Research ArticleMATERIALS SCIENCE

Nonequilibrium strongly hyperuniform fluids of circle active particles with large local density fluctuations

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Science Advances  25 Jan 2019:
Vol. 5, no. 1, eaau7423
DOI: 10.1126/sciadv.aau7423
  • Fig. 1 Absorbing-active transition.

    (A) Schematic of the 2D system of circle active particles. (B) Dynamic phase diagram in the representation of packing fraction ϕ and circle radius R. (C and D) Typical snapshots of the active and adsorbing states near the critical point with ϕ = 0.20 with R = 1.75σ, where the color indicates the self-propulsion orientation of each particle. These two states are marked as magenta and cyan solid symbols, respectively, in (E). (E) MSD as functions of time for system with R = 1.75σ started from random configurations. Red line, active state (ϕ = 0.22); blue line, absorbing state (ϕ = 0.01); green line, system near the critical point (ϕ = 0.20) in which the system ultimately falls into the absorbing state after a long simulation time. (F and G) Diffusion constant as functions of ϕ near the critical point ϕc for systems with different R. The dashed lines are the fitting of power law (ϕ − ϕc)β. (H and I) The structure factor S(q) and the orientation correlation function C(r) of active (magenta) and absorbing (cyan) states as marked by solid symbols in (E). (J) The measured critical exponent β from (G) as a function of R. For all the calculations, N = 10,000 and TR =0.

  • Fig. 2 Dynamic hyperuniform state.

    (A and D) MSD as functions of t for various R. (B and E) Density variances 〈δρ2〉 as functions of window size L for various R. The L−3 asymptotic line indicates the hyperuniform scaling, which is the same as in perfect crystals. The L−2 scaling is for normal fluids, while L0 is for clustering- or phase separation–induced large density fluctuations. (C and F) Structure factor S(q) for various R. The q2 asymptotic line indicates the hyperuniform scaling, while the q−2 line represents clustering- or phase separation–induced large density fluctuations. (G) Typical snapshots for systems at ϕ = 0.4 with various R. For all the calculations, N = 40,000 and TR.

  • Fig. 3 Dynamic microphase separation.

    (A) Growing rate κ2 as functions of q for systems at ϕ = 0.35 with various R obtained from the dynamic mean-field theory. (B) Measured heights of the first peak in S(q) for systems with different combinations of R and ϕ in computer simulations indicated by the color of the symbols. The dotted line is the fitting using Eq. 9 for the phase boundary. Inset shows the measured position of the first peak in S(q) in computer simulations (symbols) and the theoretical prediction (dotted line) based on the fitting in (B).

  • Fig. 4 Global hyperuniformity.

    (A and C) Scaled density variance 〈δρo2R2 as functions of L/R and (B and D) So(q) as functions of qR, for various R at ϕ = 0.2 (A and B) and 0.4 (C and D), respectively.

  • Fig. 5 Effect of thermal noises on hyperuniformity.

    (A) Structure factor So(q) under different reduced noise strength TR for ϕ = 0.2 and R = 3σ. Open symbols show the simulation data, while the dashed lines are the theoretical predictions of Eq. 16. (B) Normalized So(0) as functions of TR from theoretical prediction (dashed line) and the fitting of simulation results (solid symbols) for systems with ϕ = 0.2. For all the calculations, n = 40,000.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/1/eaau7423/DC1

    Section S1. Derivation of the dynamic mean-field theory for 2D system of circle active particles.

    Section S2. Linear stability analysis.

    Section S3. Calculation of So(q) for system with CMC.

    Section S4. Effect of thermal noise on So(q).

    Fig. S1. Finite-size effect on the long-time diffusion coefficient D as a function of packing fraction ϕ for systems with R = 1.75σ.

    Fig. S2. Structural comparison of active and absorbing state at R = 10σ near the critical point ϕc = 0.0194.

    Fig. S3. Structure factor S(q) for large systems with different R at φ = 0.4 and TR = 0.

    Fig. S4. Hyperunifomity in an experimentally realizable system (26) with bimodal circling-phase distribution.

    Movie S1. Active state in Fig. 1C.

    Movie S2. Absorbing state in Fig. 1D.

    Movie S3. Active state with R = 1000σ in Fig. 2G.

    Movie S4. Active state with R = 100σ in Fig. 2G.

    Movie S5. Active state with R = 50σ in Fig. 2G.

    Movie S6. Active state with R = 25σ in Fig. 2G.

    Movie S7. Active state with R = 23σ in Fig. 2G.

  • Supplementary Materials

    The PDF file includes:

    • Section S1. Derivation of the dynamic mean-field theory for 2D system of circle active particles.
    • Section S2. Linear stability analysis.
    • Section S3. Calculation of So(q) for system with CMC.
    • Section S4. Effect of thermal noise on So(q).
    • Fig. S1. Finite-size effect on the long-time diffusion coefficient D as a function of packing fraction ϕ for systems with R = 1.75σ.
    • Fig. S2. Structural comparison of active and absorbing state at R = 10σ near the critical point ϕc = 0.0194.
    • Fig. S3. Structure factor S(q) for large systems with different R at φ = 0.4 and TR = 0.
    • Fig. S4. Hyperunifomity in an experimentally realizable system (26) with bimodal circling-phase distribution.

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    Other Supplementary Material for this manuscript includes the following:

    • Movie S1 (.mp4 format). Active state in Fig. 1C.
    • Movie S2 (.mp4 format). Absorbing state in Fig. 1D.
    • Movie S3 (.mp4 format). Active state with R = 1000σ in Fig. 2G.
    • Movie S4 (.mp4 format). Active state with R = 100σ in Fig. 2G.
    • Movie S5 (.mp4 format). Active state with R = 50σ in Fig. 2G.
    • Movie S6 (.mp4 format). Active state with R = 25σ in Fig. 2G.
    • Movie S7 (.mp4 format). Active state with R = 23σ in Fig. 2G.

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