Shear modulus of two-dimensional Yukawa or dusty-plasma solids obtained from the viscoelasticity in the liquid state

Universal scaling of transverse sound speed and its isomorphic property in Yukawa fluids

Molecular dynamical simulations are performed to investigate the scaling of the transverse sound speed in two-dimensional (2D) and 3D Yukawa fluids. From the calculated diagnostics of the radial distribution function, the mean-squared displacement, and the Pearson correlation coefficient, the approximate isomorphic curves for 2D and 3D liquidlike Yukawa systems are obtained. It is found that the structure and dynamics of 2D and 3D liquidlike Yukawa systems exhibit the isomorphic property under the conditions of the same relative coupling parameter Γ/Γ_{m}=const. It is demonstrated that the reduced transverse sound speed, i.e., the ratio of the transverse sound speed to the thermal speed, is an isomorph invariant, which is a quasiuniversal function of Γ/Γ_{m}. The obtained isomorph invariant of the reduced transverse sound speed can be useful to estimate the transverse sound speed, or determine the coupling strength, with applications to dusty (complex) plasma or colloidal systems.

Observation of fast sound in two-dimensional dusty plasma liquids

Equilibrium molecular dynamics simulations are performed to study two-dimensional (2D) dusty plasma liquids. Based on the stochastic thermal motion of simulated particles, the longitudinal and transverse phonon spectra are calculated, and used to determine the corresponding dispersion relations. From there, the longitudinal and transverse sound speeds of 2D dusty plasma liquids are obtained. It is discovered that, for wavenumbers beyond the hydrodynamic regime, the longitudinal sound speed of a 2D dusty plasma liquid exceeds its adiabatic value, i.e., the so-called fast sound. This phenomenon appears at roughly the same length scale of the cutoff wavenumber for transverse waves, confirming its relation to the emergent solidity of liquids in the nonhydrodynamic regime. Using the thermodynamic and transport coefficients extracted from the previous studies, and relying on the Frenkel theory, the ratio of the longitudinal to the adiabatic sound speeds is derived analytically, providing the optimal conditions for fast sound, which are in quantitative agreement with the current simulation results.

Shear softening and hardening of a two-dimensional Yukawa solid

Langevin dynamical simulations are performed to study the elastic behaviors of two-dimensional (2D) solid dusty plasmas under the periodic shear deformation. The frequency- and strain-dependent shear moduli G(ω,γ) of our simulated 2D Yukawa solid are calculated from the ratio of the shear stress to strain in different orientations. The shear-softening and -hardening properties in different lattice orientations are discovered from the obtained G(ω,γ). The component of the elastic constant tensor corresponding to the shear deformation is also calculated, whose variation trend exactly agrees with the discovered shear-softening and -hardening features in different shear directions. It is also found that the shear modulus of the 2D Yukawa solid always increases monotonically with the frequency.

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)10.1103/PhysRevE.101.057201], 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)2470-004510.1103/PhysRevE.99.063206] 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.

Comment on "Shear modulus of two-dimensional Yukawa or dusty-plasma solids obtained from the viscoelasticity in the liquid state"

In a recent paper [Wang, Huang, and Feng, Phys. Rev. E 99, 063206 (2019)2470-004510.1103/PhysRevE.99.063206], Langevin dynamical simulation results related to the shear modulus G of a two-dimensional liquid dusty plasma were reported. The purpose of this Comment is to provide a comparison with available theoretical models to calculate G and to indicate the correct way of interpreting the numerical results.