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A method for the solution of non-spherical (fiber) particles deposition by means of the Fokker-Planck equation for ODF in a laminar flow
Kopečková, Barbora ; Knotek, Stanislav (referee) ; Jícha, Miroslav (advisor)
The Bachelor's thesis deals with a deposition efficiency for a fibers by various mechanisms of a deposition. It explains deposition efficiency by diffusion, by sedimentation and by impaction. The implementation of Peterlin's analytical solution for calculation of the ODF, which is used for individual efficiencies solution, is also mentioned. Afterwards, the thesis summarizes formulas for calculation of particular efficiencies derived for spherical particles and recomputation appropriate parameters for fibers. The purpose of the thesis is to create graphs, which illustrate deposition efficiencies dependence by various mechanisms on the aspect ratio of fibers. Another goal is the graphs creation, which shows juxtaposition for various breathing modes for given deposition mechanisms. The software MATLAB is used for the whole calculation process and graphs plotting.
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Energetics of diffusion in time-dependent parabolic potential.
Škvára, Jan ; Chvosta, Petr (advisor) ; Netočný, Karel (referee)
In this thesis we are going to study the dynamics and energetics of the dif- fusion of a Brownian particle in a time-dependent parabolic potential. Our central quantity is a random variable corresponding to the work done on the particle due to the time dependency of the potential. We present new exact analytical ex- pression for the probability density function for the work variable in a situation, where the potential is piecewise constant in the time variable. Furthermore, this result is used to develop a hierarchy of approximations which yield the density function for an arbitrary time-dependent parabolic potential. 1
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Energetics of diffusion in time-dependent parabolic potential.
Škvára, Jan ; Chvosta, Petr (advisor) ; Netočný, Karel (referee)
In this thesis we are going to study the dynamics and energetics of the dif- fusion of a Brownian particle in a time-dependent parabolic potential. Our central quantity is a random variable corresponding to the work done on the particle due to the time dependency of the potential. We present new exact analytical ex- pression for the probability density function for the work variable in a situation, where the potential is piecewise constant in the time variable. Furthermore, this result is used to develop a hierarchy of approximations which yield the density function for an arbitrary time-dependent parabolic potential. 1
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A method for the solution of non-spherical (fiber) particles deposition by means of the Fokker-Planck equation for ODF in a laminar flow
Kopečková, Barbora ; Knotek, Stanislav (referee) ; Jícha, Miroslav (advisor)
The Bachelor's thesis deals with a deposition efficiency for a fibers by various mechanisms of a deposition. It explains deposition efficiency by diffusion, by sedimentation and by impaction. The implementation of Peterlin's analytical solution for calculation of the ODF, which is used for individual efficiencies solution, is also mentioned. Afterwards, the thesis summarizes formulas for calculation of particular efficiencies derived for spherical particles and recomputation appropriate parameters for fibers. The purpose of the thesis is to create graphs, which illustrate deposition efficiencies dependence by various mechanisms on the aspect ratio of fibers. Another goal is the graphs creation, which shows juxtaposition for various breathing modes for given deposition mechanisms. The software MATLAB is used for the whole calculation process and graphs plotting.
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