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By critically examining the traditional theory of homogeneous nucleation of precipitates in solid solutions, it is revealed that the theory's assertion regarding an increase in the nucleation free energy due to elastic strain associated with the difference in atomic volumes between the two phases is applicable to coherent precipitates, but becomes incorrect when applied to incoherent precipitates. This conclusion is obtained by accounting for thermal point defects in the matrix, which can be absorbed at the interface between an incoherent particle and the matrix during nucleation, thereby relieving elastic stresses. Accordingly, a new kinetic model based on the Reiss theory for binary nucleation is proposed for predicting the nucleation rate of incoherent precipitates by agglomeration of solute atoms and point defects, with a further extension to account for excess vacancies formed under non-equilibrium conditions of quenching experiments., Comment: Published in Russian Zhurnal Eksperimental'noi i Teoreticheskoi Fiziki 165 (2024) 214-225

Dynamical equations that are valid in the vicinity of the phase transition into the superconducting state are given. Probable effects of the field of charge carriers' magnetic interactions and the field of temperature fluctuations were taken into account. The order of the phase transition is discussed. Considerations in favor of the applicability of the stochastic dynamical model A to describe the dynamics of this phase transition are given., Comment: 15 pages, 1 figure, in Russian

For the Langevin model of the dynamics of a Brownian particle with perturbations orthogonal to its current velocity, in a regime when the particle velocity modulus becomes constant, an equation for the characteristic function $\psi (t,\lambda )=M\left[\exp (\lambda ,x(t))/V={\rm v}(0)\right]$ of the position $x(t)$ of the Brownian particle. The obtained results confirm the conclusion that the model of the dynamics of a Brownian particle, which constructed on the basis of an unconventional physical interpretation of the Langevin equations, i. e. stochastic equations with orthogonal influences, leads to the interpretation of an ensemble of Brownian particles as a system with wave properties. These results are consistent with the previously obtained conclusions that, with a certain agreement of the coefficients in the original stochastic equation, for small random influences and friction, the Langevin equations lead to a description of the probability density of the position of a particle based on wave equations. For large random influences and friction, the probability density is a solution to the diffusion equation, with a diffusion coefficient that is lower than in the classical diffusion model., Comment: 11 pages, preprint, in Russian

In the framework of Gibbs statistical theory, the issue of the distribution of particle sizes forming the statistical system and the moments of this distribution are considered. This task is relevant for a wide variety of applications. The distribution for particle sizes and moments of this quantity are determined from probabilistic considerations. Particle size depends on interactions in the system, on the compressibility factor, on the number of interacting particles, on the volume of the system. The expressions for the intrinsic volume of particles are substituted into the equations of state written using the theory of excluded volume for various expressions of the exclusion factor. The equations of state thus obtained can be considered as a refinement of the equation of state, a transition to a higher level of description., Comment: 21 pages, in Russian

In this paper the detailed investigation of one of the most interesting models in the non relativistic quantum mechanics of one massive particle i.e., introduced by G. Poeschl and E. Teller in 1933 is continued; the starting point of dynamic analysis for potentials, wave functions and energy spectrum was carried on by the same authors in the paper. The generalization of these results on the case of nonzero temperature includes the approximate calculation of the partition function of the model and then also the Massieu Planck thermodynamic potential and its most important derivatives, i.e. internal energy, heat capacity and pressure. The analysis of the results is carried on separately for low and high temperature regions because of the lack of exact unifying expressions of the potential at all temperatures., Comment: 13 pages, in Russian

Work is a continuation of work TMPh, 175(2), 2013. We study the Potts model with zero external field on the Cayley tree. It is shown that for any values of the parameter all periodic Gibbs measures are translation-invariant for the q-state antiferromagnetic Potts model on the Cayley tree of order two and for the q-state ferromagnetic Potts model on the Cayley tree of order k., Comment: in Russian

In the framework of the Gibbs statistical theory, the question of the size of the particles forming the statistical system is investigated. This task is relevant for a wide variety of applications. The distribution for particle sizes and the moments of this quantity are determined from probabilistic considerations. The results are compared with different models and approximations. The particle size depends on the interactions in the system, on the compressibility factor, on the number of interacting particles. The cases of the absence and presence of a rigid incompressible particle core are considered., Comment: 16 pages, in Russian, 2 figures

We study the effects of synchronization and desynchronization in ensembles of phase oscillators with the global Kuramoto-Sakaguchi coupling under common noise driving. Since the mechanisms of synchronization by coupling and by common noise are essentially different, their interplay is of interest. In the thermodynamic limit of large number of oscillators, employing the Ott-Antonsen approach, we derive stochastic equations for the order parameters and consider their dynamics for two cases: (i) identical oscillators and (ii) small natural frequency mismatch. For identical oscillators, the stability of the perfect synchrony state is studied; a strong enough common noise is revealed to prevail over a moderate negative (repelling) coupling and to synchronize the ensemble. An inequality between the states of maximal asynchrony (zero-value of the order parameter) and perfect synchrony; the former can be only weakly stable, while the latter can become adsorbing (the transition to the synchrony becomes unidirectional). The dependence of the temporal dynamics of the transition on the system parameters is investigated. For nonidentical oscillators the perfect synchrony state becomes impossible and an absorbing state disappears; on its place, only a weakly stable state of imperfect synchrony remains. A nontrivial effect of the divergence of individual frequencies of oscillators with different natural frequencies is revealed and studied for moderate repelling coupling; meanwhile, the order parameter remains non-small for this case. In Appendix we provide an introduction to the theories of Ott-Antonsen and Watanabe-Strogatz., Comment: 31 pages, 5 figures, in Russian

The paper presents a solution to the Boltzmann kinetic equation based on the construction of its discrete conservative model. Discrete analogue of the collision integral is presented as a contraction of a tensor, which is independent from the initial distribution function, colliding with a tensor composed of medium densities in the cells. Numerical implementation of the discrete model is demonstrated on the example of the isotropic gas relaxation problem applied to the hard spheres model. The key feature of the method is independence of the collision tensor components from the distribution function. Consequently the components of the collision tensor are calculated once for various initial distribution functions, which substantially increases performance of the suggested method., Comment: in Russian

We discuss the molecular diffusion transport in infinitely dilute liquid solutions under non-isothermal conditions. This discussion is motivated by an occurring misinterpretation of thermodynamic transport equations written in terms of chemical potential in the presence of temperature gradient. The transport equations contain the contributions owned by a gauge transformation related to the fact that chemical potential is determined up to the summand of form (AT+B) with arbitrary constants A and B, where constant A is owned by the entropy invariance with respect to shifts by a constant value and B is owned by the potential energy invariance with respect to shifts by a constant value. The coefficients of the cross-effect terms in thermodynamic fluxes are contributed by this gauge transformation and, generally, are not the actual cross-effect physical transport coefficients. Our treatment is based on consideration of the entropy balance and suggests a promising hint for attempts of evaluation of the thermal diffusion constant from the first principles. We also discuss the impossibility of the "barodiffusion" for dilute solutions, understood in a sense of diffusion flux driven by the pressure gradient itself. When one speaks of "barodiffusion" terms in literature, these terms typically represent the drift in external potential force field (e.g., electric or gravitational fields), where in the final equations the specific force on molecules is substituted with an expression with the hydrostatic pressure gradient this external force field produces. Obviously, the interpretation of the latter as barodiffusion is fragile and may hinder the accounting for the diffusion fluxes produced by the pressure gradient itself., Comment: in Russian; author's version of the manuscript published in Vych. Mekh. Sploshnyh Sred -- Computational Continuum Mechanics, vol. 9, no. 1, 52-58 (2016)

From the previously obtained solutions of the Fokker - Planck equation for Rayleigh gas (small impurity of heavy particles in a thermostat of light particles) with sources and without them, the entropy production was calculated. In a system without source (isolated system) shown that it holds theorem of Prigogine, and in a system with sources (open system) implementation of the principle of Ziegler (MEPP) depends on the relaxation direction. In an open system entropy production is compensate by a negative production of entropy, i.e. by a negentropy production. The algebraic sum of entropy and negentropy productions is called the generalized entropy production. From the balance of entropy and negentropy productions in an open system formulated a possible variation of the second law for open systems in a form: "At the relaxation of an open system to a nonequilibrium steady state, a generalized entropy production decreases in absolute value and equal to zero in a nonequilibrium steady state." Keywords: Fokker-Planck equation, Prigogine theorem, principle of maximum entropy production, the second law, negentropy., Comment: in Russian. Negentropy production - is the negative production of positive entropy, that is, absorption of entropy. The term "negentropy production" introduced to emphasize absorption of entropy by irreversible processes

By example of a particle interacting with ideal gas, it is shown that statistics of collisions in statistical mechanics at any degree of the gas rarefaction qualitatively differs from that conjugated with Boltzmann's hypothetical molecular chaos and kinetic equation. In reality, probability of the particle collisions in itself is random, which results in power-law asymptotic of the particle velocity relaxation. An estimate of its exponent is suggested basing on simple kinematic reasonings, Comment: 4 pages, no figures, latex2e jetpl, submitted in Russian to JETP Letters (attached in the source tex ile)

General key problems in relation to the application of self-organizing structures theory to the analysis of current cooperative phenomena are discussed. Particularly, we present the new results of the analysis of burning problem to form a qubit network. Recently [Proc. of the Inst. of Physics and Technol. of Russian Acad. of Sci. (Trudy FTIAN), vol. 25 (accepted for publication on Jan. 15, 2015)] we have proposed a new method for quantum computer implementation based on self-organizing structures. Here we consider in detail the essence of new proposals and theoretical argumentation. We have shown that some self-organizing structures, both dissipative ones and thermodynamically equilibrium structures with off-diagonal long-range order, are promising to form a qubit network. This is confirmed by our results of the investigations relative to the following items: an open resonator with periodic boundaries, conditions to create specific distribution of the modes and the effect of the field crystallization, the use of this effect to create an proficient and coherentized system of neutral atoms traps and to achieve their precise localization; the equilibrium systems which can go, at temperatures below critical ones, into the special state with off-diagonal long-range order (i.e. to the state with macroscopic quantum coherence), phase transition (photons condensation) in the two-level atoms interacting with radiation mode in the resonator, superradiant phase transition, the order-disorder type ferroelectrics in the cavity electromagnetic field, the advantage of the systems capable to self-organization, including the suppression of the temperature influence as the decoherence factor acting on the work states of the qubits (atoms, ferroelectric molecules), and also the coherent character of the direct dipole-dipole interaction between qubits (in the case of ferroelectrics), and other items., Comment: 39 pages, in Russian

In this paper we consider various models of hydraulic hysteresis in invasive mercury porosimetry. For simulating the hydraulic hysteresis is used isotropic site percolation on three-dimensional square lattices with $(1, d)$-neighborhood. The relationship between the percolation model parameters and invasive porosimetry data is studied phenomenologically. The implementation of the percolation model is based on libraries SPSL and SECP, released under license GNU GPL-3 using the free programming language R., Comment: 16 pages, 11 figures, in Russian

In this paper we consider statistical estimates of threshold and strength of percolation clusters on square lattices. The percolation threshold $p_c$ and the strength of percolation clusters $P_\infty$ for a square lattice with $(1, d)$-neighborhood depends not only on the lattice dimension, but also on the Minkowski exponent $d$. To estimate the strength of percolation clusters $P_\infty$ proposed a new method of averaging the relative frequencies of the target subset of lattice sites. The implementation of this method is based on the SPSL package, released under GNU GPL-3 using the free programming language R., Comment: 10 pages, 5 figures, in Russian

It is shown that the results presented in the article 'The influence of the temperature and pressure on a fractal dimension of defects in crystal structures' by V.B. Fedoseev (Butlerov communications. 2010. V23. Number 14. P.36-42) are not correct, because the results are based on impracticable conditions, conflicting assumptions and incorrect distributions., Comment: 5 pages, in Russian

The equilibrium size distribution function of clusters (nanoparticles) in the system of finite number of molecules (atoms) in finite closed volume with constant total energy (isolated system) is found using methods of statistical thermodynamics. The distribution function is found from kinetic equation of nucleation using one-drop approximation for both isothermal and isolated systems. The results obtained are compared with computer simulation data of finite two-dimensional system., Comment: 14 pages, in Russian

In this paper we consider the structure of site percolation models on three-dimensional square lattices with various shapes of (1,d)-neighborhood. For these models, are proposed iso- and anisotropic modifications of the invasion percolation algorithm with (1,0)- and (1,d)-neighborhoods. All the above algorithms are special cases of the anisotropic invasion percolation algorithm on the n-dimensional lattice with a (1,d)-neighborhood. This algorithm is the basis for the package SPSL, released under GNU GPL-3 using the free programming language R., Comment: 18 pages, 4 figures, in Russian

In the paper we propose an universal bridge functional for the closure of the Ornstein-Zernike (OZ) equation for the case of infinitely diluted solutions of Lennard-Jones shperes of different size in the Lennard-Jones fluid. Bridge functional is paprameterized using the data of the Molecular Dynamics (MD) simulations. We show that for all investigated systems the bridge functional can be efficiently papameterized with the exponential function which depends only on the ratio of sizes of the solute and solvent atoms. To check the parameterization we solve the OZ equation with the closure which includes the parametrized functional and with the closure without the bridge functional (Hyper-netted chain closure). We show that introducing the bridge functional allows to obtain radial distribution functions (RDFs), which are close to the MD results and essentially improve predictions of the location and height of the first peak of the RDF., Comment: Preprint. Original (in Russian) was sent to the Russian Journal of Physical Chemistry A

This report focuses on the dependencies for the center and radius of the confidence interval that arise when estimating the mass fractal dimensions of anisotropic sampling clusters in the site percolation model., Comment: 3 pages, 1 figures, in Russian

This report focuses on the dependencies for the center and radius of the confidence interval that arise when estimating the mass fractal dimensions of isotropic sampling clusters in the site percolation model., Comment: 3 pages, 1 figures, in Russian

This paper is a natural continuation of our previous paper arXiv:1011.4173 . We illustrated earlier that in classical Hamilton mechanics, for overwhelming majority of real chaotic macroscopic systems, alignment of their thermodynamic time arrows occurs because of their low interaction. This fact and impossibility to observe entropy decrease at introspection explain the second law of thermodynamics. The situation in quantum mechanics is even a little bit easier: all closed systems of finite volume are periodic or nearly periodic. The proof in quantum mechanics is in many respects similar to the proof in classical Hamilton mechanics - it also uses small interaction between subsystems and impossibility to observe entropy decrease at introspection. However, there are special cases which were not found in the classical mechanics. In these cases one microstate corresponds to a set of possible macrostates (more precisely, their quantum superposition). Consideration of this property with use of decoherence theory and taking into account thermodynamic time arrows will introduce new outcomes in quantum mechanics. It allows to resolve basic paradoxes of quantum mechanics: (a) to explain the paradox of wave packet reduction at measurements when an observer is included in the system (introspection) (paradox of the Schrodinger cat); (b) to explain unobservability of superposition of macroscopic states by an external observer in real experiments (paradox of Wigner's friend); (c) to prove full equivalence of multi-world and Copenhagen interpretations of quantum mechanics; (d) to explain deviations from the exponential law at decay of particles and pass from one energy level to another (paradox of a kettle which will never begin to boil)., Comment: 42 pages in Enlish and in Russian

In this paper we study statistical methods of parameters estimation of the site percolation model. Advantages of the proposed method is demonstrated for the computing of the confidence interval of mass fractal dimension of a percolation clusters sampling, formed by the Monte Carlo method., Comment: 9 pages, 4 figures, in Russian

We study the implementation of a weak multiple delayed feedback for controlling coherence of chaotic oscillations. The specific system we treat is the Lorenz system with classical set of parameters. There are two reasons behind the interest to feedback with multiple (incommensurable) delay times: (1) two delay times provide more flexibility in control than the single one; (2) some dynamic systems posses an inherent internal delay (e.g., traveling-wave tube), and the introducing of the second delayed feedback is a natural measure for dealing with stray effects brought about by the inherent one. Specifically, for the Lorenz system we show that two incommensurable delay times enable achieving suppression of the phase diffusion constant (quantifying the oscillation coherence) by 2-3 orders of magnitude without destruction of chaos, while the single one does by 20 times., Comment: In Russian, 4 pages, 1 figure. Paper for the topical issue of "Izvestiya vuzov. Prikladnaya nelinejnaya dinamika" (Applied Nonlinear Dynamics) (StatInfo-2009)

A relationship of the random walks on one-dimensional periodic lattice and the correlation functions of the XX Heisenberg spin chain is investigated. The operator averages taken over the ferromagnetic state play a role of generating functions of the number of paths made by the so-called "vicious" random walkers (the vicious walkers annihilate each other provided they arrive at the same lattice site). It is shown that the two-point correlation function of spins, calculated over eigen-states of the XX magnet, can be interpreted as the generating function of paths made by a single walker in a medium characterized by a non-constant number of vicious neighbors. The answers are obtained for a number of paths made by the described walker from some fixed lattice site to another sufficiently remote one. Asymptotical estimates for the number of paths are provided in the limit, when the number of steps is increased., Comment: 16 pages, 1 figure, LaTeX. Extended talk at the Conference "Classical and Quantum Integrable Systems CQIS-08" (Protvino, Russia, January 21-24, 2008). To appear in Theoretical and Mathematical Physics in 2009 (In Russian)

The dissertation contains 4 original chapters: 1) Parametric excitation of Soret-driven convection of binary mixture in a horizontal porous layer. 2) Soret-driven convection in a horizontal porous layer from a heat or concentration source. 3) Localization of convective flows under randomly inhomogeneous heating. 4) Synchrony of nonlinear systems driven by common noise., Comment: 150 pages, 30 figures, Dissertation [in Russian] for earning the degree of Candidate of Phys.-Math. Sciences (analog of PhD; specialized field 01.02.05. "Mechanics of Fluid, Gas, and Plasma") has been successfully defended in the defense committee D 212.189.06 of Perm State University (Perm, Russia) on May 15, 2007 Scientific adviser: Prof. Dmitry V. Lyubimov