Journal
PHYSICS OF FLUIDS
Volume 35, Issue 10, Pages -Publisher
AIP Publishing
DOI: 10.1063/5.0173374
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This study focuses on the three-dimensional RTP model in a harmonic trap and derives the recurrence relation for generating moments of a stationary distribution. These moments are then used to recover the stationary distribution.
When it comes to active particles, even an ideal gas model in a harmonic potential poses a mathematical challenge. An exception is a run-and-tumble particles (RTP) model in one dimension for which a stationary distribution is known exactly. The case of two dimensions is more complex, but the solution is possible. Incidentally, in both dimensions the stationary distributions correspond to a beta function. In three dimensions, a stationary distribution is not known but simulations indicate that it does not have a beta function form. The current work focuses on the three-dimensional RTP model in a harmonic trap. The main result of this study is the derivation of the recurrence relation for generating moments of a stationary distribution. These moments are then used to recover a stationary distribution using the Fourier-Lagrange expansion.
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