The phase diagram of correlated, disordered electron systems is calculated within dynamical mean-field theory for the Anderson-Falicov-Kimball model with nearest-neighbors and next-nearestneighbors hopping. The half-filled band is analyzed in terms of the chemical potential of the system using the geometric and arithmetic averages. We also introduce the on-site energies exhibiting a long-range correlated disorder, which generates a system with similar characteristics as the one created by a random independent variable distribution. A decrease in the correlated disorder reduces the extended phase.
The external structure of the spray-flamelet can be described using the Schvab-Zel'dovich-Liñan formulation. The gaseous mixture-fraction variable as function of the physical space, Z(x i ), typically employed for the description of gaseous diffusion flames leads to non-monotonicity behaviour for spray flames due to the extra fuel supplied by vaporisation of droplets distributed into the flow. As a result, the overall properties of spray flames depend not only on Z and the scalar dissipation rate, χ, but also on the spray source term, S v . We propose a new general coordinate variable which takes into account the spatial information about the entire mixture fraction due to the gaseous phase and droplet vaporisation. This coordinate variable, Z C (x i ) is based on the cumulative value of the gaseous mixture fraction Z(x i ), and is shown to be monotonic. For pure gaseous flow, the new cumulative function, Z C , yields the well-established flamelet structure in Z-space. In the present manuscript, the spray-flamelet structure and the new equations for temperature and mass fractions in terms of Z C are derived and then applied to the canonical counterflow configuration with potential flow. Numerical results are obtained for ethanol and methanol sprays, and the effect of Lewis and Stokes numbers on the spray-flamelet structure are analyzed. The proposed formulation agrees well when mapping the structure back to physical space thereby confirming our integration methodology.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.