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We develop a finite element algorithm to solve such problems with dynamic mesh control, achieved by supplementing the free energy with an auxiliary functional that promotes mesh quality and is minimised in the null space of the energy. We apply this algorithm to a flexible capacitor, as well as to determine the shape of liquid crystal tactoids as a function of the surface tension and elastic constants. These are compared with theoretical predictions and experimental observations of tactoids from the literature.","descriptionType":"Abstract"}],"geoLocations":[],"fundingReferences":[],"xml":"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","url":"https://tandf.figshare.com/articles/dataset/Shape_minimisation_problems_in_liquid_crystals/3504914/1","contentUrl":null,"metadataVersion":4,"schemaVersion":"http://datacite.org/schema/kernel-4","source":"mds","isActive":true,"state":"findable","reason":null,"viewCount":1,"viewsOverTime":[{"yearMonth":"2025-10","total":1}],"downloadCount":0,"downloadsOverTime":[{"yearMonth":"2025-10","total":0}],"referenceCount":1,"citationCount":0,"citationsOverTime":[],"partCount":0,"partOfCount":0,"versionCount":0,"versionOfCount":0,"created":"2016-07-29T06:37:40.000Z","registered":"2016-07-29T06:37:41.000Z","published":"2016","updated":"2020-09-04T04:55:44.000Z"},"relationships":{"client":{"data":{"id":"figshare.ars","type":"clients"}},"provider":{"data":{"id":"otjm","type":"providers"}},"media":{"data":{"id":"10.6084/m9.figshare.3504914.v1","type":"media"}},"refer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