Lobachevskii Journal of Mathematics最新文献

英文中文

From Texts to Knowledge Graph in the Semantic Library LibMeta 语义图书馆 LibMeta 从文本到知识图谱

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602625

O. M. Ataeva, V. A. Serebryakov, N. P. Tuchkova

Abstract

The problem of constructing a knowledge graph for previously unprocessed scientific texts is studied. The task is to analyze the use of various machine processing methods for extracting text semantics using the example of an interdisciplinary subject area. The goal of the research is to create a semantic model of the subject area of an interdisciplinary scientific journal and use a knowledge graph to navigate through data. The semantic model is based on the ontology of the LibMeta library. Texts and metadata receive connections due to the processing procedure and become part of the ontology of the semantic library. The interdisciplinary subject area is integrated into the library content as a related area of the ‘‘mathematics’’ ontology of the LibMeta library. A comparison of texts is carried out according to different characteristics, thematic proximity, commonality of research methods and approaches, problem setting and their symbolic representation. The results of preliminary text processing and the results in the form of a knowledge graph integrated into the library content are presented. The formulation of the problem of constructing an ontology and a knowledge graph for an interdisciplinary subject area adjacent to mathematics is considered by the authors as part of the general problem of managing mathematical knowledge.

摘要研究了为以前未经处理的科学文本构建知识图谱的问题。任务是以跨学科主题领域为例，分析使用各种机器处理方法提取文本语义的情况。研究的目标是创建跨学科科学期刊主题领域的语义模型，并使用知识图谱来浏览数据。语义模型基于 LibMeta 图书馆的本体。文本和元数据在处理过程中会产生连接，并成为语义图书馆本体的一部分。跨学科主题领域作为 LibMeta 图书馆 "数学 "本体的相关领域被整合到图书馆内容中。根据文本的不同特征、主题接近性、研究方法和途径的共性、问题设置及其符号表示，对文本进行比较。初步文本处理的结果和以知识图谱的形式整合到图书馆内容中的结果都已呈现。作者认为，为邻近数学的跨学科领域构建本体和知识图谱的问题，是数学知识管理一般问题的一部分。

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引用次数: 0

Probabilistic Analysis of the Coefficients of Stochastic Differential Equations in Their Modeling of the Air–Sea Interaction in the North Atlantic 北大西洋海气相互作用模型中随机微分方程系数的概率分析

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602406

K. P. Belyaev, N. P. Tuchkova, K. A. Romashina

Abstract

The observational data for 1979–2018 in the North Atlantic regionhave been used for the analysis of the heat fluxes. The dynamicsof air-sea interaction between ocean and atmosphere has beenmodeled by the stochastic differential equation (SDE) which usethe heat fluxes observations taken from those databased. Thecoefficients of the SDE represented the diffusion stochasticprocess have been statistically defined from the original dataset.Earlier the existence and uniqueness of the solution in strongsense of SDE generated by the modeled diffusion process has beenproved. In the current work the drift and diffusion coefficientshave been smoothed and approximated by the trigonometric functionswith sought amplitude and phase characteristics within chosenyear. Their spatial and temporal intra-annual variability of thosecharacteristics has been studied and analyzed. Also, thecorresponding Fokker–Planck–Kolmogorov (FPK) equation for theSDE with smoothed coefficients has been constructed andnumerically solved. Numerical calculations realized on theLomonosov-2 supercomputer of the Lomonosov Moscow StateUniversity.

摘要利用北大西洋地区 1979-2018 年的观测数据分析了热通量。通过随机微分方程（SDE）模拟了海洋与大气之间的海气相互作用动态，并利用了这些数据中的热通量观测资料。由建模扩散过程生成的 SDE 的广义解的存在性和唯一性已经得到证明。在目前的工作中，漂移和扩散系数已被平滑化，并用三角函数近似，其振幅和相位特征在所选年份内得到了寻求。研究和分析了这些特征的空间和时间年内变率。此外，还构建并数值求解了平滑系数SDE 的相应 Fokker-Planck-Kolmogorov (FPK) 方程。数值计算在莫斯科国立罗蒙诺索夫大学的罗蒙诺索夫-2 超级计算机上实现。

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引用次数: 0

A Mathematical Model of Rod Lateral Oscillations Considering an External Tangential Load 考虑外部切向载荷的杆侧摆动数学模型

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602431

I. V. Kudinov, A. V. Pashin, Yu. A. Kryukov

Abstract

A mathematical model has been developed for lateral oscillations of a rod fixed at one end, taking into account internal friction and external tangential harmonic loading. Analysis of the results of numerical calculations has shown that when the natural oscillation of the rod coincide with the external load frequency, resonant oscillations occur, accompanied by significant increase in the amplitude of rod oscillations, limited by the friction coefficient. At load frequencies approaching to the natural oscillation frequency, the amplitude of oscillations at each point of the rod is accompanied by periodic increase and decrease, qualifying them as bifurcation-flutter oscillations (beats). When the amplitude and frequency of the load oscillation change, the rod oscillations occur in the form of wave packets with amplitude-frequency modulation. In general, rod oscillations occur with an infinitely large number of amplitudes and frequencies. The maximum frequency at minimum amplitude is observed in sections of the rod close to the fixed end.

摘要在考虑到内部摩擦和外部切向谐波载荷的情况下，为一端固定的杆的横向振荡建立了数学模型。对数值计算结果的分析表明，当杆件的自然振荡频率与外部载荷频率相吻合时，就会产生共振振荡，同时杆件振荡的振幅会显著增加，但会受到摩擦系数的限制。当载荷频率接近自然振荡频率时，杆件各点的振幅会出现周期性的增大和减小，这就是分叉-扑动振荡（节拍）。当负载振荡的振幅和频率发生变化时，杆振荡以振幅-频率调制的波包形式出现。一般来说，杆振荡的振幅和频率都是无限大的。在靠近固定端的杆段，可以观察到最小振幅下的最大频率。

引用次数: 0

Mathematical Model of Asphaltene Deposition During Oil Production 石油生产过程中沥青质沉积的数学模型

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602303

A. I. Nikiforov, G. A. Nikiforov

Abstract

Asphaltenes are heavy hydrocarbon molecules that exist naturally in petroleum reservoir fluids. Asphaltene precipitation may occur during pressure depletion or during gas injection processes to improve oil recovery. Inside the reservoir, the precipitated asphaltene can deposit onto the rock surface or remain as a suspended solid in the oil phase. Precipitated asphaltenes are one of the main causes of decreased permeability. A new approach to modeling asphaltene deposition during oil production has been developed. In the model, oil is represented by two hydrocarbon components (‘‘oil’’ and ‘‘asphaltene’’) that do not dissolve in water and the theory of an ideal solution of a binary mixture is used. Closing relations for the mass and momentum conservation equations describing porosity, permeability and mass transfer are constructed using the pore size distribution function and a model of an ideal porous medium consisting of a bundle of capillaries.

摘要沥青质是天然存在于石油储层流体中的重烃分子。沥青质析出可能发生在压力耗竭过程中，也可能发生在为提高石油采收率而注入气体的过程中。在储层内部，沉淀的沥青质可以沉积在岩石表面，也可以作为悬浮固体留在油相中。沉淀沥青质是导致渗透率下降的主要原因之一。我们开发了一种新方法来模拟石油生产过程中的沥青质沉积。在该模型中，石油由两种不溶于水的碳氢化合物成分（"石油 "和 "沥青质"）表示，并使用二元混合物理想溶液理论。利用孔径分布函数和由毛细管束组成的理想多孔介质模型，构建了描述孔隙度、渗透性和传质的质量和动量守恒方程的闭合关系。

引用次数: 0

Propagation of Acoustic Waves in a Moving Monodispersed Gas Suspension 声波在移动的单分散气体悬浮液中的传播

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602376

E. A. Teregulova

Abstract

In this work, we study the propagation of plane acoustic waves in a uniformly moving monodispersed gas suspension. A mathematical model was constructed and the dispersion relation was obtained.

摘要在这项工作中，我们研究了平面声波在均匀移动的单分散气体悬浮液中的传播。我们建立了一个数学模型，并得到了频散关系。

引用次数: 0

Metric Effects in Event Space and Einstein’s Gravitation Theory 事件空间的度量效应与爱因斯坦引力理论

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s199508022460239x

P. A. Belov, S. A. Lurie

Abstract

A variant of the mechanistic gravitation theory is considered as a 4D theory of elasticity of the event space. A 4D displacement vector is introduced, where the fourth component is the local uneven time of the physical process generating the gravitational field. An analysis of the kinematic model of the mechanistic theory of gravity is presented. It is shown that Einstein’s gravity is a particular theory of the 4D theory of elasticity of the event space with a field of defects. Kinematic models of 4D space-time continuum are proposed, allowing to formulate the variational mechanistic models of gravity. Lagrangian of gravitational field models are formulated for the kinematic variables of a defect-free space–time continuum, continuum with conserved dislocations and a 4D space-time continuum with generated dislocations and conserved disclinations.

摘要机械引力理论的一个变体被视为事件空间的 4D 弹性理论。引入了一个 4D 位移矢量，其中第四分量是产生引力场的物理过程的局部不均匀时间。对引力力学理论的运动模型进行了分析。研究表明，爱因斯坦引力是具有缺陷场的事件空间弹性 4D 理论的一种特殊理论。提出了 4D 时空连续体的运动学模型，从而可以制定万有引力的变分力学模型。针对无缺陷时空连续体、具有守恒位错的连续体以及具有生成位错和守恒位错的 4D 时空连续体的运动变量，提出了引力场模型的拉格朗日。

引用次数: 0

Numerical Simulation of Inverse Retrospective Problems for a Two-Dimensional Heat Equation 二维热方程逆回溯问题的数值模拟

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602583

S. A. Kolesnik, E. M. Stifeev

Abstract

The paper proposes a new, unique method for numerically solving inverse problems for nonlinear conditions using the example of the problem of restoring the initial condition for a two-dimensional heat equation with boundary conditions of the third kind. In this problem, the initial condition is an unknown function of two variables, and is determined from experimental temperature values. The proposed method is based on using the parametric identification method, the implicit gradient descent method and Tikhonov’s regularization method. An algorithm and a software package for numerical solution have been developed. The use of the implicit gradient descent method allowed for faster convergence (number of iterations) compared to zero-order methods. Numerous results of numerical experiments have been obtained and discussed. An analysis of the behavior of solution functions with and without the use of Tikhonov’s regularizing functional along with the impact of the regularizing parameter has been carried out. The results of computational experiments using the proposed numerical method showed that the error in the results obtained does not exceed the error in the experimental data due to the correct choice of the regularizing parameter.

摘要本文以具有第三类边界条件的二维热方程的初始条件恢复问题为例，提出了一种新的、独特的非线性条件逆问题数值求解方法。在这个问题中，初始条件是两个变量的未知函数，由实验温度值确定。所提出的方法基于参数识别法、隐式梯度下降法和 Tikhonov 正则化方法。已开发出一种算法和一个用于数值求解的软件包。与零阶方法相比，使用隐式梯度下降法可以更快地收敛（迭代次数）。获得并讨论了大量数值实验结果。对使用和不使用季霍诺夫正则函数的求解函数的行为以及正则参数的影响进行了分析。使用所提出的数值方法进行计算实验的结果表明，由于正则化参数的正确选择，所得结果的误差不会超过实验数据的误差。

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引用次数: 0

Nonlinear Resonant Gas Oscillations in Resonators with Variable Cross-section 可变截面谐振器中的非线性共振气体振荡

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602170

D. A. Gubaidullin, B. A. Snigerev

Abstract

In a number of studies, it has been shown that the geometry of an acoustic resonator strongly affects its resonant frequencies, as well as the nonlinear shape of the standing pressure waves generated inside the cavity. In this paper, we consider three resonators with different wall shapes (cone, exponential and bulb-shaped resonators) in which gas vibrations are formed due to an external periodic force. The acoustic field in the resonators is generated by the vibration of the left wall of the enclosure. The oscillation frequency of this wall is chosen so that the lowest acoustic mode can propagate along the resonator. The fully compressible form of the Navier–Stokes equations is used, and the explicit time-stepping algorithm is employed for modeling the motion of acoustic waves. The structure of acoustic flows of the second order, resulting from the interaction between the wave field and viscous effects on the walls, leads to the formation of flow patterns. These patterns can be revealed by averaging solutions over a specific period of time. To evaluate the performance of resonators, the pressure amplitude gain factor is used. This is defined as the ratio of pressure amplitude at the small end of the resonator to the pressure amplitude at its large end. It has been found that the best performance is observed in a flask-shaped resonator.

摘要大量研究表明，声共振器的几何形状对其谐振频率以及腔内产生的驻留压力波的非线性形状有很大影响。在本文中，我们考虑了三个具有不同壁形（锥形、指数形和球形谐振器）的谐振器，在这些谐振器中，气体振动是由外部周期性力引起的。谐振器中的声场由外壳左壁的振动产生。选择这面墙的振动频率是为了让最低的声学模式能够沿着谐振器传播。采用纳维-斯托克斯方程的完全可压缩形式，并使用显式时间步进算法来模拟声波的运动。二阶声波流的结构是由波场和壁面上的粘性效应相互作用产生的，从而形成了流动模式。通过对特定时间段内的解求取平均值，可以揭示这些模式。为了评估谐振器的性能，使用了压力振幅增益因子。其定义为谐振器小端压力振幅与大端压力振幅之比。研究发现，瓶形谐振器的性能最佳。

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引用次数: 0

Estimation of Oil Reservoir Transmissivity and Storativity Fields Using a Radial Basis Function Network Based on Inverse Problem Solving 利用基于逆问题求解的径向基函数网络估算油藏渗透率和储量场

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s199508022460225x

V. P. Kosyakov, D. Yu. Legostaev

Abstract

In the oil industry, there is a noticeable trend towards using proxy models to simulate various levels of complexity in order to make operational predictions. In particular, machine learning techniques are being actively developed in the context of the digitalization and automation of production processes. This paper proposes a method for combining a physically relevant fluid flow model with machine learning techniques to address the challenges of history-matching and prediction. The approach is demonstrated using synthetic oil reservoir models. The synthetic model has significant zonal inhomogeneities in the permeability and storativity fields. The simplified single-phase flow through a porous medium model was used for the proposed approach. This model was matched to the historical values of the development parameters by restoring the fields of the reservoir parameters. Properties fields were reconstructed using a radial basis functions network and a fully connected linear layer. Based on the reconstructed field, interwell connectivity coefficients were calculated, which corresponded qualitatively and quantitatively to the true interwell connectivity coefficients. The predictive characteristics of the proposed approach were evaluated by split the historical dataset into training and test time intervals.

摘要在石油工业中，一个明显的趋势是使用代理模型模拟不同程度的复杂性，以进行业务预测。特别是在生产流程数字化和自动化的背景下，机器学习技术正在得到积极发展。本文提出了一种将物理相关流体流动模型与机器学习技术相结合的方法，以应对历史匹配和预测方面的挑战。该方法使用合成油藏模型进行了演示。合成模型的渗透率和储量场具有明显的分区不均匀性。所提出的方法使用了简化的单相流流经多孔介质模型。通过恢复储层参数场，该模型与开发参数的历史值相匹配。使用径向基函数网络和全连接线性层重建属性场。根据重建的油气田，计算出了井间连通系数，这些系数在定性和定量上都与真实的井间连通系数一致。通过将历史数据集分成训练时间段和测试时间段，对所提方法的预测特性进行了评估。

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引用次数: 0

Refined Analysis of Shear Stress Distribution in Tapered Rods Accounting for Gradient Effects 考虑梯度效应的锥形杆剪应力分布精细分析

IF 0.7 Q2 MATHEMATICS

Lobachevskii Journal of Mathematics

Pub Date : 2024-08-28 DOI: 10.1134/s1995080224602522

A. V. Volkov, K. S. Golubkin, Y. O. Solyaev

Abstract

In this article, we propose to apply the strain gradient elasticity theory for the refined stress analysis in the tapered rods with variable cross section. Corresponding statement of the higher-order boundary value problem with extended set of boundary conditions is derived based on the variational approach. Considering an example for the cylindrical/conical rod loaded by self-equilibrated body and end forces, we provide the comparison between the stress distributions that can be obtained within the classical 3D elasticity, classical 1D rod theory and the established 1D rod theory with the strain gradient effects. It is shown that the last one allows to obtain the smoothed solution for the shear stresses that can be fitted to 3D elasticity solution under appropriate choice of additional length scale parameter of gradient theory. In contrast, solution of classical rod theory cannot be fitted exactly to 3D elasticity solution and contains unavoidable discontinuities of shear stresses.

摘要本文提出应用应变梯度弹性理论对变截面锥形杆进行精细应力分析。基于变分法，推导出了具有扩展边界条件集的高阶边界值问题的相应表述。考虑到圆柱形/圆锥形杆在自平衡体力和端力作用下的载荷实例，我们对经典三维弹性理论、经典一维杆理论和具有应变梯度效应的既定一维杆理论所能获得的应力分布进行了比较。结果表明，在适当选择梯度理论的附加长度尺度参数的情况下，最后一种方法可以获得与三维弹性解相匹配的剪应力平滑解。与此相反，经典杆理论的解无法与三维弹性解精确拟合，并且包含不可避免的剪应力不连续性。

引用次数: 0

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全部化学•材料生命科学医学物理工程技术环境•农林材料科学地球科学法学管理学化学环境科学与生态学计算机科学教育学经济学农林科学人文科学生物学数学物理与天体物理心理学综合性期刊其他工业工程理学历史学农学文学信息工程

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