Scaling Limits of Active Particles
S.T. Holtrop (TU Delft - Applied Sciences)
F.H.J. Redig – Mentor (TU Delft - Electrical Engineering, Mathematics and Computer Science)
J.M. Thijssen – Mentor (TU Delft - Applied Sciences)
W.G.M. Groenevelt – Graduation committee member (TU Delft - Electrical Engineering, Mathematics and Computer Science)
T. Idema – Graduation committee member (TU Delft - Applied Sciences)
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Abstract
In this thesis, the diffusive limit of active particle motion in Rd is studied via a technique based on homogenisation. Thereafter, this study is extended to active particle motion on a Riemannian manifold.
Furthermore, as an application of active particle motion, a connection is made with the Dirac equation. On the basis of this connection, a Monte Carlo method is developed to find the ground state of a Dirac equation with static potential. The core idea of this method is based on the Diffusion Monte Carlo method for the Schrödinger equation.