Instability and Contraction
Instability and Contraction
This work is devoted to the study of the generation of the equatorial noise—electromagnetic radiation below the LHR frequency observed near the equatorial plane of the magnetosphere at distances of ~4RE. According to accepted views, the generation of the equatorial noise is related to the instability of ring current protons. In this work, a logarithmic distribution of energetic protons over the magnetic moment with an empty loss cone is proposed, and arguments for the formation of such a distribution are presented. The main result of the work is the calculation and analysis of the instability increment of waves forming the equatorial noise. The increment obtained in this work significantly differs from that encountered in the literature.
Sergei P. Kurdyumov (1928–2004) and his distinguished contribution in the development of the modern interdisciplinary theory and methodology of study of complex self- organizing systems, i.e. synergetics, is under consideration in the article. The matter of a mathematical model of evolutionary dynamics of complex systems elaborated by him is demonstrated. The nonlinear equation of heat conductivity serves as a basis of the model. Under certain conditions, it describes dynamics of development of structures of different complexity in the blow-up regime. Methods of calculation of two-dimentional structures which are described by automodel solutions are considered; and their classification is given. The automodel problem is a boundary problem aiming to find eigen-values and eigen-functions for a nonlinear equation of elliptical type on a plane. Proceeding from the analysis of the model, a principle of coevolution was formulated by S.P. Kurdyumov. This is the principle of integration of simple structures into a complex one. Three notions of great significance follow from the principle, and namely: the notion of connection of space and time, the notion of complexity and its nature and the notion evolutionary cycles and switching over different regimes as a necessary mechanism of maintenance of «life» of complex structures. Approaches of possible application of this model for understanding of dynamics of complex social, demographic and geopolitical systems are viewed as well.
The evolutionary model elaborated by Sergei P. Kurdyumov is considered in the article. Some key ideas put forward by him constitute a basis for development of the methodology of sudy of complex selforganizing systems, called also synergetics. Four important theoretical notions form a fundament of this evolutionary model: connection between space and time, complexity and its nature, blow-up regimes, in which self-organization and rapid, avalanche-like growth of complexity occur, evolutionary cycles and switching of different regimes as a necessary mechanism for maintenance of “life” of complex structures. The methodology allows to understand the nature of innovative shifts in nature and society and to show a possibility of management of innovative processes and of construction of desirable future. Some approaches for possible application of this model for understanding of dynamics of complex social, demographic and geopolitical system are discussed.
The work is devoted to fundamental aspects of the classical molecular dynamics method, which was developed half a century ago as a means of solving computational problems in statistical physics and has now become one of the most important numerical methods in the theory of condensed state. At the same time, the molecular dynamics method based on solving the equations of motion for a multiparticle system proved to be directly related to the basic concepts of classical statistical physics, in particular, to the problem of the occurrence of irreversibility. This paper analyzes the dynamic and stochastic properties of molecular dynamics systems connected with the local instability of trajectories and the errors of the numerical integration. The probabilistic nature of classical statistics is discussed. We propose a concept explaining the finite dynamic memory time and the emergence of irreversibility in real systems.