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

Communications of the Byurakan Astrophysical Observatory Pub Date : 2024-01-09 DOI:10.52526/25792776-23.70.2-204

H. V. Pikichyan

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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.

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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

在本文中，借助作者之前提出的一种新方法，解决了在辐射按频率分布的一般规律下，平行于平面的无限介质在各向异性散射作用下的辐射漫反射问题。结果解决了将进入介质量子的一对自变量（即量子的频率和方向）与流出量子的一对自变量分开的可能性。与已知方法相比，这种方法的优势在于无需解决额外的分离问题，也无需对散射作用的特性进行任何特殊表述，就能实现解释变量的分离。因此，通过仅依赖于两个变量的辅助函数系统，可以明确地表达四个解释性变量的未知函数。为此，针对特别选定的和先前未知的内核，提出了特征值和特征函数的问题。新方法和传统方法的解之间存在双边关系，因此可以直接比较其准确性和效率。此外，还讨论了组织计算的总体方案。

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Communications of the Byurakan Astrophysical Observatory

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