Electronic Thesis and Dissertation Repository


Master of Science


Applied Mathematics


Dr. Colin Denniston


Simulations help us test various restrictions/assumptions placed on physical systems that would otherwise be difficult to efficiently explore experimentally. For example, the Scallop Theorem, first stated in 1977, places limitations on the propulsion mechanisms available to microscopic objects in fluids. In particular, the theorem states that when the viscous forces in a fluid dominate the inertial forces associated with a physical body, such a physical body cannot generate propulsion by means of reciprocal motion. The focus of this thesis is to firstly, explore an adaptive Multiple-timestep(MTS) scheme for faster molecular dynamics(MD) simulations, and secondly, use hybrid MD-LBM(Lattice-Boltzman Method) to test the Scallop Theorem's restrictions using an elastic spherical swimmer. The work begins with developing and demonstrating an adaptive MTS technique that reduces the run time of single timestep(STS) velocity-Verlet integration scheme. Later we discuss our simulation, which uses the MD-LBM method to simulate a spherical elastic swimmer in water-like fluid and prove that it indeed overcomes the Scallop Theorem. We investigate the relation between the swimmer's physical behaviour(speed, frequency) and it’s properties(radius, bulk modulus etc).