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 $I$ diagonal case. The 3- curvature can be understood as a generalized potential, and the Bianchi $I$ 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 $I$ 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

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

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

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

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.

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