Vol. 54 No. 2 Jul-Dec (2008): Revista Mexicana de Física E
Published:
2008-01-01
Artículos
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Sobre el caso de Euler del movimiento de un cuerpo rígido*
Abstract:This is a review paper on the rigid body motion with not torques. This subject was considered by Euler and solved by Jacobi in therms of elliptic functions known as jacobian, $\Theta$ and $H$. The purpose of this work is to complement the study published previously on that subject. In their solution new and not well known ways have been introduced. Some computations have been finished and one find unpublised and general expressions.⬇️ Scroll down to see the full summary -
Principios fundamentales, técnicas de medición y análisis de datos en un acelerador de iones
Abstract:The present work is intended to be a general reference for students and professionals interested in the field. Here, we present an introduction to the analysis techniques and fundamental principles for data processing and operation of a typical ion accelerator that operates in the low energy range. We also present a detailed description of the apparatus and propose new analysis methods for the results. In addition, we introduce illustrative simulations of the ion's trajectories in the different components of the apparatus performed with specialized software and, a new computer data acquisition and control interface.⬇️ Scroll down to see the full summary -
Solving the time-dependent Schrödinger equation using finite difference methods
Abstract:We solve the time-dependent Schrödinger equation in one and two dimensions using the finite difference approximation. The evolution is carried out using the method of lines. The illustrative cases include: the particle in a box and the harmonic oscillator in one and two dimensions. As non-standard examples we evolve two solitons and show the time-dependent solitonic behavior in one dimension and the stabilization of an atomic gas model in two dimensions. The codes used to generate the results in this manuscript are freely available under request, and we expect this material could help students to have a better grasp of the solution of partial differential equations related to dynamical systems.⬇️ Scroll down to see the full summary -
Student use of vectors in the context of acceleration
Abstract:A functional understanding of Newton's second law as a vector equation requires that students be able to reason about forces and acceleration as vectors. In this paper, we present data describing students' conceptual difficulties with vector quantities such as acceleration. These data suggest that after traditional instruction in introductory physics, some students do not recognize the vector nature of this quantity. Other students do not have the requisite procedural knowledge to determine acceleration, and are therefore unable to reason qualitatively about Newton's second law. We describe some specific procedural and reasoning difficulties we have observed in students' use of vectors quantities. In addition, we describe instructional difficulties in mechanics that we observed on the basis of our research into student understanding. Some modifications in the instruction were intended to improve students' understanding of the vector nature of acceleration, and to promote student use of vectors when solving mechanics problems. Finally, we describe initial measurements of the effectiveness of these modifications.⬇️ Scroll down to see the full summary -
On second-order mimetic and conservative finite-difference discretization schemes
Abstract:Although the scheme could be derived on the grounds of a relatively new numerical discretization methodology known as {\em Mimetic Finite-Difference Approach}, the derivation of a second-order mimetic finite difference discretization scheme will be presented in a more intuitive way, using Taylor expansions. Since students become familiar with Taylor expansions in earlier calculus and mathematical methods for physicist courses, one finds this approach of presenting this new discretization scheme to be more easily handled in courses on numerical computations of both undergraduate and graduated programs. The robustness of the resulting discretized equations will be illustrated by finding the numerical solution of an essentially hard-to-solve, one-dimensional, boundary-layer-like problem, based on the steady diffusion equation. Moreover, given that the presented mimetic discretization scheme attains second-order accuracy in the entire computational domain (including the boundaries), as a comparative exercise the discretized equations can be readily applied in solving examples commonly found in texbooks on applied numerical methods and solved numerically via other discretization schemes (including some of the standard finite-diffence discretization schemes).⬇️ Scroll down to see the full summary -
Simple assembling of organic light-emitting diodes for teaching purposes in undergraduate labs
Abstract:Electroluminescent organic molecules and polymers have emerged as advanced materials used to fabricate organic light-emitting diodes (OLEDs) whose unique technological features could revolutionize the industry of flat-panel displays. Although in many cases these novel organic materials combine low cost and ease of processing, OLEDs fabrication for educational purposes has rarely been reported. In this work, we report a simple and inexpensive method to fabricate organic electroluminescent devices intended for educational purposes at the undergraduate level of physics, chemistry and material sciences. For ease of fabrication the cathode in the diode structure was formed by either an alloy of Bi-Pb-Cd-Sn or by a Ga-In alloy in the liquid phase, or simply by silver paint, whereas we used ITO (Indium Tin Oxide) deposited on glass substrates as the anode. Substrates of flexible plastic were also used. The OLEDs were fabricated using the spin-coating technique with solutions of the fluorescent materials Alq$_3$ and MEH:PPV, as well as the phosphor complex Ru(bpy)$_3$. We report measurement data on current-voltage curves, luminescence, and efficiencies obtained by students fabricating and testing the devices under normal room conditions.⬇️ Scroll down to see the full summary -
Mathematics motivated by physics: the electrostatic potential is the Coulomb integral transform of the electric charge density
Abstract:This article illustrates a practical way to connect and coordinate the teaching and learning of physics and mathematics. The starting point is the electrostatic potential, which is obtained in any introductory course of electromagnetism from the Coulomb potential and the superposition principle for any charge distribution. The necessity to develop solutions to the Laplace and Poisson differential equations is also recognized, identifying the Coulomb potential as the generating function of harmonic functions. Correspondingly, the convenience of expressing the electrostatic potential in terms of its multipole expansion in spherical coordinates, or as integral transforms based on harmonic functions in different coordinate systems, is also established. These connections provide a motivation for teachers and students to acquire the necessary mathematics as a basic tool in the study of electromagnetic theory, optics and quantum mechanics.⬇️ Scroll down to see the full summary -
Some intricacies of the momentum operator in quantum mechanics
Abstract:In quantum mechanics textbooks, the momentum operator is defined in Cartesian coordinates and the form of the momentum operator in spherical polar coordinates is rarely discussed. Consequently one always generalizes the Cartesian prescription to other coordinates and falls into a trap. In this work, we introduce the difficulties one faces when the question of the momentum operator in general curvilinear coordinates arises. We have tried to elucidate the points related to the definition of the momentum operator, taking spherical polar coordinates as our specimen coordinate system and proposing an elementary method in which we can ascertain the form of the momentum operator in general coordinate systems.⬇️ Scroll down to see the full summary -
n-order perturbative solution of the inhomogeneous wave equation
Abstract:The exact solution of the inhomogeneous wave equation in one dimension, when the square of the velocity is a linear function of the position, can be written in terms of Bessel functions of the first kind. We use this solution as the zero order approximation for a perturbation expansion and apply it to the case when the square of the velocity can be written as a polynomial in the position. The first and second order perturbation terms, corresponding to quadratic and cubic terms for the square of the velocity, are obtained. A closed formula for the $n$-order correction in terms of integrals of the Bessel functions of the first kind was also explicitly obtained, this expression can be solved analytically for the first and second order corrections and numerically for higher terms.⬇️ Scroll down to see the full summary -
Materia extraña en el universo
Abstract:The strange quark matter hypothesis is one of the most exciting speculations of the XX Century Physics. If this hypothesis is correct, the ground state of the matter would be the strange matter, which could form the core of compact objects like neutron stars or even more exotic objects like quarks stars. Due to the high-density and low-temperature regime in these stars, the interaction between quarks through gluon exchange could favor the appearance of a color superconducting state, significantly modifying the equation of state of the system. In this paper we present a general overview of this subject, taking also into account the effect of strong magnetic fields in the quark stars.⬇️ Scroll down to see the full summary -
Uso del sistema HSI para asignar falso color a objetos en imágenes digitales
Abstract:In this manuscript are shown results of the designation of false color of objects in digital image. The change of hue is done using the color system HSI (Hue, Saturation,Intensity). In order to maintain the appearance of the original objects, the matrix S and I are not altered, and the H matrix becomes. As a result, the resulting image has the same shaded effects, changing only the tone. The system HSI associates the tone of the colors with angles.⬇️ Scroll down to see the full summary -
La materia oscura del universo: retos y perspectivas
Abstract:Understanding the nature of dark matter is one of the greatest challenges of modern physics. This paper gives an introduction to teaching this subject, doing an emphasis on the observational results that give sustenance to the existence of dark matter. We talk about candidates for this king of matter, its advantages and problems, in addition to the immediate prospects for understanding the nature of it.⬇️ Scroll down to see the full summary -
Campos eléctricos generados por elipsoides uniformemente polarizados
Abstract:The electric fields $\vec {E}(\vec {r})$, inside and outside uniformly polarised ellipsoidal electrets, dielectrics and conductors, is given in terms of elliptic integrals. The derivation, valid for homogeneous isotropic and anisotropic materials, makes no recourse to differential equations. The full expression of the $\vec {E}(\vec {r})$ induced for spherical bodies embedded in uniform aplied constant electric fields, either dielectrics or conductors, is explicity given.⬇️ Scroll down to see the full summary -
Método de múltiples reflexiones para determinar el movimiento en un riel de aire
Abstract:This work proposes an experimental set-up to explain the rectilinear and the accelerated uniform movements in the experimental laboratory. The system uses a combination of movement sensors and optics instrumentation. The proposed about this experimental work is to obtain measurements in practical laboratory using an alternative method and introducing to the students, to use different concepts of physic, in the experimental measurement.⬇️ Scroll down to see the full summary -
An alternative solution to the general tautochrone problem
Abstract:In 1658, Blaise Pascal put forward a challenge for solving the area under a segment of a cycloid and also its center of gravity. In 1659, motivated by Pascal challenge, Huygens showed experimentally that the cycloid is the solution to the tautochrone problem, namely that of finding a curve such that the time taken by a particle sliding down to its lowest point, under uniform gravity, is independent of its starting point. Ever since, this problem has appeared in many books and papers that show different solutions. In particular, the fractional derivative formalism has been used to solve the problem for an arbitrary potential and also to put forward the inverse problem: what potential is needed in order for a particular trajectory to be a tautochrone? Unfortunately, the fractional derivative formalism is not a regular subject in the mathematics curricula for physics at most of the Universities we know. In this work we develop an approach that uses the well-known Laplace transform formalism together with the convolution theorem to arrive at similar results.⬇️ Scroll down to see the full summary -
Semejanzas y diferencias entre las carreras de físico y astrónomo en la UNAM (1939-1967)
Abstract:The Faculty of Sciences at the National Autonomous University of Mexico was founded with seven scientific careers, and the astronomer and physicists majors were two of them. But because of the subjects in each of these careers were almost the same, both of them were established just as a Physics in 1967 (considering Astronomy as an specialty). This was justified because in the Astronomy career were no graduated students at that time. In fact the students interested in Astronomy field finished the mayor in Physics and then elaborate a thesis work in Astronomy from their final dissertation.⬇️ Scroll down to see the full summary -
El profesor Pedro Carrasco Garrorena
Abstract:This is a relation about the most important facts in the profesor Pedro Carrasco Garrorena's academic life, Head of the Astronomical Observatory at Madrid, and Dean of the Faculty of Sciences of the University of Madrid during the Civil War. He left Spain next to the Franco's triumph as he was pursued in exceptionally form. He arrived to Mexico in 1939, when Physics was borning in this country, and served to Science by teaching and through the publication of his scientific books.⬇️ Scroll down to see the full summary -
An early comment on the sunspot-climate connection
Abstract:In 1784, a remark on the possible relationship between sunspots and climate was published by the Mexican astronomer and meteorologist José Antonio Alzate. In this paper we wish to note that Alzate was perhaps the first 18th century scientist to suggest the possible relation between sunspots and the Earth's weather, thus preceding William Herschel's 1801 scientifically reasoned statement on this matter, the latter widely regarded as the earliest ever made.⬇️ Scroll down to see the full summary -
Comment on ``Continuous groups of transformations and time-dependent invariants''
Abstract:Some errors in a recent paper ( Rev. Mex. Fís. E 53 (2007) 112) dealing with the Noether theorem are pointed out.⬇️ Scroll down to see the full summary -
Answer to the Comment on ``Continuous groups of transformations and time-dependent invariants''
Abstract:In this paper we answer to the Comment on Continuous groups of transformations and time-dependent invariants. Additionally, in order to apply Hegel´s {\em Aufhebung} concept in physics, some remarks about what we consider the right way to write a ``Comment'' are given.⬇️ Scroll down to see the full summary
