6,843 research outputs found
Modelling crystal aggregation and deposition\ud in the catheterised lower urinary tract
Urethral catheters often become encrusted with crystals of magnesium struvite and calcium phosphate. The encrustation can block the catheter, which can cause urine retention in the bladder and reflux into the kidneys. We develop a mathematical model to investigate crystal deposition on the catheter surface, modelling the bladder as a reservoir of fluid and the urethral catheter as a rigid channel. At a constant rate, fluid containing crystal particles of unit size enters the reservoir, and flows from the reservoir through the channel and out of the system. The crystal particles aggregate, which we model using Becker–Döring coagulation theory, and are advected through the channel, where they continue to aggregate and are deposited on the channel’s walls. Inhibitor particles also enter the reservoir, and can bind to the crystals, preventing further aggregation and deposition. The crystal concentrations are spatially homogeneous in the reservoir, whereas the channel concentrations vary spatially as a result of advection, diffusion and deposition. We investigate the effect of inhibitor particles on the amount of deposition. For all parameter values, we find that crystals deposit along the full length of the channel, with maximum deposition close to the channel’s entrance
A Statistical Treatment of the Gamma-Ray Burst "No Host Galaxy" Problem: II. Energies of Standard Candle Bursts
With the discovery that the afterglows after some bursts are coincident with
faint galaxies, the search for host galaxies is no longer a test of whether
bursts are cosmological, but rather a test of particular cosmological models.
The methodology we developed to investigate the original "no host galaxy"
problem is equally valid for testing different cosmological models, and is
applicable to the galaxies coincident with optical transients. We apply this
methodology to a family of models where we vary the total energy of standard
candle bursts. We find that total isotropic energies of E<2e52~erg are ruled
out while log(E)~53 erg is favored.Comment: To appear in Ap.J., 514, 15 pages + 7 figures, AASTeX 4.0. Revisions
are: additional author, updated data, and minor textual change
The BATSE Gamma-Ray Burst Spectral Catalog. I. High Time Resolution Spectroscopy of Bright Bursts using High Energy Resolution Data
This is the first in a series of gamma-ray burst spectroscopy catalogs from
the Burst And Transient Source Experiment (BATSE) on the Compton Gamma Ray
Observatory, each covering a different aspect of burst phenomenology. In this
paper, we present time-sequences of spectral fit parameters for 156 bursts
selected for either their high peak flux or fluence. All bursts have at least
eight spectra in excess of 45 sigma above background and span burst durations
from 1.66 to 278 s. Individual spectral accumulations are typically 128 ms long
at the peak of the brightest events, but can be as short as 16 ms, depending on
the type of data selected. We have used mostly high energy resolution data from
the Large Area Detectors, covering an energy range of typically 28 - 1800 keV.
The spectral model chosen is from a small empirically-determined set of
functions, such as the well-known `GRB' function, that best fits the
time-averaged burst spectra. Thus, there are generally three spectral shape
parameters available for each of the 5500 total spectra: a low-energy power-law
index, a characteristic break energy and possibly a high-energy power-law
index. We present the distributions of the observed sets of these parameters
and comment on their implications. The complete set of data that accompanies
this paper is necessarily large, and thus is archived electronically at:
http://www.journals.uchicago.edu/ApJ/journal/.Comment: Accepted for publication: ApJS, 125. 38 pages, 9 figures;
supplementary electronic archive to be published by ApJ; available from lead
author upon reques
Target Mass Monitoring and Instrumentation in the Daya Bay Antineutrino Detectors
The Daya Bay experiment measures sin^2 2{\theta}_13 using functionally
identical antineutrino detectors located at distances of 300 to 2000 meters
from the Daya Bay nuclear power complex. Each detector consists of three nested
fluid volumes surrounded by photomultiplier tubes. These volumes are coupled to
overflow tanks on top of the detector to allow for thermal expansion of the
liquid. Antineutrinos are detected through the inverse beta decay reaction on
the proton-rich scintillator target. A precise and continuous measurement of
the detector's central target mass is achieved by monitoring the the fluid
level in the overflow tanks with cameras and ultrasonic and capacitive sensors.
In addition, the monitoring system records detector temperature and levelness
at multiple positions. This monitoring information allows the precise
determination of the detectors' effective number of target protons during data
taking. We present the design, calibration, installation and in-situ tests of
the Daya Bay real-time antineutrino detector monitoring sensors and readout
electronics.Comment: 22 pages, 20 figures; accepted by JINST. Changes in v2: minor
revisions to incorporate editorial feedback from JINS
BATSE Gamma-Ray Burst Line Search: V. Probability of Detecting a Line in a Burst
The physical importance of the apparent discrepancy between the detections by
pre-BATSE missions of absorption lines in gamma-ray burst spectra and the
absence of a BATSE line detection necessitates a statistical analysis of this
discrepancy. This analysis requires a calculation of the probability that a
line, if present, will be detected in a given burst. However, the connection
between the detectability of a line in a spectrum and in a burst requires a
model for the occurrence of a line within a burst. We have developed the
necessary weighting for the line detection probability for each spectrum
spanning the burst. The resulting calculations require a description of each
spectrum in the BATSE database. With these tools we identify the bursts in
which lines are most likely to be detected. Also, by assuming a small frequency
with which lines occur, we calculate the approximate number of BATSE bursts in
which lines of various types could be detected. Lines similar to the Ginga
detections can be detected in relatively few BATSE bursts; for example, in only
~20 bursts are lines similar to the GB 880205 pair of lines detectable. Ginga
reported lines at ~20 and ~40 keV whereas the low energy cutoff of the BATSE
spectra is typically above 20 keV; hence BATSE's sensitivity to lines is less
than that of Ginga below 40 keV, and greater above. Therefore the probability
that the GB 880205 lines would be detected in a Ginga burst rather than a BATSE
burst is ~0.2. Finally, we adopted a more appropriate test of the significance
of a line feature.Comment: 20 pages, AASTeX 4.0, 5 figures, Ap.J. in pres
Spectral Hardness Decay with Respect to Fluence in BATSE Gamma-Ray Bursts
We have analyzed the evolution of the spectral hardness parameter Epk as a
function of fluence in gamma-ray bursts. We fit 41 pulses within 26 bursts with
the trend reported by Liang & Kargatis (1996) which found that Epk decays
exponentially with respect to photon fluence. We also fit these pulses with a
slight modification of this trend, where Epk decays linearly with energy
fluence. In both cases, we found the set of 41 pulses to be consistent with the
trend. For the latter trend, which we believe to be more physical, the
distribution of the decay constant is roughly log-normal, with a mean of 1.75
+/- 0.07 and a FWHM of 1.0 +/- 0.1. Regarding an earlier reported invariance in
the decay constant among different pulses in a single burst, we found
probabilities of 0.49 to 0.84 (depending on the test used) that such invariance
would occur by coincidence, most likely due to the narrow distribution of decay
constant values among pulses.Comment: 17 pages, 7 figure pages, 2 table pages, submitted to The
Astrophysical Journa
A family of diameter-based eigenvalue bounds for quantum graphs
We establish a sharp lower bound on the first non-trivial eigenvalue of the
Laplacian on a metric graph equipped with natural (i.e., continuity and
Kirchhoff) vertex conditions in terms of the diameter and the total length of
the graph. This extends a result of, and resolves an open problem from, [J. B.
Kennedy, P. Kurasov, G. Malenov\'a and D. Mugnolo, Ann. Henri Poincar\'e 17
(2016), 2439--2473, Section 7.2], and also complements an analogous lower bound
for the corresponding eigenvalue of the combinatorial Laplacian on a discrete
graph. We also give a family of corresponding lower bounds for the higher
eigenvalues under the assumption that the total length of the graph is
sufficiently large compared with its diameter. These inequalities are sharp in
the case of trees.Comment: Substantial revision of v1. The main result, originally for the first
eigenvalue, has been generalised to the higher ones. The title has been
changed and the proofs substantially reorganised to reflect the new result,
and a section containing concluding remarks has been adde
Dynamics of nodal points and the nodal count on a family of quantum graphs
We investigate the properties of the zeros of the eigenfunctions on quantum
graphs (metric graphs with a Schr\"odinger-type differential operator). Using
tools such as scattering approach and eigenvalue interlacing inequalities we
derive several formulas relating the number of the zeros of the n-th
eigenfunction to the spectrum of the graph and of some of its subgraphs. In a
special case of the so-called dihedral graph we prove an explicit formula that
only uses the lengths of the edges, entirely bypassing the information about
the graph's eigenvalues. The results are explained from the point of view of
the dynamics of zeros of the solutions to the scattering problem.Comment: 34 pages, 12 figure
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