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Optimization of the Water Supply Network of Počátky Town
Pavelka, David ; Netušil, Lukáš (referee) ; Kučera, Tomáš (advisor)
This diploma thesis focuses on the optimization of water supply system in the town of Počátky. It describes the process of creating a mathematical model needed for the hydraulic analysis, which was used to assess the water supply system Počátky. This thesis task is to apprise reader, with a basic distribution in the drinking water supply, how to proceed in collecting data on hydraulic analysis requirements and using tools and means used in hydraulic analysis. Conclusions are processed variants for possible optimization of water supply system Počátky.
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Evaluation of particle deposition rate in cement plant ductwork
Dorniak, Michal ; Kilkovský, Bohuslav (referee) ; Vondál, Jiří (advisor)
The submitted thesis deals with calculation of pressure drop in pipeline of cement industry, which is directly correlated with energy consumption of raw mill exhaust fans. The introduction in submitted thesis describes theoretical basics of cement production. Part of theoretical analysis is about detailed study of calculations of different friction factors. Separately for gas and separately for solids. In the practical part, a mathematical model of universal configuration of pipeline for pressure drop calculations was created. The last part evaluate impacts of pressure drop on energetic demands of raw mill exhaust fans.
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Mathematical modeling of early embryogenesis processes
Dunajová, Michaela ; Šejnoha, Jiří (advisor) ; Drutovič, David (referee)
1 Abstract: Early embryogenesis is a fundamental phenomenon of developmental biology, which involves the establishment of the first structures within embryos. The work focuses on mathematical spatial models of mammalian blastulation, which were created based on spatial approach. We discuss and compare six mo- dels, which simulate the differentiation of cell lines and the formation of blas- tocyst structures. Models are based on local rules, using considerable cellular abstraction. Models focus on the processes of differentiation of the blastomere into the trophoectoderm and the inner cell mass, followed by the establishment of the structure of the epiblast and the primitive endoderm.
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Bohl-Marek decomposition applied to a class of biochemical networks with conservation properties
Papáček, Štěpán ; Matonoha, Ctirad ; Duintjer Tebbens, Jurjen
This study presents an application of one special technique, further called as Bohl-Marek decomposition, related to the mathematical modeling of biochemical networks with mass conservation properties. We continue in direction of papers devoted to inverse problems of parameter estimation for mathematical models describing the drug-induced enzyme production networks [3]. However, being aware of the complexity of general physiologically based pharmacokinetic (PBPK) models, here we focus on the case of enzyme-catalyzed reactions with a substrate transport chain [5]. Although our ultimate goal is to develop a reliable method for fitting the model parameters to given experimental data, here we study certain numerical issues within the framework of optimal experimental design [6]. Before starting an experiment on a real biochemical network, we formulate an optimization problem aiming to maximize the information content of the corresponding experiment. For the above-sketched optimization problem, the computational costs related to the two formulations of the same biochemical network, being (i) the classical formulation x˙(t) = Ax(t) + b(t) and (ii) the 'quasi-linear' Bohl-Marek formulation x˙M(t) = M(x(t)) xM(t), can be determined and compared.
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Quantifying aspects of orthosis in relation to ankle sprain
Znášiková, Ivona ; Jelen, Karel (advisor) ; Kubový, Petr (referee)
Title: Quantifying aspects of orthosis in relation to ankle sprain Objectives: To detect whether various types of ankle bracing affect dynamic postural stability. Investigation of attenuation of vertical forces in different conditions. To determine range of motion for each orthosis. Methods: Monitoring of dynamic variables by piezoelectric measuring device - Kistler recording of dynamic changes. Mathematical modeling of damping characteristics and detected variables. Measuring of range of motion by goniometer with and without orthosis. Results: Results suggest, that bracing conditions have an effect on dynamic postural stability and orthosis limit range of motion. Attenuation of vertical forces is affected by using orthosis. Keywords: ankle instability, orthosis, mathematical modeling, stabilization
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Modeling of water quality in the water supply network
Dukát, Petr ; Rajnochová, Markéta (referee) ; Ručka, Jan (advisor)
This thesis looks at water quality modelling in the water network, focusing on water age. The initial part of the work identifies the factors that lead to an increase in water age in water supply networks. The theoretical part of the work presents the mathematical relationships and logistical steps that software tools apply to simulate water quality indicators in a water supply network. In the practical part of the work, a hydraulic model of a water distribution system with a total length of 302,1 km was constructed. Measurement campaign was carried out to calibrate and verify created hydraulic model. Using this hydraulic model, water age for existing and possible scenarios was simulated. The results of the work have revealed parts of the water supply network containing high water age and are intended to encourage the progressive water distribution systems management philosophy.
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Optimization Risk Modelling in Strategic Applications
Kovalčík, Marek ; Štětina, Josef (referee) ; Popela, Pavel (advisor)
The aim of this diploma thesis is to design and efficiently implement a framework to support optimization modelling. The emphasis is placed on two-stage stochastic optimization problems and performing calculations on large data. The computing core uses the GAMS system and with using its application interface and Python programming language, the user will be able to efficiently acquire and process input and output data. The separation of the data logic and the application logic then offers a wide range of options for testing and experimenting with a general model on dynamically changing input data. The thesis is also focused on an evaluation of the framework complexity. The framework performance was evaluated by measuring the time required to complete the required task for various use cases, on the increasing sample size of input data.
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Evaluation of particle deposition rate in cement plant ductwork
Dorniak, Michal ; Kilkovský, Bohuslav (referee) ; Vondál, Jiří (advisor)
The submitted thesis deals with calculation of pressure drop in pipeline of cement industry, which is directly correlated with energy consumption of raw mill exhaust fans. The introduction in submitted thesis describes theoretical basics of cement production. Part of theoretical analysis is about detailed study of calculations of different friction factors. Separately for gas and separately for solids. In the practical part, a mathematical model of universal configuration of pipeline for pressure drop calculations was created. The last part evaluate impacts of pressure drop on energetic demands of raw mill exhaust fans.
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Optimization Models of Risk in Energy Systems
Tetour, Daniel ; Cabalka, Matouš (referee) ; Popela, Pavel (advisor)
The diploma thesis deals with mathematical modeling of the resource allocation problem in an energy system with respect to technical parameters of the used resources. The model includes random input variables affecting the amount of demand and constraints related to associated risks. The thesis addresses control of the operation of various types of boilers and also extends the system with a heat storage tank examining its impact on the behavior of the system and achieved results. The optimization model is based on a multi-period two-stage scenario model of stochastic programming and works with simulated data, which combines real data, statistically determined estimates, and the use of logistic regression. The implementation utilizes GAMS software. When comparing the achieved results with the current state, it was found that the heat storage tank has a positive effect on the function of the system as it allows for extended usage of the cheaper unregulated sources by storing surplus heat, and thus helps to reduce the overall costs of the system.
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