Analiza faznih prijelaza u kompleksnim mrežama

master's thesis

• Title (english): Phase transition analysis in complex networks
• Author: Matija Medvidović
• Mentor: Davor Horvatić (mentor)
• Committee member: Davor Horvatić (predsjednik povjerenstva)
• Committee member: Matko Milin (član povjerenstva)
• Committee member: Ivica Smolić (član povjerenstva)
• Committee member: Mihael Makek (član povjerenstva)
• Committee member: Tomislav Marketin (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2017-09-21, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

U ovom diplomskom radu promatramo modele intrigirajućih mreža koji su u širokoj primjeni u analizi i predviđanju ponašanja mreža u stvarnom svijetu, poput mapa interneta ili modela tržišta. Na odabranim primjerima koristimo matematičke metode statističke fizike kako bismo razvili generalnije formalizme tretiranja različitih klasa mreža te opisali njihovo kritično ponašanje. Modele dijelimo na statičke i dinamičke, identificirajući parametre uređenja i koristeći aproksimacije srednjeg polja pri izračunu kritičnih eksponenata. Diskusijom o ograničenjima svakog modela i primjenjivosti metoda rješavanja, uspostavljamo analogiju sa statističkom fizikom i najznačajnije primjene na stvarne mreže.

Abstract (english)

We examine a few select interacting network models with broad real-world applications ranging from internet maps to economic market modeling. Employing the mathematical formalism of statistical physics, we show its range of applicability in developing more general ways of treating classes of networks as well as describing and classifying their critical phenomena. By tackling static and dynamical models separately, we emphasize their conceptual differences manifesting in the mean-field calculations of critical exponents. Ultimately, we discuss model limitations and point out their use in terms of describing real-world network critical phenomena.

• Keywords: intrigirajuća mreža; teorija grafova; fazni prijelaz; kritični fenomeni; kompleksne mreže
• Keywords (english): interacting network; graph theory; phase transition; critical phenomena; complex networks
• Language: croatian
• URN:NBN: urn:nbn:hr:217:443018
• Study programme: Title: Physics; specializations in: Research; Course: Research; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: magistar/magistra fizike (magistar/magistra fizike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2017-10-06 11:36:57