Physics

Geometric and motivationals but especially graphics arguments are presented concerning a posible generalization to the Black Hole (BH) model. The propousals are highly linked (i think) with the spinorial formalism. As a first step, we study the BH perturbations l = 0 and l = 1 in a tridimensional version of the Penrose-Carter diagram.

The proposal, in a nutshell, is to think of the cosine as a function that arises when studying "toroidal phenomena" --like the angular momentum-- with theories based on the presumption of a topologically spherical space-time.
This conjecture, which intends to be located in the origins of General Relativ-ity, needs a correct definition of the existent here called "toroidal phenomenon". That is to say, we will have to pause a moment in the assumptions about space-time that we seek to question. Modesty aside, let's think of as an analogy in Einstein's effort to convince the scientific community that Space and Time were not two independent existents, but that one could transform one into the other according to the observer. That questioning, of the ontological type, will be the branch of this work that I would most like to emphasize.
As I have not known how to have the mathematical capabilities-or luck-to find a "perihelion of Mercury" that gives experimental value to the topological proposal that I seek to present, what I will do instead will be to analyze the conjecture using three "metaphysical frames of references", in three independent sections, hoping to convince "by convergence" (or, by insistence...):
⊕ Epistemological arguments: I will present the "toroidal phenomena" as a "mode of resonance" (or, adapting Bruno Latour, a "mode of existence" [1]) of a universe that I will assume infinitely complex.
⊕ Geometric Arguments: I will draw on a known result [2][3][4] that relates the first non-spherical mode of a non-rotating black hole perturbation with a slowly rotating black hole. This small step between one space-time and another, which turns out to be topologically identifiable with the boundary figure between a a sphere and a toroid, will be the cornerstone on which the proposed generalization will be based.
⊕ Graphical Arguments: Through the use of Penrose Diagrams --the most commonly used space-time maps in General Relativity-- I will show that the toroid is not only intuited from continuous deformations of the diagram, but even seems to suggest simple explanations for the timelike closed curves and infinite parallel universes "predicted" by classical theory.

The use of differential equations methods in the approach, treatment, and solution of problems in diverse areas of geometry, particularly in affine differential geometry is well known and prolific, where they have proven to be quite fruitful when it comes to the obtainment of definite results. It is perhaps lesser known that the same kind of those very same methods has been and is currently being used to treat developments in some specific areas of applied sciences, such as the theory of shells where, similarly, they can be proven to be quite effective as well. In this paper we precisely show that such is the case in two particular, related instances: the historic approach of the classical, Euclidean part of the theory pursued by Fritz John, in the past century, and the more recent expositions that we ourselves have dedicated to the affine counterpart of the theory.

The classical Monge-Ampère equation has been the center of considerable interest in recent years because of its important role in several areas of applied mathematics. In reflecting these developments, this works stresses the geometric aspects of this beautiful theory, using some techniques from harmonic analysis---covering lemmas and set decompositions. Moreover, Monge- Ampère type equations have applications in the areas of

El principal objetivo en la Teoría de Cáscaras, ya sea ésta euclidiana o afín, es determinar la medida de la deformación de una cáscara una vez que la solicitación ha sido aplicada a la misma. Y la mejor forma de analizar esto es mirar qué ocurre con las correspondientes superficies medias. Este problema se plantea aquí, en este trabajo, a los efectos de determinar la superficie media deformada a partir de datos conocidos que contiene la cáscara antes de deformarse de su estado original. Así se podrá cuantificar, en alguna medida, su deformación. De esa forma, se da inicio a un método general comparativo entre ambas geometrías, aclarando que, en ambos casos, se usa el respectivo Teorema Fundamental de Existencia para superficies. Para una mejor comprensión del tema deberán verse los artículos anteriores publicados por los mismos autores.

A spin echo is usually expected to exhibit a maximum at a time 2τ, where τ is the pulse spacing; for high diffusivities in presence of linear gradients, however, a maximum is observed at times 2τ. Here we show that in the presence of non-linear gradients a strong departure from the linear case is obtained. For long echo times a plateau for the maximum signal time is reached, thus a diffusion correlation time dependent both on the diffusion coefficient and the gradients strengths can be defined. Results for laser polarized 3He and 129Xe are compared with Monte Carlo simulations.Unexpected echo formation in laser polarized gas NMR prior to the conventional time is described and analyzed in detail.

Spin echo formation in magnetic field gradients in the presence of fast stochastic motion is studied for hyperpolarized 3He gas at different diffusivities. The fast translational motion leads to frequency shifts already during echo formation, which can be described analytically for a linear gradient. Despite complete signal loss at the position of the spin echo itself, considerable intensity can be preserved at an earlier time (sqrt[2]tau rather than 2tau, where tau is the pulse delay). Hence, the phenomenon is designated as a pseudo spin echo.

Distant dipolar fields among nuclear spins on macroscopic scales in the gas phase are reported for the first time. Their observation via interatomic multiple quantum coherences requires high nuclear spin polarization corresponding to spin temperatures of a few mK, which is generated in laser-polarized He3, and proper control of the gas diffusion through a heavier buffer gas. This combination of physics at low and ambient temperatures opens up new ways of studying the relative translational diffusion of atoms and of gas diffusion in structures with a large range of length scales.

Diffusion of atoms or molecules in presence of magnetic field gradients not only attenuates the NMR signal but also leads to distortions close to restricting boundaries. This phenomenon is most evident in imaging with laser polarized (LP) noble gases. Diffusion of gases can be manipulated, however, by admixing inert gases of different molecular weight. In this work we analyze the effect of mixing LP-3He with SF6 on the image quality of a phantom consisting of an arrangement of capillaries with different diameters. Admixing buffer gases of higher molecular weight changes the contrast and offers a means to record images with high spatial and time resolution. Additionally we demonstrate how distortions due to edge enhancement can be reduced even for long timed MRI-sequences.

Nuclear spins are promising candidates for quantum information processing because their good isolation from the environment precludes the rapid loss of quantum coherence. Many strategies have been developed to further extend their decoherence times. Some of them make use of decoupling techniques based on the Carr-Purcell and Carr-Purcell-Meiboom-Gill pulse sequences. In many cases, when applied to inhomogeneous samples, they yield a magnetization decay much slower than the Hahn echo. However, we have proved that these decays cannot be associated with longer decoherence times as coherences remain frozen. They result from coherences recovered after their storage as local polarization and thus they can be used as memories. We show here how this freezing of the coherent state, which can subsequently be recovered after times longer than the natural decoherence time of the system, can be generated in a controlled way with the use of field gradients. A similar behaviour of homogeneous samples in inhomogeneous fields are demonstrated. It is emphasized that the effects of inhomogeneities in solid state NMR, independently of their origin, should not be disregarded as they play a crucial role in multipulse sequences.

The NMR spin-lattice proton relaxation dispersion in the smectic mesophase of two liquid crystals, 4cyano-4'-8-alkylbiphenyl and 4,4'-bis-heptyloxyazoxybenzene, are studied over several decades of Larmor frequencies. The results show that the order fluctuation of the local smectic director contribution to T1(nu(L)) undergoes a transition between two power regimes: from T1(nu(L)) proportional, variantnu(1)(L) to nu(1/2)(L) on going from low to high Larmor frequencies. We explain this behavior by assuming, in the smectic mesophases, short coherence length nematiclike cooperative molecular reorientations.