Chinese Physics B, Volume. 29, Issue 9, (2020)

Active Brownian particles simulated in molecular dynamics

Liya Wang1,4, Xinpeng Xu2, Zhigang Li3, and Tiezheng Qian4、†
Author Affiliations
  • 1Faulty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 2203, China
  • 2Faculty of Physics, Guangdong-Technion - Israel Institute of Technology, Shantou 515063, China
  • 3Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Hong Kong, China
  • 4Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong, China
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    Figures & Tables(11)
    (a) A snapshot of the simulation showing a dilute suspension of three active particles in the simulation box. The red particles are the head particles and the blue particles are the fluid particles in the phantom regions. Fluid particles out of the phantom regions are not shown here. Due to the periodic boundary conditions, the fluid body of one active particle is separated into four parts. (b) The ABP modeled in this work. A force dipole is exerted on the head particle and the phantom region of fluid to model a pusher.
    (a) Exponential decay of the orientational time correlation function C(t) for Dr=0.05τ0−1. The red solid line represents the numerical result and the black dashed line represents the exponential fitting with τr = 10.32τ0. (b) The product Dr × τr plotted for different values of Dr in units of τ0−1. Note that for small Dr, τr is large and leads to large statistical error in a limited time duration.
    (a) Gaussian distribution of the axial velocity wA, plotted for different values of rotational diffusivity Dr (in units of τ0−1) and applied force FA (in units of εffσff−1). (b) The active velocity vA plotted as a function of the applied force FA for Dr=0.01τ0−1 and 0.02τ0−1.
    Dependence of the standard deviation σA on the size of ABP.
    Trajectories of a PBP and three ABPs with lA = 0.18σff from τr=1τ0,vA=0.18σffτ0−1, lA = 1.125σff from τr=25τ0,vA=0.045σffτ0−1, and lA = 4.5σff from τr = 50τ0, vA=0.09σffτ0−1. Each trajectory includes 100 frames with a time duration of 25τ0.
    (a) MSD for PBPs (solid line), with DT found to be 0.015σff2τ0−1 through a linear fitting (dashed line). (b) MSD for three ABPs with different values of Dr (in units of τ0−1) and FA (in units of εffσff−1). In each case, the solid line represents the simulation data and the dashed line of the same color represents the corresponding linear fitting.
    MD simulation results for the dependence of DA on vA2 for Dr=0.01τ0−1 and 0.02τ0−1. From the linear fitting (dashed lines), the prefactor α in DA≃αvA2τr is found to be 0.274 for Dr=0.01τ0−1 and 0.252 for Dr=0.02τ0−1.
    The equilibrium PDF g(r) of the confined PBP for k=εffσff−2.
    Evolution of the PDF g(r) with the increase of R1. (a) The Boltzmann-type distribution for R1 = 0.125. (b) A distribution slightly deviating from the Boltzmann-type for R1 = 0.25. (c) A distribution exhibiting a plateau in the central region for R1 = 0.5. (d) A bimodal distribution for R1 = 1 with the accumulation of probability near r = ± rB. Here the red line represents a fitting of the Boltzmann-type and the gray region is bounded by r = ± rB.
    The PDF g(r) and marginal PDF f(x). (a) g(r) for R1 = 0.5. (b) f(x) for R1 = 0.5. (c) g(r) for R1 = 2.5. (d) f(x) for R1 = 2.5. In (b) and (d), f(x) directly measured in simulations (represented by solid circles) is compared to that obtained from g(r) by the use of Eq. (23) (represented by solid line), with good agreement.
    • Table 1. Comparison between DAC and DAF.

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      Table 1. Comparison between DAC and DAF.

      R1vA/(σffτ01)x2/σff2DAC/(σff2/τ0)DAF/(σff2/τ0)Error/%
      0.1250.0915.770.0720.05819.4
      0.250.097.290.0720.05819.4
      0.50.093.050.0690.05815.9
      10.183.980.2880.20827.7
      2.50.180.980.2910.20828.5
      100.180.100.2750.20824.4
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    Liya Wang, Xinpeng Xu, Zhigang Li, Tiezheng Qian. Active Brownian particles simulated in molecular dynamics[J]. Chinese Physics B, 2020, 29(9):

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    Paper Information

    Received: May. 25, 2020

    Accepted: --

    Published Online: Apr. 29, 2021

    The Author Email: Qian Tiezheng (maqian@ust.hk)

    DOI:10.1088/1674-1056/aba60d

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