Revista Mexicana de Física E

Implementation of the Khorezmian education model in Uzbekistan: problems and solutions

Yunusali Xolboyev — 2026-01-01

The integration of science, education and production is crucial for national development whereby interdisciplinary approaches are vital to enhance learning. This article explores the significance of integrated and problem-based educational technologies, particularly through the Khorezmian model of education, which highlights the interconnectedness of disciplines. When implemented regularly, the model enables learners to develop their critical thinking and practical skills to deal with sociatal challenges, through being exposed to real-life problems. The model, also, promotes active learning, spiriting learners to identify and solve problems relevant to their lives. In the article, the problems related to the introduction of the Khorezmian education model in Uzbekistan and their solutions are discussed in detail.

Detección de habilidades de pensamiento crítico en la resolución de problemas de estudiantes de ingeniería: El caso del esquiador de Perelman

Laura Muñoz Salazar — 2026-01-01

En este estudio se analiza la forma en que estudiantes de ingeniería, quienes están iniciando el segundo semestre, resuelven el problema del esquiador, un reconocido acertijo propuesto por Yakov Perelman. La investigación se realiza sobre cuatro grupos de una Escuela Superior de Cómputo que cursaron la asignatura de física, dos de ellos con una intervención didáctica enfocada en el desarrollo del pensamiento crítico y creativo, y dos grupos control con formación tradicional. El objetivo principal es comparar el desempeño de los estudiantes en la resolución del problema e identificar si existen diferencias significativas, que evidencien un pensamiento de orden superior en los grupos expuestos a las estrategias innovadoras de desarrollo de habilidades. Los resultados obtenidos sirven para sustentar la premisa de que la introducción de métodos activos de enseñanza que fomenten el pensamiento crítico y creativo, desde los primeros semestres de la carrera, es fundamental para la formación integral de los futuros ingenieros.

This study analyzes the way in which engineering students, who are starting their second semester, solve the skier problem, a well-known puzzle proposed by Yakov Perelman. The research is carried out on four groups from a Higher School of Computing that took the physics subject, two of them with a didactic sequence focused on the development of critical and creative thinking, and two control groups with traditional training. The main objective is to compare the performance of students in solving the problem and identify if there are significant differences that evidence higher-order thinking in the groups exposed to innovative skill development strategies. The results obtained serve to support the premise that the introduction of teaching methods that encourage critical and creative thinking, from the first semesters, is essential for the comprehensive training of future engineers.

Euler's number: a new experimental estimation

Milan Kovacevic — 2026-01-01

Euler's number e is one of the most well-known integers in mathematics. The base of the natural logarithm is represented by the number e, often known as Neper's number in books. In the work of distinguished mathematician and physicist Jacob Bernoulli, the number e appears as the limit value of a number sequence that Bernoulli studied dealing with the issue of interest. Although it was primarily used for financial calculations. This remarkable number quickly began to be applied in a wide range of natural phenomena and scientific laws of physics, biology, chemistry. Students in high schools who are nearing the end of their schooling are taught that is equal to the number e=2.718... This study reports on a new experiment in physics using communicating vessels, where number e appears indirectly. For example, if in described experiment, a vessel with an area of 100 cm² is divided into N=100 smaller vessels with an area of 1 cm², we will theoretically reproduce the number e with an accuracy of 0.5%. It is also emphasized that Euler's number is currently used more frequently and may be found in a wide range of scientific fields as well as daily life.

Do the homework and explore galaxy collisions

guillermo arreaga-garcia — 2026-01-01

In this paper we test a code to model the collision of galaxies. This code is based on the program GALAXY, which is proposed in Appendix J of a well-known textbook in astrophysics. The GALAXY program is in turn based on the approximation model proposed by the Toomre brothers in 1972. With this model, it was possible to demonstrate very efficiently that the tails and bridges observed by astronomers when two galaxies collide have their origin in the gravitational tidal forces. We have made several improvements to our code with respect to the one described in Appendix J, such as (i) the possibility of evolving more than two galaxies (up to N-galaxies); (ii) the placement of stars in each of the galaxies; (iii) the rotation of the galaxies according to Euler angles; and finally, (iv) coding in ansi c rather than the original Basic language. To test the code we ran the binary collision models proposed in the homework part of the book, namely the whirlpool and cartwheel models. Then we rotated the galaxies involved in the collision and examined the differences in the results. To generate more models we change the initial velocity of the disturbing galaxy. We found geometrically and physically more interesting star configurations. In addition, we ran the Stephan model with five interacting galaxies. To show the final results of the models, we use our own algorithm to perform a density smoothing procedure and create two-dimensional isodensity plots with Python. To give the reader the opportunity to practice and visualize the different scenarios, the source programs are shared in the link: https://drive.google.com/drive/ folders/1J08YVJICYWbAZbSGceO-uOZtNrCmC7Op?usp=sharing.

Effectiveness of E-Book thermodynamics based on STEM discovery learning assisted with virtual laboratory simulation to improve high school students’ critical thinking

Lilik Kurniawan — 2026-01-01

This study aims to determine the effectiveness of the Thermodynamics E-Book assisted by a virtual lab with a STEM approach that is implemented to students and operated through student devices. The research model used is a quasi-experiment with a one-group pre-test post-test design. This study uses one experimental class and one control class that is differentiated by treatment in learning activities. Based on the analysis, it was found that the problem of developing students' critical thinking was still lacking. The results showed significant results in improving critical thinking skills in the experimental class using Thermodynamics E-Book assisted by virtual lab with STEM approach. Data from pre-test and post-test results have been tested and proven to be normally distributed and homogeneous with a significance value greater than 0.05. The N-gain score in the experimental class was 0.720 and in the control class was 0.699. The use of a virtual lab-assisted Thermodynamics E-Book with a STEM approach is able to contribute to improving critical thinking skills.

Descriptive analysis of student electronic worksheets based on STEM-entrepreneurship integrated group investigation in physics learning

Ananda Aprilia — 2026-01-01

Learning resources and models are needed to support 21^st century skills. In this research, we have used electronic worksheets (e-worksheets) based on direct instruction, group investigation, and group investigation – Science Technology Engineering Mathematics and Entrepreneurship. The aim of this research is to qualitatively compare students' e-worksheet answers toward students' creative thinking and graphical representation abilities. The method used is the descriptive qualitative method. The results show that the e-worksheets influence students' creative thinking abilities. Group investigation – Science Technology Engineering Mathematics and Entrepreneurship based e-worksheet gives the best creativity from students. The e-worksheets based on direct instruction, group investigation, and group investigation – Science Technology Engineering Mathematics and Entrepreneurship show the same results for the graphical representation ability.

Analysis of the effectiveness of website-based Technological Pedagogical Content Knowledge (TPACK) in physics learning: a meta analysis

Silvia Laeli — 2026-01-01

The use of website technology-based learning in physics learning has become an alternative method of choice to support 21st century education. However, there is still no data study on this topic. The meta analysis in this research examines the effectiveness of website technology-based learning on students' physics learning achievement. In this study, 15 primary studies from Scopus, ERIC, and Google Scholar were collected that met the inclusion and exclusion criteria. The research results show that the use of website technology-based learning has a significant influence on students' physics learning achievement. No publication bias was found in this study. So it can be concluded that website technology-based learning has a good impact on students' physics learning achievement.

Motion in the gravitational field of an oblate spheroid

Vladimir V. Ivchenko — 2026-01-01

We present the theory of motion in the gravitational field of an attracting object, considering its equatorial bulge. There is a secular precession of the orbit that occurs in the direction opposite to the orbital revolution. The precession rate increases as the gravitating body’s flattening increases and the orbit’s characteristic size decreases. Using the perturbation approach, we derive the equations for finding the precession period and the apocentric distance. We also construct the generalized version of the Laplace-Runge-Lenz vector for this type of motion.

Desempeño de algunos métodos de Runge-Kutta en la aproximación numérica de la ecuación lineal de Schrödinger

Paul Castillo — 2026-01-01

Se comparan diferentes métodos de Runge-Kutta tradicionales aplicados a la ecuación lineal de Schrödinger. Se estudia la conservación de los invariantes fı́sicos relevantes de esta ecuación haciendo uso de un problema escalar elemental, la hermiticidad del operador hamiltoniano y argumentos básicos de álgebra matricial. Además, se discute la estabilidad numérica, solubilidad y selección del paso en tiempo en estos métodos.

Different traditional Runge-Kutta methods applied to the linear Schrödinger equation are compared. The conservation of the relevant physical invariants of this equation is studied using an elementary scalar problem, the hermiticity of the Hamiltonian operator and basic arguments of matrix algebra. In addition, numerical stability, solubility and time step selection for these methods are discussed.

Uso de GROMACS para el cálculo de propiedades termodinámicas, estructurales y de transporte de iones en agua

Victor Manuel Trejos Montoya — 2026-01-01

El estudio de iones en agua sigue siendo un área de gran relevancia tanto en el contexto ambiental y biológico. En este trabajo, presentamos el uso de la paquetería GROMACS para implementar simulaciones por computadora de dinámica molecular con el fin de obtener propiedades termodinámicas, estructurales y de transporte en soluciones acuosas de sales. Se detallan los procedimientos empleados para llevar a cabo las simulaciones y se describen las propiedades analizadas en función de la concentración salina. Para modelar los iones, empleamos los parámetros moleculares del campo de fuerza Madrid-2019, mientras que el agua fue representada mediante el modelo TIP4P/2005. A partir de estas simulaciones, se calcularon propiedades como la densidad (termodinámica), las funciones de distribución radial, el número de iones en contacto y el número de hidratación de aniones y cationes (estructurales), así como el coeficiente de auto-difusión (transporte). Nuestros resultados muestran que este modelo describe con precisión la densidad en soluciones de alta molalidad, además de revelar una notable concordancia entre las propiedades estructurales obtenidas y los datos experimentales reportados en la literatura. Este trabajo busca proporcionar una herramienta útil para el estudio de soluciones iónicas mediante dinámica molecular y el software GROMACS, validando su capacidad para reproducir resultados previamente publicados y consolidando el conocimiento sobre la simulación de iones en solución.

The study of ions in water remains a topic of great relevance in both environmental and biological sciences. In this work, we employ the GROMACS package to perform molecular dynamics simulations and investigate the thermodynamic, structural, and transport properties of aqueous salt solutions. We detail the simulation procedures and analyze the properties as a function of salt concentration. To model the ions, we use the molecular parameters of the Madrid-2019 force field, while water is represented by the TIP4P/2005 model. From these simulations, we compute properties, including density (thermodynamics), radial distribution functions, the number of ions in contact, and the hydration number of anions and cations (structural), as well as the self-diffusion coefficient (transport). Our results demonstrate that this model accurately describes density in high-molality solutions, showing remarkable agreement between simulated structural properties and experimental data reported in the literature. This work provides a valuable tool for studying ionic solutions using molecular dynamics and GROMACS software, validating its ability to reproduce previously published results and reinforcing knowledge on the simulation of ions in solution.

Una introducción al cálculo fraccional con aplicaciones en la física

Pedro Oliva-Sanchez — 2026-01-01

Este trabajo ofrece una introducción a los conceptos fundamentales del cálculo fraccional, destacando las definiciones más utilizadas de la derivada fraccional y poniendo énfasis en sus propiedades y aplicaciones. En particular, se analiza la derivada fraccional de Fourier, subrayando su relativa simplicidad para la implementación numérica, y se presentan códigos en Matlab y Python basados en métodos espectrales para su cálculo. Además, se exploran aplicaciones clave de las derivadas fraccionales en física, como su uso en haces ópticos, estructuras viscoelásticas, mecánica cuántica y el oscilador armónico fraccional. Como complemento, se introducen los fundamentos de la función de Mittag-Leffler, ampliamente utilizada en el cálculo fraccional. Finalmente, se discuten posibles aplicaciones futuras del cálculo fraccional, destacando su relevancia en diversas áreas de la física.

This work provides an introduction to the fundamental concepts of fractional calculus, highlighting the most commonly used definitions of fractional derivatives and emphasizing their properties and applications. In particular, the fractional Fourier derivative is analyzed, underscoring its relative simplicity for numerical implementation, and Matlab and Python codes based on spectral methods for its calculation are presented. Additionally, key applications of fractional derivatives in physics are explored, such as their use in optical beams, viscoelastic structures, quantum mechanics, and the fractional harmonic oscillator. As a complement, the fundamentals of the Mittag-Leffler function, widely used in fractional calculus, are introduced. Finally, potential future applications of fractional calculus are discussed, highlighting its relevance in various areas of physics.

Interactive MATLAB GUI for exploring extreme values in bivariate functions

Muhammad Yousuf Tufail — 2026-01-01

This paper presents the development of a graphical user interface (GUI) in MatLab designed to assist in the 
identification and classification of extreme values and saddle points of functions of two variables. Aimed at 
supporting mathematics and Physics education for university students and instructors, the tool integrates 
symbolic differentiation and the second derivative test to provide an interactive learning experience. 
Through three representative examples, the GUI demonstrates its ability to detect multiple critical points and 
visually convey their nature, enhancing conceptual understanding. While the method is effective in most cases, 
it is limited when the discriminant D equals zero, rendering the second derivative test inconclusive. 
Furthermore, the current implementation supports only two-variable functions; adapting it to higher dimensions 
would require further development. Overall, the GUI serves as a valuable educational aid for teaching and 
learning multivariable calculus concepts.

Project-based learning approach for applying the principles of magnetism and movement in a magnetic linear motor

José Luis García-Luna — 2026-01-01

This article describes the application of the principles of magnetism and motion by working with engineering students at Tecnologico de ´ Monterrey to construct and simulate a Magnetic Linear Motor (MLM) through the Project-Based Learning (PjBL) methodology combined with STEM to facilitate experiential and collaborative learning. PjBL is a teaching methodology that applies learning to real-world problems. This approach is currently being adopted by various educational institutions, which face challenges in using pedagogical methods to foster positive relationships between students and mentors. Three phases can be distinguished in project-based methodology. Commitment: Students are motivated to participate in the importance of an MLM as a device capable of giving motion in one dimension. Research: Students engage in a research project where they design and model their ideas from different areas, such as electromagnetism, differential equations, and programming. Action: Assemble the prototype in the laboratory and evaluate its model. The differential equations of the magnetic force in the MLM prototype are used to determine its kinematic graphs and interpretation. As evidence of learning, students are required to submit two reports that are evaluated using rubrics.

Numerical solution of the Lindblad master equation using the Runge-Kutta method implemented in Python

Leonardi Hernández Sánchez — 2026-01-01

The dynamics of open quantum systems is governed by the Lindblad master equation, which provides a consistent framework for incorporating environmental effects into the evolution of the system. Since exact solutions are rarely available, numerical methods become essential tools for analyzing such systems. This article presents a step-by-step implementation of the fourth-order Runge-Kutta method in Python to solve the Lindblad equation for a single quantized field mode subject to decay. A coherent state is used as the initial condition, and the time evolution of the average photon number is investigated. The proposed methodology enables transparent and customizable simulations of dissipative quantum dynamics, emphasizing a pedagogical approach that helps readers understand the numerical structure without relying on external libraries such as QuTiP. This standalone implementation offers full control over each integration step, making it particularly suitable for educational contexts and for exploring non-standard dynamics or introducing custom modifications to the Liouvillian.

Solution of the Schrödinger equation for a particle in a uniform force field via the solution for a free particle

Gerardo Francisco Torres del Castillo — 2026-01-01

We show that the solutions of the Schrödinger equation for a free particle are related in a simple manner with the solutions of the Schrödinger equation for a particle in a uniform force field. Making use of this relation we readily obtain the so-called Airy wave packets and the propagator for a particle in a uniform force field.

Taller de conceptos básicos del Sistema Solar adaptado a grupos de nivel primaria y secundaria

Raquel Rojas — 2026-01-01

Se presenta el diseño y evaluación de un taller semanal del Sistema Solar para niños (entre 8 y 13 años) como recurso didáctico para promover en los pequeños diferentes habilidades, entre ellas: que formulen preguntas de forma relajada y divertida, practiquen la lectura, reflexionen en información nueva y manipulen material relacionado con temas astronómicos del Sistema Solar.
Los elementos didácticos utilizados en la propuesta son: historietas, construcción de modelos celestes con materiales de bajo costo y juegos de mesa; todos ellos enfocados en los temas astronómicos del Sistema Solar.
Se muestran los resultados cualitativos más relevantes de la realización de este taller lúdico en dos ocasiones, obteniendo en general que en más del 90% de las sesiones, mas del 50% de los participantes lograron alcanzar los aprendizajes esperados, además de otros alcances no previstos inicialmente.

The design and evaluation of a weekly Solar System workshop for children (aged 8-13) is presented as a teaching resource to promote different skills in children, including: formulating questions in a relaxed and fun way, practicing reading, reflecting on new information, and manipulating materials related to astronomical topics of the Solar System.
The educational elements used in the proposal include comics, construction of celestial models with low-cost materials, and board games, all focused on astronomical topics related to the Solar System.
The most relevant qualitative results are shown from the performance of this recreational workshop on two occasions, with more than 50% of the participants achieving the expected learning outcomes in more than 90% of the sessions, in addition to other achievements not initially anticipated.

Internet-based experiment to measure the muon lifetime in real time

E. Ponce — 2026-01-01

We describe a web-based experiment to measure the lifetime of cosmic-ray muons that stop in a liquid scintillator detector. Our experimental setup consists of a container filled with liquid scintillator, a photomultiplier tube, a commercial electronics board (STEMlab 125-14) that includes an ARM-based computer with a field programmable gate array (FPGA) and an analog-to-digital converter (ADC). The muons we detect arrive at the detector as part of the secondary cosmic rays that are produced high in the Earth atmosphere when energetic primary cosmic rays collide with nitrogen and oxygen nuclei. The software we use to run this experiment in real time on the web uses Python code on the computer of the Red Pitaya board and HTML/Javascript code on the webpage. The experiment is located at the Centro Interdisciplinario de Investigación y Enseñanza de la Ciencia on the campus of the Benemérita Universidad Autónoma de Puebla (BUAP) in the city of Puebla, ´ Mexico. We report a value for the effective mean lifetime of the stopping muons of 2.051 ± 0.009 µs. This result is lower than the 2.197 µs mean muon lifetime in vacuum due to the capture of negative muons by the nuclei of the atoms of the detector material. The experiment can be accessed through the webpage https://ciiec.buap.mx/Muon-Decay.

Development of Physicist-Muslim comic for Newton’s law of motion: a needs analysis from teachers' and students' perspectives

Silvi Yulia Sari — 2026-01-01

Newton’s Law of Motion is one of the challenging concepts that require the use of various types of resources as teaching and learning aids to improve students’ understanding of the concept. Hence, this research was conducted to analyze the need for developing an al-Quran integrated learning aid in the form of a comic for the Newton’s Law of Motion concept from the perspectives of teachers and students. The research design employed a survey study, utilizing teacher and student questionnaires as the primary research instruments. A total of 20 physics teachers and 384 senior high school students in West Sumatra were selected using a simple random sampling technique as the sample of this research. The data were analyzed using descriptive statistics. The findings indicated that 65% teachers and 72.9% students agreed that Newton’s Law of Motion is a difficult concept to teach and learn. The findings also showed that only 55% of teachers employed Quranic verses to teach Physics concepts, but no teachers used educational comics in their teaching and learning sessions. However, 79.4% of students assumed that the educational comic could help them enhance their understanding of the Physics concept. In addition, the findings show that 121 students have the Visual-Auditory-Kinesthetic (VAK) learning style as their most dominant learning preference; meanwhile, 95% of the learning resources only facilitate the visual learning style. Additionally, 90.6% of students state the need for the integration of the Al-Quran, which highlights the relevance of Newton’s Law. In conclusion, there is a need to develop an Al-Quran integrated learning resource in the form of a comic for the Newton’s Law of Motion concept, targeting the VAK learning style. The learning resource is designed to enhance conceptual understanding among students with diverse learning styles.