The limiting state of bodies during separation in the case of the general plane problem

Работа посвящена решению общей плоской задачи, связанной с определением предельного состояния тел при отрыве. Уравнения, определяющие условия предельного состояния принимаются функциями, зависящими от среднего давления и направлений отрыва. В результате вычислений были получены характеристические уравнения для двух случаев: при достижении предельных значений отрыва двумя главными напряжениями и при достижении предельного значения отрыва одним главным напряжением. Для двух рассмотренных случаев были получены уравнения характеристик и соотношения вдоль них. The work is devoted to the solution of the general plane problem related to the determination of the limiting state of bodies during separation. The equations defining the conditions for the limiting state are taken as functions that depend on the average pressure and directions of separation. As a result of calculations, the characteristic equations were determined for two cases: when the limiting values of separation by two main stresses are reached and when the limiting value of separation by one main stress is reached. For the two considered cases, equations of characteristics and relations along them were obtained.

Carreau's Rheological Model and A.N. Tikhonov’s Regularization Method: Parametric Identification Based on a CFD model

Introduction. Carreau's rheological model can describe the three-dimensional flows of non-Newtonian media. However, it requires modeling parameters for the viscosity of the medium at the limiting values of shear rates, which cannot be achieved by instrumental methods. The present article introduces a novel method that can identify the parameters of Carreau’s model using a regularization algorithm. Study objects and methods. The study featured fondant mass produced according to the traditional formulation for Creamy Fondant unglazed candies. Standard methods were used to describe the properties of the raw materials and semi-finished products, as well as methods of mathematical processing, modeling, and optimization. Results and its discussion. The research produced an algorithm based on A.N. Tikhonov’s regularization method of the parametric identification of Carreau's rheological model. The calculation residual was minimized by the viscometric measurements and the CFD model, which provided the calculation of the hydrodynamic flow regime at the limiting values of shear rates. The CFD model of a steady non-isothermal flow of a nonlinear viscous medium through a cylindrical capillary was based on the equations of conservation of mass, energy, and momentum. The rheological parameters of Carreau’s model were illustrated by the case of fondant mass. The error for the viscosity prediction did not exceed 14.07%. Conclusion. The parametric identification algorithm made it possible to evaluate the rheological parameters of structured liquid media with Carreau's rheological law in cases that lack experimental information on the behavior of the medium at limiting shear rates. The algorithm eliminated the computational problems typical of Ostwald and de Ville’s rheological model, which usually arise when solving practical problems of three-dimensional flows of non-Newtonian media with limiting viscosity values.

Method for Prediction of Extreme Wave Loads Based on Ship Operability Analysis Using Hindcast Wave Database

The method for the prediction of extreme vertical wave bending moments on a passenger ship based on the hindcast database along the shipping route is presented. Operability analysis is performed to identify sea states when the ship is not able to normally operate and which are likely to be avoided. Closed-form expressions are used for the calculation of transfer functions of ship motions and loads. Multiple operability criteria are used and compared to the corresponding limiting values. The most probable extreme wave bending moments for the short-term sea states at discrete locations along the shipping route are calculated, and annual maximum extreme values are determined. Gumbel probability distribution is then fitted to the annual extreme values, and wave bending moments corresponding to a return period of 20 years are determined for discrete locations. The system reliability approach is used to calculate combined extreme vertical wave bending moment along the shipping route. The method is employed on the example of a passenger ship sailing across the Adriatic Sea (Split, Croatia, to Ancona, Italy). The contribution of the study is the method for the extreme values of wave loads using the hindcast wave database and accounting for ship operational restrictions.

Equations of nonlinear dynamics of development of industrial enterprises, taking into account the amount of its maximum profit

In the published article, new modifications of economic and mathematical models of the dynamic development of enterprises are proposed, the production of which is being restored due to the introduction of their own investments. The developed models are presented in the form of systems of differential equations for an arbitrary number of production factors. Stationary solutions of these systems of equations correspond to the equilibrium states of the operation of enterprises and represent the limiting values of the factors of production. Two versions of systems of differential balance equations for enterprises, describing the growth of factors of production and output, have been established. In the first case, the growth of resources and output is limited by the limiting values of the factors of production. In the second case, the growth of resources and output is limited by the pre-calculated values of the factors of production that correspond to the value of the maximum profit of the enterprise. It is shown that the growth of production factors of the enterprise should not exceed the values corresponding to the value of the maximum profit. Otherwise, the company starts to operate at a loss. In the presented models, proportional, progressive and digressive depreciation deductions are considered. Theconstructed models make it possible to describe various modes of operation of enterprises. Such regimes include a stable output of products by enterprises, a temporary suspension of the work of enterprises during its technical re-equipment, and a temporary partial curtailment of production.

Calculation and Analytical Substantiation of the Limiting Values of Ammonium Nitrate Mass During Storage in the Warehouses and Terminals

On the basis of theory of stationary thermal explosion of A.D. Frank-Kamenetsky, depending on the temperature of the critical size of the ammonium nitrate embankment, the calculations were performed, which show that it can be stored in the large volumes at the temperatures up to 30 °C. On the contrary, at the temperatures above 100 °C (for example, at 200 °C), the decomposition of nitrate occurs with acceleration and can lead to an explosion. Based on the studies performed, it is shown that the changes and additions to the fire safety requirements for ammonium nitrate storage in the buildings and structures should be determined by the requirements for fire resistance of buildings (at least II degree of fire resistance), for the purity of the product and its packaging, for the exclusion of contacts with organic substances and materials, storage conditions. Additional fire safety requirements were developed for inclusion in the normative document regarding ammonium nitrate storage. Ammonium nitrate is allowed to be stored in one-story warehouse buildings of at least II degree of fire resistance, structural fire hazard class C0. The floor area within the fire compartment should not exceed 10 500 m2. Between the fire-fighting walls of the 1st type, it is allowed to store no more than 25 000 tons of nitrite in bulk or in the special bags, as well as in the soft specialized containers for bulk products in accordance with GOST 2—2013.The conditions for placing ammonium nitrate in the stacks should be accepted in accordance with the requirements of SP 92.13330.2012. Temperature in the storage room of ammonium nitrate should not exceed 30 °C with a relative humidity of not more than 60 %. Warehouses for storing ammonium nitrate should be equipped with general exchange supply and exhaust and (or) emergency ventilation, in order to exclude the formation of a fire and explosion hazardous environment in the room during the decomposition of ammonium nitrate. Warehouses for storing ammonium nitrate in an amount of not more than 5 thousand tons may be separated from other premises, including from the warehouses for fertilizers and pesticides, by solid (without openings) type 2 fire walls.

Why Should We Test the Wideband Transformation Accuracy of Medium Voltage Inductive Voltage Transformers?

In this paper the results of the tests of the wideband transformation accuracy of medium voltage (MV) inductive voltage transformers (VTs) in the frequencies range from 50 Hz up to 5 kHz are presented. The values of voltage error and phase displacement for transformation of the harmonics of distorted primary voltages are determined. In the case of a typical 50 Hz-type inductive VT with a rated primary voltage equal to (15/Ö3) kV and (20/Ö3) kV manufactured by an international company the limiting values of the accuracy classes extension for quality metering required by the standard IEC 61869-6 for the Low Power Instrument Transformers (LPIT) were not exceeded. While, in the same test other MV inductive VTs show poor accuracy and even resonance at multiple frequencies. Unfortunately, this problem also arises from nonlinearity of the magnetization characteristic of their magnetic core. Therefore, for transformation of the sinusoidal voltage in the secondary voltage significant but not easily detectable values of the low order higher harmonics are present. Moreover, for transformation of harmonics of distorted primary voltage the influence of connected capacitance on the obtained values of voltage error and phase displacement was tested.

Perceptibility and Acceptability of Surface Gloss Variation Under Different Illuminants

Clinical Relevance The influence of different illuminants on the perception and acceptance of surface gloss variation in composite resins remains unclear but is important if restorations are to mimic natural teeth. SUMMARY Objective: The purpose of this study was to evaluate the influence of different illuminants on the perceptibility and acceptability of surface gloss variations and to determine limiting values. Methods: Eight composite resin specimens and one human tooth specimen were polished to obtain composite resin specimens with different gloss units (GU) of 10, 20, 30, 40, 50, 60, 70, and 80 and a human tooth specimen of 80 GU. Sixty observers compared the surface gloss of the specimens in a light booth. For perceptibility testing, the specimens were randomly positioned two at a time. The acceptability of the gloss variation was determined by comparing the composite resin specimens with the tooth specimen. The observers answered specific questions to determine the level and perceptibility and acceptability limits of gloss variations. All analysis was done with two illuminants (D65 and fluorescent light) used randomly. Data were submitted to a nonlinear probit model and nonlinear probit regression estimation (α=0.05). Results: Significant differences in illuminants were observed for perceptibility (p<0.001) and acceptability (p=0.045). The perceptibility limit for D65 was 7.0 GU and 6.8 GU for fluorescent illuminant. The acceptability limit for D65 was 34.2 GU and 37.1 GU for fluorescent illuminant. Conclusions: More accurate perceptibility and acceptability judgments of the surface gloss of composite resin were made when the specimens were illuminated with D65 light.

A Non-Field Analytical Method for Solving Some Nonlinear Problems in Heat Transfer

This paper presents an extension of the non-field analytical method – known as the method of Kulish – to some nonlinear problems in heat transfer. In view of the fact that solving nonlinear problems is very complicated in general, the extension of the method is presented in the form of several important illustrative examples. Two classes of problems are considered: first are the problems, in which the heat equation contains nonlinear terms, while the second type of the problems includes some problems with nonlinear boundary conditions. From the practical viewpoint, the case considered in Section 4 is of the greatest interest. In that section, it is shown that, for complex heat transfer problems, where applications of the non-field method are practically impossible due to a large volume of necessary computations, it is still possible to analyse the solution behaviour and automatically determine similarity criteria for the limiting values of the parameters. Wherever possible the obtained solutions are compared with known solutions obtained by other methods. The practical advantages of the non-field method over other analytical methods are emphasised in each case.

Partition-theoretic formulas for arithmetic densities, II

International audience In earlier work generalizing a 1977 theorem of Alladi, the authors proved a partition-theoretic formula to compute arithmetic densities of certain subsets of the positive integers N as limiting values of q-series as q → ζ a root of unity (instead of using the usual Dirichlet series to compute densities), replacing multiplicative structures of N by analogous structures in the integer partitions P. In recent work, Wang obtains a wide generalization of Alladi's original theorem, in which arithmetic densities of subsets of prime numbers are computed as values of Dirichlet series arising from Dirichlet convolutions. Here the authors prove that Wang's extension has a partition-theoretic analogue as well, yielding new q-series density formulas for any subset of N. To do so, we outline a theory of q-series density calculations from first principles, based on a statistic we call the "q-density" of a given subset. This theory in turn yields infinite families of further formulas for arithmetic densities.

Isochoric specific heat in the Dual Model of Liquids and comparison with the Phonon theory of Liquid Thermodynamics

We continue in this paper to illustrate the implications of the Dual Model of Liquids (DML) by deriving the expression for the isochoric specific heat as a function of the collective degrees of freedom available at a given temperature and comparing it with the analogous expression obtained in the Phonon Theory of Liquid Thermodynamics. The Dual Model of Liquids has been recently proposed as a model describing the dynamics of liquids at the mesoscopic level. Bringing together the early pictures of Brillouin and Frenkel and the recent experimental outcomes obtained by means of high energy scattering, liquids are considered in the DML as constituted by a population of wave packets, responsible for the propagation of elastic and thermal perturbations, and of dynamic aggregates of molecules, in continuous re-arrangement, diving in an ocean of amorphous, disordered liquid. The collective degrees of freedom contribute to the exchange of energy and momentum between the material particles and the lattice particles, which the liquids are supposed to be composed of in the DML.First, we show that the expression obtained for the specific heat in the DML is in line with the experimental results. Second, its comparison with that of the Phonon Theory of Liquid Thermodynamics allows getting interesting insights about the limiting values of the collective degrees of freedom and on that of the isobaric thermal expansion coefficient, two quantities that appear related to each other in this framework