Effective-Medium Approach for Conductivities in Multi-Component Granular Mixtures

We apply the effective-medium theory to a multi-component mixture system, by which the effective longitudinal and Hall conductivities can be calculated. We find that there is more than one threshold in the multi-component mixture, and the maximum number of thresholds is one less than the component number. Further, the thresholds are mainly dependent on the relative volume ratio of the components when the conductivity ratios between any two components are far larger or smaller than one