ВЕСТНИК НАЦИОНАЛЬНОГО ИССЛЕДОВАТЕЛЬСКОГО ЯДЕРНОГО УНИВЕРСИТЕТА МИФИ

  • Publisher Общество с ограниченной ответственностью Международная академическая издательская компания "Наука/Интерпериодика"
  • Country Россия
  • Web https://elibrary.ru/title_about.asp?id=33583

Content

Reprocessed Uranium Re-enrichment in a Double Cascade of Gas Centrifuges Providing Its Complete Return to the Nuclear Fuel Cycle

Smirnov A. Yu., Gusev V.Е., Sulaberidze G.A., Nevinitsa V.A., Fomichenko P.А.

The problem of spent nuclear fuel recycling, specifically, reusing the regenerated uranium component, i.e., reprocessed uranium has been considered. The re-enrichment of this material requires modern separation technologies, namely, the application of the separation cascade theory to gas centrifuges. However, this process is technically difficult due to the presence of the artificial 232, 236 U isotopes and natural-born 234 U isotope, whose content in reprocessed uranium is higher than that in natural uranium. Thus, to satisfy the radiation safety requirements for the production of fuel elements and to preserve the neutron-physical characteristics of nuclear fuel, the standard uranium enrichment scheme should be modified. In this work, a modification of the double cascade of gas centrifuges has been proposed to obtain a product that satisfies the constraints for all even uranium isotopes and simultaneously consumes a determined amount of the uranium regenerate for its production. The latter condition is necessary for the complete closing of the uranium fuel cycle and the correct control over the turnover of exported fissile materials. The principle of operation for the proposed cascade scheme for reprocessed uranium enrichment after several consecutive irradiation cycles has been illustrated using the theory of cascades for isotope separation. The possibility of reaching the compliance with all specified conditions and restrictions to relevant international standards has been demonstrated. DOI: 10.1134/S2304487X18060135

Reductions and New Exact Solutions of the Convective Heat and Mass Transfer Equations with a Nonlinear Source

Polyanin A.D.

Various classes of nonlinear convective heat and mass transfer equations with variable coefficients $c(x){{u}_{t}} = {{[a(x){{u}_{x}}]}_{x}} + b(x){{u}_{x}} + p(x)f(u)$ are considered. Exact solutions with a functional separation of variables of the general form $u = U(z)$, $z = \varphi (x,t)$ are sought. It is shown that the kinetic function $f(u)$ and any three of the four coefficients $a(x)$, $b(x)$, $c(x)$ and $p(x)$ of these equations can be chosen arbitrarily, and the remaining coefficient is expressed in terms of them. The properties of the overdetermined system of differential equations for the function $\varphi (x,t)$ are investigated and all its solutions are constructed. Examples of specific equations and their exact solutions are given. The results obtained are generalized to more complex multidimensional nonlinear convective heat and mass transfer equations with variable coefficients. Some exact solutions with the functional separation of variables of nonlinear reaction–diffusion equations with delay ${{u}_{t}} = {{u}_{{xx}}} + a(x)f(u,w),\quad w = u(x,t - \tau )$, where $\tau > 0$ is the delay time and $f(u,w)$ is an arbitrary function of two arguments, are also obtained. DOI: 10.1134/S2304487X18060093

Application of the Fuchs Indices for the Construction of Exact Solutions of Nonlinear Differential Equations

Kudryashov N.A.

The basic idea of the method is to use the value of the Fuchs index that appears in the Painlevé test to construct the auxiliary equation for finding the first integrals and exact solutions of nonlinear differential equations. It allows us to obtain the first integrals and new exact solutions of some nonlinear ordinary differential equations. The main feature of the method is that we do not assign a solution function at the beginning, we find this function during calculations. This approach is conceptually equivalent to the third step of the Painlev´e test and sometimes allows us to change this step. Our approach generalizes a number of other methods for finding exact solutions of nonlinear differential equations. We demonstrate a method for finding the traveling wave solutions and the first integrals of the well-known nonlinear evolution equation for description of surface waves in a convecting liquid. The general solution of this equation at some conditions on parameters and new traveling wave solutions of the fourth-order equation are found. DOI: 10.1134/S2304487X18060056

Stationary Dissipative Structures and Diffusion Chaos in a One-Dimensional Reaction–Diffusion System with Cubic Nonlinearity

Yakushkin N.A.

—Stationary and unsteady aperiodic (diffusion chaos) dissipative structures resulting from two different bifurcations of the loss of stability of a trivial stationary solution (thermodynamic branch) of a one-dimensional reaction–diffusion system with cubic nonlinearity have been studied. Turing and Andronov–Hopf bifurcations are responsible for the occurrence of stationary and unsteady aperiodic dissipative structures, respectively. The considered bifurcations occur under quite simple conditions when the spectrum of the linearization operator of the studied reaction–diffusion system contains one or a pair of complex conjugate eigenvalues with positive real parts near the bifurcating thermodynamic branch, respectively. In spite of the simplicity of these conditions, their interpretation for a particular one-dimensional reaction–diffusion system can be technically complicated. In this work, two theorems have been formulated and proven to study quite trivially the conditions under which Turing and Andronov–Hopf bifurcations of a trivial thermodynamic branch occur in an arbitrary one-dimensional reaction–diffusion system with cubic nonlinearity. Furthermore, numerical experiments that make it possible to detect and visualize dissipative structures resulting from these bifurcations have been described. DOI: 10.1134/S2304487X18060160

First Integrals and Exact Solutions of a Two-Component Belousov–Zhabotinsky Model

Kudryashov N.A.

The popular Belousov–Zhabotinsky system of equations for description of a two component reaction is considered. The Painlevé test is applied to determine integrability of this system. It is shown that the system of equations is nonintegrable in the general case. The parameters of the mathematical model are found for the case where the system of equations passes the Painlevé test. The simplest solutions of the system of equations are presented. Additional conditions are specified under which the general solutions of the system can be found. These general solutions are found using the new generalized method for finding exact solutions and the first integrals. Two first integrals of the Belousov–Zhabotinsky system of equations are given under additional conditions on the parameters of the mathematical model. DOI: 10.1134/S2304487X18060068 REFERENCES 1. R.J. Field, R.M. Noyes, Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction, J. Chem. 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Wang, Travelling wave front solutions of Noyes-field system for Belousov–Zhabotinskii reaction, Nonlinear Analysis 11 (11) (1987) 1289–1302. 8. M. Shiwang, Traveling Wavefronts for Delayed Reaction-Diffusion Systems via a Fixed Point Theorem, Journal of Differential Equations 171 (2001) 294–314. 9. E. Trofimchuk, M. Pinto, S. Trofimchuk, Traveling waves for a model of the Belousov–Zhabotinsky reaction, Journal of Differential Equations 254 (9) (2013) 3690–3714. 10. W.C. Troy, The existence of traveling wave front solutions of a model of the Belousov–Zhabotinskii chemical reaction, Journal of Differential Equations 36 (1) (1980) 89–98. 11. L. Zhibin, He Shi, Exact solutions for Belousov-Zhabotinskii reaction–diffusion system, Appl. Math. – JCU 11B (1996) 1–6. 12. J.D. Murray, On travelling wave solutions in a model for the Belousov–Zhabotinskii reaction, Journal of Theoretical Biology 56 (2) (1976) 329–353. 13. J.D. Murray, Mathematical biology. I. An introduction, Springer-Verlag, 2001. 14. J.D. Murray, Mathematical biology. II. Spatial models and biomedical applications, Springer-Verlag, 2003. 15. N.A. Kudryashov, A.S. Zakharchenko Painlevґe analysis and exact solutions for the Belousov–Zhabotinskii reaction–diffusion system. Chaos, Soliton Fract., 65 (2014), 111–117. 16. C. Muriel, J.L. Romero, Second-order ordinary differential equations and first integrals of the form $A{{(t;x)}_{x}} + B(t;x)$, J. Nonlinear Math. Phys. 16 (2009) 209–222. 17. L.G. S. Duarte, I.C. Moreira, F.C. Santos, Linearization under nonpoint transformations, J. Phys. A. Math. Gen. 27 (1994) L739–L743. 18. N.A. Kudryashov, D.I. Sinelshchikov, On connections of the Liґenard equation with some equations of Painlevґe–Gambier type. J. Math. Analys. Appl., 449(2) (2017), 1570–1580 19. C. Muriel, J.L. Romero, Integrating factors and $\lambda $-symmetries, J. Nonlinear Math. Phys. 15 (2008) 111–125. 20. C. Muriel, J.L. Romero, A $\lambda $–symmetry methos for the linearization and determination of the first integrals of a family of second–order ordinary differential equations, J. Phys.:A: Mathh. Theor. 44 (2011) 245201–245220. 21. A. Ramani, B. Dorizzi, B, Grammaticos, T. Bountis, Integrability and the Painlevé property for low-dimensional systems, J. Math.Phys. 25(4), (1984) 878–883. 22. M. J. Ablowitz, A. Ramani, H. Segur, Nonlinear evolution equations and ordinary differential equations of Painlevé type, Lett. Nuovo cim., 23 (1984) 878–883. 23. M.J. Ablowitz, A. Ramani, H. Segur, A connection between nonlinear evolution equations and ordinary differential equations of P–type. I and II, J. Math. Phys., 21 (1980) 715–721; 1006–1015. 24. N.A. Kudryashov, Fuchs indices and the first integrals of nonlinear differential equations, Chaos, Solitons and Fractals, 26(2) (2005), 591–603. 25. N.A. Kudryashov, Simplest equation method to look for exact solutions of nonlinear differential equations, Chaos Soliton Frac. 24 (2005) 1217–1231. 26. N.A. Kudryashov, One method for finding exact solutions of nonlinear differential equations, Commun. Nonlinear Sci. Numer. Simulat. 17 (2012) 2248–2253. 27. A. Biswas, Solitary wave solution for the generalized Kawahara equation, Appl. Math. Lett. 22 (2009) 208–210. 28. E.J. Parkes, B.R. Duffy, An automated tanh-function method for finding solitary wave solutions to nonlinear evolution equations, Comput. Phys. Commun. 98 (1996) 288–300. 29. A.D. Polyanin, V.F. Zaitsev, Handbook of Nonlinear Partial Differential Equations, Second Edition, Chapman and Hall/CRC, Boca Raton, 2012. 30. W. Malfliet, W. Hereman, The tanh method: I. Exact solutions of nonlinear evolution and wave equations, Phys. Scripta. 54 (1996) 563–568. 31. N.K. Vitanov, Application of simplest equations of Bernoulli and Riccati kind for obtaining exact traveling-wave solutions for a class of PDEs with polynomial nonlinearity, Commun. Nonlinear Sci. Numer. Simulat. 15 (2010) 2050–2060. 32. N.A. Kudryashov, Solitary and Periodic Solutions of the Generalized Kuramoto-Sivashinsky Equation, Regular and Chaotic Dynamics, 13 (3), (2008), 234–238. 33. A.D. Polyanin, V.F. Zaitsev, Handbook of Exact Solutions for Ordinary Differential Equations, Boca Ration, Chapman and Hall/CRC, 2003. 34. E.L. Ince, Ordinary differential equations, Dover, New York, 1956. 35. P. Painleve, Sur les ґequations diffґerentielles du second ordre et d’ordre supґerieur dont l’intґegrale gґenґerale est uniforme. Acta Math., 25(1), (1902) 1–85. 36. B. Gambier, Sur les ґequations diffґerentielles du second ordre et du premier degrґe dont l’intґegrale gґenґerale est a points critiques fixes. Acta Math. (1910) 1–55.

Reductions and New Exact Solutions of Convection–Diffusion Equations with Variable Coefficients

Polyanin A.D.

Various classes of nonlinear convection–diffusion equations with variable coefficients $c(x){{u}_{t}} = {{[a(x){{u}_{x}}]}_{x}} + [b(x) + p(x)f(u)]{{u}_{x}}$ are considered. Exact solutions with the functional separation of variables of the general form $u = U(z)$, $z = \varphi (x,t)$ are sought. It is shown that the kinetic function $f(u)$ and any three of the four coefficients $a(x)$, $b(x)$, $c(x)$, and $p(x)$ of these equations can be chosen arbitrarily, and the remaining coefficient is expressed in terms of them. The properties of the overdetermined system of differential equations for the function $\varphi (x,t)$ are investigated and all its solutions are constructed. Examples of specific equations and their exact solutions are given. Some exact solutions with the functional separation of variables of nonlinear reaction–diffusion equations with delay, ${{u}_{t}} = {{u}_{{xx}}} + a(x)f(u,w){{u}_{x}},\,\,w = u(x,t - \tau )$, where $\tau > 0$ is the delay time and $f(u,w)$ is an arbitrary function of two arguments, are also obtained. DOI: 10.1134/S2304487X1806010X

Analytic Properties and Nonlinear Dynamics of the FitzHugh–Nagumo Model for Two Coupled Neurons

Lavrova S.F., Kudryashov N.A., Sinelshchikov D.I.

The FitzHugh–Nagumo model is used to describe impulse propagation between neurons. This model is a simplification of the Hodgkin–Huxley model, which is inconvenient for application because of a large number of variables and experimentally obtained parameters. The FitzHugh–Nagumo model describing two neurons electrically coupled by an ion flow through gap junctions between them is considered in this work. This model is the simplest example neural network, which has numerous periodic behaviors. It is described by the system of four ordinary differential equations. It is shown that this system of equations does not pass the Painlevé test. Consequently, its general solution cannot be expanded in the series of meromorphic functions on the extended complex plane. The expansion of the general solution in the Puiseux series is obtained. The stability of the trivial stationary point of the system is analyzed. It is shown that this stationary point is not necessarily stable. For some parameter regions where a solution oscillates, bifurcation diagrams are plotted and maximum Lyapunov characteristic exponents are calculated. It is shown that studied nonstationary solutions are stable limit cycles. DOI: 10.1134/S2304487X18060081

Numerical Simulation of Damage Evolution of a Metal at Treatement by High-Density Electric Current Pulses

Kukudzhanov K.V., Levitin A.L.

Processes of evolution of the intergranular and intragranular microcracks and micropores in a metal treated by a pulsed high-energy electromagnetic field are studied numerically within the coupled model of the impact of the high-energy electromagnetic field on the predamaged thermo-elastic–plastic material with an ordered system of defects. The model includes the melting and evaporation of the metal and the temperature dependence of its physical and mechanical properties. The derived system of equations is solved numerically by the finite element method with an adaptive mesh using the arbitrary Euler–Lagrange method. It has been shown that microcracks can be completely healed under certain conditions. Healing occurs through simultaneous decrease in the length of a microcrack, the ejection of the molten metal jet from the apex into the crack, and closing of microcrack shores. The influence of geometry and orientation of microdefects on the process of their healing is investigated. Using the results of the simulation, simple approximate dependences of changes in the damage of the metal treated by the pulsed high-energy electromagnetic field on its initial damage, the characteristic “length” of microdefects, and their angle of inclination are obtained. It is shown that the time dependence of damage for the same initial porosity is determined primarily by the generalized parameter equal to the projection of the initial length of the microdefect on the plane perpendicular to the current density vector. DOI: 10.1134/S2304487X1806007X

Fraud Detection in Payment Data Based on a Discrete Wavelet Transform

Khuzin A.H., Ktitrov S.V., Kolpakov V.I.

Financial fraud is rapidly developed. Annual losses from illegal online payments exceed tens of billions of dollars. Accurate and rapid fraud detection during payment transactions is a key factor in reducing these losses. A fraud detection algorithm based on the discrete wavelet transform of transaction characteristics is proposed. This algorithm analyzes the transaction profile using the energy of wavelet coefficients and detects an anomaly, comparing the difference of this energy and the average energy of previous transactions with the threshold value. The algorithm is tested on the real statistical data of payment transactions for the Haar and Daubechies-4 wavelets. To assess the quality of the classification algorithm, the percentage of correct fraud detection, the percentage of false positives, and the Matthews correlation coefficient are calculated. It is shown that by choosing the threshold, it is possible to adjust the algorithm to a higher percentage of correct fraud detection, sacrificing an increased percentage of false triggering. The quality of the classification by the developed algorithm is compared to the existing machine learning algorithms of. Using a threshold of 7.45, the algorithm has correctly detected 74% of fraudulent transactions, which exceeds a similar percentage of methods such as random forests, single-level decision trees, random trees, and linear regression. However, when selecting a threshold value of 4, the percentage of correct detection reaches 84%, which is superior to the other methods, but the percentage of false positives reaches 0.4%. DOI: 10.1134/S2304487X18060044

A Gender Identification of Text Author in Mixture of Russian Multi-Genre Texts with Distortions Using Machine Learning Models

Sboev A.G., Gudovskikh D.V., Moloshnikov I.A., Rybka R.B.

In this work we investigate a wide set of machine learning models of data-driven approaches (Long Short-Term Memory networks, Convolutional neural networks, multilayer perceptrons, Random Forest Classifiers, Logistic Regression and Gradient Boosting Classifiers with different sets of features) to identify the gender of author in Russian multi-genre texts in the case of existing style distortions and gender deceptions in training and testing sets. We consider and evaluate accuracy for the following situations: the influence of style distortions and gender deceptions in training texts for different genre, and the case when such deception is present only in test results. A comparison with known literature data is presented. The set of data corpora includes: one collected by a crowdsourcing platform, essays of Russian students (RusPersonality), Gender Imitation corpus, and the corpora used at Forum for Information Retrieval Evaluation 2017 (FIRE), containing texts from Facebook, Twitter and Reviews. We present the analysis of numerical experiments based on different features (morphological data, vector of character n-gram frequencies, LIWC and others) of input texts along with various machine learning models. The presented results, obtained on a wide set of data-driven models, establish the accuracy level for the task to identify gender of an author of a Russian text in the multi-genre case and analyzed the effect of the presence of deception in the test and training sets.

Using Machine Learning to Predict Overall Survival of Patients after Gamma Knife Radiosurgery for Brain Metastases

Vazhenin G.A., Ryabov P.N., Banov S.М., Golanov A.V., Dalechina A.V.

One of the most serious complications of oncological diseases is brain metastases, which significantly reduce the survival time of patients. The prediction of the survival rate of this category of patients is aimed at increasing the survival time and improving its quality. In this work, machine learning algorithms have been used to predict overall survival of patients at the Gamma Knife Center, Burdenko Neurosurgical Institute. The overall survival prediction is based on a regression problem built on data for 916 patients with 25 different primary features. The train set included patients with known clinical outcomes. The overall survival prediction has been made for a test sample of 437 patients. The median deviation in determining the time from the onset of the disease to an unfavorable outcome was 1.4 months. The most significant feature has been identified as the largest volume of the lesion at the time of the first radiosurgery. The machine learning approach demonstrates great potential in such cases. Furthermore, this approach makes it possible to improve the understanding of the effectiveness of medical techniques and to establish the most favorable prognostic factors. DOI: 10.1134/S2304487X18060159

Analytical Forecasting of Investment Performance in Multi-Unit Power Plants

Kharitonov V.V., Kosolapova N.V., Uljanin Yu. A.

A new economic-mathematical model is presented for analytical calculation of investment efficiency criteria in a multi-unit power plant and identification of the interrelations between them and the main engineering and economic parameters of the power units characterizing the profitability and competitiveness of the power plant at the microeconomic level. The traditional approaches of the investment analysis are modified for convenient alternative calculations of investment efficiency and the solution of the inverse problem of the determination of such combination of the engineering and economic parameters of power units at which the given efficiency estimates are achieved. The net present value is used as the main investment efficiency (profitability) criterion to derive auxiliary criteria such as the internal rate of return (IRR), levelized cost of electricity (LCOE), economic payback period, and cost–benefit ratio. The dependences of investment efficiency criteria on capital and operating costs, capacity of power units, revenues from electricity sales, number of power units, construction dates and delays in commissioning of power units, and discount rates are considered. Much attention is paid to the assessment of the investments efficiency losses into a multi-unit power plant with delays in the commissioning of power units (in application to a multi-unit nuclear power plant). The predicted investment efficiency criteria for the power and exponential functions of cash flow discounting are compared. It is shown that the internal rate of return and the levelized cost of electricity for the multi-unit power plant with identical power units are the same as for a single-block power plant. As compared to the single-unit power plant, the multi-unit power plant is characterized by increased economic risks associated with the uncertainty of the initial parameters of the power units. The number of blocks significantly affects the net present value of the power plant, but this effect per unit is relatively weak (at low discount rates typical for nuclear power plants). It is found surprisingly that the payback period measured from the beginning of the construction of the first power block of the multi-unit power plant is almost independent of the number of power units. DOI: 10.1134/S2304487X18060032

Comparison of Rate and Temporal Encoding on a Network with Spike-Timing-Dependent Plasticity Solving a Classification Task

Sboev A.G., Serenko A.V., Rybka R.B., Vlasov D.S.

On a simple toy task of Fisher’s Iris classification, two learning algorithms are considered for a spiking neural network with spike-timing-dependent plasticity (STDP), which are based on two ways to encode input data into the spiking input to the network: (i) rate encoding, where the network receives random spike sequences whose mean frequencies encode the data, and (ii) temporal encoding, where the input values are represented by moments of spikes. The learning algorithm for rate encoding is based on the stabilization of the neuron mean firing rate under STDP. The learning algorithm for temporal encoding is based on the ability of a neuron with STDP to memorize repeating spike patterns. Neuron and STDP model constants, as well as encoding parameters, are adjusted with a genetic algorithm. The classification accuracy is shown to depend more on the input encoding parameters than on the choice of STDP constants. The highest (for the learning scheme considered) accuracy is achieved with preprocessing the input data by Gaussian receptive fields, regardless of the encoding method.

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