Vol. 18 No. 2 Jul-Dec (2021): Revista Mexicana de Física E

We present some examples in the elementary Lagrangian formulation of classical mechanics where the introduction of a parameter in place of the time (sometimes called fictitious time or local time) decouples the equations of motion.

Several important statistical tools and concepts are covered in upper division undergraduate Statistical Physics courses, including those of random walks and the central limit theorem. However, some of their broad applicability tends to be missed by students as well as the connection between these and other physical concepts. In this work, we apply a 1D random walk to study the evolution of the probability that a candidate will win an election given she holds some lead over her opponent, and connect the result found to the concept of density of states and occupation probabilities. This paper is intended to serve as a guide to the Statistical Physics instructor who wishes to motivate students beyond the boundaries of the official syllabus.

A century ago Srinivasa Ramanujan --- the great self-taught
  Indian genius of mathematics --- died, shortly after returning
  from Cambridge, UK, where he had collaborated with Godfrey Hardy.
  Ramanujan contributed numerous outstanding results to different
  branches of mathematics, like analysis and number theory,
  with a focus on special functions and
  series. Here we refer to apparently weird values
  which he assigned to two simple divergent series, $\sum_{n \geq 1} n$
  and $\sum_{n \geq 1} n^{3}$. These values are sensible, however,
  as analytic continuations, which correspond to Riemann's
  $\zeta$-function. Moreover, they have applications in physics:
  we discuss the vacuum energy of the photon field, from which one
  can derive the Casimir force, which has
  been experimentally measured.
  We discuss its interpretation, which remains controversial.
  This is a simple way to illustrate the concept of renormalization,
  which is vital in quantum field theory.

En este trabajo se presenta un estudio te´orico-experimental de la din´amica del movimiento de una esfera que se mueve en una trayectoria circular vertical con fricci´on. En el estudio te´orico se resuelve una ecuaci´on diferencial de Bernoulli que permite calcular la rapidez en cualquier posici´on angular y la rapidez m´ınima necesaria para que la esfera complete una vuelta en la trayectoria circular. En el estudio experimental se utilizan fotopuertas para medir la posici´on angular de la esfera como funci´on del tiempo; a partir de esto, se obtienen de manera indirecta la rapidez y fuerza normal en cualquier posici´on angular. Al comparar los resultados te´oricos y experimentales obtenidos de forma indirecta para la rapidez y fuerza normal se observa que el modelo te ´orico describe de forma cualitativa el comportamiento experimental cuando ¹ = 0:12. Finalmente, se analiza el comportamiento te´orico de la rapidez y fuerza normal para distintos valores del coeficiente de fricci´on cin´etica, donde se observa que para ¹ ¸ 0:2 la rapidez y fuerza normal final decaen de manera abrupta.

This work presents a theoretical and experimental study of the dynamics of the motion of a sphere that moves in a vertical circular trajectory with friction. In the theoretical study, a Bernoulli differential equation is solved to calculate the velocity at any angular position and the minimum velocity necessary for the sphere to complete one turn in the circular track. In the experimental study, photogates are used to measure the angular position of the sphere as a function of time, from which the velocity and normal force are indirectly obtained in any angular position. When comparing the theoretical and experimental results obtained indirectly for the velocity and the normal force, it is observed that the theoretical model qualitatively describes the experimental behavior when ¹ = 0:12. Finally, the theoretical behavior of the speed and normal force is analyzed for different values of the coefficient of friction kinetic, where it is observed that for ¹ ¸ 0:2 the final normal speed and force decline abruptly.

The Dirac delta function is a concept that is useful throughout physics as a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum including electrodynamics, optics, and quantum mechanics. Our analysis was guided by an analytical framework focusing on how students activate, construct, execute, and reflect on the Dirac delta function in the context of classical electrodynamics problems solving. It’s applications in solving the charge density associated with a point charge as well as electrostatic point dipole field, for more advanced situations to describe the charge density of hydrogen atom were presented.

In this academic paper we present in detail the numerical solution of the accretion of a perfect fluid onto a black hole. The conditions are very simple, we consider a radial flux being accreted by a Schwarzschild black hole. We present two scenarios: 1) the test field case in which the fluid does not affect the geometry of the black hole space-time background, and 2) the full non-linear scenario, in which the geometry of the space-time evolves simultaneously with the fluid according to Einstein's equations.
In the two scenarios we describe the black hole space-time in horizon penetrating coordinates, so that it is possible to visualize that accretion actually takes place within the numerical domain.
For the evolution of matter we use the Valencia formulation of relativistic fluid dynamics. In the non-linear scenario we solve the equations of geometry using the ADM formulation of General Relativity, with very simple and intuitive gauge and boundary conditions, and include diagnostics related to the Apparent Horizon and Event Horizon growth.
In view of the recent spectacular discoveries by the Event Horizon Telescope collaboration and further discoveries to come, the aim of this paper is to provide the necessary tools for interested graduate students in Black Hole Astrophysics, to enter into the accretion modeling starting from a considerable advanced starting point.

This paper presents a comparative numerical study that demonstrates the feasibility of stochastic optimization (SO) for reconstructing the optical path difference (OPD) from a real interferogram degraded by noise, either by the maximization of the correlation coefficient or by the minimization of the Euclidean distance where the optimization achieved for each objective function corresponds to the near-optimal solution without being dominated by a local optimum. In order to show the efficacy of different SO algorithms based on evolutionary computation, we propose a solution to the maximization problem by using a genetic algorithm with the primary aberrations described by Kingslake, while for the solution of the minimization problem an evolutionary strategy with Zernike polynomials is proposed. The numerical results show the simplicity, robustness, and accuracy of both SO algorithms to calculate their corresponding aberration coefficients. Thus, this work offers an ideal opportunity to integrate the skills acquired by university students of science and engineering in subjects such as interferometric optical metrology, numerical methods, and programming with the purpose of performing interferogram analysis.

In this article, we provide a pedagogical review of the Tolman-Oppenheimer-Volkoff (TOV) equation and its solutions which describe static, spherically symmetric gaseous stars in general relativity. Our discussion starts with a systematic derivation of the TOV equation from the Einstein field equations and the relativistic Euler equations. Next, we give a proof for the existence and uniqueness of solutions of the TOV equation describing a star of finite radius, assuming suitable conditions on the equation of state characterizing the gas. We also prove that the compactness of the gas contained inside a sphere centered at the origin satisfies the well-known Buchdahl bound, independent of the radius of the sphere. Further, we derive the equation of state for an ideal, classical monoatomic relativistic gas from statistical mechanics considerations and show that it satisfies our assumptions for the existence of a unique solution describing a finite radius star. Although none of the results discussed in this article are new, they are usually scattered in different articles and books in the literature; hence it is our hope that this article will provide a self-contained and useful introduction to the topic of relativistic stellar models.

The problem of photon propagation in a medium in presence of a strong magnetic field in the frame of quantum electrodynamics is discussed in the present paper, based on previous literature in this area. The breaking of the spatial symmetry by the magnetic field determine the existence of a set of basic vectors and tensors which must satisfy the gauge and CPT invariance of quantum electrodynamics. The charge symmetric and non-symmetric cases are discussed. In the second case the Faraday effect is produced. A chiral current arises, associated to a pseudovector eigenvector of
the polarization operator (due to the breaking of the spatial symmetry by the external magnetic field), related to the so-called axial anomaly. The path integrals and functional derivation are widely used to obtain the self-energy and vertex operators, and the Dyson equations. The inadequate introduction of a chiral chemical potential in the standard model is discussed for the Weinberg-Salam model for electroweak interactions.

As we lower the temperature of water at a certain point it changes from liquid to solid. Yet under certain conditions it is possible to keep the water in a non-equilibrium, liquid-like phase, called \emph{supercooled water}, thus avoiding solidification. Water in such state may freeze under the slightless perturbation, as stirring it a little. The existence of supercooled water is usually known to the students since the introductory courses, but it seems to be difficult to attest in an elementary undergraduate laboratory. A simple method for supercooling water is, however, readily available. It is this short paper aim to describe such a method in a form that may be readily performed in a teaching laboratory.

In this work didactic principles that guided the organization and processing of materials in a physics course for biologists, according to the current program of the College of Science, UNAM, for that subject are presented. The course was designed based on the results in physics education research, which led to the implementation in the daily dynamics of modeling, contextualization, development of the concrete to the formal and active work of students both individually as in small groups. The results apply to the over 6 semesters (2016-I to 2019-I) with groups both freshmen and repeating students. The total population consists of 128 students from which 70 % are women.

The titles of the Physics books owned by Antonio de Le´on y Gama are presented. In order to establish the degree of knowledge of this discipline that this New Spain native of the second half of the 18th century reached, the content of these works is discussed. It is shown that the knowledge reached in this matter by this person, were at the height of his European peers.