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National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
Mathematical modelling of liver perfusion
 Kociánová, Barbora ; Rohan, Eduard (advisor) ; Bulíček, Miroslav (referee)
Liver perfusion can be modelled by Darcy's flow in multiple connected com- partments. The first part of the present thesis shows in detail the existence of a solution to the multi-compartmental model. The flow in each compartment in this model is characterized by a permeability tensor, which is obtained from the geometry of liver vasculature. It turns out that this tensor might be singular, which potentially causes solvability problems. The second part deals with this abnormality in one compartment. By using the theory of degenerate Sobolev spaces, an appropriate weak formulation is defined. Analogues of Poincar'e and traces inequalities in this degenerate setting are proved, which also imply the existence of the weak solutions. In addition, this part justifies another possibil- ity how to deal with degenerate permeability, which is regularizing the tensor by adding a small isotropic permeability to it. In the third part, the aim is to find subdomains of autonomous perfusion with respect to the source positions. This is formulated as a minimization problem and several numerical results are presented. 1
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Problémy a modely v předpovídání záplav
 Hokr, Milan ; Maryška, Jiří ; Šotner, O.
In the paper, we deal with the flood forecasting, in particular with determining the water flow as result of known precipitation. In the first part, we present several approaches how to express the water flow in the environment concluding underground flow, surface flow and channel flow in the ricer system (water runoff and flood routing). We discuss possibilities to simplify the shallow-water equations for slowly varying flow to either potential flow or advection-dispersion process. On the second part, we present results of two example models of 2D surface flow in the landscape, first based on the advection-dispersion representation of surface flow and the second mixed-hybrid FEM model based on potential flow approximation.
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