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Biochemical and mechanical processes in synovial fluid - modeling, analysis and computational simulations
Pustějovská, Petra ; Málek, Josef (advisor) ; Süli, Endré (referee) ; Jäger, Willi (referee) ; Maršík, František (referee)
vi Title: Biochemical and mechanical processes in synovial fluid - modeling, mathematical analysis and computational simulations Author: Petra Pustějovská (petra.pustejovska@karlin.mff.cuni.cz) Department: Matematický ústav UK, Univerzita Karlova v Praze Institut für Angewandte Mathematik, Universität Heidelberg Supervisors: prof. RNDr. Josef Málek CSc., DSc. (malek@karlin.mff.cuni.cz) Matematický ústav UK, Univerzita Karlova v Praze, Prof. Dr. Dr. h.c. mult. Willi Jäger (jaeger@iwr.uni-heidelberg.de) Institut für Angewandte Mathematik, Universität Heidelberg Abstract: Synovial fluid is a polymeric liquid which generally behaves as a viscoelastic fluid due to the presence of polysaccharide molecules called hyaluronan. In this thesis, we study the biological and biochemical properties of synovial fluid, its complex rheology and interaction with synovial membrane during filtration process. From the mathematical point of view, we model the synovial fluid as a viscous incompressible fluid for which we develop a novel generalized power-law fluid model wherein the power-law exponent depends on the concentration of the hyaluronan. Such a model is adequate to describe the flows of synovial fluid as long as it is not subjected to instantaneous stimuli. Moreover, we try to find a suitable linear viscoelastic model...
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Thermodynamic analysis of processes in Hydrogen fuel cells.
Pavelka, Michal ; Maršík, František (advisor) ; Grmela, Miroslav (referee) ; Sciacovelli, Adriano (referee)
Non-equilibrium thermodynamics, which serves as a framework for formulating evolution equations of macroscopic and mesoscopic systems, is briefly reviewed and further developed in this work. For example, the relation between the General Equation for the Nonequilibrium Reversible- Irreversible Coupling (GENERIC) and (ir)reversibility is elucidated, and Onsager-Casimir reciprocal relations are shown to be an implication of GENERIC. Non-equilibrium thermodynamics is then applied to describe fuel cells and related devices, and theoretical conclusions are compared to experimental data. Moreover, a generalization of standard exergy analysis is developed bringing a new method for revealing a map of useful work losses in electricity producing devices. This method requires a non-equilibrium thermodynamic model, and so the general theory of non- equilibrium thermodynamics and optimization of real power generating devices stand side by side.
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Application of spectral element method in fluid dynamics
Pech, Jan ; Maršík, František (advisor) ; Hron, Jaroslav (referee)
This work presents application of spectral element method (SEM) for solving partial differential equations. This method can be seen as combination of spectral method (SM) and finite element method (FEM). Computational domain is decomposed to smaller elements, what enable description of more general geometries. On each element is then used the spectral method, which brings high accuracy. In this work the basic theory is presented for SM and SEM with emphasize to facilitate application of this method in developing computer programs. Numerical scheme is presented on several appropriate examples. The result of this work is in comparison of solution of chosen problems obtained by SM and SEM from written program. Comparison with professional software is also done and shows power of spectral methods.
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Analysis of Stability of Steady and Time Periodic Flow in a Pipe
Průša, Vít ; Maršík, František (advisor) ; Neustupa, Jiří (referee) ; Healy, Jonathan (referee)
The text considers stability analysis of steady and time dependent flow in a pipe of circular cross section, whereas the steady flow is considered not only with the classical no-slip boundary condition on the pipe's wall but also with Navier's slip boundary condition. The problems are investigated both by theoretical and computational means mainly in framework of linear stability theory, and both approaches are based on detailed knowledge of spectrum of the Stokes operator that represents the damping term in stability equations. Concerning theoretical results a sufficient condition for monotone linear stability of oscillatory and steady flow (with the classical no-slip boundary condition) is derived by purely analytical means. For flow with Navier's slip boundary condition the text presents several heuristic arguments on possible influence of the choice boundary of condition on stability characteristics of the flow. The heuristic arguments are verified by computational means, and computational means are also used to investigate stability of time dependent flow with the classical no-slip boundary condition, mainly for parameter values not covered by theoretical results. In contrast with results available in literature, the numerical approach also considers nonaxisymmetric disturbances to the flow. It was...
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Elastic properties of blood veins with a scaffold
Frost, Miroslav ; Maršík, František (advisor) ; Kružík, Martin (referee)
Presented master's thesis deals with modeling of a NiTiNOL wire under thermal and uniaxial mechanical loading. NiTiNOL can undergo reversible martensitic phase transformation and thus belongs among shape memory alloys. In the form of a thin wire it is used in many applications (e.g. as a reinforcement for veins). MT is studied with respect to the extended non-equilibrium thermomechanics of mixtures and the Clusius-Clapeyron equation is derived for it. A new phenomenological model iRLOOP, developed at AS CR, simulating thermomechanical behavior of a NiTiNOL wire is mathematically formulated. Restrictions on tting functions in proposed hysteresis mechanism are derived from the second law of thermodynamics. The existence and uniqueness of the solution of an initial problem are proven for the superelasticity model. Experiments are compared with results modeled by numerical implementation of iRLOOP.
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Optimization of operation of renewable electric energy sources based on fuel cells, accumulators and FV panels for small powers.
Holeček, Martin ; Maršík, František (advisor) ; Beran, Zdeněk (referee)
The first part of the research is motivated to provide citations deeper to the literature of optimal control principles that could be linked to the system optimization problem, discuss these principles and various ways to apply them. Then we describe one fuel cell, accumulator and photovoltaic standalone system along with the most used equations from the literature. Next, we formulate the problem of optimal control for this system to optimize the system financial cost in the best case and we process to describe and discuss the numerical optimal control algorithm - multiple shooting - that will be used to solve the problem, that was not used in literature so far in conjunction with the problem. The codes and numerical simulations are also provided. Powered by TCPDF (www.tcpdf.org)
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Aerodynamic Optimization of Airfoils and Wings Using Fast Solver
Hájek, Jaroslav ; Šafařík, Pavel (advisor) ; Maršík, František (referee) ; Stebel, Jan (referee)
This thesis is concerned with aerodynamic optimization of airfoils and wings. It focuses at using very fast solvers based on hybrid potential methods to evaluate the aerodynamic performance of the airfoils and wings. Compared to more widely used CFD solvers which are more computationally demanding, use of fast solvers brings different possibilities and different problems to tackle, some of which are analyzed in this work. A state-of-the-art fast solver for airfoils is resented, and a fast solver for slender wings is developed, and some of its aspects are discussed. An innovative evolutionary optimization algorithm is presented and both solvers are hen utilized to solve real-life airfoil and wing optimization problems.
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Mathematical analysis and numerical simulation of bone remodeling
Čížek, Pavel ; Maršík, František (advisor) ; Hron, Jaroslav (referee)
In the presented work, we study a model of bone deformation caused by action of external forces. After the biological introduction, in which we describe a bone remodelling process and its connection with bone deformation, we deal with conservation laws and material characteristics of a bone. We define weak formulation. Further, we linearize the equations and prove existence and uniqueness of the solution. Consecutively, we describe the finite element method and the programming of this method for the computing of the approximate solution of the problem using the logic of object-oriented programming. We also adduce a description of the used data structures. In the conclusion, we present numerical results reached by the described program that represent deformation of femur and deformation of vertebras and intervertebral foramina.
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Modelování růstu kostní chrupavky na biodegrabilním scafoldu při mechanickém zatěžování.
Kozák, Jakub ; Maršík, František (advisor) ; Stará, Jana (referee)
In the present work we study modeling of hyaline cartilage growth. We start with exploration of the background of the problem, i.e. biology of cartilage, possibilities of cartilage healing and methods of tissue engineering. Derivation of modified mass action law follows. It provides possibility of including chemical reactions and mechanical stimuli into the model. We use this equation for mathematical formulation of the cartilage growth model, which has the form of reaction-diffusion equations. This model is analyzed then and compared with the experiment. It gives some parameters of the model which quantitatively describe cartilage growth in vitro.
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Shear layer-synthetic jet interaction.Qualitative solution
Falta, Jiří ; Maršík, František (advisor) ; Popelka, Lukáš (referee) ; Uruba, Václav (referee)
This thesis investigates possibilities of suppressing the boundary layer separation which is made by controling boundary layer stability. Orr-Sommerfeld equation is numerically solved for this purpose and its solution was tested on Blasius boundery layer which stability is described in many specialized publications. Transition to turbulence is found out by eN method. Single-variable description of velocity pro les on own surface, which is based on the aproximative properties of Falkner-Skan equation, was used. Process of transition on the aerofoil NACA 63-418 was solved as an example of using proposed computational programs.
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