A Novel Computational Approach Towards The Mill Matrix Of Distributed Comminution Models

An accurate, efficient and stable computation of the mill matrix function (eAt) is needed where mill matrix (A) is a real general matrix. Two important modeling cases in comminution where such need arises are: Heterogeneous comminution behavior of multi-component ores and ultra-fine grinding involving simultaneous attrition and fragmentation breakages. This paper presents the application of a novel splitting method in conjunction With similarity transformation technique in the form of "product formula" which is found to work in all cases and uses a most aggravating, yet interesting property of the matrix exponential in a restricted sense. Results are presented showing that this method can yield solution as accurate as those obtained With an analytical technique. The utility of this computational approach is demonstrated by parameter estimation analysis using a distributed component model in the liberation area through computer simulations.