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master's thesis
Fermi-Pasta-Ulamov model
Zagreb: University of Zagreb, Faculty of Science, 2016. urn:nbn:hr:217:015941
Čižmek, Kristina
University of Zagreb
Faculty of Science
Department of Mathematics

Cite this document

Čižmek, K. (2016). Fermi-Pasta-Ulamov model (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:015941

Čižmek, Kristina. "Fermi-Pasta-Ulamov model." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:015941

Čižmek, Kristina. "Fermi-Pasta-Ulamov model." Master's thesis, University of Zagreb, Faculty of Science, 2016. https://urn.nsk.hr/urn:nbn:hr:217:015941

Čižmek, K. (2016). 'Fermi-Pasta-Ulamov model', Master's thesis, University of Zagreb, Faculty of Science, accessed 19 April 2024, https://urn.nsk.hr/urn:nbn:hr:217:015941

Čižmek K. Fermi-Pasta-Ulamov model [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2016 [cited 2024 April 19] Available at: https://urn.nsk.hr/urn:nbn:hr:217:015941

K. Čižmek, "Fermi-Pasta-Ulamov model", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2016. Available at: https://urn.nsk.hr/urn:nbn:hr:217:015941

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Metadata
TitleFermi-Pasta-Ulamov model
AuthorKristina Čižmek
MentorSiniša Slijepčević (mentor)
Committee memberSiniša Slijepčević (predsjednik povjerenstva)
Committee memberGoran Muić (član povjerenstva)
Committee memberJosip Tambača (član povjerenstva)
Committee memberMladen Jurak (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2016-09-23, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu proučavali smo neke temeljne rezultate teorije diferencijalnih jednadždbi koje smo zatim iskoristili za objašnjenje Fermi-Pasta-Ulamovog modela. Enrico Fermi, Stanisław Ulam i Johan R. Pasta izveli su eksperiment u kojem su promatrali N identičnih kuglica (masa) od kojih su susjedne kuglice povezane oprugama, a krajnje kuglice su pričvršćene za fiksne pozicije. Dodatna pretpostavka je da je kretanje kuglica ograničeno samo na kretanje duž pravca. Na početku rada promatrali smo rješenja diferencijalne jednadžbe; njegovo postojanje i jedinstvenost. Bavili smo se geometrijskom interpretacijom i definirali neke pojmove vezane uz tu temu. Zatim smo proučavali stabilnost rješenja. Zaključke i rezultate do kojih smo došli u prvom dijelu ovog rada iskoristili smo u zadnjem poglavlju u kojem opisujemo Fermi-Pasta-Ulamov model. Njihovo očekivanje vezano uz prethodno opisani eksperiment je bilo da će se nakon početnog pobuđivanja sustava, to jest dovođenja vanjske energije doći do procesa termalizacije - procesa koji vodi do "jednake raspodjele energije". Početni cilj eksperimenta bio je odrediti vrijeme potrebno da se dogodi termalizacija. Međutim, suprotno očekivanjima, termalizacija se nije dogodila.
Abstract (english)
In this paper we observed some basic results of the theory of the differential equations and then we used them to describe Fermi-Pasta-Ulam model. Enrico Fermi, Stanisław Ulam and Johan R. Pasta made an experiment in which they observed N identical balls which were bounded by spring. The balls at the end were fixed. It was assumed that the movement of the balls is in one direction only. At the beginning of the paper we studied the solutions of differential equations, their existence and uniqueness. We described geometric interpretation and defined some terms on that subject. Then we examined the stability of the solution. The conclusions and results that we came to in the first part of the paper, we used in the last chapter, where we described Fermi-Pasta-Ulam model. They applied force to the described system and they expected that it will come to thermalization, same allocation of the energy. The main goal of the experiment was to measure the time needed for thermalization, but at the end it never came to the thermalization.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:015941
Study programmeTitle: Finance and Business 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
RepositoryRepository of the Faculty of Science
Created on2019-01-08 09:48:51

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