Characterization and Mechanism of Rigidity in Columns of Star-shaped Granular Particles by Yuchen Zhao Department of Physics Duke University Date: Approved: Joshua E. S. Socolar, Advisor Patrick Charbonneau Gleb Finkelstein Sara Haravifard Jian-Guo Liu Dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Physics in the Graduate School of Duke University 2020