{"title":"非均匀最小分区相场模型及其在液滴动力学中的应用","authors":"É. Bretin, S. Masnou","doi":"10.4171/IFB/379","DOIUrl":null,"url":null,"abstract":"We propose and analyze in this paper a new derivation of a phase-field model to approximate inhomogeneous multiphase perimeters. It is based on suitable decompositions of perimeters under some embeddability condition which allows not only an explicit derivation of the model from the surface tensions, but also gives rise to a Γ-convergence result. We propose a simple and robust scheme to simulate the gradient flow of the approximating energy. We illustrate the efficiency of our approach with a series of numerical simulations in 2D and 3D, and we address in particular the dynamics of droplets evolving on a fixed solid.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"24","resultStr":"{\"title\":\"A new phase field model for inhomogeneous minimal partitions, and applications to droplets dynamics\",\"authors\":\"É. Bretin, S. Masnou\",\"doi\":\"10.4171/IFB/379\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose and analyze in this paper a new derivation of a phase-field model to approximate inhomogeneous multiphase perimeters. It is based on suitable decompositions of perimeters under some embeddability condition which allows not only an explicit derivation of the model from the surface tensions, but also gives rise to a Γ-convergence result. We propose a simple and robust scheme to simulate the gradient flow of the approximating energy. We illustrate the efficiency of our approach with a series of numerical simulations in 2D and 3D, and we address in particular the dynamics of droplets evolving on a fixed solid.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2017-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"24\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/IFB/379\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/IFB/379","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
A new phase field model for inhomogeneous minimal partitions, and applications to droplets dynamics
We propose and analyze in this paper a new derivation of a phase-field model to approximate inhomogeneous multiphase perimeters. It is based on suitable decompositions of perimeters under some embeddability condition which allows not only an explicit derivation of the model from the surface tensions, but also gives rise to a Γ-convergence result. We propose a simple and robust scheme to simulate the gradient flow of the approximating energy. We illustrate the efficiency of our approach with a series of numerical simulations in 2D and 3D, and we address in particular the dynamics of droplets evolving on a fixed solid.
期刊介绍:
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.