Scaled Brownian motion as transient behavior of individual particle diffusion due to multiple probe-to-probe collisions

Authors

  • Adrielle Theresa DL. Cusi National Institute of Physics, University of the Philippines Diliman
  • Caesar A. Saloma National Institute of Physics, University of the Philippines Diliman

Abstract

We investigate the possible transient effect of elastic probe-to-probe collisions on the diffusion of individual probes and ensembles through the changes in the diffusion coefficient D and the anomalous exponent α . Coefficient D quantifies the diffusion speed of the system while exponent α measures the deviation from normal diffusion or pure Brownian motion (BM) where: α = 1 indicates pure BM, and α ≠ 1 indicates anomalous diffusion (AD) or scaled BM. We modeled originally pure BM ensembles subjected to collisions using a combination of time-driven BM and event-driven collisions algorithms. Using the time-averaged mean-squared displacement analysis technique of the scaled BM theory, we measured Diso and αiso from the collision-less pure BM trajectories, and Dcol and αcol from the collision-laden trajectories. Results show that the ensemble- and individual probe-levels of diffusion slow down (Dcol < Diso) due to collisions. At the ensemble-level, there is persistence of pure BM (αcol ≈ αiso = 1) despite collisions. Results at the individual-level reveal that the ensemble pure BM behavior is due to the dominant pure BM-behaving probes in the population. Yet, a significant fraction of the particle population exhibited AD (αcol ≠ αiso) at short sampling periods of T < 4590 time intervals. As T increases, the ensembles eventually reach a steady-state condition where all probes diffuse normally. We conclude that probe-to-probe collisions cause the transient AD of individual particles at short T. Thus, anomalous diffusion emerges even without complex attractive and repulsive probe-probe and probe-medium interactions.

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Article ID

SPP-2022-3G-02

Section

Complex Systems and Data Analytics

Published

2022-09-28

How to Cite

[1]
ATD Cusi and CA Saloma, Scaled Brownian motion as transient behavior of individual particle diffusion due to multiple probe-to-probe collisions, Proceedings of the Samahang Pisika ng Pilipinas 40, SPP-2022-3G-02 (2022). URL: https://proceedings.spp-online.org/article/view/SPP-2022-3G-02.