Mathematical simulation of “Shelter” object releases impacts

Methods of mathematical modeling of radiological human impacts are described. Calculation of admissible
 releases at different exploitation stages of New Safe Confinement at the existing ChNPP “Shelter” object are given. Описано методику математичного моделювання впливів на населення за всім...

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Опубліковано в: :Вопросы атомной науки и техники
Дата:2004
Автори: Batiy, V.G., Paskevich, S.A., Rudko, V.M., Sizov, A.A., Shcherbin, V.N.
Формат: Стаття
Мова:Англійська
Опубліковано: Національний науковий центр «Харківський фізико-технічний інститут» НАН України 2004
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Цитувати:Mathematical simulation of “Shelter” object releases impacts / V.G. Batiy, S.A. Paskevich, V.M. Rudko, A.A. Sizov, V.N. Shcherbin // Вопросы атомной науки и техники. — 2004. — № 5. — С. 96-100. — Бібліогр.: 4 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
_version_ 1860086725886345216
author Batiy, V.G.
Paskevich, S.A.
Rudko, V.M.
Sizov, A.A.
Shcherbin, V.N.
author_facet Batiy, V.G.
Paskevich, S.A.
Rudko, V.M.
Sizov, A.A.
Shcherbin, V.N.
citation_txt Mathematical simulation of “Shelter” object releases impacts / V.G. Batiy, S.A. Paskevich, V.M. Rudko, A.A. Sizov, V.N. Shcherbin // Вопросы атомной науки и техники. — 2004. — № 5. — С. 96-100. — Бібліогр.: 4 назв. — англ.
collection DSpace DC
container_title Вопросы атомной науки и техники
description Methods of mathematical modeling of radiological human impacts are described. Calculation of admissible
 releases at different exploitation stages of New Safe Confinement at the existing ChNPP “Shelter” object are given. Описано методику математичного моделювання впливів на населення за всіма можливими шляхами у
 результаті можливого викиду радіоактивних речовин. Надано результати розрахунку допустимих викидів на
 різних етапах експлуатації нового безпечного конфайнменту над існуючим об’єктом “Укриття”
 Чорнобильської АЕС. Описана методика математического моделирования воздействий на население по всем возможным путям
 в результате возможного выброса радиоактивных веществ. Приведены результаты расчета допустимых
 выбросов на различных этапах эксплуатации нового безопасного конфайнмента над существующим
 объектом “Укрытие” Чернобыльской АЭС.
first_indexed 2025-12-07T17:20:19Z
format Article
fulltext MATHEMATICAL SIMULATION OF “SHELTER” OBJECT RELEASES IMPACTS V.G. Batiy, S.A. Paskevich, V.M. Rudko, A.A. Sizov, V.N. Shcherbin Interdisciplinary Scientific and Technical Center “Shelter” of Ukraine’s NAS e-mail: batiy@mntc.org.ua Methods of mathematical modeling of radiological human impacts are described. Calculation of admissible releases at different exploitation stages of New Safe Confinement at the existing ChNPP “Shelter” object are given. PACS: 28.41Te 1. INTRODUCTION During practical activities aimed at operation of New Safe Confinement (NSC) of ChNPP “Shelter” object, diverse works are planned to carry out (dismantle of unstable structures, subsequent retrieval of fuel- containing materials, et al.), which can be resulted in radiation impacts to public and environment. In force of the fact that the NSC will contain a huge amount of nuclear and radioactive materials, it can be referred to radiation hazardous facilities. In conformity with NRBU-97, limitation of public exposure is implemented by way of regulating and monitoring of aerosol releases and water discharges in the course of operating radiation and nuclear facilities. To reduce the releases, admissible release (AR) of radioactive substances into environment must be established, which refers to radiation and hygienic regulations of first group. To solve that task, NSC release modeling must be conducted and impact of these releases to the public should be estimated. Besides, one should identify the critical group of public (i.e. groups, impact on which will be maximal), as well as impact ways that are most intensive in influencing a critical group. AR was evaluated from the condition of non-exceeding relevant release quotes due to all the ways of dose formation (40 µSv/year) at 10 km distance from NSC. 2. PROCEDURE FOR RELEASE IMPACT ESTIMATE To identify release impacts to public, one should estimate effective dose of human exposure with considering all dose formation ways. There are the following main release impacts to a man: • internal exposure conditioned by radioactive substance intake to human organism with food; • internal exposure due to radioactive substance inhalation; • external exposure from radionuclides precipitated on the earth; • external exposure conditioned by staying in radioactive cloud. The following foodstuff makes the basis for man’s food allowance: potable water; bread; potato; cabbage; fruits and berries; leaf vegetables; meat and its processing produce; milk; fish. 3. RADIOACTIVE SUBSTANCE CONCENTRATIONS IN THE AIR AND SOIL. CONTINUOUS RELEASES As release cloud moves, radioactive aerosol precipitate on earth surface. Surface source of external exposure is formed. Radionuclide precipitation density on the soil after release Q (Bq/s) is defined from the formula [1]: )( Z gs GGvQA Λ+= • , (1) where Q – release intensity, Bq/s ; gv – dry precipitation velocity, m/s; G – meteorological dilution factor, s/m3, under which is implied the ratio of volumetric activity of radionuclide in atmosphere to a release per time unit; Λ – wash-out constant, 1−s , depending on precipitation type, raindrop spectrum, precipitation intensity; zG – integral of dilution factor G along vertical coordinate z, s/m3, Ikkr 0=Λ , (2) where I – precipitation intensity, mm/hour; 510−=rk hour/(mm · s) – standard value of absolute rain washing-out ability (for all nuclides beside inert gases), specific for rain intensity I = 1 mm/hour; 0k – relative washing-out ability for diverse precipitation types (see Table 1). ∫= zH z dzzyxGyxG 0 ),,(),( , (3) where zH – height of cloud lower boundary – precipitation source (m). Table 1. Relative washing-out ability for diverse precipitation types [1] Precipitation type 0k Rain 1,0 Rain with thunderstorm 1,1 Snow with thunderstorm 2,4 Rainfall 2,8 Snow 3,0 Drizzle 4,5 Mist 5,0 96 PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2004, № 5. Series: Nuclear Physics Investigations (44), p. 96-100. Rough estimate of meteorological dilution factor in vicinity and at up to 10-km distance behind the zone of near-surface concentration maximum can be made using the procedure of envelope: xuhe xFG )( )2( 2 2/3 η⋅ π = , (4) where η – wind rose oblongness in specified direction; )(xF – cloud exhaustion function; h – release source height, m; u – wind average velocity, m/s; x – distance from a man to release source. This formula gives maximum (conservative) estimates in the sense, that under any law of vertical dispersion factor change and any reiteration of weather conditions, no high concentration values can be obtained. Wind rose oblongness in specified direction is defined by the following formula: 0/ nn=η , (5) where n and 0n – wind direction reiteration in a given azimuth sector under real wind rose and under round wind rose, accordingly. Function of radioactive cloud exhaustion as result of dry precipitation is defined by the following formula: , 2 exp1exp)( 0 2 2                 σ −⋅    σ ⋅−= ∫ x zz dxhAxF (6) where )(/()/2( huvA g⋅π= ; )(hu – horizontal constituent of wind velocity in dependence of effective release height, m/s; zσ – mean-square deflection of admixture distribution in release cloud due to turbulent diffusion in vertical direction, m; phuhu )2/()2()( ⋅= , (7) where )2(u – wind velocity at 2 m height, m/s; р – factor from Table 2. Table 2. Exponential factor values р for wind velocity estimate Air stability category using Pasquill A B C D E F Standard conditions 0,07 0,07 0,10 0,15 0,35 0,55 Urban conditions 0,15 0,15 0,20 0,25 0,40 0,60 Dispersion factors σz are defined in dependence of weather conditions using Smith-Hosker formula:     > ≤ = ,)x(g)x,z(f, ;)x(g)x,z(f),x(g)x,z(f )x( max z max z max z z σσ σ σ 0 00 (8) where max zσ – limiting value zσ for given category of atmospheric stability; 0z – height of underlying surface roughness, cm; x – distance from release source, m. Functions )(xg and ),( 0 xzf are estimated depending of atmosphere stability category due to the following formulae: )1()( 21 21 bb xaxaxg += , (9) [ ] [ ]    ≤+ >+ = сm.10z1 сm;10z1 021 021 0 21 21 ,)xc(xcln ,,)xc(xcln )x,z(f dd dd (10) The main factors needed for estimates are shown in Tables 3-5. Table 3. Factors applicable for estimates of jet lateral dispersion yσ and function )(xg Atmospher e stability category by Pasquill ,max zσ m a1 b1 а2 b2 А 1600 0,112 1,06 5,38·10-4 0,815 B 920 0,130 0,950 6,52·10-4 0,750 C 640 0,112 0,920 9,05·10-4 0,718 D 400 0,098 0,889 1,35·10-3 0,688 E 220 0,0609 0,895 1,96·10-3 0,684 F 100 0,0638 0,783 1,36·10-3 0,672 Table 4. Factors of function ),( 0 xzf modifying zσ for diverse roughness height 0z Roughness height 0z , cm c1 d1 c2 d2 1 1,56 0,0480 6,25·10-4 0,45 4 2,02 0,0269 7,76·10-4 0,37 10 2,73 0 0 0 40 5,16 -0,098 5,38·10-2 0,225 100 7,37 -0,00957 2,33·10-4 0,6 400 11,7 -0,128 2,18·10-5 0,78 Table 5. Roughness height 0z for diverse types of surface microrelief Microrelief 0z , cm Snow, 1 cm high lawn 0,1 Mown and low grass to 15 cm 0,6…2 High grass to 6 cm 4…9 Heterogenous surface with alternate grass areas, shrubs etc. 10…20 Park, forest to 10 m height 20…100 4. RELEASES OF RADIOACTIVE AEROSOL ADMIXTURES INTO ATMOSPHERE According to [1], individual average annual dose rate is conditioned by intake of radioactive substances in human organism with foodstuff, is defined as follows: FDs KAH ⋅= •• , (11) where – individual average annual dose rate, Sv/s; • sA – contamination intensity, Bq/(m2⋅c). igFIFD BKK ⋅= , (12) 97 where FIK – factor linking contamination level with radionuclide intake into organism, m2; igB – factor linking activity coming with foodstuff with effective dose (depends on age) [3], Sv/Bq. Effective dose rate of external exposure vH (Sv/s) due to each nuclide for a man staying on earth surface conditioned by a radioactive aerosol cloud, which was produced as result of release, is defined from the formula: ayVv BAH ~⋅= , (13) where AV – radionuclide volumetric activity, Bq/m3; γaB~ – transient dosimetric multiplier (depending on age) characterizing effective dose rate created by a radioactive aerosol cloud of single concentration at open earth surface [3], Sv m3/(s⋅Bq). Effective dose intH (Sv) conditioned by inhalation intake of radioactive aerosol, is estimated by the formula: Vageageint ATeVH τ= , (14) where ageV – breathing rate (depends on age) [4], m3/hour; T – stay time in aerosol cloud, hour; ageeτ – dose per unit of activity intake by inhalation way (depends on age) [3], Sv/Bq. Effective dose rintH _ (Sv) conditioned by inhalation intake of resuspended dust is estimated by the formula: *_ Vagerint AVTeH τ= , (15) where *VA – volumetric activity due to resuspended dust, Bq/m3. Ratio of volumetric activity produced due to resuspended dust and nuclide volumetric activity under absence of wind rise, is defined as follows:       λ + λ+λ Λ+= αα 2 2 21 1 max )(* KK H v A A Z g V V , (16) where 15 1 m10 −− α =K ; 19 2 m10 −− α =K ; 1λ – constant of deflation factor reduction for rapid phase, 17 1 c1046,1 −−⋅=λ ; 2λ – constant of its more prolonged reduction, 110 2 s102,2 −−⋅=λ ; max ZH – mixing layer height, m, which is defined by formula: maxmax )2/( zZH σ⋅π= . (17) Dose conditioned by radiation of soil contaminated surface, is defined from the formula: effSssurf BAH τ= γ •• , (18) where • surfH – expectable dose, Sv/s; effSB τγ – expectable dose per contamination unit (depends on age), Sv m2/Bq. Considering the fact that main contribution into external exposure from soil contaminated surface induces 137Cs, 71001,1 − γ ⋅=τ effSB Sv m2/Bq [1]. 5. PROCEDURE FOR ADMISSIBLE RELEASE ESTIMATE To estimate admissible release, PRC-1 program was created, which allows estimating AR with considering all described ways of dose formation from NSC releases. The program features permit working with all initial data, changing them with the help of MS Excel, as well as displaying any needed information in graphic, or table form. For more pictorial view and facilitation of work with the software, it was compiled as follows. First, single release impact to public is estimated, thereafter by way of iterations with indicated accuracy the set of releases is made to achieve required dose quote. In estimating AR, radionuclide content of NSC release is considered. Based on the fact that projected NSC existing time – 100 years, radionuclide content of releases through each 10 years of NSC operation was estimated as an assumption that radionuclide content correspond to SO fuel content [2] in the same year. 6. ADMISSIBLE RELEASE VALUES Based on above procedure, estimate of admissible release for total NSC operational life time for critical group of public was made. Besides, an estimate of admissible release for β- and α-emitting nuclides and dust fuel release from the NSC was made. Estimate results are shown in Table 6. Estimates were made for five reference ages of man (new-born, 1 year, 5 years, 10 years, 15 years, adult), and for the two sexes. Reduction with time of summary AR and β-emitting radionuclide AR is conditioned by influence of different chains of radioactive decay. Simultaneously, the main β-emitting radionuclides decay with half-life being 30 years and less. At the same time, total alpha-activity even increases due to 241Am accumulation resulted by 241Pu β-decay (maximum value will be reached approximately to the year of 2050). Because of it, contribution to dose from α-emitting radionuclides will increase, and their AR will grow. Naturally, total amount of dust fuel will also increase, whose release will lead to dose for public of 40 µSv/year at 10 km zone border. Contributions to quote due to diverse dose formation ways in the beginning (for 2010 year) and in the end of NSC operation (2110 year) are submitted in Tables 7 and 8. In the beginning of NSC operation (Table 7), dose will be, mainly, defined by internal exposure (around 34 µSv/year), in addition due to radionuclide intake through food chains (around 28 µSv/year). Under external exposure, dose due to immersion in cloud is negligible one and relatively low dose (1,1 µ Sv/year) is mainly defined by 137Cs radiation from contaminated ground surface. In estimating doses under inhalation intake of radionuclides, two mechanisms were considered too – direct exposure in radioactive cloud due to exposure release occurred and from resuspension of dust precipitated on surface. Beginning from, approximately, the third year of operation, relative contribution to inhalation intake dose directly from a cloud remains, practically, constant one, and makes around 2/3 of all inhalation doses. Ingest dose is, mainly, defined by dose conditioned by aerial way of contamination of agricultural produce (around 24 µSv/year). There are less, at a significant rate, of doses (2,2 µSv/year) due to contamination of water medium resulted by releases. Around 5,4 µ Sv/year – dose due to root way of contamination. To NSC operation end, the situation can somehow change (Table 8). Determining contribution to dose will induce ingestion intake of alpha-emitting nuclides. Dose due to that mechanism may total around 28 µSv/year, some 6 µSv/year will be defined by intake through food chains, mainly, due to alpha-emitting nuclides. One should consider that the releases from NSC operation will not be uniform in the course of a year, and will depend on type and intensity of works being implemented. In case of conduct of dust-producing works in pre-harvest period, which will be accompanied by intensive release during a short time period, annual dose can essentially increase. That fact should be considered when planning the works in NSC. The main conclusions of carried out modeling are: • before 2080, critical group is 15 year teenagers of male sex, after 2080 – adults of male sex; • during all NSC operation period is expected that most ingestion dose will be from bread consumption; • in NSC operation start, ingestion dose is mainly defined by dose conditioned by aerial way of contamination of agricultural produce; • in NSC operation end, determining contribution to dose will be induced by inhalation intake of alpha- emitting nuclides. Table 6. Main results of admissible release estimate Year Radionuclide mix AR, Ci Radionuclide mix AR, Bq Beta-emitting radionuclide AR, Ci Beta-emitting radionuclide AR, Bq Alpha-emitting radionuclide AR, Ci Alpha-emitting radionuclide AR, Ci Fuel dust AR, g 2010 8,3 3,07E+11 8,1101 3,00E+11 0,1899 7,03E+09 167,71 2020 7,6 2,81E+11 7,3581 2,72E+11 0,2419 8,95E+09 200,52 2030 7 2,59E+11 6,7033 2,48E+11 0,2967 1,10E+10 238,77 2040 6,4 2,37E+11 6,0485 2,24E+11 0,3515 1,30E+10 279,75 2050 5,85 2,16E+11 5,4415 2,01E+11 0,4085 1,51E+10 325,06 2060 5,3 1,96E+11 4,8359 1,79E+11 0,4641 1,72E+10 371,54 2070 4,8 1,78E+11 4,2789 1,58E+11 0,5211 1,93E+10 421,36 2080 4,35 1,61E+11 3,7702 1,39E+11 0,5798 2,15E+10 474,57 2090 3,9 1,44E+11 3,2676 1,21E+11 0,6324 2,34E+10 524,61 2100 3,4 1,26E+11 2,7354 1,01E+11 0,6646 2,46E+10 559,17 2110 2,95 1,09E+11 2,2613 8,37E+10 0,6887 2,55E+10 587,79 Table 7. Contribution into effective dose from admissible release of diverse nuclides and diverse ways of impact at NSC operation start Dose due to intake through vegetative and meat chains for individual radionuclides, µSv Internal exposure External exposure Dose due to intake through alimentary chains, µSv Contamination aerial way Contamination root way Dose due to consumption of fish and water, µ Sv Dose due to RS inhalation, µ Sv Dose due to immersion in cloud, µSv External dose from surface contamination 137Cs, µSv 137Cs 9,26 90Sr 16,14 Alpha-emitting nuclides 2,28 241Pu 0,36 24,34 3,65 5,4 0,08 2,05E-07 0,13 1,81E-07 1.1 5,3 4,13E-08 1,85E-03 2,25E-11 Sum 28,04 33,39 5,51 Dose sum of internal exposure 38,9 Dose sum of external exposure 1,1 99 Table 8. Contribution into effective dose from admissible release of diverse nuclides and different impact ways at NSC operation end Dose due to intake through vegetative and meat chains for individual radionuclides, µSv Internal exposure External exposure Dose due to intake through alimentary chains, µSv Contamination aerial way Contamination root way Dose due to consumption of fish and water, µ Sv Dose due to RS inhalation, µSv Dose due to immersion in cloud, µSv External dose from surface contamination 137Cs, µSv 137Cs 1,19 90Sr 3,35 Alpha- emitting nuclides 27,56 241Pu 0,04 31,03 1,10 2,21 6,79E-03 8,66E-08 2,00E-02 6,74E-08 0,5 5,14E+00 1,74E-07 1,35E-04 2,30E-12 Sum 32,13 34,34 5,17E+00 Dose sum of internal exposure 39,5 Dose sum of external exposure 0,5 Thus, when planning activities for protection of public and environment during NSC operation, radiation monitoring must be provided of NSC releases, of radionuclide concentrations in air (in first turn of 90Sr, 137Cs and 241Am), of surface contamination levels, of radionuclide content in foodstuff. It seems as inexpedient to grow cereals (except feed- preparing works), near exclusion zone borders, especially in case of reduction of its dimensions. Besides, one should consider the fact that in case of reduction of borders of 30 km exclusion zone to 10 km, practical implementation of all agricultural works must be provided on the basis of recommendations for agricultural activities on the territories that are contaminated with radionuclides. It implies that a complex of measures (counter-measures) should be implemented to minimize radionuclide intake into the products of agricultural industry and conduct of continuous radioecological monitoring. REFERENCES 1. N.G. Gusev, V.A. Belyaiev. Radioactive releases in atmosphere, reference book. M.: “Energoatomizdat”, 1986, p. 32, 91, 95-130 (in Russian). 2. The “Shelter's” current safety analysis and situation development forecast. (Updated version). Kiev: TACIS, 1998, p. 77. 3. U.S. Environmental Protection Agency, Federal Guidance. Report 13 Cancer Risk Coefficients for Environmental Exposure to Radionuclides: CD Supplement, EPA 402-C-99-001, Rev. 1. Oak Ridge National Laboratory, Oak Ridge, TN; U.S. Environmental Protection Agency, Washington, DC. 4. Norms of radiation safety of Ukraine (NRBU-97). State hygienic standards. GGN 6.6.1.-6.5.001-98. Official edition. Kiev, 1998, p. 74. МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ВОЗДЕЙСТВИЙ ПРИ ВЫБРОСАХ ИЗ ОБЪЕКТА “УКРЫТИЕ” В.Г. Батий, С.А. Паскевич, В.М. Рудько, А.А. Сизов, В.Н. Щербин Описана методика математического моделирования воздействий на население по всем возможным путям в результате возможного выброса радиоактивных веществ. Приведены результаты расчета допустимых выбросов на различных этапах эксплуатации нового безопасного конфайнмента над существующим объектом “Укрытие” Чернобыльской АЭС. МАТЕМАТИЧНЕ МОДЕЛЮВАННЯ ВПЛИВІВ ПРИ ВИКИДАХ З ОБ’ЄКТУ “УКРИТТЯ” В.Г. Батій, С.А. Паскевич, В.М. Рудько, А.О. Сізов, В.М. Щєрбін Описано методику математичного моделювання впливів на населення за всіма можливими шляхами у результаті можливого викиду радіоактивних речовин. Надано результати розрахунку допустимих викидів на різних етапах експлуатації нового безпечного конфайнменту над існуючим об’єктом “Укриття” Чорнобильської АЕС. 2. PROCEDURE FOR RELEASE IMPACT ESTIMATE 3. RADIOACTIVE SUBSTANCE CONCENTRATIONS IN THE AIR AND SOIL. CONTINUOUS RELEASES 4. RELEASES OF RADIOACTIVE AEROSOL ADMIXTURES INTO ATMOSPHERE 5. PROCEDURE FOR ADMISSIBLE RELEASE ESTIMATE 6.  ADMISSIBLE RELEASE VALUES REFERENCES
id nasplib_isofts_kiev_ua-123456789-80556
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1562-6016
language English
last_indexed 2025-12-07T17:20:19Z
publishDate 2004
publisher Національний науковий центр «Харківський фізико-технічний інститут» НАН України
record_format dspace
spelling Batiy, V.G.
Paskevich, S.A.
Rudko, V.M.
Sizov, A.A.
Shcherbin, V.N.
2015-04-18T20:27:47Z
2015-04-18T20:27:47Z
2004
Mathematical simulation of “Shelter” object releases impacts / V.G. Batiy, S.A. Paskevich, V.M. Rudko, A.A. Sizov, V.N. Shcherbin // Вопросы атомной науки и техники. — 2004. — № 5. — С. 96-100. — Бібліогр.: 4 назв. — англ.
1562-6016
PACS: 28.41Te
https://nasplib.isofts.kiev.ua/handle/123456789/80556
Methods of mathematical modeling of radiological human impacts are described. Calculation of admissible
 releases at different exploitation stages of New Safe Confinement at the existing ChNPP “Shelter” object are given.
Описано методику математичного моделювання впливів на населення за всіма можливими шляхами у
 результаті можливого викиду радіоактивних речовин. Надано результати розрахунку допустимих викидів на
 різних етапах експлуатації нового безпечного конфайнменту над існуючим об’єктом “Укриття”
 Чорнобильської АЕС.
Описана методика математического моделирования воздействий на население по всем возможным путям
 в результате возможного выброса радиоактивных веществ. Приведены результаты расчета допустимых
 выбросов на различных этапах эксплуатации нового безопасного конфайнмента над существующим
 объектом “Укрытие” Чернобыльской АЭС.
en
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
Вопросы атомной науки и техники
Применение ядерных методов
Mathematical simulation of “Shelter” object releases impacts
Математичне моделювання впливів при викидах з об’єкту “Укриття”
Математическое моделирование воздействий при выбросах из объекта “Укрытие”
Article
published earlier
spellingShingle Mathematical simulation of “Shelter” object releases impacts
Batiy, V.G.
Paskevich, S.A.
Rudko, V.M.
Sizov, A.A.
Shcherbin, V.N.
Применение ядерных методов
title Mathematical simulation of “Shelter” object releases impacts
title_alt Математичне моделювання впливів при викидах з об’єкту “Укриття”
Математическое моделирование воздействий при выбросах из объекта “Укрытие”
title_full Mathematical simulation of “Shelter” object releases impacts
title_fullStr Mathematical simulation of “Shelter” object releases impacts
title_full_unstemmed Mathematical simulation of “Shelter” object releases impacts
title_short Mathematical simulation of “Shelter” object releases impacts
title_sort mathematical simulation of “shelter” object releases impacts
topic Применение ядерных методов
topic_facet Применение ядерных методов
url https://nasplib.isofts.kiev.ua/handle/123456789/80556
work_keys_str_mv AT batiyvg mathematicalsimulationofshelterobjectreleasesimpacts
AT paskevichsa mathematicalsimulationofshelterobjectreleasesimpacts
AT rudkovm mathematicalsimulationofshelterobjectreleasesimpacts
AT sizovaa mathematicalsimulationofshelterobjectreleasesimpacts
AT shcherbinvn mathematicalsimulationofshelterobjectreleasesimpacts
AT batiyvg matematičnemodelûvannâvplivívprivikidahzobêktuukrittâ
AT paskevichsa matematičnemodelûvannâvplivívprivikidahzobêktuukrittâ
AT rudkovm matematičnemodelûvannâvplivívprivikidahzobêktuukrittâ
AT sizovaa matematičnemodelûvannâvplivívprivikidahzobêktuukrittâ
AT shcherbinvn matematičnemodelûvannâvplivívprivikidahzobêktuukrittâ
AT batiyvg matematičeskoemodelirovanievozdeistviiprivybrosahizobʺektaukrytie
AT paskevichsa matematičeskoemodelirovanievozdeistviiprivybrosahizobʺektaukrytie
AT rudkovm matematičeskoemodelirovanievozdeistviiprivybrosahizobʺektaukrytie
AT sizovaa matematičeskoemodelirovanievozdeistviiprivybrosahizobʺektaukrytie
AT shcherbinvn matematičeskoemodelirovanievozdeistviiprivybrosahizobʺektaukrytie