Simulation of continuous-time random walks with anharmonicity

  • Richmond Lin Co National Institute of Physics, University of the Philippines Diliman
  • Cristine Villagonzalo National Institute of Physics, University of the Philippines Diliman

Abstract

Anomalous diffusion processes are best described and analyzed by a continuous-time random walk (CTRW) formalism. The latter is a generalization of a transport model using random walk processes that are not limited to Markovian systems. Using a robust numerical generation of continuous trajectories based on Langevin equations, sample paths from a CTRW system encountering a nonlinear net force were generated and analyzed. The resultant force comprised of a linear repelling term and an anharmonic term, that is, f(x) = -k₁ x + k₂ x³. The effect of anharmonicity through varying the k₂ values on the trajectories was manifested on the waiting time. This is the time at which the particle is relatively stationary. At a fixed stability index α, the results show that generally, waiting times would increase as k₂ values increased and that there is an optimum value of k₂ where the waiting time is longest. These results are compared to the case when only the linear force is present.

Published
2019-05-22
How to Cite
[1]
R. Co and C. Villagonzalo. Simulation of continuous-time random walks with anharmonicity, Proceedings of the Samahang Pisika ng Pilipinas 37, SPP-2019-PB-48 (2019). URL: https://paperview.spp-online.org/proceedings/article/view/SPP-2019-PB-48.