Vol. 58 No. 1 (2012): Revista Mexicana de Física.

Published: 2012-01-01

Articles

  • Manto de invisibilidad en microondas

    E. Septién, V. Aboites
    1-5
    Abstract:
    We present experimental results of an invisibility cloak operating in the microwave range at a 10.525 GHz frequency. The theoretical analysis is based on a conformal mapping. The experimental results were obtained from the construction of a resonant metamaterial with copper rings. A good agreement is found between both results.
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  • Complex dynamics and chaos in commutable pendulum

    V.R. Nosov, H. Dominguez, J.A. Ortega-Herrera, J.A. Meda-Campaña
    6-12
    Abstract:
    This paper deals with a commutable pendulum which has two different natural frequencies in two space regions. The first region corresponds to the first three quadrants of the phase space; while the second region coincides with the fourth quadrant. This apparently trivial system shows a very complex behavior, regardless of the fact that it is based on the simple pendulum model. In the case where the two natural frequencies coincide, the flow is stable. However, just by varying the natural frequency in the fourth quadrant, the system may be asymptotically stable or unstable and also may have simple limit cycle, complex limit cycles and even chaotic behavior. In all these cases the trajectories have simple analytical descriptions.
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  • Algorithm to compute the electric field gradient tensor in ionic crystals

    J.J. Hernández-Gómez, V. Marquina, R.W. Gómez
    13-18
    Abstract:
    A simple algorithm and a computational program to numerically compute the electric field gradient and the concomitant quadrupolar nuclear splitting is developed for an arbitrary ionic crystal. The calculations are performed using a point charge model. The program provides three different ways for the data input: by Bravais lattices, by lattice parameters, or by introducing any spatial structure. The program calculates the components of the electric field gradient, the asymmetry parameter and the quadrupolar splitting for a given number of nearest neighbors with respect to the nuclear charge as origin. In addition, the program allows the use of different Sternheimer antishielding factors.
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  • Natural convection and surface thermal radiation in a tilted open shallow cavity

    J.F. Hinojosa Palafox
    19-28
    Abstract:
    In this paper the numerical calculations of heat transfer by natural convection and surface radiation in a tilted open shallow cavity are presented. The cavity maintains the opposite wall to the aperture at a constant temperature while the remaining walls are adiabatic. The results in the steady state are obtained for a Rayleigh number range from 10$^{5}$ to 10$^{7}$, inclination angles from 45$^{\circ}$ to 135$^{\circ}$ and aspect ratios equal to 2 and 4. It was found that the exchange of thermal radiation between walls is considerably more relevant that the convective phenomenon for an inclination angle of 135$^{\circ}$. Oscillations in the convective Nusselt number were observed for inclination angles of 45$^{\circ}$ (AR=4) and 90$^{\circ}$ (AR of 2 and 4) caused by the formation of thermal plumes in the bottom adiabatic wall that travel and mix with the thermal layer of the hot wall.
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  • Computer simulation of the energy dynamics of a sinusoidally perturbed double sine-Gordon equation: an application to the transmission of wave signals

    J.E. Macías-Díaz
    29-40
    Abstract:
    In this work, we employ a numerical method to approximate the solutions of a damped, double sine-Gordon equation spatially defined over a closed and bounded interval of the real line, subject to a harmonic perturbation of the Dirichlet type on one end, and a homogeneous Neumann condition on the other. The method has schemes to approximate consistently the temporal dynamics of the local energy density and the total energy of the medium, and the total energy over any finite interval of time and, additionally, it preserves the positivity of the corresponding energy operators. As an application of this method, we establish numerically that the phenomenon of nonlinear bistability (which is physically characterized by the coexistence of conducting and insulating regimes) is present in media governed by damped, double sine-Gordon equations when the systems are driven harmonically at a frequency in the forbidden band-gap. We employ this nonlinear process in order to accurately propagate localized pulses from the perturbed end to the free boundary. Two different methods for the transmission of monochromatic waves are employed in this study, and our results demonstrate that an efficient propagation of information is feasible, indeed.
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  • Structural and electronic properties of RuN/GaN superlattices: a first-principles study

    C. Ortega López, R. González-Hernández, J. Arbe, Rodríguez.
    41-45
    Abstract:
    In this work, we investigate the structural and electronic properties of RuN/GaN superlattices, using first-principles calculations within density functional theory (DFT) and generalized gradient approximation (GGA). We have employed the full potential linearized augmented plane waves (FP-LAPW) method as implemented in the \verb"WIEN2k" code. The 1$\times$1, 1$\times$2, 1$\times$3 and 1$\times$4 RuN/GaN superlattices are studied in the wurtzite phase, which is the most stable structure of the GaN. In order to determine the best parameters, we have optimized the total energy as a function of: (i) the unit cell volume, (ii) the $c/a$ ratio and (iii) the $z$-coordinate of Ga and Ru atoms. Lattices constant, bulk moduli, cohesive and formation energies are reported as a function of the period for each RuN/GaN superlattices, and trends are discussed. On the other hand, a study of the density of states show that the superlattices present a metallic behavior. The results suggest that the RuN/GaN superlattices can be used as compounds for the fabrication of semiconductor-metal-semiconductor or semiconductor-metal devices.
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  • Electronic band structure of platinum low--index surfaces: an ab initio and tight--binding study. II

    H.J. Herrera-Suárez, A. Rubio--Ponce, D. Olguín
    46-54
    Abstract:
    We present the calculated electronic band structure of ideal Pt(100) and Pt(110) surface by using density functional theory and the empirical tight--binding method. A detailed discussion of the surface-- and resonance--states is given. It is shown that the calculated surface-- and resonance--states of ideal Pt(100) surfaces agree very well with the available experimental data. For Pt(110), some of the surface-- and resonance--states are characteristic of the low symmetry of the surface and are identified as being independent of surface reconstruction effects. As in the previous paper, the density functional calculations were performed using the full potential linearized augmented plane wave method, and the empirical calculations were performed using the tight--binding method and Surface Green's Function Matching Method.
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  • On the centre of mass velocity in molecular dynamics simulations

    G.A. Méndez-Maldonado, M. González-Melchor, J. Alej, re., G.A. Chapela
    55-60
    Abstract:
    Molecular dynamics simulations are performed on a fluid at supercritical conditions to analyze the effect that the velocity of centre of mass (VCOM) of the system has on temperature and phase stability. Standard rescaling velocities and Nosé-Hoover chains of thermostats methods are used to carry out simulations on Square Well, Lennard-Jones and Soft Primitive potential models. Removing the VCOM at the beginning or during the simulation is not required for the Nosé-Hoover chain of thermostats to keep the correct temperature of the system, however, it is fundamental to keep null the VCOM when the traditional rescaling velocity scheme is used. It is shown that if the VCOM is removed only at the beginning of the simulation the internal and external temperatures are not the same for very long simulations and the fluid becomes a solid. The temperatures and physical properties obtained using the Nosé-Hoover chain method are the same as those obtained by removing the VCOM during the simulation in the rescaling velocity procedure.
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  • On singular lagrangians and Dirac's method

    J.U. Cisneros-Parra
    61-68
    Abstract:
    We show some instances of singular lagrangians from the classical mechanics of particles and apply Dirac's method for building the canonical equations. We find then the reason for the singularity, and therefore, we get the Hamilton equations with the familiar procedure, that is without the need of Dirac's procedure. Known cases of singular lagrangians in special relativity are also presented, and their non-singular alternatives.
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  • A $m$-dimensional stochastic estimator

    R. Palma Orozco, J. de J, G. Garrido Aguilar
    69-76
    Abstract:
    This paper shows the development of a optimal stochastic estimator for a black-box system in a $m$-dimensional space, observing noise with an unknown dynamics model. The results are based in state space, described by a discrete stochastic estimator and noise characterization. The proposed result gives an algorithm to construct diagonal form for the state space system. It is a new technique for a instrumental variable tool, and a diagonalization process avoiding the calculation of pseudo-inverse matrices is presented with a linear computational complexity $O(j)$ and $j$ as the diagonal matrix dimension. The results show that it is possible to reconstruct the observable signal with a probability approximation.
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  • Nature of the bonding, surface relaxation and charge transfer of Au dimmers on an MgO(100) surface

    C. Quintanar, R. Caballero, J. Ulises Reveles, S.N. Khanna
    77-85
    Abstract:
    First principles electronic structure investigations of the nature of adsorption, relaxation of the atoms near the adsorption site, and the charging of the Au$_{2}$ particle on the relaxed-rumpled MgO(100) surface have been carried out within the density functional theory-cluster-embedding approach. The investigations focus on an Au$_{2}$ molecule, perpendicular to the surface, adsorbed at different locations. Three bonding sites are studied: a five coordinated oxygen regular terrace site O$_{5c}$, an F$_{s}$ neutral color center (two electrons in an O vacancy), and an F$_{s}^{ + }$ positive charged color center (one electron in an O vacancy). The studies indicate that large relaxation of the neighboring atoms and large charge transfer occurs for an Au$_{2}$ over the color centers. An analysis of the one-electron energy levels of the Au dimer, the MgO surface and the Au$_{2}$MgO(100) complex for each absorption site allows us to rationalize the nature of the bonding, surface relaxation, calculated absorption and dimerization energies and electron charge transfers.
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  • A 1.7 MHz Chua's circuit using VMs and CF+s

    C. Sánchez López
    86-93
    Abstract:
    In this paper, a high-frequency Chua's chaotic oscillator based on unity gain cells (UGCs) is introduced. Leveraging the internal buffers of the integrated circuit AD844, a voltage mirror (VM) and a positive current follower (CF+) are designed, taking into account the parasitic elements associated to each UGC. Afterwards, the behavior of the nonlinear resistor and of the grounded inductor are designed by using several VMs, CF+s, discrete capacitors and resistors. In this way, Chua's circuit is built by coupling a nonlinear resistor and an active LC tank circuit by using an RC passive filter. Hspice simulations performed at the state space and in the time and frequency domains show that the proposed topology generates chaos at 1.7 MHz. Experimental results are given, verifying that the chaotic spectrum is extended to high-frequency and showing close agreement with theoretical analysis. The proposed topology is compared with other topologies reported in the literature, showing that a number reduced of active devices and passive elements along with smaller supply voltages can be used to generate chaotic oscillations at high-frequency. Sensitivity and Monte Carlo analysis are also done in order to research the robustness of the proposed chaotic circuit.
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  • Hermitian operators and boundary conditions

    M. Ma, a-Mendieta., J. Oliveros-Oliveros, E. Teniza-Tetlalmatzi, J. Vargas-Ubera
    94-103
    Abstract:
    The case of the hermeticity of the operators representing the physical observable has received considerable attention in recent years. In this paper we work with a method developed by Morsy and Ata [1] for obtaining Hermitian differential operators independently of the values of the boundary conditions on wave functions. Once obtained these operators, called intrinsically Hermitic operators, we build the Hamiltonian for the harmonic oscillator, hydrogen atom and the potential well of infinite walls. In the first two cases we use the factorization method of ladder operators (also intrinsically Hermitic) and show that results obtained with conventional operators, based on the annulation of the wave functions on the boundaries, are preserved. For the infinite well we show that the version of the Hamiltonian intrinsically Hermitic provides a solution to a paradox that appears in a particular wave function.
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  • Orientational distribution for dipolar and quadrupolar colloids driven by an external field

    R. Ramírez-Sanchez, H. Ruiz-Estrada, O. Alarcón-Waess
    104-112
    Abstract:
    We study the ordering in dipolar and quadrupolar colloids driven by an appropiate external field, which is low structured at zero field strength. This study consists of analyzing the predictions involved by the one body probability density function, as function of the strength of the field, which is the solution of the equilibrium Smoluchowski equation, without hydrodynamic interactions. Because of the symmetry of the dipole and quadrupole, for the former an axial nematic-like phase is predicted, wheras for the latter a biaxial nematic-like phase is predicted. In the study we consider different fields, for the dipole only the orientation of the field is changed, whereas for the quadrupole the gradient of the field is also changed. The alignment of the multipolar colloids for high values in field is independent of the different fields studied in both moments, but their alignment for low values depends on the field features. The change in curvature of the one body probability density functions for the moments analyzed is predicted in field strength values with a different meaning. For the quadrupole moment an anomalous perpendicular alignment of the particles is predicted, which does not ocurr for the dipole moment. Our results are described as a generalized point of view in the Landau-de Gennes theory for the nematic isotropic phase transition driven by an external field.
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  • Hyperfine interaction of V$_{\text{k}}$ centres in Cs$_{_{2}}$NaYCl$_{6}$ crystals

    J. Barreto, J.L. Boldú, H. del Castillo, E. Muñoz
    113-116
    Abstract:
    In this work we present the results obtained through electron paramagnetic resonance (EPR) spectroscopy of the study of the hyperfine interaction of the V$_{k}$ centres in the Cesium, sodium, yttrium hexachloride (Cs$_{2}$NaYCl$_{6}$) crystals. These electron defect centres are created by $\gamma$-irradiation at liquid nitrogen temperature of the Cs$_{2}$NaYCl$_{6}$ crystals. Our results are: $g_{\|}$=2.008, $g_{\bot}$=2.023, A$_{\|}$=91.21 (gauss) and A$_{\bot}$=3.10 (gauss) and these results are compared with those obtained by Th. Pawlik and J.M. Spaeth [24] for the same system and those of D. Shoemaker [23] for sodium chloride.
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