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Computer modeling of diffusional transport in hydrogel
Koláček, Jakub ; Sedláček, Petr (referee) ; Pekař, Miloslav (advisor)
This thesis focuses on the design of models applicable to the simulation of particle motion in a viscoelastic environment in COMSOL Multiphysics. Two approaches have been chosen for the design of these models: the first is the design of a geometry representing the porous structure of hydrogels and the second is the implementation of viscoelasticity using the mathematical concept of a continuous environment. Two elementary geometrical models are presented in this work – a three-dimensional periodic lattice and a spherical volume model. Furthermore, the possibilities of implementing the generalized Langevin equation in COMSOL Multiphysics are explored by using the interface for custom partial differential equations, by adding an auxiliary dependent variable, or by defining a custom external function written in the C language. The proposed geometric models did not prove to be suitable for the simulation of viscoelastic environment. An implementation using an external function seems to be the most promising, as it offers the most customization possibilities, and its implementation reflects the theoretical foundations. The thesis also includes a custom add-in written for COMSOL Multiphysics to facilitate the evaluation of simulation data and a modified Python script to calculate the complex shear modulus from MSD data.
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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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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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Analysis of linear ion Paul traps using 3-D FEM and the azimuthal multipole expansion
Oral, Martin ; Číp, Ondřej ; Slodička, L.
Radiofrequency (RF) Paul traps are valuable in the design and in the operation of highly stable\noptical atomic clocks based on suitable trapped ions. The traditional setup involves a single\nion in an RF trap irradiated with a laser beam. The frequency of the laser light is then fine-tuned to match that of photons coming from an electronic transition in the atomic shell. The\nachievable frequency stability is about 10-17 for laser-cooled ions. However, the stability can be\nfurther improved by using heavy atoms (such as Thorium) and the more stable frequencies of\ntheir nuclear transitions, and by setting up so-called Coulomb crystals, to improve the frequency measurement statistics by increasing the number of reference atoms. These techniques and their combination could reach relative stabilities beyond 10-20.
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