Authors:S. R. Tuikina; S. I. Solov’eva Pages: 301 - 309 Abstract: We consider the inverse problem for the two-dimensional modified FitzHugh–Nagumo model in the presence of an infarct. The inverse problem determines the myocardium excitation source function (a function of space variables and time) from a system of partial differential equations. Additional dynamic measurements of the potential are carried out on the entire inside boundary of the region representing a cross-section of the heart and its ventricles by a horizontal plane, which fits the real heart geometry. A numerical method is proposed for the solution of this inverse problem with the discrepancy functional; numerical results are reported. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9365-2 Issue No:Vol. 28, No. 3 (2017)

Authors:N. P. Savenkova; A. Yu. Mokin; V. P. Il’yutko Pages: 310 - 315 Abstract: We consider the dependence of the MHD stability of an electrolysis bath on the shape of the work space. As the optimal work-space shape we choose the one that achieves the best separation of the eigenvalues in the spectrum of the multidimensional problem posed for the kinematic equation for the electrolytealuminum interface in a particular electrolysis bath. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9366-1 Issue No:Vol. 28, No. 3 (2017)

Authors:Yu. N. Kiselev; S. N. Avvakumov; M. V. Orlov; S. M. Orlov Pages: 316 - 338 Abstract: We investigate the resource allocation problem in a two-sector economic model with a Cobb-Douglas production function with different depreciation rates. The problem is considered on a finite time horizon with an integral type functional. Optimality of the extremum solution constructed by the Pontryagin maximum principle is established. When the planning horizon is sufficiently long, the optimal control has two or three switching points, contains one singular section, and vanishes on the terminal section. A transitional “calibration” regime exists between the singular section, where the motion is along a singular ray, and the terminal section. The solution of the maximum-principle boundary-value problem is presented in explicit form, accompanied by graphs based on numerical results. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9367-0 Issue No:Vol. 28, No. 3 (2017)

Authors:A. M. Golovina; A. G. D’yakonov; O. A. Kharatsidi Pages: 339 - 349 Abstract: The article focuses on the analysis of photoplethysmograms. The quality of a photoplethysmogram is assessed by solving the classification problem, i.e., identifying the patient from the photoplethysmogram. Efficient patient identification methods are proposed, including methods based on DTW and TWED metrics. Identification accuracy reaches 70%. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9368-z Issue No:Vol. 28, No. 3 (2017)

Authors:Basant K. Jha; Babatunde Aina Pages: 350 - 367 Abstract: The present work consists of a numerical investigation of transient free convective flow in vertical channel formed by two infinite vertical parallel plates filled with porous material in the presence of thermal dispersion. The governing coupled-nonlinear equations of momentum and energy transport are solved numerically using the implicit finite difference method, while the approximate analytical solution is also presented to find the expression for velocity, temperature, skin friction, and rate of heat transfer for the steady fully developed flow using the perturbation technique. The main objective is to investigate the effects of the dimensionless time, Darcy number, thermal dispersion, and Prandtl number on the fluid flow and heat transfer characteristics. Solutions are presented in graphical form and given in terms of fluid velocity, fluid temperature, skin friction, and rate of heat transfer for various parametric values. The significant result from this study is that velocity and temperature is enhanced with increase in thermal dispersion parameter and time. Furthermore, excellent agreement is found between the steady-state solution and the transient solution at large values of time. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9369-y Issue No:Vol. 28, No. 3 (2017)

Authors:V. V. Morozov; V. A. Babin Pages: 368 - 376 Abstract: We consider a modified Merton’s model of optimal consumption that allows for the utility of continuous and terminal consumption. An explicit solution of the Hamilton-Jacoby-Bellman equation is found. An upper bound is constructed on the probability of an event involving either investor ruin or negative consumption. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9370-5 Issue No:Vol. 28, No. 3 (2017)

Authors:E. S. Kurkina Pages: 377 - 399 Abstract: We propose and investigate three mathematical models describing production cycles. They incorporate various mechanisms of endogenous fluctuations in economic systems. The models are based on ODE systems. The first model is a Keynesian IS-LM model of business cycles. The interest rate is determined by the money market and influences the relationship between savings and investments, allowing funds to flow from one to the other and vice versa. In the second case, the fluctuation mechanism is associated with time lags between investment growth, capital growth, and rate of return on capital. As a result, the economy periodically “overheats”, as rapid growth of capital suppresses the return rates, production becomes unprofitable, and investments sharply decline. Two models realizing this mechanism are proposed. One is a minimalist model based on a system of three ODEs. The other is an augmented model that sufficiently fully describes modern economic systems of developed countries and consists of nine ODEs and nine algebraic equations. It encompasses all the principal markets: labor market, capital market, financial market, and commodity market. Bifurcation analysis of the three models is carried out, oscillation regions are determined, and oscillation mechanisms are examined in detail. The model parameters are chosen so that the cycle periods are 12–17 years long. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9371-4 Issue No:Vol. 28, No. 3 (2017)

Authors:S. V. Gavrilov; S. I. Gurov; T. D. Zhukova; V. S. Rukhlov; D. I. Ryzhova; D. V. Tel’pukhov Pages: 400 - 406 Abstract: Increasing the operating reliability of integrated microcircuits (IMC) remains, on the whole, an unsolved design problem. An important aspect of this problem is the stability of the circuits under transient faults (malfunctions) in large integrated circuits. Faults appear due to various disturbances: radiation, supply voltage jumps, signal degradation over time, etc. Investigations show that the probability of an error due to these factors may vary between very wide limits: from less than 0.1% for large circuits and up to 30% for very small circuits. In this article, we consider various methods of enhancing the fault tolerance of combinational circuits and also assess the effect of a single fault and a stuck-at fault on circuit operation for the case of combinational circuits from the ISCAS’85 set. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9372-3 Issue No:Vol. 28, No. 3 (2017)

Authors:A. K. B. Chand; N. Vijender; M. A. Navascués Pages: 407 - 430 Abstract: Fractal interpolation is more general than the classical piecewise interpolation due to the presence of the scaling factors that describe smooth or non-smooth shape of a fractal curve/surface. We develop the rational cubic fractal interpolation surfaces (FISs) by using the blending functions and rational cubic fractal interpolation functions (FIFs) with two shape parameters in each sub-interval along the grid lines of the interpolation domain. The properties of blending functions and C 1-smoothness of rational cubic FIFs render C 1-smoothness to our rational cubic FISs. We study the stability aspects of the rational cubic FIS with respect to its independent variables, dependent variable, and first order partial derivatives at the grids. The scaling factors and shape parameters seeded in the rational cubic FIFs are constrained so that these rational cubic FIFs are convex/concave whenever the univariate data sets along the grid lines are convex/concave. For these constrained scaling factors and shape parameters, our rational cubic FIS is convex/concave to given convex/concave surface data. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9373-2 Issue No:Vol. 28, No. 3 (2017)

Authors:Akanksha Srivastava Pages: 431 - 447 Abstract: This article deals with the study of sign-changing solutions of the nonlinear singularly perturbed reaction-diffusion equation. Sign changing solutions of the nonlinear problem do not appear to have been previously studied in detail computationally, and it is hoped that this paper will help to provide a new idea in this direction. A variant of Newton’s method having tenth order of convergence has been established to linearize the nonlinear system of equations. Examples of the nonlinear problem having nonlinearities in homogeneous/nonhomogeneous form are considered to show the existence of solutions. PubDate: 2017-07-01 DOI: 10.1007/s10598-017-9374-1 Issue No:Vol. 28, No. 3 (2017)

Authors:F. A. Anikeev; S. V. Anpilov; F. S. Zaitsev; N. P. Savenkova; A. V. Kalmykov Pages: 185 - 194 Abstract: Numerical methods for modeling the behavior of an industrial aluminum electrolyzer are investigated and developed. Solving a prototype problem that brings out the specific features of aluminum electrolysis, we compare two approaches to investigating the relaxation of oscillations in an electrolyzer with a free boundary between the phases. The first approach is the classical finite-difference method while the second approach uses smoothed particle hydrodynamics (SPH). The SPH method had not been applied previously to model aluminum electrolysis and it required development in this context. In particular, a new algorithm was proposed for one of the SPH subproblems that allowed for the dependence of acceleration on the velocity. The computational characteristics and the accuracy of the two methods are compared for the relaxation of free interface oscillations. The strengths and weaknesses of the two methods are discussed, as well as their potential for applications. It is shown that SPH is applicable to more realistic three-dimensional problems, such as real-time feedback control of aluminum electrolysis that can ensure online prevention of the onset of MHD instability. PubDate: 2017-04-01 DOI: 10.1007/s10598-017-9356-3 Issue No:Vol. 28, No. 2 (2017)

Authors:Yu. A. Eremin Abstract: The optical theorem is generalized to the case of excitation of a local body by a multipole. To compute the extinction cross-section, it is sufficient to find the derivatives of the scattered field at the single point where the multipole is located. The relationship obtained in this article makes it possible to test software modules developed for studying wave diffraction on transparent bodies. PubDate: 2017-03-20 DOI: 10.1007/s10598-017-9354-5

Authors:Yang Jianxun Abstract: A new method for seismic data processing is considered. Surface traveling waves are recovered from these data and wave-dependent coefficients are determined. The results of the proposed method are consistent with the results reported by other Chinese researchers [4, 5]. PubDate: 2017-03-20 DOI: 10.1007/s10598-017-9361-6

Authors:M. Abdulhameed; R. Roslan; D. Vieru; S. Shafie Abstract: This study aimed to develop a mathematical model of an unsteady Burgers’ fluid in a circular cylinder with a trapezoidal pressure waveform described by an infinite Fourier series. An analytical solution was obtained for the governing equation using the Bessel transform method together with similarity arguments. The validity of the solution was verified using a numerical inversion method based on Stehfest’s method. Limiting cases were considered to examine the fluid flow performance of different fluids. Our results show that the Newtonian and Oldroyd-B fluids performed similar velocity time variation for the trapezoidal waveform of oscillating motion, whereas the velocity time variation was different for Maxwell and Burger’s fluids. Moreover, it is evident that the material constant of a Burgers’ fluid is another important factor that affects flow performance in an oscillating flow. PubDate: 2017-03-20 DOI: 10.1007/s10598-017-9357-2

Authors:S. Tapaswini; S. Chakraverty; T. Allahviranloo Abstract: This paper proposes a new method based on fuzzy center and radius for solving n th order fuzzy differential equations. First, the fuzzy differential equation is solved in term of fuzzy center and then this solution is used to find the radius of the fuzzy solution. Finally using the solution of fuzzy center and radius, one obtains the solution of the governing fuzzy differential equation. The proposed method is illustrated by considering three cases with numerical examples along with one application problem of vibration. Results obtained are also compared with solutions by existing methods and are found to be in good agreement. PubDate: 2017-03-20 DOI: 10.1007/s10598-017-9364-3

Authors:V. I. Dmitriev; L. V. Stolyarov Abstract: The article considers the inverse boundary-value problem of heat conduction which involves determining the time distribution of temperature on the boundary given the spatial distribution of the temperature at the final time instant. The problem is reduced to an integral equation of the first kind with a symmetrical kernel. The integral equation is solved by a special iterative method. Test examples demonstrate convergence and stability of the proposed method. PubDate: 2017-03-20 DOI: 10.1007/s10598-017-9352-7

Authors:I. S. Barashkov; V. I. Dmitriev Abstract: We consider finite-difference modeling of the electromagnetic field in a nonhomogeneous medium in the case of H-polarization. At the interior grid points, the finite-difference approximation binds five neighboring values of the grid functions, which correspond to the five diagonals of the linear algebraic system matrix. The matrix is banded. The linear algebraic system is solved by decomposing the matrix into a product of an upper-triangular matrix and a lower-triangular matrix. The algorithm is implemented for complex matrices using double-precision arithmetic. We show how to use the grid function values obtained by solving the linear algebraic system to find the magnetic field at the corner point of the conductivity discontinuity boundary. Calculation of the field at the corner point of the conductivity discontinuity boundary is an independent difficult problem of mathematical modeling of electromagnetic fields in nonhomogeneous media that deserves special attention. An equation is obtained for the field value at the corner point of the boundary. The numerical results obtained for the electromagnetic field in a complex nonhomogeneous medium confirm the validity of this equation. PubDate: 2017-03-20 DOI: 10.1007/s10598-017-9362-5

Authors:N. Sarkar Abstract: A three-dimensional problem for a homogeneous isotropic thermoelastic half-space solids with temperature-dependent mechanical properties subject to a time-dependent heat sources on the boundary of the half-space which is traction free is considered in the context of the generalized thermoelasticity with dual-phase-lag effects. The normal mode analysis and eigenvalue approach techniques are used to solve the resulting non-dimensional coupled field equations. Numerical results for the temperature, thermal stresses and displacement distributions are represented graphically and discussed. A comparison is made with the result obtained in the absence of the temperature dependent elastic modulus. Various problems of generalized thermoelasticity and conventional coupled dynamical thermoelasticity are deduced as special cases of our problem. PubDate: 2017-03-20 DOI: 10.1007/s10598-017-9358-1

Authors:T. V. Zakharova; P. I. Karpov; V. M. Bugaevskii Abstract: The article discusses the development of noninvasive preoperative methods for the localization of eloquent areas in the human brain. The accuracy with which such areas are localized directly determines the outcome of surgery. An analytical formula is derived for the solution of the forward problem that computes the magnetic field on the surface of the head from the known location and orientation of a current dipole in the low-frequency approximation in the spherical model. The inverse problem is also solved, reconstructing the location and orientation of the source given the magnetic field on the surface of the head. Qualitative analysis of the ellipsoidal model is carried out. PubDate: 2017-03-20 DOI: 10.1007/s10598-017-9353-6

Authors:A. A. Lukianitsa Abstract: We consider descriptors in polar and log-polar coordinates that produce compact description of the image near interest points. These descriptors may be used to establish one-to-one correspondence between points in two images. Algorithms to compute these descriptors are described and the results of a numerical experiment comparing them with SIFT and SURF descriptors are reported. The numerical experiment suggests that the proposed descriptors are highly efficient for finding conjugate points in two images. PubDate: 2017-03-20 DOI: 10.1007/s10598-017-9360-7