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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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Finite element solution of the nonlinear 2DOFs dynamic system under random Gaussian excitation using the Fokker-Planck equation
Král, Radomil ; Náprstek, Jiří
Papers published until now are dealing with single degree of freedom (SDOF) systems. So the respective FP equation includes two independent space variables only (x1, x2). Nevertheless stepping over this limit and entering into a true multi-dimensionality a number of specific problems must be overcome. While in usual FEM practice the number of space variables is two or three, investigating FP equation, so 2n independent space variables emerges. It means for instance 12 space variables when random motion of a rigid body in space with six degrees of freedom is studied. Many requirements should be respected which are out of a conventional practice of Finite Element employment.
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