On the Grain-Modified Magnetic Diffusivities in Protoplanetary Disks

Weakly ionized protoplanetary disks (PPDs) are subject to non-ideal-magnetohydrodynamic (MHD) effects including Ohmic resistivity, the Hall effect and ambipolar diffusion (AD), and the resulting magnetic diffusivities ($\eta_O, \eta_H$ and $\eta_A$) largely control the disk gas dynamics. The presence of grains not only strongly reduces disk ionization fraction, but also modify the scalings of $\eta_H$ and $\eta_A$ with magnetic field strength. We derive analytically asymptotic expressions of $\eta_H$ and $\eta_A$ in both strong and weak field limits and show that towards strong field, $\eta_H$ can change sign (at a threshold field strength $B_{\rm th}$), mimicking a flip of field polarity, and AD is substantially reduced. Applying to PPDs, we find that when small $\sim0.1$ ($0.01$)$\mu$m grains are sufficiently abundant [mass ratio $\sim0.01$ ($10^{-4}$)], $\eta_H$ can change sign up to $\sim2-3$ scale heights above midplane at modest field strength (plasma $\beta\sim100$) over a wide range of disk radii. Reduction of AD is also substantial towards the AD dominated outer disk and may activate the magneto-rotational instability. We further perform local non-ideal MHD simulations of the inner disk (within 10 AU) and show that with sufficiently abundant small grains, magnetic field amplification due to the Hall-shear instability saturates at very low level near the threshold field strength $B_{\rm th}$. Together with previous studies, we conclude by discussing the grain-abundance-dependent phenomenology of PPD gas dynamics.Comment: 12 pages, 6 figures. submitted to Ap

Jamming of packings of frictionless particles with and without shear

By minimizing the enthalpy of packings of frictionless particles, we obtain jammed solids at desired pressures and hence investigate the jamming transition with and without shear. Typical scaling relations of the jamming transition are recovered in both cases. In contrast to systems without shear, shear-driven jamming transition occurs at a higher packing fraction and the jammed solids are more rigid with an anisotropic force network. Furthermore, by introducing the macro-friction coefficient, we propose an explanation of the packing fraction gap between sheared and non-sheared systems at fixed pressure.Comment: 6 pages, 5 figure