Schwinger and Pegg-Barnett approaches and a relationship between angular and Cartesian quantum descriptions: II. Phase spaces

Following the discussion-in state-space language-presented in a preceding paper, we work on the passage from the phase-space description of a degree of freedom described by a finite number of states (without classical counterpart) to one described by an infinite (and continuously labelled) number of states. With this it is possible to relate an original Schwinger idea to the Pegg-Barnett approach to the phase problem. In phase-space language, this discussion shows that one can obtain the Weyl-Wigner formalism, for both Cartesian and angular coordinates, as limiting elements of the discrete phase-space formalism.

The Dirac-Hestenes equation for spherical symmetric potentials in the spherical and Cartesian gauges

In this paper, using the apparatus of the Clifford bundle formalism, we show how straightforwardly solve in Minkowski space-time the Dirac-Hestenes equation - which is an appropriate representative in the Clifford bundle of differential forms of the usual Dirac equation - by separation of variables for the case of a potential having spherical symmetry in the Cartesian and spherical gauges. We show that, contrary to what is expected at a first sight, the solution of the Dirac-Hestenes equation in both gauges has exactly the same mathematical difficulty. © World Scientific Publishing Company.

O legado de Descartes

The criticism of Cartesian philosophy is correlated on four pillars: the fragmentation of knowledge, the separation between mind and body, the impossibility of the reductionist method for explanation of natural phenomena, and in the superiority of the reason as the only valid form of knowledge. These last two pillars, as many environmentalists claim, contributed decisively to the devaluation of the res extensa over the res cogitans. To check this we used as a theoretical framework the following texts: Discourse on Method, Rules for Conduct of the Spirit and Metaphysical Meditations. By reading these works it was found that the first two pillars (the fragmentation of knowledge and the separation between mind and body) there are no theoretical basis in texts. The failure of the reductionist method to explain the ecological and atomic phenomena and the overcoming of reason as the only valid form of knowledge are supported in their philosophy.

Is global workspace a cartesian theater? How the neuro-astroglial interaction model solves conceptual issues

The Global Workspace Theory (GWT) proposed by Bernard Baars (1988) along with Daniel Dennett’s (1991) Multiple Drafts Model (MDM) of consciousness are renowned cognitive theories of consciousness bearing similarities and differences. Although Dennett displays sympathy for GWT, his own MDM does not seem to be fully compatible with it. This work discusses this compatibility, by asking if GWT suffers from Daniel Dennett’s criticism of what he calls a “Cartesian Theater”. We identified in Dennett 10 requirements for avoiding the Cartesian Theater. We believe that some of these requirements are violated by GWT, but not all, hence there is partial incompatibility with MDM, and it is nonsense to answer if GWT is or is not a Cartesian Theater. However, by asking such question we conclude that the issues around this discussion involve fuzzy claims about degrees of consciousness and we show how the Neuro-Astroglial Interaction Model (NAIM) is fit for solving such conceptual issues.

Algumas considerações sobre as críticas ao conhecimento científico moderno no contexto do processo educativo e a temática ambiental

Este trabalho aponta algumas críticas feitas ao conhecimento científico moderno no âmbito do movimento ambientalista, com especial destaque às idéias filosóficas cartesianas. Entendendo ser o processo educativo uma etapa fundamental para amenizar ou reverter o quadro de degradações ambientais, analisamos alguns limites dessas críticas como a não contextualização histórico-social de tais idéias. Por fim observamos a inadequação que causa a repetição dessas críticas à ciência moderna para o processo educativo.

Heat transfer in laminar flow of non-Newtonian fluids in ducts of elliptical section

Laminar forced convection inside tubes of various cross-section shapes is of interest in the design of a low Reynolds number heat exchanger apparatus. Heat transfer to thermally developing, hydrodynamically developed forced convection inside tubes of simple geometries such as a circular tube, parallel plate, or annular duct has been well studied in the literature and documented in various books, but for elliptical duct there are not much work done. The main assumption used in this work is a laminar flow of a power flow inside elliptical tube, under a boundary condition of first kind with constant physical properties and negligible axial heat diffusion (high Peclet number). To solve the thermally developing problem, we use the generalized integral transform technique (GITT), also known as Sturm-Liouville transform. Actually, such an integral transform is a generalization of the finite Fourier transform where the sine and cosine functions are replaced by more general sets of orthogonal functions. The axes are algebraically transformed from the Cartesian coordinate system to the elliptical coordinate system in order to avoid the irregular shape of the elliptical duct wall. The GITT is then applied to transform and solve the problem and to obtain the once unknown temperature field. Afterward, it is possible to compute and present the quantities of practical interest, such as the bulk fluid temperature, the local Nusselt number and the average Nusselt number for various cross-section aspect ratios. (C) 2006 Elsevier. SAS. All rights reserved.

Análise da fidelidade do traçado predictivo em pacientes submetidos à cirurgia ortognática em mandíbula

OBJETIVO: a proposta desse trabalho foi analisar a fidelidade dos traçados predictivos realizados para cirurgias ortognáticas, por meio de análise cefalométrica do pré e pós-operatório de sete dias, em pacientes submetidos à correção de deformidade mandibular. MÉTODOS: foram utilizadas telerradiografias cefalométricas de perfil de 17 pacientes submetidos à cirurgia ortognática de mandíbula. Foram realizados traçados cefalométricos do pré e do pós-operatório de 7 dias com marcação dos pontos côndilo (Co), pogônio (Pog), goníaco (Go), mento (Me), ponto B (B) e incisivo (I). A análise foi baseada na diferença obtida pela sobreposição dos traçados pré-operatório, predictivo e pós-operatório. Os pontos foram projetados em um plano cartesiano para medição das suas distâncias em milímetros. Os dados obtidos foram submetidos à análise estatística por meio do teste t de Student pareado (± = 0,05). RESULTADOS: no eixo horizontal, foi observada diferença média, entre a mudança planejada e a obtida nos traçados cefalométricos pós-operatórios, estatisticamente significativa nos pontos Pog (p = 0,014) e I (p = 0,008). No eixo vertical, não verificou-se diferença estatística significativa para os pontos cefalométricos marcados (p > 0,05). CONCLUSÕES: o traçado predictivo contribuiu para a avaliação pré-operatória do paciente e, consequentemente, para a otimização do tratamento. Entretanto, ele não se mostrou totalmente fiel nos casos analisados, com leve subestimação das alterações esqueléticas horizontais. Essas alterações devem ser consideradas no planejamento e acompanhamento pós-operatório dos pacientes submetidos à cirurgia ortognática em mandíbula.

CHARGED PARTICLE DYNAMICS IN TIME DEPENDENT MAGNETIC FIELDS

In this work we study the behavior of charged particles immersed in a peculiar configuration of magnetic fields, which has a main constant field B(0) and a superimposed, transversal perturbation field B(1) sin(omega(p)t), with B(1) << B(0). By taking Cartesian coordinates and placing B(0) along the z axis and B(1) sin (omega(p)t) on the x axis, an analytical solution for y(t) may be obtained by solving an integrodifferential equation. Besides, the solution z(t) also exhibits a very interesting dynamics, and the entire system is conditioned by resonances between the particle orbit frequencies and the frequency of the magnetic transversal perturbation, omega(p). In this work we also discuss numerical simulations for the related particle trajectories, as well as potential applications in the context of separation phenomena.

Duality between coordinates and Dirac field

The duality between the Cartesian coordinates on the Minkowski space-time and the Dirac field is investigated. Two distinct possibilities to define this duality are shown to exist. In both cases, the equations satisfied by prepotentials are of second order. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Discrete and canonical quantum variables

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Simulation of free surface flows in a distributed memory environment

A parallel technique, for a distributed memory machine, based on domain decomposition for solving the Navier-Stokes equations in cartesian and cylindrical coordinates in two dimensions with free surfaces is described. It is based on the code by Tome and McKee (J. Comp. Phys. 110 (1994) 171-186) and Tome (Ph.D. Thesis, University of Strathclyde, Glasgow, 1993) which in turn is based on the SMAC method by Amsden and Harlow (Report LA-4370, Los Alamos Scientific Laboratory, 1971), which solves the Navier-Stokes equations in three steps: the momentum and Poisson equations and particle movement, These equations are discretized by explicit and 5-point finite differences. The parallelization is performed by splitting the computation domain into vertical panels and assigning each of these panels to a processor. All the computation can then be performed using nearest neighbour communication. Test runs comparing the performance of the parallel with the serial code, and a discussion of the load balancing question are presented. PVM is used for communication between processes. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Thermally developing forced convection of non-Newtonian fluids inside elliptical ducts

Laminar-forced convection inside tubes of various cross-section shapes is of interest in the design of a low Reynolds number heat exchanger apparatus. Heat transfer to thermally developing, hydrodynamically developed forced convection inside tubes of simple geometries such as a circular tube, parallel plate, or annular duct has been well studied in the literature and documented in various books, but for elliptical duct there are not much work done. The main assumptions used in this work are a non-Newtonian fluid, laminar flow, constant physical properties, and negligible axial heat diffusion (high Peclet number). Most of the previous research in elliptical ducts deal mainly with aspects of fully developed laminar flow forced convection, such as velocity profile, maximum velocity, pressure drop, and heat transfer quantities. In this work, we examine heat transfer in a hydrodynamically developed, thermally developing laminar forced convection flow of fluid inside an elliptical tube under a second kind of a boundary condition. To solve the thermally developing problem, we use the generalized integral transform technique (GITT), also known as Sturm-Liouville transform. Actually, such an integral transform is a generalization of the finite Fourier transform, where the sine and cosine functions are replaced by more general sets of orthogonal functions. The axes are algebraically transformed from the Cartesian coordinate system to the elliptical coordinate system in order to avoid the irregular shape of the elliptical duct wall. The GITT is then applied to transform and solve the problem and to obtain the once unknown temperature field. Afterward, it is possible to compute and present the quantities of practical interest, such as the bulk fluid temperature, the local Nusselt number, and the average Nusselt number for various cross-section aspect ratios.

Remarks on orthotropic elastic models applied to wood

Wood is generally considered an anisotropic material. In terms of engineering elastic models, wood is usually treated as an orthotropic material. This paper presents an analysis of two principal anisotropic elastic models that are usually applied to wood. The first one, the linear orthotropic model, where the material axes L (Longitudinal), R(radial) and T(tangential) are coincident with the Cartesian axes (x, y, z), is more accepted as wood elastic model. The other one, the cylindrical orthotropic model is more adequate of the growth caracteristics of wood but more mathematically complex to be adopted in practical terms. Specifically due to its importance in wood elastic parameters, this paper deals with the fiber orientation influence in these models through adequate transformation of coordinates. As a final result, some examples of the linear model, which show the variation of elastic moduli, i.e., Young's modulus and shear modulus, with fiber orientation are presented.

State Dependent Riccati Equation (SDRE) control method applied in cancellation of a parametric resonance in a magnetically levitated body

Here, a simplified dynamical model of a magnetically levitated body is considered. The origin of an inertial Cartesian reference frame is set at the pivot point of the pendulum on the levitated body in its static equilibrium state (ie, the gap between the magnet on the base and the magnet on the body, in this state). The governing equations of motion has been derived and the characteristic feature of the strategy is the exploitation of the nonlinear effect of the inertial force associated, with the motion of a pendulum-type vibration absorber driven, by an appropriate control torque [4]. In the present paper, we analyzed the nonlinear dynamics of problem, discussed the energy transfer between the main system and the pendulum in time, and developed State Dependent Riccati Equation (SDRE) control design to reducing the unstable oscillatory movement of the magnetically levitated body to a stable fixed point. The simulations results showed the effectiveness of the (SDRE) control design. Copyright © 2011 by ASME.

Alternate treatments of jacobian singularities in polar coordinates within finite-difference schemes

Jacobian singularities of differential operators in curvilinear coordinates occur when the Jacobian determinant of the curvilinear-to-Cartesian mapping vanishes, thus leading to unbounded coefficients in partial differential equations. Within a finite-difference scheme, we treat the singularity at the pole of polar coordinates by setting up complementary equations. Such equations are obtained by either integral or smoothness conditions. They are assessed by application to analytically solvable steady-state heat-conduction problems.