|
|
Nonlinear diffusion equations
Polášek, Radek ; Hájek, Jiří (referee) ; Franců, Jan (advisor)
This work is focused on various types of diusion equations. The diffusion equations are derived for various assumptions of media. We describe in detail Barenblatt solution for slow diffusion equation, whose features are demonstrated.
|
|
|
Computational analysis of pressurized water reactor core behaviour using PARCS code
Novotný, Filip ; Ing. Jan Frýbort, Ph.D., KJR FJFI ČVUT v Praze (referee) ; Katovský, Karel (advisor)
The Master Thesis performs search concerning advanced small and medium power light-water reactors’ designs, including different possibilities to gain a license for their development and operation. The work covers the principal theory about the area of neutronics calculations, principal equations and simplifications. There are several different methods for solution of neutronics calculations. The thesis gives an overview of two principal groups of codes – deterministic methods and Monte Carlo method. The survey shows computational codes examples based on mentioned methods. The computational code PARCS is chosen for further study, which contained description of the input and output file, process of the model creation and conditions for neutronics calculation the of selected reactor design. Based on these facts, the transient calculation has been prepared within the thesis. Thee analyses are described – reactor emergency shutdown, reactor shutdown with stuck group of control and emergency shutdown rods and reactor shutdown with faulty reaction of emergency shutdown rods.
|
|
|
Relation between Schrödinger equation and diffusion equation
Poprocký, Mojmír ; Stránský, Pavel (advisor) ; Cejnar, Pavel (referee)
The Schrodinger's equation and the diffusion equation can be written in a similar form. While the Schrodinger's equation is complex, the diffusion equation is real. In this thesis we wish to outline similarities of both equations. We present a way to treat a problem in non-relativistic quantum mechanics as a diffusion process. This shows that under certain circumstances both theories are equivalent. We demonstrate this on a few simple examples.
|
|
|
Computational analysis of pressurized water reactor core behaviour using PARCS code
Novotný, Filip ; Ing. Jan Frýbort, Ph.D., KJR FJFI ČVUT v Praze (referee) ; Katovský, Karel (advisor)
The Master Thesis performs search concerning advanced small and medium power light-water reactors’ designs, including different possibilities to gain a license for their development and operation. The work covers the principal theory about the area of neutronics calculations, principal equations and simplifications. There are several different methods for solution of neutronics calculations. The thesis gives an overview of two principal groups of codes – deterministic methods and Monte Carlo method. The survey shows computational codes examples based on mentioned methods. The computational code PARCS is chosen for further study, which contained description of the input and output file, process of the model creation and conditions for neutronics calculation the of selected reactor design. Based on these facts, the transient calculation has been prepared within the thesis. Thee analyses are described – reactor emergency shutdown, reactor shutdown with stuck group of control and emergency shutdown rods and reactor shutdown with faulty reaction of emergency shutdown rods.
|
|
|
Nonlinear diffusion equations
Polášek, Radek ; Hájek, Jiří (referee) ; Franců, Jan (advisor)
This work is focused on various types of diusion equations. The diffusion equations are derived for various assumptions of media. We describe in detail Barenblatt solution for slow diffusion equation, whose features are demonstrated.
|
|
|
On Two Methods for the Parameter Estimation Problem with Spatio-Temporal FRAP Data
Papáček, Š. ; Jablonský, J. ; Matonoha, Ctirad
FRAP (Fluorescence Recovery After Photobleaching) is a measurement technique for determination of the mobility of fluorescent molecules (presumably due to the diffusion process) within the living cells. While the experimental setup and protocol are usually fixed, the method used for the model parameter estimation, i.e. the data processing step, is not well established. In order to enhance the quantitative analysis of experimental (noisy) FRAP data, we firstly formulate the inverse problem of model parameter estimation and then we focus on how the different methods of data pre- processing influence the confidence interval of the estimated parameters, namely the diffusion constant $p$. Finally, we present a preliminary study of two methods for the computation of a least-squares estimate $\hat{p}$ and its confidence interval.
|
|
| |
|
| |
guest ::
