572 research outputs found
Kaluza-Klein dimensional reduction and Gauss-Codazzi-Ricci equations
In this paper we imitate the traditional method which is used customarily in
the General Relativity and some mathematical literatures to derive the
Gauss-Codazzi-Ricci equations for dimensional reduction. It would be more
distinct concerning geometric meaning than the vielbein method. Especially, if
the lower dimensional metric is independent of reduced dimensions the
counterpart of the symmetric extrinsic curvature is proportional to the
antisymmetric Kaluza-Klein gauge field strength. For isometry group of internal
space, the SO(n) symmetry and SU(n) symmetry are discussed. And the
Kaluza-Klein instanton is also enquired.Comment: 15 page
Jacobi multipliers, non-local symmetries and nonlinear oscillators
Constants of motion, Lagrangians and Hamiltonians admitted by a family of
relevant nonlinear oscillators are derived using a geometric formalism. The
theory of the Jacobi last multiplier allows us to find Lagrangian descriptions
and constants of the motion. An application of the jet bundle formulation of
symmetries of differential equations is presented in the second part of the
paper. After a short review of the general formalism, the particular case of
non-local symmetries is studied in detail by making use of an extended
formalism. The theory is related to some results previously obtained by
Krasil'shchi, Vinogradov and coworkers. Finally the existence of non-local
symmetries for such two nonlinear oscillators is proved.Comment: 20 page
Homogeneous Solutions of Quadratic Gravity
It is believed that soon after the Planck time, Einstein's general relativity
theory should be corrected to an effective quadratic theory. In this work we
present the 3+1 decomposition for the zero vorticity case for arbitrary
spatially homogenous spaces. We specialize for the particular Bianchi
diagonal case. The 3- curvature can be understood as a generalized potential,
and the Bianchi case is a limiting case where this potential is negligible
to the dynamics. The spirit should be analogous, in some sense to the BKL
solution. In this sense, a better understanding of the Bianchi case could
shed some light into the general Bianchi case.Comment: talk presented in the 8th Friedmann Seminar, 30 May - 03 June 2011,
Rio de Janeiro, Brazi
Dulce de Leche—Chemistry and Processing Technology
Originally hailing from Latin America, dulce de leche (DL) is one of the most widely manufactured dairy products in South America, where it is marketed as a paste or bar. Due to DL’s low moisture content, the product can be safely stored at room temperature, which facilitates storage and transportation logistics. The primary ingredients used to manufacture DL are milk, sucrose, and an acidity reducer. Needless to say, the raw materials must be of good quality from reliable suppliers in order for the final product to have the desired characteristics. The milk used to make DL must be microbiologically safe, remain stable during thermal processing, and preferably exhibit a high solid content. Dulce de leche is defined as a product made with or without the addition of other food substances that is obtained from milk or reconstituted milk and added sucrose (either partially substituted or not by monosaccharides and/or other disaccharides) via concentration and heat action at normal or reduced pressure. This chapter aims to explore the chemistry, processing technology, and most common industrial practices for manufacturing DL in South America
Exact Foldy-Wouthuysen transformation for gravitational waves and magnetic field background
We consider an exact Foldy-Wouthuysen transformation for the Dirac spinor
field on the combined background of a gravitational wave and constant uniform
magnetic field. By taking the classical limit of the spinor field Hamiltonian
we arrive at the equations of motion for the non-relativistic spinning
particle. Two different kinds of the gravitational fields are considered and in
both cases the effect of the gravitational wave on the spinor field and on the
corresponding spinning particle may be enforced by the sufficiently strong
magnetic field. This result can be relevant for the astrophysical applications
and, in principle, useful for creating the gravitational wave detectors based
on atomic physics and precise interferometry
3D-printed products for topical skin applications : from personalized dressings to drug delivery
3D printing has been widely used for the personalization of therapies and on-demand production of complex pharmaceutical forms. Recently, 3D printing has been explored as a tool for the development of topical dosage forms and wound dressings. Thus, this review aims to present advances related to the use of 3D printing for the development of pharmaceutical and biomedical products for topical skin applications, covering plain dressing and products for the delivery of active ingredients to the skin. Based on the data acquired, the important growth in the number of publications over the last years confirms its interest. The semisolid extrusion technique has been the most reported one, probably because it allows the use of a broad range of polymers, creating the most diverse therapeutic approaches. 3D printing has been an excellent field for customizing dressings, according to individual needs. Studies discussed here imply the use of metals, nanoparticles, drugs, natural compounds and proteins and peptides for the treatment of wound healing, acne, pain relief, and anti-wrinkle, among others. The confluence of 3D printing and topical applications has undeniable advantages, and we would like to encourage the research groups to explore this field to improve the patient’s life quality, adherence and treatment efficacy
Morgan-Morgan-NUT disk space via the Ehlers transformation
Using the Ehlers transformation along with the gravitoelectromagnetic
approach to stationary spacetimes we start from the Morgan-Morgan disk
spacetime (without radial pressure) as the seed metric and find its
corresponding stationary spacetime. As expected from the Ehlers transformation
the stationary spacetime obtained suffers from a NUT-type singularity and the
new parameter introduced in the stationary case could be interpreted as the
gravitomagnetic monopole charge (or the NUT factor). As a consequence of this
singularity there are closed timelike curves (CTCs) in the singular region of
the spacetime. Some of the properties of this spacetime including its particle
velocity distribution, gravitational redshift, stability and energy conditions
are discussed.Comment: 18 pages, 5 figures, RevTex 4, replaced with the published versio
The Formation of non-Keplerian Rings of Matter about Compact Stars
The formation of energetic rings of matter in a Kerr spacetime with an
outward pointing acceleration field does not appear to have previously been
noted as a relativistic effect. In this paper we show that such rings are a
gravimagneto effect with no Newtonian analog, and that they do not occur in the
static limit. The energy efficiency of these rings can, depending of the
strength of the acceleration field, be much greater than that of Keplerian
disks. The rings rotate in a direction opposite to that of compact star about
which they form. The size and energy efficiency of the rings depend on the
fundamental parameters of the spacetime as well as the strength the
acceleration field.Comment: 19 pages, 7 figures, 1 diagram. Figures are included in the text
using the "graphicx" package. If you do not have this package you can use
epsfig, or another package as long as you alter the tex file appropriately.
Alternatively you could print the figures out seperatel
Periastron shift in Weyl class spacetimes
The periastron position advance for geodesic motion in axially symmetric
solutions of the Einstein field equations belonging to the Weyl class of vacuum
solutions is investigated. Explicit examples corresponding to either static
solutions (single Chazy-Curzon, Schwarzschild and a pair of them), or
stationary solution (single rotating Chazy-Curzon and Kerr black hole) are
discussed. The results are then applied to the case of S2-SgrA binary
system of which the periastron position advance will be soon measured with a
great accuracy.Comment: To appear on General Relativity and Gravitation, vol. 37, 200
Noether symmetries and analytical solutions in f(T)-cosmology: A complete study
We investigate the main features of the flat
Friedmann-Lema{\i}tre-Robertson-Walker cosmological models in the f(T)
teleparallel gravity. In particular, a general approach to find out exact
cosmological solutions in f (T) gravity is discussed. Instead of taking into
account phenomenological models, we consider as a selection criterion, the
existence of Noether symmetries in the cosmological f(T) point-like Lagrangian.
We find that only power-law models admit extra Noether symmetries. A complete
analysis of such cosmological models is developed.Comment: 16 pages, 1 figure, to be published in Phys. Rev.
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