Detail publikačního výsledku
Statistics of fractal systems
ZMEŠKAL, O.; NEŠPŮREK, S.; VESELÝ, M.; DZIK, P.
Originální název
Statistics of fractal systems
Anglický název
Statistics of fractal systems
Druh
Článek recenzovaný mimo WoS a Scopus
Originální abstrakt
Distribution functions are used for the description of energy distribution of elementary particles, atoms, and molecules in dynamic systems. These distribution functions depend on the energy of the system and on its properties. The paper focuses on the generalization of the relationships commonly used to study the statistical properties of particles in 3D space so that they become generally applicable onto an E-dimensional space. These relationships can then be applied e.g. for studying the properties of the particles in 2D and in 1D space. Two approaches are discussed to describe the classic (Maxwell Boltzmann) and quantum (Fermi-Dirac, Einstein-Bose) distribution functions. The first approach is based on standard theory of probability, the second one on the fractal theory. We have shown that both approaches lead to the same results for defined boundary conditions. But the validity of the second one, i.e. the fractal approach, is much more general.
Anglický abstrakt
Distribution functions are used for the description of energy distribution of elementary particles, atoms, and molecules in dynamic systems. These distribution functions depend on the energy of the system and on its properties. The paper focuses on the generalization of the relationships commonly used to study the statistical properties of particles in 3D space so that they become generally applicable onto an E-dimensional space. These relationships can then be applied e.g. for studying the properties of the particles in 2D and in 1D space. Two approaches are discussed to describe the classic (Maxwell Boltzmann) and quantum (Fermi-Dirac, Einstein-Bose) distribution functions. The first approach is based on standard theory of probability, the second one on the fractal theory. We have shown that both approaches lead to the same results for defined boundary conditions. But the validity of the second one, i.e. the fractal approach, is much more general.
Klíčová slova
fractal physics, classic and quantum statistics, classical theory of statistics, fractal theory of statistics
Klíčová slova v angličtině
fractal physics, classic and quantum statistics, classical theory of statistics, fractal theory of statistics
Autoři
ZMEŠKAL, O.; NEŠPŮREK, S.; VESELÝ, M.; DZIK, P.
Vydáno
23.06.2014
Nakladatel
Springer
Místo
Heidelberg
ISSN
2194-5357
Periodikum
Advances in Intelligent Systems and Computing
Svazek
289
Číslo
1
Stát
Švýcarská konfederace
Strany od
55
Strany do
63
Strany počet
9
Plný text v Digitální knihovně
BibTex
@article{BUT109916,
author="Oldřich {Zmeškal} and Stanislav {Nešpůrek} and Michal {Veselý} and Petr {Dzik}",
title="Statistics of fractal systems",
journal="Advances in Intelligent Systems and Computing",
year="2014",
volume="289",
number="1",
pages="55--63",
issn="2194-5357"
}