SUPERLOCALIZED CHARACTER OF THE VISCOUS DAMPING OF FRACTONS

The damping of the vibrations of very irregular discretized-systems em bedded in a viscous fluid is studied in the particular case of the vib rations of a percolation cluster. We develop a formal description for the ''regularity'' of a vibrational mode. This permits us to measure n umerically how the local fluctuations in the vibration amplitude incre ase the viscous damping. We find that a major part of the dissipation is localized in a small fraction of the next-nearest-neighbour pairs. This is a qualitative indication of the existence of a ''localization within localization'' of the dissipation. The fact that the regularity is found to be larger than that of a single localized state on a line ar chain is qualitatively indicative of the structure of the percolati on cluster made of blobs and red bonds.