Boundary identification criteria and geometry analysis of Al 7050 stretch zone from elevation profiles

This article describes the development of a method for analysis of the shape of the stretch zone surface based on parallax measurement theory and using digital image processing techniques. Accurate criteria for the definition of the boundaries of the stretch zone are established from profiles of fracture surfaces obtained from crack tip opening displacement tests on Al-7050 alloy samples. The elevation profiles behavior analysis is based on stretch zone width and height parameters. It is concluded that the geometry of the stretch zone profiles under plane strain conditions can be described by a semi-parabolic relationship. (C) Elsevier B.V., 1999. All rights reserved.

Differential geometry of intersection curves in R(4) of three implicit surfaces

We present algorithms for computing the differential geometry properties of intersection Curves of three implicit surfaces in R(4), using the implicit function theorem and generalizing the method of X. Ye and T. Maekawa for 4-dimension. We derive t, n, b(1), b(2) vectors and curvatures (k(1), k(2), k(3)) for transversal intersections of the intersection problem. (C) 2008 Elsevier B.V. All rights reserved.

Desenvolvimento de dobras e falhas em ambiente distensional: Aplicação da modelagem física

The geological modeling allows, at laboratory scaling, the simulation of the geometric and kinematic evolution of geological structures. The importance of the knowledge of these structures grows when we consider their role in the creation of traps or conduits to oil and water. In the present work we simulated the formation of folds and faults in extensional environment, through physical and numerical modeling, using a sandbox apparatus and MOVE2010 software. The physical modeling of structures developed in the hangingwall of a listric fault, showed the formation of active and inactive axial zones. In consonance with the literature, we verified the formation of a rollover between these two axial zones. The crestal collapse of the anticline formed grabens, limited by secondary faults, perpendicular to the extension, with a curvilinear aspect. Adjacent to these faults we registered the formation of transversal folds, parallel to the extension, characterized by a syncline in the fault hangingwall. We also observed drag folds near the faults surfaces, these faults are parallel to the fault surface and presented an anticline in the footwall and a syncline hangingwall. To observe the influence of geometrical variations (dip and width) in the flat of a flat-ramp fault, we made two experimental series, being the first with the flat varying in dip and width and the second maintaining the flat variation in width but horizontal. These experiments developed secondary faults, perpendicular to the extension, that were grouped in three sets: i) antithetic faults with a curvilinear geometry and synthetic faults, with a more rectilinear geometry, both nucleated in the base of sedimentary pile. The normal antithetic faults can rotate, during the extension, presenting a pseudo-inverse kinematics. ii) Faults nucleated at the top of the sedimentary pile. The propagation of these faults is made through coalescence of segments, originating, sometimes, the formation of relay ramps. iii) Reverse faults, are nucleated in the flat-ramp interface. Comparing the two models we verified that the dip of the flat favors a differentiated nucleation of the faults at the two extremities of the mater fault. V These two flat-ramp models also generated an anticline-syncline pair, drag and transversal folds. The anticline was formed above the flat being sub-parallel to the master fault plane, while the syncline was formed in more distal areas of the fault. Due the geometrical variation of these two folds we can define three structural domains. Using the physical experiments as a template, we also made numerical modeling experiments, with flat-ramp faults presenting variation in the flat. Secondary antithetic, synthetic and reverse faults were generated in both models. The numerical modeling formed two folds, and anticline above the flat and a syncline further away of the master fault. The geometric variation of these two folds allowed the definition of three structural domains parallel to the extension. These data reinforce the physical models. The comparisons between natural data of a flat-ramp fault in the Potiguar basin with the data of physical and numerical simulations, showed that, in both cases, the variation of the geometry of the flat produces, variation in the hangingwall geometry

The Fermi pseudo-potential in one dimension

Wu and Yu recently examined point interactions in one dimension in the form of the Fermi pseudo-potential. on the other hand there are point interactions in the form of self-adjoint extensions (SAEs) of the kinetic energy operator. We examine the relationship between the point interactions in these two forms in the one-channel and two-channel cases. In the one-channel case the pseudo-potential leads to the standard three-parameter family of SAEs. In the two-channel case the pseudo-potential furnishes a ten-parameter family of SAEs.

Spinorial field and Lyra geometry

The Dirac field is studied in a Lyra space-time background by means of the classical Schwinger Variational Principle. We obtain the equations of motion, establish the conservation laws, and get a scale relation relating the energy-momentum and spin tensors. Such scale relation is an intrinsic property for matter fields in Lyra background.

Free electromagnetic field in Riemannian space-time via DKP theory

We study the massless Duffin-Kemmer-Petiau (DKP) equation in Riemannian space-times, particularly the massless spin 1 sector which reproduces the free Maxwell's equations.

Conformal invariance of massless Duffin-Kemmer-Petiau theory in Riemannian spacetimes

We investigate the conformal invariance of massless Duffin-Kemmer-Petiau theory coupled to Riemannian spacetimes. We show that, as usual, in the minimal coupling procedure only the spin I sector of the theory - which corresponds to the electromagnetic field - is conformally invariant. We also show that the conformal invariance of the spin 0 sector can be naturally achieved by introducing a compensating term in the Lagrangian. Such a procedure - besides not modifying the spin I sector - leads to the well-known conformal coupling between the scalar curvature and the massless Klein-Gordon-Fock field. Going beyond the Riemannian spacetimes, we briefly discuss the effects of a nonvanishing torsion in the scalar case.

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.

A Contribution to the Estimation of Binary Halide and Pseudo-Halide Equilibrium Constants using a Linear Extrapolation Methodology

The molar single ion activity coefficient (y(F)) of fluoride ions was determined at 25 degrees C and ionic strengths between 0.100 and 3.00 mol L(-1) NaClO(4) using an ion-selective electrode. The activity coefficient dependency on ionic strength was determined to be Phi(F) = log y(F) = 0.2315I-0.041I(2). The function Phi(F)(I), combined with functions obtained in previous work for copper (Phi(Cu)) and hydrogen (Phi(H)), allowed us to make the estimation of the stoichiometric and thermodynamic protonation constants of some halides and pseudo-halides as well as the formation constants of some pseudo-halides and fluoride 1:1 bivalent cation complexes. The calculation procedure proposed in this paper is consistent with critically-selected experimental data. It was demonstrated that it is possible to use Phi(F)(I) for predicting the thermodynamic equilibrium parameters independently of Pearson's hardness of acids and bases.

Clivagem dos ciclopaladados diméricos [Pd(dmba)(m-X)]2 (dmba = N,N-dimetilbenzilamina; X = Cl, N3, NCO) por tiouréia

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Dichloro(cyclohexilidene-1-methylene)(phenyl)Te(IV). Looking for the theoretical treatment

C(13)H(16)Cl(2)Te,M(r)=370.76,P2(1)/a, a = 8.1833(8), b = 8.4163(8), c = 20.787(2) A, beta = 99.52(1)degrees, Z = 4, R(1) = 0,0275. The primary coordination around the Te(IV) atom is consistent with a pseudo-trigonal bipyramidal bond configuration with two Cl atoms occupying axial positions while the C atoms and the lone pair of electrons occupy the equatorial positions. The Te(IV) atom is involved in an intermolecular secondary interaction resulting in the self assembly of zigzag-chains supramolecular array. In order to determine the theoretical basis set for the Te atom which leads to the best agreement with the experimental data, a large series of geometry optimizations were performed on dichloro dimethyl Te(IV), as a model compound, and the results compared with the mean distances and angles obtained from 45 X-ray structures. The Ahlrichs basis set plus the Hay & Wadt ECP was selected and used for a series of calculations performed on the title compound.

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.

Hamiltonian hierarchy of pseudo-potentials

The general structure of the Hamiltonian hierarchy of the pseudo-Coulomb and pseudo-Harmonic potentials is constructed by the factorization method within the supersymmetric quantum mechanics (SQMS) formalism. The excited states and spectra of eigenfunctions of the potentials are obtained through the generation of the members of the hierarchy. It is shown that the extra centrifugal term added to the Coulomb and Harmonic potentials maintain their exact solvability.