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In the context of nonextensive Tsallis statistics, sensible examples are employed in order to compare the variational method proposed in Phys. Rev. Lett. 80 (1998) 218 with the one in J. Phys. A 26 (1993) L893. These examples are such that they can be solved exactly. Thus, a comparison of the exact result with the approximated ones is possible. The analysis of these examples indicates that the calculation related to the first variational method is easier to work with than the other method. In particular, when one is trying to apply the last variational method, the calculation of the approximated case can be more cumbersome than solving the exact one. [Copyright &y& Elsevier]

Abstract: In this work, we address modal parameter fluctuations in statistical distributions describing charge-to-breakdown and/or time-to-breakdown during the dielectric breakdown regime of ultra-thin oxides, which are of high interest for the advancement of electronic technology. We reobtain a generalized Weibull distribution (q-Weibull), which properly describes data when oxide thickness fluctuations are present, in order to improve reliability assessment of ultra-thin oxides by time-to-breakdown extrapolation and area scaling. The incorporation of fluctuations allows a physical interpretation of the q-Weibull distribution in connection with the Tsallis statistics. In support to our results, we analyze data of -based MOS devices obtained experimentally and theoretically through a percolation model, demonstrating an advantageous description of the dielectric breakdown by the q-Weibull distribution. [Copyright &y& Elsevier]

Abstract: We analyze a multidimensional nonlinear diffusion equation taking a spatial time dependent diffusion coefficient and external forces into account. We obtain new exact classes of solutions and investigate the transverse effects induced by an external force applied in the system. We also connect the solutions found here with the distribution that emerges from the nonextensive statistics. [Copyright &y& Elsevier]