Let V be a real finite-dimensional vector space. We introduce some physical problems that may be described by V-valued homogeneous and isotropic random fields on R3. We propose a general method for calculation of expectations and two-point correlation functions of such fields. Our results are equivalent to classical results by Robertson, when V = R3, and those by Lomakin, when V is the space of symmetric second-rank tensors over R3. Our solution involves an analogue of the classical Clebsch-Gordan coefficients.
- Godunov-Gordienko coefficients
- Group representation
- Isotropic tensor random field
ASJC Scopus subject areas
- Civil and Structural Engineering
- Numerical Analysis
- Computational Mathematics