Teaching 3-Dimensional Modeling of 2 Concentrations of Substances with Diffusion Reaction System
DOI:
https://doi.org/10.58797/cser.020205Keywords:
finite difference method, numerical methods, partial differential equations, reaction-diffusion, three-dimensional spaceAbstract
This research models the concentration of two substances in three-dimensional space with a reactiondiffusion system. The underlying partial differential equations (PDEs) are solved numerically using the finite difference method. Simulation results show the spatial and temporal variation of the concentrations of the substances, influenced by the diffusion, reaction, and boundary constants. This study introduces an innovative 3-dimensional modeling tool specifically designed to enhance students' understanding of complex diffusion reaction systems. Through the interactive 3-dimensional modeling tool students can observe how these substances diffuse and react over time, offering a dynamic way to explore complex scientific concepts. The result of the research with this tool is that it can significantly improve the learning process by transforming theoretical knowledge into practical, real-world understanding.
References
Ahn, S.-J., Lee, H., & Cho, K.-J. (2024). 3D printing with a 3D printed digital material filament for programming functional gradients. Nature Communications, 15(1). https://doi.org/10.1038/s41467-024-47480-5
Alexander, S. M., Pogson‐Morowitz, K. B., & Johnson, C. S. (2024). Three‐dimensional modeling in anatomy—Tool or terror? Anatomical Sciences Education, 17(4), 878–882. https://doi.org/10.1002/ase.2403
Ali, I., & Saleem, M. T. (2023). Spatiotemporal Dynamics of Reaction–Diffusion System and Its Application to Turing Pattern Formation in a Gray–Scott Model. Mathematics, 11(6), 1459–1459. https://doi.org/10.3390/math11061459
Ding, P., Yan, Y., Liang, Z., & Yan, Y. (2023). Finite difference method for time-fractional Klein–Gordon equation on an unbounded domain using artificial boundary conditions. Mathematics and Computers in Simulation, 205, 902–925. https://doi.org/10.1016/j.matcom.2022.10.030
Gray, P., & Scott, S. K. (2012). Autocatalytic reactions in the isothermal, continuous stirred tank reactor. Chemical Engineering Science, 39(6), 1087–1097. https://doi.org/10.1016/0009-2509(84)87017-7
John, D., Heuveline, V., & Schober, M. (2019). GOODE: A Gaussian Off-The-Shelf Ordinary Differential Equation Solver. International Conference on Machine Learning, 3152–3162.
Kalogeris, I., & Papadopoulos, V. (2021). Diffusion maps-aided Neural Networks for the solution of parametrized PDEs. Computer Methods in Applied Mechanics and Engineering, 376, 113568. https://doi.org/10.1016/j.cma.2020.113568
Li, A., Chen, R., Farimani, A. B., & Zhang, Y. J. (2020). Reaction diffusion system prediction based on convolutional neural network. Scientific Reports, 10(1). https://doi.org/10.1038/s41598-020-60853-2
Lian, V., Varoy, E., & Giacaman, N. (2022). Learning Object-Oriented Programming Concepts Through Visual Analogies. IEEE Transactions on Learning Technologies, 15(1), 1–1. https://doi.org/10.1109/tlt.2022.3154805
Mahmudah, M.S., Yacobi, M.A.A., & Steeven, D. (2024). Enhancing Learning of Electromagnetic Wave Propagation through 3D Visualization in Physics Education. (2024). Current STEAM and Education Research, 2(1), 43-52. https://doi.org/10.58797/cser.020104
Muñoz-Gil, G., Garcia-March, M. A., Manzo, C., Celi, A., & Lewenstein, M. (2019). Diffusion Through a Network of Compartments Separated by Partially-Transmitting Boundaries. Frontiers in Physics, 7. https://doi.org/10.3389/fphy.2019.00031
Oktavia, D. (2018). Solusi Asimtotik Pada Persamaan Difusi Dengan Waktu Singkat. Jurnal Matematika UNAND, 7(1), 59. https://doi.org/10.25077/jmu.7.1.59-63.2018
Olaye, O., & Ojo, O. A. (2021). Time variation of concentration-dependent interdiffusion coefficient obtained by numerical simulation analysis. Materialia, 16, 101056. https://doi.org/10.1016/j.mtla.2021.101056
Park, I., Triulzi, G., & Magee, C. L. (2022). Tracing the emergence of new technology: A comparative analysis of five technological domains. Technological Forecasting and Social Change, 184, 122014. https://doi.org/10.1016/j.techfore.2022.122014
Pinar, Z. (2021). An Analytical Studies of the Reaction- Diffusion Systems of Chemical Reactions. International Journal of Applied and Computational Mathematics, 7(3). https://doi.org/10.1007/s40819-021-01028-z
Raviprakash, K., Huang, B., & Prasad, V. (2022). A hybrid modelling approach to model process dynamics by the discovery of a system of partial differential equations. Computers & Chemical Engineering, 164, 107862–107862. https://doi.org/10.1016/j.compchemeng.2022.107862
Raya, A.G., Rahmah, A., Izzati, R.D., Zalianty, S.X., Firmansyah, F. (2024). Simulation of Optical Waveguide on Communication Signal Wave Delivery Between Airplane and Airport Through Tower. (2024). Current STEAM and Education Research, 2(1), 53-68. https://doi.org/10.58797/cser.020105
Riggi, M., Torrez, R. M., & Iwasa, J. H. (2024). 3D animation as a tool for integrative modeling of dynamic molecular mechanisms. Structure, 32(2), 122–130. https://doi.org/10.1016/j.str.2023.12.007
Saylors, R., & Trafimow, D. (2020). Why the Increasing Use of Complex Causal Models Is a Problem: On the Danger Sophisticated Theoretical Narratives Pose to Truth. Organizational Research Methods, 24(3), 109442811989345. https://doi.org/10.1177/1094428119893452
Schmitt, O., Nitzsche, C., Eipert, P., Prathapan, V., Hütt, M.-T., & Hilgetag, C. C. (2022). Reaction-diffusion models in weighted and directed connectomes. PLoS Computational Biology, 18(10), e1010507. https://doi.org/10.1371/journal.pcbi.1010507
Vargas, A. (2022). Finite difference method for solving fractional differential equations at irregular meshes. Mathematics and Computers in Simulation, 193, 204–216. https://doi.org/10.1016/j.matcom.2021.10.010
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Astrid Sovana Situmorang, Desy Dwi Ariyanti, Muhamad Syeha Nursidiq
This work is licensed under a Creative Commons Attribution 4.0 International License.
