Rosenbluth Algorithm Studies of Self-Avoiding Walks

In this thesis we used self-avoiding walks as a model of linear polymers to study some of the most fundamental questions about polymers- namely the quantification of polymer entropy. We introduced scaling formulas for the number of walks and other polymer properties such as radius of gyration and end-to-end distance. Then, we calculated these quantities using a Monte Carlo simulation and estimated the critical exponents in the scaling formulas.

There is a pressure field in the vicinity of a polymer and a particle placed close to the polymer will accelerate away from it due to the pressure gradient. The scaling of the pressure as a function of distance from the polymer and length of the polymer is determined and tested numerically. Also, we modeled the relationship between velocity and the position of the particle in the 2-dimensional lattice and estimated the limiting speed.