Vol. 53 No. 1 (2007): Revista Mexicana de Física.

Published: 2007-01-01

Articles

  • Obtaining time-dependent invariants by the Sarlet-Bahar method for a non-linear equation

    E. González-Acosta, M.G. Corona-Galindo
    1-0
    Abstract:
    Applying the Sarlet-Bahar method one obtains the invariant of equations of motion of the type $\overset{..}{\rho}+ \omega^{2}(t)\rho/2$ = $\alpha(t)F(\beta(t)\rho).$ The corresponding auxiliary equation for the Ermakov system is also obtained, and the results obtained by other authors are generalized.
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  • The Maxwell equations in a uniformly accelerated frame

    G.F. Torres del Castillo, C.I. Pérez Sánchez
    4-0
    Abstract:
    The solution of the source-free Maxwell equations in a uniformly accelerated frame of reference is expressed in terms of a single complex scalar potential that obeys a second-order equation. The field of a static electric charge is obtained as an example of a stationary axisymmetric field.
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  • Extended \pmb{$\alpha \beta $} associative memories

    J.H. Sossa Azuela, R. Barrón Fernández
    10-0
    Abstract:
    The $\alpha \beta $ associative memories recently developed in Ref. 10 have proven to be powerful tools for memorizing and recalling patterns when they appear distorted by noise. However they are only useful in the binary case. In this paper we show that it is possible to extend these memories now to the gray-level case. To get the desired extension, we take the original operators $\alpha $ and $\beta $, foundation of the $\alpha \beta $ memories, and propose a more general family of operators. We find that the original operators $\alpha $ and $\beta $ are a subset of these extended operators. For this we first formulate a set of functional equations in terms of the original properties of operators $\alpha $ and $\beta.$ Next we solve this system of equations and find a family of solutions. We show that the $\alpha $ and $\beta $ originally proposed in Ref. 10 are just a particular case of this new family. We present the properties of the new operators. We then use these operators to build a new set of extended memories. We also give the conditions under which the extended memories are able to recall a pattern either from the pattern's fundamental set or from altered versions of them. We give real examples with images where the proposed memories show their efficiency. We compare the proposal with other similar works, and show the ours performs much better.
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  • On the anisotropy in the HRTEM images of a decagonal quasicrystalline phase of the Al-Cu-Co-Si system

    R. García-García, M.M. Martínez, J. Re, es-Gasga.
    21-0
    Abstract:
    Experimental evidence of an electrical and/or magnetic anisotropy was observed in the high resolution transmission electron microscope (HRTEM) images of a decagonal quasicrystalline (DQC) phase of the Al-Cu-Co-Si system. X-ray energy dispersive spectroscopy (EDS) spectra indicated a composition of Al$_{60}$Cu$_{23}$Co$_{15}$Si$_{2}$ for this phase. The anisotropy was responsible for poor contrast quality in the HRTEM images along the periodic direction of this phase, whereas good image contrast was observed in the quasi-aperiodic ten-fold plane. Comparing these results to findings previously reported for the Al$_{62}$Cu$_{20}$Co$_{15}$Si$_{3 }$DQC, we conclude that the observed anisotropy is strongly dependent on the selected chemical composition. After analyzing both the electrical and magnetic effects presented by a sample which is observed with an electron microscope, we conclude that the electrical properties of the DQC phase might be responsible for these observations.
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  • Thoughts on duality and fundamental constants

    J.A. Nieto, L. Ruiz, J. Silvas
    25-0
    Abstract:
    We consider some fundamental constants from the point of view of the duality symmetry. Our analysis of duality is focused on three issues: the maximum radiated power of gravitational waves, the cosmological constant, and the magnetic monopole mass. We show that the maximum radiated power of gravitational waves implies that the Planck time is a minimal time. Furthermore, we prove that duality implies a quantization of the cosmological constant. Finally, by using one of the Euler series for the number $\pi $, we show that the Dirac electric-magnetic charge quantization implies a mass for the magnetic monopole (or neutrino) of the order of $10^{-5}$ the mass of the electron.
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  • Non-isolated pair model for upconversion energy transfer processes

    S.O. Vásquez
    31-0
    Abstract:
    The description of the temporary evolution of upconversion energy transfer processes in solid samples including doped luminescent centers is revised using a simple but non-restrictive pair model. The formalism is related to upconversion processes between a collective of donor and acceptor optical centers, and leads to analytic expressions for the temporary behavior of the emission intensities from the intermediate excited states and the up converted excited state. From a microscopic viewpoint, the results of the model are compared with numerical solutions of the system of differential equations and with those obtained from kinetic type equations, showing the limits of directly using the latter in the analysis of upconversion processes. The proposed model makes it possible to obtain average macroscopic solutions, explicitly dependent on the concentration of dopant luminescent centers in the crystalline lattice, and permits an adequate prediction of the shapes of the decay curves. It would improve the determination of the upconversion energy transfer rates from experimental data.
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  • Time dependent quantum harmonic oscillator subject to a sudden change of mass: continuous solution

    H. Mo, a-Cessa., M. Fernández Guasti
    42-0
    Abstract:
    We show that a harmonic oscillator subject to a sudden change of mass produces squeezed states. Our study is based on an approximate analytic solution to the time-dependent harmonic oscillator equation with a subperiod function parameter. This continuous treatment differs from former studies that involve the matching of two time-independent solutions at the discontinuity. This formalism requires an ad hoc transformation of the original differential equation and is also applicable for rapid, although not necessarily instantaneous, mass variations.
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  • From embedded solitons to 4d dynamical systems

    E. Cabrera, S. González-Pérez-S, i., J. Fujioka
    47-0
    Abstract:
    The term ``embedded soliton'' was coined in 1999 to describe a new type of soliton (discovered in 1997) whose internal frequencies lie within the spectrum of the radiation modes of certain nonlinear systems. In 2005 it was discovered that ``embedded lattice solitons'' (ELS) can also exist in discrete systems. The present communication shows that a discrete higher-order NLS equation with exact ELS leads naturally to a four-dimensional dynamical system that can be cast in the form $\phi _{n+4}=F\left( \phi _{n},\ldots,\phi _{n+3}\right) $, where F is a nonlinear function. In all the particular cases studied in this communication, at least two of the four Lyapunov coefficients associated with the system are positive, thus indicating a chaotic behavior.
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  • Low-complexity chaotic encryption system

    R. Hasimoto-Beltrán
    58-0
    Abstract:
    Secure multimedia communication presents new challenges that are difficult to handle using by currently adopted encryption schemes (RSA---Rivest-Shamir-Adelman, AES---Advanced Encryption Standard, and IDEA---International Data Encryption algorithm) [28]. It requires the processing of huge amounts of information at speeds ranging from Kilobits/sec (Kbs) to the order of Megabits/sec (Mbs). With this in mind, we propose a secure low-complexity encryption system based on a 4-array of independently iterated chaotic logistic maps with a new Spatiotemporal feedback scheme as a diffusion process. The robustness of the system to opponents' attack is enhanced by using a periodic three-level pseudo-random perturbation scheme, one at the system-key level and two at the map array level. An analysis of the proposed scheme regarding its vulnerability to attacks, statistical properties and implementation performance is presented. To the best of our knowledge we provide a simple and secure encryption system for real-time multimedia communications with the fastest software execution time reported in the literature.
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  • Flatness measurement using a grazing incidence interferometer

    N. Alcalá Ochoa, G. Mendiola, J.E.A. L, grave.
    66-0
    Abstract:
    The purpose of this work is to report results of flatness measurements using a grazing incidence interferometer. We show that this interferometer provides enough accuracy to measure nominally flat polishing tools and rough surfaces. In order to calculate the deformation of the surface under test, an interferogram is analyzed with digital imaging techniques based on Fourier methods. We found experimentally that the entire surface topography can be recovered with errors lower than $\sim 0.6 \mu $m, or $\sim \lambda_{eqv} / 6$, where $\lambda _{eqv} = 3.6441 \mu$m is the equivalent wavelength of the interferometer.
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  • A noise tolerant technique for submicron dynamic digital circuits

    F. Mendoza-Hernández, M. Linares-Ar, a.
    72-0
    Abstract:
    Signal integrity issues are a main concern in high performance circuits due to technological advancement. The smaller size of the CMOS transistors together with the increasing use of dynamic logic has brought signal integrity issues to the forefront. Hence it is necessary to develop noise-tolerant circuit techniques that will tolerate noise effects with slight performance penalties. In this paper a new noise tolerant dynamic digital circuit technique is proposed and demonstrated. Simulation results for CMOS AND gate show that the proposed technique has an improvement in the ANTE metric of 3.4x over conventional dynamic logic. A one-bit carry look-ahead adder implemented with the proposed technique has been designed and fabricated using an AMS 0.35$\mu $m CMOS N-well process. The experimental results show the noise immunity improvements of ANTE by 2.1x over the conventional dynamic circuit.
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