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The kinetics of deformation processes on the yield plateau is studied in aluminum alloy 1550. It is found out that in the general case, the Luders band fronts move discretely and only in the phase of specimen unloading. A continuous motion of the deformation fronts is possible if the relaxation rate of the applied stresses due to the test machine is higher than or equal to the rate of their decrease controlled by the internal processes at a lower scale level. The discrete motion of the Luders fronts in the 1550 alloy suggests that they are not purely switching autowaves.

The paper focuses on the investigation of the strain kinetics at the yield point of materials with shear dislocations and martensitic transformations at a microlevel. In both cases, the autowave propagation and localized plastic deformation occur. The autowave propagation velocity depends on the nonlinear speed of the crosshead movement. It is found that its nature is the same both in low carbon mild steel and titanium nickelide.

General patterns of localized plastic flow development are described at linear work hardening stages of nineteen metals. Correlations between the position of the element in the periodic table of elements and the parameters of the autowave localized plastic flow have been established and discussed. The observed correlations indicate the existence of dependences of the localized plastic flow in a deformable medium on the lattice parameters of the elements and their electronic structures.

A new approach is suggested for explanation of autowave processes during plastic deformation of metals. It is based on the postulate that a quasiparticle corresponds to a localized flow autowave. Characteristics of the quasiparticle are determined, and a number of consequences from the postulate are considered. The relations have been established for the processes on micro- and macro-level in the course of plastic deformation.

The deformation behavior of TRIP steel at the macroscopic level is experimentally investigated. It has been established that the deformation-induced austenite → martensite phase transformation is developed by shaping localized deformation fronts and can be described in terms of the propagation of the Luders and Portevin–Le Chatelier bands; therefore, the theory of autowave localized plasticity is applicable to them. On the elastoplastic transition, the transformation is realized in the form of auto-switching waves, which originate, propagate, and annihilate. With further loading of the zone of origin of auto-switching waves, they become sources of excitation autowaves.

The regularities in the inhomogeneous development of plastic deformation at the front of the Luders band at the yield plateau in Hadfield steel single crystals are considered. It has been established that the Luders front moves in jumps under these conditions. This character of motion is associated with the rearrangement of the inhomogeneous distributions of the components of the plastic distortion tensor components at the deformation front. A plausible estimate of the frequency of oscillations in the development of the Luders front has been obtained.

This paper reports the results of acoustic parameter measurements in a deformed material with simultaneous recording of autowave patterns of localized plastic deformation for steels of various compositions. It discusses the possibility of using an autowave model for the derivation of structural strength criteria of materials. It was shown that the time and place of future fracture in steel specimens can be predicted from the kinetic dependences of localized deformation sites at the prefracture stage long before visible necking. It was found that the ultrasonic velocity vs. strain curve has a kink in the elastic–plastic transition in low-carbon steels. This kink may serve as an acoustic criterion for the onset of irreversible deformation in metal forming and non-destructive testing of components and structures.

Macroscopic laws of the development of plastic flow localization autowaves in metals, alloys, alkali halide crystals, and rocks are investigated. It is shown that the characteristics of elastic and plastic waves form an elastoplastic invariant. The nature of the invariant is explained, and it is demonstrated that its existence is determined by changes in the entropy of a deformable system in the process of generation of localized plastic flow autowaves. It has been established that the main features of the deformation and deformation hardening processes can be considered as a consequence of the elastoplastic invariant.

We investigate the dynamics and conditions of emergence of complex autowave solutions in bistable reaction-diffusion systems with time fractional derivatives. It is shown that fractional reaction-diffusion systems have new properties in comparison with standard systems with derivatives of integer order. In particular, in bistable systems with fractional derivatives, we have found new types of autowave solutions, which cannot exist in standard reaction-diffusion systems. Results of the linear theory are substantiated by using computer simulation of a system with cubic nonlinearity, which enables us to simulate characteristic feedbacks and main types of autowave solutions. On the basis of the computational experiment, we show that the order and relation between time fractional derivatives change qualitatively the conditions of instability and nonlinear dynamics of bistable systems.

A stress-deformed state of zirconium alloy in a cold rolling site is investigated considering the process of evolution of localized deformation autowaves and changes in the ultrasound velocity. It is established that transition from the upsetting to reduction region is accompanied by significant exhaustion of the plasticity margin of the material; therefore, fracture of the material is most probable exactly in this region. It is stated that traditional methods of estimating the plasticity margin from the mechanical characteristics cannot reveal this region; comprehensive analysis of plastic strain macrolocalization and results of acoustic measurements are required.

A mathematical model of autowave processes in a heterogeneous medium with chemical reactions in the gas phase and on the catalyst is constructed. The coefficients of heat and mass transfer between the phases and the thermal conductivity of the solid phase are determined from the current values of system parameters. The model describes three types of autowaves: waves due to filtration combustion of gases in the low-velocity regime, waves due to a catalytic reaction, and hybrid waves. The behavior of phase trajectories of the dynamic system is studied by methods of qualitative and numerical analysis, and an effective technique is developed for searching for a physically grounded autowave solution of the problem. The laws of propagation of autowaves due to filtration combustion of gases and hybrid autowaves are numerically examined, and the effect of system parameters on the basic technological characteristics of autowave processes is studied.

A simplified system of equations is used to investigate the properties of autowaves of slow nuclear burn, which under certain circumstances can propagate in a medium containing 238U (or 232Th). It is shown that the reactor spectrum and the presence of other substances in the medium which determine the critical concentration of plutonium (or 233U) affect the appearance of a wave.

A mathematical model is developed to describe autowave processes in a catalytic fixed bed, which takes into account changes in coefficients of interphase heat and mass transfer and thermal conductivity of the catalytic bed, depending on the current values of system parameters. The behavior of the phase trajectories of the dynamic system is studied by methods of qualitative and numerical analysis, and an effective technique is proposed for searching for a phase trajectory corresponding to the autowave solution of the problem. Numerical studies of the mathematical model of autowave processes are performed, and the effect of system parameters on technological characteristics of the process, such as the maximum temperature and wave-propagation velocity, is considered.

This paper proposes a novel binary image thinning algorithm by using the autowaves generated by Pulse Coupled Neural Network (PCNN). Once the autowaves travelling in different directions meet, the PCNN delivers the thinning results. Four meeting conditions are given for autowaves meeting. If a neuron satisfies one of the four conditions, the pixel corresponding to this neuron belongs to the thinning result. Moreover, the specification of the PCNNs parameters is given, which makes the implementation of the proposed thinning algorithm easy. Experimental results show that the proposed algorithm is efficient in extracting the skeleton of images (such as Chinese characters, alphabet letters, numbers, fingerprints, etc.). Finally, a rate called "R MSkel" is given to evaluate the performance of different thinning algorithms, and comparisons show that the proposed algorithm has higher "R MSkel" and costs less time.

Modelling of soft tissue deformation is of great importance to virtual reality based surgery simulation. This paper presents a new methodology for simulation of soft tissue deformation by drawing an analogy between autowaves and soft tissue deformation. The potential energy stored in a soft tissue as a result of a deformation caused by an external force is propagated among mass points of the soft tissue by non-linear autowaves. The novelty of the methodology is that (i) autowave techniques are established to describe the potential energy distribution of a deformation for extrapolating internal forces, and (ii) non-linear materials are modelled with non-linear autowaves other than geometric non-linearity. Integration with a haptic device has been achieved to simulate soft tissue deformation with force feedback. The proposed methodology not only deals with large-range deformations, but also accommodates isotropic, anisotropic and inhomogeneous materials by simply changing diffusion coefficients.

A biologically inspired single layer cellular neural network (CNN) with trigger wave formation capability is presented. A novel compact MOS cell circuit is proposed which exhibits a third order I-V characteristic with negative differential resistance (NDR). Certain D.C. characteristics of both the proposed cell and the network are described and corresponding theoretical estimations are presented. It is shown that the CNN formed by resistive coupling of these cells has very low complexity and realizes a reaction-diffusion system. The dynamical network behavior is demonstrated by transient simulations of a 2D cell array at the circuit level.

The thermodynamic properties of an active distributed kinetic system are considered, and the entropy balance equation for laminar‐combustion autowaves is derived for arbitrary Lewis number. Qualitative and numerical analyses of the local and complete entropy production in a dynamic system with a three‐dimensional phase space were performed. It is shown that the complete entropy production in the system is a functional of the autowave solution of the problem. Of the one‐parameter family of mathematically equivalent solutions, a single physically meaningful solution corresponds to the minimum of the functional. A variational formulation of the problem is given, which is solved without using the method of zeroing the reaction rate at low temperatures. The results of computational experiments are compared with literature data.

Thermodynamics of physicochemical processes in a reversibly reacting distributed kinetic system is considered, and nonequilibrium entropy of autowaves of laminar combustion is constructed. A qualitative and numerical analysis of the local and total entropy production in the system is performed. The total entropy production is shown to be a functional on integral curves, possessing extreme properties, whose minimum corresponds to the only physically meaningful solution of the problem. The results of solving problems with kinetic equations that take into account the reversible or irreversible character of the chemical reaction are compared.

Statistical lattice models which imitate oscillatory and wave dynamics in the adsorbed layer during of carbon monoxide oxidation over Pt(100) and Pd(110) single crystals differing in the mechanism of autooscillation formation are compared. In the case of platinum, oscillations are due to phase transitions of the catalyst surface structure and surface reconstruction under the action of the reaction medium. In the case of palladium, the driving force of oscillations is phase transitions in the adsorbed layers on the catalyst surface, namely, the reversible formation of subsurface oxygen in the course of the reaction, which modifies the adsorption and catalytic properties of the surface. It is shown that, according to the proposed models, a change in the coverages (COads ↔ Oads) in the autooscillation regimes occurs via the formation of a surface wave whose front is characterized by the high concentration of catalytically active sites that provide the maximal rate of CO2 molecule formation. Under certain conditions, the formation of various spatiotemporal structures is observed in simulation experiments.

Heat transfer is investigated under conditions of autowave change from a metastable boiling mode to a stable one. The classification of boiling curves is suggested that depends on the temperature gradient and on the directions of flow velocity and velocity of temperature wave motion. A hypothesis is advanced according to which a considerable variation of regularities of heat transfer in the zone of temperature waves is caused by local disequilibrium of boiling. Experimental investigations are performed of heat transfer under conditions of water boiling in pipes upon autowave change of boiling modes in the pressure range from 3 to 10 MPa and in a wide range of values of steam quality and mass velocity. It is demonstrated that the change of boiling modes in pipes in the form of autowave is observed at less-than-boundary values of steam quality. The possibility is discussed of using the obtained data in simulating emergency conditions in the reactor core.

The self-propagating high-temperature synthesis was applied for the production of foam materials under the conditions of microgravity aboard the Mirstation. The materials obtained have a porous bimodal structure. The results of space experiments predicted using the interpolation method are checked. An unpredicted phase separation of the combustion products is discovered. The autowave combustion of suspended nickel-clad aluminum solids is observed for the first time. The combustion products were found to have a frame structure.

Within the framework of the Zel'dovich–Frank‐Kamenetskii theory of thermal propagation of flame, thermodynamic properties of an open nonlinear system are considered, and nonequilibrium entropy of a steady combustion wave is constructed. The nonequilibrium dynamic system is analyzed qualitatively and quantitatively, and the distribution functions of local entropy production in terms of the spatial variable are constructed. It is shown that total entropy production in the system is a functional on integral curves that possess extreme properties, and its minimum corresponds to a unique physically sustainable solution of the problem. The procedure of “cutting” (vanishing) of the reaction rate is justified by methods of nonequilibrium thermodynamics. A variational formulation of the problem is presented for calculation of a steady combustion wave.

We consider the evolution of the electric field and charge in a one-dimensional electrohydrodynamic (EHD) distributed-parameter system which serves as a simple model of a thundercloud. A diffusion equation for the electric field is proposed which, under reasonable assumptions on the nonlinear dependence of the dissipation current on the electric field (caused by the corona effect around aerosol particles in strong fields), has autowave solutions describing the dynamics of spatially separated electric-charge regions in the thundercloud. The nonlinear set of equations describing the electric-field dynamics in an ensemble of colliding aerosol particles and light ions is reduced to a rather simple basic model which admits solutions in the form of traveling fronts and traveling pulses. We find the asymptotic values of the velocity and thickness of the space-charge front, which are determined by the diffusion and the separation and conductivity currents. Using these values, we estimate the electrostatic-energy growth rate in a thunderstorm cell at the stage of its intensive electrification. A possibility is shown of the formation of a traveling pulse of field and conductivity in such an EHD system with allowance for inductive and noninductive mechanisms of aerosol-particle charging.

Plastic-strain localization of fcc, bcc, and hcp single crystalline and polycrystalline materials is investigated in different stages in the loading curve under active uniaxial tension. Localization patterns are found to be of an ordered character and can be classified into four types, each corresponding to a certain stage in the loading curve. The regularities observed are interpreted in terms of self-organization in open systems. It is shown that all types of localization patterns can be treated as autowaves of plastic flow. The wave parameters are analyzed and the fundamental difference from the well-known waves of plasticity under shock loading is demonstrated.

Space-time self-organization phenomena can be observed in open nonideal systems far away from the thermodynamic equilibrium [1–10]. The study of the spontaneous and forced destruction of old nonequilibrium states and the generation of qualitatively new ones is of considerable interest in basic science and technical applications. The constructive definition of conditions for the existence of qualitatively different nonequilibrium stabilized states and possible evolution transitions between them via control parameters is a reliable foundation for the control of systems with multivariant dynamic behavior [10]. Simple mathematical models play a substantial role in the analysis of nontrivial phenomena. Examples of such models for the case of a bistable medium were given in [11, 12]. Of the simplest models, we can try to extract a minimal model that, on the one hand, describes the main properties of a nontrivial phenomenon and, on the other hand (which is also important), permits one to find solutions of key problems and conditions for their existence and uniqueness conditions in elementary functions. Exact solutions have no competitors when used in debugging numerical algorithms of nonlinear analysis and problem-oriented software. In the present paper, we suggest and analyze minimal deterministic models of homogeneous and heterogeneous bistable media. We find stationary and autowave solutions and derive conditions for the existence of such solutions in elementary functions. Unlike simple models considered earlier [9, 11, 12], our model of a heterogeneous medium permits one to find the exact critical size of an inhomogeneity for the forced heterogeneous nucleation of a new stable state from a metastable state and obtain exact conditions under which the autowave of transition from the metastable state to the new stable state can be arrested by a local imperfection of the medium.

A thermal fluctuation theory has been developed for damage to metal-insulator-metal diode structures, which has been employed to determine the critical electrophysical parameters for oscillating structural changes arising in the insulator in a steady external electric field. The electronic processes giving rise to microdefects are of autowave origin and are accompanied by current oscillations, acoustic emission, and electromagnetic radiation. This can be used in remote-sensing nondestructive testing, and also for the elimination of manufacturing defects in solid-state electronic devices and the insulation in electrotechnical instruments.

The thermodynamic description of the physicochemical processes in a fixed catalytic bed is considered in the approximation of the simplest (quasihomogeneous) model in the presence of a first-order reversible reaction. It is shown that the physical nature of slow heat waves is amenable to the second law of thermodynamics, and the total entropy production in a distributed open and strongly nonequilibrium system is a functional of the autowave solution of a mathematical model. Of the one-parameter family of autowave solutions, the minimum value of the functional corresponds to the unique physically valid solution. The methods of nonequilibrium thermodynamics are used to substantiate the technique of “cutting off” the reaction function. At the same time, a variational problem that is solved without using this technique is formulated.

We study the mathematical model of a vessel having an N-type static pressure-radius relationship. Due to the presence of a descending part in the characteristics, long-wave instability of autowave nature may appear in the vessel-fluid system. As a result, the nonlinear solution is close to a stationary wave of the vessel-aperture contraction, which is also confirmed by numerical analysis. The fluid-transport effect is estimated.

Fast self sustained waves (autowaves) associated with chemical or phase transformations are observed in many situations in condensed matter. They are governed neither by diffusion of matter or heat (as in combustion processes) nor by a travelling shock wave (as in gaseous detonation). Instead, they result from a coupling between phase transformation and the stress field, and may be classified as gasless detonation autowaves in solids. We propose a simple model to describe these regimes. The model rests on the classical equations of elastic deformations in a 1-dimensional solid bar, with the extra assumption that the phase (chemical) transformation induces a change of the sound velocity. The transformations are assumed to occur through a chain branched mechanism, which starts when the mechanical stress exceeds a given threshold. Our investigation shows that supersonic autowaves exist in this model. In the absence of diffusion (dissipation factor, losses), a continuum of travelling wave solutions is found. In the presence of diffusion, a steady state supersonic wave solution is found, along with a slower wave controlled by diffusion.

A material under loading is treated as a dissipative bistable medium described by a nonlinear equation of the reaction-diffusion type for order parameters. The coefficients of the equation are temperature and stress dependent. It is shown that in the easy glide stage I deformation the plastic flow occurs by the switching wave propagation mechanism. The action of the temperature on the critical shear stress and on the length of the region of easy glide under quasi-static loading is analyzed.

We study theoretical and numerical propagation of autowave fronts in excitable two-variable (activator-inhibitor) systems with anisotropic diffusion. A general curvature-velocity relation is derived for the case that the inhibitor diffusion is neglected. This relation predicts the break of an activation front when the front curvature exceeds a critical value, which is corroborated by computer simulations of a particular reaction-diffusion model. Some qualitative effects associated with the inhibitor diffusion are studied numerically. It is found that the critical value of curvature decreases with an increase in the inhibitor diffusion coefficient. The core of a spiral wave increases in size and turns through an angle which depends on the inhibitor diffusion coefficient. PACS Numbers: 05.50. +q, 05.70. Ln., 82.40. -g, 87.10. +e

Weak periodic external perturbations of an autowave medium can cause large-distance directed motion of the spiral wave. This happens when the period of the perturbation coincides with, or is close to the rotation period of a spiral wave, or its multiple. Such motion is called resonant or parametric drift. It may be used for low-voltage defibrillation of heart tissue. Theory of the resonant drift exists, but so far was used only qualitatively. In this paper, we show good quantitative agreement of the theory with direct numerical simulations. This is done for Complex Ginzburg-Landau Equation, one of the simplest autowave models.

Spiral waves in excitable media may drift due to interaction with medium inhomogeneities. We describe this drift asymptotically, within the kinematic (eikonal) approximation.

The problems of heterogeneous catalysis are considered using mathematical modeling of catalytic reactions beginning from the atomic and molecular level. Some problems of the nonlinear dynamics of heterogeneous catalytic reactions are discussed. Mathematical models of these systems were designed using a combination of laboratory and computer experiments. The results of simulation of the nonlinear phenomena involved in the reactions NO+CO, NO+H2, and CO+O2, which are important for environmental catalysis, are discussed.

A mathematical model of autowave propagation of solid-state low-temperature chlorination of butyl chloride is proposed. The model is of a coupled character and includes nonlinear equations of thermal conductivity and chemical kinetics and a balance equation for defectiveness of the medium with corresponding boundary conditions. The eigenvalues and eigenfunctions of the problem are found by a numerical method. The inverse problem is solved, and possible magnitudes of the heat effects of the chemical reactions and fracture are determined. The calculation results are in qualitative agreement with the experimental data.

Structural transformations in solidifying binder systems are considered in the context of the thermodynamics of irreversible processes. It is shown that the coagulation-condensation structure emerging in the binder system in the period of hydratation acceleration is a dissipative structure. The emergence of instability in the binder system is accompanied by the development of oscillation phenomena, and the formation of a dissipative structure corresponds to an autowave process in the form of a standing electromagnetic wave. The structure formation schemes proposed in the paper make it possible to realize deliberate selection of external technological actions on binder systems.

A correct method for constructing autowave solutions is proposed for single-temperature models of unsteady processes in a dissipative medium with Arrhenius type chemical reactions. It is based on extending the temperature range to 0 K and using the Kolmogorov-Petrovskii-Piskunov approach. Solutions that are not inconsistent with the Nernst theorem are selected from the obtained finite spectrum of autowave solutions. For a quasihomogeneous model of gas filtration in a dissipative heterogeneous medium with a single irreversible chemical reaction, such an autowave solution is unique. A nondimensional parameter is found whose critical value for the selected Zel’dovich number defines the existence condition for this self-similar solution. A criterion is obtained for the initial temperature range in which the chemical transformations in the reaction are negligibly small for autowave processes.

We have performed a qualitative and numerical analysis of the simplest model of slow heat waves propagating in a fixed catalytic bed in the presence of a first-order reversible reaction. A one-parameter family of autowave solutions subject to the boundary conditions of the problem is shown to exist. From the continuum of solutions, one can choose a unique physically reasonable solution that is a slow heat wave. The existence conditions for slow heat waves and the effect of the model parameters on the velocity of their propagation have been studied.

The mechanisms of solid-phase reactions that have been experimentally and theoretically studied during recent decades and can be directly related to the formation of organic substances in space and their delivery to Earth and to the problems of prebiotic evolution are considered. Among these mechanisms are molecular tunneling (hypothesis of the cold prehistory of life), polycondensation of solid monomers by shock waves (problem of the delivery of organic substances to Earth by meteorites), thermal and thermal-wave explosions. and oscillations of temperature and radical concentrations in small cold particles under radiation exposure, mechanochemical explosions and autowave propagation of chemical reactions due to the positive feedback between fragile destruction of solids and reactions at freshly formed surfaces.

We study spatially uniform autowave processes in a generalized model of an active medium. These processes are interpreted as global synchronization in a chain of discrete dynamic systems, which is a discrete analog of a distributed system. We obtain sufficient conditions of global synchronization for different coupling types. Analytical results are illustrated by a numerical experiment carried out for a chain of circuits with individual chaotic dynamics.

Here we show a new interaction mechanism of colliding population waves. It provides a stable coexistence of two similar but different species competing for the same limiting resource during their asexual propagation in a limited homogeneous environment under constant conditions. The revealed mechanism opens new opportunities in conservation biology.

The critical change in the temperature of a 120 mm long and 15 mm thick brass plate at different distances from the nitrogen boiling surface is investigated experimentally.

It is shown that for the same initial reagent concentrations autooscillations in miscible solutions and autowaves in immiscible solutions have nearly equal periods in the reaction system consisting of sodium bromate-malonic acid-tris-2,2′ -bipyridyl iron-sulfuric acid.

Structural transformations in the front of an autowave mode of synthesis of organic powders in a condensed phase are studied. A mode of the front stopping and an initial acceleration section are considered. The dynamics of structural transformations and the effect of the heat exchange rate on the autowave mode are established.

A comparison is made between the autowave processes of self-propagating high-temperature synthesis (SHS), conbustion of pyrotechnic composititions, and self-propagating synthesis in organic mixtures. It is shown that autowave modes in organic mixtures involve a variation in the electrophysical properties of a composition. Studying the latter allows one to determine the stages of microkinetic transformations based on the results of dynamic investigations of the self-propagating synthesis.

A study has been made of an oscillatory reaction in a chemical system consisting of iodate, hydrogen peroxide, manganese(II) sulfate, malonic acid, and sulfuric acid (Briggs-Rausher reaction) in unstirred solutions in the bulk and in a thin layer (distributed media). Autowave structures formed in the system at 20–25 °C are described for the first time, as well as changes in color of the solution as a result of local action of light.

The concentration dependences of autowave parameters have been established for the Belousov-Zhabotinsky reactions involving Fe(phen)32+ and Fe(dipy)32+ as catalysts and malonic or α-ketoglutaric acid as a reductant. Plots of autowave parameters against reactant concentration and solution viscosity in such systems containing agar-agar and SiO2 gel are given.