Description Of Breakage Research Articles

Copula-based approximation of particle breakage as link between DEM and PBM

Abstract In process engineering, the breakage behavior of particles is needed for the modeling and optimization of comminution processes. A popular tool to describe (dynamic) processes is population balance modeling (PBM), which captures the statistical distribution of particle properties and their evolution over time. It has been suggested previously to split up the description of breakage into a machine function (modeling of loading conditions) and a material function (modeling of particle response to mechanical stress). Based on this idea, we present a mathematical formulation of machine and material functions and a general approach to compute them. Both functions are modeled using multivariate probability distributions, where in particular so-called copulas are helpful. These can be fitted to data obtained by the discrete element method (DEM). In this paper, we describe the proposed copula-based breakage model, and we construct such a model for an artificial dataset that allows to evaluate the prediction quality.

Computational Insights into the Role of the Frontiers Orbital in the Chemistry of Tridentate Ligands

The FERM O concept emerges as a powerful and innovative implement to investigate the role of molecular orbitals applied in the description of breakage and formation of chemical bonds. In this work, Hartree-Fock (HF) and Density Functional Theory (DFT) calculations were carried out for a series of four tridentate ligands and their behavior was analyzed using molecular orb ital (M O) energies. It was observed that HOMO energies are inadequate to describe the Pearsons Hard and Solf acid-base (HSA B) p ricinple behavior of these compounds. By using the frontier effective-for-reaction molecular orbital (FERM O) concept, the reactions that are driven by HOM O, and those that are not, can be better exp lained, independent of the calculation method used, since both HF and Kohn-Sham methodologies lead to the same FERM O.

Erratum: The role of the frontier orbitals in acid-base chemistry of organic amines probed by ab initio and chemometric techniques

The Frontier effective-for-reaction molecular orbital (FERMO) concept emerges as a powerful and innovative implement to investigate the role of molecular orbitals (MOs) applied in the description of breakage and formation of chemical bonds. In this work, theoretical calculations were carried out for conjugated acids of 18 amines and their acid–base behavior was analyzed using MO energies. We observed that highest occupied MO (HOMO) energies are inadequate to describe the acid–base behavior of these compounds. By using the FERMO concept, the reactions that are driven by HOMO, and those that are not, can be better explained, independent of the calculation method used, as independent of the calculation method used, both HF and Kohn–Sham methodologies lead to the same FERMO. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010

The role of the Frontier orbitals in acid–base chemistry of organic amines probed by ab initio and chemometric techniques

AbstractThe Frontier effective‐for‐reaction molecular orbital (FERMO) concept emerges as a powerful and innovative implement to investigate the role of molecular orbitals (MOs) applied in the description of breakage and formation of chemical bonds. In this work, theoretical calculations were carried out for conjugated acids of 18 amines and their acid–base behavior was analyzed using MO energies. We observed that highest occupied MO (HOMO) energies are inadequate to describe the acid–base behavior of these compounds. By using the FERMO concept, the reactions that are driven by HOMO, and those that are not, can be better explained, independent of the calculation method used, as independent of the calculation method used, both HF and Kohn–Sham methodologies lead to the same FERMO. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2010