Multi scaling of Fractal Dimension and Relative Entropy as Diagnostic Tools for Irradiated Carbon Nano-tubes

Linear and nonlinear dissipative structures emerge in the irradiated single and multi walled carbon nano-tubes in the form of collision cascades and thermal spikes. These are diagnosed by the information theoretic tools of fractal dimension and relative entropy by the probabilistic description of dissipative structures using the measure that depends upon the energy of the irradiating ion and the incremental energy step. Multi scaling of the measure of the probability distributions is shown to induce variability of fractal dimension of the sputtered carbon atoms and clusters. Fractal dimension and relative entropy care shown to unambiguously distinguish and identify the information generating collision cascades and thermal spikes.