{"title":"简化Pn方程的理论方面","authors":"R. McClarren","doi":"10.1080/00411450.2010.535088","DOIUrl":null,"url":null,"abstract":"In celebration of the 50th anniversary of the simplified Pn equations (SPn), this work reviews the theory underpinning the SPnequations for neutral particle transport. We recount the derivation of these equations by Gelbard’s formal procedure and by more recent asymptotic and variational analyses. The relation between the SPn equations and several other low order approximations is discussed. Also, the conditions under which the SPn equations are equivalent to the full Pn equations of the same order are discussed as well as the accuracy of the SPnequations. Several open problems in the theory of the SPn equations are posed.","PeriodicalId":49420,"journal":{"name":"Transport Theory and Statistical Physics","volume":"39 1","pages":"109 - 73"},"PeriodicalIF":0.0000,"publicationDate":"2010-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/00411450.2010.535088","citationCount":"78","resultStr":"{\"title\":\"Theoretical Aspects of the Simplified Pn Equations\",\"authors\":\"R. McClarren\",\"doi\":\"10.1080/00411450.2010.535088\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In celebration of the 50th anniversary of the simplified Pn equations (SPn), this work reviews the theory underpinning the SPnequations for neutral particle transport. We recount the derivation of these equations by Gelbard’s formal procedure and by more recent asymptotic and variational analyses. The relation between the SPn equations and several other low order approximations is discussed. Also, the conditions under which the SPn equations are equivalent to the full Pn equations of the same order are discussed as well as the accuracy of the SPnequations. Several open problems in the theory of the SPn equations are posed.\",\"PeriodicalId\":49420,\"journal\":{\"name\":\"Transport Theory and Statistical Physics\",\"volume\":\"39 1\",\"pages\":\"109 - 73\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/00411450.2010.535088\",\"citationCount\":\"78\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transport Theory and Statistical Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1080/00411450.2010.535088\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transport Theory and Statistical Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1080/00411450.2010.535088","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Theoretical Aspects of the Simplified Pn Equations
In celebration of the 50th anniversary of the simplified Pn equations (SPn), this work reviews the theory underpinning the SPnequations for neutral particle transport. We recount the derivation of these equations by Gelbard’s formal procedure and by more recent asymptotic and variational analyses. The relation between the SPn equations and several other low order approximations is discussed. Also, the conditions under which the SPn equations are equivalent to the full Pn equations of the same order are discussed as well as the accuracy of the SPnequations. Several open problems in the theory of the SPn equations are posed.
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