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Negative Poisson's ratio and percolating structures

100%

Wojciechowski K. W. , Novikov V. V.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2001

tom Vol. 5, No 1

5-11

Elastic properties of non-uniform, two-component systems are studied in frames of a model of percolation on a simple cubic lattice. It is shown that as the ratio of the bulk moduli of the components tends to zero, kappa =K/sub s//K/sub h/ to 0 (where s,h denote the softer and harder phase, respectively), the Poisson's ratio of the system tends to 0.2 at the percolation threshold of the harder phase, no matter what the values are of the Poisson's ratios of the components. A qualitatively new, collective mechanism leading to negative Poisson's ratio is suggested.

Anomalous relaxation in dielectrics. Equations with fractional derivatives

80%

Novikov V. V. , Wojciechowski K. W. , Komkova O. A. , Thiel T.

Materials Science Poland

2005

tom Vol. 23, No. 4

977--984

It has been shown that anomalous relaxation in dielectrics can be described in terms of equations with fractional derivatives. The solutions of the resulting equation with fractional derivatives are expressed by the Mittag-Leffler function and the Fox function. The conditions of a change from the Debye relaxation to "slow" (anomalous) relaxation with a power time dependence have been examined in the limits t › 0 and t › ∞.

Chaotic fractal models generated by rectangular cells

80%

Novikov V. V. , Wojciechowski K. W. , Privalko V. P.

Computational Methods in Science and Technology

2004

tom Vol. 10, nr 1

91-100

Properties of some chaotic fractal models constructed on hierarchies of rectangular cells (the latter being rectangular subsets of the square lattice) are investigated. Fractal dimensionalities and average neighbour numbers of structures generated by small rectangular cells Lx x Ly (2 less-than or equal to L x less-than or equal to 4, 1 less-than or equal to Ly less-than or equal to 4) are derived. Generating probability functions and critical indices for the correlation length as well as for the percolation cluster density are calculated for the models considered. The calculations show that structures generated by anisotropic (rectangular) initial cells show much broader range of critical indices and other characteristic parameters than structures generated by 'isotropic' (square) initial cells.