52,034 research outputs found
Entropy "floor" and effervescent heating of intracluster gas
Recent X-ray observations of clusters of galaxies have shown that the entropy
of the intracluster medium (ICM), even at radii as large as half the virial
radius, is higher than that expected from gravitational processes alone. This
is thought to be the result of nongravitational processes influencing the
physical state of the ICM. In this paper, we investigate whether heating by a
central AGN can explain the distribution of excess entropy as a function of
radius. The AGN is assumed to inject buoyant bubbles into the ICM, which heat
the ambient medium by doing pdV work as they rise and expand. Several authors
have suggested that this "effervescent heating" mechanism could allow the
central regions of clusters to avoid the ``cooling catastrophe''. Here we study
the effect of effervescent heating at large radii. Our calculations show that
such a heating mechanism is able to solve the entropy problem. The only free
parameters of the model are the time-averaged luminosity and the AGN lifetime.
The results are mainly sensitive to the total energy injected into the cluster.
Our model predicts that the total energy injected by AGN should be roughly
proportional to the cluster mass. The expected correlation is consistent with a
linear relation between the mass of the central black hole(s) and the mass of
the cluster, which is reminiscent of the Magorrian relation between the black
hole and bulge mass.Comment: accepted for Ap
Testing Foundations of Biological Scaling Theory Using Automated Measurements of Vascular Networks
Scientists have long sought to understand how vascular networks supply blood
and oxygen to cells throughout the body. Recent work focuses on principles that
constrain how vessel size changes through branching generations from the aorta
to capillaries and uses scaling exponents to quantify these changes. Prominent
scaling theories predict that combinations of these exponents explain how
metabolic, growth, and other biological rates vary with body size.
Nevertheless, direct measurements of individual vessel segments have been
limited because existing techniques for measuring vasculature are invasive,
time consuming, and technically difficult. We developed software that extracts
the length, radius, and connectivity of in vivo vessels from contrast-enhanced
3D Magnetic Resonance Angiography. Using data from 20 human subjects, we
calculated scaling exponents by four methods--two derived from local properties
of branching junctions and two from whole-network properties. Although these
methods are often used interchangeably in the literature, we do not find
general agreement between these methods, particularly for vessel lengths.
Measurements for length of vessels also diverge from theoretical values, but
those for radius show stronger agreement. Our results demonstrate that vascular
network models cannot ignore certain complexities of real vascular systems and
indicate the need to discover new principles regarding vessel lengths
An Algorithmic Study of Manufacturing Paperclips and Other Folded Structures
We study algorithmic aspects of bending wires and sheet metal into a
specified structure. Problems of this type are closely related to the question
of deciding whether a simple non-self-intersecting wire structure (a
carpenter's ruler) can be straightened, a problem that was open for several
years and has only recently been solved in the affirmative.
If we impose some of the constraints that are imposed by the manufacturing
process, we obtain quite different results. In particular, we study the variant
of the carpenter's ruler problem in which there is a restriction that only one
joint can be modified at a time. For a linkage that does not self-intersect or
self-touch, the recent results of Connelly et al. and Streinu imply that it can
always be straightened, modifying one joint at a time. However, we show that
for a linkage with even a single vertex degeneracy, it becomes NP-hard to
decide if it can be straightened while altering only one joint at a time. If we
add the restriction that each joint can be altered at most once, we show that
the problem is NP-complete even without vertex degeneracies.
In the special case, arising in wire forming manufacturing, that each joint
can be altered at most once, and must be done sequentially from one or both
ends of the linkage, we give an efficient algorithm to determine if a linkage
can be straightened.Comment: 28 pages, 14 figures, Latex, to appear in Computational Geometry -
Theory and Application
Certified quantum non-demolition measurement of material systems
An extensive debate on quantum non-demolition (QND) measurement, reviewed in
Grangier et al. [Nature, {\bf 396}, 537 (1998)], finds that true QND
measurements must have both non-classical state-preparation capability and
non-classical information-damage tradeoff. Existing figures of merit for these
non-classicality criteria require direct measurement of the signal variable and
are thus difficult to apply to optically-probed material systems. Here we
describe a method to demonstrate both criteria without need for to direct
signal measurements. Using a covariance matrix formalism and a general noise
model, we compute meter observables for QND measurement triples, which suffice
to compute all QND figures of merit. The result will allow certified QND
measurement of atomic spin ensembles using existing techniques.Comment: 11 pages, zero figure
Entangled photons, nonlocality and Bell inequalities in the undergraduate laboratory
We use polarization-entangled photon pairs to demonstrate quantum nonlocality
in an experiment suitable for advanced undergraduates. The photons are produced
by spontaneous parametric downconversion using a violet diode laser and two
nonlinear crystals. The polarization state of the photons is tunable. Using an
entangled state analogous to that described in the Einstein-Podolsky-Rosen
``paradox,'' we demonstrate strong polarization correlations of the entanged
photons. Bell's idea of a hidden variable theory is presented by way of an
example and compared to the quantum prediction. A test of the Clauser, Horne,
Shimony and Holt version of the Bell inequality finds , in
clear contradiciton of hidden variable theories. The experiments described can
be performed in an afternoon.Comment: 10 pages, 6 figure
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