{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:03:49Z","timestamp":1760241829678,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2018,9,20]],"date-time":"2018-09-20T00:00:00Z","timestamp":1537401600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Spanish Ministry of Economy and Competitiveness","award":["TEC2017-89403-C2-2-R"],"award-info":[{"award-number":["TEC2017-89403-C2-2-R"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this work, we have obtained a new constitutive matrix to calculate the induced Lorentz electric current of in a conductive disk in movement within a magnetic field using the cell method in 3D. This disk and a permanent magnet act as a magnetic brake. The results obtained are compared with those obtained with the finite element method (FEM) using the computer applications Getdp and femm. The error observed is less than 0.1173%. Likewise, a second verification has been made in the laboratory using Hall sensors to measure the magnetic field in the proximity of the magnetic brake.<\/jats:p>","DOI":"10.3390\/s18103185","type":"journal-article","created":{"date-parts":[[2018,9,21]],"date-time":"2018-09-21T11:00:25Z","timestamp":1537527625000},"page":"3185","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["New Constitutive Matrix in the 3D Cell Method to Obtain a Lorentz Electric Field in a Magnetic Brake"],"prefix":"10.3390","volume":"18","author":[{"given":"Jos\u00e9 Miguel","family":"Monz\u00f3n-Verona","sequence":"first","affiliation":[{"name":"Electrical Engineering Department, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain"},{"name":"Institute for Applied Microelectronics, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pablo Ignacio","family":"Gonz\u00e1lez-Dom\u00ednguez","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain"},{"name":"Institute for Applied Microelectronics, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Santiago","family":"Garc\u00eda-Alonso","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering and Automatics (DIEA), University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,9,20]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1109\/TMAG.2005.860782","article-title":"Parametric analysis of eddy-current brake performance by 3-d finite-element analysis","volume":"42","author":"Gay","year":"2006","journal-title":"IEEE Trans. Magn."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3004","DOI":"10.1109\/TMAG.2003.816723","article-title":"Comparison of three types of permanent magnet linear eddy-current brakes according to magnetization pattern","volume":"39","author":"Jang","year":"2003","journal-title":"IEEE Trans. Magn."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2528\/PIER00080101","article-title":"Finite formulation of the electromagnetic field geometric methods in computational electromagnetics","volume":"32","author":"Tonti","year":"2001","journal-title":"PIER"},{"key":"ref_4","first-page":"237","article-title":"A direct discrete formulation of field laws: The cell method","volume":"2","author":"Tonti","year":"2001","journal-title":"Comput. Model. Eng. Sci."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"9102","DOI":"10.3390\/s101009102","article-title":"Electro-quasistatic analysis of an electrostatic induction micromotor using the cell method","volume":"10","year":"2010","journal-title":"Sensors"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1260","DOI":"10.1016\/j.jcp.2013.08.016","article-title":"Why starting from differential equations for computational physics?","volume":"257","author":"Tonti","year":"2014","journal-title":"J. Comput. Phys."},{"key":"ref_7","unstructured":"Woodson, H., and Melcher, J. (1968). Electromechanical Dynamic, Part I Discrete System, Wiley."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"7401","DOI":"10.1016\/j.jcp.2010.06.023","article-title":"A new set of basis functions for the discrete geometric approach","volume":"229","author":"Codecasa","year":"2010","journal-title":"J. Comput. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1109\/TMAG.2004.824107","article-title":"Geometric interpretation of discrete approaches to solving magnetostatic problems","volume":"40","author":"Trevisan","year":"2004","journal-title":"IEEE Trans. Magn."},{"key":"ref_10","unstructured":"Balay, S., Abhyankar, S., Adams, M.F., Brown, J., Brune, P., Buschelman, K., Dalcin, L., Eijkhout, V., Gropp, W.D., and Kaushik, D. (2018, September 17). PETSc, Available online: http:\/\/www.mcs.anl.gov\/petsc."},{"key":"ref_11","unstructured":"Geuzaine, C. (2007, January 16\u201320). GetDP: A general finite-element solver for the de Rham complex. Proceedings of the Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Z\u00fcrich, Switzerland."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1002\/nme.2579","article-title":"Gmsh: A three-dimensional finite element mesh generator with built-in pre- and post-processing facilities","volume":"79","author":"Geuzaine","year":"2009","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1016\/j.agsy.2005.11.004","article-title":"Assessment of the adequacy of mathematical models","volume":"89","author":"Tedeschi","year":"2006","journal-title":"Agric. Syst."},{"key":"ref_14","first-page":"315","article-title":"Errores frecuentes en la interpretaci\u00f3n del coeficiente de determinaci\u00f3n lineal","volume":"38","year":"2005","journal-title":"Anuario Jur\u00eddico y Econ\u00f3mico Escurialense"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1016\/j.ecolmodel.2008.05.006","article-title":"How to evaluate models: Observed vs. predicted or predicted vs. observed?","volume":"216","author":"Perelman","year":"2008","journal-title":"Ecol. Model."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"885","DOI":"10.13031\/2013.23153","article-title":"Model evaluation guidelines for systematic quantification of accuracy in watershed simulations","volume":"50","author":"Moriasi","year":"2007","journal-title":"Trans. Asabe"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.jhydrol.2009.08.003","article-title":"Decomposition of the mean squared error and performance criteria: Implications for improving hydrological modelling","volume":"377","author":"Gupta","year":"2009","journal-title":"J. Hydrol."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Jolliffe, T., and Stephenson, D.B. (2012). Forecast Verification: A Practitioner\u2019s Guide in Atmospheric Science, John Wiley & Sons. [1st ed.].","DOI":"10.1002\/9781119960003"},{"key":"ref_19","first-page":"211","article-title":"A bounded version of the Nash-Sutcliffe criterion for better model assessment on large sets of basins","volume":"307","author":"Mathevet","year":"2006","journal-title":"IAHS Publ."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"79","DOI":"10.3354\/cr030079","article-title":"Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance","volume":"30","author":"Willmott","year":"2005","journal-title":"Clim. Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1016\/j.ijforecast.2006.03.001","article-title":"Another look at measures of forecast accuracy","volume":"22","author":"Hyndman","year":"2006","journal-title":"Int. J. Forecast."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.5194\/gmd-7-1247-2014","article-title":"Root mean square error (RMSE) or mean absolute error (MAE)? Arguments against avoiding RMSE in the literature","volume":"7","author":"Chai","year":"2014","journal-title":"Geosci. Model Dev."},{"key":"ref_23","first-page":"18","article-title":"Calibraci\u00f3n y validaci\u00f3n de modelos de pron\u00f3stico de heladas en el valle del Mantaro","volume":"3","author":"Sanabria","year":"2006","journal-title":"ECIPERU"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"344","DOI":"10.2307\/1238512","article-title":"On the use of theil\u2019s inequality coefficients","volume":"57","author":"Leuthold","year":"1975","journal-title":"Am. J. Agric. Econ."},{"key":"ref_25","first-page":"124","article-title":"Metropolitan maquiladora econometric forecast accuracy","volume":"13","author":"Fullerton","year":"2010","journal-title":"Rom. J. Econ. Forecast."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1177\/002224377301000413","article-title":"Theil\u2019s forecast accuracy coefficient: A clarification","volume":"10","author":"Bliemel","year":"1973","journal-title":"J. Market. Res."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"2088","DOI":"10.1002\/joc.2419","article-title":"Short communication: A refined index of model performance","volume":"32","author":"Willmott","year":"2012","journal-title":"Int. J. Climatol."},{"key":"ref_28","first-page":"255","article-title":"Comparaci\u00f3n de medidas de desviaci\u00f3n para validar modelos sin sesgo, sesgo constante o proporcional","volume":"26","author":"Medina","year":"2010","journal-title":"Univ. Cienc."},{"key":"ref_29","unstructured":"Yangzhou Positioning Tech. Co., Ltd. (2018, September 17). 49E Hall Effect Linear Position Sensor. Available online: http:\/\/www.pst888.com."},{"key":"ref_30","unstructured":"Supermagnete (2018, September 17). Data Sheet Article S-04-05-Z. Available online: https:\/\/www.supermagnete.es\/."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/10\/3185\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:21:46Z","timestamp":1760196106000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/10\/3185"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,9,20]]},"references-count":30,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2018,10]]}},"alternative-id":["s18103185"],"URL":"https:\/\/doi.org\/10.3390\/s18103185","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2018,9,20]]}}}