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National Repository of Grey Literature 2 records found  Search took 0.00 seconds. 
Numerical Analysis of a polydisperse sedimentation problem
 Dvořák, Daniel ; Felcman, Jiří (advisor) ; Feistauer, Miloslav (referee)
The problem of the polydisperse sedimentation as the system of the partial differential equations is formulated. The hyperbolicity of the problem and the determination of the eigenvalues of the Jacobi matrix of the flux function is studied. Based on the conservation laws of the mass and momentum completed by the constitutive relations the so called MLB model is derived. The one- dimensional problem is formulated. The Sherman-Morrison formula is used to find the inverse matrix of the sum of the diagonal matrix and the matrix being the product of two vectors. In order to find the eigenvalues of the Jacobi matrix of the flux function the rank two perturbation of the diagonal matrix is used. In such a way the problem of the determination of the eigenvalues is reformulated as the solution of the so called secular equation. The eigenvalues can be localized and the strong hyperbolicity of the problem under certain conditions is proved. 1
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Numerical solution of a secular equation for rayleigh waves in a thin semi-infinite medium made of a composite material
 Červ, Jan ; Adámek, V. ; Valeš, František ; Parma, Slavomír
The traditional way of deriving the secular equation for Rayleigh waves propagating along the stress-free edge of a thin semi-infinite composite is presented. It means that it is necessary to find a general steady-state solution that vanishes at infinity. The secular equation is then obtained by vanishing of the surface traction at the stress-free edge. For the solution of such secular equation it is necessary to precompute some roots of characteristic quartic equation. The method shown in this paper, based on displacement formulation, leads to the so-called implicit secular equation. The numerical approach to the solution is shown.
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