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

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

Authors:S. R. Jena; D. Nayak; M. M. Acharya Abstract: This paper is concerned with the problem of determining the approximate solution of real definite integrals by means of the mixed quadrature rule, which has been implemented with the quasi-type singular integral of electromagnetic field problems. The main advantage of the proposed numerical integration method over electromagnetic field problems is its efficiency, less functional evaluation and simple applicability. Five test numerical examples are provided to compare the accuracy with other researchers. PubDate: 2017-03-20 DOI: 10.1007/s10598-017-9363-4

Authors:V. S. Laponin; N. P. Savenkova Abstract: The Gross–Pitaevskii equation is at the core of the mathematical problem of the propagation of a Bose–Einstein condensate (BEC). In this article, we look for an analytical soliton solution in the three-dimensional Gross–Pitaevskii equation. We compare our analytical solution with the various numerical soliton solutions (dark solitons, light solitons, reflected solitons) reported by many researchers for the case of BEC interacting with an external potential (an obstacle, a magnetic trap, etc.). Our analytical solution can be applied to find both the main and the reflected soliton solution. PubDate: 2017-03-20 DOI: 10.1007/s10598-017-9359-0

Authors:D. Yu. Zagurskii; I. G. Zakharova; V. A. Trofimov Abstract: A conservative difference scheme is constructed for the system of equations that describe, in the semi-classical approximation, resonance and nonresonance interaction of an electromagnetic pulse with matter. The conservativity of the scheme is proved. A cascade mechanism for the excitation of high energy levels in the medium under the impact of a narrow-spectrum electromagnetic pulse is demonstrated. In the cascade mechanism, if the spectrum does not contain a pulse of sufficiently high frequencies to trigger direct transitions from the ground state to high excited states, the molecules of the medium may still reach the high states through a series of successive transitions between nearer lying energy levels. This may lead to the appearance in the transmitted pulse of higher frequencies than those observed in the incident pulse. For a medium whose length is comparable with the spatial extent of the pulse, distortion of the transmitted pulse spectrum is observed. The absolute phase of the small-period pulse substantially affects the transformation of the pulse spectrum during the transmission through the matter. If the matter contains several close energy levels, the corresponding transition rates will depend on the absolute phase of the field. We demonstrate and explain the generation of the third harmonic during the interaction of the electromagnetic pulse with the medium due to the nonstationary and nonlinear character of the response. PubDate: 2017-03-20 DOI: 10.1007/s10598-017-9355-4

Authors:A. G. Belov Abstract: We investigate the properties of multiple linear regression estimators obtained by the Ordinary Least Squares method (OLS) and the Generalized Least Squares method (GLS, Aitken estimator) assuming substantially different errors in input data. We illustrate the mechanism that leads to fallacious conclusions about the quality of OLS and Aitken estimators based on visual graphical analysis of experimental data. Numerical simulation and comparative analysis of the estimators is carried out for simple and parabolic regression models. PubDate: 2016-12-19 DOI: 10.1007/s10598-016-9346-x

Authors:Mohamed El Amine Bencheikh Le Hocine; Mohamed Haiour Abstract: This paper deals with the numerical analysis of the problem of parabolic quasi-variational inequalities related to impulse control problems. An optimal L ∞ -convergence of a piecewise linear finite element method is established using the concept of subsolution. PubDate: 2016-12-17 DOI: 10.1007/s10598-016-9349-7

Authors:Ali Taghavi; Afshin Babaei; Alireza Mohammadpour Abstract: In this article, a coupled method based on the Laplace and differential transformations is applied to solve a class of time fractional convection-diffusion equations. The fractional derivatives are described in the Caputo sense. The method consists of implementing the Laplace transformation at first, then performing the differential transform method (DTM) on the resulting equations. Several examples are given to validate the proposed method. PubDate: 2016-12-17 DOI: 10.1007/s10598-016-9350-1

Authors:A. A. Voronenko; N. K. Voronova; V. P. Il’yutko Abstract: The article describes the construction of discrete functions which, by some of their values, specify (generate) arbitrary linear functions. The cases of prime and sufficiently large composite k have been considered previously. In the present study we finally solve the problem of existence of such functions for almost all k and n variables. The proof of the probabilistic upper bound and the general approach are due to A. A. Voronenko. The proof for small k has been developed by N. K. Voronova. The proof for k from 21 to 48 is the result of indispensable cooperation of V. P. Il’yutko and A. A. Voronenko. PubDate: 2016-12-17 DOI: 10.1007/s10598-016-9347-9

Authors:Elsayed M. E. Zayed; Yasser A. Amer Abstract: In this article, we apply two powerful methods, namely the first integral method and a direct algebraic method for constructing many exact solutions for the higher-order nonlinear Schrödinger equation with non-Kerr terms that describes the propagation of femtosecond optical pulses in nonlinear optical fibers. Using a simple transformation, we reduce the given equation to a nonlinear ordinary differential equation (ODE). Various solutions of the resulting nonlinear ODE are obtained by using the above two methods. A comparison between our recent results and the well-known results is given. PubDate: 2016-12-17 DOI: 10.1007/s10598-016-9351-0

Abstract: We consider a linear control problem with a partially known initial condition. Kalman’s observability theory of linear controlled system is applied to derive constructive sufficient conditions under which the control process to attain a terminal set M can be decomposed into the following stages: first collect information on system output, then apply this information to reconstruct the system’s initial state, and finally proceed with active control to attain the terminal set M. PubDate: 2016-12-16 DOI: 10.1007/s10598-016-9341-2

Abstract: The Godunov method of first order accuracy continues to attract the attention of researchers both because of its simple implementation and its sufficiently high numerical accuracy subject to relatively modest resource requirements. However, it is necessary to constantly verify that the method indeed produces acceptable accuracy. We test the method on a number of one- and two-dimensional prototype problems and compare the results with analytical and numerical solutions obtained by higher accuracy schemes. The results for the method tested are quite acceptable. We also compare the solutions of applied problems on flows in supersonic, freely expanding jets and on supersonic flow past blunt bodies. The results for these problems are also positive. PubDate: 2016-12-16 DOI: 10.1007/s10598-016-9342-1