Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki最新文献

{"title":"Solution of the Problem of Gradient Thermoelasticity for a Coated Strip","authors":"A. Vatulyan, S. A. Nesterov","doi":"10.26907/2541-7746.2021.2.181-196","DOIUrl":"https://doi.org/10.26907/2541-7746.2021.2.181-196","url":null,"abstract":"The formulation of a one-parameter problem of gradient thermoelasticity for the “thermal protective coating – substrate” system which is modeled by a composite strip is presented. The lower boundary of the strip is rigidly clamped and maintained at zero temperature, and on the upper boundary, free of stresses, a heat flux localized over small segment acts, while the rest of the upper boundary is thermally insulated. First, the Fourier transform in the horizontal coordinate is applied to the equilibrium and heat conduction equations and the boundary conditions. After finding the temperature transformant, the transformants of horizontal and vertical displacement are determined. The Vishik–Lyusternik’s asymptotic approach is used to find the transformants of displacements, taking into account the presence of boundary layer solutions in the vicinity of the strip boundaries. The numerical inversion of the transformants is based on the compound quadrature formula of Philon. A comparison is made of the distribution of Cauchy displacements and stresses obtained on the basis of solving the problem in the classical formulation and in the gradient formulation. It is found that a change in the gradient parameter insignificantly affects the distribution of displacements, but strongly on the distribution of Cauchy stresses and moment stresses. The displacements are continuous, equal to zero in the containment, have certain symmetry when distributed along the horizontal coordinate, and attenuate with distance from the source. Near the termination, the Cauchy stresses decrease exponentially to zero in accordance with the boundary conditions, experience a jump on the mate line. Since displacements and deformations are continuous on the line of conjugation of the strips, due to the jump in thermomechanical characteristics, a Cauchy stress jump occurs in the vicinity of the line of conjugation of the strips. The magnitude of the Cauchy stress jump also depends on the ratio between the gradient parameter and the coating thickness. It is revealed that when the thickness of the coating is less than two gradient parameters, the stress jump changes exponentially and then goes to a stationary value. The moment stresses are continuous and peak at the interface of the materials.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"9 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87685790","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":"Two-Phase Flow in a Narrow Annular Channel between Stationary and Rotating Cylinders","authors":"I. V. Morenko","doi":"10.26907/2541-7746.2021.2.143-152","DOIUrl":"https://doi.org/10.26907/2541-7746.2021.2.143-152","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"1986 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89846699","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":"Optimization of Periodic Synchronization of UAV’s Clock by Differential Phase Method","authors":"A. I. Sulimov","doi":"10.26907/2541-7746.2021.3-4.231-249","DOIUrl":"https://doi.org/10.26907/2541-7746.2021.3-4.231-249","url":null,"abstract":"The article considers the problem of designing a synchronized aerial wireless sensor network of unmanned aerial vehicles (UAVs) with centralized control by a master unit. A 10-ns synchronization precision must be ensured for all units within the aerial network in the time intervals of at least 100 s. To achieve it, the master unit periodically generates a synchronizing signal with two coherent sine tones of different frequencies that helps the slave UAVs to adjust their clocks. High-stability oven-controlled crystal quartz oscillators (OCXO) are used as onboard clocks for the UAVs. The study aims to assess the optimal frequency separation of the coherent synchronizing tones that provides the best possible noise immunity of the measured data with a reliable ambiguity resolution of the carrier phase. The problem is solved using a computer simulation of periodic synchronization of the slave UAVs by differential phase measurements associated with the reference time scale of the master UAV in order to suppress possible random clock offsets.According to the simulation results, aside from the positioning errors of the UAVs, the systematic Doppler phase shift of the synchronizing signal in the propagation channel is the main obstacle to differential phase synchronization. Depending on the efficiency of the Doppler phase shift compensation, the optimum frequency separation of the synchronizing tones ranges from 10 to 1500 MHz with the correspondent synchronization precision achieved from 0.25 to 2.65 ns at the observation time of up to 100 s. It is shown that the effective compensation for the Doppler shift requires periodic channel estimation for at least every 10 ms. For most prac-tical applications, however, adjusting the slave clock every 5 s using two coherent synchronizing sine tones separated by 400–500 MHz results in a satisfactory quality of synchronization.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"20 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90333869","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":"Numerical Study of the Process of Gas Hydrate Decomposition under the Thermal Impact on the Hydrate-Containing Region of a Porous Formation","authors":"N. Musakaev, D. S. Belskikh","doi":"10.26907/2541-7746.2021.2.153-166","DOIUrl":"https://doi.org/10.26907/2541-7746.2021.2.153-166","url":null,"abstract":"A mathematical model that describes, in a two-dimensional approximation, the thermal impact (a temperature increase at the upper boundary of the reservoir) on the region of the porous medium containing methane and its hydrate in the initial state is proposed. The boundaries of the region are impermeable to decomposition products of the gas hydrate (gas and wa-ter). The gas reality and the non-isothermal effects during the movement of gas and water in the porous medium are considered. The methane hydrate decomposition is assumed to be in equilibrium. A numerical study of non-isothermal filtration flow is performed considering the dissociation of methane gas hydrate in the porous medium. The obtained results show that a frontal mode of phase transitions is observed under the thermal impact. The region containing the products of gas hydrate decomposition grows along with the increase in the values of temperature at the upper boundary of the formation and its initial permeability, as well as with the decrease in the hydrate saturation.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"6 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88320402","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":"Convergence of the Galerkin Method for Solving a Nonlinear Problem of the Eigenmodes of Microdisk Lasers","authors":"A. Repina","doi":"10.26907/2541-7746.2021.1.5-20","DOIUrl":"https://doi.org/10.26907/2541-7746.2021.1.5-20","url":null,"abstract":"This paper investigates an eigenvalue problem for the Helmholtz equation on the plane modeling the laser radiation of two-dimensional microdisk resonators. It was reduced to an eigenvalue problem for a holomorphic Fredholm operator-valued function A ( k ). For its numerical solution, the Galerkin method was proposed, and its convergence was proved. Namely, a sequence of the finite-dimensional holomorphic operator functions A n ( k ) that converges regularly to A ( k ) was constructed. Further, it was established that there is a sequence of eigenvalues k n of the operator-valued functions A n ( k ) converging to k 0 for each eigenvalue k 0 of the operator-valued function A ( k ). If { k n } n ∈ N is a sequence of eigenvalues of the operator-valued functions A n ( k ) converging to a number of k 0 , then k 0 is an eigenvalue of A ( k ). The estimates for the rate of convergence of { k n } n ∈ N to k 0 depend either on the or-der of the pole k 0 of the operator-valued function A − 1 ( k ), or on the algebraic multiplicities of all eigenvalues of A n ( k ) in a neighborhood of k 0 , or on the number of different eigenvalues of A n ( k ) in this neighborhood. The reasoning is based on the fundamental results of the theory of holomorphic operator-valued functions and is important for the theory of microdisk lasers, because it significantly expands the class of devices interesting for applications that allow mathematical modeling based on numerical methods that are strictly justified.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"51 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84595993","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":"Numerical Simulation of Experiments on Determining the Type of Initial Anisotropy of an Elastic Material","authors":"D. Khristich, D. Sukhorukov, M. Sokolova","doi":"10.26907/2541-7746.2021.2.214-225","DOIUrl":"https://doi.org/10.26907/2541-7746.2021.2.214-225","url":null,"abstract":"The concept of canonical axes of anisotropy of the material, in which the largest number of elements of the elastic compliance tensor is equal to zero, is introduced. A program of experiments that allows one to determine the type of an anisotropic material without finding all the components of the elastic compliance tensor in an arbitrary laboratory coordinate system and, simultaneously, to detect the position of the canonical axes of anisotropy in the material is developed. A program of mechanical experiments is proposed to identify the type of initial elastic anisotropy of a material based on the results of experiments in the canonical axes of anisotropy for the case when they coincide with the axes of the laboratory coordinate system. Computer numerical simulation of the experiments is performed. The influence of experimental measurement errors on the identification results is investigated. It is shown that the developed criteria for identifying the type of material are applicable in the presence of measurement errors.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"62 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87178141","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 Quantum Collision Resistant Function","authors":"M. Ablayev","doi":"10.26907/2541-7746.2021.1.90-94","DOIUrl":"https://doi.org/10.26907/2541-7746.2021.1.90-94","url":null,"abstract":"In the classical hashing theory, collision is a coincidence of the values of a function with different arguments. This paper formulates a quantum analogue of the collision property. A variant of formalization of the concept of quantum function resistant to collisions was proposed. Within the framework of this formalization, the theorem (sufficient condition) on the quantum function that is resistant to collisions was proved.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"61 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86119776","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":"Structure and Relations of a Multi-Level Mathematical Model for Describing Microcracks Formation during Polycrystals Deformation","authors":"K. A. Kurmoiartseva, N. Kotelnikova, P. Volegov","doi":"10.26907/2541-7746.2021.2.197-213","DOIUrl":"https://doi.org/10.26907/2541-7746.2021.2.197-213","url":null,"abstract":"The mechanical behavior of parts is significantly affected by the material’s internal defective structure and its evolution. The paper aims to build a complex physically based mathematical model for describing the behavior of metals in the deformation and destruction pro-cess. The main deformation mechanisms of metals and alloys are considered. The mechanism and criterion for the microcrack nucleation, as well as a method for microcracks describing, are outlined. The structure and main relations of the developed model are presented, inclu-ding a description of the most significant mechanisms carriers evolution implemented at each structural-scale level. A submodel of the evolution of dislocation densities during deformation due to such mechanisms as the new dislocations generation and opposite dislocations anni-hilation on close slipping systems is described. The algorithm for implementing the model and the results of modeling the dislocation structure evolution are presented. The multi-level approach based on the crystal plasticity and the introduction of internal variables is found to be sufficiently effective for describing both the propagation and nucleation of microcracks in metals.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"104 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87988415","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":"Mathematical Modeling of Sorption Processes Considering the Transformation of the Porous Matrix","authors":"M. Kravchenko, M. I. Ivlev, K.D. Pantelei","doi":"10.26907/2541-7746.2021.2.128-142","DOIUrl":"https://doi.org/10.26907/2541-7746.2021.2.128-142","url":null,"abstract":"The paper addresses the results of the polymer flooding process hydrodynamic modeling considering changes in the reservoir properties of the porous matrix and the fluids properties. Application of a multiphase filtration mathematical model requires the system closure considering the data of oil displacement with a specific type of polymer. A method for processing the results of the experiment on core samples with displacement process modeling, considering the real-time transformation of the pore size distribution curve during polymer adsorption, is suggested. Based on the hydrodynamic calculations, we estimate the dependence of the rate of the adsorption process on the concentration of the polymer solution, the rate of pumping of the surfactant through the sample, the processing time, and the current thickness of the polymer film formed for the specific compositions and structure of the sample used. A comparison of the simulation results with the data of dynamic experiments on oil displacement with Gum Arabic polymer solution showed a good correlation of the calculated and experimental data, which confirms the possibility of using a hydropercolation approach to predict the oil recovery coefficient when using various polymer substances at specific fields.","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"119 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89550892","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":"Evolution of Acoustic Pulses in Damaged Underground Pipelines","authors":"V. Shagapov, E. Galiakbarova, Z. R. Chakimova","doi":"10.26907/2541-7746.2021.1.48-58","DOIUrl":"https://doi.org/10.26907/2541-7746.2021.1.48-58","url":null,"abstract":"","PeriodicalId":41863,"journal":{"name":"Uchenye Zapiski Kazanskogo Universiteta-Seriya Fiziko-Matematicheskie Nauki","volume":"137 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86588707","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}