Penroseovo popločavanje i struktura kvazikristala

undergraduate thesis

• Title (english): Penrose tiling and quasicrystals
• Author: Katja Čemerin
• Mentor: Erna Begović Kovač (mentor)
• Committee member: Erna Begović Kovač (predsjednik povjerenstva)
• Committee member: Miroslav Jerković (član povjerenstva)
• Committee member: Dajana Kučić Grgić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Chemical Engineering and Technology; Zagreb
• Defense date and country: 2021-09-22, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Popločavanje predstavlja prekrivanje prostora geometrijskih likovima bez rupa i preklapanja te ga je moguće primijeniti na proučavanje struktura čvrstih odnosno kristalnih tvari. Struktura kristala ponavlja se u svim smjerovima na periodičan način, a osnovna prostorna jedinica kristala je jedinična ćelija. Do 80-ih godina vjerovalo se da sve čvrste stvari posjeduju ovakve savršene strukture, no proučavajući legure metala otkriveno je da mnoge tvari posjeduje nedopuštene rotacijske simetrije te je njihova struktura u stvarnosti kvaziperiodična. Za razumijevanje ovakvih struktura potrebno je primijeniti neperiodična popločavanja koja je proučavao matematičar Roger Penrose. Kod neperiodičnog popločavanja nikada neće doći do ponavljanja uzorka, a Penrose uspjeva neperiodično popločavanje svesti na korištenje samo dva oblika koje naziva „zmaj“ i „strijela“.

Abstract (english)

Tiling is the covering of space with geometric figures without holes and overlaps, and it can be applied to the study of the structures of solid or crystalline substances. The structure of the crystal is repeated in all directions in a periodic manner, and the basic spatial unit of the crystal is the unit cell. Until the 1980s, all solids were believed to possess such perfect structures, but studying metal alloys revealed that many substances possess impermissible rotational symmetries and their structure is in fact quasi-periodic. To understand such structures it is necessary to apply the non-periodic tiling studied by the mathematician Roger Penrose. With non-periodic tiling, the pattern will never be repeated and Penrose manages to reduce the non-periodic tiling to using only two shapes, which he calls "kite" and "dart".

• Keywords: neperiodičnost; Penroseovo popločavanje; kvazikristali; ikosaedar
• Keywords (english): non-periodicity; Penrose tiling; quasicrystals; icosahedron
• Language: croatian
• URN:NBN: urn:nbn:hr:149:578166
• Study programme: Title: Environmental Engineering - Undergraduate study; Study programme type: university; Study level: undergraduate; Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka ekoinženjerstva (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka ekoinženjerstva)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2023-03-27 06:31:36