Target Search of Single Active Brownian Particles

Active propulsion allows living micro-organisms, bacteria or unicellular protozoa, to explore their local environment and forage nutrients. Responding to chemical gradients or other stimuli is essential for such active agents to optimize survival strategies in complex media. In recent years, there has been enormous experimental progress to build artificial swimmers or self-propelled particles and monitor their behavior in well-controlled environments. The interest in such active agents is manifold originating from understanding true non-equilibrium processes at a fundamental level, manipulating and controlling the phase behavior of collections of active particles as a new state of matter, as well as their anticipated fundamental role in the nanotechnology of the 21st century, in particular, for biomedical engineering, controlled drug delivery, and environmental cleansing of soil and polluted water. The current project aims at analytical as well as simulational progress for two paradigmatic models for active particles in the context of the target-search problem. The active Brownian particle (ABP) model extends the diffusive motion of a passive particle by the directed self-propelled motion. While the diffusive motion is often compared to the random walk of drunken sailor taking random steps, the active Brownian particles resembles more a drunk driver moving at constant speed, however the direction of driving evolves randomly. This model is appropriate for synthetic active particles, whose directed motion is induced by converting chemical energy or induced by irradiation with laser light. The second model, the run-and-tumble agent, is an accurate model for bacterial motion. Here the bacteria move essentially along straight paths interrupted by regular or random tumbling events where the bacteria remains at the same position and finds a new direction to move. Here we will develop analytical tools for simple geometries for target search. For example we want to solve analytically what is the probability for an active Brownian particle to reach for the first time a wall separated at a distance. A second problem is to determine the probability distribution for the first passage of a run-and-tumble agent in chemotaxis, i.e. when a chemical nutrient attracts the agent toward a certain direction. We also intend to perform new simulations for active agents in complex landscapes, for example, when the active particle has to overcome an energy barrier before reaching the target. Then the target-search problem becomes a rare event and brute-force simulations are inefficient. To circumvent this difficulty we will rely on advanced sampling methods that are know to work for passive particles. The scientific challenge here is to find suitable algorithms that transfer to active particles without introducing artefacts that could distort the probabilities to find the target.