97 research outputs found
Monotone contractions of the boundary of the disc
In this paper, we study contractions of the boundary of a Riemannian 2-disc where the maximal length of the intermediate curves is minimized. We prove that with an arbitrarily small overhead in the lengths of the intermediate curves, there exists such an optimal contraction that is monotone, i.e., where the intermediate curves are simple closed curves which are pairwise disjoint. This proves a conjecture of Chambers and Rotman
Drawing Planar Graphs with a Prescribed Inner Face
Given a plane graph (i.e., a planar graph with a fixed planar embedding)
and a simple cycle in whose vertices are mapped to a convex polygon, we
consider the question whether this drawing can be extended to a planar
straight-line drawing of . We characterize when this is possible in terms of
simple necessary conditions, which we prove to be sufficient. This also leads
to a linear-time testing algorithm. If a drawing extension exists, it can be
computed in the same running time
Random geometric complexes
We study the expected topological properties of Cech and Vietoris-Rips
complexes built on i.i.d. random points in R^d. We find higher dimensional
analogues of known results for connectivity and component counts for random
geometric graphs. However, higher homology H_k is not monotone when k > 0. In
particular for every k > 0 we exhibit two thresholds, one where homology passes
from vanishing to nonvanishing, and another where it passes back to vanishing.
We give asymptotic formulas for the expectation of the Betti numbers in the
sparser regimes, and bounds in the denser regimes. The main technical
contribution of the article is in the application of discrete Morse theory in
geometric probability.Comment: 26 pages, 3 figures, final revisions, to appear in Discrete &
Computational Geometr
Irreducible triangulations of surfaces with boundary
A triangulation of a surface is irreducible if no edge can be contracted to
produce a triangulation of the same surface. In this paper, we investigate
irreducible triangulations of surfaces with boundary. We prove that the number
of vertices of an irreducible triangulation of a (possibly non-orientable)
surface of genus g>=0 with b>=0 boundaries is O(g+b). So far, the result was
known only for surfaces without boundary (b=0). While our technique yields a
worse constant in the O(.) notation, the present proof is elementary, and
simpler than the previous ones in the case of surfaces without boundary
The Effects of Atmospheric Dispersion on High-Resolution Solar Spectroscopy
We investigate the effects of atmospheric dispersion on observations of the
Sun at the ever-higher spatial resolutions afforded by increased apertures and
improved techniques. The problems induced by atmospheric refraction are
particularly significant for solar physics because the Sun is often best
observed at low elevations, and the effect of the image displacement is not
merely a loss of efficiency, but the mixing of information originating from
different points on the solar surface. We calculate the magnitude of the
atmospheric dispersion for the Sun during the year and examine the problems
produced by this dispersion in both spectrographic and filter observations. We
describe an observing technique for scanning spectrograph observations that
minimizes the effects of the atmospheric dispersion while maintaining a regular
scanning geometry. Such an approach could be useful for the new class of
high-resolution solar spectrographs, such as SPINOR, POLIS, TRIPPEL, and ViSP
Can induced gravity isotropize Bianchi I, V, or IX Universes?
We analyze if Bianchi I, V, and IX models in the Induced Gravity (IG) theory
can evolve to a Friedmann--Roberson--Walker (FRW) expansion due to the
non--minimal coupling of gravity and the scalar field. The analytical results
that we found for the Brans-Dicke (BD) theory are now applied to the IG theory
which has ( being the square ratio of the Higgs to
Planck mass) in a cosmological era in which the IG--potential is not
significant. We find that the isotropization mechanism crucially depends on the
value of . Its smallness also permits inflationary solutions. For the
Bianch V model inflation due to the Higgs potential takes place afterwads, and
subsequently the spontaneous symmetry breaking (SSB) ends with an effective FRW
evolution. The ordinary tests of successful cosmology are well satisfied.Comment: 24 pages, 5 figures, to be published in Phys. Rev. D1
Domain Wall Spacetimes: Instability of Cosmological Event and Cauchy Horizons
The stability of cosmological event and Cauchy horizons of spacetimes
associated with plane symmetric domain walls are studied. It is found that both
horizons are not stable against perturbations of null fluids and massless
scalar fields; they are turned into curvature singularities. These
singularities are light-like and strong in the sense that both the tidal forces
and distortions acting on test particles become unbounded when theses
singularities are approached.Comment: Latex, 3 figures not included in the text but available upon reques
Oligarchic growth of giant planets
Runaway growth ends when the largest protoplanets dominate the dynamics of
the planetesimal disk; the subsequent self-limiting accretion mode is referred
to as ``oligarchic growth.'' Here, we begin by expanding on the existing
analytic model of the oligarchic growth regime. From this, we derive global
estimates of the planet formation rate throughout a protoplanetary disk. We
find that a relatively high-mass protoplanetary disk ( 10
minimum-mass) is required to produce giant planet core-sized bodies ( 10
M) within the lifetime of the nebular gas (\la 10 million years).
However, an implausibly massive disk is needed to produce even an Earth mass at
the orbit of Uranus by 10 Myrs. Subsequent accretion without the dissipational
effect of gas is even slower and less efficient. In the limit of
non-interacting planetesimals, a reasonable-mass disk is unable to produce
bodies the size of the Solar System's two outer giant planets at their current
locations on {\it any} timescale; if collisional damping of planetesimal random
velocities is sufficiently effective, though, it may be possible for a
Uranus/Neptune to form in situ in less than the age of the Solar System. We
perform numerical simulations of oligarchic growth with gas, and find that
protoplanet growth rates agree reasonably well with the analytic model as long
as protoplanet masses are well below their estimated final masses. However,
accretion stalls earlier than predicted, so that the largest final protoplanet
masses are smaller than those given by the model. Thus the oligarchic growth
model, in the form developed here, appears to provide an upper limit for the
efficiency of giant planet formation.Comment: ScienceDirect already has the final published version here:
dx.doi.org/10.1016/S0019-1035(02)00043-
Performance of novel VUV-sensitive Silicon Photo-Multipliers for nEXO
Liquid xenon time projection chambers are promising detectors to search for
neutrinoless double beta decay (0), due to their response
uniformity, monolithic sensitive volume, scalability to large target masses,
and suitability for extremely low background operations. The nEXO collaboration
has designed a tonne-scale time projection chamber that aims to search for
0 of \ce{^{136}Xe} with projected half-life sensitivity of
~yr. To reach this sensitivity, the design goal for nEXO is
1\% energy resolution at the decay -value (~keV).
Reaching this resolution requires the efficient collection of both the
ionization and scintillation produced in the detector. The nEXO design employs
Silicon Photo-Multipliers (SiPMs) to detect the vacuum ultra-violet, 175 nm
scintillation light of liquid xenon. This paper reports on the characterization
of the newest vacuum ultra-violet sensitive Fondazione Bruno Kessler VUVHD3
SiPMs specifically designed for nEXO, as well as new measurements on new test
samples of previously characterised Hamamatsu VUV4 Multi Pixel Photon Counters
(MPPCs). Various SiPM and MPPC parameters, such as dark noise, gain, direct
crosstalk, correlated avalanches and photon detection efficiency were measured
as a function of the applied over voltage and wavelength at liquid xenon
temperature (163~K). The results from this study are used to provide updated
estimates of the achievable energy resolution at the decay -value for the
nEXO design
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