Print Email Facebook Twitter Ergodic theory and hydrodynamic limit for run-and-tumble particle processes Title Ergodic theory and hydrodynamic limit for run-and-tumble particle processes Author van Wiechen, Hidde (TU Delft Electrical Engineering, Mathematics and Computer Science) Contributor Redig, F.H.J. (mentor) Degree granting institution Delft University of Technology Programme Applied Mathematics Date 2021-08-19 Abstract In this thesis we will study the ergodic measures and the hydrodynamic limit of independent run-and-tumble particle processes, i.e., an interacting particle system for particles with an internal energy source, which makes them move in a preferred direction that changes at random times. We start by providing some basic concepts and theory of Markov processes and interacting particle systems. Afterwards, we define our model on the particle state space $\mathbb{Z}^d \times S$, with $S$ a finite space of internal states, by giving its generator, and we prove a duality result with a similar process which we will use repeatedly throughout this thesis. Then we show that the product Poisson measures with constant parameter are ergodic, and are also the only ergodic probability measures for this process in the space of so-called tempered measures, i.e., measures with bounded factorial moments. Lastly we prove the hydrodynamic limit of this process on $\mathbb{Z} \times S$ by showing that the evolution of the macroscopic density is a weak solution to a PDE. Subject Interacting Particle SystemsRun-and-Tumble ParticlesErgodic TheoryHydrodynamic LimitDuality To reference this document use: http://resolver.tudelft.nl/uuid:d1cfed8d-fa5a-4d99-ba9d-49ea66a48a3e Part of collection Student theses Document type master thesis Rights © 2021 Hidde van Wiechen Files PDF Hidde_van_Wiechen_Thesis_.pdf 646.74 KB Close viewer /islandora/object/uuid:d1cfed8d-fa5a-4d99-ba9d-49ea66a48a3e/datastream/OBJ/view