Effect of Inertial Mass on Velocity Correlations of Shear Driven Soft-Core Disks Approaching the Athermal Jamming Transition

It was found numerically that overdamped, frictionless, soft-core disks undergoing uniform shear driven flow, show differences in behavior depending on how the viscous dissipation is introduced into the numerical simulation. When dissipation is with respect to a sheared external reservoir (the so-called ``mean-field'' approximation), velocity correlations are found to determine a finite length scale $\xi$ that diverges as the jamming transition is approached[1]. However, when dissipation is modeled by inter-particle inelastic collisions, the velocity correlations show no characteristic length other than the length of the system[2]. To study the relation between these two models of dissipation, we remove the overdamped constraint and consider particles with finite inertial mass $m$, and study how velocity correlations behave as the overdamped limit $m\to 0$ is approached. \newline [1] P. Olsson and S. Teitel, Phys.\ Rev.\ Lett.\ {\bf 99}, 178001 (2007). \newline [2] B. P. Tighe et al.\ Phys.\ Rev.\ Lett.\ {\bf 105}, 088303 (2010).