  The Abelian Sandpile Model is a discrete diffusion process defined on graphs
(Dhar [10], Dhar et al. [11]) which serves as the standard model of
self-organized criticality. The transience class of a sandpile is defined as
the maximum number of particles that can be added without making the system
recurrent ([3]). Using elementary combinatorial arguments and symmetry
properties, Babai and Gorodezky (SODA 2007,[2]) demonstrated a bound of O(n^30)
on the transience class of an nxn grid. This was later improved by Choure and
Vishwanathan (SODA 2012,[7]) to O(n^7) using techniques based on harmonic
functions on graphs. We improve this bound to O(n^7 log n). We also demonstrate
tight bounds on certain resistance ratios over grid networks. The tools used
for deriving these bounds may be of independent interest.
