Spivak A. The structurization and dynamic processes in many-body micro-mechanical systems under the influence of external perturbations

Theoretical models of multi-particle micro-mechanical (granular) systems under the influence of external perturbations where structured eigen-states and transitions between them are carried out has been studied. The influence of initial and external conditions on the structure of such states and a Lindemann type criterion of structural ordering were investigated. The kinetics of compaction in granular materials were studied by uses the free-volume model and the adapted Ginzburg-Landau phase transition theory. By means of comparison of the obtained data with the results of experiments it is shown the fractional character of the kinetics of corresponding relaxation processes. The model of bi-dispersed micro-mechanical mixture which based on the Kirkwood-Buff approach has been developed in order to describe and parameterize their compressibility and packing at arbitrary values of volume fraction of the components. For the nonhomogeneous one dimensional force chain with nonlinear contacts the dynamics of external mechanical impulse which perturb the system were studied. The conditions of formation of the resonant modes in linearized inhomogeneous disordered force chain which looks as a wave packets formed from cylindrical waves has been found. A solitonic solution of the Nesterenko type and expression for the amplitude of scattering of excitation from isotopic defect were obtained. The results of the analysis of the pulse scattering amplitude on the heavy defect agree well with the corresponding experimental data.