A salient issue facing contemporary urban development in many countries is that the physical areas of major cities are growing at a faster rate than their populations. The popularity of the green belt concept among advocates is that it can effectively counter urban sprawl while safeguarding the countryside from urban development. This paper is intended to measure the efficacy of the green belt in preventing urban sprawl through an international comparative study in three cities of different sizes, and which have experienced different urban growth pressures, namely Frankfurt am Main (Germany), London (UK), and Seoul (South Korea). The study adopts the urban sprawl measurement methodological framework defined by Jaeger et al. to process GHSL data in order to examine the urban sprawl index in the three case study cities. This quantitative evidence-based comparative study demonstrates that the designation of green belts has failed to prevent urban sprawl both within urban centers and at a wider regional level.

The nature of charge degrees-of-freedom distinguishes scenarios for interpreting the character of a second order magnetic transition at zero temperature, that is, a magnetic quantum critical point (QCP). Heavy-fermion systems are prototypes of this paradigm, and in those, the relevant question is where, relative to a magnetic QCP, does the Kondo effect delocalize their f-electron degrees-of-freedom. Herein, we use pressure-dependent Hall measurements to identify a finite-temperature scale Eloc that signals a crossover from f-localized to f-delocalized character. As a function of pressure, Eloc(P) extrapolates smoothly to zero temperature at the antiferromagnetic QCP of CeRhIn5 where its Fermi surface reconstructs, hallmarks of Kondo-breakdown criticality that generates critical magnetic and charge fluctuations. In 4.4% Sn-doped CeRhIn5, however, Eloc(P) extrapolates into its magnetically ordered phase and is decoupled from the pressureinduced magnetic QCP, which implies a spin-density-wave (SDW) type of criticality that produces only critical fluctuations of the SDW order parameter. Our results demonstrate the importance of experimentally determining Eloc to characterize quantum criticality and the associated consequences for understanding the pairing mechanism of superconductivity that reaches a maximum Tc in both materials at their respective magnetic QCP.

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