Large scale heterogeneous networks, the Davis-Wielandt shell, and graph separation

We consider a large scale network of interconnected heterogeneous dynamical components. Scalable stability conditions are derived that involve the input/output properties of individual subsystems and the interconnection matrix. The analysis is based on the Davis-Wielandt shell, a higher dimensional version of the numerical range with important convexity properties. This can be used to allow heterogeneity in the agent dynamics while relaxing normality and symmetry assumptions on the interconnection matrix. The results include small gain and passivity approaches as special cases, with the three dimensional shell shown to be inherently connected with corresponding graph separation arguments. © 2012 Society for Industrial and Applied Mathematics.

Electronic structure of the layered ferroelectric perovskite SrBi2Ta2O9

The band structure of the Bi layered perovskite SrBi2Ta2O9 (SBT) has been calculated by the tight binding method. We find both the valence and conduction band edges to consist of states primarily derived from the Bi-O layer rather than the perovskite Sr-Ta-O block. The valence band maximum arises from O p and some Bi s states, while the conduction band minimum consists of Bi p states, with a band gap of 5.1 eV. It is argued that the Bi-O layers largely control the electronic response of SBT while the ferroelectric response originates from the perovskite Sr-Ta-O block. Bi and Ta centered traps are calculated to be shallow, which may account in part for the excellent fatigue properties of SBT.

Electronic structure of the ferroelectric layered perovskite SrBi2Ta2O9

The band structure of the layered perovskite SrBi2Ta2O9 (SBT) was calculated by tight binding and the valence band density of states was measured by x-ray photoemission spectroscopy. We find both the valence and conduction band edges to consist of states primarily derived from the Bi-O layer rather than the perovskite Sr-Ta-O blocks. The valence band maximum arises from O p and some Bi s states, while the conduction band minimum consists of Bi p states, with a wide band gap of 5.1 eV. It is argued that the Bi-O layers largely control the electronic response whereas the ferroelectric response originates mainly from the perovskite Sr-Ta-O block. Bi and Ta centered traps are calculated to be shallow, which may account in part for its excellent fatigue properties. © 1996 American Institute of Physics.