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Complete System of Navier–Stokes Equations: Linearization and Construction of Solutions Navier-Stokes方程组的完备系统:线性化和解的构造
IF 0.4 4区 物理与天体物理 Q4 PHYSICS, NUCLEAR Pub Date : 2026-03-04 DOI: 10.1134/S1063778825100047
A. A. Bugaenko, I. Yu. Krutova

Modeling of atmospheric phenomena based on systems of ordinary differential equations and partial differential equations with their subsequent numerical study has been carried out. As a result of discretization of these equations, we arrive at systems with millions and even billions of unknowns. Owing to the nonlinearity of the complete Navier–Stokes system of equations, construction of its solutions is very labor-intensive. As a consequence, a linearization procedure on the exact solution (homogeneous rest) has been applied. For a linearized system, the emergence and development of ascending swirling flows of different intensities has been numerically simulated using blowing up the pipe with allowance for the action of gravity and Coriolis forces. Numerical calculation of the velocity characteristics of a three-dimensional unsteady flow of viscous heat-conducting gas in an ascending swirling flow initiated by vertical blowing has shown that the gas swirl occurs in the positive direction and is caused by the presence of terms describing the Coriolis acceleration in the linearized complete system of Navier–Stokes equations. Thus, the scheme of the emergence of an ascending swirling flow has been numerically confirmed once again. A conclusion about the possibility of applying this approach to the study of ascending swirling flows of the tornado and tropical cyclone types has also been made.

基于常微分方程和偏微分方程系统的大气现象模拟及其随后的数值研究已经开展。由于这些方程的离散化,我们得到了具有数百万甚至数十亿未知数的系统。由于完全Navier-Stokes方程组的非线性,构造它的解是非常费力的。因此,应用了精确解(齐次休息)的线性化过程。对于线性化系统,在考虑重力和科里奥利力作用的情况下,对管道进行吹胀,数值模拟了不同强度的上升旋流的产生和发展。对垂直吹风引起的上升旋流中粘性导热气体三维非定常流场的速度特性进行了数值计算,结果表明,在线性化的Navier-Stokes方程完备系统中,由于存在描述科里奥利加速度的项,气体的旋流发生在正方向上。因此,上升旋涡流出现的方案再次得到了数值证实。并对该方法应用于龙卷风和热带气旋上升旋流研究的可能性作了总结。
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引用次数: 0
Production of a Charged Hadron Beam in the Momentum Range of 2–13 GeV/c at the U-70 Accelerator U-70加速器产生2-13 GeV/c动量范围的带电强子束
IF 0.4 4区 物理与天体物理 Q4 PHYSICS, NUCLEAR Pub Date : 2026-03-04 DOI: 10.1134/S1063778825110043
S. F. Reshetnikov, E. V. Barnov, A. N. Vasiliev, V. A. Maisheev, V. V. Moiseev, V. V. Mochalov, Yu. A. Chesnokov

A method for obtaining a beam of charged hadrons in the momentum range of 2–13 GeV/c has been implemented at the SPASCHARM facility of the U-70 accelerator complex for methodological studies. A scheme for obtaining such a beam has been demonstrated using a crystal deflector placed in the vacuum chamber of the U-70 strong focusing accelerator to extract primary protons onto an external aluminum target. It has been shown that this method allows for obtaining beams of charged particles in the specified momentum range for methodological studies.

在U-70加速器综合体的SPASCHARM设施上实现了一种获得2-13 GeV/c动量范围的带电强子束的方法,用于方法学研究。利用放置在U-70强聚焦加速器真空室中的晶体偏转器将初级质子提取到外部铝靶上,证明了一种获得这种光束的方案。已经证明,这种方法可以获得在特定动量范围内的带电粒子束,用于方法学研究。
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引用次数: 0
Features and Methods of Protection against the Technogenic Acoustic Background Influencing the Character of γ Spectra Recorded by a Xenon γ Spectrometer 影响氙γ能谱仪记录的γ光谱特征的技术声背景的特点和防护方法
IF 0.4 4区 物理与天体物理 Q4 PHYSICS, NUCLEAR Pub Date : 2026-03-04 DOI: 10.1134/S1063778825100229
A. I. Majidov, S. E. Ulin, A. P. Elokhin, A. E. Shustov

In this paper, the influence of a technogenic acoustic background on the formation of a γ spectrum recorded by a xenon γ spectrometer is considered. It is shown that the technogenic acoustic background significantly deforms the spectrum to broaden the total absorption peak and decrease its amplitudes as compared to the spectrum recorded in the absence of acoustic load. Such deformation of the total absorption peak leads to deliberately underestimated values for the parameters of radioactive contamination of the environment under the conditions of radiation accidents and, in the long run, to wrong decisions when ensuring the nuclear safety of personnel and population located near nuclear facilities where the radiation accident occurred. The observed deformation of the γ spectrum requires a protective coating of the γ spectrometer with porous rubber used to absorb acoustic loads. The results have proven to be satisfactory as a whole, but the weight and overall dimensions of the γ spectrometer have substantially increased. As an alternative protection instead of porous rubber, the authors propose to place the detector in a metallic thin-wall capsule and evacuate the air from it, i.e., to protect the xenon γ spectrometer with a “vacuum shell” formed in the absence of an elastic medium (air) in the capsule. This method of protection is characterized by simplicity and availability and does not require high financial expenditures.

本文考虑了技术声背景对氙γ谱仪记录的γ谱形成的影响。结果表明,与无声负荷时相比,技术声背景显著地使光谱变形,使总吸收峰变宽,并使其幅度减小。总吸收峰的这种变形,导致在辐射事故条件下,故意低估环境放射性污染参数的值,从长远来看,会导致在确保辐射事故发生地点核设施附近人员和人口的核安全时做出错误的决策。观察到的γ谱的变形需要用多孔橡胶来吸收声载荷的γ谱仪的保护涂层。结果总体上是令人满意的,但是γ谱仪的重量和整体尺寸大大增加了。作为多孔橡胶的替代保护,作者建议将探测器放置在金属薄壁胶囊中并从中抽出空气,即在胶囊中没有弹性介质(空气)的情况下形成“真空壳”来保护氙γ光谱仪。这种保护方法的特点是简单易行,不需要很高的财政支出。
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引用次数: 0
Peculiarities of Anisotropic Ultrasonic Radiation Passage in Deep-Water Sea Areas 深水区各向异性超声辐射通道特性
IF 0.4 4区 物理与天体物理 Q4 PHYSICS, NUCLEAR Pub Date : 2026-03-04 DOI: 10.1134/S1063778825100102
A. P. Elokhin, S. E. Ulin, A. E. Shustov, N. M. Sveshnikov

It has been necessary to solve the problem of transmitting to the operator the information received by the underwater dosimetric complex within the framework of the studies devoted to estimations of radioactive contamination of the bottom surface of deep-sea areas. The use of a standard radio channel under these conditions has been impossible, and therefore, it is expedient to use an ultrasonic channel of information transmission. Thus, the issue of ultrasonic anisotropic radiation transmission in deep-water sea areas has been considered. Anisotropy of radiation is necessary to reduce the error and increase the reliability of information transmission. A boundary value problem to estimate the ultrasound pressure on the aquatic medium has been formulated and its solution as a wave equation in seawater has been provided. Attention has been paid to such characteristics of seawater areas as water salinity, liquid column pressure determining its density, temperature, and range of radiation propagation with allowance for its frequency characteristics. The problem has been solved by the known method of separation of variables in spherical geometry with allowance for the anisotropy of radiation, the specified characteristics of which are determined on the basis of the optimal selection of the radiation direction to the ultrasonic buffer device located on the water surface of the water area that is determined experimentally. The results of calculations have shown that, at the radiation frequency of 1 kHz, the detector reliably registers the signal at a distance of ~1 km. As the frequency increases, the signal is noticeably absorbed and, at a radiation frequency of ~40 kHz, begins to drop sharply from a distance of ~20 m. Similar results have been obtained when the problem is solved in the form of radiation of a wide beam. The results of solving the problems make it possible to formulate certain requirements for the design of ultrasonic detectors used for underwater transmission of information, which will make it possible to implement the method of information transmission from deep-water areas when using an underwater dosimetric complex and, in addition, to develop a sound method of communication in deep-water areas, which will play a significant role in solving the problems of information transmission under these specific conditions.

有必要在专门估计深海地区底表面放射性污染的研究框架内,解决向操作者传送水下剂量测量复合体收到的资料的问题。在这些条件下使用标准的无线电信道是不可能的,因此,使用超声波信道进行信息传输是权宜之计。因此,研究了深水区超声各向异性辐射传输问题。辐射的各向异性是减小误差和提高信息传输可靠性所必需的。本文提出了一个估算水介质超声压力的边值问题,并给出了其在海水中的波动方程的解。在考虑到其频率特性的情况下,关注了海水区域的水盐度、决定其密度、温度和辐射传播范围的液柱压力等特性。在考虑辐射各向异性的情况下,利用球面几何中已知的分离变量方法解决了这一问题,在实验确定的水面上超声波缓冲装置的辐射方向的最优选择的基础上确定了辐射各向异性的规定特性。计算结果表明,在1 kHz的辐射频率下,探测器可以可靠地记录到距离约1 km的信号。随着频率的增加,信号被明显吸收,在~40 kHz的辐射频率处,信号在~20 m的距离处开始急剧下降。当以宽光束辐射的形式解决问题时,也得到了类似的结果。这些问题的解决结果,为水下信息传输用超声波探测器的设计提出了一定的要求,使利用水下剂量计复合体实现深水区域信息传输的方法成为可能,并使深水区域的通信方法得到完善。这将对解决这些特定条件下的信息传递问题起到重要作用。
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引用次数: 0
Simulation Results of Dry Deposition of Radioactive Aerosols in the Arctic Regions of the Far North 远北北极地区放射性气溶胶干沉降的模拟结果
IF 0.4 4区 物理与天体物理 Q4 PHYSICS, NUCLEAR Pub Date : 2026-03-04 DOI: 10.1134/S1063778825100333
D. A. Pripachkin, I. D. Sadofev

This study presents modeling of the dry deposition of radioactive aerosols in the Arctic regions of the Far North using a model of aerosol dry deposition on heterogeneous underlying surfaces. The model accounts for the influence of aerosol particle size and density, surface roughness characteristics, and the dynamic friction velocity determined on the basis of boundary-layer and surface-layer parameterization in the applied version of the WRF-ARW model. Estimates have been obtained of radioactive aerosol contamination of the ground surface for particle sizes of 0.1, 1, and 10 μm in Arctic regions of the Far North (the Yamal and Kola peninsulas) with heterogeneous underlying surfaces under real meteorological conditions during summer and winter. It is shown that radioactive aerosol contamination of the ground surface on the Yamal and Kola peninsulas depends on particle size and the type of underlying surface in summer and winter. The greatest spatial heterogeneity of contamination and its dependence on the type of underlying surface are observed for particles smaller than 1 μm, while for larger particles, the determining factors are terrain and meteorological conditions at the time of release. The results of numerical modeling will reduce the uncertainty in estimates of radioactive aerosol contamination of terrain and improve their reliability for purposes of analysis and ensuring public safety, including assessment of environmental impacts of radioactive aerosols generated at nuclear energy facilities currently operating and planned for operation in the Arctic regions of the Far North.

本研究采用非均质下垫面的气溶胶干沉降模式,对远北北极地区放射性气溶胶的干沉降进行模拟。该模式考虑了WRF-ARW模式应用版本中基于边界层和表层参数化确定的气溶胶粒径和密度、表面粗糙度特征以及动态摩擦速度的影响。在夏季和冬季的真实气象条件下,获得了远北地区(亚马尔半岛和科拉半岛)具有非均匀下垫面的北极地区地表粒径为0.1、1和10 μm的放射性气溶胶污染的估计。结果表明,亚马尔半岛和科拉半岛夏季和冬季地表放射性气溶胶污染与颗粒物大小和下垫面类型有关。对于小于1 μm的颗粒,污染的空间异质性和对下垫面类型的依赖性最大,而对于较大的颗粒,污染的决定因素是释放时的地形和气象条件。数值模拟的结果将减少对地形放射性气溶胶污染估计的不确定性,并提高其分析和确保公共安全的可靠性,包括评估目前在远北北极地区运行和计划运行的核能设施产生的放射性气溶胶对环境的影响。
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引用次数: 0
Full-Scale ZR-6 and BFS-49/1A Critical Assemblies Calculations Using MNT-CUDA 3.0 Program 基于MNT-CUDA 3.0的全尺寸ZR-6和BFS-49/1A关键组件计算
IF 0.4 4区 物理与天体物理 Q4 PHYSICS, NUCLEAR Pub Date : 2026-03-04 DOI: 10.1134/S1063778825100448
V. A. Varfolomeeva, I. E. Ivanov, O. N. Andrianova, S. A. Bychkov, A. V. Pryanichnikov

The article presents the results on MNT-CUDA 3.0 verification and validation on full-scale calculations of light-water ZR-6 and ZR-6M and fast-neutron BFS-49/1A critical assemblies. MNT-CUDA 3.0—a newly developed high-precision engineering code—is aimed at conducting neutron-physical core calculations of various types of nuclear reactors using the multi-group Monte Carlo method. The leverage of graphic processing units’ (GPUs) parallel processing capabilities significantly reduces calculation time. MNT-CUDA 3.0 has a flexible module architecture. Modules of multi-group libraries generation allow to conduct calculations using the data either prepared by the MCU precise code or from multi-group constants library of general purpose ABBN-RF. For full-scale calculations a preprocessor was developed allowing to build a system’s geometry from primitives created by user. It provides the opportunity to describe benchmark models of ZR-6 and BFS critical assemblies without using any significant simplifications. The comparison between multiplication factor calculation results and experimental ones are presented in the paper as well as the discrepancies in flux in every fuel rod, generation rates in every out of 65 energy groups, radial and axial flux distributions between MNT-CUDA calculation results and MCU and MCNP precise codes calculations.

本文介绍了MNT-CUDA 3.0对轻水ZR-6、ZR-6M和快中子BFS-49/1A临界组件全尺寸计算的验证结果。MNT-CUDA 3.0是一种新开发的高精度工程代码,旨在使用多群蒙特卡罗方法进行各种类型核反应堆的中子物理堆芯计算。图形处理单元(gpu)的并行处理能力显著减少了计算时间。MNT-CUDA 3.0具有灵活的模块架构。多组库生成模块允许使用MCU精确代码或通用ABBN-RF多组常数库准备的数据进行计算。对于全尺寸计算,开发了一个预处理器,允许从用户创建的原语构建系统的几何形状。它提供了描述ZR-6和BFS关键组件的基准模型的机会,而无需使用任何重要的简化。本文将乘法系数计算结果与实验结果进行了比较,并比较了MNT-CUDA计算结果与MCU和MCNP精确代码计算结果在各燃料棒通量、65个能量组中各能量组的产生率、径向和轴向通量分布等方面的差异。
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引用次数: 0
Estimation of the Capabilities of the SPHERE-3 Cherenkov Telescope for Determining the Parameters of the Primary Cosmic Particle 估算SPHERE-3切伦科夫望远镜确定主要宇宙粒子参数的能力
IF 0.4 4区 物理与天体物理 Q4 PHYSICS, NUCLEAR Pub Date : 2026-03-04 DOI: 10.1134/S1063778825100023
E. A. Bonvech, O. V. Cherkesova, D. V. Chernov, E. L. Entina, V. I. Galkin, V. A. Ivanov, T. A. Kolodkin, N. O. Ovcharenko, D. A. Podgrudkov, T. M. Roganova, M. D. Ziva

New results of modeling the operation of the new SPHERE-3 Cherenkov telescope are presented. The telescope will be able to detect cosmic particles by direct and reflected Cherenkov light of the extensive air showers (EAS). Dual detection improves the accuracy of determining the parameters of the primary particle. The study is based on the data bank of distributions of the EAS Cherenkov light obtained on the Lomonosov-2 supercomputer. The accuracy of determining the energy and type of the primary particle from the reflected and direct flux of Cherenkov light is estimated.

介绍了新的SPHERE-3切伦科夫望远镜运行建模的新结果。望远镜将能够通过直接和反射切伦科夫光的广泛的空气阵雨(EAS)来探测宇宙粒子。双重检测提高了测定主粒子参数的准确性。该研究基于在罗蒙诺索夫-2超级计算机上获得的EAS切伦科夫光分布数据库。估计了由切伦科夫光的反射通量和直接通量确定主粒子能量和类型的精度。
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引用次数: 0
Multidimensional Nonlinear Schrödinger Equations with Potential and Dispersion of General Form: Exact Solutions and Reductions 具有一般形式的势和色散的多维非线性Schrödinger方程:精确解和约简
IF 0.4 4区 物理与天体物理 Q4 PHYSICS, NUCLEAR Pub Date : 2026-03-04 DOI: 10.1134/S1063778825100278
A. D. Polyanin, N. A. Kudryashov

Multidimensional nonlinear Schrödinger equations of general form with potential and dispersion specified by one or two arbitrary functions are studied. The equations under consideration naturally generalize a number of related nonlinear partial differential equations encountered in different areas of theoretical physics, including nonlinear optics, superconductivity, and plasma physics. One- and multidimensional non-symmetry reductions leading the studied nonlinear Schrödinger equations to simpler equations of lower dimensions or ordinary differential equations (or systems of ordinary differential equations) are described. Particular attention is paid to the search for solutions with radial symmetry. Using methods of generalized and functional separation of variables, new exact solutions are found in quadratures or elementary functions for two- and n-dimensional Schrödinger equations of general form.

研究了由一个或两个任意函数指定势和色散的一般形式的多维非线性Schrödinger方程。所考虑的方程自然地推广了在理论物理的不同领域中遇到的一些相关的非线性偏微分方程,包括非线性光学、超导和等离子体物理。描述了将所研究的非线性Schrödinger方程转化为更简单的低维方程或常微分方程(或常微分方程系统)的一维和多维非对称约简。特别注意的是寻找具有径向对称性的解。利用变量的广义分离和泛函分离的方法,找到了二维和n维Schrödinger一般形式方程的正交或初等函数的新的精确解。
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引用次数: 0
Justification of Steam‑Generator Level Setpoints for the V‑392M Reactor Unit during Normal Operation and during Deviations from Normal Operation V - 392M反应堆机组在正常运行和偏离正常运行期间的蒸汽发生器液位设定值的论证
IF 0.4 4区 物理与天体物理 Q4 PHYSICS, NUCLEAR Pub Date : 2026-03-04 DOI: 10.1134/S106377882510031X
P. V. Povarov

The ability to carry load through transients without reaching the actuation conditions of reactor safety systems and emergency shutdown is termed the dynamic stability of an NPP power unit. The water level in steam generators of the VVER‑1200 reactor unit (V‑392M) is regulated to maintain a balance among steam removal, blowdown, and feedwater supply. A change in steam‑generator water level caused by transients can reach technological protection and blocking setpoints, followed by a trip of the main circulation pump and a load reduction. Analysis of commissioning tests at the Novovoronezh, Leningrad, and Belarusian NPP units, together with recorded main‑equipment trips due to steam‑generator level deviations, made it possible to identify ways to enhance the dynamic stability of VVER‑1200 units. Maintaining the nominal water level in the steam generator prevents admission of steam to the turbine with humidity exceeding 1%. There are realistic prospects to improve the dynamic stability of VVER‑1200 units by upgrading the shutoff valves at the steam‑generator feed unit to increase their speed of response and by making corresponding adjustments to steam‑generator water‑level setpoints. Enhancing the dynamic stability of VVER‑1200 units will provide a significant additional contribution to the economic attractiveness of the improved domestically designed NPP project.

在不达到反应堆安全系统的驱动条件和紧急停机的情况下,核电机组的动态稳定性被称为核电机组的动态稳定性。VVER - 1200反应堆机组(V - 392M)蒸汽发生器的水位是调节的,以保持蒸汽去除、排污和给水供应之间的平衡。瞬变引起的蒸汽发生器水位变化可达到技术保护设定值和堵塞设定值,随后主循环泵跳闸并减少负荷。通过对新沃罗涅日、列宁格勒和白俄罗斯核电站机组调试试验的分析,以及由于蒸汽发生器液位偏差导致的主要设备行程记录,可以确定提高VVER - 1200机组动态稳定性的方法。保持蒸汽发生器的标称水位,防止湿度超过1%的蒸汽进入汽轮机。通过升级蒸汽发生器给水装置的关闭阀以提高其响应速度,并对蒸汽发生器水位设定值进行相应的调整,提高VVER - 1200机组的动态稳定性具有现实的前景。提高VVER - 1200机组的动态稳定性将为改进后的国产核电站项目的经济吸引力提供重要的额外贡献。
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引用次数: 0
Void Reactivity Effect in the MTIR-SKD Multipurpose Test Research Reactor MTIR-SKD多用途试验研究堆中的空洞反应性效应
IF 0.4 4区 物理与天体物理 Q4 PHYSICS, NUCLEAR Pub Date : 2026-03-04 DOI: 10.1134/S1063778825100205
A. S. Lapin, Yu. N. Volkov, S. A. Subbotin

The problem of the positive void reactivity effect is considered for reactors operating in the fast neutron spectrum, in particular, for the VVER-SKD reactor. The relevance of the study is explained by the need to ensure the safety of these reactors under the conditions of out-of-design accidents. The study is focused on the MTIR-SKD reactor application as an experimental platform for analysis of the void reactivity effect. It is shown that void reactivity effects with the opposite signs can be obtained by changing the composition of the fuel and reflectors. It is expected that a negative void reactivity effect will be implemented to ensure safety at the first stage of work with the reactor, and it may be changed later to the positive one. In the first part of the work, the neutron balances have been calculated, which reveal the mechanisms of the void reactivity effect formation. It is shown that a steel reflector and the plutonium-240 isotope significantly affect the positive void reactivity effect. Options to achieve negative and zero void reactivity effects are discussed, whereas the positive effect can be achieved using high-background plutonium, which eliminates the risk of uncontrolled reactor runaway. The results can be used as a basis for justifying safe operation of the VVER-SKD reactor with a positive void reactivity effect. This work has both scientific and practical significance for the development and design of safe new-generation nuclear reactors that provide reliable reactivity control under various operating conditions.

在快中子谱中运行的反应堆,特别是VVER-SKD反应堆,考虑了正空洞反应性效应的问题。研究的意义在于,需要确保这些反应堆在超出设计的事故条件下的安全。重点研究了MTIR-SKD反应器作为空泡反应效应分析实验平台的应用。结果表明,通过改变燃料和反射器的组成,可以获得相反符号的空洞反应性效应。预计在反应堆工作的第一阶段将实施负空性反应性效应,以确保安全,之后可能会改为正空性反应性效应。在第一部分的工作中,计算了中子平衡,揭示了空洞反应性效应形成的机制。结果表明,钢反射镜和钚-240同位素显著影响了正空穴反应性效应。讨论了实现负空洞反应性效应和零空洞反应性效应的方案,而使用高本底钚可以实现正空洞反应性效应,从而消除了反应堆失控失控的风险。研究结果可作为VVER-SKD反应器安全运行的依据。这项工作对于开发和设计在各种工况下提供可靠反应性控制的安全的新一代核反应堆具有重要的科学意义和现实意义。
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引用次数: 0
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Physics of Atomic Nuclei
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