Regularity-Chaos Transition Temperature and Guisbiers-Buchaillot Equation

Abstract

A focus of frontline interdisciplinary research today is the development of the conceptual framework and the experimental background of the science of nanostructured materials and the perspectives of its technological applications. G. Guisbiers and L. Buchaillot found out the general equation (GBE) which was based only on the surface area to volume ratio of nanostructures and statistics (Fermi-Dirac or Bose-Einstein) followed by the particles involved in the considered phenomena (melting, ferromagnetism, vibration and superconductivity). In this paper, we consider another phenomenon, the regularity-chaos transition, and find its connection with GBE. We have performed the computational experiments with one hydrogen molecule and one graphene sheet. H 2 -C interactions are described by Lennard-Jones potential. The main goal of our experiments is find out the critical temperatures of regularity-chaos transition. The results of computation derived using Runge-Kutta-Fehlberg method show approximate agreement with GBE.