A CLOSED-FORM SOLUTION TO THE ONE-DIMENSIONAL LINEAR AND NONLINEAR RADIATIVE TRANSFER PROBLEM

1999 ◽  
Vol 1 (1) ◽  
pp. 18 ◽  
Author(s):  
Marco T. Vilhena ◽  
L. B. Barichello
Keyword(s):  
Radiative Transfer ◽  
Closed Form ◽  
Transfer Problem ◽  
Closed Form Solution ◽  
Form Solution ◽  
Radiative Transfer Problem ◽  
One Dimensional ◽  
Linear And Nonlinear ◽  
The One

scholarly journals Analytical solution of the simple nonlinear radiative transfer problem

2018 ◽  
pp. 364-372
Author(s):  
H. V. Pikichyan
Keyword(s):  
Radiative Transfer ◽  
Analytical Solution ◽  
Transfer Problem ◽  
Internal Field ◽  
Field Problem ◽  
Radiative Transfer Problem ◽  
Absorbing Medium ◽  
One Dimensional ◽  
Radiation Beams ◽  
Finite Optical Thickness

Exploring the "Principle of invariance" and the method of "Linear images", the simple nonlinear conservative problem of radiative transfer is analyzed. The solutions of nonlinear reection-transmission and internal field problems of one dimensional scattering-absorbing medium of finite optical thickness are obtained, whereas both boundaries of medium illuminated by powerful radiation beams. Using two different approaches - a direct and inverse problem, the analytical solution of the internal field problem is derived.

New exact results for the defective square lattice

1976 ◽  
Vol 80 (2) ◽  
pp. 365-381 ◽  
Author(s):  
G. Ronca
Keyword(s):  
Closed Form Solution ◽  
Exact Result ◽  
Form Solution ◽  
Square Lattice ◽  
Zero Temperature ◽  
Real Crystal ◽  
One Dimensional ◽  
Resonance Modes ◽  
The One ◽  
Dimensional Crystal

Since the publication of the fundamental papers by Lifshitz (1, 2) and Montroll and Potts (3, 4) many authors have investigated the effect of an isotopic impurity on the lattice vibrations of a harmonic crystal at zero temperature. A fairly broad knowledge is now available on scattering amplitudes, localized modes and resonance modes (6, 7). Nevertheless, as pointed out by Maradudin and Montroll (see (7), p. 430), a closed form solution to the problem has been found only for the one-dimensional crystal, the work done on two and three-dimensional crystals being predominantly numerical. Unfortunately the one-dimensional crystal, as an approximation for a real crystal is an oversimplified model, incapable as it is of exhibiting resonance modes. To the author's knowledge the most significant exact result concerning the classical behaviour at zero temperature of crystals having a dimensionality higher than one is the connexion, calculated by Mahanty et al. (5) between localized mode frequency and impurity mass for the case of a square lattice undergoing planar vibrations.

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