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Stability and cost optimality of power generation and supply systems must not be considered independently from one another. Simple examples show that optimizing cost without considering stability may result in modes of operation that, while economically optimal, are unstable. We demonstrate that stability, robustness, and optimality can be considered systematically and simultaneously by combining bifurcation theory and nonlinear optimization. Essentially, the proposed method enforces a backoff distance between the optimal point of operation and operational or stability boundaries in the space of the optimization variables, where bifurcation theory is used to describe nonlinear stability boundaries.
Cost optimal meter placement in low and medium voltagte grids considering stochastic dependencies
(2013)
Despite their overwhelming complexity, living cells display a high degree of internal mechanical and functional organization which can largely be attributed to the intracellular biopolymer scaffold, the cytoskeleton. Being a very complex system far from thermodynamic equilibrium, the cytoskeleton's ability to organize is at the same time challenging and fascinating. The extensive amounts of frequently interacting cellular building blocks and their inherent multifunctionality permits highly adaptive behavior and obstructs a purely reductionist approach. Nevertheless (and despite the field's relative novelty), the physics approach has already proved to be extremely successful in revealing very fundamental concepts of cytoskeleton organization and behavior. This review aims at introducing the physics of the cytoskeleton ranging from single biopolymer filaments to multicellular organisms. Throughout this wide range of phenomena, the focus is set on the intertwined nature of the different physical scales (levels of complexity) that give rise to numerous emergent properties by means of self-organization or self-assembly.