Closed form solution of the diffusion transport equation in multiple scattering
β Scribed by V. Tulovsky; L. Papiez
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 478 KB
- Volume
- 14
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
β¦ Synopsis
The solution of the Yang transport equation of the multiple scattering theory of charged particles is discussed. The method of Lie groups is utilized for the purpose of the construction of the solution of this equation. The fundamental solution of the Yang equation is provided as the closed form expression valid in the neighborhood of the center of coordinates.
π SIMILAR VOLUMES
In this paper, the hypergeometric matrix differential equation z( 1 -t)W" -zAW' + W'(C -z(B + I)) -AWB = 0 is studied. First it is proved that if matrix C is invertible and no negative integer is one of its eigenvalues, then the hypergeometric matrix function F(A, B; C; z) is an analytic solution in
In this manuscript the one dimensional fractional transport equation in which the prescribed source and angular flux are spatially quadratic is investigated within the generalized quadratic form method. It is reported that the angular flux satisfies Fick's law and the corresponding scalar flux satis
By using appropriate transformations in combination with specific Abel equations solvable in closed form containing arbitrary functions, an implicit solution as well as the associated sufficient condition are derived for certain differential equations of the Abel class of the first kind.
## The shape of a caustic and its initial curve about a crack in fracture mechanicsjor plane elastic media is defined by a pair of equations, theJirst of which does not in general possess a closed-form solution, being ojjijth or higher degree and, frequently, transcendental. A closedform solution of