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The flow of magnetic liquid with Bingham model application
Stejskal, Jan ; Krausová, Hana (referee) ; Haluza, Miloslav (advisor)
Main topic of this thesis are magnetic fluids. These are specific type of fluids which can simplistically be considered as Bingham fluids. Main issues regarding the magnetic fluids mentioned in this thesis are: rheological properties of the magnetic fluids, behaviour of the magnetic fluids and the use of the magnetic fluids in industrial applications. Main goal is to apply Binghams model on the the magnetic fluids assuming that this model can be applied with a good accuracy. Equations which describe behaviour of the Bingham fluids are constructed. Some assumptions which have to be respected to use this analytical equations for magnetic fluids are formulated. Flow of bingham fluid is analytically solved in some simplificated cases with consideration of laminar flow. Analytical results are confronted with numerical ones obtained from CFD software Fluent for the purpose of verification.
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The Shadow Vector in the Lanczos Method
Tichý, Petr
The left starting vector, also called shadow vector, is one of the parameters of Krylov subspace methods for solving systems of linear equations based on the nonsymetric Lanczos process. We will shov various choices of this vector that cause equality of certain residual vectors of another Krylov subspace method like GMRES.
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Structure and dynamics of shell sources in general relativity
Turnovec, Aleš ; Žofka, Martin (advisor) ; Langer, Jiří (referee)
Cylindrically symmetric shell sources are studied and a general form of induced energy-momentum tensor of a collapsing shell is presented. The actual movement of the shell is numerically solved for a case when dynamics of the system is determined by energy conservation per unit length. It is then shown that additional assumptions can prevent the collapse, e. g. induced energy-momentum tensor as perfect fluid or null dust of counter-rotating particles. Collapse can be prevented also by introducing Thorne's C-energy into the system.
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Water column separation under hydraulic turbine runner during unsteady operating regimes.
Vašek, Lubomír ; Rudolf, Pavel (referee) ; Habán, Vladimír (advisor)
In this diploma thesis called Water column separation under the hydraulic turbine runner during unsteady operating regimes are solved the pressure pulsations of the reverse water hamer. In the thesis is deduced a mathematical relationship of elaboration the numerice model which is based on equations of continuity and equations of forces equilibrium. Numerical model is created in MS Excel uses for computation the numerical method Lax-Wendrof that allows consideration of variable sound speed as function of static pressure and allows variable lenght step in computation domain. Reverse water hammer is in the thesis solved with consideration of rotating flow behind shut-off valve, where we expect forming of vortex rope. This situation can be applied on the closing water turbine which has vertex rope under turbine runner. Specifically for this thesis was carried out the experiment of the reverse water hammer. Constants going into numerical solution are optimalized with using experiment and pressure pulsation are compared between numerical solution and experiment.
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Fenomén nehomogenity materiálu v NMR
Fiala, P. ; Kroutilová, E. ; Steinbauer, M. ; Dohnal, P. ; Bartušek, Karel
This article deals with the verification of experimental results obtained by numerical simulation. We solved the effect of changes in the homogeneity of magnetic fields evoked by different samples from conductive and/or magnetic materials and the different types of inhomogeneity in the MR tomograph. Moreover, the paper will describe the suitable magnetic resonance techniques.
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A note on tension spline
Segeth, Karel
Spline theory is mainly grounded on two approaches: the algebraic one (where splines are understood as piecewise smooth functions) and the variational one (where splines are obtained via minimization of quadratic functionals with constraints). We show that the general variational approach called smooth interpolation introduced by Talmi and Gilat covers not only the cubic spline but also the well known tension spline (called also spline in tension or spline with tension). We present the results of a 1D numerical example that show the advantages and drawbacks of the tension spline.
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Modifications of the limited-memory BFGS method based on the idea of conjugate directions
Vlček, Jan ; Lukšan, Ladislav
Simple modifications of the limited-memory BFGS method (L-BFGS) for large scale unconstrained optimization are considered, which consist in corrections of the used difference vectors (derived from the idea of conjugate directions), utilizing information from the preceding iteration. For quadratic objective functions, the improvement of convergence is the best one in some sense and all stored difference vectors are conjugate for unit stepsizes. The algorithm is globally convergent for convex sufficiently smooth functions. Numerical experiments indicate that the new method often improves the L-BFGS method significantly.
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2D finite element formulation of elastic string vibrations with large displacements
Michálek, Jakub ; Horáček, Jaromír (advisor) ; Matyska, Ctirad (referee)
The thesis addresses the numerical solution of the oscillation of the vocal fold at finite strain, whereas the literature has so far been concerned with infinitesimal strain only. The geometry concerned corresponds to the easiest situation of falsetto, since we observe an isolated vocal fold. The vocal fold is treated as non-linear and non-isotropic continuum in 2D space. To demonstrate the function of the model, we simulate the behaviour of the vocal fold with the linear constitutive equation numerically. The vocal fold is modelled by the finite element method with quadratic elements for static and dynamic surface load. We show that a proper simulation of vocal fold tissue deformation requires the equations with finite strain term. Numerical simulation of the vocal fold can be used e.g. for the construction of artificial vocal folds, and for the optimization of their function. Understanding the phonatory mechanism is also essential for discovering the causes of the disorders such as the vocal nodules and for the scientific foundation of phoniatrics and education of singers. The thesis is interdisciplinary and synthesises the facts from mechanics of continuum, anatomy and education of singers.
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