1,337,322 research outputs found
The minimal volume orientable hyperbolic 2-cusped 3-manifolds
We prove that the Whitehead link complement and the (-2, 3, 8) pretzel link
complement are the minimal volume orientable hyperbolic 3-manifolds with two
cusps, with volume 3.66... = 4 x Catalan's constant. We use topological
arguments to establish the existence of an essential surface which provides a
lower bound on volume and strong constraints on the manifolds that realize that
lower bound.Comment: 10 pages, 5 figures, incorporated referees comments, includes
hyperref link
Volume Effects on the Glass Transition Dynamics
The role of jamming (steric constraints) and its relationship to the
available volume is addressed by examining the effect that certain
modifications of a glass-former have on the ratio of its isochoric and isobaric
activation enthalpies. This ratio reflects the relative contribution of volume
(density) and temperature (thermal energy) to the temperature-dependence of the
relaxation times of liquids and polymers. We find that an increase in the
available volume confers a stronger volume-dependence to the relaxation
dynamics, a result at odds with free volume interpretations of the glass
transition.Comment: 9 pages 5 figure
Figures of merit for present and future dark energy probes
We compare current and forecasted constraints on dynamical dark energy models
from Type Ia supernovae and the cosmic microwave background using figures of
merit based on the volume of the allowed dark energy parameter space. For a
two-parameter dark energy equation of state that varies linearly with the scale
factor, and assuming a flat universe, the area of the error ellipse can be
reduced by a factor of ~10 relative to current constraints by future
space-based supernova data and CMB measurements from the Planck satellite. If
the dark energy equation of state is described by a more general basis of
principal components, the expected improvement in volume-based figures of merit
is much greater. While the forecasted precision for any single parameter is
only a factor of 2-5 smaller than current uncertainties, the constraints on
dark energy models bounded by -1<w<1 improve for approximately 6 independent
dark energy parameters resulting in a reduction of the total allowed volume of
principal component parameter space by a factor of ~100. Typical quintessence
models can be adequately described by just 2-3 of these parameters even given
the precision of future data, leading to a more modest but still significant
improvement. In addition to advances in supernova and CMB data, percent-level
measurement of absolute distance and/or the expansion rate is required to
ensure that dark energy constraints remain robust to variations in spatial
curvature.Comment: 9 pages, 7 figures; submitted to Phys. Rev.
Warm DBI Inflation
We propose a warm inflationary model in the context of relativistic D-brane
inflation in a warped throat, which has Dirac-Born-Infeld (DBI) kinetic term
and is coupled to radiation through a dissipation term. The perturbation
freezes at the sound horizon and the power spectrum is determined by a
combination of the dissipative parameter and the sound speed parameter. The
thermal dissipation ameliorates the {\it eta} problem and softens theoretical
constraints from the extra-dimensional volume and from observational bounds on
the tensor-to-scalar ratio. The warm DBI model can lead to appreciable
non-Gaussianity of the equilateral type. As a phenomenological model, ignoring
compactification constraints, we show that large-field warm inflation models do
not necessarily yield a large tensor-to-scalar ratio.Comment: 5 pages, 1 figure, IPMU-10-019
Why multi-tracer surveys beat cosmic variance
Galaxy surveys that map multiple species of tracers of large-scale structure
can improve the constraints on some cosmological parameters far beyond the
limits imposed by a simplistic interpretation of cosmic variance. This
enhancement derives from comparing the relative clustering between different
tracers of large-scale structure. We present a simple but fully generic
expression for the Fisher information matrix of surveys with any (discrete)
number of tracers, and show that the enhancement of the constraints on
bias-sensitive parameters are a straightforward consequence of this
multi-tracer Fisher matrix. In fact, the relative clustering amplitudes between
tracers are eigenvectors of this multi-tracer Fisher matrix. The diagonalized
multi-tracer Fisher matrix clearly shows that while the effective volume is
bounded by the physical volume of the survey, the relational information
between species is unbounded. As an application, we study the expected
enhancements in the constraints of realistic surveys that aim at mapping
several different types of tracers of large-scale structure. The gain obtained
by combining multiple tracers is highest at low redshifts, and in one
particular scenario we analyzed, the enhancement can be as large as a factor of
~3 for the accuracy in the determination of the redshift distortion parameter,
and a factor ~5 for the local non-Gaussianity parameter. Radial and angular
distance determinations from the baryonic features in the power spectrum may
also benefit from the multi-tracer approach.Comment: New references included; 9 pages, 9 figure
Are Small Hyperbolic Universes Observationally Detectable?
Using recent observational constraints on cosmological density parameters,
together with recent mathematical results concerning small volume hyperbolic
manifolds, we argue that, by employing pattern repetitions, the topology of
nearly flat small hyperbolic universes can be observationally undetectable.
This is important in view of the facts that quantum cosmology may favour
hyperbolic universes with small volumes, and from the expectation coming from
inflationary scenarios, that is likely to be very close to one.Comment: 5 pages, 1 figure, LaTeX2e. A reference and two footnotes added. To
appear in Class. Quantum Grav. 18 (2001) in the present for
Topological gravity localization on a delta-function like Brane
Besides the String Theory context, the quantum General Relativity can be
studied by the use of constrained topological field theories. In the celebrated
Plebanski formalism, the constraints connecting topological field theories and
gravity are imposed in space-times with trivial topology. In the braneworld
context there are two distinct regions of the space-time, namely, the bulk and
the braneworld volume. In this work we show how to construct topological
gravity in a scenario containing one extra dimension and a delta-function like
3-brane which naturally emerges from a spontaneously broken discrete symmetry.
Starting from a D=5 theory we obtain the action for General Relativity in the
Palatini form in the bulk as well as in the braneworld volume. This result is
important for future insights about quantum gravity in brane scenarios.Comment: 4 page
Volume fluctuations and geometrical constraints in granular packs
Structural organization and correlations are studied in very large packings
of equally sized acrylic spheres, reconstructed in three-dimensions by means of
X-ray computed tomography. A novel technique, devised to analyze correlations
among more than two spheres, shows that the structural organization can be
conveniently studied in terms of a space-filling packing of irregular
tetrahedra. The study of the volume distribution of such tetrahedra reveals an
exponential decay in the region of large volumes; a behavior that is in very
good quantitative agreement with theoretical prediction. I argue that the
system's structure can be described as constituted of two phases: 1) an
`unconstrained' phase which freely shares the volume; 2) a `constrained' phase
which assumes configurations accordingly with the geometrical constraints
imposed by the condition of non-overlapping between spheres and mechanical
stability. The granular system exploits heterogeneity maximizing freedom and
entropy while constraining mechanical stability.Comment: 5 pages, 4 figure
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