  A random search is a stochastic process representing the random motion of a
particle (denoted as the searcher) that is terminated when it reaches (detects)
a target particle or area the first time. In intermittent search the random
motion alternates between two or more motility modes, one of which is
non-detecting. An example is the slow diffusive motion as the detecting mode
and fast, directed ballistic motion as the non-detecting mode, which can lead
to much faster detection than a purely diffusive search. The transition rate
between the diffusive and the ballistic mode (and back) together with the
probability distribution of directions for the ballistic motion defines a
search strategy. If these transition rates and/or probability distributions
depend on the spatial coordinates within the search domain it is a spatially
inhomogeneous search strategy, if both are constant, it is a homogeneous one.
Here we study the efficiency, measured in terms of the mean first-passage time,
of spatially homogeneous and inhomogeneous search strategies for three
paradigmatic search problems: 1) the narrow escape problem, where the searcher
has to find a small area on the boundary of the search domain, 2) reaction
kinetics, which involves the detection of an immobile target in the interior of
a search domain, and 3) the reaction-escape problem, where the searcher first
needs to find a diffusive target before it can escape through a narrow region
on the boundary. Using families of spatially inhomogeneous search strategies,
partially motivated by the spatial organization of the cytoskeleton in living
cells with a centrosome, we show that they can be made almost always more
efficient than homogeneous strategies.
