|
|
Diffuse interface models in theory of interacting continua
Řehoř, Martin ; Průša, Vít (advisor) ; Garcke, Harald (referee) ; Rohde, Christian (referee)
We study physical systems composed of at least two immiscible fluids occu- pying different regions of space, the so-called phases. Flows of such multi-phase fluids are frequently met in industrial applications which rises the need for their numerical simulations. In particular, the research conducted herein is motivated by the need to model the float glass forming process. The systems of interest are in the present contribution mathematically described in the framework of the so-called diffuse interface models. The thesis consists of two parts. In the modelling part, we first derive standard diffuse interface models and their generalized variants based on the concept of multi-component continuous medium and its careful thermodynamic analysis. We provide a critical assessment of assumptions that lead to different models for a given system. Our newly formulated class of generalized models of Cahn-Hilliard-Navier-Stokes-Fourier (CHNSF) type is applicable in a non-isothermal setting. Each model belonging to that class describes a mixture of separable, heat conducting Newtonian fluids that are either compressible or incompressible. The models capture capillary and thermal effects in thin interfacial regions where the fluids actually mix. In the computational part, we focus on the development of an efficient and robust...
|
|
|
Approximations by low-rank matrices and their applications
Outrata, Michal ; Tůma, Miroslav (advisor) ; Rozložník, Miroslav (referee)
Consider the problem of solving a large system of linear algebraic equations, using the Krylov subspace methods. In order to find the solution efficiently, the system often needs to be preconditioned, i.e., transformed prior to the iterative scheme. A feature of the system that often enables fast solution with efficient preconditioners is the structural sparsity of the corresponding matrix. A recent development brought another and a slightly different phe- nomenon called the data sparsity. In contrast to the classical (structural) sparsity, the data sparsity refers to an uneven distribution of extractable information inside the matrix. In practice, the data sparsity of a matrix ty- pically means that its blocks can be successfully approximated by matrices of low rank. Naturally, this may significantly change the character of the numerical computations involving the matrix. The thesis focuses on finding ways to construct Cholesky-based preconditioners for the conjugate gradi- ent method to solve systems with symmetric and positive definite matrices, exploiting a combination of the data and structural sparsity. Methods to exploit the data sparsity are evolving very fast, influencing not only iterative solvers but direct solvers as well. Hierarchical schemes based on the data sparsity concepts can be derived...
|
|
|
Incomplete Cholesky factorization
Hoang, Phuong Thao ; Tůma, Miroslav (advisor) ; Tichý, Petr (referee)
The thesis is about the incomplete Cholesky factorization and its va- riants, which are important for preconditioning a system with symmetric and positive definite matrix. Our main focus is on solving these systems, which arise in many technical applications and natural sciences, using preconditioned Con- jugate Gradients. Besides many other ways we can apply Cholesky factorization approximately, incompletely. In this thesis we study existence of the incomplete Cholesky factorization and we evaluate behaviour and potential of different vari- ants of the generic algorithm. 1
|
|
|
Optimation of inoculation process of ductile iron
Ulm, Daniel ; Pecina, Vladimír (referee) ; Roučka, Jaromír (advisor)
The master‘s thesis deals in theoretical part with the casting classification, ductile iron casting, its inoculation and modification and quality evaluation using thermal analysis, image analysis and testing of mechanical properties. The aim of the practical part was to test the effects of preconditioning on the properties of ductile iron and to find out whether it is able to replace the current method of inoculation or to increase the mechanical properties of ductile iron castings. The state of the ductile iron was under control by spectral and thermal analysis. The mechanical properties and image analysis were checked on finished casting.
|
|
|
Algebraic preconditioning for Biot-Barenblatt poroelastic systems
Blaheta, Radim ; Luber, Tomáš
Poroelastic systems describe fluid flow through porous medium coupled with deformation of the porous matrix. In this paper, the deformation is described by linear elasticity, the fluid flow is modelled as Darcy flow. The main focus is on the Biot-Barenblatt model with double porosity/double permeability flow, which distinguishes flow in two regions considered as continua. The main goal is in proposing block diagonal preconditionings to systems arising from the discretization of the Biot-Barenblatt model by a mixed finite element method in space and implicit Euler method in time and estimating the condition number for such preconditioning. The investigation of preconditioning includes its dependence on material coefficients and parameters of discretization.
|
|
|
Cardioprotection induced by changes in abiotic environmental factors
Kubátová, Hana ; Vybíral, Stanislav (advisor) ; Žurmanová, Jitka (referee)
Cardiovascular diseases are one of the most frequent causes of death worldwide. Methods of limiting the ischemia-reperfusion injury, which occurs as a result of acute myocardial infarction (MI), have therefore been receiving significant attention. Preconditioning through ischemia application, cold exposure or physical exercise reduces the size of an infarction and the occurrence of ventricular arrhythmias. The exact mechanism behind this process has not yet been fully comprehended; nevertheless important roles are played by factors such as the maintenance of calcium homeostasis, the opening of ATP-dependent potassium channels (KATP) and the prevention of the Mitochondrial Permeability Transition pore (MPTP) opening. Chronic hypoxia and exercise have also been proven to have a cardioprotective effect, which is to be at least partially attributed to the intensified activity of antioxidant enzymes and the opening of KATP. During winter the risk of MI is increased for a wide range of patients. In winter swimmers, the stress caused by a cold stimulus is reduced. However, a mild stress is necessary to initiating cardioprotection. At present, there is unfortunately insufficient information available regarding the effects of long term cold adaptation on the size reduction of MI. Some studies suggest,...
|
|
|
Cardiac ischemic tolerance of hypertensive rats
Jelínek, Jan ; Neckář, Jan (advisor) ; Sotáková, Dita (referee)
The aim of this thesis is to summarize current knowledge about the influence of the ischemic- reperfusion injury at the myocard of hypertensive subjects. First part of this thesis is focused on the description of ischemia, reperfusion and changes in the myocardial metabolism during these processes. These changes in the myocardial metabolism are for example necrosis or apoptosis of the myocardial cells. The second part describes the currently known cardioprotective phenomena. This part also compares their effects. The signalization of preconditioning, the second window of preconditioning and the postconditioning are described here in more details. Third part is focused on the description of the risk factors connected to the ICHS and hypertension. It describes also classes of hypertension, clinical and experimental methods of hypertension treatment, description of the laboratory breeds of hypertensive rats. In the last part of this thesis I describe the influence of hypertension on the I-R injury in current laboratory studies. In the most studies spontaneously hypertensive rats (SHR) were used. As a normotensive controls Wistar-Kyoto rats were mostly used. For some other experiments transgenic genetic rats (TGR) were used. Powered by TCPDF (www.tcpdf.org)
|
|
|
Effect of morphine on the resistance of the heart to ischemia
Mošovská, Linda ; Neckář, Jan (advisor) ; Žurmanová, Jitka (referee)
2. Abstract Opioids are considered as dangerous and addictive substances, mainly due to synthetic opioids such as heroin. It was discovered, that these substances can play an important role in myocardial ischemia because they can limit the damage of the heart tissue that occurs during a heart attack. Since that heart attack is the most common cardiovascular disease, the protective effect is significant. Cardioprotective effect is mainly mediated through δ opioid receptors, but the few studies have shown cardioprotective effect mediated through κ opioid receptors. The protective effect occurs by activation of opioid receptors by their agonists (eg. morphine or TAN-67), either before ischemia (opioid preconditioning) or before reperfusion (opioid postconditioning). The signaling pathway of cardioprotection include mitochondrial KATP channel, Gi/o proteins, protein kinase C, tyrosine kinases and reactive oxygen species.
|
|
|
The role of mitochondria in cardioprotective effect induced by hypoxia in rat
Lomnický, Matouš ; Žurmanová, Jitka (advisor) ; Hlaváčková, Markéta (referee)
Aerobic organisms need sufficient oxygen supply to maintain homeostasis. These organisms are frequently exposed in hypoxic environments naturally, and also occur in hypoxic states in various pathological conditions. Cardioprotective effect of hypoxia had been recognised more than 30 years ago; and later on, cardioprotective effects of ischemic preconditioning were discovered. Long term exposure to hypobaric hypoxia activates cardioprotective mechanisms, which lower the aftermathes of short term ischemia of myocardia and the effects of further health complications. The core of protective mechanisms has not yet been fully clarified. This work deals with the significance of mitochondria on cardioprotection during hypobaric hypoxia adaptation. This work describes physiological adaptive processes on selected animals on natural hypoxic conditions and also molecular mechanisms, examined on experimental models. Molecular mechanisms of the origins of cardioprotective effects discovered so far, mainly indicate PKC signal pathways through thyrosine kinase and mitogenes of activated kinase and also indicate an activation of sarcKATP-channels and mitoKATP-channels. Opening of these channels can protect mitochondria against a Ca2+ overload, or can lead to an increase in mitochondrial capacity which is possibly connected...
|
|
|
Algebraic Error in Matrix Computations in the Context of Numerical Solution of Partial Differential Equations
Papež, Jan ; Strakoš, Zdeněk (advisor) ; Ramage, Alison (referee) ; Vejchodský, Tomáš (referee)
Title: Algebraic Error in Matrix Computations in the Context of Numerical Solution of Partial Differential Equations Author: Jan Papež Department: Department of Numerical Mathematics Supervisor: prof. Ing. Zdeněk Strakoš, DrSc., Department of Numerical Mathe- matics Abstract: Solution of algebraic problems is an inseparable and usually the most time-consuming part of numerical solution of PDEs. Algebraic computations are, in general, not exact, and in many cases it is even principally desirable not to perform them to a high accuracy. This has consequences that have to be taken into account in numerical analysis. This thesis investigates in this line some closely related issues. It focuses, in particular, on spatial distribution of the errors of different origin across the solution domain, backward error interpretation of the algebraic error in the context of function approximations, incorporation of algebraic errors to a posteriori error analysis, influence of algebraic errors to adaptivity, and construction of stopping criteria for (preconditioned) iterative algebraic solvers. Progress in these issues requires, in our opinion, understanding the interconnections between the phases of the overall solution process, such as discretization and algebraic computations. Keywords: Numerical solution of partial...
|
guest ::
