Reply to “Comment on ‘Shear modulus of two-dimensional Yukawa or dusty-plasma solids obtained from the viscoelasticity in the liquid state' ”

In the preceding Comment [Khrapak and Klumov, preceding Comment, Phys. Rev. E 101, 057201 (2020)], a completely different method is used to calculate the shear modulus of two-dimensional Yukawa solids. Here the results of the shear modulus of two-dimensional Yukawa solids obtained in a previous work [Wang et al., Phys. Rev. E 99, 063206 (2019)] are compared with the results in the preceding Comment. It is found that the two empirical fits from the two methods are in extremely close agreement, supporting the consistency of these two methods.

Figure 1

Infinite-frequency shear modulus $G_{\infty }$ of 2D Yukawa liquids versus the screening parameter $\kappa$ for different values of the coupling parameter: (a) $\mathrm{\Gamma }=8$, (b) $\mathrm{\Gamma }=20$, and (c) $\mathrm{\Gamma }=68$. The squares correspond to the potential portion of the infinite-frequency shear modulus $G_{\infty }^{pp}$ from our simulation results in [2]. The solid curve is the candidate for the shear modulus for 2D Yukawa crystals from our phenomenological fitting of the transverse sound speed [2]. The black dashed curve is the fit of Eq. (4) in [1]. Clearly, our phenomenological fitting data almost completely overlap with the fit of Eq. (4) in [1], suggesting that our choice of the candidate for the shear modulus for 2D Yukawa crystals agree well with the final conclusion of [1].