Pub Date : 2026-03-04DOI: 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.
{"title":"Complete System of Navier–Stokes Equations: Linearization and Construction of Solutions","authors":"A. A. Bugaenko, I. Yu. Krutova","doi":"10.1134/S1063778825100047","DOIUrl":"10.1134/S1063778825100047","url":null,"abstract":"<p>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.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"88 12","pages":"2425 - 2436"},"PeriodicalIF":0.4,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147352688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-04DOI: 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.
{"title":"Production of a Charged Hadron Beam in the Momentum Range of 2–13 GeV/c at the U-70 Accelerator","authors":"S. F. Reshetnikov, E. V. Barnov, A. N. Vasiliev, V. A. Maisheev, V. V. Moiseev, V. V. Mochalov, Yu. A. Chesnokov","doi":"10.1134/S1063778825110043","DOIUrl":"10.1134/S1063778825110043","url":null,"abstract":"<p>A method for obtaining a beam of charged hadrons in the momentum range of 2–13 GeV/<i>c</i> 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.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"88 12","pages":"2534 - 2539"},"PeriodicalIF":0.4,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147352743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-04DOI: 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.
{"title":"Features and Methods of Protection against the Technogenic Acoustic Background Influencing the Character of γ Spectra Recorded by a Xenon γ Spectrometer","authors":"A. I. Majidov, S. E. Ulin, A. P. Elokhin, A. E. Shustov","doi":"10.1134/S1063778825100229","DOIUrl":"10.1134/S1063778825100229","url":null,"abstract":"<p>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.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"88 11","pages":"2317 - 2320"},"PeriodicalIF":0.4,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147352802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-04DOI: 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.
{"title":"Peculiarities of Anisotropic Ultrasonic Radiation Passage in Deep-Water Sea Areas","authors":"A. P. Elokhin, S. E. Ulin, A. E. Shustov, N. M. Sveshnikov","doi":"10.1134/S1063778825100102","DOIUrl":"10.1134/S1063778825100102","url":null,"abstract":"<p>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.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"88 11","pages":"2150 - 2162"},"PeriodicalIF":0.4,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147352806","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-04DOI: 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.
{"title":"Simulation Results of Dry Deposition of Radioactive Aerosols in the Arctic Regions of the Far North","authors":"D. A. Pripachkin, I. D. Sadofev","doi":"10.1134/S1063778825100333","DOIUrl":"10.1134/S1063778825100333","url":null,"abstract":"<p>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.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"88 11","pages":"2328 - 2332"},"PeriodicalIF":0.4,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147352645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-04DOI: 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.
{"title":"Full-Scale ZR-6 and BFS-49/1A Critical Assemblies Calculations Using MNT-CUDA 3.0 Program","authors":"V. A. Varfolomeeva, I. E. Ivanov, O. N. Andrianova, S. A. Bychkov, A. V. Pryanichnikov","doi":"10.1134/S1063778825100448","DOIUrl":"10.1134/S1063778825100448","url":null,"abstract":"<p>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.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"88 12","pages":"2456 - 2463"},"PeriodicalIF":0.4,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147352689","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-04DOI: 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.
{"title":"Estimation of the Capabilities of the SPHERE-3 Cherenkov Telescope for Determining the Parameters of the Primary Cosmic Particle","authors":"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","doi":"10.1134/S1063778825100023","DOIUrl":"10.1134/S1063778825100023","url":null,"abstract":"<p>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.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"88 12","pages":"2522 - 2528"},"PeriodicalIF":0.4,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147352741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-04DOI: 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.
{"title":"Multidimensional Nonlinear Schrödinger Equations with Potential and Dispersion of General Form: Exact Solutions and Reductions","authors":"A. D. Polyanin, N. A. Kudryashov","doi":"10.1134/S1063778825100278","DOIUrl":"10.1134/S1063778825100278","url":null,"abstract":"<p>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 <i>n</i>-dimensional Schrödinger equations of general form.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"88 12","pages":"2437 - 2444"},"PeriodicalIF":0.4,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147352747","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-04DOI: 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.
{"title":"Justification of Steam‑Generator Level Setpoints for the V‑392M Reactor Unit during Normal Operation and during Deviations from Normal Operation","authors":"P. V. Povarov","doi":"10.1134/S106377882510031X","DOIUrl":"10.1134/S106377882510031X","url":null,"abstract":"<p>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.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"88 12","pages":"2358 - 2362"},"PeriodicalIF":0.4,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147352748","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-03-04DOI: 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.
{"title":"Void Reactivity Effect in the MTIR-SKD Multipurpose Test Research Reactor","authors":"A. S. Lapin, Yu. N. Volkov, S. A. Subbotin","doi":"10.1134/S1063778825100205","DOIUrl":"10.1134/S1063778825100205","url":null,"abstract":"<p>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.</p>","PeriodicalId":728,"journal":{"name":"Physics of Atomic Nuclei","volume":"88 12","pages":"2346 - 2353"},"PeriodicalIF":0.4,"publicationDate":"2026-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147352785","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}