A model of intermittent ballistic-Brownian particle transport and its asymptotic approximation

A mean-field model of intermittent transport of particles, molecules or organelles is proposed. A particle may be in one of two phases: the first is a ballistic (active) phase, when the particle runs with constant velocity in some direction, and the second is a Brownian (passive) phase, when the particle diffuses freely. The particle can instantly change the phase of motion. The distribution of the duration of the passive phase (the free path distribution) is exponential, while that of the active phase is arbitrary. In the case that transitions between the phases are very frequent an approximation to the model is derived. An example is given which shows that the use of the exponential distribution of free paths, when it is actually non-exponential, may lead to significant errors in solutions.