master's thesis
Catastrophe Theory in the Phase Transition Phenomena

Milica Cvjetović (2016)
Metadata
TitleTeorija katastrofe u fenomenima faznih prijelaza
AuthorMilica Cvjetović
Mentor(s)Ivica Martinjak (thesis advisor)
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.
Keywordssmooth function nondegenrate point fold cusp phase transition Van de Waals’s model Ising model Zeeman model
Parallel title (English)Catastrophe Theory in the Phase Transition Phenomena
Committee MembersNenad Šuvak (committee chairperson)
Ivica Martinjak (committee member)
Snježana Majstorović (committee member)
GranterSveučilište Josipa Jurja Strossmayera u Osijeku
Odjel za matematiku
PlaceOsijek
StateCroatia
Scientific field, discipline, subdisciplineNATURAL SCIENCES
Mathematics
Other Mathematical Disciplines
Study programme typeuniversity
Study levelgraduate
Study programmeMathematics; specializations in: Financial and Statistical Mathematics, Mathematics and Computer Science, Industrial and Applied Mathematics
Study specializationFinancial and Statistical Mathematics
Academic title abbreviationmag.math.
Genremaster's thesis
Language Croatian
Defense date2016-11-04
Parallel 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.
Parallel keywords (Croatian)glatka funkcija nedegenerativna točka nabor šiljak fazni prijelaz Van der Waalsov model Isingov model Zeemanov model
Resource typetext
Access conditionOpen access
Terms of usehttp://rightsstatements.org/vocab/InC/1.0/
URN:NBNhttps://urn.nsk.hr/urn:nbn:hr:126:743764
CommitterMirna Šušak Lukačević