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Microrheology modeling with COMSOL Multiphysics package
Koláček, Jakub ; Sedláček, Petr (referee) ; Pekař, Miloslav (advisor)
This bachelor thesis focuses on modeling Brownian motion using the COMSOL Multiphysics package and its Particle Tracing module. The aim of the work is to design and create elementary models that will be able to suitably simulate the movement of microparticles in viscous and viscoelastic environments, which can later be used for modeling passive microrheology. Within this work, Matlab scripts were created for the calculation of MSD from the simulation results, validation of the viscous model was performed on experimental data and elementary models for the simulation of the viscoelastic environment were also designed. Two different approaches were chosen for the design of these models, namely the use of rigid obstacles under the assumption of a discrete environment and a mathematical model assuming continuous environment. Data from the viscous model showed good agreement with the experimental results. The results of viscoelastic simulations are presented, and further possible development of these models is discussed. The continuous mathematical model is considered closest to modeling viscoelastic behavior because of a characteristic curvature that was observed in the evaluation of MSD.
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Passive microrheology of colloidal systems based on biopolymers.
Bjalončíková, Petra ; Burgert, Ladislav (referee) ; Mravec, Filip (advisor)
Diploma thesis was aimed to deal with evaluation of microrheology method in the research of biopolymer-protein. Used biopolymer was sodium hyaluronate and proteins were trypsin and chymotrypsin. For measuring of microrheology were used particles with different radius (0,5 m and 1 m). It was found, that both substances have viscous charakter. Passive microrheology is suitable for measuring the viscoelastic properties of biopolymers.
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Fractals in Computer Graphics
Šelepa, Jan ; Venera, Jiří (referee) ; Sumec, Stanislav (advisor)
The goal of this work is to give introduction and specification of fractals. The first chapter presents the basics of fractal geometry. The second chapter maps the history of fractals and points out the most important people of fractal science. The third chapter presents fractal classification based on several criteria and gives basic examples. The fourth chapter is a summary of widely used applications for fractal creation. The last chapter describes the application that was made to demonstrate given algorithms and fractals mentioned in this thesis.
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Stochastic ordinary differential equations
Bahník, Michal ; Kolářová, Edita (referee) ; Franců, Jan (advisor)
Diplomová práce se zabývá problematikou obyčejných stochastických diferenciálních rovnic. Po souhrnu teorie stochastických procesů, zejména tzv. Brownova pohybu je zaveden stochastický Itôův integrál, diferenciál a tzv. Itôova formule. Poté je definováno řešení počáteční úlohy stochastické diferenciální rovnice a uvedena věta o existenci a jednoznačnosti řešení. Pro případ lineární rovnice je odvozen tvar řešení a rovnice pro jeho střední hodnotu a rozptzyl. Závěr tvoří rozbor vybraných rovnic.
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Simulations of synthetic diffusion MRI data based on Brownian motion
Valla, Radek ; Mikl, Michal (referee) ; Labounek, René (advisor)
This master thesis focuses on dMRI (diffusion magnetic resonance imaging) and its dependance on diffusion in human brain tissue. It is described how to retrieve an image from gained data and its properties, advantages and disadvantages. It mentions problem in detecting kissing fibres due to its similarity with crossing fibres. Design of mathematical models of axons is decribed and suggested measurement to detect difference in signals for kissing and crossing fibres. It describes new simulator of diffusion-weighted MRI (dMRI) data which is able to generate it based on random walk algorithm with geometrical constraints not only for crossing fiber geometry, but also as o novelty for bending and kissing fiber geometries. This study contains results of simulations and disscusion about their usefulness with suggestions for simulator improvement. Simulated dMRI data shows significant difference in certain gradients. Data reconstruction shows, that these reults cannot be reconstructed into the same geometry as it was simulated for.
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Transitional motion analysis of the optically trapped particle in under-damped regime
Sűsserová, Martina ; Damková, Jana (referee) ; Harabiš, Vratislav (advisor)
This bachelor thesis deals with the analysis of the transition phenomenon, which occurs when the nanoparticles enter the laser beam. Thereafter the particle is anchored around the point of focus of this beam. The main objectives of the thesis were to illustrate the dependence of the trajectory positions in relation to its instantaneous values and to obtain the parameters of the attenuated harmonic oscillator whose character is characteristic for the particle inserting the beam. Another objective of the thesis was to apply frequency filters to signal data and to observe their effects on phase diagrams and also to visualize the behavior of the particle in the vicinity of the focus in the stationary state.
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Correlation analysis of optically trapped particle motion
Koudelníček, Karel ; Jákl,, Petr (referee) ; Harabiš, Vratislav (advisor)
This bachelor’s thesis deals with the description of random (Brownian) motion of microscopic particle trapped by optical trap. This thesis provides overview of possible usage in biology. The major part of the thesis is dedicated to description of methods that allow characterize optical trap with etc. stiffness thanks to the random motion. First, the estimation methods are tested on the simulated data. Before using these methods for real data, it was necessary to modify them, specifically to eliminate crosstalk and frequency noise. The differences in the estimation of the stiffness from the autocorrelation function and the power spectrum were described in the conclusion.
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Microrheology in systems of polymeric colloids
Bjalončíková, Petra ; Sedláček, Petr (referee) ; Venerová, Tereza (advisor)
My bachelor’s thesis was aimed to deal with evaluation of microrheology method in the research of polymer colloids. Used polymers were poly(sodium 4-styrenesulfonate) and sodium carboxymethyl celullose. For measuring of microrheology were used particles with different radius (1 m and 4 m). The results obtained with passive microrheology were compared with results obtained with clasical rheology. It was found, that both substances have viscous charakter. The values of polymer viscosity were similar for dilute solutions in both methods, but for concentrated solutions deviations were found. The reason are polymer nets, which do not allow sufficient movement of particles in concentrated solutions.
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Stochastic Calculus and Its Applications in Biomedical Practice
Klimešová, Marie ; Růžičková, Miroslava (referee) ; Dzhalladova, Irada (referee) ; Baštinec, Jaromír (advisor)
V předložené práci je definována stochastická diferenciální rovnice a jsou uvedeny její základní vlastnosti. Stochastické diferenciální rovnice se používají k popisu fyzikálních jevů, které jsou ovlivněny i náhodnými vlivy. Řešením stochastického modelu je náhodný proces. Cílem analýzy náhodných procesů je konstrukce vhodného modelu, který umožní porozumět mechanismům, na jejichž základech jsou generována sledovaná data. Znalost modelu také umožňuje předvídání budoucnosti a je tak možné kontrolovat a optimalizovat činnost daného systému. V práci je nejdříve definován pravděpodobnostní prostor a Wienerův proces. Na tomto základě je definována stochastická diferenciální rovnice a jsou uvedeny její základní vlastnosti. Závěrečná část práce obsahuje příklad ilustrující použití stochastických diferenciálních rovnic v praxi.
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