Survival time of active Brownian particles on flat curves

We find the average time for an overdamped active Brownian particle (OABP) moving on any flat curve with metric, to first reach a given point on the curve (so called mean-first passage time, MFPT). This problem can also be interpreted as the survival time an OABP has, before it is absorbed at a give point on the curve. From this analysis, a general MFPT equation depending on the curve’s geometry is found and solved for three particular cases, namely, a circle, an ellipse, and a second order limacon. The results are also validated by using Brownian dynamics simulations.