlets in earlier models. We find that K-flat direction has
This shift symmetry is broken by interactions coming from
the superpotential and gauge fields. This direction fails to produce successful
inflation in the MSSM but produces a viable model in the NMSSM. The model is
specifically interesting in the Peccei-Quinn (PQ) limit of the NMSSM. In this
limit the model can be confirmed or ruled-out not just by cosmic microwave
background observations but also by axion searches.Comment: matches the published version at JCA
Asymptotic Expansions for the Sojourn Time Distribution in the -PS Queue
We consider the queue with a processor sharing server. We study the
conditional sojourn time distribution, conditioned on the customer's service
requirement, as well as the unconditional distribution, in various asymptotic
limits. These include large time and/or large service request, and heavy
traffic, where the arrival rate is only slightly less than the service rate.
Our results demonstrate the possible tail behaviors of the unconditional
distribution, which was previously known in the cases and (where it
is purely exponential). We assume that the service density decays at least
exponentially fast. We use various methods for the asymptotic expansion of
integrals, such as the Laplace and saddle point methods.Comment: 45 page
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