Fractions of the particles with n b bonds p 1(n b ) and p 2(n b ) for the species 1 and 2 at T = 0.24.
Fractions of the B and BL particles, ϕ b (t) and , respectively, together with 1 − F b (t) and 1 − F s (t) on a double logarithmic scale for T = 0.24. Here, for t ≲ 103 and for t ≳ 103. From F b (τ b ) = e −1 and F s (τα) = e −1, we have τ b = 2.7 × 105 and τα = 1.1 × 105.
Typical time-smoothed vibration lengths S i (t) in Eq.(4.4) in time interval [t 0, t 0 + 500] for three non- B particles without bond breakage, where Δt = 40 (left) and 100 (right) for T = 0.24 (top) and T = 0.20 (bottom).
(a) Particles with vibration length S i (t 0) in Eq. (4.4) exceeding 0.16 at a time t 0 for T = 0.24, where those with 0.16 < S i (t 0) < 0.25 have colors according to the color bar and those with S i (t 0) > 0.25 are written in red. Arrows represent the displacements of the BL particles. (b) BL particles in the same run, which are determined in one of ten time intervals [t k , t k + 1] with t k = t 0 + k × 103 (0 ⩽ k ⩽ 9) and . At jump time , they undergo large displacements (>0.8). Their colors represent according to the color bar. Arrows represents .
Displacement vectors of the BL particles for T = 0.24. Data are the same as in Fig. 4 . Colors represent (red for ).
Snapshots of S i (t) exceeding 0.16 at (a) t = t 0 + 104, (b) t = t 0 + 5 × 104, (c) t = t 0 + 105, and (d) t = t 0 + 2 × 105, where T = 0.24. Snapshot of S i (t 0) is given in Fig. 7(a) . Arrows are displacement vectors . These four snapshots are taken consecutively in the same run, indicating slow time-evolution of the mesoscopic vibrational heterogeneity.
Structure factor S vi(q) for the vibration amplitude in Eq. (4.7) (left) and structure factor S b (q, t) for bond breakage in Eq.(4.8) with t = 104 and 2 × 104 (right) for T = 0.24. Solid curves represent the Ornstein-Zernike fitting.
(a) Distributions P 1(S) and P 2(S) of the thermal vibration length S i (t) for the small and large particles in Eq. (4.9) on a semilogarithmic scale for T = 0.24. The small particles are more mobile than the larger ones. (b) Distribution P 1(S, n b ) in Eq. (4.11) for n b = 9, 10, 11, and 12 on a semilogarithmic scale for T = 0.24.
Distribution P(S) = P 1(S) + P 2(S) for the thermal vibration length S i (t) (upper curve) and conditional probability distribution in Eq. (4.14) at t = 104 (lower curve) on a semi-logarithmic scale, where T = 0.24. Inset gives P(S) on a linear scale. Here, approaches P(S) for S ≳ 0.2, indicating close correlation between structure and slow dynamics.
(a) Surviving fraction vs t for the particles with and S i (t 0) > λ in Eq. (4.17) for various λ at T = 0.24. Here, is the conditional probability of undergoing stringlike motions for particles with S i (t 0) > λ, so (see Fig. 2 ). (b) Surviving fraction of the particles with and in Eq. (4.18) as functions of t for T = 0.24.
Fraction of the B L particles at time t 0 + t with initial S i (t 0) larger than λ. For λ = 0, it becomes the fraction of the total BL particles in Fig. 2 .
Numbers of particles with S i (t 0) > λ and S i (t 1) > λ with λ = 0.16 or 0.20 in the same run, where t 1 − t 0 = 102, 103, 104, 5 × 104, 105, and 2 × 105. The initial particle numbers with S i (t 0) > λ is 1207 for λ = 0.16 and 274 for λ = 0.20 in Fig. 4(a) . See Fig. 6 for the subsequent particle configurations at the later four times.
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