Characterization of multiple reflections and phase space properties for a periodically corrugated waveguide

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Scaling invariance for the escape of particles from a periodically corrugated waveguide

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Husserl on Geometry and Spatial Representation

Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally motivated psychic functions), that of physical geometry (or idealized perceptual space), the space of the mathematical science of physical nature (in which science, not only raw perception has a word) and the abstract spaces of mathematics (free creations of the mathematical mind), each of them with its peculiar geometrical structure. Perceptual space is proto-Euclidean and the space of physical geometry Euclidean, but mathematical physics, Husserl allowed, may find it convenient to represent physical space with a non-Euclidean structure. Mathematical spaces, on their turn, can be endowed, he thinks, with any geometry mathematicians may find interesting. Many other related questions are addressed here, in particular those concerning the a priori or a posteriori character of the many geometric features of perceptual space (bearing in mind that there are at least two different notions of a priori in Husserl, which we may call the conceptual and the transcendental a priori). I conclude with an overview of Weyl's ideas on the matter, since his philosophical conceptions are often traceable back to his former master, Husserl.

Determination of Glyphosate in Water Samples by Multi-pumping Flow System Coupled to a Liquid Waveguide Capillary Cell

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Erbium and ytterbium co-doped SiO2 : GeO2 planar waveguide prepared by the sol-gel route using an alternative precursor

The sol-gel method combined with a spin-coating technique has been successfully applied for the preparation of rare-earth doped silica:germania films used for the fabrication of erbium-doped waveguide amplifiers (EDWA), presenting several advantages over other methods for the preparation of thin films. As with other methods, the sol-gel route also shows some drawbacks, such as cracks related to the thickness of silica films and high hydrolysis rate of certain precursors such as germanium alkoxides. This article describes the preparation and optical characterization of erbium and ytterbium co-doped SiO2:GeO2 crack-free thick films prepared by the sol-gel route combined with a spin-coating technique using a chemically stable non-aqueous germanium oxide solution as an alternative precursor. The non-crystalline films obtained are planar waveguides exhibiting a single mode at 1,550 nm with an average thickness of 3.9 mu m presenting low percentages of porosity evaluated by the Lorentz-Lorenz Effective Medium Approximation, and low stress, according to the refractive index values measured in both transversal electric and magnetic polarizations. Weakly confining core layers (0.3% < Delta n < 0.75%) were obtained according to the refractive index difference between the core and buffer layers, suggesting that low-loss coupling EDWA may be obtained. The life time of the erbium I-4(13/2) metastable state was measured as a function of erbium concentration in different systems and based on these values it is possible to infer that the hydroxyl group was reduced and the formation of rare-earth clusters was avoided.

Numerical simulation of magnetic-field-enhanced plasma immersion ion implantation in cylindrical geometry

Recent studies have demonstrated that the sheath dynamics in plasma immersion ion implantation (PIII) is significantly affected by an external magnetic field. In this paper, a two-dimensional computer simulation of a magnetic-field-enhanced PHI system is described. Negative bias voltage is applied to a cylindrical target located on the axis of a grounded vacuum chamber filled with uniform molecular nitrogen plasma. A static magnetic field is created by a small coil installed inside the target holder. The vacuum chamber is filled with background nitrogen gas to form a plasma in which collisions of electrons and neutrals are simulated by the Monte Carlo algorithm. It is found that a high-density plasma is formed around the target due to the intense background gas ionization by the magnetized electrons drifting in the crossed E x B fields. The effect of the magnetic field intensity, the target bias, and the gas pressure on the sheath dynamics and implantation current of the PHI system is investigated.

Fluctuating commutative geometry

We use the framework of noncommutative geometry to define a discrete model for fluctuating geometry. Instead of considering ordinary geometry and its metric fluctuations, we consider generalized geometries where topology and dimension can also fluctuate. The model describes the geometry of spaces with a countable number n of points. The spectral principle of Connes and Chamseddine is used to define dynamics. We show that this simple model has two phases. The expectation value , the average number of points in the universe, is finite in one phase and diverges in the other. Moreover, the dimension delta is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, < 2. We also address another discrete model defined on a fixed d = 1 dimension, where topology fluctuates. We comment on a possible spontaneous localization of topology.

Study of plasma immersion ion implantation into silicon substrate using magnetic mirror geometry

The effect of magnetic field enhanced plasma immersion ion implantation (PIII) in silicon substrate has been investigated at low and high pulsed bias voltages. The magnetic field in magnetic bottle configuration was generated by two magnetic coils installed outside the vacuum chamber. The presence of both, electric and magnetic field in PIII creates a system of crossed E x B fields, promoting plasma rotation around the target. The magnetized electrons drifting in crossed E x B fields provide electron-neutral collision. Consequently, the efficient background gas ionization augments the plasma density around the target where a magnetic confinement is achieved. As a result, the ion current density increases, promoting changes in the samples surface properties, especially in the surface roughness and wettability and also an increase of implantation dose and depth. (C) 2012 Elsevier B. V. All rights reserved.

Quantum geometry of chiral bosons on a circle

We extend the geometric treatment done for the Majorana-Weyl fermions in two dimensions by Sanielevici and Semenoff to chiral bosons on a circle. For this case we obtain a generalized Floreanini-Jackiw Lagrangian density, and the corresponding gravitational (or Virasoro) anomalies are found as expected. © 1989 The American Physical Society.

On the geometry of non-classical curves

In this paper we relate the numerical invariants attached to a projective curve, called the order sequence of the curve, to the geometry of the varieties of tangent linear spaces to the curve and to the Gauss maps of the curve. © 1992 Sociedade Brasileira de Matemática.

Combining genetic algorithm and simulated annealing: A molecular geometry optimization study

We introduce a new hybrid approach to determine the ground state geometry of molecular systems. Firstly, we compared the ability of genetic algorithm (GA) and simulated annealing (SA) to find the lowest energy geometry of silicon clusters with six and 10 atoms. This comparison showed that GA exhibits fast initial convergence, but its performance deteriorates as it approaches the desired global extreme. Interestingly, SA showed a complementary convergence pattern, in addition to high accuracy. Our new procedure combines selected features from GA and SA to achieve weak dependence on initial parameters, parallel search strategy, fast convergence and high accuracy. This hybrid algorithm outperforms GA and SA by one order of magnitude for small silicon clusters (Si6 and Si10). Next, we applied the hybrid method to study the geometry of a 20-atom silicon cluster. It was able to find an original geometry, apparently lower in energy than those previously described in literature. In principle, our procedure can be applied successfully to any molecular system. © 1998 Elsevier Science B.V.

Finite element analysis of anisotropic optical waveguide with arbitrary index profile

This work presents the application of a scalar finite element formulation for Ex (TE-like) modes in anisotropic planar and channel waveguides with diagonal permittivity tensor, diffused in both transversal directions. This extended formulation considers explicitly both the variations of the refractive index and their spatial derivates inside of each finite element. Dispersion curves for Ex modes in planar and channel waveguides are shown, and the results compared with solutions obtained by other formulations.

Energy and angular momentum of the gravitational field in the teleparallel geometry

The Hamiltonian formulation of the teleparallel equivalent of general relativity is considered. Definitions of energy, momentum and angular momentum of the gravitational field arise from the integral form of the constraint equations of the theory. In particular, the gravitational energy-momentum is given by the integral of scalar densities over a three-dimensional spacelike hypersurface. The definition for the gravitational energy is investigated in the context of the Kerr black hole. In the evaluation of the energy contained within the external event horizon of the Kerr black hole, we obtain a value strikingly close to the irreducible mass of the latter. The gravitational angular momentum is evaluated for the gravitational field of a thin, slowly rotating mass shell. © 2002 The American Physical Society.

Gravitational energy of Kerr and Kerr anti-de Sitter space-times in the teleparallel geometry

In the context of the hamiltonian formulation of the teleparallel equivalent of general relativity we compute the gravitational energy of Kerr and Kerr Anti-de Sitter (Kerr-AdS) space-times. The present calculation is carried out by means of an expression for the energy of the gravitational field that naturally arises from the integral form of the constraint equations of the formalism. In each case, the energy is exactly computed for finite and arbitrary spacelike two-spheres, without any restriction on the metric parameters. In particular, we evaluate the energy at the outer event horizon of the black holes. © SISSA/ISAS 2003.