Derivatives iterative averaging method

A number of interesting results have been obtained (due to our fractal model of structure and the iterative averaging method) for the Hall properties of the composite for example, use of a logarithmic derivative allows one to obtain critical exponents for the effective Hall coefficient (Fig. 39) for various values of the magnetic field H. When cti = a2 (Fig. 40) the effective conductivity is a constant if H = 0 and tends to zero if H —> oo near the percolation threshold. On the left of the percolation threshold (p < pc) the rise in the Hall coefficient is more rapid as the magnetic field increases (Fig. 40). On the right of the percolation threshold (p > pc) the Hall coefficient is practically independent of the concentration p. 

We carried out non-spin-polarized molecular orbital calculations using a DV-Xa code called SCAT (7). In the DV-Xa method, matrix elements in the secular equation are derived from the weighted sum of integrand values at sampling points. Hence numerical atomic orbitals can be used as basis sets. These atomic orbitals were generated on each iteration in atomic-like potentials derived from spherically averaging the molecular potential around each nucleus (7). The numerical wave functions thus obtained can be used efficiently for the molecular orbitals and have a practical character making them suitable for... 

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