|
| |
|
| |
|
|
Characterisation of the Physical Chemical Processes Using the Fractal and Harmonic Analysis
Haderka, Jan ; Nešpůrek, Stanislav (referee) ; Mikula,, Milan (referee) ; Zmeškal, Oldřich (advisor)
Existuje mnoho různých způsobů jak analyzovat disperzní systémy a fyzikálně chemické processy ke kterým v takových systémech dochází. Tato práce byla zaměřena na charakterizaci těchto procesů pomocí metod harmonické fraktální analýzy. Obrazová data sledovaných systémů byly analyzovány pomocí waveletové analýzy. V průběhu práce byly navrženy různé optimalizace samotné analýzy, převážně zaměřené na odstranění manuálních operací během analýzy a tyto optimalizace byly také inkorporovány do softérového vybavení pro Harmonickou Fraktální Analýzu HarFA, který je vyvíjen na Fakultě chemické, VUT Brno.
|
|
| |
|
| |
|
|
Fractal Analysis of Track Geometry
Nejezchlebová, Jitka ; Holcner, Petr (referee) ; Svoboda, Richard (advisor)
The master’s thesis deals with the fractal analysis of track geometry. The theoretical part is primarily focused on introducing the basics of fractal geometry. There is also concisely described the current methodology for evaluating track geometry. In the practical part is verified the accuracy of the methods for determining the fractal dimension of the curve. For different curves with the same standard deviation is calculated the fractal dimension to demonstrate the possible advantages of using this analysis. Further is researched the use of the fractal dimension for the analysis of track geometry data. All mathematical procedures are done using the MATLAB system.
|
|
|
A guide to fractal geometry
Hajmová, Kateřina ; Pokorný, Dušan (advisor) ; Boček, Leo (referee)
This text is intended for the general public. The aim of this work is acquaint readers with foundations of the fractal geometry. The thesis explains important terminology, such as the coastline paradox or the fractal dimension. A great emphasis is placed on explaining the concept of the box-counting dimension. The thesis includes the construction methods of the L-systems, IFS, TEA and random fractals. In addition, it shows the use of fractal geometry in practice. The text is completed with illuminating figures drawn in most cases in Geogebra software and Wolfram Mathematica.
|
|
|
Hausdirff metric and its application in fractals
Roháľ, Branislav Ján ; Hušek, Miroslav (advisor) ; Pyrih, Pavel (referee)
Title: Hausdorff metric and its application in fractals Author: Branislav Ján Roháľ Department: Department of Mathematical Analysis Supervisor: prof. RNDr. Miroslav Hušek, DrSc., Department of Mathematical Analysis Abstract: In this thesis we focus on the themes naturally connected with the con- cept of a fractal. In the first part of the thesis we pay attention to Banach fixed point theorem and to the Hausdorff metric which are later used when studying self-similar sets. There are included parts on the Hausdorff, similarity, and box- counting dimension, too. In the second part of the thesis the new approaches to fractal dimension and some their properties are refered. We introduce generaliza- tion of this concept for any space admitting a fractal structure and for a distance space where also the "size" of sets on each level of fractal structure is considered. In the last chapter the contribution of new approache is demonstrated, - this enables defining the notion needed and counting fractal dimension where it was not possible under the classical approaches, too. Application to the domain of words and counting of dimensions of a language generated by a regular expresion are presented. Keywords: Hausdorff metric, Banach fixed point theorem, self-similar set, Hausdorff dimension, fractal dimension
|
|
| |
|
|
X-ray micro-tomography characterization of voids caused by three-point bending in selected alkali-activated aluminosilicate composite
Kumpová, Ivana ; Rozsypalová, I. ; Keršner, Z. ; Rovnaníková, P. ; Vopálenský, Michal
This paper deals with the pilot characterization of a special alkali-activated aluminosilicate composite composed of waste brick powder, brick rubble and a solution of potassium water glass. Fracture tests were conducted on the specimens via three-point bending and fracture parameters were evaluated. Selected specimen was investigated using micro-tomography to supplement the results with visual information about the inner structure of this newly designed material before and after the mechanical loading. Tomographic measurements and image processing were conducted for a qualitative and quantitative assessment of changes in the internal structure with an emphasis on the calculation of porosimetric parameters and visualization of the fracture surface. Fractal dimension of fracture surface was estimated.
|
guest ::
