2019/06/12 by Sanhedrai, Hillel, Maayan, Yafit, Shekhtman, Louis · 1 citation
#FOS: Physical sciences #Physics and Society (physics.soc-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.1906.04974
We study a greedy forager who consumes food throughout a region. If the forager does not eat any food for S time steps it dies. We assume that the forager moves preferentially in the direction of greatest smell of food. Each food item in a given direction contributes towards the total smell of food in that direction, however the smell of any individual food item decays with its distance from the forager. We assume a power-law decay of the smell with the distance of the food from the forager and vary the exponent α governing this decay. We find, both analytically and through simulations, that for a forager living in one dimension, there is a critical value of α, namely αc, where for ααc the forager has a nonzero probability to live infinite time. We calculate analytically, the critical value, αc, separating these two behaviors and find that αc depends on S as αc=1 + 1/\lceil S/2 \rceil. We determine analytically that at α=αc the system has an essential singularity. We also study, using simulations, a forager with long-range decaying smell in two dimensions (2D) and find that for this case the forager always dies within finite time. However, in 2D we observe indications of an optimal α for which the forager has the longest lifetime.