Vol. 62 No. 1 Jan-Jun (2016): Revista Mexicana de Física E

Published: 2016-01-01

Artículos

  • On thermal waves' velocity: some open questions in thermal waves' physics

    E. Marín, L.S. Vaca-Oyola, O. Delgado-Vasallo
    1-4
    Abstract:
    This paper presents some considerations about the truly character of thermal waves. Starting from the comparison of typical characteristic velocities, it is shown why a limiting frequency must exists, above which the parabolic treatment of the heat transfer in presence of time varying periodical heat sources is no longer valid due to the constancy of the speed of light in vacuum. Although it is demonstrated that this frequency is much smaller than that at which the thermal wave velocity can become the speed of light, many questions remain open, such as the behavior of thermal waves at intermediary frequencies. The discussion presented here can be useful to stimulate further discussion on this theme among students, teachers and scientists dealing with heat transport under non-stationary conditions.
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  • About the calculation of the second-order susceptibility $\chi^{(2)}$ tensorial elements for crystals using group theory

    E.S. Jatirian-Foltides, J.J. Escobedo-Alatorre, P.A. Márquez-Aguilar, H. Hardhienata, K. Hingerl, A. Alejo-Molina
    5-13
    Abstract:
    In this work we discuss the way in which, in principle, the nonzero elements in the second-order susceptibility tensor are calculated in a crystal. Group Theory predicts which one of these elements will be zero based on the symmetry of the crystal. However, the position of these zeros in the tensor are intrinsically associated to a fixed system of reference chosen ``a priori'' for a particular crystal.
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  • Tesis de Física presentadas en la Real y Pontificia Universidad de México. 1774-1791.

    M.A. Moreno Corral
    14-22
    Abstract:
    Some of the most overlooked aspects of the historical development of Physics in Mexico, are when, how, and what was taught of it in New Spain, in particular in the last third of the eighteenth century, which was when New Spain's culture began to adapt to the new scientific paradigms. One way to establish reliable information about the subjects that high school students learned from that period, which was the only school level where physics was taught, is to analyze the content of the theses in Physics presented at the Royal and Pontifical University of Mexico. Those documents, virtually unknown today, have been difficult to trace and still harder to get, but, as discussed in this work, they provide clear, reliable information on how, when, and where the physics arising from the Scientific Revolution entered the classrooms of our nation.
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  • Coexistence curve of monodisperse gases

    R.A. Méndez Álvarez, Ó Vázquez-Rodríguez., J.N. Herrera
    23-30
    Abstract:
    We present and discuss two equations of state for monodisperse systems. The first one is a general, semi-empiric, cubic equation of state written in terms of three constant parameters and a temperature dependent function for which the second virial coefficient may be used to obtain an analytically manipulable expression. The second equation is obtained by means of the mean spherical approximation (MSA) and depends on two parameters, one for the range, and the other for the amplitude, of the interaction potential. The aim of this paper is to present the mathematical and numerical techniques used to obtain the coexistence curve of monodisperse gases. This is made for the two equations of state and the corresponding appropriate methods to obtain the coexistence curve: Maxwell's equal-area rule, for the cubic equation, and the equilibrium condition of the chemical potential of the coexisting phases, for the MSA result. We compare our results with recently reported experimental data for Ar. With this work, we intend to acquaint the reader with both equations and their application possibilities, and also with the mathematical and computational tools required to find the coexistence curves.
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  • Sobre la naturaleza, tensorial o no tensorial, de los símbolos de Christoffel

    L. Patiño, J. Söhle
    31-39
    Abstract:
    From the first approach to General Relativity we learn about the Christoffel symbols, and it is easy to notice that their coordinated components do not transform as a tensor. It is then confusing to find renowned books on the subject that refer to these symbols as if they were indeed a tensor. A prominent example of such a book is the one written by Rober Wald \cite{GeneralRelativity}, which has been embraced as a textbook on the matter by a large amount of prestigious institutions around the globe. The simplest alternative would be to think that the books just mentioned provide a wrong description of the Christoffel symbols, but this is not the case. Understanding the mathematical foundation of why some authors treat the Christoffel symbols as a tensor provides valuable insight about the nature of the metric connection in General Relativity, and that is why in this paper we dedicate the space to provide the needed analysis. The discussion provided here is aimed to those that have already taken at least one class in General Relativity, hence some of the theoretical tools will be taken as known by the reader.
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  • Two-dimensional harmonic and Green's functions on a spherical surface

    Ch. Esparza-López, E. Ley-Koo, P.L. Rendón
    40-43
    Abstract:
    The solutions of the Laplace-Beltrami equation on a spherical surface are constructed by the method of separation of variables, as the products of the Fourier basis functions of the azimuthal angle and the integer powers of tangent or cotangent functions of half the polar angle. The Legendre operator acting on the latter functions yields zero. The construction of the Green's function as the solution of the corresponding Poisson-Beltrami equation with a unit point source on the spherical surface is also constructed using the two-dimensional spherical harmonic basis.
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  • Experimental aspects of the gyroscope's movement

    P. Morales, D.E. Jaramillo, J. Osorio
    44-50
    Abstract:
    In presence of a uniform gravitational field, Euler equations for a gyroscope can be written as a non-linear equation for the components of Riemann's stereographic projection of the symmetry axis over a horizontal plane. Under the approximation of nutations with low amplitude, the solution of this equation corresponds to the sum of two rotating vectors with angular frequencies related to both angular velocities of nutation and precession. Such velocities are functions of rotation rapidity and inertia momentum of the gyroscope. From pictures of the movement projection of a commercial gyroscope, and using a laser that turn on during half revolution cycle of a disk, we can determine all kinematic quantities of the gyroscope, velocities of: rotation, precession and nutation, along with the angle of average inclination from axis. After complete a total of 120 experiments, we corroborate that the expressions given for velocities of precession and nutation, in function of rotation, match with experimental data. This is an easy experiment to implement, and can be used in advanced courses of mechanic.
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  • Difracción de luz por esferas dieléctricas: micro- y nano-partículas

    R. Rodríguez-Mijangos, R. García-Llamas
    51-59
    Abstract:
    The light diffraction associated to excitation of whispering gallery modes in dielectric spheres or nanoparticles is studied theoretically. The named nanojets in dielectric micro spheres are also studied, these are a sub-wavelength volumetric regions of high light field intensity located near to the sphere. The excitation WGM for dielectric spheres are observed as peaks in the total scattering cross section. Under excitation condition, the modes are behaved as waves which are propagating along the circumference, but in the sphere, its intensity is highly confined to the surface.
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  • The Einstein nanocrystal

    D.S. Bertoldi A, E.N. Miranda
    60-65
    Abstract:
    We study the simplest possible model of nanocrystal consisting in a simple cubic lattice with a small number of atoms ($N_A \sim 10-10^3$), where each atom is linked to its nearest neighbor by a quantum harmonic potential. Some properties (entropy, temperature, specific heat) of the nanocrystal are calculated numerically but exactly within the framework of the microcanonical ensemble. We find that the presence of a surface in the nanocrystal modifies the thermostatistic properties to a greater extent than the small number of atoms in the system. The specific heat $C_v$ behaves similarly to the Einstein solid, with an asymptotic value for high temperatures that differs from that of the Dulong-Petit law by a term of the order of $N_A^{-1/3}$ and that can be explained easily in terms of the surface. The entropy is non-additive, but this is due to the presence of the surface and we show that the additivity is recovered in the thermodynamic limit. Finally, we find that, when calculations follow the canonical ensemble, results differ little for small systems ($N_A = 27$) and are inexistent for larger systems ($N_A = 1000$).
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