Scaling laws for flows of jammed frictionless granular materials between parallel plates

We theoretically study the flows of jammed frictionlessu granular materials driven by an external force between parallel plates. Using a continuum model, we analytically derive a scaling law that characterizes the critical behavior of the mass flux. When the external force is below a critical threshold, the mass flux remains zero, while it increases above this threshold, following a power-law dependence on the distance from the critical point. This scaling law is numerically verified using the discrete element method.