Self-similar cosmologies in 5D: spatially flat anisotropic models

In the context of theories of Kaluza-Klein type, with a large extra dimension, we study self-similar cosmological models in 5D that are homogeneous, anisotropic and spatially flat. The "ladder" to go between the physics in 5D and 4D is provided by Campbell-Maagard's embedding theorems. We show that the 5-dimensional field equations $R_{AB} = 0$ determine the form of the similarity variable. There are three different possibilities: homothetic, conformal and "wave-like" solutions in 5D. We derive the most general homothetic and conformal solutions to the 5D field equations. They require the extra dimension to be spacelike, and are given in terms of one arbitrary function of the similarity variable and three parameters. The Riemann tensor in 5D is not zero, except in the isotropic limit, which corresponds to the case where the parameters are equal to each other. The solutions can be used as 5D embeddings for a great variety of 4D homogeneous cosmological models, with and without matter, including the Kasner universe. Since the extra dimension is spacelike, the 5D solutions are invariant under the exchange of spatial coordinates. Therefore they also embed a family of spatially {\it inhomogeneous} models in 4D. We show that these models can be interpreted as vacuum solutions in braneworld theory. Our work (I) generalizes the 5D embeddings used for the FLRW models; (II) shows that anisotropic cosmologies are, in general, curved in 5D, in contrast with FLRW models which can always be embedded in a 5D Riemann-flat (Minkowski) manifold; (III) reveals that anisotropic cosmologies can be curved and devoid of matter, both in 5D and 4D, even when the metric in 5D explicitly depends on the extra coordinate, which is quite different from the isotropic case.Comment: Typos corrected. Minor editorial changes and additions in the Introduction and Summary section

Equivalence Between Space-Time-Matter and Brane-World Theories

We study the relationship between space-time-matter (STM) and brane theories. These two theories look very different at first sight, and have different motivation for the introduction of a large extra dimension. However, we show that they are equivalent to each other. First we demonstrate that STM predicts local and non-local high-energy corrections to general relativity in 4D, which are identical to those predicted by brane-world models. Secondly, we notice that in brane models the usual matter in 4D is a consequence of the dependence of five-dimensional metrics on the extra coordinate. If the 5D bulk metric is independent of the extra dimension, then the brane is void of matter. Thus, in brane theory matter and geometry are unified, which is exactly the paradigm proposed in STM. Consequently, these two 5D theories share the same concepts and predict the same physics. This is important not only from a theoretical point of view, but also in practice. We propose to use a combination of both methods to alleviate the difficult task of finding solutions on the brane. We show an explicit example that illustrate the feasibility of our proposal.Comment: Typos corrected, three references added. To appear in Mod. Phys. Let

Tailored gamification and serious game framework based on fuzzy logic for saving energy in connected thermostats

Connected thermostats (CTs) often save less energy than predicted because consumers may not know how to use them and may not be engaged in saving energy. Additionally, several models perform contrary to consumers’ expectations and are thus not used the way they are intended to. As a result, CTs save less energy and are underused in households. This paper reviews aspects of gamification and serious games focused on engaging consumers. A gamification and serious games framework is proposed for saving energy that is tailored by a fuzzy logic system to motivate connected thermostat consumers. This intelligent gamification framework can be used to customize the gamification and serious game strategy to each consumer so that fuzzy logic systems can be adapted according to the requirements of each consumer. The framework is designed to teach, engage, and motivate consumers while helping them save electrical energy when using their thermostats. It is described the proposed framework as well as a mockup that can be run on a cellphone. Although this framework is designed to be implemented in CTs, it can be translated to their energy devices in smart homes

Stellar models with Schwarzschild and non-Schwarzschild vacuum exteriors

A striking characteristic of non-Schwarzschild vacuum exteriors is that they contain not only the total gravitational mass of the source, but also an {\it arbitrary} constant. In this work, we show that the constants appearing in the "temporal Schwarzschild", "spatial Schwarzschild" and "Reissner-Nordstr{\"o}m-like" exteriors are not arbitrary but are completely determined by star's parameters, like the equation of state and the gravitational potential. Consequently, in the braneworld scenario the gravitational field outside of a star is no longer determined by the total mass alone, but also depends on the details of the internal structure of the source. We show that the general relativistic upper bound on the gravitational potential $M/R < 4/9$, for perfect fluid stars, is significantly increased in these exteriors. Namely, $M/R < 1/2$, $M/R < 2/3$ and $M/R < 1$ for the temporal Schwarzschild, spatial Schwarzschild and Reissner-Nordstr{\"o}m-like exteriors, respectively. Regarding the surface gravitational redshift, we find that the general relativistic Schwarzschild exterior as well as the braneworld spatial Schwarzschild exterior lead to the same upper bound, viz., $Z < 2$. However, when the external spacetime is the temporal Schwarzschild metric or the Reissner-Nordstr{\"o}m-like exterior there is no such constraint: $Z < \infty$. This infinite difference in the limiting value of $Z$ is because for these exteriors the effective pressure at the surface is negative. The results of our work are potentially observable and can be used to test the theory.Comment: 19 pages, 3 figures and caption

Brane world solutions of perfect fluid in the background of a bulk containing dust or cosmological constant

The paper presents some solutions to the five dimensional Einstein equations due to a perfect fluid on the brane with pure dust filling the entire bulk in one case and a cosmological constant (or vacuum) in the bulk for the second case. In the first case, there is a linear relationship between isotropic pressure, energy density and the brane tension, while in the second case, the perfect fluid is assumed to be in the form of chaplygin gas. Cosmological solutions are found both for brane and bulk scenarios and some interesting features are obtained for the chaplygin gas on the brane which are distinctly different from the standard cosmology in four dimensions.Comment: 10 Latex pages, 5 figure

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

Photoluminescence of near-lattice-matched GaN/AlInN quantum wells grown on free-standing GaN and on sapphire substrates

Near-lattice-matched GaN/Al1−xInxN single quantum wells, grown using both free-standing GaN and conventional GaN-on-sapphire substrates, are studied by photoluminescence (PL) and PL excitation spectroscopies. PL spectra distinguish luminescence originating in the wells, barriers, and underlying GaN buffer layers. The spectra also reveal significant differences between structures grown simultaneously on the different substrates. The quantum well transition energy decreases as the well width increases due to the intense in-built electric fields, estimated to be 3.0±0.5 MeV/cm, that persist in strain free GaN/Al1−xInxN. Screening of these fields is studied using the excitation power dependence of the P

Tosio Kato (1917–1999)

Tosio Kato was born August 25, 1917, in Kanuma City, Tochigi-ken, Japan. His early training was in physics. He obtained a B.S. in 1941 and the degree of Doctor of Science in 1951, both at the University of Tokyo. Between these events he published papers on a variety of subjects, including pair creation by gamma rays, motion of an object in a fluid, and results on spectral theory of operators arising in quantum mechanics. His dissertation was entitled “On the convergence of the perturbation method”. Kato was appointed assistant professor of physics at the University of Tokyo in 1951 and was promoted to professor of physics in 1958. During this time he visited the University of California at Berkeley in 1954–55, New York University in 1955, the National Bureau of Standards in 1955–56, and Berkeley and the California Institute of Technology in 1957–58. He was appointed professor of mathematics at Berkeley in 1962 and taught there until his retirement in 1988. He supervised twenty-one Ph.D. students at Berkeley and three at the University of Tokyo. Kato published over 160 papers and 6 monographs, including his famous book Perturbation Theory for Linear Operators [K66b]. Recognition for his important work included the Norbert Wiener Prize in Applied Mathematics, awarded in 1980 by the AMS and the Society for Industrial and Applied Mathematics. He was particularly well known for his work on Schrödinger equations of nonrelativistic quantum mechanics and his work on the Navier-Stokes and Euler equations of classical fluid mechanics. His activity in the latter area remained at a high level well past retirement and continued until his death on October 2, 1999

The Effective Energy-Momentum Tensor in Kaluza-Klein Gravity With Large Extra Dimensions and Off-Diagonal Metrics

We consider a version of Kaluza-Klein theory where the cylinder condition is not imposed. The metric is allowed to have explicit dependence on the "extra" coordinate(s). This is the usual scenario in brane-world and space-time-matter theories. We extend the usual discussion by considering five-dimensional metrics with off-diagonal terms. We replace the condition of cylindricity by the requirement that physics in four-dimensional space-time should remain invariant under changes of coordinates in the five-dimensional bulk. This invariance does not eliminate physical effects from the extra dimension but separates them from spurious geometrical ones. We use the appropriate splitting technique to construct the most general induced energy-momentum tensor, compatible with the required invariance. It generalizes all previous results in the literature. In addition, we find two four-vectors, J_{m}^{mu} and J_{e}^{mu}, induced by off-diagonal metrics, that separately satisfy the usual equation of continuity in 4D. These vectors appear as source-terms in equations that closely resemble the ones of electromagnetism. These are Maxwell-like equations for an antisymmetric tensor {F-hat}_{mu nu} that generalizes the usual electromagnetic one. This generalization is not an assumption, but follows naturally from the dimensional reduction. Thus, if {F-hat}_{mu nu} could be identified with the electromagnetic tensor, then the theory would predict the existence of classical magnetic charge and current. The splitting formalism used allows us to construct 4D physical quantities from five-dimensional ones, in a way that is independent on how we choose our space-time coordinates from those of the bulk.Comment: New title, editorial changes made as to match the version to appear in International Journal of Modern Physics