{"id":{"repo_id":"toronto-retro","oai_identifier":"oai:utoronto.scholaris.ca:1807/128007"},"canonical_url":"https://search.dev.ndltd.org/etd/toronto-retro/oai:utoronto.scholaris.ca:1807/128007","repository":{"repo_id":"toronto-retro","name":"University of Toronto","base_url":"https://utoronto.scholaris.ca/server/oai/request"},"display":{"title":"On Local Order in Particle Packings","abstract":"A great many physical systems take the form of a particle packing. The structure of such systems is often characterized through the study of local order. The current thesis makes progress towards a formal understanding of this physical phenomenon. It is demonstrated that particle packings cannot have global order without also having local order around every particle. A formal definition for local order parameters is proposed and an information-theoretic quantity that satisfies this definition is derived. This quantity is approximated with a simple coefficient $E$ that depends only on the number of neighbours and different bond angles associated with a particle. By generalizing $E$ to $n$ particles, a metric model of the space of three-dimensional coordination geometries is conceived and a taxonomy that is consistent with geometric intuition is recovered. An application of $E$ to an open problem in glass physics is considered. In particular, the variance of $E$ is used to characterize short-time structural relaxation in Kob-Andersen-type mixtures. This variance is found to be nearly composition independent at the onset temperature of glassy dynamics. It is also observed to behave like a heuristic measure of glass-forming ability, which could prove useful when exact methods are intractable.","abstract_html":"A great many physical systems take the form of a particle packing. The structure of such systems is often characterized through the study of local order. The current thesis makes progress towards a formal understanding of this physical phenomenon. It is demonstrated that particle packings cannot have global order without also having local order around every particle. A formal definition for local order parameters is proposed and an information-theoretic quantity that satisfies this definition is derived. This quantity is approximated with a simple coefficient $E$ that depends only on the number of neighbours and different bond angles associated with a particle. By generalizing $E$ to $n$ particles, a metric model of the space of three-dimensional coordination geometries is conceived and a taxonomy that is consistent with geometric intuition is recovered. An application of $E$ to an open problem in glass physics is considered. In particular, the variance of $E$ is used to characterize short-time structural relaxation in Kob-Andersen-type mixtures. This variance is found to be nearly composition independent at the onset temperature of glassy dynamics. It is also observed to behave like a heuristic measure of glass-forming ability, which could prove useful when exact methods are intractable.","abstract_has_math":true,"creators":["Çamkıran, John"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Materials Science and Engineering","school":null,"contributors":[],"advisors":["Hibbard, Glenn D","Parsch, Fabian"],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023-06","date_published":"2023-06","updated_at":"2026-07-27T21:28:11Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/1807/128007","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Hibbard, Glenn D","Parsch, Fabian"]},{"key":"dc:contributor.department","label":"Department","values":["Materials Science and Engineering"]},{"key":"dc:creator","label":"Author","values":["Çamkıran, John"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2023-06"]},{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2023-06-27T15:50:45Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2023-06-27T15:50:45Z"]},{"key":"dc:date.issued","label":"Date","values":["2023-06"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/1807/128007"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["A great many physical systems take the form of a particle packing. The structure of such systems is often characterized through the study of local order. The current thesis makes progress towards a formal understanding of this physical phenomenon. It is demonstrated that particle packings cannot have global order without also having local order around every particle. A formal definition for local order parameters is proposed and an information-theoretic quantity that satisfies this definition is derived. This quantity is approximated with a simple coefficient $E$ that depends only on the number of neighbours and different bond angles associated with a particle. By generalizing $E$ to $n$ particles, a metric model of the space of three-dimensional coordination geometries is conceived and a taxonomy that is consistent with geometric intuition is recovered. An application of $E$ to an open problem in glass physics is considered. In particular, the variance of $E$ is used to characterize short-time structural relaxation in Kob-Andersen-type mixtures. This variance is found to be nearly composition independent at the onset temperature of glassy dynamics. It is also observed to behave like a heuristic measure of glass-forming ability, which could prove useful when exact methods are intractable."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph.D."]},{"key":"dc:title","label":"Title","values":["On Local Order in Particle Packings"]}]}],"canonical_facts":{"dc:contributor.advisor":["Hibbard, Glenn D","Parsch, Fabian"],"dc:contributor.department":["Materials Science and Engineering"],"dc:creator":["Çamkıran, John"],"dc:date":["2023-06"],"dc:date.accessioned":["2023-06-27T15:50:45Z"],"dc:date.available":["2023-06-27T15:50:45Z"],"dc:date.issued":["2023-06"],"dc:description.abstract":["A great many physical systems take the form of a particle packing. The structure of such systems is often characterized through the study of local order. The current thesis makes progress towards a formal understanding of this physical phenomenon. It is demonstrated that particle packings cannot have global order without also having local order around every particle. A formal definition for local order parameters is proposed and an information-theoretic quantity that satisfies this definition is derived. This quantity is approximated with a simple coefficient $E$ that depends only on the number of neighbours and different bond angles associated with a particle. By generalizing $E$ to $n$ particles, a metric model of the space of three-dimensional coordination geometries is conceived and a taxonomy that is consistent with geometric intuition is recovered. An application of $E$ to an open problem in glass physics is considered. In particular, the variance of $E$ is used to characterize short-time structural relaxation in Kob-Andersen-type mixtures. This variance is found to be nearly composition independent at the onset temperature of glassy dynamics. It is also observed to behave like a heuristic measure of glass-forming ability, which could prove useful when exact methods are intractable."],"dc:description.degree":["Ph.D."],"dc:identifier.uri":["http://hdl.handle.net/1807/128007"],"dc:title":["On Local Order in Particle Packings"],"dc:type":["Thesis"]},"updated_at":"2026-07-27T21:28:11Z"}