2019/01/20 by Vladimir Mityushev, Mityushev, Vladimir, Wojciech Nawalaniec +1
Chemistry · Engineering · #74Q15 #Asphalt Pavement Performance Evaluation #Electrostatics and Colloid Interactions #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.1901.06652
openalex publication_date 2019/01/20 · openalex created_date 2022/07/30 · openalex updated_date 2026/07/28
Randomly distributed non-overlapping perfectly conducting spheres are embedded in a conducting matrix with the concentration of inclusions f. Jeffrey (1973) suggested an analytical formula valid up to O(f3) for macroscopically isotropic random composites. A conditionally convergent sum arose in the spatial averaging. In the present paper, we apply a method of functional equations to random composites and correct Jeffrey's formula. The main revision concerns the proper investigation of the conditionally convergent sum and correction the f2-term. A new model of symbolic computations is developed in order to compute the effective conductivity tensor. The corresponding algorithm is realized up to O(f^\frac103). The obtained formulae explicitly demonstrate the dependence of the effective conductivity tensor on the deterministic and probabilistic distributions of inclusions in the f2-term, and in the f3-term. This leads to the conclusion that some previous formulae presented as universal, i.e., valid for all random composites, may be actually applied only to dilute or to special composites when interaction between inclusions do not matter.