Figure 1 Structure of a pulsating combustion wave
In 1972, in the Department of Theoretical Physics of the Lebedev Physical Institute, the Sector for Theoretical Biophysics Problems was formed on the initiative of D.S.Chernavsky and with the support of the head of the OTF Academician V.L. Ginzburg. Initially, the Sector was engaged in the research of biological systems, in particular, the problem of the appearance of biological rhythms, the study of possible mechanisms of biological self-organization, the mechanism of charge transfer in biological macromolecules, and the mechanism of the functioning of enzymes. In the future, the range of tasks to be solved has expanded considerably and has gone beyond purely biological ones. A number of important results have been obtained, both of a general nature, concerning the fundamental mechanisms of spatio-temporal self-organization in open nonequilibrium systems and relating to specific systems of a different nature: physical, chemical, biological.
In 2015, the Sector was transformed into a Laboratory nonlinear dynamics and theoretical biophysics. The main area of work is the study of the mechanisms of formation of space-time structures in nonlinear dissipative dynamical systems. Within the framework of this direction, fundamental problems of self-organization are being solved, and mathematical models that describe specific systems are being developed. In particular, recently, the objects of the theoretical study of the Laboratory were complex spatio-temporal regimes experimentally observed in chemical reactions, such as the Belousov-Zhabotinsky reaction, as well as on the propagating combustion front, the growth and progression of the malignant tumor, taking into account its interaction with surrounding tissues and with blood vessels, complex autooscillatory regimes, including dynamic chaos, in ensembles of coupled oscillators.
Self-organization phenomena, i.e. transition of the system to a different, as a rule, more ordered state, are observed in systems of a different nature: physical chemical, biological. An essential property of such systems is that they are open and far from the state of thermodynamic equilibrium. This is precisely the prerequisite for the appearance in them of various nontrivial space-time regimes. The system can self-organize itself in time: for example, it changes from stationary to oscillatory mode, and in space: in particular, it can go from spatially homogeneous to an inhomogeneous steady state, or in it various autowave regimes can arise. Often, the emergence of dynamic chaos is also attributed to self-organization phenomena.
Essentially, all the activities of our laboratory lie in the mainstream of studies of self-organization in various systems. At the same time, it is necessary to emphasize the direction connected with the study of spatio-temporal self-organization in chemical systems. This is due to the fact that, on the one hand, there are a number of chemical reactions to date that demonstrate complex spatio-temporal behavior in experiments (a clear example is the Belousov-Zhabotinsky reaction), and on the other, because of their relative simplicity (compared to biological systems) they allow a correct study of the corresponding mechanisms of self-organization with the help of mathematical models.
Specific tasks that are solved within the framework of this direction is the study of the mechanisms of origin complex space-time regimes observed in experiments with the Belousov-Zhabotinsky reaction, which takes place, in particular, in the water-oil microemulsion, as well as the mechanisms of the appearance of structures on the moving front of the reaction, for example, on the front of the combustion wave.
For more than ten years we have been actively studying nonlinear wave processes associated with combustion. Our research is aimed at analyzing the stability, structure, and dynamics of laminar flames in mixtures and diffusion flames. In addition, we have extensive experience in studying nonlinear wave phenomena in active media and reaction-diffusion systems. Based on the results of our work, more than 50 articles have been published. P>
We first used the Evans function method to analyze the diffusion-thermal stability of premixed and diffusion flames. In particular, we first investigated the stability of combustion waves in the Zel'dovich-Linian and Zeldovich-Barenblatt models with a two-stage chain reaction mechanism, which are the basic fundamental representation of hydrocarbon flames with a chain reaction mechanism. In the parameter space, the critical values of the parameters for the loss of stability were found, the types of bifurcations that led to the appearance of complex dynamic modes of propagation of combustion waves were established, and the properties of these regimes were investigated. The analysis of flame extinguishing scenarios is carried out. It has been established that there are three scenarios for suppression of combustion waves: the standard folding-related folding bifurcation; The case when the flame velocity decreases continuously to zero at finite values of the parameters; dynamic scenario. The latter is associated with the creation of a chaotic flame propagation regime and the crisis of a strange attractor in the scenario of transition chaos. P>
Later, we applied, the knowledge gained for the analysis of the stability of rich hydrogen-air flames within the models with reduced and detailed kinetics. New results were obtained in the field of studying the critical phenomena of loss of stability and quenching of deflagration waves in mixtures with a chain kinetic mechanism of the reaction, and a new method for verifying the kinetic mechanisms of combustion reactions in such systems was proposed. P>
The main areas of current research include:
-Investigation of the dynamics and structure of combustion waves and diffusion flames
-Development of new methods of reduction and verification of kinetic mechanisms
-Investigation of processes of inhibition and interaction of a flame with walls
-Examination of the propagation of combustion waves in composite solid energy materials
-Investigations of the fundamentals of energy-efficient hydrocarbon fuel combustion technologies for practical applications
-Investigation of combustion processes in microgravity and simulation of experiments
-Development of low-dimensional kinetic schemes of combustion of hydrocarbon fuels, study of inhibition processes and dynamics of flames in the framework of these models
Наши исследования в области теории детонации направлены на построение асимптотических и качественных моделей нестационарной детонации. При этом проводится анализ на линейную неустойчивость используя традиционный метод нормальных мод, а также разрабатываются новые подходы. Для исследования динамики детонации в нелинейных режимах, проводится анализ уравнений Эйлера или Навье-Стокса в различных асимпоточеских приближениях: слабая нелинейность, медленная эволюция, малая кривизна фронта, большая энергия активации и т.д. Помимо асимптотических моделей, мы также предложили простые качественные модели, которые оказались способны воспроизвести широкий спектр динамических свойств газовой детонации, включая неустойчивость решений в виде бегущих волн, наличие каскада бифуркаций удвоения периода с переходом в хаос, образование ячеистых структур и другие.
Кроме детонации, нас интересует динамика ударных волн в самых различных системах. Это и гидравлические скачки, дорожные пробки, волны в квантовых жидкостях, нелинейные волны в магнитных материалах и другие явления, описываемые в первом приближении гиперболическими уравнениями, но с возможными дополнительными факторами, связанными с дисперсией или диссипацией.