Pinning Susceptibility Near the Jamming Transition*

The study of jamming in the presence of pinned obstacles is of both practical and theoretical interest. In simulations of soft, bidisperse disks and spheres, we pin a small fraction, $n_f$ of particles prior to the equilibration process. The presence of pinned particles is known to lower the critical packing fraction, $\phi_J$, for jamming. Further, around this threshold there is a peak in a quantity which we have termed the ``pinning susceptibility'': $\chi_P = \lim_{n_f \rightarrow 0} \frac{\partial P_J (\phi, n_f)}{\partial n_f}$. In the thermodynamic limit, we have posited that $\chi_P \propto |\Delta \phi |^{-\gamma_P} $. Finite-size scaling calculations, involving careful fits of $P_J$ to logistic sigmoidal functions, yield a value for the critical exponent, $\gamma_P$. This new exponent is proposed to be independent of inter-particle potential. Its dependence on dimensionality (2 vs. 3 dimensions) will be discussed.