Target-searching on the percolation

TL;DR

This study investigates a target-searching process on a percolation cluster, revealing a scaling law for search time dependent on percolation connectivity and hunter sensitivity, with search efficiency decreasing below a critical threshold.

Contribution

It introduces a model of odor-based target searching on percolation clusters and identifies how connectivity and sensitivity affect search efficiency and scaling behavior.

Findings

Scaling law for search time at high percolation connectivity

Search probability drops significantly below a critical percolation threshold

Hunter becomes trapped in percolation clusters at low connectivity

Abstract

We study target-searching processes on a percolation, on which a hunter tracks a target by smelling odors it emits. The odor intensity is supposed to be inversely proportional to the distance it propagates. The Monte Carlo simulation is performed on a 2-dimensional bond-percolation above the threshold. Having no idea of the location of the target, the hunter determines its moves only by random attempts in each direction. For lager percolation connectivity $p\gtrsim 0.90$, it reveals a scaling law for the searching time versus the distance to the position of the target. The scaling exponent is dependent on the sensitivity of the hunter. For smaller $p$, the scaling law is broken and the probability of finding out the target significantly reduces. The hunter seems trapped in the cluster of the percolation and can hardly reach the goal.