Author: Yaroslav Tsekhmister

Publisher:

Published: 2015

Total Pages: 0

ISBN-13:

Understanding the fundamentals and principles for self-organization in open systems with different nature (physical, chemical, biological, etc.), being far from equilibrium state, has become the significant achievement in development of science for recent years. A system is called open, if it exchanges the substance, energy and information with the environment. Now we can already speak about establishment of a new interdisciplinary sphere of science - synergetics that studies the general principles for formation of space, time and space-time structures in such open systems. There are a great number of examples for ordered structures in open systems, in particular: • In physics - phase transformations and critical phenomena, in particular, superconduction and superfluidity phenomena; convective instability; losses in gas discharges; coherent laser radiation; • In astrophysics - Jupiter red spot; Aurora Borealis; • In chemistry - Belousov-Zhabotynskyy periodic oxidation-reduction reaction; • In biology - periodic processes at glycolysis and photosynthesis; morphogenesis; vibrational dynamics in magnitude of populations; • In medicine - formation of reverberators (spiral waves) in myocardium, hexagonal structures in eye retina; etc.; Among the most advanced methods that are applied in synergetics we should mention the following ones: 1) methods from theory of nonlinear vibrations; 2) methods of kinetic models; 3) methods from theory of phase transitions. Anomalously large susceptibility of systems that are subject to phase transitions and are near the stability border is characteristic for bioobjects, which important specificity is the significant influence of various external effects on their properties. This crucial circumstance distinguishes the method from theory of phase transitions among abovementioned methods of synergetics. A certain analogy between ordering processes in open systems and phase transitions is based on determinative role of fluctuations in order parameter (control mode), corrected at large distances and in time. Thus this research pays the special attention to construction and analysis of kinetic models, agreed with the theory of phase transitions. In fact, the kinetic models of “brusselator”, “oregonator”, Girer-Meinheim, etc., which are widely used at modeling of self-organizing and ordering processes in bioobjects, are not agreed with the main concepts in physics of phase transitions that they cannot be received from fluctuation part of free energy (Landau-Ginzburg Hamiltonian) for the system with some interacting order parameters, in other words, for some coordinates (degree of completeness) of biochemical reactions. It is the determinative defect of the abovementioned models as the modern synergetic approach interprets the processes for formation of coherent structures in open systems of different nature as the non-equilibrium phase transitions. The consecutive analysis of fluctuations in self-organizing and ordering processes allows creating the strict molecular theory of coherent structures in open systems, as well as taking into consideration the influence of external fields on ordered structures.