Solution of some problems of continuum mechanics by the method of invariant imbedding

1987 ◽  
Vol 23 (2) ◽  
pp. 120-126
Author(s):  
S. K. Nikitin ◽  
V. K. Chibiryakov
Keyword(s):  
Continuum Mechanics ◽  
Invariant Imbedding ◽  
Method Of Invariant Imbedding

Inelastic High-Energy Electron Spectrafrom Plane-Parallel Layer-Nonhomogeneous Surfaces

1991 ◽  
Vol 46 (10) ◽  
pp. 851-857 ◽  
Author(s):  
V. P. Afanas’ev ◽  
D. Naujoks
Keyword(s):  
Solid Angle ◽  
High Energy ◽  
Initial Energy ◽  
Energy Spectra ◽  
Invariant Imbedding ◽  
Adequate Description ◽  
Reflection Function ◽  
Plane Parallel ◽  
Parallel Layer ◽  
Method Of Invariant Imbedding

AbstractWe consider inelastic backscattering of electrons with initial energy of tens and hundreds of keV by plane-parallel homogeneous and sandwiched targets. Basing on the invariance principle, we find expressions that describe the dynamics of the changes in the energy spectra of electrons reflected into a given solid angle that occur with increase of the thickness of films of different materials on substrates of finite and infinite thickness. We substantiate a procedure of linearizing the equations for the reflection function obtained by the method of invariant imbedding. We obtain an analytical solution of linearized equations in the form of a series in Legendre polynomials. A comparison with experimental data shows that the theory developed gives an adequate description of the process of electron backscattering.

Deep Penetration of Radiation by the Method of Invariant Imbedding

1967 ◽  
Vol 27 (2) ◽  
pp. 263-270 ◽  
Author(s):  
D. R. Mathews ◽  
K. F. Hansen ◽  
E. A. Mason
Keyword(s):  
Deep Penetration ◽  
Invariant Imbedding ◽  
Method Of Invariant Imbedding
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