Negative moments of current distribution in random resistor networks

Scaling behaviors of the voltage distribution in dielectric breakdown networks

We study the distribution of voltage drops across bonds in dielectric breakdown networks and its qth moments in the two-dimensional Euclidean space. Performing numerical simulations, we find that the distribution is composed of three different power-law regimes which are distinguished by two crossover voltages V(1) and V(2). The scaling behaviors of these crossover voltages with respect to the system size govern those of the qth moments of the voltage distribution. This feature differs from the multifractal behavior of the qth moment in random resistor networks. We discuss the implications of these scaling behaviors in relation to the application of the dielectric breakdown network to memory devices.

Advective transport in percolation clusters

We simulate advective transport in bond percolation clusters at the critical point. We compute the histogram of flow speeds in each bond of the backbone and find the multifractal spectrum for two-dimensional lattices with linear dimension L2000 and in three dimensions for L250 . We demonstrate that in the limit of large systems all the negative moments of the velocity distribution become ill-defined. However, to model transport, the velocity histogram should be weighted by the flux to obtain a well-defined mean travel time. Finally, we use continuous time random walk theory to demonstrate that anomalous transport is observed whose characteristics can be related to the multifractal properties of the system.