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Projection method applied to modelling blood flow in cerebral aneurysm
Hrnčíř, Jakub ; Hron, Jaroslav (advisor) ; Knobloch, Petr (referee)
This thesis is motivated by a problem of cerebral aneurysms, which are abnormal bulges on the arteries which supply blood for our brain. These aneurysms can rupture and cause death or permanent neurological deficits. To study the evolution of aneurysms and assess the risk of rupture, mathematical modelling might be used to compute otherwise unobtainable information about blood flow inside the aneurysm. For this reason it is essential to be able to model blood flow in sufficiently high resolution. A goal of this thesis was to implement standard projection method for the solution of unsteady incompressible Navier-Stokes equations using the free finite element software FEniCS to create a working code adjusted to the need of this particular application. The incremental pressure correction scheme was chosen. Various shortcomings of this method are described and a proper choice of boundary conditions and other implementation issues are discussed. A comparison of computed important hemodynamic indicator wall shear stress using new and previously used solution approach are compared. A test of the new code for parallel efficiency and performance on finer meshes for a real medical case was conducted. Powered by TCPDF (www.tcpdf.org)
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Projection method applied to modelling blood flow in cerebral aneurysm
Hrnčíř, Jakub ; Hron, Jaroslav (advisor) ; Knobloch, Petr (referee)
This thesis is motivated by a problem of cerebral aneurysms, which are abnormal bulges on the arteries which supply blood for our brain. These aneurysms can rupture and cause death or permanent neurological deficits. To study the evolution of aneurysms and assess the risk of rupture, mathematical modelling might be used to compute otherwise unobtainable information about blood flow inside the aneurysm. For this reason it is essential to be able to model blood flow in sufficiently high resolution. A goal of this thesis was to implement standard projection method for the solution of unsteady incompressible Navier-Stokes equations using the free finite element software FEniCS to create a working code adjusted to the need of this particular application. The incremental pressure correction scheme was chosen. Various shortcomings of this method are described and a proper choice of boundary conditions and other implementation issues are discussed. A comparison of computed important hemodynamic indicator wall shear stress using new and previously used solution approach are compared. A test of the new code for parallel efficiency and performance on finer meshes for a real medical case was conducted. Powered by TCPDF (www.tcpdf.org)
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Replicator dynamics with mutations
Hrnčíř, Jakub ; Pražák, Dalibor (advisor) ; Kaplický, Petr (referee)
This thesis deals with the subject of implementing simplified principle of mutations into the replicator dynamics. In this thesis, I have shown the derivation of the basic replicator dynamics and on this basis I have derived generalized replicator dynamics with a deterministic model of mutations. Thesis also contains an analysis of general properties of these two models. Consequences of implementing mutations are demonstrated by means of analysis of three typical examples from the evolutionary game theory. I used the models called Hawk-Dove, Rock-Scissors-Paper and a modification of the Repeated Prisoner's Dilemma, to which I have paid the closest attention. The analysis shows in what ways the number of stationary points and their stability changes. Powered by TCPDF (www.tcpdf.org)
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