Cuadernos de Ingeniería Matemática Vol. 01 Núm. 04 (2024)

URI permanente para esta colección

https://hdl.handle.net/10784/34769

Editor Jefe: Paula Escudero Marín - pescuder@eafit.edu.co

Editor Operativo: Amelia Hoyos Vélez - ahoyosv2@eafit.edu.co

Contacto: Cuadernos de Ingeniería Matemática - cuadernos.ing.mat@eafit.edu.co

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Mostrando 1 - 7 de 7

Light Pathways in Inhomogeneous and Anisotropic Media
(2024) Martinod, T.; Riascos, J.F.; Universidad EAFIT
In this study, we first revisit Fermat’s principle and reformulate it as a variational calculus problem for inhomogeneous media, establishing a bridge with Lagrangian mechanics. We then apply this framework to explore light trajectories in materials with spatially dependent refractive indices. Finally, we extend the analysis to anisotropic media by modeling the refractive index as a tensor field, deriving the corresponding geodesic and eikonal equations to capture the directional dependence of light propagation. This approach offers a rigorous basis for analyzing light paths in complex media, with potential applications in advanced optical design and material science. En este estudio, primero revisitamos el principio de Fermat y lo reformulamos como un problema de cálculo variacional para medios inhomogéneos, estableciendo un vínculo con la mecánica lagrangiana. Luego, aplicamos este marco teórico para explorar trayectorias de la luz en materiales con índices de refracción dependientes del espacio. Finalmente, ampliamos el análisis a medios anisotrópicos modelando el índice de refracción como un campo tensorial, derivando las ecuaciones correspondientes de geodésicas y eikonales para capturar la dependencia direccional de la propagación de la luz. Este enfoque ofrece una base rigurosa para analizar trayectorias de luz en medios complejos, con aplicaciones potenciales en diseño óptico avanzado y ciencia de materiales.
Analysis Of The Spread Of Alcohol Consumption Among Students Through Agent-based Models
(2024) Leiva R, María Alejandra; Galvis, Diego Esteban; Castano, Juan Pablo; Universidad EAFIT
Alcohol abuse is a critical issue in schools worldwide, with students starting to drink at younger ages. Key factors such as social pressure, household conditions, and emotional stability significantly influence student drinking behavior, often leading to compulsive drinking. This study investigates how peer influence contributes to compulsive drinking among students and explores preventive measures. To explore these interventions, we utilized agent-based modeling to simulate alcohol consumption dynamics among students. Each student is modeled as an agent with attributes like susceptibility to peer pressure and drinking status. The model, implemented in NetLogo, follows a discrete-time process where agents move and interact, updating their behavior based on peer influence. Recovery workshops were tested to evaluate their impact on reducing compulsive drinking. Specifically, when the initial percentage of binge drinkers was set to 20% and the social influence radius was increased to 7, nearly all students from groups 1 to 4 became binge drinkers at an accelerated rate. However, implementing recovery workshops where 50% of binge drinkers reduced their alcohol intake led to a visible slowdown in compulsive drinking rates, significantly mitigating the spread. These results highlight the importance of early, targeted interventions in schools to transform societal drinking patterns, promoting a healthier, more stable student population. This research provides valuable insights for policymakers and educators working to combat underage drinking and its social consequences.
Medidas De Ciberdecepción Para Sistemas Digitales Interconectados: Un Modelo Basado En Agentes Y Grafos De Ataque Bayesiano
(2024) Álvarez, J. A.; González, E.; Universidad EAFIT
This study proposes a hybrid model based on Bayesian Attack Graphs (BAGs) and Agent-Based Modeling (ABMs) to analyze worm attacks on interconnected networks with a mesh topology. The model, developed in NetLogo, simulates the spread of malware in a structured network, evaluating the impact of various defense policies, such as using decoy nodes to divert attacks, reducing connections between devices to limit malware spread, and periodically conducting a full inventory of devices on the network. Through a detailed sensitivity analysis, the critical variables influencing cybersecurity measures are identified. The results demonstrate that the implementation of cyber deception techniques significantly reduces the impact of attacks.
Evaluación Operativa De Colas En La Estación Aguacatala Del Metro De Medellín
(2024) Cantellón, Jesús D.; Serna, Emanuel; Toro, Juan E.; Universidad EAFIT
The increase in the supply of services and the resulting queues at the Aguacatala station of the Medellín Metro highlights the importance of designing solutions that ensure efficient, comfortable, and safe circulation for users. The study presented in this document proposes to address this challenge by modeling the operation of the Aguacatala station, focusing specifically on queue management, using the Discrete Event Simulation (DES) methodology. The impact of the available services at the station is evaluated through a baseline scenario, measuring wait times and queue lengths on the platform. As a result, visual outputs are generated to identify under which situations wait times and crowding conditions would exceed certain thresholds.
Sound-Based Imaging Regularization Approaches in Near-field Acoustic Holography
(2024) Martinod, T.; Universidad EAFIT
Regularization of the inverse problem is a complex issue when using Near-field Acoustic Holography (NAH) techniques to identify vibrating sources. This article aims to compare and implement various regularization methods in the context of NAH. Specifically, it compares commonly used Tikhonov regularization, sparsity-based regularization, and neural networks (NN) regularization for a planar NAH array with measurements obtained from an experimental setup. Additionally, it theoretically introduces Green’s function-based regularization. The first three types of regularization methods yield images consistent with the results, and statistical indicators are used to determine which method performs best at different frequencies.
Integración Manufactura – Envasado En El Área De Gran Volumen En Prebel Usando Des
(2024) Valencia, M.; Cano, S. M.; Martinod, T.; Universidad EAFIT
Prebel, as a cosmetics manufacturing company, faces delays in its packaging process due to the unavailability of fixed tanks, which affects the fulfillment of production orders. This work presents a discrete event simulation (DES) model developed in SIMUL8 to analyze the packaging area's operation and propose solutions to optimize the process. The study is based on real data and focuses on identifying the main causes of stoppages and their impact on production. The results show that reorganizing staff breaks could increase efficiency by 10%, suggesting that optimizing existing resources is more effective than increasing tank or personnel capacity.
On the Biharmonic Equation
(2024) Fierro, A.; Posada, C.; Sanchez, J.J; Martinod T.; Universidad EAFIT
This article provides a comprehensive introduction to the biharmonic equation, focusing on its origins in elasticity and fluid mechanics. We derive the equation from physical principles of linear deformations and Stokes flow, illustrating its applicability in modeling phenomena such as plate bending and stream functions in viscous media. Solutions are developed in polar and spherical coordinates with radial symmetry, including boundary conditions for spherical domains, as well as in general 2D Cartesian coordinates and the biharmonic wave equation for structural mechanics. Throughout, we highlight practical applications across engineering fields, showcasing the biharmonic equation’s role in predicting stress, displacement, and flow patterns.

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