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. 2015 Jun 12;6:7392. doi: 10.1038/ncomms8392

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(a) The dynamic correlation length ξ₄(τ_α) versus the translational relaxation time τ_α. The circles are the results for the 2D system where the underlying dynamics is Newtonian (green) and Brownian (blue). The lines are fits to a power law . The red squares are results for the 3D system where the underlying dynamics is Newtonian. The red line is a fit to ξ₄(τ_α)=b[ln(τ_α/τ_o)]^2/3. (b) The dynamic susceptibility χ₄(τ_α) versus the dynamic correlation length ξ₄(τ_α) for the 2D system where the underlying dynamics are Newtonian (green circles) and Brownian (blue circles). The red squares are results for the 3D system. The lines are fits to the power laws χ₄(τ_α)∼ξ₄(τ_α)³ in 3D and χ₄(τ_α)∼ξ₄(τ_α)^1.5 in 2D. (c) The relaxation time τ_α and the dynamic correlation length ξ₄(τ_α) where the underlying dynamics are Newtonian (green) and Brownian (blue) for the 2D system, and Newtonian for the 3D system (red). The error bars in all the figures are standard errors computed from four independent trajectories. (a–c) Results are for the Kob–Andersen mixtures.

Inline graphic — (a) The dynamic correlation length ξ₄(τ_α) versus the translational relaxation time τ_α. The circles are the results for the 2D system where the underlying dynamics is Newtonian (green) and Brownian (blue). The lines are fits to a power law . The red squares are results for the 3D system where the underlying dynamics is Newtonian. The red line is a fit to ξ₄(τ_α)=b[ln(τ_α/τ_o)]^2/3. (b) The dynamic susceptibility χ₄(τ_α) versus the dynamic correlation length ξ₄(τ_α) for the 2D system where the underlying dynamics are Newtonian (green circles) and Brownian (blue circles). The red squares are results for the 3D system. The lines are fits to the power laws χ₄(τ_α)∼ξ₄(τ_α)³ in 3D and χ₄(τ_α)∼ξ₄(τ_α)^1.5 in 2D. (c) The relaxation time τ_α and the dynamic correlation length ξ₄(τ_α) where the underlying dynamics are Newtonian (green) and Brownian (blue) for the 2D system, and Newtonian for the 3D system (red). The error bars in all the figures are standard errors computed from four independent trajectories. (a–c) Results are for the Kob–Andersen mixtures.