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Title: Lattice Monte Carlo simulation of Galilei variant anomalous diffusion

The observation of an increasing number of anomalous diffusion phenomena motivates the study to reveal the actual reason for such stochastic processes. When it is difficult to get analytical solutions or necessary to track the trajectory of particles, lattice Monte Carlo (LMC) simulation has been shown to be particularly useful. To develop such an LMC simulation algorithm for the Galilei variant anomalous diffusion, we derive explicit solutions for the conditional and unconditional first passage time (FPT) distributions with double absorbing barriers. According to the theory of random walks on lattices and the FPT distributions, we propose an LMC simulation algorithm and prove that such LMC simulation can reproduce both the mean and the mean square displacement exactly in the long-time limit. However, the error introduced in the second moment of the displacement diverges according to a power law as the simulation time progresses. We give an explicit criterion for choosing a small enough lattice step to limit the error within the specified tolerance. We further validate the LMC simulation algorithm and confirm the theoretical error analysis through numerical simulations. The numerical results agree with our theoretical predictions very well.
Authors:
 [1] ;  [2] ;  [3] ;  [3]
  1. School of Information System and Management, National University of Defense Technology, Changsha, 410073 (China)
  2. (Germany)
  3. Institute of Computer Science, University of Rostock, Albert Einstein Str. 22, Rostock, 18059 (Germany)
Publication Date:
OSTI Identifier:
22465623
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics; Journal Volume: 288; Other Information: Copyright (c) 2015 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; ABSORPTION; ALGORITHMS; ANALYTICAL SOLUTION; COMPUTERIZED SIMULATION; DIFFUSION BARRIERS; ERRORS; GRAPH THEORY; MONTE CARLO METHOD; PARTICLE TRACKS; STOCHASTIC PROCESSES; TRAJECTORIES