Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics最新文献

{"title":"Evaluation of local mechanical properties of SiO2-based ceramic refractories using microscale modeling","authors":"A. Grigoriev, A. Dmitriev, E. V. Shil’ko","doi":"10.17223/19988621/80/7","DOIUrl":"https://doi.org/10.17223/19988621/80/7","url":null,"abstract":"The development of multiscale mechanical models of promising refractory materials is an urgent problem in the mechanics of solids. One of the reasons is the applicability of these models when creating digital twins of advanced refractories. The authors of this paper recently developed and validated a mesoscopic model of the SiO2-based refractory material that is widely used in metallurgy. This model takes into account the characteristic structural features of SiO2 refractory in the scale range of 10-5 - 10-2 m and the mechanical behavior features in a wide range of strain rates. However, the full use of the model requires knowledge of local mechanical properties of mesoscopic structural elements, in particular, the highly porous regions, which are formed by fine grains less than 102 pm in size. An experimental study of effective mechanical characteristics of such regions is an extremely difficult task. Therefore, the purpose of this work is to obtain the theoretical estimate using the microscale numerical simulation of highly porous regions of SiO2 refractory material and to determine their integral mechanical characteristics. To study this problem, the two-dimensional model samples are developed that simulate fine-grained regions of the refractory and are characterized by different porosity and pore structure types (channel-like or closed type). The intervals of the variation of Young’s modulus and strength characteristics of the samples are obtained depending on the porosity and morphology of the pore space. The contribution of the closed-type porosity to the integral mechanical characteristics of the refractory is determined; though, the volume fraction of such pores is low as compared to that of the channel-like pores. The obtained data will be used as input parameters of mesoscale refractory models for solving the urgent problems related to the study of the effect of microstructure parameters on the macroscopic mechanical and thermomechanical properties of SiO2-based refractories.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"18 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90145933","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the finite support property of Gul’ko-Khmyleva’s homeomorphism","authors":"Valeriya S. Ametova, Vadim Lazarev","doi":"10.17223/19988621/80/1","DOIUrl":"https://doi.org/10.17223/19988621/80/1","url":null,"abstract":"It is established that for the homeomorphism of the spaces c0 and s × c0 constructed by S.P. Gulko and T.E. Khmylyov, the image of the first coordinate functional under the adjoint mapping has no finite support. As a consequence, we see that this homeomorphism does not have the finite support property. In addition, it is shown that the images of all other coordinate functionals under the adjoint mapping have finite supports. The authors thank S.P. Gubko and T.E. Khmyleva, as well as A.V. Osipov for their kind attention to this work. The authors thank S.P. Gubko and T.E. Khmyleva, as well as A.V. Osipov for their kind attention to this work.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"40 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91174696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A study of the ignition and combustion of high-density charges under constant volume conditions","authors":"K. Rogaev, A. S. D’yachkovskiy, A. Ishchenko, N. Samorokova, E. Stepanov, N. R. Gimaeva","doi":"10.17223/19988621/81/11","DOIUrl":"https://doi.org/10.17223/19988621/81/11","url":null,"abstract":"The study of combustion and ignition of charges with promising propellants or powder compositions in terms of initial conditions is an urgent problem of modern ballistics. Generally, combustion and ignition of charges are tested in a manometric closed vessel. The charge ignition conditions may affect the subsequent reactions. When designing a shot with a new charge, it is necessary to know what determines the moment of ignition (gas pressure, time, pressure rise rate, type of igniter, etc.) and which factor has a greater effect on the ignition. This paper presents a study of some features of high-density charge ignition under constant volume conditions. A brief description of the manometric setup is given. The effect of mass and type of igniter and combustion surface area on the high-density charge ignition and subsequent combustion is studied. The pressure-time dependences corresponding to high-density charge combustion in a textolite container with different diameters are presented and analyzed. The ignition of the paste high-density charge is revealed to be affected by the geometric dimensions of the container. The parametric experimental study results show that the ignition conditions of a model high-density propellant (MHDP) strongly depend on the method of initiation, namely the number of burning particles and ambient pressure; however, these factors do not affect the dependence of the MHDP combustion rate on pressure. The ignition momentum is obtained as a function of the ratio of the container burning surface circumference to the burning surface area.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"66 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90362076","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Passive convective ventilation in a double air-porous layer with internal heat generation depending on solid fraction","authors":"E. Kolchanova, N. Kolchanov","doi":"10.17223/19988621/82/9","DOIUrl":"https://doi.org/10.17223/19988621/82/9","url":null,"abstract":"The convective stability of a two-layered system consisting of a heat-generating porous region underlying an air region has been numerically studied. The linear dependence of the heat release on the solid volume fraction is taken into account in the porous region. The equal constant temperature values are fixed on the external impermeable boundaries of the system. The critical internal Rayleigh-Darcy number at which the convection is induced in the system in the form of two-dimensional roll patterns with a given wave number has been determined. The convective flow is possible due to the formation of unstable density stratification in the presence of internal heat release. Two types of stationary convection, namely, the local and the large-scale convection, have been studied. The local flow arises in the air sublayer and scarcely penetrates into the porous sublayer. The large-scale convection covers both sublayers. The change in the convective regime occurs with the growth of one or another parameter of the system and indicates the variation of the instability type. It is accompanied by an abrupt (by times and tens of times) change in the critical wave number of roll patterns. Numerical calculations show a decrease in the onset value for both types of convection with increasing solid volume fraction ϕ in the porous sublayer and increasing relative thickness d of the air sublayer. The growth of the Darcy number (the dimensionless per-meability of the porous sublayer) also causes destabilization of the air motionless state at the given ϕ and d. The variation of the convection regime from a large-scale flow to a local one occurs with increasing relative thickness of the air sublayer, whereas an opposite transition from the local to the large-scale convection regime is observed with increasing Darcy number.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"63 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90371233","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Peculiarities of the flame formation of a propane-air mixture in a narrow channel","authors":"K. M. Moiseeva, Aruzhan I. Kantarbaeva, A. Krainov","doi":"10.17223/19988621/82/11","DOIUrl":"https://doi.org/10.17223/19988621/82/11","url":null,"abstract":"This paper presents a numerical study of the features of propane-air mixture flame propagation in a narrow cylindrical channel. The main purpose of the study is to determine the effect of the channel width on the combustion characteristics of a propane-air mixture with a composition close to stoichiometric. The problem is formulated using the methods of reactive gas dynamics. The solution method is based on the Van Leer method for determining flows on the faces of computational cells. The peculiarities of the combustion front formation and its propagation along the channel are revealed and analyzed. The formation of the curved flame front is shown to have a cyclical nature. The visible flame velocity is obtained as a function of the channel radius. The proposed physical and mathematical model can be used to determine the thermal conditions of operating cylindrical burners.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"9 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90720138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Determination of the values of transfer characteristics in multicomponent media on the basis of micro-process analysis","authors":"Irina V. Anisimova, Victor N. Ignat'ev, Elena Yu. Lapteva","doi":"10.17223/19988621/81/5","DOIUrl":"https://doi.org/10.17223/19988621/81/5","url":null,"abstract":"This paper proposes a two-level approach for mathematical modeling of processes in multicomponent gas mixtures. It involves a combination of the description of conservation laws based on macro-equations and the determination of the corresponding transfer coefficients using the analysis of micro-processes. The main purpose of this work is to develop an algorithm for determining transport characteristics in multicomponent media based on the analysis of inner micro-processes. Hence, the kinetic molecular theory of gases and liquids is used, namely, the collision part of the Boltzmann equation. It includes multiple improper integrals taking into account the effect of micro-processes in the medium on the values of transport coefficients. When integrating the Boltzmann equation by the Chapman-Enskog method, the transport coefficients are expressed through integral brackets of the Sonin polynomials, which represent the linear combinations of molecular collision integrals. Their calculations require the use of efficient mathematically sound ways including the elements of parallel computing.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"2 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88632509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Engineering calculation of a midwater fishing trawl","authors":"Aleksey Razhev, A. Nedostup","doi":"10.17223/19988621/81/12","DOIUrl":"https://doi.org/10.17223/19988621/81/12","url":null,"abstract":"This paper presents a method for calculating the power and geometric properties of a midwater fishing trawl, which is a complicated engineering structure made up of tied flexible (threads, ropes, flap) and rigid (rigging, trawl boards) elements. A computational model, the functional relations for internal forces and geometric characteristics of the trawl, and a calculation procedure based on the finite element method are proposed. The computational algorithm is implemented on a graphics processing unit of a personal computer with the use of DirectCompute, Shader Model 5, and high-level shader language. The performance and resource intensity of the algorithm applied in the computer-aided design system for industrial fishing gear are assessed in terms of the number of trawl nodes and computing equipment. A comparative analysis of the calculated and experimentally obtained characteristics of the trawl physical model is presented. According to the results, the computational error in geometric characteristics and internal forces is less than 3 and 5%, respectively.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"11 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81402936","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"METHODS AND ALGORITHMS FOR SOLVING THE PROBLEM OF OPTIMIZING THE CHARGE DESIGN INTENDED TO INCREASE THE INITIAL VELOCITY OF A PROJECTILE","authors":"I. G. Rusyak, V. Tenenev","doi":"10.17223/19988621/82/13","DOIUrl":"https://doi.org/10.17223/19988621/82/13","url":null,"abstract":"A mathematical model of the structural and parametric synthesis of a charge composed of sequentially arranged tubular and granular powder elements is formulated for increasing the muzzle velocity of a projectile. A target parameter (the muzzle velocity) and the controlled parameters (the maximum pressure behind the shot) are determined from the solution of a gas-dynamic problem of internal ballistics for a combined charge at various loading schemes. The developed method for the optimization problem solving is based on a genetic algorithm. The operability of the proposed optimization algorithm along with the solution of the main problem of internal ballistics in a gas-dynamic formulation is examined and confirmed. The general scheme and the basic steps of the algorithm implementation are tested on a benchmark problem. Four components of the charge consisting of single-channel tubular and seven-channel grained gunpowder are considered. The components differ in the burning rate, geometry of the powder elements, and powder mass. The rest of the characteristics remain the same. The potential for increasing the muzzle velocity of the projectile using the structural and parametric optimization of the combined charge design is shown.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"8 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86692841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Statistical evaluation of mechanical characteristics of hot-pressed ceramics in ZrB2–SiC system","authors":"Sukyas S. Ordan’yan, D. D. Nesmelov, E. S. Novoselov","doi":"10.17223/19988621/82/12","DOIUrl":"https://doi.org/10.17223/19988621/82/12","url":null,"abstract":"The effect of the addition of 5 mol.% LaB6 on the Weibull modulus of hot-pressed ceramics in ZrB2-SiC is studied in this paper. The samples with a relative density of 91–92%, a flexural strength of 300–315 MPa, and a Vickers hardness of 14–15 GPa are obtained by hot pressing at an isothermal holding temperature of 1900°C and a pres-sure of 30 MPa within 15 minutes in an argon atmosphere. The addition of LaB6 induces an increase in the Weibull modulus of ceramics from 9.5 up to 15.5 when calculating using the bending strength, and from 22.0 up to 31.4 when calculating using the hardness. The values calculated using the hardness are somewhat overestimated due to the local impact of the Vickers pyramid. An increase in the Weibull modulus with the addition of LaB6 is associated with increasing homogeneity of the ceramic structure due to the formation of a more developed system of interphase boundaries in three-component samples.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"86 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88535308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The set Kp in some finite groups","authors":"A. I. Zabarina, E. A. Fomina","doi":"10.17223/19988621/81/1","DOIUrl":"https://doi.org/10.17223/19988621/81/1","url":null,"abstract":"The study of the properties of the set Kp consisting of elements of a non-Abelian group that commute with exactly p elements of the group G is continued. In particular, this question is considered for groups of order p1p2...pk, k ≥ 3 and p2q, where рі, q are prime numbers. It is also proved that the set K5 is non-empty in the three-dimensional projective special linear group. This group has the same order as the alternating group A8, in which the set K5 is empty.","PeriodicalId":43729,"journal":{"name":"Vestnik Tomskogo Gosudarstvennogo Universiteta-Matematika i Mekhanika-Tomsk State University Journal of Mathematics and Mechanics","volume":"75 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86114038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}