Quantitative analysis of the gain in probability of escaping for ideal phototactic swimmers due to chaotic dynamics

We study the dynamics of ideal phototactic swimmers in a steady two-dimensional model flow with transport barriers. We consider a distant light source, in which case the self-propulsion velocity of the swimmers is, at any instant, along a predetermined direction. The probability of transport along that direction emerges from the competing effects of the swimmers' self-propulsion and the flow's transport barriers. For swimmers bounded to have the same time average self-propulsion speed, temporal modulation of that speed increases the probability of escaping due to the formation of a stochastic layer which fosters transport. We use separatrix-map techniques to calculate the gain in the probability of escaping.