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master's thesis
Teorija katastrofe u fenomenima faznih prijelaza
2016. urn:nbn:hr:126:743764
Cvjetović, Milica
Josip Juraj Strossmayer University of Osijek
Department of Mathematics

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Cvjetović, M. (2016). Teorija katastrofe u fenomenima faznih prijelaza (Master's thesis). Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics. Retrieved from https://urn.nsk.hr/urn:nbn:hr:126:743764

Cvjetović, Milica. "Teorija katastrofe u fenomenima faznih prijelaza." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:743764

Cvjetović, Milica. "Teorija katastrofe u fenomenima faznih prijelaza." Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, 2016. https://urn.nsk.hr/urn:nbn:hr:126:743764

Cvjetović, M. (2016). 'Teorija katastrofe u fenomenima faznih prijelaza', Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:126:743764

Cvjetović M. Teorija katastrofe u fenomenima faznih prijelaza [Master's thesis]. Osijek: Josip Juraj Strossmayer University of Osijek, Department of Mathematics; 2016 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:126:743764

M. Cvjetović, "Teorija katastrofe u fenomenima faznih prijelaza", Master's thesis, Josip Juraj Strossmayer University of Osijek, Department of Mathematics, Osijek, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:126:743764

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Metadata
TitleTeorija katastrofe u fenomenima faznih prijelaza
Title (english)Catastrophe Theory in the Phase Transition Phenomena
AuthorMilica Cvjetović
MentorIvica Martinjak (mentor)
Committee memberNenad Šuvak (predsjednik povjerenstva)
Committee memberIvica Martinjak (član povjerenstva)
Committee memberSnježana Majstorović (član povjerenstva)
GranterJosip Juraj Strossmayer University of Osijek
Department of Mathematics
Osijek
Defense date and country2016-11-04, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Abstract
U ovom radu proučavamo kako različiti tipovi stacionarnih točaka glatke funkcije opisuju ponašanje sustava kojeg ta funkcija karakterizira. Definirat ćemo degenerativne i nedegenerativne kritične točke. Zatim ćemo se upoznati s naborom i šiljkom, univerzalnim perturbacijama kritičnih točaka koje spadaju u 7 elementarnih katastrofa. Gravitacijski stroj i Zeemanov stroj katastrofe jednostavni su fizikalni sustavi opisani navedenim perturbacijama. U drugom dijelu rada opisujemo nekoliko sustava u kojima se događa fazni prijelaz. Temeljne pojmove uvodimo i ilustriramo na primjeru procesa grananja. Drugi primjer je Van der Waalsova jednadžba stanja fluida, koja očituje katastrofu šiljka. Idući primjer je Isingov model feromagnetizma u kojem se od jednadžbe stanja magneta također dolazi do katastrofe šiljka. Na kraju rada opisujemo nestabilno ponašanje tržišta Zeemanovim modelom baziranim na teoriji katastrofe.
Abstract (english)
In this thesis we study how different types of stationary points of smooth function describes behaviour of the system that is characterised whit this function. We define degenerate and nondegenerate critical points. After that we get to know fold and cusp catastrophe, universal unfoldings of critical points which are also known as two of 7 elementary catastrophes. Gravitational catastrophe machine and Zeeman catastrophe machine are simple physical systems exhibiting typical catastrophic behaviour. In the second part of thesis we describe several systems in which the phase transition occurs. We start with simple example of branching process. Second example is Van der Waals equation of state of gas from which we can easily get cusp catastrophe. Also there is Ising model of ferromagnetism in which we can also find cusp catastrophe. In the end we describe unstable behaviour of stock exchange with a model based on catastrophe theory.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:126:743764
Study programmeTitle: Mathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Course: Financial and Statistical Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2016-11-10 08:05:38