A multicomponent film model incorporating a general matrix method of solution to the Maxwell-Stefan equations

AIChE Journal ◽  
1976 ◽  
Vol 22 (2) ◽  
pp. 383-389 ◽  
Author(s):  
Rajamani Krishna ◽  
G. L. Standart
Keyword(s):  
Matrix Method ◽  
General Matrix ◽  
Film Model ◽  
Method Of Solution

Equations de bilan dépendentes du temps appliquées aux collisions inélastiques

1982 ◽  
Vol 60 (5) ◽  
pp. 654-658
Author(s):  
A. Lupaşcu ◽  
St. Tudorache ◽  
I. M. Popescu
Keyword(s):  
Cross Sections ◽  
Matrix Method ◽  
Inelastic Collisions ◽  
Time Dependent ◽  
Rate Equations ◽  
General Matrix ◽  
Dependent Rate ◽  
Minimal Information

A general matrix method for the time dependent rate equations applied to inelastic collisions is presented. The minimal information needed to compute the collisional cross-sections is deduced and used to study the particular case of two excited levels.

Dynamic Theory of Asymetric X-Ray Diffraction for Strained Crystal Wafers

1987 ◽  
Vol 31 ◽  
pp. 161-165 ◽  
Author(s):  
D. W. Berreman ◽  
A. T. Macrander
Keyword(s):  
Numerical Solution ◽  
Matrix Method ◽  
Dynamic Theory ◽  
Grazing Incidence ◽  
Dynamical Theory ◽  
Matrix Approach ◽  
X Ray Diffraction ◽  
General Matrix ◽  
X Ray ◽  
Strained Crystal

A very accurate 8X8 matrix approach to dynamical theory of X-ray diffraction in which fewer approximations are made than in the classic vonLaue approach, is described here. The method is related to the very general matrix method of Kokushima and Yamakito, and is particularly suited to numerical solution with a computer. It can be used to solve problems in ideal, undistorted crystals with high precision even at near grazing incidence without special consideration of refraction or external reflection. It is also easy to apply to problems where periodicity of oblique Bragg planes varies in the direction normal to the surface. Such strain may be induced, for example, by variation of composition with depth. Certain problems wherein simultaneous diffraction by two sets of Bragg planes occurs can also be treated by this approach.

A Matrix Method for the Numerical Solution of Linear Differential Equations with Variable Coefficients

1957 ◽  
Vol 61 (554) ◽  
pp. 133-134
Author(s):  
E. A. Winn
Keyword(s):  
Differential Equations ◽  
Matrix Method ◽  
High Speed ◽  
Input Function ◽  
Variable Coefficients ◽  
Linear Differential Equations ◽  
Order Of Accuracy ◽  
The Matrix ◽  
Method Of Solution ◽  
Linear Differential

A method of solution of linear differential equations is derived which requires no special starting procedure, and which is, in principle at least, capable of extension to any order of accuracy. Further advantages of the method are that boundary conditions are easy to satisfy, and that the solution of families of equations differing only in the input function requires little extra computation. The method requires the reciprocation of a matrix of order equal to the number of points for which a solution is to be obtained, but this can be much simplified by suitably partitioning the matrix, and with most automatic high-speed computers the reciprocation of a matrix is in any case an easily programmed operation.

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