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Conformational behavior of dendritic branched polymers in aqueous solutions (Dissipative particle dynamics)
Suchá, Lucie ; Limpouchová, Zuzana (advisor) ; Posel, Zbyšek (referee)
Bakalářská práce se věnuje studiu konformačního chování polymerních den- drimer· ve vodných roztocích. Polymerní roztoky byly simulovány pomocí di- sipativní částicové dynamiky. Všechny simulace byly provedeny pomocí pro- gramu DL−MESO. Pro generování vstupních soubor· a zpracování výsledk· simulací byly napsány vlastní programy. Správná funkce programu a správné nastavení simulačních parametr· bylo ověřeno pomocí parametrické studie nekonečně zředěných roztok· homopolymerních dendrimer· v dobrém roz- pouštědle. 'kálovací exponent gyračního poloměru získaný pomocí simulací je v souladu s publikovanými daty. Dále bylo porovnáváno konformační chování homopolymerního a kopolymerního dendrimeru. Klíčová slova: Počítačové simulace, disipativní částicová dynamika, dendri- mer, konformační chování, vodné roztoky, větvený polymer
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Mathematical analysis and computer simulations of deformation of nonlinear elastic bodies in the small strain range
Kulvait, Vojtěch ; Málek, Josef (advisor)
Title: Mathematical analysis and computer simulations of deformation of nonlinear elastic bodies in the small strain range. Author: Vojtěch Kulvait Department: Mathematical Institute of Charles University Supervisor: prof. RNDr. Josef Málek, CSc., Dsc. Abstract: Implicit constitutive theory provides a suitable theoretical framework for elastic materials that exhibit a nonlinear relationship between strain and stress in the range of small strains. We study a class of power-law models, where the nonlinear dependence of strain on the deviatoric part of the stress tensor and its trace are mutually separated. We show that these power-law models are capable to describe the response of a wide variety of beta phase titanium alloys in the small strain range and that these models fit available experimental data exceedingly well. We also develop a mathematical theory regarding the well-posedness of boundary value problems for the considered class of power-law solids. In particular, we prove the existence of weak solutions for power law exponents in the range (1, ∞). Finally, we perform computer simulations for these problems in the anti-plane stress setting focusing on the V-notch type geometry. We study the dependence of solutions on the values of power law exponents and on the V-notch opening angle. We achieve...
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Optimisation of light conditions in buildings
Vajkay, František ; Mohelníková, Jitka (advisor)
Building physics as a branch of architecture must ensure an indoor comfort of each user and inhabitant of a building object. This involves, acoustics, indoor thermal conditions and among others also daylighting and artificial lighting of buildings. Light as a particle and an electromagnetic wave, is required by the different aspects of the human organism. It allows the living beings to see, influences skin and bones, the biorhythms, etc. Therefore, it is necessary for the engineering community to predict the correct illuminance and luminance levels acting insides. The thesis deals with such issues. More precisely, it assesses the quality of design tools and methodologies, either against CIE reference cases described in CIE 171/2006 and against real measurements done over the working plane of an indoor space located in the attic of Building D of the Institute of Building Structures, Faculty of Civil Engineering, Brno University of Technology, too. The tools tested throughout the solution of the dissertation did involve three computer programs: RADIANCE, WDLS v3.1 and WDLS v4.1, and one numerographical approach, namely the Daniljuk’s innovated methodology (sometimes even combined with the theories of BRS). In addition several software’s have had been created alongside the process assessment, just to mention the “RADIANCE Script”, “RADIANCE Data Evaluation Script” or “MuuLUX“. The later was written as a communication software allowing the connection of the KONICA-MINOLTA T10 illuminance meter to a computer with the aim of data collection while long term observation. The solution did also require the establishment of a measuring element for the determination of the light reflectance values of surfaces. The solutions, results and conclusions do describe how well did the design approaches deal while predicting the resulting awaited daylight factor levels in points over the working plane.
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Mathematical analysis and computer simulations of deformation of nonlinear elastic bodies in the small strain range
Kulvait, Vojtěch ; Málek, Josef (advisor)
Title: Mathematical analysis and computer simulations of deformation of nonlinear elastic bodies in the small strain range. Author: Vojtěch Kulvait Department: Mathematical Institute of Charles University Supervisor: prof. RNDr. Josef Málek, CSc., Dsc. Abstract: Implicit constitutive theory provides a suitable theoretical framework for elastic materials that exhibit a nonlinear relationship between strain and stress in the range of small strains. We study a class of power-law models, where the nonlinear dependence of strain on the deviatoric part of the stress tensor and its trace are mutually separated. We show that these power-law models are capable to describe the response of a wide variety of beta phase titanium alloys in the small strain range and that these models fit available experimental data exceedingly well. We also develop a mathematical theory regarding the well-posedness of boundary value problems for the considered class of power-law solids. In particular, we prove the existence of weak solutions for power law exponents in the range (1, ∞). Finally, we perform computer simulations for these problems in the anti-plane stress setting focusing on the V-notch type geometry. We study the dependence of solutions on the values of power law exponents and on the V-notch opening angle. We achieve...
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Mathematical analysis and computer simulations of deformation of nonlinear elastic bodies in the small strain range.
Kulvait, Vojtěch ; Málek, Josef (advisor) ; Kovtunenko, Victor A. (referee) ; Kružík, Martin (referee)
Title: Mathematical analysis and computer simulations of deformation of nonlinear elastic bodies in the small strain range. Author: Vojtěch Kulvait Department: Mathematical Institute of Charles University Supervisor: prof. RNDr. Josef Málek, CSc., Dsc. Abstract: Implicit constitutive theory provides a suitable theoretical framework for elastic materials that exhibit a nonlinear relationship between strain and stress in the range of small strains. We study a class of power-law models, where the nonlinear dependence of strain on the deviatoric part of the stress tensor and its trace are mutually separated. We show that these power-law models are capable to describe the response of a wide variety of beta phase titanium alloys in the small strain range and that these models fit available experimental data exceedingly well. We also develop a mathematical theory regarding the well-posedness of boundary value problems for the considered class of power-law solids. In particular, we prove the existence of weak solutions for power law exponents in the range (1, ∞). Finally, we perform computer simulations for these problems in the anti-plane stress setting focusing on the V-notch type geometry. We study the dependence of solutions on the values of power law exponents and on the V-notch opening angle. We achieve...
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Bingham-Korteweg fluids - modeling, analysis and computer simulations
Los, Tomáš ; Málek, Josef (advisor) ; Bulíček, Miroslav (referee)
Flow of granular materials is usually initiated when the shear stress is large enough and exceeds certain critical value. This can result in the presence of the dead-zones in which the flow itself does not take place. Motions of such materials are frequently described by Bingham model. Flows of granular fluids are frequently connected with the presence of free surface. In the thesis Bingham model is incorporated into a more general framework of Bingham-Korteweg fluids, which is a suitable way how to transfer free- boundary problems into the problems on fixed domains. A part of the thesis concerns mathematical analysis of interesting relevant problems for incompressible fluids. 1
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Conformational behavior of branched polymers
Wang, Xiu ; Limpouchová, Zuzana (advisor) ; Cifra, Peter (referee) ; Kolafa, Jiří (referee)
This PhD thesis is devoted to the study of the conformational behavior of branched polymers in confined volumes. This behavior depends not only on polymer architecture and composition but also on steric confinement and on interaction of polymer segments with the confining wall. Better understanding of complex entropy-to-enthalpy interplay can elucidate the mechanism of the chromatographic separation at the microscopic level. An unambiguous size-exclusion chromatography (SEC) analysis of mixtures containing different polymer architectures is difficult because the sizes of polymer coils, which determine the separation, depend not only on molar mass but also on the polymer architecture. Modern chromatographic methods combine the SEC with the interaction chromatography (IC). They exploit the fact that polymer interactions with pore walls, which are the prerequisite for efficient IC separation, depend strongly on polymer architecture. The knowledge of the conformational behavior of linear and branched polymers in confined volumes and of their interactions with confining medium enables to find optimum conditions either for enhancing or for suppressing the role of individual factors that influence the separation. We have shown that the complex entropy-to-enthalpy interplay in polymer solutions in confined...
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Stochastic modelling of epidemics
Drašnar, Jan ; Staněk, Jakub (advisor) ; Hlubinka, Daniel (referee)
This thesis uses a simple deterministic model represented by an ordinary di- fferential equation with two equilibrium points - depending on the initial state the illness either vanishes or persists forever. This model is expanded by adding some diffusion coefficients leading to different stochastic differential equations. They are analyzed to show how the choice of diffusion coefficients changes be- havior of the model in proximity of its equilibria and near the boundary of area with biological meaning. The theoretical results are than illustrated by computer simulations. 1
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Spatial agent-based models of common pool resources
Vach, Dominik ; Gregor, Martin (advisor) ; Červinka, Michal (referee)
This thesis examines the application of the spatial aspect applied in the com- petitive models in the context of the natural resource economics. At first, the spatial models are thoroughly derived in one dimension. Then also their general properties such as the choice of the agents' location or their payoff function are examined. These properties are investigated for various distri- butions of the resource, and therefore they depend also on their parameters. The Nash equilibrium and local stability conditions are derived for the basic setups. In the second part, these competitive models are numerically tested also in a two-dimensional space. One of the results also suggests, that in the setup where the players have perfect information, the beginning player is not necessarily always better off than the second player. Throughout the entire thesis it is also comprehensively examined whether the existence of corners of the strategy space has an impact on the existence of the competition which was successfully demonstrated on several cases. JEL Classification Q20, Q22, C62, C68, C72 Keywords spatial models, natural resource exploitation, Nash equilibrium, fishery, computer simulations Author's e-mail vach.dominik@gmail.com Supervisor's e-mail martin.gregor@fsv.cuni.cz 1
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Korteweg fluids - modeling, analysis and computer simulations
Blaškovičová, Monika ; Málek, Josef (advisor) ; Řehoř, Martin (referee)
We present two possible thermodynamical approaches towards a derivation of a model, proposed by Korteweg at the beginning of the 20th century, that is suitable to describe phase transitions liquid-vapor with non-sharp interfaces. The first approach (Dunn, Serrin (1985)) is based on classical rational continuum thermodynamics. The second approach (Heida, Málek (2010)) stems from the principles of classical nonequilibrium continuum thermodynamics. We compare both approaches in favor of the second one. The considered constitutive equation for the Cauchy stress is nonlinear. Nonlinearity and higher order derivatives of the density makes the analysis of relevant problems for the Navier-Stokes- Korteweg (NSK) fluid more difficult in comparison to problems concerning Navier-Stokes equations. Special attention is devoted to the appropriate choice of the boundary conditions. We also investigate the influence of compressibility on the stability of bubbles by comparing numerical simulations for compressible NSK fluid and its incompressible variant. Instabilities observed for a compressible NSK fluid are due to the pressure that has a different meaning for incompressible fluid. Powered by TCPDF (www.tcpdf.org)
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