{"title":"拉伸-扭曲-褶皱流单位球面上的相图","authors":"J. Llibre, C. Valls","doi":"10.15388/namc.2023.28.33088","DOIUrl":null,"url":null,"abstract":"The so-called stretch-twist-fold flow consists in a Stokes flow depending on two parameters defined in a unit closed ball B that is associated with the motion of a fluid particle coming from the dynamo theory, and it models a mechanism for studying the magnetic field of the Earth and the Sun. Here for the first time, we classify all the local phase portraits of its equilibrium points, and we provide the global phase portraits on the 2-dimensional sphere of the boundary of the ball B.","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Phase portraits on the unit sphere of the stretch-twist-fold flow\",\"authors\":\"J. Llibre, C. Valls\",\"doi\":\"10.15388/namc.2023.28.33088\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The so-called stretch-twist-fold flow consists in a Stokes flow depending on two parameters defined in a unit closed ball B that is associated with the motion of a fluid particle coming from the dynamo theory, and it models a mechanism for studying the magnetic field of the Earth and the Sun. Here for the first time, we classify all the local phase portraits of its equilibrium points, and we provide the global phase portraits on the 2-dimensional sphere of the boundary of the ball B.\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2023-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.15388/namc.2023.28.33088\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.15388/namc.2023.28.33088","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
Phase portraits on the unit sphere of the stretch-twist-fold flow
The so-called stretch-twist-fold flow consists in a Stokes flow depending on two parameters defined in a unit closed ball B that is associated with the motion of a fluid particle coming from the dynamo theory, and it models a mechanism for studying the magnetic field of the Earth and the Sun. Here for the first time, we classify all the local phase portraits of its equilibrium points, and we provide the global phase portraits on the 2-dimensional sphere of the boundary of the ball B.
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