The influence of spatially anisotropic randomness on the solution of one-dimensional stochastic differential and integral equations

IF 1.9 3区工程技术 Q1 NUCLEAR SCIENCE & TECHNOLOGY

Annals of Nuclear Energy Pub Date : 2024-11-20 DOI:10.1016/j.anucene.2024.111058

M.M.R. Williams

引用次数: 0

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.

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空间各向异性随机性对一维随机微分方程和积分方程求解的影响

我们证明了一维随机问题的概念，即只使用介质在一个方向上的统计特性，是不符合实际情况的。尽管统计平均量（如均值和协方差）可能只取决于一个空间维度，但必须包括介质在其他两个方向上的统计特性。我们用一个基于二阶微分方程的简单例子来说明这一点，并辅以数值计算。这个问题与空间随机介质中的辐射和中子输运的相关性是显而易见的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Nuclear Energy 工程技术-核科学技术

CiteScore

4.30

自引率

21.10%

发文量

632

审稿时长

7.3 months

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.