Vol. 17 No. 2 Jul-Dec (2020): Revista Mexicana de Física E
02 Education in Physics
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Desarrollo de competencias genéricas y específicas en estudiantes de ingeniería en el marco del laboratorio de física
Abstract:⬇️ Scroll down to see the full summaryEl objetivo de este artículo es describir el desarrollo de competencias específicas y genéricas a través de la implementación de experiencias de laboratorio en el marco del curso de física básica de estudiantes de ingeniería de la Facultad de Ingeniería y Arquitectura de la Universidad Católica Luis Amigó, Medellín-Colombia. En el texto se describen las actividades y se presenta un análisis estadístico comparativo del rendimiento académico de los estudiantes cuando no se implementaron y cuando sí se implementaron estas actividades en el período lectivo. Nos permitimos concluir que la inclusión de las experiencias de laboratorio y su complementación con ayudas multimedias afianzan el aprendizaje de los contenidos del curso y ayuda en el desarrollo del pensamiento científico del estudiante.
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Massless Majorna bispinors and two-qubit entangled states
Abstract:This is a pedagogical paper, where bispinors solutions to the four-dimensional massless Dirac equation are considered in relativistic quantum mechanics and in quantum computation, taking advantage of the common mathematical description of four-dimensional spaces. First, Weyl and massless Majorana bispinors are shown to be unitary equivalent, closing a gap in the literature regarding their equivalence. A discrepancy in the number of linearly independent solutions reported in the literature is also addressed. Then, it is shown that Weyl bispinors are algebraically equivalent to two-qubit direct product states, and that the massless Majorana bispinors are algebraically equivalent to maximally entangled sates (Bell states), with the transformations relating the two bispinors types acting as entangling gates in quantum computation. Different types of entangling gates are presented, highlighting a set that fulfills the required properties for Majorana zero mode operators in topological quantum computation. Based on this set, a general topological quantum computation model with four Majorana operators is presented, which exhibits all the required technical and physical properties to obtain entanglement of two logical qubits from tpological operations.⬇️ Scroll down to see the full summary -
El límite de Chandrasekhar para principiantes
Abstract:En un breve artículo publicado en 1931 y ampliado en 1935, el astrofísico hindú Subrahmanyan Chandrasekhar hizo público un importante descubrimiento astronómico donde introducía lo que en nuestros días se conoce como límite de Chandrasekhar. Este límite establece la masa máxima que puede alcanzar una enana blanca, que es el remanente estelar que se genera cuando una estrella de baja masa ha agotado su combustible nuclear. El presente trabajo tiene un doble propósito. El primero es presentar una derivación heurística del límite de Chandrasekhar. El segundo es clarificar la génesis del descubrimiento de Chandrasekhar, así como los aspectos conceptuales del tema. La exposición solo utiliza de álgebra de secundaria, así como de algunas nociones generales de física clásica y teoría cuántica.⬇️ Scroll down to see the full summary -
Schrödinger and Planck oscillators: not quite the same physics for a modified Einstein solid
Abstract:⬇️ Scroll down to see the full summaryIn the statistical mechanics of quantum harmonic oscillators, the zero-point energy can either be included (Schrödinger oscillators) or omitted (Planck oscillators). For the usual results, the type of oscillator makes no difference but, looking more closely, it turns out that including or not this energy is not without consequences.
A simple model is introduced that we called the modified Einstein solid (MES). In this model the frequency of the oscillators change with the volume of the solid, and this change is characterized by a certain value of the Grüneisen parameter. The specific heat is the same as in the standard Einstein model, but the pressure, equation of state and bulk modulus can be evaluated in the MES. Using Planck oscillators, the pressure shows an anomalous behavior in terms of the volume, and the bulk modulus becomes negative for certain temperature and volume values, which is physically incorrect. When Schrödinger oscillators are used, the bulk modulus is always positive. Therefore, the different behavior of both types of oscillators indicates that only Schrödinger oscillators lead to correct results.
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Addendum to complete electromagnetic multipole expansion including toroidal moments Rev. Mex. Fis E 52 (2006) 188-197
Abstract:This Addendum reports exact and complete solutions for the electromagnetic field of poloidal currents uniformly distributed on spherical toroidal surfaces, which has been a pending task of Section 3 in [1]. This result is important by⬇️ Scroll down to see the full summary
itself, and also because it allows the identification of new and alternative solutions and the reasons behind them. -
Relating simple harmonic motion and uniform circular motion with Tracker
Abstract:⬇️ Scroll down to see the full summaryIn this study, we demonstrate an interesting relationship between simple harmonic motion and uniform circular motion trough a simple experiment. The experiment requires a low cost-easily found materials and free software, Tracker. To represent uniform circular motion, we use a tape that is stick on a fan moving with the constant angular speed. Meanwhile, spring and pendulum motion are used to represent simple harmonic motion. Through Video Tracker analysis, we have shown that the positions (x and y coordinates) of an object undergoes uniform circular motion fit to the sinusoidal function of time, as same as shown in simple harmonic motion. This simple experiment can be used in high school physics course to lead students in developing a conceptual understanding of uniform circular motion with a less mathematical approach.
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Applications of the double and the dual numbers. The Bianchi models
Abstract:We show that by using complex, double, and dual numbers one can find the invariant one-forms employed in the metrics of the Bianchi cosmological models. The result is equivalent to find, locally, all the Lie groups of dimension three.⬇️ Scroll down to see the full summary -
Particle physics phenomenology with Python 3: $e^- + \bar{\nu}_e \to e^- + \bar{\nu}_e$ scattering in the Fermi theory
Abstract:In this work, we develop an algorithm in Python 3 to compute the theoretical prediction of the electron and electron anti-neutrino scattering cross section using two different numerical methods: {\it i)} Riemann sums and {\it ii)} Monte Carlo integration. We compare the precision among these two methods and the theoretical result. Finally, the theoretical prediction is compared with the result obtained with MadGraph 5 which is commonly used to provide theoretical predictions for the LHC. With this project, we would like to encourage students to use programming languages as a tool for the study of new physics.⬇️ Scroll down to see the full summary -
Horizontal projectile motion: comparing free fall and drag resistance
Abstract:The motion of a particle that is projected into a resistant medium and subjected to a uniform gravitational field is considered. The drag force that acts upon the particle within the medium is proportional to the particle’s speed, the density of the medium, and the cross-section area of the projectile. We review the problem of a horizontal motion with a drag force that is linear in speed. The problem is formulated in terms of particle speed, mass, height, time, and expelled gas velocity. The equations of motion are solved analytically, and a case study is discussed. As a result, we obtain the deviation of the projectile as a function of time because of the expelled gases with or without drag force.⬇️ Scroll down to see the full summary -
Implementación de un método numérico para la solución de una ecuación del tráfico
Abstract:Los estudiantes de licenciatura y posgrado en ciencias tienen conocimientos muy heterogéneos de herramientas computacionales para resolver problemas matemáticos. Generalmente los profesores no conocen el manejo de todos los programas computacionales existentes, así que deben mediar entre las herramientas que ellos conocen y las que dominan los alumnos para que el curso avance sin dificultad y sin detenerse a enseñar un solo tipo de herramienta. Se aborda esta problemática utilizando la siguiente metodología: se explica el algoritmo general que resuelve el problema, se implementa en un lenguaje de programación fácil de aprender, de libre distribución y en el que se grafican los resultados directamente. Se implementa en el modelo de tráfico vehicular de Greenberg. Los resultados se contrastan con los datos del artículo original de Greenberg y algunos tomados directamente en la Ciudad de México.⬇️ Scroll down to see the full summary -
Spatial and temporal dynamics of Belousov-Zhabotinsky reaction: A STEM approach
Abstract:An integrative methodology for teaching science is proposed through the STEM methodology (Science-Technology-EngineeringMathematics).The STEM methodology provides students the opportunity to combine knowledge in an interdisciplinary and collaborative manner, allowing the development of creative and systemic thinking. As a model we propose the experimental reproduction of the Belousov-Zhabotinsky reaction (BZ), which is the standard prototype of non-linear chemistry, in addition we used the Python V2.7 programming software and the Jupyter platform for the computational reproduction of the BZ reaction. The STEM methodology could help the development of new competences for students, that is, it will provide them with tools to solve complex current problems that require of the interdisciplinarity⬇️ Scroll down to see the full summary -
Numerical study of the fundamental fiber soliton propagation
Abstract:This work presents a numerical approach to understand the self-regeneration mechanism of the fundamental soliton propagation driven by the nonlinear Schr\"odinger equation in the nonlinear fiber formalism. This approach shows that the interplay between dispersion and nonlinearity results in a compensation effect in the phase and the instantaneous frequency representation of the pulse envelope. For a better understanding of this compensation process, 3D mapping propagation graphs are presented.⬇️ Scroll down to see the full summary -
Modelación de sistemas dinámicos de la mecánica clásica
Abstract:Los sistemas dinámicos tienen su origen en la Mecánica Clásica. La segunda Ley de Newton representada matemáticamente por una ecuación de movimiento o ecuación diferencial de segundo orden, modela la evolución en el tiempo de los sistemas dinámicos de la Mecánica Clásica constituidos por uno o más cuerpos masivos sujetos a fuerzas externas. El tratamiento de los sistemas dinámicos de la Mecánica Clásica o abreviadamente sistemas mecánicos, mediante la ecuación de movimiento y su solución correspondiente, permite establecer el comportamiento dinámico de los sistemas mecánicos en el tiempo. Para obtener la modelación completa de un sistema mecánico en particular es fundamental obtener la solución de la ecuación de movimiento, ya sea por medio de métodos matemáticos analíticos o numéricos. Sin embargo, los métodos analíticos frecuentemente requieren de una matemática más compleja que la utilizada en los métodos numéricos y que es más difícil de conocer y aplicar para cualquier sistema dinámico. Por este motivo, aquí le damos preferencia al desarrollo de los métodos numéricos de solución de la ecuación de movimiento que se adaptan muy adecuadamente al estudio de diferentes sistemas mecánicos modelados en este trabajo y que sufren muy pocas variaciones al aplicarlos de un sistema mecánico a otro.⬇️ Scroll down to see the full summary -
Learning about wave optics: the effects of combining external visualizations with extreme case reasoning
Abstract:⬇️ Scroll down to see the full summaryIn this study we investigated whether combining external visualizations with extreme case reasoning may facilitate developing of conceptual understanding about wave optics. For purposes of answering our research question we conducted a pretest-posttest quasi-experiment which included 179 students from a first year introductory physics course at the University of Zagreb, Croatia. Students who were guided through extreme case reasoning in their wave optics seminars significantly outperformed their peers who received conventional teaching treatment. Findings from our study suggest that combining external visualizations with extreme case reasoning facilitates development of visually rich internal representations which are a good basis for performing mental simulations about wave optics phenomena. In addition, it has been also found that many students use the “closer to the source implicates greater effect” p-prim when reasoning about certain relationships, such as the relationship between fringes’ dimension and slits-screen separation.
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ESPResSo: una herramienta para la docencia y la investigación
Abstract:ESPResSo es un software especializado para realizar simulaciones computacionales⬇️ Scroll down to see the full summary
de dinámica molecular en el área de la materia condensada blanda; en particular
fue creado para simulaciones del tipo grano grueso. Tradicionalmente, este software,
ha sido utilizado como una poderosa herramienta para investigación básica, aplicada
y como una plataforma fácil de extender acorde a las necesidades del usuario.
Sin embargo, dada su inherente versatilidad y facilidad para implementar un sistema,
es posible también utilizarlo como una plataforma didáctica que sirva como un
primer acercamiento a la simulación computacional, o bien, como herramienta de apoyo
en la docencia. En este trabajo mostraremos las características y uso básico del
software, a través de la implementación de algunos sistemas básicos y del cálculo de
observables estándar como la función de distribución radial y el desplazamiento
cuadrático medio.
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Análisis del Experimento de Millikan
Abstract:Este experimento demostró la cuantización de la carga y midió la magnitud de la carga del electrón. Es un experimento que se repite en laboratorios escolares, causando muchas decepciones; pero es interesante interpretar los datos presentados en su recepción del premio Nobel y en un artículo en Physical Review. Millikan paso muchos años perfeccionando el experimento, reduciendo las corrientes de convección y el tamaño de las gotas de aceite, usado para reducir la evaporación de la gota. Sus mejores datos corresponden a gotas tan pequeñas que tardaban 120 segundos en caer 1.303 cm, las que pueden hacerse subir con 1 a 4 electrones. En laboratorios escolares se obtienen tiempos de 10 a 3 segundos y la carga mínima para vencer a la gravedad corresponde a decenas de electrones, lo que requiere mucha precisión en la medida de las velocidades. Se requiere un buen aislamiento térmico para reducir la convección y un atomizador capaz de producir gotas sumamente pequeñas.⬇️ Scroll down to see the full summary -
Dark matter with n-body numerical simulations
Abstract:The development of numerical N-body simulations have allowed studying the formation process and evolution of galaxies at different scales. This paper presents the fundamental concepts of N-body systems applied to the cosmological evolution of the ¤-Cold Dark Matter (¤CDM) model. To perform structure formation in the Universe, we provide an introduction to the basic equations and their implementation on the GADGET-2 software. We also present a simple guide to modifying this code. First, we briefly describe the dark matter in the Universe as well as the theoretical and experimental basis of the ¤CDM model. Then, we focus on the simulation codes and provide the equations that govern most of the N-body simulations to model the dark matter. We describe the Smoothed Particle Hydrodynamics method used for simulating the gas, star dynamics, and structure formation in these simulations. Then, cautiously, we guide the reader to the installation of GADGET-2 on a Linux-based computer, as well as to carry out a couple of examples to operate the code. Finally, by using a computational cluster, we show several results of a large structure simulation, analyze the outputs to display the matter power spectrum, and compare the outcome with theoretical predictions.⬇️ Scroll down to see the full summary -
Development of physics comic based on local wisdom: Hopscotch (engklek) game android-assisted to improve mathematical representation ability and creative thinking of high school students
Abstract:Comic can be an effective educational tool at various levels of Education. Developmental trends of technology can be used as a learning medium. In this research the comics are designed for operated using an android. This study aims to produce a local wisdom based physics comic media: hopscotch game that is suitable for learning impulse and momentum material in high school, and to know the effectiveness of the media used to improve mathematical representation and creative thinking of students. This research is a Research and Development (R&D) using the Borg & Gall model. Research instruments include product assessment sheets, questionnaire, mathematical representation and creative thinking tests. The data analysis technique used is the MANOVA test. The results show that the product is a media that is operated using a smartphone/ android with the EPUB-Reader application or a computer with an internet browser. The comic media contains impulse and momentum material, videos, examples, and practice questions. The product is categorized as suitable to be used in the physics learning process. There is a difference between the experimental and control classes. This shows that the local wisdom based Physics comic: android-assisted can improve mathematical representation and creative thinking of high school students.⬇️ Scroll down to see the full summary -
On the quantum description of the early universe
Abstract:⬇️ Scroll down to see the full summaryWhy is it interesting to try to understand the origin of the universe? Everything we observe today, including our existence, arose from that event. Although we still do not have a theory that allows us to describe the origin itself, the study of the very early era of the universe involves the ideal terrain to analyze the interface between two of today’s most successful physical theories, General Relativity and Quantum physics. But it is also an area in which we have a large number of observational data to test our theoretical ideas. Two of the fathers of Quantum physics, Niels Bohr and Werner Heisenberg, shared some thoughts that could be described with these words: Quantum physics tells us that there is a line between the observed and the observer, and therefore science should be limited to what is observed. We must give up a complete, objective and realistic theory of the world. This article will orbit around these ideas and summarizes how it is that today, from recent works, we are in a position to try to challenge them (at least in part) through cosmology, seeking the quantum description of the early universe.
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Confined free motion under a dipole potential
Abstract:The classical motion of a particle in a dipolar potential, $U_{\hbox{dip}}(q) = - {k}/{q^2}$, and free motion along a curve in phase space are proven to be equivalent. We also prove that the singularity at $q=0$ in the dipolar potential is strong enough as to prevent the flow of particles from one side of the singularity to the other. This effect does not depende on whether the dipole potential is regarded as attractive ($k>0$) or as repulsive ($k<0$). All the proofs are given using the Hamitonian formalism, therefore they may be used for illustrating the power the Hamiltonian approach may confer in analysing different mecanical systems. The discussion is keep within the reach of advanced undergraduate or graduate students of Hamiltonian mechanics.⬇️ Scroll down to see the full summary -
El problema de la Braquistócrona en el cilindro S1 × R con varias vueltas
Abstract:Presentamos brevemente el problema del braquistócrona en un plano vertical. A seguir presentamos la formulación paramétrica del problema de la braquistócrona sobre la superficie de un cilindro vertical de radio R y encontramos la curva que resuelve este problema. Enseguida formulamos el problema del tautócrona en el cilindro y demostramos que la curva tipo braquistócrona encontrada anteriormente tiene conportamiento tautócrono, esto es, dos partículas sueltas del reposo de puntos distintos de la curva braquistócrona, llegan al punto más bajo de la trajectoria en forma simultánea.⬇️ Scroll down to see the full summary
Se verifica también que la curva tipo braquistócrona en un plano vertical (cicloide invertida) es límite de la curva tipo braquistócrona encontrada en la superficie cilíndrica cuando el radio del
cilindro tiende al infinito. Posteriormente analizamos el problema del braquistócrona entre dos pontos fijos A y B sobre la superficie cilíndrica con la condición adicional de que la partícula antes de llegar al punto final B deve dar um cierto número de vueltas previamente definido. Encontramos la curva que resuelve este problema y adicionalmente encontramos uma relación matemática que determina cuantos vueltas como máximo puede haber si fijamos los valores de las coordenadas del punto inicial (A), final (B), el radio del cilindro y g (la aceleración de la gravedad). -
Exploring Fraunhofer diffraction through Tracker and spreadsheet: An alternative lab activity for distance learning
Abstract:⬇️ Scroll down to see the full summaryIn this paper, we present an alternative for physics laboratory activity related to Fraunhofer diffraction in distance learning. The activity utilizes a demonstration video from MIT Open CourseWare, Tracker software, and spreadsheet. An online demonstration video is used because it is the most accessible resource during undesirable conditions such as COVID 19 pandemic. In the activity, students can explore diffractions phenomena with multiple slits. The effect of slit spacing and slit numbers to the intensity of light is investigated trough spectral analysis with Tracker. The investigation is followed by a discussion through the mathematical approach and visualization with spreadsheets. It will enrich students with a theoretical explanation of the observation. This distance learning activity allows students to develop their science process skills, mathematical and computational thinking skills, and conceptual understanding of Fraunhofer diffraction.
