{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,21]],"date-time":"2026-03-21T13:18:06Z","timestamp":1774099086401,"version":"3.50.1"},"reference-count":59,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,17]],"date-time":"2021-10-17T00:00:00Z","timestamp":1634428800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100006108","name":"Kult\u00farna a Edukacn\u00e1 Grantov\u00e1 Agent\u00fara M\u0160VVa\u0160 SR","doi-asserted-by":"publisher","award":["023\u017dU-4\/2020: Development of advanced virtual models for studying and investigation of transport means operation characteristics"],"award-info":[{"award-number":["023\u017dU-4\/2020: Development of advanced virtual models for studying and investigation of transport means operation characteristics"]}],"id":[{"id":"10.13039\/501100006108","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100006109","name":"Vedeck\u00e1 Grantov\u00e1 Agent\u00fara M\u0160VVa\u0160 SR a SAV","doi-asserted-by":"publisher","award":["1\/0558\/18: Research of the interaction of a braked railway wheelset and track in simulated opera-tional conditions of a vehicle running in a track on the test bench"],"award-info":[{"award-number":["1\/0558\/18: Research of the interaction of a braked railway wheelset and track in simulated opera-tional conditions of a vehicle running in a track on the test bench"]}],"id":[{"id":"10.13039\/501100006109","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The main objective of this work is to study the possibilities of improving the running safety of a railway wagon with independently rotating wheels by changing their design symmetrically mounted on an axle. The article provides a discussion of the advantages and disadvantages of using the independently rotating wheels in a bogie of railway wagons. Their increasing tendency of derailment is described. The influence of a perspective constructive scheme (PKS) of railway wagon wheels in comparison with a traditional constructive scheme (TKS) on running safety due to the climbing of a wheel flange onto a rail is studied. This work introduces a conceptual proposition of a technical solution to railway wheel design as well as containing the results of both analytical calculations as well as the results of multibody simulations. A PKS wheel design for a railway wheel is designed that allows independent rotation of its tread surface and of a guiding surface (i.e., of a flange) to each other, which both are arranged symmetrically on a wheelset axle. It brings features of the distribution of friction forces generating in a flange contact when the wheel with a TKS and with PKS move on a rail. It is possible to conclude with the help of the obtained results that the use of wheels with the PKS is advisable for the reduction of the running resistance as well as for increasing the running safety of railway wagons.<\/jats:p>","DOI":"10.3390\/sym13101955","type":"journal-article","created":{"date-parts":[[2021,10,17]],"date-time":"2021-10-17T23:25:15Z","timestamp":1634513115000},"page":"1955","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["A Study of Improving Running Safety of a Railway Wagon with an Independently Rotating Wheel\u2019s Flange"],"prefix":"10.3390","volume":"13","author":[{"given":"Evgeny","family":"Mikhailov","sequence":"first","affiliation":[{"name":"Department of Logistics and Traffic Safety, Educational and Scientific Institute of Transport and Building, Volodymyr Dahl East Ukrainian National University, Central Avenue 59A\/403, 93400 Severodonetsk, Ukraine"}]},{"given":"Stanislav","family":"Semenov","sequence":"additional","affiliation":[{"name":"Department of Logistics and Traffic Safety, Educational and Scientific Institute of Transport and Building, Volodymyr Dahl East Ukrainian National University, Central Avenue 59A\/403, 93400 Severodonetsk, Ukraine"}]},{"given":"Hanna","family":"Shvornikova","sequence":"additional","affiliation":[{"name":"Department of Logistics and Traffic Safety, Educational and Scientific Institute of Transport and Building, Volodymyr Dahl East Ukrainian National University, Central Avenue 59A\/403, 93400 Severodonetsk, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3928-0567","authenticated-orcid":false,"given":"Juraj","family":"Gerlici","sequence":"additional","affiliation":[{"name":"Department of Transport and Handling Machines, Faculty of Mechanical Engineering, University of \u017dilina, Univerzitn\u00e1 8215\/1, 010 26 \u017dilina, Slovakia"}]},{"given":"Maxim","family":"Kovtanets","sequence":"additional","affiliation":[{"name":"Department of Railway and Road Technology, Lift and Care Systems, Educational and Scientific Institute of Transport and Building, Volodymyr Dahl East Ukrainian National University, Central Avenue 59A\/410, 93400 Severodonetsk, Ukraine"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9433-392X","authenticated-orcid":false,"given":"J\u00e1n","family":"Di\u017eo","sequence":"additional","affiliation":[{"name":"Department of Transport and Handling Machines, Faculty of Mechanical Engineering, University of \u017dilina, Univerzitn\u00e1 8215\/1, 010 26 \u017dilina, Slovakia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3936-7507","authenticated-orcid":false,"given":"Miroslav","family":"Blatnick\u00fd","sequence":"additional","affiliation":[{"name":"Department of Transport and Handling Machines, Faculty of Mechanical Engineering, University of \u017dilina, Univerzitn\u00e1 8215\/1, 010 26 \u017dilina, Slovakia"}]},{"given":"Jozef","family":"Haru\u0161inec","sequence":"additional","affiliation":[{"name":"Department of Transport and Handling Machines, Faculty of Mechanical Engineering, University of \u017dilina, Univerzitn\u00e1 8215\/1, 010 26 \u017dilina, Slovakia"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,17]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1080\/00423119208969013","article-title":"Independently rotating wheel systems for railway vehicles\u2014A state-of-the-art review","volume":"21","author":"Dukkipati","year":"1992","journal-title":"Veh. Syst. Dyn."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Liang, B., and Iwnicki, S.D. (2007, January 5\u20138). An experimental study of independently rotating wheels for railway vehicles. Proceedings of the International Conference on Mechatronics and Automation 2007, Harbin, China.","DOI":"10.1109\/ICMA.2007.4303908"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Zaazaa, K.E., and Whitten, B. (2007, January 11\u201315). Effect of independently rotating wheels on the dynamic performance of railroad vehicles. Proceedings of the ASME International Mechanical Engineering Congress and Exposition 2007, Seattle, WA, USA.","DOI":"10.1115\/IMECE2007-43645"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Farhat, N., Ward, C., Shaebi, O., Crosbee, D., Stow, J., Wang, R., Goodall, R., and Whitley, M. (2020). Controlling a Rail Vehicle with Independently-Rotating Wheels. Advances in Dynamics of Vehicles on Roads and Tracks, Springer.","DOI":"10.1007\/978-3-030-38077-9_4"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"23","DOI":"10.4203\/ijrt.5.1.2","article-title":"Railway Wheelsets: History, Research and Developments","volume":"5","author":"Bracciali","year":"2016","journal-title":"Int. J. Railw. Technol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1076\/0042-3114(200001)33:1;1-5;FT057","article-title":"Solid Axle and Independently-Rotating Railway Wheelsets\u2014A Control Engineering Assessment of Stability","volume":"33","author":"Goodall","year":"2000","journal-title":"Veh. Syst. Dyn."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1177\/0954409718777374","article-title":"Robust active guidance control using the \u03bc-synthesis method for a tram with independently rotating wheelsets","volume":"233","author":"Lu","year":"2019","journal-title":"Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/s00419-017-1301-6","article-title":"Simulation study of wheels wear in low-floor tram with independently rotating wheels","volume":"88","author":"Chudzikiewicz","year":"2018","journal-title":"Arch. Appl. Mech."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"113","DOI":"10.20858\/tp.2017.12.3.11","article-title":"Analysis of dynamics of a metro vehicle model with differential wheelsets","volume":"12","author":"Melnik","year":"2017","journal-title":"Transp. Probl."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/j.proeng.2017.06.076","article-title":"Numerical dynamics study of a rail vehicle with differential gears","volume":"192","author":"Kostrzewski","year":"2017","journal-title":"Procedia Eng."},{"key":"ref_11","first-page":"19","article-title":"Research on the safety factor against derailment of railway vehicles","volume":"6","author":"Sapronova","year":"2017","journal-title":"East. Eur. J. Enterp. Technol."},{"key":"ref_12","unstructured":"Nozhenko, O.S., Hauser, V., Kravchenko, K.O., and Loulova, M. (2017, January 20\u201322). Proposal of wheel with additional tread for vehicle to strongly curved track interaction improvement. Proceedings of the XXIII Konference s Mezinarodni Ucasti: Soucasne Problemy v Kolejovych Vozidlech 2017\/23rd Conference: Current Problems in Rail Vehicles 2017, Ceska Trebova, Czech Republic."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.wear.2016.03.037","article-title":"Contact mechanics issues of a vehicle equipped with partially independently rotating wheelsets","volume":"366","author":"Bracciali","year":"2016","journal-title":"Wear"},{"key":"ref_14","first-page":"143","article-title":"Contribution to random vibration numerical simulation and optimisation of nonlinear mechanical systems","volume":"103","author":"Saga","year":"2019","journal-title":"Sci. J. Sil. Univ. Technol. Ser. Transp."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/j.arcontrol.2004.02.004","article-title":"Combined active steering and traction for mechatronic bogie vehicles with independently rotating wheels","volume":"28","author":"Perez","year":"2004","journal-title":"Annu. Rev. Control"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"03019","DOI":"10.1051\/matecconf\/201929403019","article-title":"Study of rail vehicles movement characteristics improvement in curves using fuzzy logic mechatronic systems","volume":"294","author":"Kapitsa","year":"2019","journal-title":"MATEC Web Conf."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"020009","DOI":"10.1063\/1.5140870","article-title":"Mechatronic System of Control Position of Wheel Pairs by Railway Vehicles in the Rail Track","volume":"2198","author":"Mikhailov","year":"2019","journal-title":"AIP Conf. Proc."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s40534-020-00207-w","article-title":"Active suspension in railway vehicles: A literature survey","volume":"28","author":"Fu","year":"2020","journal-title":"Railw. Eng. Sci."},{"key":"ref_19","first-page":"391","article-title":"Analysis of a tramcar ride when passing a point frog and when entering small radius arc by specific rail geometry","volume":"19","author":"Hauser","year":"2019","journal-title":"Manuf. Technol."},{"key":"ref_20","unstructured":"Dvorak, Z., Leitner, B., and Novak, L. (2015, January 7\u20138). Software support for railway traffic simulation under restricted conditions of the rail section. Proceedings of the 9th International Scientific Conference TRANSBALTICA 2015, Vilnius, Lithuania."},{"key":"ref_21","first-page":"33","article-title":"Reduced wear wheels and rails","volume":"7","author":"Upadhyay","year":"2000","journal-title":"Int. Railw. J."},{"key":"ref_22","first-page":"85","article-title":"Proposal and application of methodology of revitalisation of regional railway track in Slovakia and Serbia. Part 1: Theoretical approach and proposal of methodology for revitalisation of regional railways","volume":"10","author":"Kendra","year":"2015","journal-title":"Transp. Probl."},{"key":"ref_23","unstructured":"Leitner, B., M\u00f4cov\u00e1, L., and Hromada, M. (2017, January 4\u20135). A new Approach to Identification of Critical Elements in Railway Infrastructure. Proceedings of the 10th International Scientific Conference on Transportation Science and Technology TRANSBALTICA 2017, Vilnius, Lithuania."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1111","DOI":"10.24425\/amm.2019.129502","article-title":"The evaluation of the wear mechanism of high-carbon hard facing layers","volume":"64","author":"Winczek","year":"2019","journal-title":"Arch. Metall. Mater."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"554","DOI":"10.1080\/00423114.2002.11666262","article-title":"Passive non-linear elastic suspension devices for improved hunting stability of railway bogies","volume":"37","author":"Scheffel","year":"2003","journal-title":"Veh. Syst. Dyn."},{"key":"ref_26","first-page":"1","article-title":"Improved curving performance of an innovative two-axle vehicle: A reasonable feedforward active steering approach","volume":"58","author":"Giossi","year":"2020","journal-title":"Veh. Syst. Dyn."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"102457","DOI":"10.1016\/j.mechatronics.2020.102457","article-title":"Estimating the wheel lateral position of a mechatronic railway running gear with nonlinear wheel-rail geometry","volume":"73","author":"Keck","year":"2021","journal-title":"Mechatronics"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Wilson, N., Shu, X., and Kramp, K. (2004, January 13\u201319). Effects of Independently Rolling Wheels on Flange Climb Derailment. Proceedings of the ASME International Mechanical Engineering Congress and Exposition 2004, Anahaim, CA, USA.","DOI":"10.1115\/IMECE2004-60293"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"39","DOI":"10.5604\/08669546.1218792","article-title":"Study of the derailment safety index Y\/Q of the low-floor tram bogies with different types of guidance of independently rotating wheels","volume":"38","author":"Opala","year":"2016","journal-title":"Arch. Transp."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1080\/00423110600882738","article-title":"Enhancing the resistance to derailment and side-wear for a tramway vehicle with independently rotating wheels","volume":"44","author":"Shen","year":"2006","journal-title":"Veh. Syst. Dyn."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Iwnicki, S. (2006). Railway vehicle derailment and prevention. Handbook of Railway Vehicle Dynamics, Taylor & Francis. [1st ed.].","DOI":"10.1201\/9781420004892"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1080\/00423114.2019.1566558","article-title":"Study on the derailment behaviour of a railway wheelset with solid axles in a railway turnout","volume":"58","author":"Xu","year":"2020","journal-title":"Veh. Syst. Dyn."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Mikhailov, E., Semenov, S., Sapronova, S., and Tkachenko, V. (2019, January 2\u20133). On the Issue of Wheel Flange Sliding along the Rail. Proceedings of the International Conference TRANSBALTICA 2019, Vilnius, Lithuania.","DOI":"10.1007\/978-3-030-38666-5_40"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Mikhailov, E., Semenov, S., Kliuiev, S., Di\u017eo, J., Blatnick\u00fd, M., Gerlici, J., Haru\u0161inec, J., and Kovtanets, M. (2020). Clarification of features of the wheel movement with a perspective constructive scheme on a rail. Appl. Sci., 10.","DOI":"10.3390\/app10196758"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"01011","DOI":"10.1051\/matecconf\/201824401011","article-title":"Static analysis of transmission tower beam structure","volume":"244","author":"Jakubovicova","year":"2018","journal-title":"MATEC Web Conf."},{"key":"ref_36","unstructured":"Dukkipati, R. (2000). Vehicle Dynamics, Narosa Publishing House. [1st ed.]."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"00033","DOI":"10.1051\/matecconf\/201823500033","article-title":"Reduction of Kinematic Resistance to Movement of the Railway Vehicles","volume":"235","author":"Mikhailov","year":"2019","journal-title":"MATEC Web Conf."},{"key":"ref_38","unstructured":"Mikhailov, E., Semenov, S., Di\u017eo, J., and Kravchenko, K. (2019, January 29\u201331). Research of possibilities of reducing the driving resistance of a railway vehicle by means of the wheel construction improvement. Proceedings of the 13th International Scientific Conference on Sustainable, Modern and Safe Transport TRANSCOM 2019, High Tatras, Slovak Republic."},{"key":"ref_39","first-page":"176","article-title":"Improvement of high speed stability and curving performance by parameter control of trucks for rail vehicles considering independently rotating wheelsets and unsymmetric structure","volume":"33","author":"Suda","year":"1990","journal-title":"JSME Int. J."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2633","DOI":"10.1299\/kikaic.57.2633","article-title":"Dynamic stability and steering ability of trucks for rail vehicles with longitudinally unsymmetric structure","volume":"57","author":"Suda","year":"1991","journal-title":"Trans. Jpn. Soc. Mech. Ser. C"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"2846","DOI":"10.1299\/kikaic.61.2846","article-title":"Dynamic behavior of a heavy haul railway vehicle with forced steering trucks used in a Factory Yard (In case of trucks with a link-type mechanism for axle supporting)","volume":"61","author":"Tanafuji","year":"1995","journal-title":"Trans. Jpn. Soc. Mech. Ser. C"},{"key":"ref_42","unstructured":"Goodal, R., and Mei, T.X. (2001, January 8\u201312). Mechatronic strategy for controlling-railway wheelsets with independently rotating wheels. Proceedings of the IEEE\/ASME International Conference on Advanced Intelligent Mechatronics, (AIM), Como, Italy."},{"key":"ref_43","unstructured":"Mei, T.X., and Goodall, R.M. (September, January 30). Wheelset control strategies for a two-axle railway vehicle. Proceedings of the 16th Symposium of the International Association for Vehicle System Dynamics, Pretoria, South Africa."},{"key":"ref_44","first-page":"1","article-title":"Independently rotating wheels with induction motors for high-speed trains","volume":"2011","author":"Liang","year":"2011","journal-title":"J. Control Sciebce Eng."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Liu, X.Y., Goodall, R., and Iwnicki, S. (2021). Yaw compensation and yaw relaxation controls for active steering of railway wheelsets via electromechanical actuators. Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit, 1\u201310.","DOI":"10.1177\/09544097211004322"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"21","DOI":"10.17531\/ein.2021.1.3","article-title":"Identification of safety hazards and operating conditions of the low-floor tram with independently rotating wheels with various drive control algorithms","volume":"23","author":"Konowrocki","year":"2021","journal-title":"Exsploatacja Niezawodn\u2014Maint. Reliab."},{"key":"ref_47","unstructured":"Kalinowski, D., Szolc, T., and Konowrocki, R. (2019, January 2\u20133). The new simulation approach to tramway safety againts deraolment evaluation in term of vehicle dynamics. Proceedings of the 11th Transbaltica International Scientific Conference-Transportation Science and Technology, Vilnius, Lithuania."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"276","DOI":"10.1177\/0954409718801265","article-title":"Benefits of mechatronically guided vehicles on railway track switches","volume":"234","author":"Farhat","year":"2020","journal-title":"Proc. Inst. Mech. Eng. Part. F J. Rail Rapid Transit"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.mechatronics.2018.03.008","article-title":"The benefits of mechatronically-guided railway vehicles: A multi-body physics simulation study","volume":"51","author":"Farhat","year":"2018","journal-title":"Mechatronics"},{"key":"ref_50","first-page":"1","article-title":"Modelling the dynamics of an unconventional rail vehicle bogie with independently rotating wheels with the use of Boltzmann-Hamel equations","volume":"58","author":"Chudzikiewicz","year":"2020","journal-title":"Veh. Syst. Dyn."},{"key":"ref_51","unstructured":"Chudzikiewicz, A., and Sowinski, B. (2015, January 17\u201321). Modelling nad simulation of trams bogies with fully independently rotating wheels. Proceedings of the 24th Symposium of the International Association for Vehicle System Dynamics, Graz, Austria."},{"key":"ref_52","unstructured":"Uhl, T., and Chudzikiewicz, A. (2001, January 20\u201324). Analytical and experimental investigation of low floor tram dynamics. Proceedings of the 17th Symposium of the International Association for Vehicle System Dynamics, Lyngby, Denmark."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"748","DOI":"10.1080\/00423114.2016.1156135","article-title":"An alternative to FASTSIM for tangential solution of the wheel-rail contact","volume":"54","author":"Sichani","year":"2016","journal-title":"Veh. Syst. Dyn."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/s11044-018-09635-3","article-title":"A fast method for determination of creep forces in non-Hertzian contact of wheel and rail based on a book of tables","volume":"45","author":"Piotrowski","year":"2019","journal-title":"Multibody Syst. Dyn."},{"key":"ref_55","unstructured":"Lack, T., and Gerlici, J. (2015, January 16\u201318). A Modified Strip Method to Speed up the Tangential Stress between Wheel and Rail Calculation. Proceedings of the 22nd International Conference on Current Problems in Rail Vehicles, Prorail, Zilina, Slovakia."},{"key":"ref_56","doi-asserted-by":"crossref","unstructured":"Lack, T., and Gerlici, J. (2015, January 16\u201318). Speeding up of the rail\/wheel contact stress computation by means of modified strip method. Proceedings of the 22nd International Conference on Current Problems in Rail Vehicles, Prorail, Zilina, Slovakia.","DOI":"10.26552\/com.C.2014.3A.33-39"},{"key":"ref_57","unstructured":"Nadal, M.J. (1908). Locomotives a Vapeur, Collection Encyclopedie Scientifique, Biblioteque de Mecanique Appliquee et Genie."},{"key":"ref_58","unstructured":"Mikhailov, E., Semenov, S., Di\u017eo, J., Kravchenko, K., and Blatnick\u00fd, M. (2019, January 17\u201319). Possibilities of reducing of a rail vehicle running resistance by means of a new wheel design. Proceedings of the 24th International Conference \u201cCurrent Problems in Rail Vehicles\u2014PRORAIL 2019\u201d, \u017dilina, Slovak Republic."},{"key":"ref_59","unstructured":"Strazovec, P., Gerlici, J., Lack, T., and Harusinec, J. (2019, January 29\u201331). Innovative solution for experimental research of phenomena resulting from the wheel and rail rolling. Proceedings of the 13th International Scientific Conference on Sustainable, Modern and Safe Transport TRANSCOM 2019, Novy Smokovec, Slovakia."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/10\/1955\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T07:16:24Z","timestamp":1760166984000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/10\/1955"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,10,17]]},"references-count":59,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2021,10]]}},"alternative-id":["sym13101955"],"URL":"https:\/\/doi.org\/10.3390\/sym13101955","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,10,17]]}}}