Monte-Carlo simulations of defect-rich tilings of polydisperse squares
Monte-Carlo simulations of defect-rich tilings of polydisperse squares
Date
2018
Authors
Editors
Journal ISSN
Electronic ISSN
ISBN
Bibliographical data
Publisher
Series
URI (citable link)
International patent number
Link to the license
EU project number
Project
Open Access publication
Collections
Title in another language
Publication type
Bachelor thesis
Publication status
Published
Published in
Abstract
Two-dimensional systems have long been a subject of research, as they exhibit interesting behavior not found in three dimensions. The thesis presented here examines two-dimensional, hard core potential systems of squares. These squares are anisotropic and exclusively driven by entropic forces. Their equilibrium behavior is accessed through Monte-Carlo simulations. The different thermodynamic phases of this system are analyzed and the thesis reports an intermediate phase between the solid and the fluid called the tetratic phase [1]. Defects in the system are evaluated. It is found that the point defect density increases with the packing fraction to values of up to 1.4%. Finally, the dispersion relations of the lattice vibrations are calculated via an elasticity theory for real crystals [2]. Most interestingly the frequency of the angular vibrations in the solid phase does not tend to zero in the hydrodynamic limit. In the tetratic phase however, the same branch tends to zero in this limit case.
Summary in another language
Subject (DDC)
530 Physics
Keywords
Conference
Review
undefined / . - undefined, undefined. - (undefined; undefined)
Cite This
ISO 690
DANNERT, Felix Aron, 2018. Monte-Carlo simulations of defect-rich tilings of polydisperse squares [Bachelor thesis]. Konstanz: Universität KonstanzBibTex
@mastersthesis{Dannert2018Monte-47191, year={2018}, title={Monte-Carlo simulations of defect-rich tilings of polydisperse squares}, address={Konstanz}, school={Universität Konstanz}, author={Dannert, Felix Aron} }
RDF
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/47191"> <dc:contributor>Dannert, Felix Aron</dc:contributor> <dcterms:title>Monte-Carlo simulations of defect-rich tilings of polydisperse squares</dcterms:title> <dc:creator>Dannert, Felix Aron</dc:creator> <dc:rights>terms-of-use</dc:rights> <dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/47191/3/Dannert_2-1jyxw7ee20mwc4.pdf"/> <dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/47191/3/Dannert_2-1jyxw7ee20mwc4.pdf"/> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2019-10-11T08:17:32Z</dc:date> <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/41"/> <bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/47191"/> <dc:language>eng</dc:language> <dcterms:abstract xml:lang="eng">Two-dimensional systems have long been a subject of research, as they exhibit interesting behavior not found in three dimensions. The thesis presented here examines two-dimensional, hard core potential systems of squares. These squares are anisotropic and exclusively driven by entropic forces. Their equilibrium behavior is accessed through Monte-Carlo simulations. The different thermodynamic phases of this system are analyzed and the thesis reports an intermediate phase between the solid and the fluid called the tetratic phase [1]. Defects in the system are evaluated. It is found that the point defect density increases with the packing fraction to values of up to 1.4%. Finally, the dispersion relations of the lattice vibrations are calculated via an elasticity theory for real crystals [2]. Most interestingly the frequency of the angular vibrations in the solid phase does not tend to zero in the hydrodynamic limit. In the tetratic phase however, the same branch tends to zero in this limit case.</dcterms:abstract> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2019-10-11T08:17:32Z</dcterms:available> <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/41"/> <dcterms:issued>2018</dcterms:issued> <foaf:homepage rdf:resource="http://localhost:8080/"/> <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/> </rdf:Description> </rdf:RDF>
Internal note
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Examination date of dissertation
University note
Konstanz, Universität Konstanz, Bachelor thesis, 2018