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CONDITIONS OF ERGODICITY FOR RANDOM DIFFUSION-TYPE FIELDS

机译:随机扩散型场的刚性条件

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摘要

We introduce the concept of random diffusion-type field and study its homogeneity. In analyzing ergodic and quasiergodic fields, we establish the conditions necessary for the introduction of a physically small representative element of the body and the conditions of replacement of averaging over the ensemble by averaging over the body. The statistically homogeneous random diffusion-type fields are investigated and the effective radius of correlation is determined. The spectral expansions of random diffusion fields are presented and it is shown that the spectral amplitudes are delta-correlated in density for homogeneous random fields.
机译:介绍随机扩散型场的概念,研究其均匀性。在分析遍历和拟遍历场时,我们建立了引入身体上物理上较小的代表元素所必需的条件,以及通过对整个身体求平均来替换对整体求平均的条件。研究统计上均匀的随机扩散型场,并确定相关的有效半径。给出了随机扩散场的频谱扩展,结果表明,对于均匀随机场,频谱幅度在密​​度上是三角相关的。

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