Many living systems, such as bacteria or eukaryotic cells, utilize self-propulsion to enhance transport, find nutrients, or avoid threats. However, cells often inhabit complex and heterogeneous spaces---e.g. gels and tissues in the body, or soil sediments in the environment---that impede rapid transport. Additionally, many biologically and industrially relevant complex materials are opaque and difficult to characterize, indicating the need for adequate computational and analytical models to guide experimental efforts.
In this dissertation, I utilize theory and simulation to study the structure and motion of microscopic self-propelled (or active) species in confinement, including bacteria, synthetic swimmers, and cytoskeletal filaments. Active matter systems are inherently nonequilibrium and traditional theories of Brownian motion in porous media fail to accurately describe the swimmers' dispersion. Active particles accumulate along boundaries due to their self-propulsion, even in the absence of attractive interactions. This mechanism traps the active particles at regions of high concavity, coupling the diffusivity of the swimmer to the microstructure of the confining walls.
I then extend these theories to study the motion of anisotropic active particles (like cytoskeletal filaments or rod-shaped bacteria) in the presence of soft confinement. I develop a Smoluchowski model that demonstrates the connection between the long-time self-diffusivity and active rod nematic order. Finally, I use these results to examine the partitioning of bacteria in an aqueous two-phase system, and the nematic ordering of F-actin filaments on topographically patterned channels.
