Mamikon Mnatsakanian:
III. RADIATION TRANSFER THEORY

V. Ambartsumian is the father of
Soviet Theoretical Astrophysics, whose main subject
is 'Radiation Transfer Theory' (RTT). It is used to
analyze the properties of planetary and stellar
atmospheres based on the transformed information
carried to us through light radiation.
In 1941, Ambartsumian introduced
his 'principle of invariance' and used it to solve
some basic theoretical problems. Later it was
deeply explored by Sobolev, Ivanov, and others, at
Leningrad University, USSR, and Chandrasekhar,
Bellman, Kalaba, and others in the USA.
In 1972 I solved the same
problems by a simpler method, reducing them to
linear instead of the classical nonlinear
integral equations [13]. Thus, for problems in
finite thickness layers, instead of principle of
invariance, I introduced a reduction method  reducing them' to a particular, much
simpler and solvable even analytically, case for a
semiinfinite layer. For the latter case only, I
modified Ambartsumian's principle into a general
'apparatus' of
invariance [5]. The reduction method can also be
applied to solve similar pure mathematical problems
[4].
My method is extremely efficient
both for numerical
calculations and for
analytic solutions of
very high accuracy [610]. With hand calculations,
I obtained Chandrasekhar's numeric computer
solutions published in several volumes in Ap. J.
Suppl, with three digits accuracy which fully
suffices for practical applications considering
that the problems in question are idealized
compared to the real ones. In a very special case,
Yamamoto's puzzling intuitive solution follows.
My methods were successfully
applied furter to solve both numerically and
analytically the problems with an anisotropic
scattering [9, 21] using Chandrasekhar's idea of
pseudoindicatrix and Sobolev's transformations, as
well as my simple geometricprobabilistic
interpretation
of pseudoindicatrix. They were also extended to
problems with nonmonochromatic scatterings [1012], in particular, with
complete frequency redistribition law of scattering
(for Doppler, Lorenz, etc., profiles).
In 1978 I have also solved a
nonlinear
transfer problem [5]. Soon, I was invited to 'Joint
Institute of Nuclear Research' in Dubna, because I
actually approached a problematic issue in Quantum
Field Theory in an elementary manner, with
simple
geometric
considerations, The solution is mathematically
equivalent to important GellMann and Low equation
in Quantum Electrodynamics (QED). My approach
established analogies
between SemiGroups
intoduced in [5,13] in nonlinear RTT and the
Renormalization Group in QED, in the frames of
Shirkov's Functional SelfSimilarity.
In a series of papers [1317], I
established both formal and physical
parallels between Ambartsumian's invariance
principle presented in a form of diagrams for
elementary light scattering acts, and Feynman's
famous diagrams in QED, 'Milne's solution' and
'naked charge' in QED, the 'critical thickness' and
'ghost pole', 'infrared catastrophee' the
'semiinfinite nonlinear solution' and the
'asymptotic freedom', and more. These are
onetoone analogies, which allow one to use the
solutions in nonlinear RTT to draw certain
conclusions in the corresponding counterpart
problems of QED and other sciences.
In 1981, I organized
International Symposium 'Principle Invariance and
its Applications', at Byurakan Observatory. Was
editor of its Proceedings. My work on RTT was
nominated in 1985 to Soviet State Prize by
Marchuk, the President of the USSR Academy of
Sciences. It was the topic of my Doctoral
Dissertation [21]. In 198488, at Ambartsumian's
suggestion, I lectured on this work at Yerevan
State University, Armenia.

Publications by Mamikon
Mnatsakanian: III.
Radiation Transfer Theory. Twenty two
papers are published on this theme, originally in
Russian.

1. On the Solution of
OneDimentional Transport Problem, Soob.
Byurakan Obs., 46, 1975, pp 93100, English
Abstract

2. On the
Reduction of Radiative Transfer Problem in a Finite
Layer to the Problem for a Half Space,
Docl. Acad. Sci. USSR , 225, No. 5, 1975, pp
10491052, English pp 833835

3. On the Solution of the Light
Diffusion Problem in Optically Finite Shell
(Danielian, E. Kh.). Soob. Byurakan Obs., 46, 1975,
pp 101114, English Abstract

4. On the Linear Problems of
Transfer (Yengibarian, N.B.), Docl. Acad.
Sci. USSR, Math., 217, No.3, 1974, pp 533535

5. On the Solution of Radiative
Transfer Problems in SemiInfinite Media,
Soob. Byurakan. Obs., 50, 1978, pp 5978, English
Abstract

6. The Quasiasymptotic Solutions
of the Radiative Transfer Problem in an Optically
Finite Shell. I. Conservative Scattering.
Astrophysics, 11, 1975, 659678, English pp 434448

7. The Quasiasymptotic Solutions
of the Radiative Transfer Problem in an Optically
Finite Shell. II. NonConservative
Scattering. Astrophysics, 12, 1976, 451473,
English pp 295311

8. Analytic
Solutions of High Accuracy to the Problem of
Monochromatic Scattering of Light in a Plane
Layer. Astrophysics, 16, No.3, 1980, pp
513533, English pp 271285

9. On the Theory of Anisotropic
Scattering in a Plane Layer. HighAccuracy Analytic
Solutions. Int. Sym. 1981 'Principle
Invariance and its Applications', Eds.
Mnatsakanian, Pikichian Yerevan, Acad. Sci.
Armenian SSR, 1988, pp 445456, English Abstract

10. Solution of Radiative
Transfer Problem in a Plane Layer for the Model of
Complete Frequency Redistribution. I.
OneDimensional Medium. (Gabrielian, R.G.,
Mkrtchian, A.R., Kotandjian, Kh.V.) Astrophysics,
28, 1988, pp 193204, English pp 112119

11. Solution
of Radiative Transfer Problem in a Plane Layer for
the Model of Complete Frequency Redistribution. II.
Three Dimensional Medium. (Gabrielian,
R.G., Mkrtchian, A.R., Kotandjian, Kh.V.)
Astrophysics, 28, 1988, pp 443454, English pp
262268

12. Nearly
Exact Analytical Solutions of the Problem of
Radiation Transfer in a Plane Layer for the Model
of Complete Frequency
Redistribution.
(Gabrielian, R. G., Mkrtchian, A. R., Kotandjian,
Kh.V.). Izv. Ac. Sci. Arm., 22, No.4, 1987, pp
191197, English Abstract

13. Nonlinear
Tranfer Problems and the Renormalization
Group. Docl. Acad. Sci. USSR, 262, No.4,
1982, pp 856860, English pp 262856

14.
RenormGroup Analogies in Astrophysics.
Int. Conf. 'Renormalization Group86', Dubna, USSR,
2629 August 1986, World Sci. Publ., pp. 437465,
in English

15. On the Solution of a
NonLinear Reflection Problem. (Melikian,
A.O.). Soviet Conf. Young Astrophys., Yerevan,
Acad. Sci. Arm, 1979, p. 22

16. On Analogies Between the
Problems of NonLinear Transfer Theory and the
Theory of Interacting Quantized Fields. Int.
Sym. Modern Problems of Quantum Field Theory,
Alushta, 1981, Uspekhi Phys. Sci., 136, No.3, 1982,
pp 542543

17. NonLinear Tranfer Problems
and the Problems of the Theory of Quantized
Fields. Int. Sym. 1981 'Principle Invariance
and its Applications', Eds. Mnatsakanian, M. A.,
Pikichian, O.V., Yerevan, Acad. Sci. Armenian SSR,
1988, pp 445456, English Abstract

18. On the Problem of Random
Walk on Lattice. Int. Sym. 1981 'Principle
of Invariance and its Applications', Eds.
Mnatsakanian M. A., Pikichian, O. V., Yerevan,
1988, pp 445456, English Abstract

19. On Some Representations of
the Source Function. Soob. Byurakan Obs.,
61, 1975, pp 113116, English Abstract

20. About One Peculiarity of the
Solution of Conservative Anisotropic Scattering
Problems. Astrophysics, 17, 1981, pp
179183, English Abstract

21. New Apparatus of Transfer
Theory in a Plane Layer. Soviet Doctoral
Dissertation in Theoretical and Mathematical
Physics/Astrophysics; Manuscript, Yerevan, 1983,
320 pages; Annotations, Byurakan, 1984, 32 pages

