For each odd integer r greater than one and not divisible by three we give explicit examples of infinite families of simply and tangentially homotopy equivalent but pairwise non-homeomorphic closed homogeneous spaces with fundamental group isomorphic to Z/r. As an application we construct the first examples of manifolds which possess infinitely many metrics of nonnegative sectional curvature with pairwise non-homeomorphic homogeneous souls of codimension three with trivial normal bundle, such that their curvatures and the diameters of the souls are uniformly bounded. These manifolds are the first examples of manifolds fulfilling such geometric conditions and they serve as solutions to a problem posed by I. Belegradek, S. Kwasik and R. Schultz.
The generation and supply of electricity is currently about to undergo a fundamental transition that includes extensive development of smart grids. Smart grids are huge and complex networks consisting of a vast number of devices and entities which are connected with each other. This opens new variations of disruption scenarios which can increase the vulnerability of a power distribution network. However, the network topology of a smart grid has significant effects on urban resilience particularly referring to the adequate provision of infrastructures. Thus, topology massively codetermines the degree of urban resilience, i.e. different topologies enable different strategies of power distribution. Therefore, this article introduces a concept of criticality adapted to a power system relying on an advanced metering infrastructure. The authors propose a two-stage operationalization of this concept that refers to the design phase of a smart grid and its operation mode, targeting at an urban resilient power flow during power shortage.
In this article, we analyze “digital massification” in smart cities, that is, an ever‐growing number of market participants, consumers, and Internet of Things devices with simultaneous accommodation of users to increasing disturbances and inconveniences due to data congestion—as a driver for systemic risk. We argue that digital massification phenomena largely escape societal awareness due to their protracted evolution and are therefore still in the blind spot of long‐term governance. Our analysis makes methodological use of historical and relational analogy, and we introduce and elaborate concepts and terms that allow us to discuss the evolutionary nature of massification, that is, the foreseeable increasing probability of the occurrence of trigger events. Using the analogy to the history of road traffic congestion, we deduce that digital massification will most likely lead to a future “risk transition” where tolerated disturbances and inconveniences of the present will turn into systemic impacts. This insight calls for heightened sensitivity in governance to massification phenomena to ensure the long‐term resilience of smart cities.
The generation and supply of electricity is currently about to undergo a fundamental transition that includes extensive development of smart grids. Smart grids are huge and complex networks consisting of a vast number of devices and entities which are connected with each other. This fact opens new variations of disruption scenarios which can increase the vulnerability of a power distribution network. However, the network topology of a smart grid has significant effects on urban resilience particularly referring to the adequate provision of infrastructures whereby the way in which a distribution network is divided into interconnected microgrids is of particular importance. Such decompositions enable the systematic protection of important infrastructures and furthermore allow new forms of resilient power supply avoiding large-scale power blackouts. Therefore, the authors introduce a concept of criticality adapted to a power system relying on an advanced metering infrastructure and thereby propose a metric for an integrated resilience assessment of power distribution networks.
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