Ninth Annual Graduate Student Miniconference in Computational Mathematics
Erik Palmer
University of South Carolina http://people.math.sc.edu/etpalmer/ 

Abstract 
A stochastic model for high performance computing of polymer gel behavior
Hydrogels have attracted attention as "smart" materials for their tunable mechanical properties that respond to environmental stimuli such as pH, UV, or temperature; making them ideal for a variety of biomedical and sensor technology applications. Consisting of mostly water, the viscoelastic properties of hydrogels are the product of a network of polymer chains attaching and detaching at various entanglement points. Due to this complexity at the microscale, many previous polymer simulations rely on mathematical simplifications of chain dynamics to produce results. In this poster we explore the potential for a meanfield model to capture the properties that emerge from a mixture of hydrogels using massively parallel computation on graphics processing units. This approach abstracts away the network positions and uses stochastic differential equations derived from physical properties to capture the breaking and reforming behavior of attached segments, thereby keeping the nonlinear microscale polymer dynamics intact. 