From the perspective of D-brane physics, we consider the role of the real intrinsic Riemannian geometry and describe the statistical nature of gauge and exotic instanton vacuum fluctuations. For the Veneziano-Yankielowiz/ Affleck-Dine-Seiberg and non-perturbative instanton superpotentials, the issue of the wall (in)stabilities is analysed for marginal and threshold like vacua, and their arbitrary linear combinations. Physically, for both the stationary and non-stationary statistical configurations with and without the statistical fluctuations of the gauge and exotic instanton curves, the...

This book is a short introduction to power system planning and operation using advanced geometrical methods. The approach is based on well-known insights and techniques developed in theoretical physics in the context of Riemannian manifolds.
The proof of principle and robustness of this approach is examined in the context of the IEEE 5 bus system.
This work addresses applied mathematicians, theoretical physicists and power engineers interested in novel mathematical approaches to power network theory.