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Updated: Jan 1, 2026

MPI CyberMotion Simulator: Implementation of a Novel Motion Simulator to Investigate Multisensory Path Integration in Three Dimensions
Published on: May 10, 2012
Run-and-tumble motion in one dimension with space-dependent speed
L Angelani1,2, R Garra3
1ISC-CNR, Institute for Complex Systems, Piazzale Aldo Moro 2, 00185 Rome, Italy.
Abstract:
We consider a particle performing run-and-tumble dynamics with space-dependent speed. The model has biological relevance as it describes motile bacteria or cells in heterogeneous environments. We give exact expression for the probability density function in the case of free motion in unbounded space. We then analyze the case of a particle moving in a confined interval in the presence of partially absorbing boundaries, reporting the probability density in the Laplace (time) domain and the mean time to absorption. We also discuss the relaxation to the steady state in the case of confinement with reflecting boundaries and drift effects due to direction-dependent tumbling rates, modeling taxis phenomena of cells. The case of diffusive particles with spatially variable diffusivity is obtained as a limiting case.
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