Organodynamics	Grant Holland, Apr 25, 2014
Slide: Topological State – Example from Chemistry	Nav Refs Top Bottom Previous Next 90m 90m 45m 45m 25m 25m
Challenge: Mathematically Modeling Molecular Compositional Dynamics (MCD) Representing how a closed collection of atoms changes molecular organization over time. Viewing a closed set of atoms as being organized into molecules; having those atoms reorganized into other configurations of molecules over time. An underlying set S: A closed finite collection of assorted atomic structures Note: Two ways to articulate the concept of system organization: - Compartmentalization of the components (atoms) of the system S - Interrelationships among the components (atoms)	Molecular Dynamics There is a discipline of chemistry named molecular dynamics. It focuses rates of change from one molecular configuration to another. It focuses on the time domain. But, organodynamics is not focused on rates of change. Rather it is focused on the organization of an underlying set, and on how that organization changes. While rates are characterized by real numbers, organization is characterized by complex constructs such as configurations, interrelationships, covers, geometries or topologies. Some counting distributions are meaningful to MCD. But in general, organizations in MCD are not associated with numbers.
The concept of molecule could be used in this MCD example to provide this compartmentalization of the atoms. The covalent, ionic and other bonding forces in physical chemistry can be used to suggest sets of interrelationships between and among the components (atomic structures) of our underlying set.	Candidate mathematical constructs Use a topology on the underlying set of atoms to represent compartmentalization into molecules. Use set-theoretic relations on the underlying set of atoms to represent network interrelationships among atoms. (Analog of graph theory.) Somehow combine the two ideas into a single structure to involve both meanings.

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