Spatio-Temporally Adaptive Transport in Complex Systems
Multiple-scale mobility is ubiquitous in nature, from human travelling to molecular transport. Adapting to the environment, the characteristics of the mobility vary spatially and temporally. For example, intracellular vesicles perform a Lévy walk and a Brownian random walk when they are on and off the cytoskeletal filaments. Traditional analysis based on a single type of stochastic process failed to capture the complexity of the mobility. In this project, we focus on developing a generalized stochastic model where the persistent length and the velocity change according to the environmental conditions. By properly choosing the persistent length and the velocity, we aim to develop generalized models able to describe a random walk, a Lévy walk and other types of intermittent walk. We are particularly interested in understanding how hidden structures of space partitions space influence the mobility and the long-run probability distribution of the transport? This fundamental understanding has potential impact in a variety of natural and engineered systems. For example, it can help understand how molecular motors accurately navigate through cytoskeletal networks and ensure efficient protein distribution inside the cell. This knowledge can also help understand nanotransport in complex engineered systems.