1,338 research outputs found
Convergence to Equilibrium States for Fluid Models of Many-server Queues with Abandonment
Fluid models have become an important tool for the study of many-server
queues with general service and patience time distributions. The equilibrium
state of a fluid model has been revealed by Whitt (2006) and shown to yield
reasonable approximations to the steady state of the original stochastic
systems. However, it remains an open question whether the solution to a fluid
model converges to the equilibrium state and under what condition. We show in
this paper that the convergence holds under a mild condition. Our method builds
on the framework of measure-valued processes developed in Zhang (2013), which
keeps track of the remaining patience and service times
Cool transition region loops observed by the Interface Region Imaging Spectrograph
We report on the first Interface Region Imaging Spectrograph (IRIS) study of
cool transition region loops. This class of loops has received little attention
in the literature. A cluster of such loops was observed on the solar disk in
active region NOAA11934, in the Si IV 1402.8 \AA\ spectral raster and 1400 \AA\
slit-jaw (SJ) images. We divide the loops into three groups and study their
dynamics and interaction. The first group comprises relatively stable loops,
with 382--626\,km cross-sections. Observed Doppler velocities are suggestive of
siphon flows, gradually changing from -10 km/s at one end to 20 km/s at the
other end of the loops. Nonthermal velocities from 15 to 25 km/s were
determined. These physical properties suggest that these loops are impulsively
heated by magnetic reconnection occurring at the blue-shifted footpoints where
magnetic cancellation with a rate of Mx/s is found. The released
magnetic energy is redistributed by the siphon flows. The second group
corresponds to two footpoints rooted in mixed-magnetic-polarity regions, where
magnetic cancellation occurred at a rate of Mx/s and line profiles
with enhanced wings of up to 200 km/s were observed. These are suggestive of
explosive-like events. The Doppler velocities combined with the SJ images
suggest possible anti-parallel flows in finer loop strands. In the third group,
interaction between two cool loop systems is observed. Evidence for magnetic
reconnection between the two loop systems is reflected in the line profiles of
explosive events, and a magnetic cancellation rate of Mx/s
observed in the corresponding area. The IRIS observations have thus opened a
new window of opportunity for in-depth investigations of cool transition region
loops. Further numerical experiments are crucial for understanding their
physics and their role in the coronal heating processes.Comment: Accepted for publication in Ap
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