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This article deals with the cost optimal commitment of power systems. System stability is often only considered after solving the commitment problem. We show by example that a cost optimization may result in a mode of operation that, while economically optimal, is unstable or has otherwise unacceptable dynamics. As a remedy, we propose to use the so-called normal vector method, which has been developed for the optimization of nonlinear dynamical systems with stability boundaries and uncertain parameters. We apply the method to a small sample power grid, where the optimization goal is to minimize the energy production costs for a given power consumption.
Großstadt-Surfen in München - Der Film »Keep Surfing« illustriert den Strukturwandel des Sports
(2011)
Cell migration is associated with the dynamic protrusion of a thin actin-based cytoskeletal extension at the cell front, which has been shown to consist of two different substructures, the leading lamellipodium and the subsequent lamellum. While the formation of the lamellipodium is increasingly well understood, organizational principles underlying the emergence of the lamellum are just beginning to be unraveled. We report here on a 1D mathematical model which describes the reaction-diffusion processes of a polarized actin network in steady state, and reproduces essential characteristics of the lamellipodium-lamellum system. We observe a steep gradient in filament lengths at the protruding edge, a local depolymerization maximum a few microns behind the edge, as well as a differential dominance of the network destabilizer ADF/cofilin and the stabilizer tropomyosin. We identify simple and robust organizational principles giving rise to the derived network characteristics, uncoupled from the specifics of any molecular implementation, and thus plausibly valid across cell types. An analysis of network length dependence on physico-chemical system parameters implies that to limit array treadmilling to cellular dimensions, network growth has to be truncated by mechanisms other than aging-induced depolymerization, e.g., by myosin-associated network dissociation at the transition to the cell body. Our work contributes to the analytical understanding of the cytoskeletal extension's bisection into lamellipodium and lamellum and sheds light on how cells organize their molecular machinery to achieve motility.
Despite its impressive complexity the cytoskeleton succeeds to persistently organize itself and thus the cells' interior. In contrast to classical man-made machines, much of the cellular organization originates from inherent self-assembly and self-organization allowing a high degree of autonomy for various functional units. Recent experimental and theoretical studies revealed numerous examples of cytoskeleton components that arrange and organize in a self-regulative way. In the present review we want to shortly summarize some of the principle mechanisms that are able to inherently trigger and regulate the cytoskeleton organization. Although taken individually most of these regulative principles are rather simple with intuitively predictable consequences, combinations of two or more of these mechanisms can quickly give rise to very complex, unexpected behavior and might even be able to explain the formation of different functional units out of a common pool of available building blocks.
The synthesis of Nb-doped TiO2 nanoparticles by spray drying: an efficient and scalable method
(2011)
Designing core ontologies
(2011)