Search efficiency of Brownian and Levy strategies with drift

Problem of target search has a long history. There are many theoretical and experimental works which discuss whether Levy flights, Brownian motion or intermittent search strategy is the most efficient way for a particle or predator to find the target. We introduce a new convenient measure of search efficiency and compute it for Brownian and Levy search with and without potential bias. This measure shows non-trivial behavior which depends on Levy flights exponent, initial distance of a particle from the target and drift velocity. Analytical and numerical results show that either Brownian or Levy flights can be efficient depending on the initial conditions. Cumulative probability to reach a target ever is also calculated. Analytical and numerical results are obtained from fractional Fokker-Planck equation and supported by Monte-Carlo simulations