3 research outputs found
Intermittent random walks for an optimal search strategy: One-dimensional case
We study the search kinetics of an immobile target by a concentration of
randomly moving searchers. The object of the study is to optimize the
probability of detection within the constraints of our model. The target is
hidden on a one-dimensional lattice in the sense that searchers have no a
priori information about where it is, and may detect it only upon encounter.
The searchers perform random walks in discrete time n=0,1,2, ..., N, where N is
the maximal time the search process is allowed to run. With probability \alpha
the searchers step on a nearest-neighbour, and with probability (1-\alpha) they
leave the lattice and stay off until they land back on the lattice at a fixed
distance L away from the departure point. The random walk is thus intermittent.
We calculate the probability P_N that the target remains undetected up to the
maximal search time N, and seek to minimize this probability. We find that P_N
is a non-monotonic function of \alpha, and show that there is an optimal choice
\alpha_{opt}(N) of \alpha well within the intermittent regime, 0 <
\alpha_{opt}(N) < 1, whereby P_N can be orders of magnitude smaller compared to
the "pure" random walk cases \alpha =0 and \alpha = 1.Comment: 19 pages, 5 figures; submitted to Journal of Physics: Condensed
Matter; special issue on Chemical Kinetics Beyond the Textbook: Fluctuations,
Many-Particle Effects and Anomalous Dynamics, eds. K.Lindenberg, G.Oshanin
and M.Tachiy
Efficient search by optimized intermittent random walks
We study the kinetics for the search of an immobile target by randomly moving
searchers that detect it only upon encounter. The searchers perform
intermittent random walks on a one-dimensional lattice. Each searcher can step
on a nearest neighbor site with probability "alpha", or go off lattice with
probability "1 - \alpha" to move in a random direction until it lands back on
the lattice at a fixed distance L away from the departure point. Considering
"alpha" and L as optimization parameters, we seek to enhance the chances of
successful detection by minimizing the probability P_N that the target remains
undetected up to the maximal search time N. We show that even in this simple
model a number of very efficient search strategies can lead to a decrease of
P_N by orders of magnitude upon appropriate choices of "alpha" and L. We
demonstrate that, in general, such optimal intermittent strategies are much
more efficient than Brownian searches and are as efficient as search algorithms
based on random walks with heavy-tailed Cauchy jump-length distributions. In
addition, such intermittent strategies appear to be more advantageous than
Levy-based ones in that they lead to more thorough exploration of visited
regions in space and thus lend themselves to parallelization of the search
processes.Comment: To appear in J. Phys.: Condensed Matter, special issue on "Random
Search Problem: Trends and Perspectives", eds.: MEG da Luz, E Raposo, GM
Viswanathan and A Grosber