{"title":"运动学守恒定律系统","authors":"P. Prasad","doi":"10.18520/cs/v123/i12/1441-1447","DOIUrl":null,"url":null,"abstract":"In a wide range of physical phenomena, we find surfaces Ω t evolving in time t , which need mathematical treat-ment. Here, we briefly review the theory of a system of conservation laws known as the kinematical conservation laws (KCLs), which govern the evolution of these surfaces. KCLs are the most general equations in conservation form which govern the evolution of Ω t with physically realistic singularities. A special type of singularity is a kink, which is a point on Ω t when it is a curve in two dimensions and a curve on Ω t when it is a surface in three dimensions. Across a kink, the normal direction n to Ω t and the normal velocity m of Ω t are discontinuous. This article is aimed at non-experts in the field. Readers may refer to the literature for more details.","PeriodicalId":11194,"journal":{"name":"Current Science","volume":"7 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2022-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"System of kinematical conservation laws\",\"authors\":\"P. Prasad\",\"doi\":\"10.18520/cs/v123/i12/1441-1447\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In a wide range of physical phenomena, we find surfaces Ω t evolving in time t , which need mathematical treat-ment. Here, we briefly review the theory of a system of conservation laws known as the kinematical conservation laws (KCLs), which govern the evolution of these surfaces. KCLs are the most general equations in conservation form which govern the evolution of Ω t with physically realistic singularities. A special type of singularity is a kink, which is a point on Ω t when it is a curve in two dimensions and a curve on Ω t when it is a surface in three dimensions. Across a kink, the normal direction n to Ω t and the normal velocity m of Ω t are discontinuous. This article is aimed at non-experts in the field. Readers may refer to the literature for more details.\",\"PeriodicalId\":11194,\"journal\":{\"name\":\"Current Science\",\"volume\":\"7 1\",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2022-12-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Current Science\",\"FirstCategoryId\":\"103\",\"ListUrlMain\":\"https://doi.org/10.18520/cs/v123/i12/1441-1447\",\"RegionNum\":4,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Current Science","FirstCategoryId":"103","ListUrlMain":"https://doi.org/10.18520/cs/v123/i12/1441-1447","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
In a wide range of physical phenomena, we find surfaces Ω t evolving in time t , which need mathematical treat-ment. Here, we briefly review the theory of a system of conservation laws known as the kinematical conservation laws (KCLs), which govern the evolution of these surfaces. KCLs are the most general equations in conservation form which govern the evolution of Ω t with physically realistic singularities. A special type of singularity is a kink, which is a point on Ω t when it is a curve in two dimensions and a curve on Ω t when it is a surface in three dimensions. Across a kink, the normal direction n to Ω t and the normal velocity m of Ω t are discontinuous. This article is aimed at non-experts in the field. Readers may refer to the literature for more details.
期刊介绍：
Current Science, published every fortnight by the Association, in collaboration with the Indian Academy of Sciences, is the leading interdisciplinary science journal from India. It was started in 1932 by the then stalwarts of Indian science such as CV Raman, Birbal Sahni, Meghnad Saha, Martin Foster and S.S. Bhatnagar. In 2011, the journal completed one hundred volumes. The journal is intended as a medium for communication and discussion of important issues that concern science and scientific activities. Besides full length research articles and shorter research communications, the journal publishes review articles, scientific correspondence and commentaries, news and views, comments on recently published research papers, opinions on scientific activity, articles on universities, Indian laboratories and institutions, interviews with scientists, personal information, book reviews, etc. It is also a forum to discuss issues and problems faced by science and scientists and an effective medium of interaction among scientists in the country and abroad. Current Science is read by a large community of scientists and the circulation has been continuously going up.
Current Science publishes special sections on diverse and topical themes of interest and this has served as a platform for the scientific fraternity to get their work acknowledged and highlighted. Some of the special sections that have been well received in the recent past include remote sensing, waves and symmetry, seismology in India, nanomaterials, AIDS, Alzheimer''s disease, molecular biology of ageing, cancer, cardiovascular diseases, Indian monsoon, water, transport, and mountain weather forecasting in India, to name a few. Contributions to these special issues ‘which receive widespread attention’ are from leading scientists in India and abroad.
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