Numerical Studies on Collective Motion and Polymer Statistics

Abstract

This thesis aims to study two areas in computational biology, namely the collective motion and polymer statistics.

The first part of the thesis focuses on collective motion which is the common coordinated behaviour observed in many scenarios. Models of different complexities are studies and simulated. We focus on the Vicsek model with repulsion and the model generated from the Navier-Stokes system. We also simulate a large system of rigid self-propelling rods in different domains. Finally we simulate particles in viscous fluids.

The second part of the thesis deals with polymer statistics. We use a path integral approach to map the problem to a quantum rotor on a unit sphere to get the 3d end to end distribution of the worm like chain. With the distribution at hand, we can get the force extension relationship and free energies of the chains with different conformations.