Two new analytic approximations of the Chandrasekhars H function for isotropic scattering
Само за регистроване кориснике
2008
Чланак у часопису (Објављена верзија)
Метаподаци
Приказ свих података о документуАпстракт
The Chandrasekhars H functions play a central role in theoretical descriptions of radiative transfer in planetary and stellar atmospheres. In the present work our aim is to obtain in a simple way new analytic approximations of the Chandrasekhars function for isotropic scattering, which would be sufficiently simple but more accurate than the existing approximations. We apply the mean value theorem for definite integrals in the nonlinear integral equation for the Chandrasekhars H function. In this way the integral equation is formally solved but the solution depends on a new unknown parameter. We determine this parameter approximately, from the condition that the obtained H function matches the zero-order moment of the H function, which is known exactly, as accurately as possible in the whole range of the single particle albedo. The result gives our first analytic approximation for the H function. Using it as a starting approximation in the corresponding integral equation, after only one... iteration which may be performed analytically, we obtain our second analytic approximation. The maximum relative error of our first analytic. approximation, which is very simple in structure, is below 2.5%. The accuracy of our second approximation is within 0.07%, so that it highly surpasses the accuracy of the other analytic approximations available in the literature. (c) 2007 Elsevier Inc. All rights reserved.
Кључне речи:
radiative transferИзвор:
Icarus, 2008, 194, 1, 389-397Финансирање / пројекти:
- Добијање и карактеризација површина наноструктурних материјала (RS-MESTD-MPN2006-2010-141001)
- Квантна и оптичка интерферометрија (RS-MESTD-MPN2006-2010-141003)
- Заштита од зрачења-фундаментални, теоријски и експериментални физички аспекти (RS-MESTD-MPN2006-2010-141041)
DOI: 10.1016/j.icarus.2007.09.024
ISSN: 0019-1035
WoS: 000253504400031
Scopus: 2-s2.0-39049116704
Колекције
Институција/група
VinčaTY - JOUR AU - Davidović, Dragomir A. AU - Vukanić, Jovan V. AU - Arsenović, Dušan PY - 2008 UR - https://vinar.vin.bg.ac.rs/handle/123456789/3370 AB - The Chandrasekhars H functions play a central role in theoretical descriptions of radiative transfer in planetary and stellar atmospheres. In the present work our aim is to obtain in a simple way new analytic approximations of the Chandrasekhars function for isotropic scattering, which would be sufficiently simple but more accurate than the existing approximations. We apply the mean value theorem for definite integrals in the nonlinear integral equation for the Chandrasekhars H function. In this way the integral equation is formally solved but the solution depends on a new unknown parameter. We determine this parameter approximately, from the condition that the obtained H function matches the zero-order moment of the H function, which is known exactly, as accurately as possible in the whole range of the single particle albedo. The result gives our first analytic approximation for the H function. Using it as a starting approximation in the corresponding integral equation, after only one iteration which may be performed analytically, we obtain our second analytic approximation. The maximum relative error of our first analytic. approximation, which is very simple in structure, is below 2.5%. The accuracy of our second approximation is within 0.07%, so that it highly surpasses the accuracy of the other analytic approximations available in the literature. (c) 2007 Elsevier Inc. All rights reserved. T2 - Icarus T1 - Two new analytic approximations of the Chandrasekhars H function for isotropic scattering VL - 194 IS - 1 SP - 389 EP - 397 DO - 10.1016/j.icarus.2007.09.024 ER -
@article{ author = "Davidović, Dragomir A. and Vukanić, Jovan V. and Arsenović, Dušan", year = "2008", abstract = "The Chandrasekhars H functions play a central role in theoretical descriptions of radiative transfer in planetary and stellar atmospheres. In the present work our aim is to obtain in a simple way new analytic approximations of the Chandrasekhars function for isotropic scattering, which would be sufficiently simple but more accurate than the existing approximations. We apply the mean value theorem for definite integrals in the nonlinear integral equation for the Chandrasekhars H function. In this way the integral equation is formally solved but the solution depends on a new unknown parameter. We determine this parameter approximately, from the condition that the obtained H function matches the zero-order moment of the H function, which is known exactly, as accurately as possible in the whole range of the single particle albedo. The result gives our first analytic approximation for the H function. Using it as a starting approximation in the corresponding integral equation, after only one iteration which may be performed analytically, we obtain our second analytic approximation. The maximum relative error of our first analytic. approximation, which is very simple in structure, is below 2.5%. The accuracy of our second approximation is within 0.07%, so that it highly surpasses the accuracy of the other analytic approximations available in the literature. (c) 2007 Elsevier Inc. All rights reserved.", journal = "Icarus", title = "Two new analytic approximations of the Chandrasekhars H function for isotropic scattering", volume = "194", number = "1", pages = "389-397", doi = "10.1016/j.icarus.2007.09.024" }
Davidović, D. A., Vukanić, J. V.,& Arsenović, D.. (2008). Two new analytic approximations of the Chandrasekhars H function for isotropic scattering. in Icarus, 194(1), 389-397. https://doi.org/10.1016/j.icarus.2007.09.024
Davidović DA, Vukanić JV, Arsenović D. Two new analytic approximations of the Chandrasekhars H function for isotropic scattering. in Icarus. 2008;194(1):389-397. doi:10.1016/j.icarus.2007.09.024 .
Davidović, Dragomir A., Vukanić, Jovan V., Arsenović, Dušan, "Two new analytic approximations of the Chandrasekhars H function for isotropic scattering" in Icarus, 194, no. 1 (2008):389-397, https://doi.org/10.1016/j.icarus.2007.09.024 . .