Application of the Qualitative Theory of Dynamic Systems to Investigation of Disoriented Structures Evolution in Crystals
by
S. N. Kolupaeva, T. V. Onipchenko, V. A. Starenchenko
Tomsk State University of Architecture and Building, Solyanaya pl., 2, 634003, Tomsk, RUSSIA

The methods of the stability theory and qualitative analysis of dynamic systems for analysis of a mathematical model of disoriented structures evolution are used. The model is based on a set of ordinary differential equations of deformation defects balance. The system of equations has glued-together character depending on a physical condition. All parameters of model equations have clear physical or geometrical sense. It is shown that two stationary points (stable nodes) can be observed in the phase space of the model variables. The results of analysis show that there are eight different scenarios of deformation defects subsystem behavior in phase space of glued-together system depending on relative position of stationary points and gluing boundaries.

The parametric analysis for dynamic system was done. A modification of structure of phase space is observed for physically realizable values of material parameters.

The different types of deformation defect structures are observed in physical experiment including similar to structures which are obtained by the model.

Date received: February 28, 2003