Vol. 51 No. 1 (2005): Revista Mexicana de Física.

Published: 2005-01-01

Articles

  • The Casimir operator of SO(1,2) and the Pöschl-Teller potential: an AdS approach

    R. da Rocha, E. Capelas de Oliveira
    1-0
    Abstract:
    We present and discuss some features of the anti-de Sitter spacetime, that is jointly with de Sitter and Minkowski is only, the unique maximal isotropic manifold. Among all possible lorentzian manifolds, we restrict our attention to the anti-de Sitter (AdS) spacetime, with metric diag(1,$-1,-1$). We start by presenting the conformal time metric on AdS and we then show how we can obtain the Schrödinger formalism~\cite{sch}. The Lie algebra $\mathfrak{so}$(1,2) is introduced and used to construct spin and ladder operators. After presenting the unitary representations, the AdS(1,2) spacetime is suitably parametrized and a representation of SO(1,2) is obtained, from which the Schrödinger equation with Pöschl-Teller potential is immediately deduced. Finally, we discuss some relations between the relativistic harmonic oscillator and the Klein-Gordon equation, using the AdS(1,2) static frame. Possible applications of the presented formalism are provided.
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  • Síntesis y caracterización estructural de las elpasolitas estequiométricas de Dy$^{3+}$ y Ho$^{3+}$

    R.Acevedo., A.Soto-Bubert., G.Navarro., V.Martín.
    5-0
    Abstract:
    In this research paper, we report an updated set of experimental data, mainly structural in character, accurately determined for pure elpasolite systems such as Cs$_{2}$NaLnCl$_{6}$; M$^{3+}=$Dy$^{3+}(f^{9})$, Ho$(f^{10})$, where the trivalent lanthanide ions occupy sites of octahedral symmetries. There is a vast amount of experimental data from spectroscopic techniques for this type of systems both, pure and doped as well as several attempts leading to the identification and assignment of the various peaks for the associated spectra. The understanding of the experimental data, is central and most relevant, when the many complexities observed in both, the absorption and emission spectra are taken into account showing up the need for carrying out new experiments and developing more general physical models in the spectroscopy of solid state physics. These models should be able to accommodate both the long and short range interactions as well as to include, in an explicit form, the coupling between the internal and the external vibrations for these systems. A further reason to preclude more comprehensive theoretical studies in this area is the well known fact that, for these systems the experimental data available obtained from X-ray and spectroscopic studies is both scarce and incomplete. In the current research paper, we report updated experimental data, essentially structural in character, obtained in our laboratory utilizing X rays diffraction for powders and we also report a neutron diffraction pattern for the Cs$_{2}$NaHoCl$_{6}$.
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  • Adsorption-desorption kinetics with multiple site occupation

    S. Manzi, G. Costanza, V.D. Pere, ra.
    14-0
    Abstract:
    The adsorption-desorption kinetics with multiple site occupation in a one-dimensional network is formulated in the framework of the kinetic lattice gas model. The kinetic equations that describe the time evolution of the correlators are obtained by use of the so called Local Evolution Rules, that take into account the adsorption, desorption, and diffusion of the adsorbed molecules. After truncating the infinite hierarchy of equations, different cases are analyzed. Equilibrium solutions are obtained and the exact expression for adsorption isotherms as well as the nearest-neighbor correlations are presented. The asymptotic approach to the equilibrium is also discussed. Finally, we analyzed the desorption kinetics throughout the thermal desorption spectra.
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  • Self-similarity in a Kantowski-Sachs universe with a string cloud

    Héctor Martínez., Carlos Peralta.
    22-0
    Abstract:
    We study a cosmological model with very simple solutions characterized by string clouds. Assuming self-similar symmetry for a Kantowski-Sachs spacetime we study the gravitational effects of the cosmic strings. It is also assumed that the primitive universe enters in a false vacuum-dominated era, accelerating the expansion in a time period of the order of $10^{-35}$ {\rm sec} (a phase transition), satisfying all the energy conditions. Finally, we examine the possibility that in the last stages of this evolution, the geometry of the universe could be flat.
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  • Asymptotic behavior of the daily increment distribution of the IPC, the mexican stock market index

    H.F. Coronel-Brizio, A.R. Hernández-Monto, a.
    27-0
    Abstract:
    In this work, a statistical analysis of the distribution of daily fluctuations of the IPC, the Mexican Stock Market Index is presented. A sample of the IPC covering the 13-year period 04/19/1990 - 08/21/2003 was analyzed and the cumulative probability distribution of its daily logarithmic variations studied. Results show that the cumulative distribution function for extreme variations, can be described by a Pareto-Lev\'y model with shape parameters $\alpha=3.634 \pm 0.272$ and $\alpha=3.540 \pm 0.278$ for its positive and negative tails, respectively. This result is consistent with previous studies, where it has been found that $2.5<\alpha<4$ for other financial markets worldwide.
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  • The fundamental optimal relations and the bounds of the allocation of heat exchangers and efficiency for a non-endoreversible brayton cycle

    G. Aragón-González, A. Canales-Palma, A. León-Galicia, M. Musharrafie-Martínez
    32-0
    Abstract:
    In this paper we analyze a Brayton cycle with external and internal irreversibilities. The external ones come from heat transfer with counterflow heat exchangers in the cold and hot sides; the internal irreversibilities are given by the isentropic efficiencies of the compressor and turbine. Optimization is carried out with respect to the pressure ratio and the total inventory of the heat transfer units, using the $\varepsilon$-NTU method. We show the analytical expressions for the efficiency that mazimizes work and the optimal allocation (size) of heat exchangers. We also analyze the asymptotic behavior of these expressions. The results obtained extend a Bejan's model and are more general and useful.
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  • Air shower array at the university of Puebla for the study of cosmic rays

    J. Cotzomi, O. Martínez, E. Moreno, H. Salazar, L. Villaseñor
    38-0
    Abstract:
    We describe the design and performance of an extensive air shower detector array built in the Campus of the University of Puebla (located at 19$^\circ$N, 90$^\circ$W, 800 g/cm$^{2}$) to measure the energy and arrival direction of primary cosmic rays with energies around 10$^{15}$~eV, known as the knee of the cosmic ray spectrum. The array consists of 18 liquid scintillator detectors (12 in the first stage), and 3 water Cherenkov detectors (one of 10 m$^{2}$ cross section and two smaller ones of 1.86 m$^{2}$ cross section), distributed in a square grid with a detector spacing of 20 m over an area of 4000 m$^{2}$. In this paper, we discuss the calibration and stability of the array and report on preliminary measurements of the arrival directions and energies of cosmic ray showers detected with the first stage of the array consisting of 12 liquid scintillator and 3 water Cherenkov detectors. Our results show that the array is efficient in detecting primary cosmic rays with energies in the range of 10$^{14}$ to 10$^{16}$~eV, with an angular resolution lower than 5.5$^\circ$ for zenithal angles in the range of 20$^\circ$ to 60$^\circ$. We also point out that the capability of water Cherenkov detectors to separate electromagnetic from muon components of extensive air showers. Finally we remark that this facility is also used to train students interested in the field of cosmic rays.
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  • Response matrix of a multisphere neutron spectrometer with an $^{3}$He proportional counter

    H.R. Vega-Carrillo, E. Manzanares-Acuña, V. Martín Hernández-Dávila, G.A. Mercado Sánchez
    47-0
    Abstract:
    The response matrix of a Bonner sphere spectrometer was calculated by use of the MCNP code. As thermal neutron counter, the spectrometer has a 3.2 cm-diameter $^{3}$He-filled proportional counter which is located at the center of a set of polyethylene spheres. The response was calculated for 0, 3, 5, 6, 8, 10, 12, and 16 inches-diameter polyethylene spheres for neutrons whose energy goes from 10$^{ - 9}$ to 20 MeV. The response matrix was compared with a set of responses measured with several monoenergetic neutron sources. In this comparison the calculated matrix agrees with the experimental results. The matrix was also compared with the response matrix calculated for the PTB C spectrometer. Even though that calculation was carried out using a detailed model to describe the proportional counter; both matrices do agree, but small differences are observed in the bare case because of the difference in the model used during calculations. Other differences are in some spheres for 14.8 and 20 MeV neutrons, probably due to the differences in the cross sections used during both calculations.
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  • Exciton spectrum of surface-corrugated quantum wells: the adiabatic self-consistent approach

    N. Atenco-Analco, N.M. Makarov, F. Pérez-Rodríguez
    53-0
    Abstract:
    A theory for calculating the relaxation frequency $\nu$ and the shift $\delta\omega$ of exciton resonances in quantum wells with finite potential barriers and adiabatic surface disorder is developed. The adiabaticity implies that the correlation length $R_c$ for the well width fluctuations is much larger than the exciton radius $a_0$ ($R_c\gg a_0$). Our theory is based on the self-consistent Green's function method, and therefore takes into account the inherent action of the exciton scattering on itself. The self-consistent approach is shown to describe quantitatively the sharp exciton resonance. It also gives the qualitatively correct resonance picture for the transition to the classical limit, as well as within the domain of the classical limit itself. We present and analyze results for $hh$-exciton in a GaAs quantum well with Al$_{0.3}$Ga$_{0.7}$As barriers. It is established that the self-consistency and finite height of potential barriers significantly influence on the line-shape of exciton resonances, and make the values of $\nu$ and $\delta\omega$ be quite realistic. In particular, the relaxation frequency $\nu$ for the ground-state resonance has a broad, almost symmetric maximum near the resonance frequency $\omega _0$, while the surface-induced resonance shift $\delta\omega$ vanishes near $\omega_0$, and has different signs on the sides of the exciton resonance.
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  • Integración sensorial utilizando clasificación difusa en tareas de ensamblado en robótica

    J.A. García Muñoz, M.A. LLama Leal, J.A. Padilla Medina
    64-0
    Abstract:
    Some approaches to the automation of assembly tasks with robots have been proposed. However, nearly all of them face the same problem: the need of identifying the current contact situation from sensory data. The confidence of assembly tasks with robotic manipulators is affected by uncertainty. The knowledge of the generalized reaction force is the natural complement to configuration information in the presence of geometric uncertainty, since a reaction force indicates a constraint in Configuration Space. Sensorial integration techniques have as objective to use information provided for several sensors to build and update a world model in order to achieve a goal. In this paper we present an approach to multisensory integration based on fuzzy c-means clustering algorithm for detection and identification of states during a dexterous manipulation task in robotics, considering modeling and sensing uncertainties.
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  • The general relativistic geometry of the Navarro-Frenk-White model

    Tonatiuh~Matos., Darío~Núñez.
    71-0
    Abstract:
    We derive the space time geometry associated with the Navarro-Frenk-White dark matter galactic halo model. We discuss several properties of this geometry, paying particular attention to the corresponding Newtonian limit and stressing the qualitative and quantitative nature of the differences between the relativistic and Newtonian descriptions. We also discuss the characteristics of the possible stress energy tensors which could produce such a geometry, using Einstein's equations.
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  • Improvement of the signal-to-noise ratio in digital holography

    Jorge Garcia-Sucerquia., Jorge Herrera Ramírez., Daniel Velásquez Prieto.
    76-0
    Abstract:
    A fundamental problem in optical and digital holography is the presence of speckle noise in the reconstruction process, which essentially diminishes the signal to noise ratio (SNR). For many applications, that reduction of the SNR makes the digital holography impractical, so great number of approaches have been carried out in order to overcome such a problem. They range from modifying the spatial coherence of the illumination to the application of image processing techniques. In this paper we propose the merged use of digital image processing techniques in order to increase this SNR by reducing the speckle noise in the digital reconstruction of optically recorded Fresnel's holograms. The proposed techniques are illustrated with experimental results.
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  • Two stream approximation to radiative transfer equation: An alternative method of solution

    J.I. Jiménez-Aquino, J.R. Varela
    82-0
    Abstract:
    An alternative analytical method of solution to radiative transfer equation in the two-stream approximation is studied. The method is formulated in terms of the diffusion-type equation for radiative transfer associated with the fluxes ( irradiances) $F_{d}=F^{+}-F^{-}$ and $F_{s}=F^{+}+F^{-}$, where $F^{+}$ and $F^{-}$ are defined as the upward and downward fluxes respectively. The diffusion-type equations are independent and therefore the method of solution is algebraically easier and faster than that used to solve the two coupled differential equations associated with $F^{+}$ and $F^{-}$.
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  • On the viscous steady flow around a circular cylinder

    F. M, ujano., R. Peralta-Fabi
    87-0
    Abstract:
    A series truncation method is proposed to obtain approximate solutions to the flow past a circular cylinder. This procedure is based on a change in the radial coordinate ($x$), such that this new coordinate is defined in a finite interval. Solutions are truncated power series in $x$, so that the full Navier-Stokes equations are transformed into three recurrence relations with two independent coefficients. The boundary conditions on the cylinder's surface are satisfied in trivially way, and the conditions at infinity lead to a system of two non linear ordinary differential equations. These are solved using Fourier series in the angular variable and, for the sake of argument, in a power series in $R_{e}$. Results on the convergence of the series, with varying order of truncation, and comparison with earlier results are discussed.
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  • Elastic scattering of low-energy electrons from ammonia

    Jorge L.S. Lino
    100-0
    Abstract:
    We report an application of the Schwinger variational principle with plane waves as a trial basis set [J.L.S. Lino, M.A.P. Lima, Braz. J. Phys. 32, 432 (2000)]. Differential cross sections are obtained for electron-NH$_3$ collisions from 8.5 to 30~eV. Differential cross sections are found to be in reasonable agreement with existing measurements.
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  • Apodization of the flat mirror support of a newton telescope

    F. Gracia Témich, A. Cornejo Rodríguez, F. Granados Agustín, H. John Caulfield
    104-0
    Abstract:
    An analysis of different structures of the spiders supporting the flat mirror of a Newton type telescope was made, in order to reduce the diffraction effects of the spider on the images produced by the telescope. After applying different numerical solutions used by different authors, and without satisfactory results, a novel solution based on the analysis of the diffraction pattern of a circular aperture allowed us to find a satisfactory reduction of the diffraction pattern in the image produced by the support of the secondary flat mirror. Experimental laboratory results will be shown, using white and He-Ne laser light sources.
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  • Optical properties of paper at 337.1nm

    J. de la Rosa, F.J. Bautista
    110-0
    Abstract:
    Here, we are reporting on the 337.1 nm radiation scattering and fluorescence spectra for white and colored bond paper (100~$\mu$m thick) using an N$_{2}$ laser of 1~$\mu$J pulse energy (t$_{FWHM}$ = 3.8 ns). Fluorescence lifetimes in the order of 10 ns and transit-times in the order of 1 ns were obtained. No fluorescence changes were caused by the short term paper irradiation.
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  • Calibración de un interferómetro fizeau: cálculo de incertidumbres

    J. García-Márquez, N. Alcalá, M. Monto, a., C. Pérez, M. Gutiérrez, J. Mo, a.
    114-0
    Abstract:
    A study on the calibration of Fizeau interferometer in order to obtain its accreditation as a flatness measuring instrument is presented. The interferometer will be used for measuring and calibrating optical flats with a maximum aperture diameter of 15 cm. It is shown here that the uncertainty contribution due to both, the interferometer and the measuring method employed is small as compared to the optical flats used in the calibration procedure.
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