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- 2015 (31) (entfernen)
The distinguishing structural feature of single-layered black phosphorus is its puckered structure, which leads to many novel physical properties. In this work, we first present a new parameterization of the Stillinger–Weber potential for single-layered black phosphorus. In doing so, we reveal the importance of a cross-pucker interaction term in capturing its unique mechanical properties, such as a negative Poisson's ratio. In particular, we show that the cross-pucker interaction enables the pucker to act as a re-entrant hinge, which expands in the lateral direction when it is stretched in the longitudinal direction. As a consequence, single-layered black phosphorus has a negative Poisson's ratio in the direction perpendicular to the atomic plane. As an additional demonstration of the impact of the cross-pucker interaction, we show that it is also the key factor that enables capturing the edge stress-induced bending of single-layered black phosphorus that has been reported in ab initio calculations.
When working on urban planning projects there are usually multiple aspects to consider. Often these aspects are contradictory and it is not possible to choose one over the other; instead, they each need to be fulfilled as well as possible. In this situation ideal solutions are not always found because they are either not sought or the problems are regarded as being too complex for human capabilities.To improve this situation we propose complementing traditional design approaches with a design synthesis process based on evolutionary many-criteria optimization methods that can fulfill formalizable design requirements. In addition we show how self-organizing maps can be used to visualize many-dimensional solution spaces in an easily analyzable and comprehensible form.The system is presented using an urban planning scenario for the placement of building volumes.