## No 1 (2016)

**Year:**2016**Articles:**10**URL:**https://ered.pstu.ru/index.php/amcs/issue/view/394**DOI:**https://doi.org/10.15593/2499-9873/2016.1

Mathematical modeling of the formal analogy wave functions

#### Abstract

It is shown that, in accordance with a priori approach to establishing physical phenomena construction formal mathematical model may be preceded by the experimental data obtained. The aim is to construct a mathematical model of a formal analogue of the wave function of the particle-free inert and compare it with the actual wave function. Reasons why this is the fact that the logic of wave-generalization, lies at the origin of the current version of the description of the wave function, it is not certain. The formal analogue of the wave function is obtained from a series of successive transformations of the classical equation of rectilinear uniform motion of a free nonrelativistic particle inert. Further transformations possible to obtain an analog of the Schrodinger equation for a free particle. His comparative analysis of the existing version of the Schrödinger equation revealed a contradiction in the existing version and half to adjust the value of the phase velocity.

**Applied Mathematics and Control Sciences**. 2016;(1):9-14

Thermomechanics of phase transitions in ferromagnetic shape memory alloys under finite deformations

#### Abstract

In the framework of finite deformations a model has been constructed to describe the behaviour of ferromagnetic material, which undergoes the austenite-to-martensite phase transformation in the process of its deformation under the action of temperature and magnetic fields. The kinematic and constitutive equations, satisfying the principles of thermodynamics and objectivity, have been developed both, for the martensitic and austenitic phases and also for the mixed austenitic-martensitic state, which takes place in the process of smeared phase transition of the first order. Relations, describing the shift of characteristic temperature of the phase transition according to the generalized Clausius-Clapeyron law, have been derived. This shift is defined by the stresses generated in the body in the process of its deformation and is controlled by the internal magnetic field induced in the material by the external magnetic field. The available experimental data for ferromagnetic shape memory alloys have been used to verify the proposed model.

**Applied Mathematics and Control Sciences**. 2016;(1):15-24

Modeling of technological plastic metal hot-forming of a large size ingot

#### Abstract

The results of numerical modeling the technological process of plastic metal working of a large size ingot made of steel 30HGSA are presented. The modeling process has been carried out in accordance with a manufacturing scheme that involves the air cooling of the ingot during its transportation from the furnace to the deforming equipment, and two metal forming operations - free upsetting and open-die forging, during which the ingot is shaped into a circular configuration. The ingot was upset between the upper flat and lower annular dies to reach a diameter of 1060 mm. Then, using a combination of different dies the ingot was pressed to the desired dimensions no less than 860 mm. Examination of changes in the ingot shape and its heat and stress-strain states was carried out using an engineering software Deform-3D. A compression force required for implementation of forming operations during the technological process of plastic metal working was calculated.

**Applied Mathematics and Control Sciences**. 2016;(1):25-33

Numerical simulation of high-speed gas flow in the region with moving boundaries

#### Abstract

Numerical simulation of high-speed gas flow in a region with moving boundaries characterized by large computational requirements in numerical simulations. The complexity of the process due to the minimum necessary value of the time step. Obtained numerical solution of a nonstationary problem of the flow of supersonic gas flow. The approach used, consisting in replacing the overall decision on the sequence of decisions at different time steps. Each of these solutions is a non-stationary task of thermal conductivity with fixed walls. Numerical solution of ANSYS CFX using the k-ε turbulence model. For averaging the results of the solution at each point on the moving boundary of the solid body used the Matlab application package.

**Applied Mathematics and Control Sciences**. 2016;(1):34-42

On ability of discrete atomistic approach to discribe elastic anisotropy by the examples of plain quasi-crystalline structures

#### Abstract

Prediction of physical and mechanical properties of nanostructured materials is usually realized within discrete atomistic simulation. Such approach often provides a unique way of studying nanomaterials and requires some restrictions for the used interatomic potentials. A huge amount of different potentials has been used, i.e. pairwise, many-particle potentials, embedded atom method, covalent bond potentials etc. It is well known that computed mechanical properties in some cases may differ from experimental data, even qualitatively. The paper aims at the demonstration of different potentials ability to explain elastic anisotropy by studying invariant representation of tensor of elastic moduli in the exact form which has been built using different potentials of interatomic interaction. It makes it possible to study the prospects of different potentials for describing anisotropy of material elastic response. The authors demonstrated the abilities of two-particle or multi-particle potentials of interatomic interaction based on the Morse potential in describing anisotropy of materials elastic properties using the obtained invariant representation by the examples of two-dimensional quasi-crystalline structures. The pair-wise potentials in contrast to the many-particle embedded atom potential are shown to be unable to explain elastic anisotropy.

**Applied Mathematics and Control Sciences**. 2016;(1):43-56

About one method of determination of distribution of functions of random variables set

#### Abstract

A problem of distribution of functions of several random variables is considered. Statement and general algorithm of problem solving is shown, as numeric method what allows to evaluate numerical values of sought probability density function. Intercomparison of results carried out from numerical and analytical solutions for the problem, what allows analytical solution. Developed technique is used to solving problem about distribution of rigidity-to-torsion modulus of the cylindrical shaft with random radius and elastic modulus.

**Applied Mathematics and Control Sciences**. 2016;(1):59-66

Rationale for selection factors of AAC quality management

#### Abstract

In article the problem of a choice of factors of management of technological process of production of an autoclave aerated concrete by criterion of quality is considered. By results of an expert assessment it is established that the best results on improvement of quality of a ready-made product will be reached at management of process of dispensing of components of an autoclave gas concrete. Justification of a choice of factors of quality management of an autoclave gas concrete at a dispensing stage, among which ratios of n, Cb and the content of active silicon dioxide (SiO2) in sand is given.

**Applied Mathematics and Control Sciences**. 2016;(1):69-80

Model development of multifamily residential building curtilage landscape in the context of modern cities

#### Abstract

The article develops problem of multifamily residential building curtilage landscape in the context of modern city. The author is concerned in relevance of the problem. The main ways of procuring a receipt from curtilage landscape use is offered. There are backgrounds of researching. The results of marketing research of consumers’ preferences is showed. Based on the results, the model, which allowed is offered to make a choise of the optimal variant of landscape with an allowance for residents, is showed.

**Applied Mathematics and Control Sciences**. 2016;(1):83-90

The analysis of economic efficiency of the decisions made at management of commercial real estate (on the example of shopping malls)

#### Abstract

The new problem definition of shopping malls management taking into account consumer appeal where as criterion function the profit of tenants of trade and entertaining rooms is used is formulated. This problem definition corresponds to economic reality as in practice of management of commercial real estate the form of interaction between management company and tenants in the form of the fixed rental rate and percent from sales of tenants is widespread. The accounting of consumer appeal is provided thanks to modeling of preferences of shopping mall visitors. For search of optimum control the graphic-analytical method of the analysis of economic efficiency of the decisions made at commercial real estate objects management based on the analysis of sensitivity of indicators of efficiency to change of controlled factors is offered. Efficiency of application of this method and a possibility of finding of optimum control of shopping mall is visually shown.

**Applied Mathematics and Control Sciences**. 2016;(1):93-108

About the economic agent’s preferences models verification

#### Abstract

The procedures of verification of models of preferences of economic agents, formalized by a comprehensive evaluation matrix mechanism in the form of a consistent set of binary matrix convolution factors influencing management decisions. Identification of the parameters of the mathematical model of preferences made during a behavioral experiment, and verification of models of preferences is carried out by comparing their results with the results of a computational experiment behavioral experiment. The information about the software tools created by the authors provides. Using these software tools can be carried out the collection, storage and processing of the results of behavioral and computational experiments. Also the information about the program provides, using which can perform computations with economic agent’s preferences models. Verification procedure is illustrated by the example where the agent or preferences carrier acts as an investor and he has to choose perspective companies to invest in alternative businesses, each of which is considered a risk and profitability.

**Applied Mathematics and Control Sciences**. 2016;(1):109-121