Numerical Approaches of Cluster Statistics for Stochastic Manganese Deposits

Abstract

Abstract In terms of origin, the most important manganese deposits are sedimentary deposits which grow on the surface and/or fractures of the natural magnesite ore. They reveal various morphological characteristic according to their location in origin. Some of them may be fractal in appearance. Although several studies have been completed with regards to their growth mechanism, it may be safe to say that their cluster statistics and scaling properties have rarely been subject an academic scrutiny. Hence, the subject of this study has been designed to calculate cluster statistics of manganese deposits by first; transferring the images of manganese deposits into a computer and then scaling them with the help of software. Secondly, the root-mean square (rms) thickness (also called as expected value in systems), the number of particles, clusters and cluster sizes are computed by means of scaling method. In doing so it has been found that the rms thickness and the number of particles are in correlation, a result which is called as power-law behaviour, T~N-ε (the critical exponent is computed as ε = 1.743). It has also been found that the correlation between the number of clusters and their sizes are determined with the power-law behaviour n(s)~s-τ (the critical exponent t may vary between 1.054 and 1.321). Finally, the distribution functions of natural manganese clusters on the magnesite subtract have been determined. All that may point to the fact that the manganese deposits may be formed according to a Poisson distribution. The results found and the conclusion reached in this study may be used to compare various natural deposits in geophysics.