{"title":"各向同性散射条件下半无限介质漫反射问题中的频率变量分离与频率辐射再分布的一般规律","authors":"H. V. Pikichyan","doi":"10.52526/25792776-23.70.2-204","DOIUrl":null,"url":null,"abstract":"Inthepresentedwork,withthehelpofanewapproachpreviouslyproposedbytheauthor,theproblem ofdiffusereflectionofradiationfromaplane-parallelsemi-infinitemediumunderisotropicscatteringinthe caseofthegeneral lawofradiationredistributionbyfrequenciesissolved.Resultingsolutionimplements thepossibilityof separatingapair of independent variables (namely, the frequencyanddirectionof thequantum)of enteringthemediumquantafromthesamepairof exitingquanta. Theadvantageof thisapproach inrelationtotheknownmethods is that the separationof theexplanatoryvariables is achievedwithouttheneedtosolvetheadditionalproblemofseparationoranyspecial representationof thecharacteristicsofasingleactofscattering.Here, inanexpandedformissoughtnamelythesolutionof themodifiedinitialproblem, insteadofapreliminarydecompositionofthecharacteristicsofasingleact ofscattering.Asaresult, theunknownfunctionofthefourexplanatoryvariables isexpressedexplicitly throughasystemofauxiliaryfunctionsthatdependononlytwovariables. Forthispurpose,aproblem foreigenvaluesandeigenfunctions is formulatedforaspeciallyselectedandpreviouslyunknownkernel. Bilateral relationshipsbetweenthe solutionsof thenewandtraditionallyusedmethodsareobtained, whichmakes itpossible todirectlycompare theiraccuracyandefficiency. Thegeneral schemeof the organizationofcalculationsisalsodiscussed.","PeriodicalId":412578,"journal":{"name":"Communications of the Byurakan Astrophysical Observatory","volume":"31 4","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Separation of Frequency Variables in the Problem of Diffuse Reflection from a Semi-Infinite Medium under Isotropic Scattering with a General Law of Radiation Redistribution by Frequencies\",\"authors\":\"H. V. Pikichyan\",\"doi\":\"10.52526/25792776-23.70.2-204\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Inthepresentedwork,withthehelpofanewapproachpreviouslyproposedbytheauthor,theproblem ofdiffusereflectionofradiationfromaplane-parallelsemi-infinitemediumunderisotropicscatteringinthe caseofthegeneral lawofradiationredistributionbyfrequenciesissolved.Resultingsolutionimplements thepossibilityof separatingapair of independent variables (namely, the frequencyanddirectionof thequantum)of enteringthemediumquantafromthesamepairof exitingquanta. Theadvantageof thisapproach inrelationtotheknownmethods is that the separationof theexplanatoryvariables is achievedwithouttheneedtosolvetheadditionalproblemofseparationoranyspecial representationof thecharacteristicsofasingleactofscattering.Here, inanexpandedformissoughtnamelythesolutionof themodifiedinitialproblem, insteadofapreliminarydecompositionofthecharacteristicsofasingleact ofscattering.Asaresult, theunknownfunctionofthefourexplanatoryvariables isexpressedexplicitly throughasystemofauxiliaryfunctionsthatdependononlytwovariables. Forthispurpose,aproblem foreigenvaluesandeigenfunctions is formulatedforaspeciallyselectedandpreviouslyunknownkernel. Bilateral relationshipsbetweenthe solutionsof thenewandtraditionallyusedmethodsareobtained, whichmakes itpossible todirectlycompare theiraccuracyandefficiency. Thegeneral schemeof the organizationofcalculationsisalsodiscussed.\",\"PeriodicalId\":412578,\"journal\":{\"name\":\"Communications of the Byurakan Astrophysical Observatory\",\"volume\":\"31 4\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-01-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications of the Byurakan Astrophysical Observatory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.52526/25792776-23.70.2-204\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications of the Byurakan Astrophysical Observatory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.52526/25792776-23.70.2-204","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Separation of Frequency Variables in the Problem of Diffuse Reflection from a Semi-Infinite Medium under Isotropic Scattering with a General Law of Radiation Redistribution by Frequencies
Inthepresentedwork,withthehelpofanewapproachpreviouslyproposedbytheauthor,theproblem ofdiffusereflectionofradiationfromaplane-parallelsemi-infinitemediumunderisotropicscatteringinthe caseofthegeneral lawofradiationredistributionbyfrequenciesissolved.Resultingsolutionimplements thepossibilityof separatingapair of independent variables (namely, the frequencyanddirectionof thequantum)of enteringthemediumquantafromthesamepairof exitingquanta. Theadvantageof thisapproach inrelationtotheknownmethods is that the separationof theexplanatoryvariables is achievedwithouttheneedtosolvetheadditionalproblemofseparationoranyspecial representationof thecharacteristicsofasingleactofscattering.Here, inanexpandedformissoughtnamelythesolutionof themodifiedinitialproblem, insteadofapreliminarydecompositionofthecharacteristicsofasingleact ofscattering.Asaresult, theunknownfunctionofthefourexplanatoryvariables isexpressedexplicitly throughasystemofauxiliaryfunctionsthatdependononlytwovariables. Forthispurpose,aproblem foreigenvaluesandeigenfunctions is formulatedforaspeciallyselectedandpreviouslyunknownkernel. Bilateral relationshipsbetweenthe solutionsof thenewandtraditionallyusedmethodsareobtained, whichmakes itpossible todirectlycompare theiraccuracyandefficiency. Thegeneral schemeof the organizationofcalculationsisalsodiscussed.
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