Dynamical Theory in Incident-Spherical-Wave Approximation

1978 ◽  
pp. 179-212
Author(s):  
Zinovii Grigorievich Pinsker
Keyword(s):  
Spherical Wave ◽  
Dynamical Theory ◽  
Wave Approximation

A simple view of the spherical wave in dynamical theory

1999 ◽  
Vol 55 (3) ◽  
pp. 561-563 ◽  
Author(s):  
J. P. Guigay
Keyword(s):  
Multiple Scattering ◽  
Spherical Wave ◽  
Dynamical Theory ◽  
Simple View ◽  
Wave Approach ◽  
Straightforward Method

The results of the Kato spherical-wave approach to the dynamical theory for perfect crystals are obtained by a simple and straightforward method based on the multiple-scattering expansion.

Transient Response of a Point-Excited Submerged Spherical Shell

1973 ◽  
Vol 40 (4) ◽  
pp. 1078-1084 ◽  
Author(s):  
Y. K. Lou ◽  
J. M. Klosner
Keyword(s):  
Spherical Shell ◽  
Spherical Wave ◽  
Cylindrical Wave ◽  
Branch Points ◽  
Wave Approximation ◽  
Mode Method ◽  
The Laplace Transform ◽  
Long Time ◽  
Impulse Load ◽  
Short Time

The transient responses of a submerged spherical shell to a concentrated impulse and Heaviside load are obtained by using the classical mode method and the Laplace transform. For long time solutions, only a relatively small number of modes are sufficient, while for the short time response, a large number of modes must be used in order to achieve acceptable accuracy. For the lower modes, the inversion integral involves only simple poles and can be evaluated by Cauchy’s residue theorem. For the higher modes it is necessary to use asymptotic approximations and the inversion involves branch points and poles. A spherical wave approximation, similar to Haywood’s cylindrical wave approximation, is also used to solve the transient problem. It is found that the approximation accurately predicts the maximum peak response for the impulse load, while it underestimates the response for the Heaviside load.

Systematic Reflections and the Two Beam Concept of Extinction Distance

1967 ◽  
Vol 25 ◽  
pp. 332-333
Author(s):  
S. S. Sheinin ◽  
C. D. Cann
Keyword(s):  
Dynamical Theory ◽  
Beam Intensity

The effects of systematic reflections on the variation of diffracted beam intensity with depth in a crystal can only be taken into account by using the multi-beam dynamical theory. The results of calculations of this kind, which are presented here, indicate that the intensity profiles obtained are not periodic. Since extinction distance is a concept strictly applicable only when the diffracted beam intensity varies periodically with depth, its use as a parameter in describing multi-beam intensity profiles must be carefully considered.

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