Kazan Federal University Science Tatarstan / Каза́нский федера́льный университе́т Science Tatarstan (E-Journal)
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The Calculation of the Ellipsoidal Shell Based FEM with Vector Interpolation of Displacements When the Variable Parameterisation of the Middle Surface
No full textThe algorithm for the formation of the stiffness matrix of a four-sided finite element, which is a fragment of an ellipsoidal shell, the middle surface of which was represented by two variants of parametrization, is presented. In the first variant of parametrization of the middle surface of the ellipsoidal shell, the axial coordinate and the angle measured from the applicate axis to the radius vector of the cross-section of the shell are used. In the second version of the representation of the middle surface, the ellipse parameter of the cross section of the ellipsoidal shell was used instead of the angle. The components of the displacement vector and their first derivatives were taken as nodal unknowns of the four-sided finite element. The approximation of the required quantities was carried out in a vector formulation using Hermite polynomials of the third degree. The approximating relations for individual components were obtained using matrix expressions between the basis vectors of the nodal points of a finite element and the basis vectors of its arbitrary point. On the example of calculation of the elliptical cylinder the advantage of the second variant of parametrization of the middle surface of the ellipsoidal shell is shown, as well as the efficiency of the vector formulation of obtaining approximating expressions of the required quantities by the finite element method in curvilinear coordinate systems is demonstrated
Polar Decomposition of Wiener Measure and Schwarzian Integrals
No full textIn this paper are considered the polar decomposition of the Wiener measure by quasi- invariance measure on the group of diffeomorphisms
Calculation of Waves in an Elastic-Plastic Body Based on ENO Modifications of the Godunov Method
No full textA numerical study of the efficiency of two ENO modifications of the Godunov method for calculation axisymmetric problems of the dynamics of elastic-plastic bodies, namely a UNO scheme of the second-order of accuracy and a TVD scheme of the second order of accuracy outside the solution extremes, where it decreases to the first order. The efficiency of the modifications is estimated by comparing the results of calculation of a number of problems on the propagation of spherical and cylindrical waves in a body with the results of reference solutions and the Godunov method. The exact and numerical solutions are used as reference solutions, the latter are obtained on fine grids. It is shown that for all the problems considered, the solutions by the TVD and UNO schemes are much closer to the reference ones than those by the Godunov method. The TVD and UNO schemes are characteristic of significantly less smearing of sharp wave fronts and a more accurate resolution of extrema. At the same time, the wave profiles and the extrema are reproduced by the UNO scheme somewhat better than by the TVD scheme
Associative steganography. Durability of associative protection of information
No full textThe case of analysis of associatively protected cartographic scenes is considered. Protection of objects and their coordinates is achieved masking binary matrices of their code symbols. The set of inverse mask matrices is the recognition key. This allows such protection to be attributed to associative steganography. A message is considered to be unconditionally steadfast if it is statistically indistinguishable from a random sequence. Therefore, the study of its steadfastness is carried out using statistical tests of randomness NIST. If a pseudo-random sequence successfully passes the test of all 15 tests, then it is considered random («white»). If there is a failure at least on one test, then it is considered «black». But in the case of the application of the basic masking algorithm, this cannot help the disclosure of the stegomessage. The effect of masking redundancy introduced with the aim of improving noise immunity on the durability of mapping objects to the effects of various attacks is considered. It is established that associative steganography retains the property of provable (computational) stability in this case as well. Recommendations for its use to protect the text characteristics of objects are given
Mathematical modeling of natural and anthropogenic processes in the Arctic zone
No full textThe article presents a review of publications on the mathematical modeling of the effects produced by natural phenomena on industrial objects in the Arctic zone of the Northern seas of the Russian Federation and those related to addressing the issues of the industrial development of the Arctic shelf. Numerical methods for the solution of the relevant and associated problems are discussed and the calculation results are reported. A list of the most urgent computational problems in developing Russian Arctic shelf is presented
Critical Phenomena in Filtration Processes of Real Gases
No full textSteady adiabatic filtration of real gases is studied. Thermodynamical states of real gases are presented by Legendrian surfaces in 5-dimensional thermodynamical contact space. The relation between phase transitions and singularities of projection of the Legendrian surfaces on the plane of intensive variables is shown. The constructive method of finding solutions of the Dirichlet filtration problem together with analysis of critical phenomena is presented. Case of van der Waals gas is discussed in details
An approach to ensuring vortex safety of an aircraft
No full textThe paper aims to create a mathematical model of a wake vortex behind a civil aircraft and to determine the parameters of a flight zone that would be dangerous for the following aircraft in terms of a possible encounter. The model employs half-empirical and analytic approaches. The model obtained is suitable for using in various flight simulators
Muller Boundary Integral Equations for Solving Generalized Complex-Frequency Eigenvalue Problem
No full textThe current paper claries the connection between the generalized complex-frequencyeigenvalue problem and the eigenvalue problem for the Muller boundary integral equations. It isproved that these problems are spectrally equivalent if a specially tailored eigenvalue problem does not have any solution
Complex Waves in Dielectric Layer
No full textThe propagation of monochromatic TE-polarized waves in a partially shielded dielectric layer is considered. The existence of infinitely many complex leaky waves is proved as well as the absence of complex surface waves
Mathematical modeling of kinetics and optimization of grain material separation processes on sieve classifiers
No full textA mathematical model of the kinetics of thin-layer separation of granular materials onmultiple-deck sieve classifiers was constructed based on the theory of Markovian processes. Weidentified the kinetic models using the oversize residues from sieves. The problem of optimizationis formulated and solved in a multi-criteria formulation, where the criteria are selected deviceperformance and the separation efficiency on its sieves