Examinando por Autor "Martinod, T."

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    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.
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    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.
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    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.