Kazan Federal University Science Tatarstan / Каза́нский федера́льный университе́т Science Tatarstan (E-Journal)
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Information Graph Visualization Using AlgoView Software Tool
No full textOne of the approaches to the study of the information structure of algorithms is theanalysis of information graphs. These are complex objects, the understanding of the structure of which can signicantly facilitate their visualization. However, it is difficult to visualize large graphs, while maintaining clarity of the information structure of the algorithm is generally very difficult. Therefore, we are developing a tool for three-dimensional interactive visualization of information graphs called AlgoView, designed to facilitate this task. At the moment, AlgoView is embedded as a visualizer on separate pages of the AlgoWiki Open encyclopedia of parallel algorithmic features, and in the near future it is planned to obtain a stand-alone version of this system
Influence of a liquid film covering a solid on liquid jet impact against its surface
No full textThe impact of a cylindrical liquid jet with a hemispherical tip on an elastic-plastic body uniformly covered in the impact domain by a liquid film has been studied, depending on the thickness of the film. The jet is directed orthogonally to the body surface, which is plane. The liquid in the jet and the film is water; the material of the body is Monel 400. The radius of the jet is , its velocity is V = 300 m/s. The film thickness is varied in the range 0 - 0.2R. The action of the jet is considered until it becomes nearly stationary. A similar configuration can occur during the collapse of cavitation bubbles nearby a solid. The dynamics of the liquid (in the jet and the film) and the surrounding gas is calculated by the CIP-CUP method without xplicit interface tracking using dynamically adaptive Soroban grids. The body is modeled by an ideal elastic-plastic semi-space, in which the deformations are considered to be small; the plasticity effect is realized according to the Mises condition. The dynamics of the body is calculated by a UNO-modification of the Godunov method of the second order of accuracy. Some features of the body surface loading and the corresponding response of the body (the deformation of its surface, the changes in its stress state) resulting from varying the liquid film thickness have been revealed. It is shown, in particular, that the body surface pressure profiles, initially very different for various , after the time moment t \approx R/V become approximately the same (with a small exception at the periphery) and closely correspond to the profile arising under the stationary action of a similar jet of incompressible liquid. The jet impact results in the formation of a very shallow pit on the body surface (with a depth of about 10^{-3}R). At d = 0, the depth of the pit in its center is approximately two times greater than at d=0.2R
Point estimators for the cross-product ratio of Binomial proportions under different sampling schemes
No full textWe consider a general problem of the interval estimation for a cross-product ratio according to data from two independent samples. Each sample may be obtained in the framework of direct or inverse Binomial sampling schemes. Asymptotic confidence intervals are constructed in accordance with different types of sampling schemes, with parameter estimators demonstrating exponentially decreasing bias. Our goal is to investigate the cases when the normal approximations (which are relatively simple) for estimators of the cross-product ratio are reliable for the construction of confidence intervals. We use the closeness of the confidence coefficient to the nominal confidence level as our main evaluation criterion, and use the Monte-Carlo method to investigate the key probability characteristics of intervals corresponding to all possible combinations of sampling schemes. We present estimations of the coverage probability, expectation and standard deviation of interval widths in tables and provide some recommendations for applying each obtained interval
Numerical Study of the Dynamics of a Gas Bubble Near a Wall Under Ultrasound Excitation
No full textA numerical study of the dynamics of a gas bubble in water near a plane rigid wallunder ultrasound excitation has been performed. The bubble dynamics is excited at the naturalfrequency of the radial oscillations of the bubble in the absence of the wall. The dynamics ofthe bubble with the formation on its surface of a cumulative liquid jet directed to the wallis considered. A regime of the ultrasound excitation is investigated, at which the cumulativejet impact against the bubble surface part closer to the wall is realized at the moment of thebeginning of the second expansion of the bubble. At this moment two known mechanisms ofemitting pressure pulses into liquid by a bubble start working simultaneously. The rst one isdue to the bubble expansion. The second one results from the impact of the cumulative jet. Theboundary element method is used. The study has revealed the dependences of the ultrasoundexcitation amplitude, at which the indicated regime is realized, on the distance between thebubble and the wall, as well as the inuence of the bubble-to-wall distance on the jet impactvelocity and the pressure inside the bubble corresponding to that regime
ABOUT THE RELIABILITY OF CIRCUITS WITH TYPE 0 FAULTS AT THE OUTPUTS OF THE ELEMENTS IN THE COMPLETE FINITE BASIS CONTAINING AN ESSENTIAL LINEAR FUNCTION
No full textWe consider the the implementation of Boolean functions by circuits from unreliable functional elements in a complete finite basis, which contains a linear function essentially dependent on at least two variables. We assume that all elements of a circuit are exposed to the faults of type at the outputs with probability independently of each other. We prove that almost any Boolean function can be implemented by an asymptotically optimal in reliability circuit functioning with the unreliability which is asymptotically equal to with $\varepsilon \to 0
Asymptotics of the solution to the Roben problem for a ring with regularly singular boundary
No full textThe aim of the research is the development of the asymptotic method of boundary functions to Robin problem for a ring with regularly singular boundary. This work is devoted to constructing complete asymptotic expansions of the solutions of Robin problem for singular perturbed inhomogeneous linear second order elliptic equation with regularly singular boundary. Singularities of the equation: the presence of a small parameter at the Laplace operator and the corresponding unperturbed (limit) the differential equation of first order has a singularity at the border ring. Bisingularly problems of the Robin studied in the ring. Full asymptotic expansion of the solution of bisingularly problems constructed by modification method of boundary functions. The resulting solutions are asymptotic in the sense Erdei. The resulting asymptotic expansions of the solutions of boundary value problems justified by the principle of maximum
Riesz Basisness of Root Functions of a Sturm Liouville Operator With Conjugate Conditions
No full textIn this paper we are interested in Riesz basisness of root functions of the non-selfadjoint a discontinuous Sturm Liouville operator with periodic boundary condition which are not strong regular and with conjugate conditions. Here we assume that the potentials are complex valued and continuously differentiable functions . One of conjugate conditions have different finite one-sided limits at point zero. In order to prove Riesz basisness of root functions, we firstly obtain asymptotic expressions of fundamental solutions. Putting these solutions into characteristic determinant, we get asymptotic formulas of eigenvalues by means of Rouche theorem. Asymptotic formulas of eigenfunctions acquired by obtained relation and fundamental solutions. By the aid of asymptotic formulas of eigenfunctions and Bessel properties of eigenfunctions we prove the basisness of the root functions of the boundary value problem. We also prove the Riesz basisness of root functions of the same operator with antiperiodic boundary conditions and with same conjugate conditions
Tricomi problem for second kind parabolic hyperbolic type equation
No full textYou shouldn't use formulas and citations in the abstract.In this article, the Tricomi problem for a parabolic-hyperbolictype equation in a mixed domain is investigated. The solution ofthe problem in the hyperbolic subdomain is found as a solution tothe Cauchy problem, and in a parabolic subdomain as a solution tothe first boundary value problem
Simulation of drop oscillation using the Lattice Boltzmann method
No full textWe simulate the oscillation of the viscous drop in the viscous liquid. We combine methods of chromodynamics model and Shan-Chen pseudo-potential for the immiscible fluids. We measure the frequency of the first nontrivial eigenmode using the initial ellipsoid form of the drop. Drop oscillates about the equilibrium spherical form of radius . Computed frequency as a function of the radius follows to the well known Rayleigh formula. We discuss the simulation setup in the framework of the Lattice Boltzmann method
Acoustothermal effect in an open tube with section leap for nonlinear gas oscillations
No full textПредставлены результаты теоретических и экспериментальных исследований вторичных тепловых эффектов, возникающих при нелинейных колебаниях газа в открытой трубе с поперечным сечением перехода вблизи собственных частот. Построены зависимости обтекания трубки по первой и второй гармоникам. Показано удовлетворительное согласие между теоретическим расчетом теплового потока и полученными экспериментальными данными