The investigators will work on several closely related subjects that will address important problems with respect to the structure and chemical and dynamical evolution of the Earth's mantle. The work will entail a combination of approaches using geochemical reservoir models that take into account the dispersion in both radiogenic isotope ratios and parent/daughter ratios in the mantle to obtain a simple theory that can combine fluxes and residence time estimates from traditional geochemical reservoir models with mixing times from three dimensional mantle convection models. Test results for the Nd and Sr isotopic systems demonstrate the validity of this approach. It is also proposed to combine reservoir models for isotopic transport and evolution with a parameterized convection model that will integrate the chemical evolution with thermal evolution. The parameterized models will include important effects that have only recently been identified, such as the bending of the lithosphere.