397 research outputs found
An analytic model for the transition from decelerated to accelerated cosmic expansion
We consider the scenario where our observable universe is devised as a
dynamical four-dimensional hypersurface embedded in a five-dimensional bulk
spacetime, with a large extra dimension, which is the {\it generalization of
the flat FRW cosmological metric to five dimensions}. This scenario generates a
simple analytical model where different stages of the evolution of the universe
are approximated by distinct parameterizations of the {\it same} spacetime. In
this model the evolution from decelerated to accelerated expansion can be
interpreted as a "first-order" phase transition between two successive stages.
The dominant energy condition allows different parts of the universe to evolve,
from deceleration to acceleration, at different redshifts within a narrow era.
This picture corresponds to the creation of bubbles of new phase, in the middle
of the old one, typical of first-order phase transitions. Taking today, we find that the cross-over from deceleration to acceleration
occurs at , regardless of the equation of state in the very
early universe. In the case of primordial radiation, the model predicts that
the deceleration parameter "jumps" from to at . At the present time and the equation of state of the
universe is , in agreement with observations and some
theoretical predictions.Comment: The abstract and introduction are improved and the discussion section
is expanded. A number of references are adde
Wave-like Solutions for Bianchi type-I cosmologies in 5D
We derive exact solutions to the vacuum Einstein field equations in 5D, under
the assumption that (i) the line element in 5D possesses self-similar symmetry,
in the classical understanding of Sedov, Taub and Zeldovich, and that (ii) the
metric tensor is diagonal and independent of the coordinates for ordinary 3D
space. These assumptions lead to three different types of self-similarity in
5D: homothetic, conformal and "wave-like". In this work we present the most
general wave-like solutions to the 5D field equations. Using the standard
technique based on Campbell's theorem, they generate a large number of
anisotropic cosmological models of Bianchi type-I, which can be applied to our
universe after the big-bang, when anisotropies could have played an important
role. We present a complete review of all possible cases of self-similar
anisotropic cosmologies in 5D. Our analysis extends a number of previous
studies on wave-like solutions in 5D with spatial spherical symmetry
Lorentz violation and the speed of gravitational waves in brane-worlds
Lorentz violation in a brane-world scenario is presented and used to obtain a
relationship between the speed of gravitational waves in the bulk and that on
the brane. Lorentz violating effects would manifest themselves in gravitational
waves travelling with a greater speed in the bulk than on the brane and this
effect is independent of the signature of the extra dimension.Comment: 8 pages, to appear in PL
Modern cosmologies from empty Kaluza-Klein solutions in 5D
We show that the empty five-dimensional solutions of
Davidson-Sonnenschtein-Vozmediano, {\em Phys. Rev.} {\bf D32} (1985)1330, in
the "old" Kaluza-Klein gravity, under appropriate interpretation can generate
an ample variety of cosmological models in 4D, which include the
higher-dimensional modifications to general relativity predicted by "modern"
versions of noncompactified 5D gravity as, e.g., induced-matter and braneworld
theories. This is the first time that these solutions are investigated in a
systematic way as embeddings for cosmological models in 4D. They provide a
different formulation, which is complementary to the approaches used in current
versions of 5D relativity.Comment: Accepted for publication in JHE
Cosmological Implications of a Non-Separable 5D Solution of the Vacuum Einstein Field Equations
An exact class of solutions of the 5D vacuum Einstein field equations (EFEs)
is obtained. The metric coefficients are found to be non-separable functions of
time and the extra coordinate and the induced metric on = constant
hypersurfaces has the form of a Friedmann-Robertson-Walker cosmology. The 5D
manifold and 3D and 4D submanifolds are in general curved, which distinguishes
this solution from previous ones in the literature. The singularity structure
of the manifold is explored: some models in the class do not exhibit a big
bang, while other exhibit a big bang and a big crunch. For the models with an
initial singularity, the equation of state of the induced matter evolves from
radiation like at early epochs to Milne-like at late times and the big bang
manifests itself as a singular hypersurface in 5D. The projection of comoving
5D null geodesics onto the 4D submanifold is shown to be compatible with
standard 4D comoving trajectories, while the expansion of 5D null congruences
is shown to be in line with conventional notions of the Hubble expansion.Comment: 8 pages, in press in J. Math. Phy
Static wormholes on the brane inspired by Kaluza-Klein gravity
We use static solutions of 5-dimensional Kaluza-Klein gravity to generate
several classes of static, spherically symmetric spacetimes which are analytic
solutions to the equation , where is the
four-dimensional Ricci scalar. In the Randall & Sundrum scenario they can be
interpreted as vacuum solutions on the brane. The solutions contain the
Schwarzschild black hole, and generate new families of traversable Lorenzian
wormholes as well as nakedly singular spacetimes. They generalize a number of
previously known solutions in the literature, e.g., the temporal and spatial
Schwarzschild solutions of braneworld theory as well as the class of self-dual
Lorenzian wormholes. A major departure of our solutions from Lorenzian
wormholes {\it a la} Morris and Thorne is that, for certain values of the
parameters of the solutions, they contain three spherical surfaces (instead of
one) which are extremal and have finite area. Two of them have the same size,
meet the "flare-out" requirements, and show the typical violation of the energy
conditions that characterizes a wormhole throat. The other extremal sphere is
"flaring-in" in the sense that its sectional area is a local maximum and the
weak, null and dominant energy conditions are satisfied in its neighborhood.
After bouncing back at this second surface a traveler crosses into another
space which is the double of the one she/he started in. Another interesting
feature is that the size of the throat can be less than the Schwarzschild
radius , which no longer defines the horizon, i.e., to a distant observer
a particle or light falling down crosses the Schwarzschild radius in a finite
time
Teaching vs. Research: Toward the Reconciliation of an Academic Dilemma
A line of thought that compares two major changes in Higher Education and the societal environments surrounding them is presented. A model, currently taking place, associated with the perceived controversy between teaching and research is introduced and discussed. The need to foster appropriate procedures where university constituencies are brought together to participate in the process of reshaping the university model guaranteeing its survivability is recognized. Finally, options for teaching comparable with the scale established for research are proposed as a reconciliatory model to solve this academic dilemma
Effective spacetime from multi-dimensional gravity
We study the effective spacetimes in lower dimensions that can be extracted
from a multidimensional generalization of the Schwarzschild-Tangherlini
spacetimes derived by Fadeev, Ivashchuk and Melnikov ({\it Phys. Lett,} {\bf A
161} (1991) 98). The higher-dimensional spacetime has
dimensions, where and are the number of "internal" and "external" extra
dimensions, respectively. We analyze the effective spacetime obtained
after dimensional reduction of the external dimensions. We find that when
the extra dimensions are compact (i) the physics in lower dimensions is
independent of and the character of the singularities in higher dimensions,
and (ii) the total gravitational mass of the effective matter distribution
is less than the Schwarzshild mass. In contrast, when the extra dimensions
are large this is not so; the physics in does explicitly depend on
, as well as on the nature of the singularities in high dimensions, and the
mass of the effective matter distribution (with the exception of wormhole-like
distributions) is bigger than the Schwarzshild mass. These results may be
relevant to observations for an experimental/observational test of the theory.Comment: A typo in Eq. (24) is fixe
Quality indices for (practical) clustering evaluation
WOS:000271584000004 (Nº de Acesso Web of Science)Clustering quality or validation indices allow the evaluation of the quality of clustering in order to support the selection of a specific partition or clustering structure in its natural unsupervised environment, where the real solution is unknown or not available. In this paper, we investigate the use of quality indices mostly based on the concepts of clusters' compactness and separation, for the evaluation of clustering results (partitions in particular). This work intends to offer a general perspective regarding the appropriate use of quality indices for the purpose of clustering evaluation. After presenting some commonly used indices, as well as indices recently proposed in the literature, key issues regarding the practical use of quality indices are addressed. A general methodological approach is presented which considers the identification of appropriate indices thresholds. This general approach is compared with the simple use of quality indices for evaluating a clustering solution
The 3D printing of a polymeric electrochemical cell body and its characterisation
An undivided flow cell was designed and constructed using additive manufacturing technology and its mass transport characteristics were evaluated using the reduction of ferricyanide, hexacyanoferrate (III) ions at a nickel surface. The dimensionless mass transfer correlation Sh = aRebScdLee was obtained using the convective-diffusion limiting current observed in linear sweep voltammetry; this correlation compared closely with that reported in the literature from traditionally machined plane parallel rectangular flow channel reactors. The ability of 3D printer technology, aided by computational graphics, to rapidly and conveniently design, manufacture and re-design the geometrical characteristics of the flow cell ishighlighted
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