## Vol 5, No 3 (2011)

**Year:**2011**Articles:**28**URL:**https://journals.eco-vector.com/1991-8615/issue/view/1255

Articles

On some conjugation problems of parabolic and hyperbolic equations with integro-differential conditions on the separating boundary

#### Abstract

The one-valued solvability of the conjugation problems of parabolic and hyperbolic equations in ﬁnite domains was proved by the method of equivalent reduction to Volterra integral equation of the second kind.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):8-25

On one non-local problem for axisymmetric Helmholtz equation

#### Abstract

Non-local boundary problem for the axisymmetric Helmholtz equation is explored. The uniqueness of the solution is proved by the spectral method. The conditions of solvability are found. The solution of the problem is constructed in the form of the biorthogonal series.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):26-34

The Goursat problem for one hyperbolic system of the third order differential equations with two independent variables

#### Abstract

The solution of the Goursat problem for the system of the diﬀerential equations of the third order is received on the basis of Riemann method. The Riemann matrix expressed in terms of hypergeometric functions with matrix argument is received, using it the solution of Goursat problem for the system of the linear hyperbolic equations of the third order is constructed.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):35-41

On the essential spectrum of a model operator associated with the system of three particles on a lattice

#### Abstract

A model operator H associated with the system of three-identical particles on a lattice ℤ3 is considered. The location of the essential spectrum of H is described by the spectrum of the corresponding Friedrichs model, that is, the two-particle and three-particle branches of the essential spectrum of H are singled out. It is proved that the essential spectrum of H consists of no more than three bounded closed intervals. An appearance of two-particle branches on the both sides of the three-particle branch is shown. Moreover, we obtain an analogue of the Faddeev equation and its symmetric version, for the eigenfunctions of H.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):42-51

Influence of the direction of rolling in the target material on its destruction under dynamic loads

#### Abstract

In the work, the comparative analysis of elasticoplastic deformation and fracture of target materials with diﬀerent directions of rolling relating to the direction of target loading was conducted. The dynamic loading of materials targets, characterized by the initial anisotropy of mechanical properties as the result of rolling was simulated numerically, in the three-dimensional formulation. The modeling was performed using the ﬁnite element method.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):52-61

Algorithm of motion on the parameter of rigidity in stability problem on the border of Winklers mediums

#### Abstract

To solve the stability problem of one-dimensional elements of construction on the border of diﬀerent elastic ambiences the algorithm of motion on the parameter of one ambience is suggested. Evolution of triple half-wave eigenform of longitudinal compressed rod is studied according to S. P. Timoshenko models using boundary conditions of articulate and rigid ﬁxing.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):62-71

Finite element modeling of residual stress distribution in solid hardened cylindrical samples and samples with semicircular notch

#### Abstract

We give a method for solving the problem of the distribution of residual stresses in a continuous surface hardened cylindrical samples and samples with a semicircular notch based on the ﬁnite element method. As the initial information the experimentally determined alone and / or two components of residual stresses in a hardened layer is used. By the example of a cylindrical specimen made of St. 45 and D16T steels the results of calculations performed by the proposed method are compared with the experimental data and the results of calculations by other methods.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):72-78

Investigation of human coronary arteries and heart ventricles mode of deformation and haemodynamics

#### Abstract

Mechanical properties of coronary arteries and heart tissues, computer 3D models of CA and heart ventricles were investigated. Numerical analysis of coronary arteries and heart ventricles mode of deformation and haemodynamics was made. The material of the arteries and heart tissue was assumed as linear isotropic, the blood as a Newtonian ﬂuid. Comparative analysis of numerical data for cases of spatially unﬁxed coronary arteries and ﬁxed coronary arteries of passive myocardium and for pathological and healthy heart ventricles was conducted.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):79-88

An influence of the false bottom on the nonlinear dynamics of the water freezing process

#### Abstract

The current paper casts the light on the processes of structural-phase transitions during the freezing salt water, including the false bottom eﬀects. A nonlinear mathematical model of heat and mass transfer was obtained. It takes into account the presence of three moving boundaries of phase transition and turbulent ﬂuid ﬂows from the ocean side by the surface of the false bottom. The exact analytical solutions of the nonlinear model were obtained - in their turn, they takes into account the time dependence of temperature and salinity at the depth and ﬂuctuations of friction velocity. The distribution of temperature and salinity, the concentration of solids, the laws of motion of the boundaries of the phase transition, salt water - the two-phase zone, two-phase zone - melted water and melt-water - ice were found. The heat ﬂux at the lower boundary of a false bottom was speciﬁed. The latter can change its direction at the time oscillations of the sea water temperature and friction velocity. Also it was shown, that structural transitions in the ice thickness are strictly associated with the processes of evolution of a false bottom

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):89-99

Maximal order of accuracy of (m, 1)-methods for solving stiff problems

#### Abstract

We investigate (m, 1)-methods for solving stiff problems in which the right part of system of the diааerential equations is calculated one times on each step. It is shown that the maximal order of accuracy of the L-stability (m, 1)-method is equal to two, and the method of the maximal order is constructed

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):100-107

Problem of iterative procedure convergence in parametric identification of the systems with turbulent friction

#### Abstract

The problem of convergence of iterative procedure for clariﬁcation of coefficients of the ﬁnite-difference equation in numerical technique for determination of the differential operator parameters for the systems with turbulent friction is considered. Theorem about a sufficient condition of iterative procedure convergence is deﬁned and demonstrated. During theorem proving contracting mapping and fundamental sequence properties are used. As a corollary of the theorem formulas describing prior and posterior estimate of the approximation error are received

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):108-116

Natural space of the micro-object

#### Abstract

The immutability of classical dynamical laws for the microscopic object in the space which coordinate axes are the transition matrix elements of the corresponding coordinates is proved. It is stated that measurement is a micro-object localization process in the classical space when it interacts with the device. The description of the wave function reduction is obtained using the path integrals. The mechanism of the probability arising on measurement is oﬀered, where the hidden parameter that is the cause of the measurement randomness of microscopic characteristics relates to the interaction process of classical instrument with micro-object. Both types of quantum mechanics processes - evolution and reduction of the wave functions - are described in a uniﬁed approach

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):117-128

The exact cosmological solutions for phantom fields

#### Abstract

The application of the method of super-potential to solution of the problems of cosmology with phantom ﬁelds is examined. The classes of exact solutions are found and the periods of time with the predominance of dark energy are established.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):129-135

Prospects for the use of solid-state nitrogen generators to create periodic-action iodine-oxygen laser

#### Abstract

In this paper we assessed the prospects of using low-temperature solid-state nitrogen generators in the two-stage scheme to obtain high-temperature nitrogen for the construction of molecular generator of iodine. The power characteristics of metals IV-V of the periodic system, used for heating the low-temperature nitrogen due to heat reactions of nitrides origin were analyzed. Based on the experimental results on the ﬁltration combustion of metals in nitrogen, the estimates of operating characteristics of two-stage generator working body of periodic-action iodine-oxygen laser were made. It was shown for heating nitrogen to high temperatures using of titanium is preferable.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):136-142

Thermodynamic calculation of temperature and composition of the combustion products of pyrotechnic and gas generating cartridges for pressurization powder fire extinguishers

#### Abstract

The main results of thermodynamic calculations of combustion reaction of pyrotechnic gas generating cartridges for powder ﬁre extinguishers are presented in the paper. Adiabatic temperature and combustion products are determined based on the calculations. Chemical compounds for the gas generating cartridge with low temperature generated gases are deﬁned.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):143-148

Calculation of hypergeometric series with quasi-linear time and linear space complexity

#### Abstract

A simple for practical implementation algorithm with the time complexity O(M(n)log(n)2) and space complexity O(n) for the evaluation of hypergeometric series with rational coefficients on the Schönhage machine is constructed (here M(n) is the complexity of integer multiplication). It is shown that this algorithm is suitable in practical informatics for constructive analogues of often used constants of analysis.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):149-156

On the problem for mixed type equation with M. Saigo operators

#### Abstract

In this paper boundary value problem with M. Saigo operators is considered for the equation of the mixed type. This equation is represented as an equation of fractional diffusion in upper half-plane and as an equation of moisture transfer in lower halfplane. One-valued solvability of the problem is proved.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):157-161

The control problem for the system of telegraph equations

#### Abstract

The boundary control problem for the system of telegraph equations was considered in the rectangular region. The control functions transferring the process described by this system from the given initial state to the ﬁnal state were constructed using the Riemann method. The ambiguity of the obtained controls consists in the way the conditions are continued in the initial line.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):162-166

Solution of the Cauchy problem for system of Euler-Poisson-Darboux equations

#### Abstract

The system of Euler-Poisson-Darboux equations is considered, the Cauchy problem is solved for the case, when characteristic numbers of matrix-coefficient are complex conjugate and having real part in the interval (−1/2, 0).

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):167-170

Multilevel models of endurance limits prediction for heterogeneous materials under complex stress state

#### Abstract

The coupled boundary-value problem of composite micromechanics is presented and formulated. The problem is closed by kinetic equations, which describe possible scenarios of damage evolution. The results of biaxial (i.e buckling and torsion) high-cycle fatigue tests with powder-iron samples and quasistatic tests under uniaxial tension and torsion are presented at the paper. Based on the dates of quasistatic tests theoretical method for cyclical durability prediction is developed, and theoretical Wöhlers curves are plotted for powder-iron. The comparison of mathematical simulation results and the dates of high-cycle fatigue tests is carried out.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):171-175

Computer modeling of compression for large cell spatially reinforced composite specimen enclosed in the ring for elimination of edge effects influence

#### Abstract

Article is dedicated to numerical simulation of compression test of the prismatic specimen of the spatially reinforced composite material in which the mechanisms leading to collapse of basic surfaces are weakened. It is shown that areas of the maximum stresses settle down in a working part of the specimen, initiating macrodestruction by a cut. The structural-phenomenological approach is applied to the description of deformation and fracture of the specimen.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):176-180

Influence of air shot blasting and temperature exposure on residual stresses and fatigue strength of notched specimens from alloys V95 and D16T

#### Abstract

The effect of air shot blasting and temperature exposure without load on residual stresses and limit endurance of smooth specimens and specimens with semicircular notches of aluminum D16T and V95 alloys was investigated experimentally. This research was done for the symmetric loading cycle in terms of bending and tensioncompression tests and the base of 107 cycles. The check of the calculated mean integral residual criterion stress to estimate the increment of the endurance limit of hardened parts with stress concentrators was completed. It was established experimentally and theoretically, that there is increment of increase in endurance limit hardened parts with stress concentrators in comparison with non-reinforced specimens, and temperature exposure leads to residual stresses relaxation and reduce the increment of the endurance limit.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):181-184

Research into the mechanical properties of continuous basalt fibre relating to composit materials manufacture

#### Abstract

The questions on the mechanical properties of continuous basalt ﬁbres are considered in the work relating to the manufacture of composite materials. Durability of a plait, consisting of 4000 continuous basalt ﬁbres is investigated. The deﬁnition technique of the mechanical characteristics of a continuous basalt ﬁbres plait is oﬀered.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):185-188

High volatile markets analysis with using berg method and Chebyshev type ii filters, and statistical modeling of the risk of loss for its tools

#### Abstract

We describe the method of technical analysis of highly volatile markets in the framework of signal processing theory, which uses Chebyshev ﬁlter. Berg method is used to estimate spectral density of the signal power. The algorithm of optimal AR-model order calculation is given. The method for proﬁt rate estimation based on artiﬁcial noise generation, preserving its structure, is developed.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):189-192

On one method for analytical solution of Graetz-Nusselt problem

#### Abstract

An approximate analytic solution of heat transfer problem for ﬂuid ﬂow in a circular tube is found using the method of separation of variables, based on the introduction of additional boundary conditions. It is shown that already in the fourth approximation over the range of dimensionless axial coordinate 0,0025 ≤ x < ∞, the difference between the exact and the obtained solution does not exceed 3%.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):193-198

On the mathematical modeling of the contaminated groundwater fractal migration in natural porous systems

#### Abstract

The problems of the mathematical modeling of the contaminated groundwater migration, which cannot be described in the context of the mass transfer theory classical approach, are considered. For the study of space-time conformity of nonlinear effects, determined by scaled invariance, the well-set nonlocal boundary problem for the model differential equation of nonlinear migration is proposed.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):199-201

Using the database of coordinates of the major planets for the numerical integration of the equations of celestial bodies motion

#### Abstract

Databases of major planets coordinates are created on the basis of the numerical theory of movement of planets DE405. Numerical integration of the motion equations of small bodies of Solar system is realized using the received databanks. Extra efficiency of usage of databanks of major planets coordinates is shown at numerical integration of motion equations of celestial bodies.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):202-207

Structural recognition algorithm for prefractal graph

#### Abstract

In the article the recognition problem for prefractal graph formed by two full alternating fuses is considered. Mathematical statement is made, metric characteristics are received, the effective algorithm of recognition is developed, the question on computing complexity is investigated.

**Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences**. 2011;5(3):208-211