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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.

A new autosoliton view is developed for the seismic process. In physical terms, faults correspond to stationary autosolitons, and inter- and intrafault deformation disturbances are traveling autosolitons. Slow dynamics reveals itself only on large time scales because slow autosoliton disturbances, as a rule, have velocities 4–7 orders of magnitude lower than the sound velocity. It is shown that, in the loaded strong medium, slow autowave and autosoliton disturbances are generated by short dynamic actions (pulses) at interfaces. In real geomaterials, these are block boundaries and various-scale faults. Dynamic movements of structural elements cause the deformation autowaves and autosolitons to propagate from the interfaces into blocks and along faults. Velocities of such deformation autowaves and autosolitons are low and proportional to velocities of the related movements of structural elements in the geomedium. Propagating in structural elements that are in a certain stress-strain state, deformation autowaves and autosolitons can be taken as small disturbances of the existing fields of the stress-strain state. A mathematical model is represented for the geomaterial treated as a nonequilibrium randomly inhomogeneous medium. Special features of the generation and propagation of deformation autosolitons in such media are studied.

We consider the regularities of a plastic flow in materials with strain-induced phase transformation in titanium nickelide and trip steel as examples. The experimental analysis of plastic deformation processes has been carried out using the technique of digital correction of speckle images, which makes it possible to describe quantitatively the behavior of plasticity fronts associated with phase transformation in the given materials. The mechanisms of formation of the Luders fronts as well as the Portevin–Le Chatelier fronts at different stages of the plastic flow are considered.

Addition of a 20-μL drop of a mixture containing 1 mM Fe2+ + 0.5 M glutathione to the surface of 0.5 M S-nitrosoglutathione solution, which is expected to form dinitrosyl iron complexes with glutathione, generated short-lived (0.2 s) concentric ring-shaped structures in the S-nitrosoglutathione solution. The number of the ring-like structures exceeded the number of concentric circles spread across the water surface (mechanical waves) when droplets of water fall into a body of an aqueous solution. It appears likely that the ring-shaped structures observed in the S-nitrosoglutathione solution are associated with an autowave distribution of products generated during the formation of dinitrosyl iron complexes with glutathione.

The kinetics of deformation processes at the yield plateau in the aluminum alloy 1550 studied. It is established that in the general case, the motion of the Lüders band fronts occurs discretely and only in the phase of sample unloading. Continuous motion of the deformation fronts is possible if the rate of relaxation of the applied stresses due to the test machine is greater than or equal to the rate of their decline, controlled by internal processes at a lower scale level. The discrete motion of the Lüders fronts in the 1550 alloy suggests that they are not pure autowaves of switching.

The behavior of localized plastic flow autowaves in a Fe–Ni–Cr alloy at temperatures 143 K ≤ T ≤ 420 K is considered. The temperature variation of the autowave propagation velocity is studied. It is found that, for the region of low temperatures, the autowave velocity is inversely proportional to the work hardening coefficient and the quadratic dispersion law takes place. The elastoplastic strain invariant does not depend on temperature.

An approach and a model of the birth and development of deformation bands and their fronts under plastic deformation due to phase transformation are proposed. A solid body is considered as an open nonequilibrium system the relaxation of which is determined both by vibrational and by electronic degrees of freedom. Electron transitions between different states of the system of nuclei and electrons under deformation initiate excitation of the unstable vibrational mode of atomic displacements into positions peculiar to the martensitic phase.

The behavior of characteristics of localized plastic flow autowaves in a Fe–Cr–Ni alloy in the temperature interval of 143 ≤ T ≤ 420 K (0.34 ≤ T/ΘD ≤ 1), where ΘD = 420 K is the Debye temperature (parameter), is considered. It is shown that the product of the length and propagation rate of the autowave λVaw in this interval decreases with temperature. At the same time, the ratio of this quantity to viscosity of the photon gas in the metal in the investigated temperature interval remains almost constant. This indicates that the elastoplastic strain invariant does not depend on temperature.

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.

Self-organized criticality is considered as a threshold stage of autowave self-organization in the evolutionary process. The proposed model defines self-organized criticality as a set of threshold parameters of the autowave system of equations. Consequently, it is associated with the formation of a qualitatively new biological structure (a new species). Experimental data on the mutation rate for groups of mice and unicellular eukaryotes that are published in the scientific literature are used to construct an autowave model of speciation at the population level. This model approach demonstrates compliance with the available experimental data in the process of fixing recessive mutations: there are three stages of fixation of mutations (accumulation of phenotypic differences, the threshold level of the mutation rate, and elimination of mutation carriers) and the maximum mutation rate when the mismatch repair system and the DNA polymerase $$\delta$$ proofreading activity are disabled. The percolation model of mutations with a delayed mutation rate is used to analyze the dynamics of the number of mutants in generations. The results demonstrate exact correspondence between the use of autowave model and percolation model of mutation fixation for calculating and analyzing the dynamics of the mutation rate and the number of mutation carriers.

Topical problems of the formation of slow deformation waves and their connection with recent geodynamic (deformational) processes are discussed. It is shown that the term “diffusion of stresses (displacements, strains)” is ill defined from the standpoint of physics of transfer phenomena because in the case of diffusion, mass transfer takes place, whereas the wave processes transfer energy. It is noted that the existing models describing the “diffusion of stresses” are solved based on the mathematical formalism of heat conduction theory which relies on the phenomenon of energy transfer. It is demonstrated that applying the term “wave” to the “stress diffusion” processes is untenable because in the classical sense, wave processes describe undamped (sustained, continuous) oscillations propagating in a homogeneous medium at constant velocity. The processes describing the “diffusion of stresses” form strongly damped oscillations whose propagation velocity substantially decreases with time. As a mechanism corresponding to the wave canonical concepts, a model of autowave deformation processes is proposed that implement the relay-race transfer and successive re-initiation of deformation activity from a fault to a fault or from one activated segment of a fault to another segment. Problematic issues of identifying the slow deformation waves are discussed, and the recommendations are proposed for constructing a network of observation points for the in situ measurements of spatiotemporal migration of the Earth’s surface deformations. It is substantiated that the existence of slow deformation waves does not explain the entire observed spatiotemporal spectrum of recent movements of the Earth’s surface.

An analytical method for determining the amplitude and velocity of an autowave pulse emerging in isentropically unstable heat-releasing media is presented. The method is suitable for any values of acoustic dispersion and growth rate and requires the knowledge of heat-loss function only without the need for a numerical solution of a complete system of gas-dynamic equations.

Basic concepts of the autowave model of development of a localized plastic flow of solids of different natures are considered. It is shown that plastic deformation develops in a localized (at the macroscale level) way throughout the process. The form of the observed localization patterns is related to stages of strain hardening of the material. The patterns are projections of different modes of the localized plastic flow autowave on the observation surface. An elastoplastic strain invariant is introduced, which is considered as the main equation of the autowave plasticity model, and its physical nature is discussed.

The paper investigates a model simulating crustal fault dynamics and strain wave generation in a fault block geological medium, the parameters determining sliding regimes in faults, and the physics of transitions between different deformation regimes. The model comprises the most important mechanisms responsible for the interaction of fault walls: friction, geometric irregularities (roughness and asperities on the fault surface), and external load, which govern sliding along the fault. The results of field and laboratory studies of deformation migration on the macro/mesoscale are consistent with the concept of localized deformation propagation in the form of solitary waves (kinks, solitons) and autowaves. The conditions are defined which make possible the transition from the model simulating solitary waves in a conservative medium with low “friction” (soliton-like behavior of the system) toward the model of solitary waves in an active medium with diffusion (autowave-like behavior of the system). Two possible deformation regimes of the fault block structure in the high-friction limit are considered. The fault wall displacement is stopped due to this friction, but the adjacent blocks move relative to each other in the core of the fault. It is shown that in the high-friction limit a perturbed sine-Gordon equation applied for fault dynamics modeling is reduced to a reaction-diffusion equation, whereas the system goes from the soliton regime to the autowave regime. In the case of high friction and a lack of energy supply to the fault from an external source, the transfer of localized deformation is changed by a diffusive dissipation of stress.

The relationship between the spatial parameter of the development of a localized plastic flow (the length of the localized plasticity autowave) and the length of the deformed sample is studied. According to experiments carried out on polycrystalline samples of a zirconium alloy and commercial purity aluminum, these quantities are related to each other by a logarithmic law valid at the stage of parabolic strain hardening.

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.

The infrared thermography method was used to study changes in the temperature of austenitic stainless steel in the process of tensile deformation. It was revealed that the temperature of the sample stops growing in the transition region between the linear stages of strain hardening. This phenomenon can be connected with a change in the entropy of the deformed medium as a result of a reconstruction of the ordered autowave structures. In the region of true deformation exceeding 0.4, a phenomenon of discontinuous flow (Portevin–Le Chậtelier effect) is observed, which is accompanied by the motion of the single fronts of localized deformation. The observed fronts are heat sources, and the value of the temperature at the arbitrary point of the sample is determined by its position relative to the front of deformation.

A diffusion neuron model representing a system of $$m,$$ $$m \geqslant 2$$ , identical nonlinear delay differential equations coupled by linear diffusion terms is considered. It is shown that, with a suitable choice of the diffusion coefficient, the system has a set of $$m$$ stable relaxation cycles.

Velocity and amplitude are two basic characteristics of any autowave, and their relationship reflects the internal regulation of the autowave system. This study proposes an approach to approximately estimate steady velocity–amplitude (VA) relation without deriving separate formulas for V and A. The approach presumes constructing an ansatz which represents the “petal” form of phase trajectory and contains V, A, and a free parameter (parameters). After substituting this ansatz, integration of model equations leads to a VA relation analytically. A free parameter (parameters) can be determined by comparing the analytical VA relation to the numerical data. As an example, we used the simplest autowave model possessing threshold, that is, the Gray–Scott model (cubic autocatalysis with linear inhibition) in isolated conditions with an immobilized precursor and a diffusible reactant. For all values of the inhibition rate constant allowing autowave solution (i.e., except approaching zero), the free parameter of ansatz belongs to a narrow interval has little effect on VA relation and can be regarded as fixed. Assumption of precursor immobilization does not influence the results qualitatively. This approach will be useful in investigations of more complex active media systems in biochemistry, combustion, and disease control.

A review of physical regularities in formation of the the spatial structure of proteins during their folding, that is, the folding of a homochiral polypeptide chain into a unique native configuration, is presented, including the mathematical models of this process. The materials of this review are summarized in a new phenomenological model for the formation of hierarchies of sign-alternating chiral structures and also in a new mathematical model for the formation of α-helices as autowave structures. Some folding thermodynamic aspects associated with symmetry factors are discussed.

TiAl-based composite materials have been produced by spin-casting self-propagating high-temperature synthesis metallurgy methods using thermite-type mixtures, general relationships in the formation of their composition and structure have been investigated, the synthesis conditions have been optimized, a method for obtaining large ingots has been proposed, and their composition and structure have been determined. We have obtained cast Nb- and Cr-doped TiAl-based composite materials using mixtures of Ti, Nb, Cr, and Ca oxides with a combined reducing agent (Al and Ca) under the effect of an overload above 200g. It has been shown that partial Ca substitution for Al in the starting mixture ensures complete reduction of the TiO2, and the resultant metallic phase contains calculated amounts of Ti and Al. Mixtures of optimized composition make it possible to produce a cast composite material similar in composition to alloy 4822.

This work is devoted to the phenomenon of liquid-liquid phase separation (LLPS), which has come to be recognized as fundamental organizing principle of living cells. We distinguish separation processes with different dimensions. Well-known 3D-condensation occurs in aqueous solution and leads to membraneless organelle (MLOs) formation. 2D-films may be formed near membrane surfaces and lateral phase separation (membrane rafts) occurs within the membranes themselves. LLPS may also occur on 1D structures like DNA and the cyto- and nucleoskeleton. Phase separation provides efficient transport and sorting of proteins and metabolites, accelerates the assembly of metabolic and signaling complexes, and mediates stress responses. In this work, we propose a model in which the processes of polymerization (1D structures), phase separation in membranes (2D structures), and LLPS in the volume (3D structures) influence each other. Disordered proteins and whole condensates may provide membrane raft separation or polymerization of specific proteins. On the other hand, 1D and 2D structures with special composition or embedded IDRs can nucleate condensates. We hypothesized that environmental change may trigger a LLPS which can propagate within the cell interior moving along the cytoskeleton or as an autowave. New phase propagation quickly and using a low amount of energy adjusts cell signaling and metabolic systems to new demands. Cumulatively, the interconnected phase separation phenomena in different dimensions represent a previously unexplored system of intracellular communication and regulation which cannot be ignored when considering both physiological and pathological cell processes.

The paper considers the question of the possibility of recovering symmetric stable states of a bistable medium in the inverse problem for a nonlinear singularly perturbed autowave equation by data given on the position of an autowave front propagating through it. It is shown that under certain conditions, this statement of the problem is ill-posed in the sense of the non-uniqueness of the solution. A regularizing approach to its solution was proposed.

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.

Cellular neural network is a well-known mathematical model for investigation of deterministic, stochastic and chaotic processes in nonlinear dynamic systems. The turn to a reaction-diffusion cellular neural network (RDCNN) enables to model different types of autowave processes (concentric, circular and spiral waves, Turing structures, etc.) RDCNN is a convenient architecture for the mathematical description of the systems of nonlinear differential equations with diffusion and their solution based on numerical methods. Running circular and spiral waves in RDCNN are synthesized and their properties are demonstrated (preservation of the shape and amplitude of the running waves, as well as the destruction of waves which results from their collision.) Autowaves are built in the MATLAB system on using the fourth-order Runge–Kutta numerical method.

The notions of plastic flow localization are reviewed here. It have been shown that each type of localized plasticity pattern corresponds to a given stage of deformation hardening. In the course of plastic flow development a changeover in the types of localization patterns occurs. The types of localization patterns are limited to a total of four pattern types. A correspondence has been set up between the emergent localization pattern and the respective flow stage. It is found that the localization patterns are manifestations of the autowave nature of plastic flow localization process, with each pattern type corresponding to a definite type of autowave. Propagation velocity, dispersion and grain size dependence of wavelength have been determined experimentally for the phase autowave. An elastic-plastic strain invariant has also been introduced to relate the elastic and plastic properties of the deforming medium. It is found that the autowave’s characteristics follow directly from the latter invariant. A hypothetic quasi-particle has been introduced which correlates with the localized plasticity autowave; the probable properties of the quasi-particle have been estimated. Taking the quasi-particle approach, the characteristics of the plastic flow localization process are considered herein.

The kinetics of the martensitic transformation fronts in transformation-induced plasticity (TRIP) steel was studied in relation to preliminary thermomechanical treatment using the digital image correlation method. It was found that warm rolling of steel to 40&ndash, 63% reduction significantly increases the stress of the onset of strain-induced phase transformation and changes the loading curve stages. The strain-induced phase transformation in TRIP steel occurring through the formation of L&uuml, ders and Portevin&ndash, Le Chatelier bands is shown to be an autowave process of localized plasticity. The austenite &rarr, martensite transformation at the elastic-plastic transition occurs in the form of several switching localized plasticity autowaves. At the jerky flow stage, excitation autowaves of localized plasticity are generated and propagate repeatedly until the strain-induced austenite &rarr, martensite transformation is completed. It is shown for the first time that the sources of excitation autowaves in the material are the sites of nucleation or annihilation of switching autowaves.