We study the structure of the Liouville quantum gravity (LQG) surfaces that are cut out as one explores a conformal loop-ensemble
We present a proof of concept for a spectrally selective thermal mid-IR source based on nanopatterned graphene (NPG) with a typical mobility of CVD-grown graphene (up to 3000
- NSF-PAR ID:
- 10305551
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- Scientific Reports
- Volume:
- 10
- Issue:
- 1
- ISSN:
- 2045-2322
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract for$$\hbox {CLE}_{\kappa '}$$ in (4, 8) that is drawn on an independent$$\kappa '$$ -LQG surface for$$\gamma $$ . The results are similar in flavor to the ones from our companion paper dealing with$$\gamma ^2=16/\kappa '$$ for$$\hbox {CLE}_{\kappa }$$ 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$$\kappa $$ in terms of stable growth-fragmentation 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 “$$\hbox {CLE}_{\kappa '}$$ CLE Percolations ” described the law of interfaces obtained when coloring the loops of a independently into two colors with respective probabilities$$\hbox {CLE}_{\kappa '}$$ p and . This description was complete up to one missing parameter$$1-p$$ . The results of the present paper about CLE on LQG allow us to determine its value in terms of$$\rho $$ p and . It shows in particular that$$\kappa '$$ and$$\hbox {CLE}_{\kappa '}$$ are related via a continuum analog of the Edwards-Sokal coupling between$$\hbox {CLE}_{16/\kappa '}$$ percolation and the$$\hbox {FK}_q$$ q -state Potts model (which makes sense even for non-integerq between 1 and 4) if and only if . This provides further evidence for the long-standing belief that$$q=4\cos ^2(4\pi / \kappa ')$$ and$$\hbox {CLE}_{\kappa '}$$ represent the scaling limits of$$\hbox {CLE}_{16/\kappa '}$$ percolation and the$$\hbox {FK}_q$$ q -Potts model whenq and are related in this way. Another consequence of the formula for$$\kappa '$$ is the value of half-plane arm exponents for such divide-and-color models (a.k.a. fuzzy Potts models) that turn out to take a somewhat different form than the usual critical exponents for two-dimensional models.$$\rho (p,\kappa ')$$ -
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$$\mathrm{km}^2$$ ) is about twice that of the SOC decrease rate (− 0.5$$\mathrm{g\,C}/\mathrm{m}^2/\mathrm{year}$$ ) in the surrounding natural watershed. Over a 50-year co-evolution 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$$\mathrm{g\,C}/\mathrm{m}^2/\mathrm{year}$$ compared to the current 0.4$$\mathrm{g\,C}/\mathrm{m}^2/\mathrm{year}$$ . The success for the completion of all gully consolidation would lead to as high as 26.67$$\mathrm{g\,C}/\mathrm{m}^2/\mathrm{year}$$ sequestrated into soils. This work, therefore, not only provides an assessment and guidance of the long-term sustainability of the ‘time zero’ landscapes but also a solution for sequestration$$\mathrm{Gg\,C}/\mathrm{year}$$ into soils.$$\hbox {CO}_2$$ -
Abstract The double differential cross sections of the Drell–Yan lepton pair (
, dielectron or dimuon) production are measured as functions of the invariant mass$$\ell ^+\ell ^-$$ , transverse momentum$$m_{\ell \ell }$$ , and$$p_{\textrm{T}} (\ell \ell )$$ . The$$\varphi ^{*}_{\eta }$$ observable, derived from angular measurements of the leptons and highly correlated with$$\varphi ^{*}_{\eta }$$ , is used to probe the low-$$p_{\textrm{T}} (\ell \ell )$$ region in a complementary way. Dilepton masses up to 1$$p_{\textrm{T}} (\ell \ell )$$ are investigated. Additionally, a measurement is performed requiring at least one jet in the final state. To benefit from partial cancellation of the systematic uncertainty, the ratios of the differential cross sections for various$$\,\text {Te\hspace{-.08em}V}$$ ranges to those in the Z mass peak interval are presented. The collected data correspond to an integrated luminosity of 36.3$$m_{\ell \ell }$$ of proton–proton collisions recorded with the CMS detector at the LHC at a centre-of-mass energy of 13$$\,\text {fb}^{-1}$$ . Measurements are compared with predictions based on perturbative quantum chromodynamics, including soft-gluon resummation.$$\,\text {Te\hspace{-.08em}V}$$ -
Abstract We prove that the Hilbert scheme of
k points on ($${\mathbb {C}}^2$$ ) is self-dual under three-dimensional mirror symmetry using methods of geometry and integrability. Namely, we demonstrate that the corresponding quantum equivariant K-theory is invariant upon interchanging its Kähler and equivariant parameters as well as inverting the weight of the$$\hbox {Hilb}^k[{\mathbb {C}}^2]$$ -action. First, we find a two-parameter family$${\mathbb {C}}^\times _\hbar $$ of self-mirror quiver varieties of type A and study their quantum K-theory algebras. The desired quantum K-theory of$$X_{k,l}$$ is obtained via direct limit$$\hbox {Hilb}^k[{\mathbb {C}}^2]$$ and by imposing certain periodic boundary conditions on the quiver data. Throughout the proof, we employ the quantum/classical (q-Langlands) correspondence between XXZ Bethe Ansatz equations and spaces of twisted$$l\longrightarrow \infty $$ -opers. In the end, we propose the 3d mirror dual for the moduli spaces of torsion-free rank-$$\hbar $$ N sheaves on with the help of a different (three-parametric) family of type A quiver varieties with known mirror dual.$${\mathbb {P}}^2$$ -
Abstract Measurements of the associated production of a W boson and a charm (
) quark in proton–proton collisions at a centre-of-mass energy of 8$${\text {c}}$$ are reported. The analysis uses a data sample corresponding to a total integrated luminosity of 19.7$$\,\text {TeV}$$ collected by the CMS detector at the LHC. The W bosons are identified through their leptonic decays to an electron or a muon, and a neutrino. Charm quark jets are selected using distinctive signatures of charm hadron decays. The product of the cross section and branching fraction$$\,\text {fb}^{-1}$$ , where$$\sigma (\text {p}\text {p}\rightarrow \text {W}+ {\text {c}}+ \text {X}) {\mathcal {B}}(\text {W}\rightarrow \ell \upnu )$$ or$$\ell = \text {e}$$ , and the cross section ratio$$\upmu $$ are measured in a fiducial volume and differentially as functions of the pseudorapidity and of the transverse momentum of the lepton from the W boson decay. The results are compared with theoretical predictions. The impact of these measurements on the determination of the strange quark distribution is assessed.$$\sigma (\text {p}\text {p}\rightarrow {{\text {W}}^{+} + \bar{{\text {c}}} + \text {X}}) / \sigma (\text {p}\text {p}\rightarrow {{\text {W}}^{-} + {\text {c}}+ \text {X}})$$