10,476 research outputs found
Cosmic acceleration in asymptotically Ricci flat Universe
We analyze the evolution of a Friedmann-Robertson-Walker spacetime within the
framework of metric gravity using an exponential model. We show that
gravity may lead to a vanishing effective cosmological constant in the
far future (i.e. ) and yet produce a transient accelerated
expansion at present time with a potentially viable cosmological history. This
is in contrast with several models which, while viable, produce in
general a non-vanishing effective cosmological constant asymptotically in time
(). We also show that relativistic {stars in
asymptotically flat spacetimes can be supported within this framework without
encountering any singularity, notably in the Ricci scalar .Comment: 12 pages, 18 figures in 9 panel
A model capturing novel strand symmetries in bacterial DNA
Chargaff's second parity rule for short oligonucleotides states that the
frequency of any short nucleotide sequence on a strand is approximately equal
to the frequency of its reverse complement on the same strand. Recent studies
have shown that, with the exception of organellar DNA, this parity rule
generally holds for double stranded DNA genomes and fails to hold for
single-stranded genomes. While Chargaff's first parity rule is fully explained
by the Watson-Crick pairing in the DNA double helix, a definitive explanation
for the second parity rule has not yet been determined. In this work, we
propose a model based on a hidden Markov process for approximating the
distributional structure of primitive DNA sequences. Then, we use the model to
provide another possible theoretical explanation for Chargaff's second parity
rule, and to predict novel distributional aspects of bacterial DNA sequences.Comment: This is a pre-copy-editing, author-produced preprint of an article
accepted for publication in Biochemical and Biophysical Research
Communications. The definitive publisher-authenticated version is available
online at: http://dx.doi.org/10.1016/j.bbrc.2011.06.072 or
http://www.sciencedirect.com/science/article/pii/S0006291X1101045X. 9 pages,
1 figur
The free boundary Euler equations with large surface tension
We study the free boundary Euler equations with surface tension in three
spatial dimensions, showing that the equations are well-posed if the
coefficient of surface tension is positive. Then we prove that under natural
assumptions, the solutions of the free boundary motion converge to solutions of
the Euler equations in a domain with fixed boundary when the coefficient of
surface tension tends to infinity.Comment: to appear in Journal of Differential Equation
On the limit of large surface tension for a fluid motion with free boundary
We study the free boundary Euler equations in two spatial dimensions. We
prove that if the boundary is sufficiently regular, then solutions of the free
boundary fluid motion converge to solutions of the Euler equations in a fixed
domain when the coefficient of surface tension tends to infinity
Channel Metrization
We present an algorithm that, given a channel, determines if there is a
distance for it such that the maximum likelihood decoder coincides with the
minimum distance decoder.
We also show that any metric, up to a decoding equivalence, can be
isometrically embedded into the hypercube with the Hamming metric, and thus, in
terms of decoding, the Hamming metric is universal.Comment: 17 pages, 3 figures, presented shorter version at WCC 201
Motion of slightly compressible fluids in a bounded domain. II
We study the problem of inviscid slightly compressible fluids in a bounded
domain. We find a unique solution to the initial-boundary value problem and
show that it is near the analogous solution for an incompressible fluid
provided the initial conditions for the two problems are close. In particular,
the divergence of the initial velocity of the compressible flow at time zero is
assumed to be small. Furthermore we find that solutions to the compressible
motion problem in Lagrangian coordinates depend differentiably on their initial
data, an unexpected result for this type of non-linear equations.Comment: to appear in Communications in Contemporary Mathematic
A Distance Between Channels: the average error of mismatched channels
Two channels are equivalent if their maximum likelihood (ML) decoders
coincide for every code. We show that this equivalence relation partitions the
space of channels into a generalized hyperplane arrangement. With this, we
define a coding distance between channels in terms of their ML-decoders which
is meaningful from the decoding point of view, in the sense that the closer two
channels are, the larger is the probability of them sharing the same
ML-decoder. We give explicit formulas for these probabilities
About matter and dark-energy domination eras in R^n gravity or lack thereof
We provide further numerical evidence which shows that R^n models in f(R)
metric gravity whether produces a late time acceleration in the Universe or a
matter domination era (usually a transient one) but not both. Our results
confirm the findings of Amendola et al. (2007), but using a different approach
that avoids the mapping to scalar-tensor theories of gravity, and therefore,
dispense us from any discussion or debate about frames (Einstein vs Jordan)
which are endemic in this subject. This class of models has been used
extensively in the literature as an alternative to the dark energy, but should
be considered ruled out for being inconsistent with observations. Finally, we
discuss a caveat in the analysis by Faraoni (2011), which was used to further
constrain these models by using a chameleon mechanism.Comment: 6 pages, 6 figures in 2 panels. Accepted for publication in Phys.
Rev.
f(R) Cosmology revisited
We consider a class of metric f(R) modified gravity theories, analyze them in
the context of a Friedmann-Robertson-Walker cosmology and confront the results
with some of the known constraints imposed by observations. In particular, we
focus in correctly reproducing the matter and effective cosmological constant
eras, the age of the Universe, and supernovae data. Our analysis differs in
many respects from previous studies. First, we avoid any transformation to a
scalar-tensor theory in order to be exempted of any potential pathologies (e.g.
multivalued scalar potentials) and also to evade any unnecessary discussion
regarding frames (i.e. Einstein vs Jordan). Second, based on a robust approach,
we recast the cosmology equations as an initial value problem subject to a
modified Hamiltonian constraint. Third, we solve the equations numerically
where the Ricci scalar itself is one of the variables, and use the constraint
equation to monitor the accuracy of the solutions. We compute the "equation of
state" (EOS) associated with the modifications of gravity using several
inequivalent definitions that have been proposed in the past and analyze it in
detail. We argue that one of these definitions has the best features. In
particular, we present the EOS around the so called "phantom divide" boundary
and compare it with previous findings.Comment: 35 pages; 33 figures; revte
Spherically symmetric black holes in gravity: Is geometric scalar hair supported ?
We discuss with a rather critical eye the current situation of black hole
(BH) solutions in gravity and shed light about its geometrical and
physical significance. We also argue about the meaning, existence or lack
thereof of a Birkhoff's theorem in this kind of modified gravity. We focus then
on the analysis and quest of (i.e. hairy)
(AF) BH solutions in static and spherically symmetric
(SSS) spacetimes in vacuum having the property that the Ricci scalar does
vanish identically in the domain of outer communication. To do so, we provide
and enforce the at the horizon in order to prevent
the presence of singular solutions there. Specifically, we consider several
classes of models like those proposed recently for explaining the
accelerated expansion in the universe and which have been thoroughly tested in
several physical scenarios. Finally, we report analytical and numerical
evidence about the of in AFSSSBH solutions in
those models. First, we submit the models to the available no-hair
theorems, and in the cases where the theorems apply, the absence of hair is
demonstrated analytically. In the cases where the theorems do not apply, we
resort to a numerical analysis due to the complexity of the non-linear
differential equations. Within that aim, a code to solve the equations
numerically was built and tested using well know exact solutions. In a future
investigation we plan to analyze the problem of hair in De Sitter and Anti-De
Sitter backgrounds.Comment: 32 pages, 11 figure
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