{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:42:26Z","timestamp":1760146946701,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,12,26]],"date-time":"2024-12-26T00:00:00Z","timestamp":1735171200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>This paper presents an innovative approach to modelling the fiber optic fusion effect using the Network Simulation Method (NSM). An analogy between the heat conduction equations and electrical circuits is developed, allowing a complex physical problem to be transformed into an equivalent electrical system. Using NGSpice, thermal interactions in an anisotropic optical fiber under high optical power conditions are simulated. The methodology addresses the distribution of the temperature in the system, considering thermal variations and temperature-dependent material characteristics. In an NSM equivalent circuit, the effect of applying the spark is modelled by a switch that switches the spark-generating source on and off. It can be seen that temperature variation with time, or temperature rise rate (K\/s), depends on the applied power. In addition, the mathematical method of nondimensionalization is used to study the real influence of each parameter of the problem on the solution and the relationship between the variables. Four optical fiber cases are analysed, each characterised by different areas and refractive indices, revealing how these variables affect the propagation of the melting phenomenon. The results highlight the effectiveness of the NSM in solving nonlinear and coupled problems in thermal engineering, providing a solid framework for future research in the optimisation of optical communication systems.<\/jats:p>","DOI":"10.3390\/axioms14010002","type":"journal-article","created":{"date-parts":[[2024,12,26]],"date-time":"2024-12-26T03:10:49Z","timestamp":1735182649000},"page":"2","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Study Using the Network Simulation Method and Nondimensionalization of the Fiber Fuse Effect"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3382-8165","authenticated-orcid":false,"given":"Juan Francisco","family":"Sanchez-P\u00e9rez","sequence":"first","affiliation":[{"name":"Department of Applied Physics and Naval Technology, Universidad Polit\u00e9cnica de Cartagena (UPCT), Campus Muralla del Mar, 30202 Cartagena, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2136-5159","authenticated-orcid":false,"given":"Joaqu\u00edn","family":"Solano-Ram\u00edrez","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Materials and Manufacturing, Universidad Polit\u00e9cnica de Cartagena (UPCT), Campus Muralla del Mar, 30202 Cartagena, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8145-516X","authenticated-orcid":false,"given":"Fulgencio","family":"Mar\u00edn-Garc\u00eda","sequence":"additional","affiliation":[{"name":"Department of Automation Engineering, Electrical Engineering and Electronic Technology, Universidad Polit\u00e9cnica de Cartagena (UPCT), Campus Muralla del Mar, 30202 Cartagena, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7477-9414","authenticated-orcid":false,"given":"Enrique","family":"Castro","sequence":"additional","affiliation":[{"name":"Department of Applied Physics and Naval Technology, Universidad Polit\u00e9cnica de Cartagena (UPCT), Campus Muralla del Mar, 30202 Cartagena, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,26]]},"reference":[{"key":"ref_1","unstructured":"Duarte, F.J. (1988). Self-propelled self-focusing damage in the optical fibres. Lasers 1987, Proceedings of the Tenth International Conference on Lasers and Applications, Lake Tahoe, NV, USA, 7\u201311 December 1987, STS Press."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1049\/el:19880032","article-title":"Observation of catastrophic self-propelled self-focusing in optical fibres","volume":"24","author":"Kashyap","year":"1988","journal-title":"Electron. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Kashyap, R., Sayles, A.H., and Cornwell, G.F. (1997). Heat-flow modeling and visualization of catastrophic self-propagating damage in single-mode optical fibers at low powers. Laser-Induced Damage in Optical Materials: 1996, SPIE.","DOI":"10.1117\/12.274219"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Starikova, V.A., Konin, Y.A., Petukhova, A.Y., Aleshkina, S.S., Petrov, A.A., and Perminov, A.V. (2023). Mathematical Model of Fuse Effect Initiation in Fiber Core. Algorithms, 16.","DOI":"10.3390\/a16070331"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Todoroki, S. (2014). Fiber Fuse, Springer.","DOI":"10.1007\/978-4-431-54577-4"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1536","DOI":"10.1364\/OL.36.001536","article-title":"Fiber fuse effect in hollow optical fibers","volume":"36","author":"Ha","year":"2011","journal-title":"Opt. Lett."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2781392","DOI":"10.1155\/2016\/2781392","article-title":"End Face Damage and Fiber Fuse Phenomena in Single-Mode Fiber-Optic Connectors","volume":"2016","author":"Shuto","year":"2016","journal-title":"J. Photonics"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Xiao, Q., Tian, J., Yan, P., Li, D., and Gong, M. (2019). Exploring the initiation of fiber fuse. Sci. Rep., 9.","DOI":"10.1038\/s41598-019-47911-0"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"672","DOI":"10.1364\/JOT.88.000672","article-title":"Structural characteristics of internal microcavities produced in optical fiber via the fuse effect","volume":"88","author":"Konin","year":"2021","journal-title":"J. Opt. Technol."},{"key":"ref_10","first-page":"162","article-title":"Fiber Fuse Simulation in Multi-Core Fibers for Space Division Multiplexed Transmission","volume":"10","author":"Shuto","year":"2022","journal-title":"J. Electr. Electron. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"8962","DOI":"10.1364\/OE.22.008962","article-title":"Harnessing the fiber fuse for sensing applications","volume":"22","author":"Lin","year":"2014","journal-title":"Opt. Express"},{"key":"ref_12","unstructured":"Mizuno, Y., Lee, H., Hayashi, N., Nakamura, K., and Todoroki, S.-I. (2024, November 20). Plastic Optical Fiber Fuse and Its Impact on Sensing Applications. Available online: http:\/\/www.youtube.com\/."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2100210","DOI":"10.1002\/adpr.202100210","article-title":"Sensing Applications of Polymer Optical Fiber Fuse","volume":"3","author":"Marques","year":"2022","journal-title":"Adv. Photonics Res."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"573","DOI":"10.1109\/LPT.2020.2985585","article-title":"An Efficient Non-Invasive Method to Fabricate In-Fiber Microcavities Using a Continuous-Wave Laser","volume":"32","author":"Xiao","year":"2020","journal-title":"IEEE Photonics Technol. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2513","DOI":"10.1364\/PRJ.465896","article-title":"On the initiation of fiber fuse damage in high-power ytterbium-doped fiber lasers","volume":"10","author":"Tian","year":"2022","journal-title":"Photonics Res."},{"key":"ref_16","first-page":"81","article-title":"Fiber Fuse Damage Effect in Fiber Lasers: A Review","volume":"48","author":"Tian","year":"2021","journal-title":"Chin. J. Lasers-Zhongguo Jiguang"},{"key":"ref_17","unstructured":"Peusner, L. (1987). The Principles of Network Thermodynamics: Theory and Biophysical Applications, Entropy Limited."},{"key":"ref_18","unstructured":"Nagel, L. (1973, January 12). SPICE (Simulation Program with Integrated Circuit Emphasis). Proceedings of the 16th Midwest Symposium on Circuit Theory, Waterloo, ON, Canada."},{"key":"ref_19","unstructured":"Nagel, L.W. (1975). SPICE2: A Computer Program to Simulate Semiconductor Circuits, College of Engineering, University of California."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"105201","DOI":"10.1016\/j.cnsns.2020.105201","article-title":"Universal curves for the solution of chlorides penetration in reinforced concrete, water-saturated structures with bound chloride","volume":"84","author":"Alhama","year":"2020","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"378","DOI":"10.1115\/1.3225900","article-title":"Conduction of heat in solids","volume":"108","author":"Carslow","year":"1986","journal-title":"J. Eng. Mater. Technol."},{"key":"ref_22","unstructured":"Davis, D.D., Mettler, S.C., and DiGiovanni, D.J. (November, January 30). Experimental data on the fiber fuse. Proceedings of the 27th Annual Boulder Damage Symposium: Laser-Induced Damage in Optical Materials, Boulder, CO, USA."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1356","DOI":"10.1063\/1.336107","article-title":"Formation mechanism of drawing-induced E\u2032 centers in silica optical fibers","volume":"58","author":"Hanafusa","year":"1985","journal-title":"J. Appl. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1109\/JQE.2004.831635","article-title":"Fiber fuse phenomenon in step-index single-mode optical fibers","volume":"40","author":"Shuto","year":"2004","journal-title":"IEEE J. Quantum Electron."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1002\/j.1538-7305.1977.tb00534.x","article-title":"Loss analysis of single-mode fiber splices","volume":"56","author":"Marcuse","year":"1977","journal-title":"Bell Syst. Tech. J."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/j.applthermaleng.2018.04.124","article-title":"A thermal-electrical analogy transient model of district heating pipelines for integrated analysis of thermal and power systems","volume":"139","author":"Hao","year":"2018","journal-title":"Appl. Therm. Eng."},{"key":"ref_27","unstructured":"Kreith, F., and Bohn, M.S. (1986). Principles of Heat Transfer, Harper and Row Publishers Inc."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"988","DOI":"10.1115\/1.1495520","article-title":"Electric Network Representation of the Unsteady Cooling of a Lumped Body by Nonlinear Heat Transfer Modes","volume":"124","author":"Alhama","year":"2002","journal-title":"J. Heat Transf."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1002\/cae.20159","article-title":"A powerful and versatile educational software to simulate transient heat transfer processes in simple fins","volume":"16","author":"Alhama","year":"2008","journal-title":"Comput. Appl. Eng. Educ."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/s002310100254","article-title":"Network simulation method for solving phase-change heat transfer problems with variable thermal properties","volume":"38","author":"Alhama","year":"2002","journal-title":"Heat Mass Transf."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"S\u00e1nchez-P\u00e9rez, J.F., Mar\u00edn, F., Morales, J.L., C\u00e1novas, M., and Alhama, F. (2018). Modeling and simulation of different and representative engineering problems using Network Simulation Method. PLoS ONE, 13.","DOI":"10.1371\/journal.pone.0193828"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Solano, J., Balibrea, F., Moreno, J.A., and Mar\u00edn, F. (2023). Dry Friction Analysis in Doped Surface by Network Simulation Method. Mathematics, 11.","DOI":"10.3390\/math11061341"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Fern\u00e1ndez-Grac\u00eda, M., S\u00e1nchez-P\u00e9rez, J.F., del Cerro, F., and Conesa, M. (2023). Mathematical Model to Calculate Heat Transfer in Cylindrical Vessels with Temperature-Dependent Materials. Axioms, 12.","DOI":"10.3390\/axioms12040335"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"1907","DOI":"10.1109\/TSG.2022.3210014","article-title":"Distributed Dispatch of Integrated Electricity-Heat Systems with Variable Mass Flow","volume":"14","author":"Zheng","year":"2023","journal-title":"IEEE Trans. Smart Grid"},{"key":"ref_35","unstructured":"Holger, V., Atkinson, G., Nenzi, P., and Warning, D. (2024, November 20). Software \u201cNgSpice\u201d. Available online: https:\/\/ngspice.sourceforge.io\/index.html."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"176","DOI":"10.1145\/362566.362571","article-title":"The automatic integration of ordinary differential equations","volume":"14","author":"Gear","year":"1971","journal-title":"Commun. ACM"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Solano, J., Mulas-P\u00e9rez, J., Balibrea, F., and Moreno-Nicol\u00e1s, J.A. (2024). Truncation Error of the Network Simulation Method: Chaotic Dynamical Systems in Mechanical Engineering. 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