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Viscosity calculated in simulations of strongly-coupled dusty plasmas with gas friction

A two-dimensional strongly-coupled dusty plasma is modeled using Langevin and frictionless molecular dynamical simulations. The static viscosity $η$ and the wave-number-dependent viscosity $η(k)$ are calculated from the microscopic shear in the random motion of particles. A recently developed method of calculating the wave-number-dependent viscosity $η(k)$ is validated by comparing the results of $η(k)$ from the two simulations. It is also verified that the Green-Kubo relation can still yield an accurate measure of the static viscosity $η$ in the presence of a modest level of friction as in dusty plasma experiments.