Density functional energy decomposition into one- and two-atom contributions

The present work provides a generalization of Mayer's energy decomposition for the density-functional theory (DFT) case. It is shown that one- and two-atom Hartree-Fock energy components in Mayer's approach can be represented as an action of a one-atom potential VA on a one-atom density ρ A or ρ B. To treat the exchange-correlation term in the DFT energy expression in a similar way, the exchange-correlation energy density per electron is expanded into a linear combination of basis functions. Calculations carried out for a number of density functionals demonstrate that the DFT and Hartree-Fock two-atom energies agree to a reasonable extent with each other. The two-atom energies for strong covalent bonds are within the range of typical bond dissociation energies and are therefore a convenient computational tool for assessment of individual bond strength in polyatomic molecules. For nonspecific nonbonding interactions, the two-atom energies are low. They can be either repulsive or slightly attractive, but the DFT results more frequently yield small attractive values compared to the Hartree-Fock case. The hydrogen bond in the water dimer is calculated to be between the strong covalent and nonbonding interactions on the energy scale

Robustness against large-scale failures in communications networks

This thesis studies robustness against large-scale failures in communications networks. If failures are isolated, they usually go unnoticed by users thanks to recovery mechanisms. However, such mechanisms are not effective against large-scale multiple failures. Large-scale failures may cause huge economic loss. A key requirement towards devising mechanisms to lessen their impact is the ability to evaluate network robustness. This thesis focuses on multilayer networks featuring separated control and data planes. The majority of the existing measures of robustness are unable to capture the true service degradation in such a setting, because they rely on purely topological features. One of the major contributions of this thesis is a new measure of functional robustness. The failure dynamics is modeled from the perspective of epidemic spreading, for which a new epidemic model is proposed. Another contribution is a taxonomy of multiple, large-scale failures, adapted to the needs and usage of the field of networking.