- Title Information
- Title
- Combinatorial and Geometric Structure in the Self-Assembly of Polyhedra
- Name:
Personal
- Name Part
- Johnson, Daniel C
- Role
- Role Term:
Text
- creator
- Origin Information
- Copyright Date
- 2015
- Physical Description
- Extent
- xiii, 108 p.
- digitalOrigin
- born digital
- Note
- Thesis (Ph.D. -- Brown University (2015)
- Name:
Personal
- Name Part
- Menon, Govind
- Role
- Role Term:
Text
- Director
- Name:
Personal
- Name Part
- Gidas, Basilis
- Role
- Role Term:
Text
- Reader
- Name:
Personal
- Name Part
- Holmes-Cerfon, Miranda
- Role
- Role Term:
Text
- Reader
- Name:
Corporate
- Name Part
- Brown University. Applied Mathematics
- Role
- Role Term:
Text
- sponsor
- Genre (aat)
- theses
- Abstract
- We consider a discrete attachment model for the self-assembly of polyhedra called the Building Game. The combinatorial configuration space of the model is computed for the Polyhedra in the Platonic, Archimedean, and Catalan solids of up to 30 faces and several novel enumerative results are generated. Further, we extend the Building Game to include geometric information in the form of a polygonal linkage. Using systems of constraints to specify the linkage, the geometric configuration space is given as a solution manifold. A random walk scheme is used to simulate reflected Brownian motion on the geometric configuration space manifolds. The combinatorial and geometric aspects of the Building Game are combined and used in a Markov
process model for measuring statistics of the self-assembly process.
- Subject
- Topic
- Self-Assembly
- Subject (FAST)
(authorityURI="http://id.worldcat.org/fast", valueURI="http://id.worldcat.org/fast/1070511")
- Topic
- Polyhedra
- Record Information
- Record Content Source (marcorg)
- RPB
- Record Creation Date
(encoding="iso8601")
- 20150601
- Language
- Language Term:
Code (ISO639-2B)
- eng
- Language Term:
Text
- English
- Identifier:
DOI
- 10.7301/Z0ZK5F37
- Access Condition:
rights statement
(href="http://rightsstatements.org/vocab/InC/1.0/")
- In Copyright
- Access Condition:
restriction on access
- Collection is open for research.
- Type of Resource (primo)
- dissertations