471 research outputs found
The Percolation Signature of the Spin Glass Transition
Magnetic ordering at low temperature for Ising ferromagnets manifests itself
within the associated Fortuin-Kasteleyn (FK) random cluster representation as
the occurrence of a single positive density percolating network. In this paper
we investigate the percolation signature for Ising spin glass ordering -- both
in short-range (EA) and infinite-range (SK) models -- within a two-replica FK
representation and also within the different Chayes-Machta-Redner two-replica
graphical representation. Based on numerical studies of the EA model in
three dimensions and on rigorous results for the SK model, we conclude that the
spin glass transition corresponds to the appearance of {\it two} percolating
clusters of {\it unequal} densities.Comment: 13 pages, 6 figure
Towards a formalism for mapping the spacetimes of massive compact objects: Bumpy black holes and their orbits
Observations have established that extremely compact, massive objects are
common in the universe. It is generally accepted that these objects are black
holes. As observations improve, it becomes possible to test this hypothesis in
ever greater detail. In particular, it is or will be possible to measure the
properties of orbits deep in the strong field of a black hole candidate (using
x-ray timing or with gravitational-waves) and to test whether they have the
characteristics of black hole orbits in general relativity. Such measurements
can be used to map the spacetime of a massive compact object, testing whether
the object's multipoles satisfy the strict constraints of the black hole
hypothesis. Such a test requires that we compare against objects with the
``wrong'' multipole structure. In this paper, we present tools for constructing
bumpy black holes: objects that are almost black holes, but that have some
multipoles with the wrong value. The spacetimes which we present are good deep
into the strong field of the object -- we do not use a large r expansion,
except to make contact with weak field intuition. Also, our spacetimes reduce
to the black hole spacetimes of general relativity when the ``bumpiness'' is
set to zero. We propose bumpy black holes as the foundation for a null
experiment: if black hole candidates are the black holes of general relativity,
their bumpiness should be zero. By comparing orbits in a bumpy spacetime with
those of an astrophysical source, observations should be able to test this
hypothesis, stringently testing whether they are the black holes of general
relativity. (Abridged)Comment: 16 pages + 2 appendices + 3 figures. Submitted to PR
Pattern densities in fluid dimer models
In this paper, we introduce a family of observables for the dimer model on a
bi-periodic bipartite planar graph, called pattern density fields. We study the
scaling limit of these objects for liquid and gaseous Gibbs measures of the
dimer model, and prove that they converge to a linear combination of a
derivative of the Gaussian massless free field and an independent white noise.Comment: 38 pages, 3 figure
DNA electrophoresis studied with the cage model
The cage model for polymer reptation, proposed by Evans and Edwards, and its
recent extension to model DNA electrophoresis, are studied by numerically exact
computation of the drift velocities for polymers with a length L of up to 15
monomers. The computations show the Nernst-Einstein regime (v ~ E) followed by
a regime where the velocity decreases exponentially with the applied electric
field strength. In agreement with de Gennes' reptation arguments, we find that
asymptotically for large polymers the diffusion coefficient D decreases
quadratically with polymer length; for the cage model, the proportionality
coefficient is DL^2=0.175(2). Additionally we find that the leading correction
term for finite polymer lengths scales as N^{-1/2}, where N=L-1 is the number
of bonds.Comment: LaTeX (cjour.cls), 15 pages, 6 figures, added correctness proof of
kink representation approac
New Black Hole Solutions in Brans-Dicke Theory of Gravity
Existence check of non-trivial, stationary axisymmetric black hole solutions
in Brans-Dicke theory of gravity in different direction from those of Penrose,
Thorne and Dykla, and Hawking is performed. Namely, working directly with the
known explicit spacetime solutions in Brans-Dicke theory, it is found that
non-trivial Kerr-Newman-type black hole solutions different from general
relativistic solutions could occur for the generic Brans-Dicke parameter values
-5/2\leq \omega <-3/2. Finally, issues like whether these new black holes carry
scalar hair and can really arise in nature and if they can, what the associated
physical implications would be are discussed carefully.Comment: 20 pages, no figure, Revtex, version to appear in Phys. Rev.
Relationship of ankle blood pressures to cardiovascular events in older adults.
BACKGROUND AND PURPOSE - Low values of ankle-arm systolic blood pressure ratio predict mortality and cardiovascular events. High values, associated with arterial calcification, also carry risk for mortality. We focus on the extent to which low and high ankle-arm index values as well as noncompressible arteries are associated with mortality and cardiovascular events, including stroke in older adults. METHODS - We followed 2886 adults aged 70 to 79 for a mean of 6.7 years for vital status and cardiovascular events (coronary heart disease, stroke, and congestive heart failure). RESULTS - Normal ankle-arm index values of 0.91 to 1.3 were found in 80%, low values of ≤0.9 were found in 13%, high values of >1.3 were obtained in 5%, and noncompressible arteries were found in 2% of the group. Increased mortality was associated with both low and high ankle-arm index values beginning at levels of <1.0 or ≥1.4. Subjects with low ankle-arm index values or noncompressible arteries had significantly higher event rates than those with normal ankle blood pressures for all end points. For coronary heart disease, hazard ratios associated with a low ankle-arm index, high ankle-arm index, and noncompressible arteries were 1.4, 1.5, and 1.7 (P<0.05 for all) after controlling for age, gender, race, prevalent cardiovascular disease, diabetes, and major cardiovascular risk factors. Noncompressible arteries carried a particularly high risk of stroke and congestive heart failure (hazard ratio=2.1 and 2.4, respectively). CONCLUSIONS - Among older adults, low and high ankle-arm index values carry elevated risk for cardiovascular events. Noncompressible leg arteries carry elevated risk for stroke and congestive heart failure specifically. © 2008 American Heart Association, Inc
Elasticity of Semiflexible Biopolymer Networks
We develop a model for gels and entangled solutions of semiflexible
biopolymers such as F-actin. Such networks play a crucial structural role in
the cytoskeleton of cells. We show that the rheologic properties of these
networks can result from nonclassical rubber elasticity. This model can explain
a number of elastic properties of such networks {\em in vitro}, including the
concentration dependence of the storage modulus and yield strain.Comment: Uses RevTeX, full postscript with figures available at
http://www.umich.edu/~fcm/preprints/agel/agel.htm
Cluster Monte Carlo study of multi-component fluids of the Stillinger-Helfand and Widom-Rowlinson type
Phase transitions of fluid mixtures of the type introduced by Stillinger and
Helfand are studied using a continuum version of the invaded cluster algorithm.
Particles of the same species do not interact, but particles of different types
interact with each other via a repulsive potential. Examples of interactions
include the Gaussian molecule potential and a repulsive step potential.
Accurate values of the critical density, fugacity and magnetic exponent are
found in two and three dimensions for the two-species model. The effect of
varying the number of species and of introducing quenched impurities is also
investigated. In all the cases studied, mixtures of -species are found to
have properties similar to -state Potts models.Comment: 25 pages, 5 figure
Reconstruction of Black Hole Metric Perturbations from Weyl Curvature
Perturbation theory of rotating black holes is usually described in terms of
Weyl scalars and , which each satisfy Teukolsky's complex
master wave equation and respectively represent outgoing and ingoing radiation.
On the other hand metric perturbations of a Kerr hole can be described in terms
of (Hertz-like) potentials in outgoing or ingoing {\it radiation
gauges}. In this paper we relate these potentials to what one actually computes
in perturbation theory, i.e and . We explicitly construct
these relations in the nonrotating limit, preparatory to devising a
corresponding approach for building up the perturbed spacetime of a rotating
black hole. We discuss the application of our procedure to second order
perturbation theory and to the study of radiation reaction effects for a
particle orbiting a massive black hole.Comment: 6 Pages, Revtex
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