核反应堆中子扩散方程的非定域效应

IF 0.7 4区工程技术 Q3 MATHEMATICS, APPLIED

Journal of Computational and Theoretical Transport Pub Date : 2020-09-18 DOI:10.1080/23324309.2020.1816551

R. El-Nabulsi

{"title":"核反应堆中子扩散方程的非定域效应","authors":"R. El-Nabulsi","doi":"10.1080/23324309.2020.1816551","DOIUrl":null,"url":null,"abstract":"Abstract In this study, a nonlocal approach to neutron diffusion equation with a memory is constructed in terms of moments of the displacement kernel with a modified geometric buckling. This approach leads to a family of partial differential equations which belong to the class of Fisher-Kolmogorov and Swift-Hohenberg equations. The stability of the problem depends on the signs of the second and fourth moments. The energy is a conserved quantity along orbits and a constant of integration is obtained. It was observed that the buckling is affected by the types of the kernel moment and for an explicit symmetric kernel, the ratio between the maximum and the average flux for a slab reactor is less than the ratio obtained using the conventional local diffusion equation, a result which is motivating technically in nuclear reactor engineering.","PeriodicalId":54305,"journal":{"name":"Journal of Computational and Theoretical Transport","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2020-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/23324309.2020.1816551","citationCount":"8","resultStr":"{\"title\":\"Nonlocal Effects to Neutron Diffusion Equation in a Nuclear Reactor\",\"authors\":\"R. El-Nabulsi\",\"doi\":\"10.1080/23324309.2020.1816551\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract In this study, a nonlocal approach to neutron diffusion equation with a memory is constructed in terms of moments of the displacement kernel with a modified geometric buckling. This approach leads to a family of partial differential equations which belong to the class of Fisher-Kolmogorov and Swift-Hohenberg equations. The stability of the problem depends on the signs of the second and fourth moments. The energy is a conserved quantity along orbits and a constant of integration is obtained. It was observed that the buckling is affected by the types of the kernel moment and for an explicit symmetric kernel, the ratio between the maximum and the average flux for a slab reactor is less than the ratio obtained using the conventional local diffusion equation, a result which is motivating technically in nuclear reactor engineering.\",\"PeriodicalId\":54305,\"journal\":{\"name\":\"Journal of Computational and Theoretical Transport\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2020-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/23324309.2020.1816551\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Computational and Theoretical Transport\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1080/23324309.2020.1816551\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Computational and Theoretical Transport","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1080/23324309.2020.1816551","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 8

摘要

摘要在本研究中，根据具有修正几何屈曲的位移核的矩，构造了一种求解具有记忆的中子扩散方程的非局部方法。这种方法导出了一类偏微分方程，属于Fisher-Kolmogorov和Swift-Hohenberg方程。问题的稳定性取决于第二个和第四个矩的符号。能量是沿轨道的守恒量，并得到积分常数。研究发现，屈曲受到核矩类型的影响，对于显式对称核，板状反应堆的最大通量和平均通量之间的比率小于使用传统局部扩散方程获得的比率，这一结果在核反应堆工程中具有技术激励作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Nonlocal Effects to Neutron Diffusion Equation in a Nuclear Reactor

Abstract In this study, a nonlocal approach to neutron diffusion equation with a memory is constructed in terms of moments of the displacement kernel with a modified geometric buckling. This approach leads to a family of partial differential equations which belong to the class of Fisher-Kolmogorov and Swift-Hohenberg equations. The stability of the problem depends on the signs of the second and fourth moments. The energy is a conserved quantity along orbits and a constant of integration is obtained. It was observed that the buckling is affected by the types of the kernel moment and for an explicit symmetric kernel, the ratio between the maximum and the average flux for a slab reactor is less than the ratio obtained using the conventional local diffusion equation, a result which is motivating technically in nuclear reactor engineering.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Computational and Theoretical Transport Mathematics-Mathematical Physics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Emphasizing computational methods and theoretical studies, this unique journal invites articles on neutral-particle transport, kinetic theory, radiative transfer, charged-particle transport, and macroscopic transport phenomena. In addition, the journal encourages articles on uncertainty quantification related to these fields. Offering a range of information and research methodologies unavailable elsewhere, Journal of Computational and Theoretical Transport brings together closely related mathematical concepts and techniques to encourage a productive, interdisciplinary exchange of ideas.