Modeling of Discrete Dynamical Systems with Self-Organization

A general mathematical model of an evolution for discrete nonlinear self-organizing dynamic system under the condition of a long-period relaxation was developed. This activity was connected closely with the progress on the field of synthetic metastable systems (molecular engines, carbon nanotubes). Both the analytical treatment and numerical modeling for the characteristics of a self-organization process were given. It was shown that the effective self-organization with reduction of the model ensemble entropy is possible only under condition of a long-period integral memory.

Lattice Dynamics of Nanocontacts and Quantum Phonon Transport

The atomic frequency distribution functions of the nanocrystal placed between two solids were calculated. The heat flux was calculated with the quantum phonon transport in point contact and the impurity monolayer separated the crystals being taken into account. It is shown that the weak impurity-crystal interaction results in a resonance-type frequency dependence of the phonon energy transmission coefficient. The analog of Landauer formula for the phonon conductivity has been derived for the heat flux through the point contact. The research is carried out within the frames of agreement on scientific collaboration between ILTPE and the P.J. Safarik University (Kosice, Slovak Republic).

Theory of Point Contact Spectroscopy of Metals

It is shown that for an arbitrary electron elastic scattering length the second derivative of the current with respect to voltage at the point contact is proportional to the electron-phonon transport function. The result signifies that the point-contact spectroscopy should be feasible in metals with arbitrarily small elastic scattering length. The effect of nonequilibrium of the phonon system on the spectroscopy of electron-phonon interaction was investigated in collaboration with Dprt.19 (ILTPE).

Statistical Mechanics of Long Polymer Chains

Path-integral method was adopted to calculate the cross-section of the light scattering by optically anisotropic polymer chains in solution. The excluded volume problem, with respect to the viscometric data, was investigated in collaboration with Dprt.18 (ILTPE).

Books:

1. A.G. Shkorbatov, D. B. Kucher, Chaotic Evolution and Self-Organization of Discrete Systems with Memory, 215 pp., ICSRD Preprint, Kharkov , 2002.
2. Yu.P.Blagoj, V.L. Galkin, G.O. Gladchenko, S.V. Kornilova, V.A. Sorokin, A.G. Shkorbatov, Metal Ion-Nuclear Acid Complexes in Solutions, 270 pp., Naukova Dumka Publ. House, Kiev, 1991, (in Russian).