Self-Avoiding Walks Used as Simulations to Polymers

Author: Adalis Castro Santiago, Department of Mathematics, University of Puerto Rico at Humacao, Puerto Rico 00791 Faculty mentor: José O. Sotero Esteva, Department of Mathematics, University of Puerto Rico at Humacao, Puerto Rico 00791

Linear polymers are molecules that form in long chains of basic units called monomers. Chains can be quite long, and scientists want to know how many different configurations a chain of n-monomers can take. Self-avoiding walks can help enumerate configurations and understand the behavior of molecules when used as a simulation for polymers. A self-avoiding walk (SAW) is a sequence of moves on a lattice, which does not visit the same point more than once. Molecular modeling and simulations facilitate predictions and provide explanations of experimentally observed macromolecular structure, dynamics, thermodynamics, and microscopic and macroscopic material properties.


In this work we apply transfer matrix techniques to develop an algorithm to enumerate two SAWs with one of their ends fixed at one of the sides of the lattice.  The transfer matrix allows us to study the variation in space of a segment. The idea is to start with a term we call Cn to determine the possible SAWs that can be taken based on n-steps. We define Cn as the number of n-step self-avoiding walks beginning at origin. Also, we can use symmetry to calculate half of the lattice. A modification of the algorithm using  GPUs was also implemented. This way we can understand the behavior of polymers and use these results to inform, guide, and complement macromolecular materials design and discovery efforts. These results will help us to predict different behaviors of polymer molecules.


Additional Abstract Information

Presenter: Adalis Santiago

Institution: University of Puerto Rico at Humacao

Type: Oral

Subject: Computer Science

Status: Approved

Time and Location

Session: Oral 11
Date/Time: Wed 3:00pm-4:00pm
Session Number: 1111
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