A mathematical programming approach for lattice molecular simulations
Abstract
Computer simulation of molecular systems is essential for testing the predictions of various theories and for explaining observations. At a low resolution, polymer chains may be modeled as self avoiding (non overlapping) walks on a lattice. Simulation methods for generating such a self avoiding walks face serious limitations for generation of long walks and in the case of dense systems. Various instances of dense simulations arise in the investigations of globular proteins, the collapsed state of homopolymers and polymer melts in addition to other polymeric systems with solvents that are widely studied in the literature. Existing simulation methods are impractical for generation of chains in a compact shape, and it is essential to develop algorithms because of the increasing interest in compact chains. In this thesis, an alternate approach for lattice simulations has been investigated based on ideas from mathematical programming and graph theory. An effective algorithm has been developed for the case of a lattice filling chain. With the combinatorial method developed in this thesis, one can explore chains of length 215999 (filling a 60 x 60 x 60 cubic lattice) in a sparc-2 workstation. A dynamic simulation method has been developed for this problem, which is probably ergodic. The combinatorial simulation methods explored in this thesis perform extremely well in the presence of geometrical constraints where the existing growth methods do not perform well. Possible extensions of this approach are discussed in terms to potential impacts of combinatorial methods in simulation studies.
Degree
Ph.D.
Advisors
Pekny, Purdue University.
Subject Area
Chemical engineering|Industrial engineering|Molecules|Polymers
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