{"title":"The influence of spatially anisotropic randomness on the solution of one-dimensional stochastic differential and integral equations","authors":"M.M.R. Williams","doi":"10.1016/j.anucene.2024.111058","DOIUrl":null,"url":null,"abstract":"<div><div>We demonstrate that the concept of a one-dimensional stochastic problem, in which only the statistical properties of the medium in one direction are used, is an unphysical situation. Even though the statistically averaged quantities, such as mean value and covariance, may depend only on one space dimension, the statistical properties of the medium in the other two directions must be included. A simple example, based on a second order differential equation, is used to illustrate the point and is supported by numerical calculations. The relevance of this matter to radiation and neutron transport in spatially stochastic media is made clear.</div></div>","PeriodicalId":8006,"journal":{"name":"Annals of Nuclear Energy","volume":"212 ","pages":"Article 111058"},"PeriodicalIF":1.9000,"publicationDate":"2024-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Nuclear Energy","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0306454924007217","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"NUCLEAR SCIENCE & TECHNOLOGY","Score":null,"Total":0}
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Abstract
We demonstrate that the concept of a one-dimensional stochastic problem, in which only the statistical properties of the medium in one direction are used, is an unphysical situation. Even though the statistically averaged quantities, such as mean value and covariance, may depend only on one space dimension, the statistical properties of the medium in the other two directions must be included. A simple example, based on a second order differential equation, is used to illustrate the point and is supported by numerical calculations. The relevance of this matter to radiation and neutron transport in spatially stochastic media is made clear.
期刊介绍：
Annals of Nuclear Energy provides an international medium for the communication of original research, ideas and developments in all areas of the field of nuclear energy science and technology. Its scope embraces nuclear fuel reserves, fuel cycles and cost, materials, processing, system and component technology (fission only), design and optimization, direct conversion of nuclear energy sources, environmental control, reactor physics, heat transfer and fluid dynamics, structural analysis, fuel management, future developments, nuclear fuel and safety, nuclear aerosol, neutron physics, computer technology (both software and hardware), risk assessment, radioactive waste disposal and reactor thermal hydraulics. Papers submitted to Annals need to demonstrate a clear link to nuclear power generation/nuclear engineering. Papers which deal with pure nuclear physics, pure health physics, imaging, or attenuation and shielding properties of concretes and various geological materials are not within the scope of the journal. Also, papers that deal with policy or economics are not within the scope of the journal.
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