{"title":"用平均法研究非线性氙振荡","authors":"Yoshiro Asahi , A.Ziya Akcasu","doi":"10.1016/0022-3107(73)90030-0","DOIUrl":null,"url":null,"abstract":"<div><p>A nonlinear analysis of xenon-temperature controlled nuclear reactor dynamics is presented. The set of equations in question belongs to a general class of rate equations with quadratic nonlinearities. Boundedness of the solutions is examined. The mean value of periodic solutions for the flux is shown to be always less than the equilibrium value. The Bogoliubov's method of averaging as extended by Case is applied to obtain approximate solutions. The mechanism of the existence of relaxation oscillations in the linear stability region is analyzed. Computer calculations are performed and found in good agreement with the approximate solutions obtained by means of the method of averaging.</p></div>","PeriodicalId":100811,"journal":{"name":"Journal of Nuclear Energy","volume":"27 12","pages":"Pages 839-855"},"PeriodicalIF":0.0000,"publicationDate":"1973-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/0022-3107(73)90030-0","citationCount":"4","resultStr":"{\"title\":\"An investigation of nonlinear xenon oscillation by method of averaging\",\"authors\":\"Yoshiro Asahi , A.Ziya Akcasu\",\"doi\":\"10.1016/0022-3107(73)90030-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A nonlinear analysis of xenon-temperature controlled nuclear reactor dynamics is presented. The set of equations in question belongs to a general class of rate equations with quadratic nonlinearities. Boundedness of the solutions is examined. The mean value of periodic solutions for the flux is shown to be always less than the equilibrium value. The Bogoliubov's method of averaging as extended by Case is applied to obtain approximate solutions. The mechanism of the existence of relaxation oscillations in the linear stability region is analyzed. Computer calculations are performed and found in good agreement with the approximate solutions obtained by means of the method of averaging.</p></div>\",\"PeriodicalId\":100811,\"journal\":{\"name\":\"Journal of Nuclear Energy\",\"volume\":\"27 12\",\"pages\":\"Pages 839-855\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1973-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/0022-3107(73)90030-0\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Nuclear Energy\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/0022310773900300\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Nuclear Energy","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/0022310773900300","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
An investigation of nonlinear xenon oscillation by method of averaging
A nonlinear analysis of xenon-temperature controlled nuclear reactor dynamics is presented. The set of equations in question belongs to a general class of rate equations with quadratic nonlinearities. Boundedness of the solutions is examined. The mean value of periodic solutions for the flux is shown to be always less than the equilibrium value. The Bogoliubov's method of averaging as extended by Case is applied to obtain approximate solutions. The mechanism of the existence of relaxation oscillations in the linear stability region is analyzed. Computer calculations are performed and found in good agreement with the approximate solutions obtained by means of the method of averaging.
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