Generalized run-and-tumble model in 1D geometry for an arbitrary distribution of drift velocities

In this work, we investigate extensions of the run-and-tumble particle model in 1D. In its simplest version, particle drift is limited to two velocities v = +/- v (0) and the model is exactly solvable. Extension of the model to three drifts v = 0, +/- v (0) yields the exact solution but the complexity of the expressions indicates that analytical treatment of higher-state models under the same procedure is impractical. Consequently, we modify our goal and consider a generalized version of the model for an arbitrary distribution of states P(v). To analyze such a system, we reformulate the Fokker-Planck equation as a self-consistent relation. The self-consistent relation is then analyzed by means of Laplace transform techniques.

Automated summary

The study investigates extensions of the run-and-tumble particle model in 1D, finding that expanding the model to three drifts leads to complexity. Therefore, the researchers modified their goal and considered a version of the model with an arbitrary distribution of states, analyzing the system through self-consistent relations and Laplace transform techniques.