THEORETICAL-STUDIES OF SELF-ORGANIZED CRITICALITY

We study various aspects of the self-organized critical phenomena. A continuous-energy model is analyzed using a self-consistent effective medium method. We find that energy is homogeneously and isotropically distributed in space. We have calculated analytically the critical energy, which is very close to that of numerical simulations. We found that the critical energy is quite universal whereas the energy distribution per site depends on particular models. Using scaling arguments we have estimated the various exponents. We have also performed a detailed study of the noise spectrum. The result shows a 1/f2 behavior in the frequency region that we have probed.