Self-assembly is the process by which complex systems are formed and behave due to the interactions of relatively simple units. In this thesis, we explore multiple augmentations of well known models of self-assembly to gain a better understanding of the roles that geometry and space play in their dynamics. We begin in the abstract Tile Assembly Model (aTAM) with some examples and a brief survey of previous results to provide a foundation. We then introduce the Geometric Thermodynamic Binding Network model, a model that focuses on the thermodynamic stability of its systems while utilizing geometrically rigid components (dissimilar to other thermodynamic models). We show that this model is computationally universal, an ability conjectured to be impossible in similar models with non-rigid components. We continue by introducing the Flexible Tile Assembly Model, a generalization of the 2D aTAM that allows bonds between tiles to flex and assemblies to therefore reconfigure. We show how systems in this model can deterministically assemble shapes that adhere to a number of certain restrictions. Finally, we introduce the Spatial abstract Tile Assembly Model, a variation of the 3D aTAM that restricts tiles from attaching without a diffusion path. We show that this model is intrinsically universal, a property of computational models to simulate themselves which has been shown for the 3D aTAM and other similar models. We conclude this thesis with a summary of the presented results, a brief impact analysis, and potential directions for future research within this area.
","abstract_html":"<p>Self-assembly is the process by which complex systems are formed and behave due to the interactions of relatively simple units. In this thesis, we explore multiple augmentations of well known models of self-assembly to gain a better understanding of the roles that geometry and space play in their dynamics. We begin in the abstract Tile Assembly Model (aTAM) with some examples and a brief survey of previous results to provide a foundation. We then introduce the Geometric Thermodynamic Binding Network model, a model that focuses on the thermodynamic stability of its systems while utilizing geometrically rigid components (dissimilar to other thermodynamic models). We show that this model is computationally universal, an ability conjectured to be impossible in similar models with non-rigid components. We continue by introducing the Flexible Tile Assembly Model, a generalization of the 2D aTAM that allows bonds between tiles to flex and assemblies to therefore reconfigure. We show how systems in this model can deterministically assemble shapes that adhere to a number of certain restrictions. Finally, we introduce the Spatial abstract Tile Assembly Model, a variation of the 3D aTAM that restricts tiles from attaching without a diffusion path. We show that this model is intrinsically universal, a property of computational models to simulate themselves which has been shown for the 3D aTAM and other similar models. We conclude this thesis with a summary of the presented results, a brief impact analysis, and potential directions for future research within this area. </p>","abstract_has_math":false,"creators":["Sharp, Michael"],"institution":null,"degree_name":"Master of Science in Computer Science (MS)","degree_level":"Thesis","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Gauch, John M.","Luu, Khoa"],"advisors":["Patitz, Matthew J."],"committee_chairs":[],"committee_members":[],"year":2019,"date_issued":"2019-12-01T08:00:00Z","date_published":"2019-12-01T08:00:00Z","updated_at":"2026-07-24T01:00:28Z","subjects":["aTAM","computational theory","dna nanotechnology","nanostructures","self-assembly","tile assembly models","Numerical Analysis and Scientific Computing","Systems Architecture","Theory and Algorithms"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholarworks.uark.edu/etd/3517","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Gauch, John M.","Luu, Khoa"]},{"key":"dc:contributor.advisor","label":"Advisor","values":["Patitz, Matthew J."]},{"key":"dc:creator","label":"Author","values":["Sharp, Michael"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2019"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2024-02-06T08:00:00Z"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Thesis"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Master of Science in Computer Science (MS)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["aTAM","computational theory","dna nanotechnology","nanostructures","self-assembly","tile assembly models","Numerical Analysis and Scientific Computing","Systems Architecture","Theory and Algorithms"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholarworks.uark.edu/etd/3517"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Self-assembly is the process by which complex systems are formed and behave due to the interactions of relatively simple units. In this thesis, we explore multiple augmentations of well known models of self-assembly to gain a better understanding of the roles that geometry and space play in their dynamics. We begin in the abstract Tile Assembly Model (aTAM) with some examples and a brief survey of previous results to provide a foundation. We then introduce the Geometric Thermodynamic Binding Network model, a model that focuses on the thermodynamic stability of its systems while utilizing geometrically rigid components (dissimilar to other thermodynamic models). We show that this model is computationally universal, an ability conjectured to be impossible in similar models with non-rigid components. We continue by introducing the Flexible Tile Assembly Model, a generalization of the 2D aTAM that allows bonds between tiles to flex and assemblies to therefore reconfigure. We show how systems in this model can deterministically assemble shapes that adhere to a number of certain restrictions. Finally, we introduce the Spatial abstract Tile Assembly Model, a variation of the 3D aTAM that restricts tiles from attaching without a diffusion path. We show that this model is intrinsically universal, a property of computational models to simulate themselves which has been shown for the 3D aTAM and other similar models. We conclude this thesis with a summary of the presented results, a brief impact analysis, and potential directions for future research within this area.
"]},{"key":"dc:title","label":"Title","values":["Contrasting Geometric Variations of Mathematical Models of Self-assembling Systems"]}]}],"canonical_facts":{"dc:contributor":["Gauch, John M.","Luu, Khoa"],"dc:contributor.advisor":["Patitz, Matthew J."],"dc:creator":["Sharp, Michael"],"dc:date":["2019"],"dc:date.available":["2024-02-06T08:00:00Z"],"dc:description.abstract":["Self-assembly is the process by which complex systems are formed and behave due to the interactions of relatively simple units. In this thesis, we explore multiple augmentations of well known models of self-assembly to gain a better understanding of the roles that geometry and space play in their dynamics. We begin in the abstract Tile Assembly Model (aTAM) with some examples and a brief survey of previous results to provide a foundation. We then introduce the Geometric Thermodynamic Binding Network model, a model that focuses on the thermodynamic stability of its systems while utilizing geometrically rigid components (dissimilar to other thermodynamic models). We show that this model is computationally universal, an ability conjectured to be impossible in similar models with non-rigid components. We continue by introducing the Flexible Tile Assembly Model, a generalization of the 2D aTAM that allows bonds between tiles to flex and assemblies to therefore reconfigure. We show how systems in this model can deterministically assemble shapes that adhere to a number of certain restrictions. Finally, we introduce the Spatial abstract Tile Assembly Model, a variation of the 3D aTAM that restricts tiles from attaching without a diffusion path. We show that this model is intrinsically universal, a property of computational models to simulate themselves which has been shown for the 3D aTAM and other similar models. We conclude this thesis with a summary of the presented results, a brief impact analysis, and potential directions for future research within this area.
"],"dc:identifier":["https://scholarworks.uark.edu/etd/3517"],"dc:subject":["aTAM","computational theory","dna nanotechnology","nanostructures","self-assembly","tile assembly models","Numerical Analysis and Scientific Computing","Systems Architecture","Theory and Algorithms"],"dc:title":["Contrasting Geometric Variations of Mathematical Models of Self-assembling Systems"],"thesis:degree_level":["Thesis"],"thesis:degree_name":["Master of Science in Computer Science (MS)"]},"updated_at":"2026-07-24T01:00:28Z"}