I'd like to study two aspects of analysis on Lie groups: multiplier which has been developed over the past 20 years and has already been implemented as an industrial technique. A large-scale application is e.g. the Ni-SiC coatings in the automotive industry. However the scientific insight into the mechanism of codeposition has not yet resulted into a predictive model. This would be helpful to achieve a better controlled degree of codeposition and to increase the process reproducibility. Moreover no unified theory explains nowadays the effect of additives in composite plating. As such the aim of this doctoral research to investigate the role of additives in composite plating and to understand the way how they can promote or hinder the codeposition of small particles (like oxides and polymeric particles) with metals (like copper a nickel) using advanced investigation techniques like the atomic force microscope and centrifuge plating cell.