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Non-equilibrium Thermodynamics of Hyperbolic Systems
Sýkora, Martin ; Pavelka, Michal (advisor) ; Hütter, Markus (referee) ; Lukáčová - Medvidová, Mária (referee)
Continuum mechanics and thermodynamics have been used in many fields from sci- ence to industry to medicine. While simple materials have already been described, for instance by the famous Navier-Stokes equations, more complex materials like superfluids are still not completely understood. Multiple frameworks, often based on balance laws and thermodynamic closures, are used. In this thesis, an alternative General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) framework is studied. We apply this method, based on Hamiltonian mechanics and gradient dynamics, to a wide range of settings from a simple continuum to mixtures, superfluids and non-Fourier heat conduction. We study the symmetric hyperbolicity of the resulting equations, as it guarantees the well-posedness of the system, and suggest extensions to the already-known symmetric hyperbolic equations. We derive new models, compare them to more classical theories and study what phenomena they can and cannot describe, both analytically and numerically. 1
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Mathematical modeling of blood coagulation process
Čapek, Marek ; Hron, Jaroslav (advisor) ; Bodnár, Tomáš (referee) ; Lukáčová Medvídová, Mária (referee)
On vessel wall injury the complex process of blood coagulation is set off. It is composed of vasoconstriction, primary hemostasis, secondary hemostasis and fibrinolysis. This work enriches current model of primary hemostasis of Storti. The previous model used ALE formalism for tracing of development of platelet plug. The phase field method is used for tracing of the development of interface blood-thrombus. Storti's primary hemostasis was extended to capture the fact, that the platelets can be activated in the blood flow in the area of reactive surface not only by influence of chemical agents like thromboxane, ADP and thrombin but also by their exposure to elevated values of shear stress. In our first approach we deal the emerging thrombus as a fluid with very high viscosity. In the second approach it was assumed, that platelet plug develops as a viscoelastic material according to constitutive equations of clot introduced by Kempen. In this manner platelet clot matures into blood clot. In both approaches the blood is represented as a non-Newtonian fluid. The framework of the phase field method was applied also to the model of high shear rate thrombosis of Weller. Weller's original model of Weller took advantage of the cylindrical symmetry of computational domains for its computations, hence the...
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