Monte-Carlo simulations of defect-rich tilings of polydisperse squares

Dannert, Felix Aron

Monte-Carlo simulations of defect-rich tilings of polydisperse squares

Files

Dannert_2-1jyxw7ee20mwc4.pdf(4.56 MB)

Date

2018

Publication type

Bachelor thesis

Publication status

Published

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.

Subject (DDC)

530 Physics

Cite This

ISO 690

DANNERT, Felix Aron, 2018. Monte-Carlo simulations of defect-rich tilings of polydisperse squares [Bachelor thesis]. Konstanz: Universität Konstanz

BibTex

@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>

University note

Konstanz, Universität Konstanz, Bachelor thesis, 2018