Revista Mexicana de Física E

Linear and angular momentum stored in a distribution of charges in a magnetic field. The other side of the story

Gerardo Francisco Torres del Castillo, Claudia Elizabeth Mendoza-Luna — Wed, 01 Jan 2025 00:00:00 +0000

The linear or the angular momentum stored in an arbitrary electric charge distribution in the presence of a magnetic field is defined by calculating the linear or the angular momentum transferred to the electric charge distribution by a time-dependent magnetic field, which is initially zero and after some time reaches the desired final value. The component of the transferred linear momentum along some axis depends only on the final magnetic field if and only if the magnetic field is invariant under translations along this axis. Similarly, the component of the transferred angular momentum along some axis depends only on the final magnetic field if and only if the magnetic field is invariant under rotations about this axis.

Cadabra and python algorithms in general relativity and cosmology I: Generalities

O. Castillo-Felisola, D. T. Price, M. Scomparin — Wed, 01 Jan 2025 00:00:00 +0000

The aim of this work is to present a series of concrete examples which illustrate how the computer algebra system Cadabra can be used to manipulate expressions appearing in General Relativity and other gravitational theories. We highlight the way in which Cadabra's philosophy differs from other systems with related functionality. The use of various new built-in packages is discussed, and we show how such packages can also be created by end-users directly using the notebook interface.

The current paper focuses on fairly generic applications in gravitational theories, including the use of differential forms, the derivation of field equations and the construction of their solutions.

Aspectos básicos del método de amplitudes I: caso sin masa

Jonathan Reyes Pérez — Wed, 01 Jan 2025 00:00:00 +0000

En este trabajo se revisa el formalismo de los espinores de helicidad o el método de amplitudes en el espacio de cuatro dimensiones (D=4), en el contexto de la Electrodinámica Cuántica (QED, por sus siglas en inglés). Se muestran los cálculos explícitos de la amplitud del proceso físico e⁺ e^- ---> mu⁺ mu^- a nivel árbol como un ejemplo de motivación a este método en el límite de altas energías o ultra-relativista. El objetivo es introducir a estudiantes de física en las nuevas técnicas de cálculo que se desarrollan a partir del formalismo de amplitudes.

In this work, the helicity spinors formalism or just amplitudes is reviewed in four-dimensional space (D = 4), in the context of Quantum Electrodynamics (QED). Explicit calculations for the amplitude of the physical process e +e − → µ +µ − at the tree level in the high energy or ultra-relativistic limit are shown as an example of motivation for study this method. The objective is to introduce particle physics students to the new calculation techniques that are developed from the amplitude program.

Teaching free-falling motion with LibreOffice Calc

Kan Sornbundit — Wed, 01 Jan 2025 00:00:00 +0000

The aim of this work is to demonstrate how to use LibreOffice Calc, a freeware spreadsheet, to teach physics of free-falling motion. Although free-falling motion is experienced in our daily lives, students often misunderstand the calculations, mainly because of the use of signs for related physical parameters. For example, the velocity can be positive, negative, or even zero, depending on the direction of motion. To help students learn, we have used the embedded VLOOKUP function in LibreOffice to create a simulation of the object's trajectory. We have found that the software can be used to create snapshots of consecutive vertical motions of the object. The direction of the object's movement can be determined using the IF function. Moreover, the software can be used to solve equations that are often found in problems in this class. By using the Goal Seek function, the numerical value of the parameter of interest can be obtained.

Quantitative characterization of light through a homemade spectrometer: A STEM project-based learning activity

Ana R. Romero Castellanos, H. E. Castellanos, C. E. Alvarez-Salazar — Wed, 01 Jan 2025 00:00:00 +0000

This paper introduces students to quantitative spectrometry using a hands-on approach, building a simple, low-cost spectrometer to characterize discrete or continuous light spectra, using a smartphone or laptop camera. This project-based learning activity is performed without any specialized equipment (favoring inclusive education at high school and university levels) and allows students to develop scientific skills through the measurement and characterization of light sources, reinforces technological and engineering skills through the construction of the optical instrument and the analysis of light spectra through free software, and applies mathematical competences through the statistical analysis of data. The project is an inclusive and integrative STEM activity, building contextualized and quantitative knowledge in these areas.

Simulación de un sistema básico de detección de muones usando software libre

P. Patiño, R. Benavides, A. Tapia, D. Mart´ınez-Caicedo — Wed, 01 Jan 2025 00:00:00 +0000

Particle detectors built with plastic scintillator bars have been used in high-energy physics applications for a long time because they have a fast response to photon production, are easy to fabricate, and are inexpensive. They are generally used with light sensors, such as silicon photo-sensors (SiPM), which have been used in recent years for their high efficiency and low operating voltage, among other advantages. SiPMs are usually located at the end of the bar to collect the light and thus create an electronic output signal. The objective of this work is to simulate the light collection process, starting from when optical photons are produced by a flow of muons passing through a scintillator bar, their journey through a wavelength-shifted optical fiber, up to their detection by the SiPM. This simulation implemented in free and open source software such as GEANT4 can serve as an important guide for Latin American students who are interested in learning the physics of elementary particle detectors.

Los detectores de partículas construidos con barras centelladoras plásticas se han utilizado en aplicaciones de física de altas energías por mucho tiempo, ya que poseen una respuesta rápida a la producción de fotones, son fáciles de fabricar y son de bajo costo. Se utilizan generalmente con sensores de luz, como los foto-sensores de silicio (SiPM), los cuales se han utilizado en los últimos años por su alta eficiencia y su bajo voltaje de operación, entre otras ventajas. Generalmente, los SiPM se encuentran en un extremo de la barra para colectar la luz y de esta manera crear una señal electrónica de salida. El objetivo de este trabajo es simular el proceso de recolección de luz, partiendo desde el momento cuando los fotones ópticos son producidos por el flujo de muones atravesando una barra centelladora, su viaje a través de una fibra óptica de corrimiento de longitud de onda, hasta su detección por parte del SiPM. Esta simulación implementada en un software libre y de código abierto como lo es GEANT4 puede servir como una guía importante para estudiantes latinoamericanos que estén interesados en aprender la física de detectores de partículas elementales.

pymcabc: A particle physics toy toolbox for the ABC model

Aman Desai — Wed, 01 Jan 2025 00:00:00 +0000

We present the pymcabc software, which is a Monte Carlo event generator for the ABC toy model. The ABC model consists of three scalar particles of arbitrary masses. The only interaction among these particles occurs when all three of them are present together. The pymcabc software can calculate all the leading-order cross-sections as well as decay widths within the ABC model and it can simulate all the scattering processes within the ABC model. Moreover, it simulates the decays associated with the heavy-particle final state, leading to a 2 → 3 or a 2 → 4 type final states within the ABC model. We also apply toy detector effects to simulate the detector response of a toy tracker for three-momentum measurements and a toy calorimeter for energy measurements. Using the results of the pymcabc software, we also illustrate some well-known physics analyses techniques such as the analysis of the lineshape of a heavy propagator and the recoil mass reconstruction technique.

GUI of Complex plane on Excel spreadsheets

M. Y. Tufail, S. Gul — Wed, 01 Jan 2025 00:00:00 +0000

In this paper we provide two spreadsheets in Excel for university students and teachers. These spreadsheets 
contains the geometrical representation of complex numbers, conversion in polar and rectangular forms and four 
basic math operation that are addition, subtraction, multiplication and division. Further we also established 
that complex number satisfies the parallelogram law

Broad spectrum attenuated total reflectance: numerical and experimental demonstration

Wed, 01 Jan 2025 00:00:00 +0000

Nano-optics is one of the most rapidly expanding fields in physics. Providing students with a basic knowledge of nano-optics and its practical applications, bridges the gap between theoretical concepts and real-world technological advancements, making the study of this branch of physics more tangible and exciting. In this study, we present a comprehensive analysis of the reflectivity of light from a thin-multilayered system across a broad spectrum. We theoretically examined the reflection of incident plane waves at interfaces between different media using the T-matrix method. We compared our theoretical findings with experimental results obtained from an attenuated total reflection (ATR) setup, which employed a supercontinuum laser as light source. This setup allowed us to observe both angular and spectral dependence of reflectivity. The sample under study, fabricated using e-beam physical vapor deposition, consisted of a BK-7 glass substrate, a 3 nm Cr layer, a 30 nm Au layer, and air as the superstrate. The obtained results demonstrate the accuracy of both, experimental and numerical methods. Our study not only serves as a valuable didactic resource, but also opens new perspectives for sensing applications where spectral shift of plasmonic resonances is a subject of interest.

The Kepler problem on the lattice

D. Sanjinés, E. Mamani, J. Velasco — Wed, 01 Jan 2025 00:00:00 +0000

We study the motion of a particle in a 3-dimensional lattice in the presence of a potential −V₁/r, but we demonstrate semiclassicaly that the trajectories will always remain in a plane which can be taken as a rectangular lattice. The Hamiltonian model for this problem is the conservative tight-binding one with lattice constants a, b and hopping elements A, B in the XY axes, respectively. We use the semiclassical and quantum formalisms; for the latter we apply the pseudo-spectral algorithm to integrate the Schrödinger equation. Since the lattice discrete subspace is not isotropic, the angular momentum is not conserved, which has interesting consequences as chaotic trajectories and precession trajectories, similar to the astronomical precession trajectories due to non-central gravitational forces, notably, the non-relativistic Mercury’s perihelion precession. Although the elements of the mass tensor are naturally different in a rectangular lattice, these can be chosen to be still different in the continuum, which permits to study the motion with kinetic energies p_i²/2m_i (i = x,y). We calculate also the contour plots of an initial Gaussian wavepacket as it moves in the lattice and we propose an “intrinsec angular momentum” S associated to its asymmetrical deformation, such that the quantum and semiclassical angular momenta, L_q, L_c, respectively, could be related as L_q = L_c+ αS.

Wavelet eXtropy of fractal signals

Julio Ramirez-Pacheco — Wed, 01 Jan 2025 00:00:00 +0000

Recently, the concept of eXtropy was proposed as a complementary dual of Shannon entropy. This article extends the standard time-domain eXtropy concept to the time-scale domain and then obtains a closed-form expression for this wavelet eXtropy for fractal signals of parameter α. A didactic study of the wavelet eXtropy of fractal signals reveals that this infomation-theory quantifier increases for short-memory fractal signals, is maximum for white noise (α = 0) and decreases for long-memory fractal processes. Compared to the standard wavelet entropy, wavelet eXtropy performs similar, however has lower variability for stationary fractal signals and higher variability for nonstationary ones. Moreover, the computation of fractality based eXtropy planes allows to highlight further properties and also potential applications for the analysis/estimation of fractals.

Impacto de la educación remota en la percepción y rendimiento de estudiantes universitarios en un curso de física

Wed, 01 Jan 2025 00:00:00 +0000

The postponement of face-to-face classes due to COVID-19 during 2020-2021, triggered urgent changes in the teaching-learning processes in the university context. Likewise, the return of university life to face-to-face attendance demanded and still demands changes in the pedagogical and didactic processes that contribute to the adaptation of those students who attend on-campus classes for the first time. Considering the above, this study seeks to unveil and analyze the perceptions of undergraduate students about the effect of remote education on the learning of physics during the pandemic and their academic performance at the beginning of the post-pandemic period. This study includes 139 third-semester students of Engineering and Geology attending a private University in Colombia, in a heat-wave physics course developed during the first academic semester of 2022. The implementation of a generalized linear model (GLM) revealed that the perception of comprehension is higher among students coming from private schools. Similarly, students who completed high school in person during the pandemic perceive that they understood the concepts studied in physics and have a better valuation of their understanding of the heat-wave physics subject. On the other hand, students who prefer virtual remote classes negatively value their understanding of heat-wave physics concepts.

El aplazamiento de las clases presenciales en el sistema educativo, por causa de la COVID-19 durante el 2020 y 2021, fomentó cambios urgentes en los procesos de enseñanza-aprendizaje en el contexto universitario. Igualmente, el retorno de la vida universitaria a la presencialidad exigió y exige aún, una adecuación en los procesos pedagógicos y didácticos que permita la adaptación de aquellos estudiantes que por primera vez asisten al campus universitario. Teniendo en cuenta lo anterior, en este estudio se busca conocer y analizar la percepción de 139 estudiantes universitarios de Ingeniería y Geología de tercer semestre de una universidad privada de Colombia, en un curso de física calor-ondas en el primer semestre académico del 2022, acerca del efecto de la educación remota en su aprendizaje de la física en tiempo de pandemia y en su desempeño académico al inicio de postpandemia en la universidad a través de un modelo lineal generalizado (MLG). Los resultados muestran que la percepción sobre la comprensión es mayor entre los estudiantes que provienen de colegios privados. Asimismo, los estudiantes que realizaron su bachillerato en forma presencial durante la pandemia perciben haber comprendido los conceptos estudiados en física y tienen una mejor valoración de su comprensión en la asignatura física calor-ondas. Por otro lado, los estudiantes que prefieren las clases remotas virtuales valoran negativamente su comprensión de los conceptos de física calor-ondas.

A toy model for determining the critical size condition in fission chain reaction

O. Ozer, W. A. Sheekhoo, G. Sayın — Wed, 01 Jan 2025 00:00:00 +0000

The geometric Buckling in the analytical solutions of the steady-state one group neutron diffusion equation are used to compare with numerical results of the Monte Carlo Method in the determination of the size condition yielding the minimum critical mass in three basic geometries. The survival fraction value, ƒ_s (which is also called as the multiplication factor, k) is calculated for the criticality condition in these geometries and the results are tabulated for each one. Our numerical results by Monte Carlo Method show that the minimum critical mass is obtained in the case of spherical shape of fuel element, and they are in agreement with those of analytical solutions.

Non conventional coherent states

A. Plastino, G. L. Ferri — Wed, 01 Jan 2025 00:00:00 +0000

We analyze properties of excited states of a special Hamiltonian H, endowed with a displaced quadratic potential V such that its ground state is a HO-Glauber coherent state of amplitude α. For large enough real α, we show that the first excited state of this Hamiltonian is also a coherent state of minimum uncertainty.

The effectiveness of green technology-based STEAM projects to improve scientific literacy

Wed, 01 Jan 2025 00:00:00 +0000

Indonesian students' scientific literacy is classified as low in terms of international and regional research results. This research aims to increase students' scientific literacy through learning green technology-based STEAM (Science, Technology, Engineering, Art, Mathematics)-projects. This research is a quasi-experimental study using a nonequivalent pretest-posttest control-group design. The research sample consisted of 288 junior high school students in Yogyakarta. The details of sample involved in this study were 144 students from the experimental class and 144 students from the control class. The sampling technique is cluster random sampling because the population is divided into regions or clusters. The instrument is in the form of scientific literacy test questions. The test items were analyzed using the gain score test and the Independent Sample T-Test with SPSS 22. The results showed that green technology-based STEAM projects can increase scientific literacy in the high category. The increase in students' scientific literacy in the experimental class was higher than in the control class. The results of the study also showed that there were differences in scientific literacy between the experimental class and the control class. Green technology-based STEAM projects can be an alternative for teachers to develop student's scientific literacy.

Comparison of cooperative learning types in physics teaching: a short literature review

A. Aprilia, W. S. Brams Dwandaru — Wed, 01 Jan 2025 00:00:00 +0000

A short literature review has been carried out on the comparison of cooperative learning types in physics learning. The purpose of this literature review is to discuss the type of cooperative learning that is effectively used in terms of the dependent variable measured. The method used in this study is a literature review. Literature review is done by searching for keywords related to the theme raised. This keyword search is done through Google Scholar, Base, and Core search engines. A number of 27 articles have been retrieved that match the keywords and have been screened with limitations on the year of publication, namely the last 10 years. Through this literature review, it is obtained that the success of the type of cooperative learning depends on the measured variables (dependent variables). The GI type of cooperative learning model is more effective for improving physics learning outcomes, scientific attitudes, and learning activities. The STAD type is better at increasing student learning motivation and cognitive learning outcomes. The NHT type is better at improving students’ affective, cognitive learning outcomes, and critical thinking skills. And, the Jigsaw type is effective in improving problem solving abilities, performance, attitude, and retention in physics.

Diseño y construcción de una estación enfocada a la enseñanza de: Análisis Frecuencial, Interferencia, Lissajous y análisis de circuitos dependientes de la frecuencia

J. M. Alvarado Reyes, C. M. Sune Reimer López — Wed, 01 Jan 2025 00:00:00 +0000

El uso de instrumentación en los laboratorios de enseñanza, nivel medio y medio superior, generalmente son de alto costo y en ocasiones el precario presupuesto destinado a la enseñanza experimental dificulta la adquisición de estos instrumentos. Los conceptos teóricos generalmente dependerán, directamente del orador o pedagogo, y sus conocimientos o lenguaje para expresar una determinada información. La enseñanza experimental es más compleja, ésto es debido a que, a pesar de haber comprendido el concepto teórico, el desarrollo experimental requiere diseñar y construir. En este simple proceso, diseñar y construir, es probable que la imaginación y la realidad se confronten. Esta breve reflexión, tiene el fin único analizar las dificultades que afrontan los profesores de laboratorios para diseñar y construir sistemas eléctricos, electrónicos o mecánicos para transmitir un determinado concepto. En este trabajo se presenta una estación que consta de dos instrumentos diseñados y construidos para fomentar la enseñanza de cuatro conceptos de manera experimental: la transformada de Fourier, figuras de Lissajous, interferencia de señales y ancho de banda (y sus aplicaciones). Estos conceptos generalmente son revisados de manera teórica y rara vez es posible estudiarlos experimentalmente, la razón única, por la que no es posible estudiar estos conceptos experimentalmente; es porque no existen instrumentos, incluso de patente, que permita realizar este tipo de experimentos, en el mejor de los casos que existieran, sin duda serían de alto costo. Para transmitir conocimiento no se requieren instrumentos de alto costo; un instrumento de bajo costo podría ser suficiente para transmitir un gran conocimiento.

The use of instrumentation in teaching laboratories, middle and high school level, is generally high cost and sometimes the precarious budget allocated to experimental teaching makes the acquisition of these instruments difficult. Theoretical concepts will generally depend directly on the speaker, or pedagogue, and their knowledge or language to express certain information. Experimental teaching is more complex, this is because, despite having understood the theoretical concept, experimental development requires designing and building. In this simple process, designing and building, it is possible that imagination and reality conflict. This brief reflection has the sole purpose of analyzing the difficulties that laboratory teachers face when designing and building electrical, electronic or mechanical systems to transmit a certain concept. This work presents a station that consists of two instruments designed and built to promote the teaching of four concepts experimentally: The Fourier transform, Lissajous figures, signal interference and bandwidth (and their applications). These concepts are generally reviewed theoretically and it is rarely possible to study experimentally, the only reason why it is not possible to study these concepts experimentally; It is because there are no instruments, even patented, that allow this type of experiments to be carried out; in the best of cases, if they existed, they would undoubtedly be high-cost. To transmit knowledge, high-cost instruments are not required; a low-cost instrument could be enough to transmit great knowledge.

Ley de enfriamiento de Newton con temperatura variable

Pablo Moreira, Othon Ortega — Wed, 01 Jan 2025 00:00:00 +0000

En este trabajo se presenta un estudio teórico-experimental sobre la ley de enfriamiento de Newton, con temperatura variable. En el estudio teórico se resolvió una ecuación diferencial ordinaria lineal la cual permite calcular la temperatura de un objeto a lo largo de un periodo de tiempo. Para la sección experimental del estudio se realizaron dos modelos experimentales, donde se uso un modelo senoidal para la temperatura ambiente y se comparo con la respuesta teórica, después de 22 y 52 horas respectivamente. En el estudio se compararon los resultados experimentales con las soluciones de las ecuaciones diferenciales, en diferentes lapsos de tiempo. El objetivo del presente, fomenta la reflexión por parte de los estudiantes y docentes, dando libre camino, a la modificación del modelo de temperatura y otros análogos para el estudio de ecuaciones diferenciales ordinarias y sus aplicaciones.

This work presents a theoretical-experimental study on the applicability of Newton’s cooling law in prolonged time periods, considering a sinusoidal variable ambient temperature. In the theoretical study, a linear ordinary differential equation that describes the heat transfer between an object and its environment was solved. The solution of this equation allows calculating the object’s temperature over time, considering a variable ambient temperature. In the experimental part, two experimental models were built to evaluate Newton’s cooling law. A sinusoidal model was used to represent the ambient temperature, which represents a non-traditional initial condition. The experimental results were compared with the theoretical solution obtained in the first part of the study, considering 22 and 52 hours. The objective of this work is to evaluate the validity of Newton’s cooling law in situations that have not been explored in depth previously. The incorporation of a sinusoidal temperature as an initial condition provides a new perspective on the study of this phenomenon and opens the door to the modification of temperature models and other analogous models in the field of ordinary differential equations and their applications.

An analysis of problem solving strategy using magic card science media on free falling topic

Wed, 01 Jan 2025 00:00:00 +0000

This study looked at how well physics teacher candidates used magic card scientific media to solve problems when learning about free fall motion. This kind of study is known as a quasi-experiment. 26 students from the Physics Education study program who were enrolled in an experimental class and a control group using magic scientific material made up the sample. methods for gathering data that make use of test and documentation methods. N-gain data analysis techniques. According to the study's findings, the experimental class's N-gain was 0.77 in the high category and the control class's N-gain was 0.37 in the medium group. The experimental class's N-Gain-Present of 77.30% indicates that learning magic science was effective, whereas the control class's N-Gain-Present of 37.36% indicates that it was ineffective.

About the force on a magnetic dipole

José Antonio Eduardo Roa Neri, José Luis Jiménez Ramírez, Ignacio Campos Flores — Wed, 01 Jan 2025 00:00:00 +0000

There is disagreement about which is the correct expression for the force on a magnetic dipole, and at least two expressions for this force have been proposed, generating a controversy between Vaidman [1985] and Franklin [2018]. Our view here exposed is that the macroscopic Maxwell equations and the constitutive relations imply, via electromagnetic momentum balance equations, several force densities which include those proposed by some authors. Therefore, the question is not which one is correct, since all are legitimate deductions of Maxwell´s equations, but under what conditions they may be useful to explain some phenomena. The discussion of conceptual problems of electromagnetism is very useful to both graduate students and researchers.

La búsqueda de los componentes básicos de la materia, desde la campana de vidrio a la lámina de oro

J. P. Calderón, A. Sánchez, A. V. Porta, Susana Orozco — Wed, 01 Jan 2025 00:00:00 +0000

In this work, we show how the study of electrical discharges through gases led to the discovery of the matter constituents. We present a review of fundamental experiments to the discovery of the blocks that constitute all materials. Our narrative begins with the stoichiometry experiments of Antoine Lavoisier, who observing chemical reactions in controlled environments within a glass bell, managed to highlight the importance of precise measurements and to know some fundamental concepts involved in chemical reactions. Our presentation of the discoveries is not historical, instead is an essay of the hypotheses behind the experiments, some specific details of them, a discussion of the concepts involved, and how their results contributed to the modification of the ideas established. The essay is finished with the ideas of Ernest Rutherford about the atomic structure, which were conceived from the results of the experiments with gold sheets and alpha particles.

En este trabajo mostramos como el estudio de las descargas eléctricas a través de los gases condujo al descubrimiento de los constituyentes de la materia. Presentamos una revisión de experimentos fundamentales para el descubrimiento de los bloques que constituyen todos los materiales. La narración comienza con los experimentos de Lavoisier, quien al realizar reacciones químicas en ambientes controlados dentro de campanas de vidrio logró destacar la importancia de las medidas precisas y conocer algunos conceptos fundamentales involucrados en las reacciones químicas. Nuestra presentación de los descubrimientos no es histórica; sino que es un relato de las hipótesis que motivaron los experimentos, algunos detalles específicos de los mismos, una discusión de los conceptos involucrados y la forma en la que sus resultados contribuyeron a la modificación de las ideas establecidas. Concluimos con las ideas de Rutherford sobre la estructura de los átomos y sus experimentos con partículas alfa y láminas de oro.

Teorías de gauge (norma) en los mercados financieros, una revisión histórica

A. Raya, M. B. Flores Romero, J. López-Chacón — Wed, 01 Jan 2025 00:00:00 +0000

In the present work we make a historical review of economic studies, in particular, of the financial market, in which the tools and concepts developed in the context of gauge or norm theories are used, which constitute the cornerstone of the development of the fundamental physics. This vision allows us to understand the financial market as a dielectric material that, through the rearrangement of charges, polarizes to self-regulate and balance when arbitrage opportunities arise.

En el presente trabajo hacemos una revisión histórica de estudios económicos, en particular, del mercado financiero, en los que se emplean las herramientas y conceptos desarrollados en el contexto de las teorías de gauge o de norma, que constituyen la piedra angular del desarrollo de la física fundamental. Esta visión permite entender al mercado financiero como un material dieléctrico que, mediante el reacomodo de cargas, se polariza para auto-regularse y equilibrarse cuando se presentan oportunidades de arbitraje.