We study the structure of the Liouville quantum gravity (LQG) surfaces that are cut out as one explores a conformal loopensemble
We present a proof of concept for a spectrally selective thermal midIR source based on nanopatterned graphene (NPG) with a typical mobility of CVDgrown graphene (up to 3000
 NSFPAR ID:
 10305551
 Publisher / Repository:
 Nature Publishing Group
 Date Published:
 Journal Name:
 Scientific Reports
 Volume:
 10
 Issue:
 1
 ISSN:
 20452322
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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Abstract for$$\hbox {CLE}_{\kappa '}$$ ${\text{CLE}}_{{\kappa}^{\prime}}$ in (4, 8) that is drawn on an independent$$\kappa '$$ ${\kappa}^{\prime}$ LQG surface for$$\gamma $$ $\gamma $ . The results are similar in flavor to the ones from our companion paper dealing with$$\gamma ^2=16/\kappa '$$ ${\gamma}^{2}=16/{\kappa}^{\prime}$ for$$\hbox {CLE}_{\kappa }$$ ${\text{CLE}}_{\kappa}$ in (8/3, 4), where the loops of the CLE are disjoint and simple. In particular, we encode the combined structure of the LQG surface and the$$\kappa $$ $\kappa $ in terms of stable growthfragmentation trees or their variants, which also appear in the asymptotic study of peeling processes on decorated planar maps. This has consequences for questions that do a priori not involve LQG surfaces: In our paper entitled “$$\hbox {CLE}_{\kappa '}$$ ${\text{CLE}}_{{\kappa}^{\prime}}$CLE Percolations ” described the law of interfaces obtained when coloring the loops of a independently into two colors with respective probabilities$$\hbox {CLE}_{\kappa '}$$ ${\text{CLE}}_{{\kappa}^{\prime}}$p and . This description was complete up to one missing parameter$$1p$$ $1p$ . The results of the present paper about CLE on LQG allow us to determine its value in terms of$$\rho $$ $\rho $p and . It shows in particular that$$\kappa '$$ ${\kappa}^{\prime}$ and$$\hbox {CLE}_{\kappa '}$$ ${\text{CLE}}_{{\kappa}^{\prime}}$ are related via a continuum analog of the EdwardsSokal coupling between$$\hbox {CLE}_{16/\kappa '}$$ ${\text{CLE}}_{16/{\kappa}^{\prime}}$ percolation and the$$\hbox {FK}_q$$ ${\text{FK}}_{q}$q state Potts model (which makes sense even for nonintegerq between 1 and 4) if and only if . This provides further evidence for the longstanding belief that$$q=4\cos ^2(4\pi / \kappa ')$$ $q=4{cos}^{2}(4\pi /{\kappa}^{\prime})$ and$$\hbox {CLE}_{\kappa '}$$ ${\text{CLE}}_{{\kappa}^{\prime}}$ represent the scaling limits of$$\hbox {CLE}_{16/\kappa '}$$ ${\text{CLE}}_{16/{\kappa}^{\prime}}$ percolation and the$$\hbox {FK}_q$$ ${\text{FK}}_{q}$q Potts model whenq and are related in this way. Another consequence of the formula for$$\kappa '$$ ${\kappa}^{\prime}$ is the value of halfplane arm exponents for such divideandcolor models (a.k.a. fuzzy Potts models) that turn out to take a somewhat different form than the usual critical exponents for twodimensional models.$$\rho (p,\kappa ')$$ $\rho (p,{\kappa}^{\prime})$ 
Abstract Massive gully land consolidation projects, launched in China’s Loess Plateau, aim to restore 2667
agricultural lands in total by consolidating 2026 highly eroded gullies. This effort represents a social engineering project where the economic development and livelihood of the farming families are closely tied to the ability of these emergent landscapes to provide agricultural services. Whether these ‘time zero’ landscapes have the resilience to provide a sustainable soil condition such as soil organic carbon (SOC) content remains unknown. By studying two watersheds, one of which is a control site, we show that the consolidated gully serves as an enhanced carbon sink, where the magnitude of SOC increase rate (1.0$$\mathrm{km}^2$$ ${\mathrm{km}}^{2}$ ) is about twice that of the SOC decrease rate (− 0.5$$\mathrm{g\,C}/\mathrm{m}^2/\mathrm{year}$$ $g\phantom{\rule{0ex}{0ex}}C/{m}^{2}/\mathrm{year}$ ) in the surrounding natural watershed. Over a 50year coevolution of landscape and SOC turnover, we find that the dominant mechanisms that determine the carbon cycling are different between the consolidated gully and natural watersheds. In natural watersheds, the flux of SOC transformation is mainly driven by the flux of SOC transport; but in the consolidated gully, the transport has little impact on the transformation. Furthermore, we find that extending the surface carbon residence time has the potential to efficiently enhance carbon sequestration from the atmosphere with a rate as high as 8$$\mathrm{g\,C}/\mathrm{m}^2/\mathrm{year}$$ $g\phantom{\rule{0ex}{0ex}}C/{m}^{2}/\mathrm{year}$ compared to the current 0.4$$\mathrm{g\,C}/\mathrm{m}^2/\mathrm{year}$$ $g\phantom{\rule{0ex}{0ex}}C/{m}^{2}/\mathrm{year}$ . The success for the completion of all gully consolidation would lead to as high as 26.67$$\mathrm{g\,C}/\mathrm{m}^2/\mathrm{year}$$ $g\phantom{\rule{0ex}{0ex}}C/{m}^{2}/\mathrm{year}$ sequestrated into soils. This work, therefore, not only provides an assessment and guidance of the longterm sustainability of the ‘time zero’ landscapes but also a solution for sequestration$$\mathrm{Gg\,C}/\mathrm{year}$$ $\mathrm{Gg}\phantom{\rule{0ex}{0ex}}C/\mathrm{year}$ into soils.$$\hbox {CO}_2$$ ${\text{CO}}_{2}$ 
Abstract We prove that the Hilbert scheme of
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Abstract Measurements of the associated production of a W boson and a charm (
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