Stochastic Search in 1D: Optimizing the search time

ORAL

Abstract

We investigate the efficiency of several search strategies in one dimension. First we simulate an unbiased stochastic search with multiple searchers. We consider an infinitely long one-dimensional line where N searchers are launched from an initial position x $=$ L at t $=$ 0 in an attempt to reach a target at x $=$ 0. We simulate this process computationally for multiple searchers to find the optimal number of searchers to minimize the search cost and compare our computational results to the analytical results from Meerson and Redner, 2014. We find that the distribution of the search cost follows a power law distribution on a log-log scale. Secondly, we consider a biased search with one biased random walker that is reset to its starting point with rate r and the direction of the bias alternates with every reset. We simulate the case without diffusion computationally for various rates to find the optimum resetting rate r* and compare our results with analytical results. Lastly, we consider a resetting search with a fixed diffusion and vary the magnitude of the bias in both directions to determine how the minimum search time corresponding to each optimal resetting rate is affected as the magnitude of the bias increases.

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Authors

  • Christy Contreras

    Arizona State University

  • Scott D. Bergesen

    Santa Fe Institute, Arizona State University, Department of Physics and Center for Biological Physics, Arizona State University, Brigham Young University Department of Physics and Astronomy, Brigham Young University, Utah Valley University, Dixie State College, Advisor, Student, Massachusetts Institute of Technology, Thomas Jefferson National Accelerator Laboratory, Colorado College, United States Air Force Academy, Georgia Institute of Technology, Utah State University, Brigham Young University - Idaho, Utah State University- Logan, National Institute of Standards and Technology, Humboldt State University, UC Santa Cruz, Institut de Chimie des Substances Naturelles, Arizona State Univ, University of Colorado at Colorado Springs, National Jewish Health, Department of Physics, The University of Texas at Austin, Department of Physics, New Mexico State University, U. S. Air Force Academy, Brigham Young Univ - Provo, University of New South Wales, University of Texas, University of Warwick, University of Louisiana, Department of Physics and Astronomy, Brigham Young University, Provo, Utah 84602, USA., Center for Materials Genomics, Department of Mechanical Engineering and Materials Science and Department of Physics, Duke University, Durham, North Ca, Duke University, Durham, North Carolina., Brigham Young University -- Provo, Utah, General Atomics -- San Diego, California, Department of Mathematics, University of British Columbia, Department of Physics, Arizona State University, UC Riverside, UMASS, STScI, NOAO, UT Austin, Texas A&M, Arizona State Univeristy, New Mexico State Univ, Los Alamos National Laboratory, Colorado State Univ, Department of Physics, Oregon State University, Colorado School of Mines, University of Alaska, Fairbanks, The Peac Institute of Multiscale Modeling, UNSW Canberra