The paper has two parts, in the first part, we apply the localisation technique to the Rozansky–Witten theory on compact hyperkähler targets. We do so via first reformulating the theory as some ...supersymmetric sigma-model. We obtain the exact formula for the partition function with Wilson loops on
S
1
×
Σ
g
and the lens spaces, the results match with earlier computations using Feynman diagrams on K3. The second part is motivated by a very curious paper (Gukov in J Geom Phys 168, 104311, 2021), where the equivariant index formula for the dimension of the Hilbert space of the Rozansky–Witten theory is interpreted as a kind of Verlinde formula. In this interpretation, the fixed points of the target hyperkähler geometry correspond to certain ‘states’. We extend the formalism of part one to incorporate equivariance on the target geometry. For certain non-compact hyperkähler geometry, we can apply the tilting theory to the derived category of coherent sheaves, whose objects label the Wilson loops, allowing us to pick a basis for the latter. We can then compute the fusion products in this basis and we show that the objects that have diagonal fusion rules are intimately related to the fixed points of the geometry. Using these objects as basis to compute the dimension of the Hilbert space leads back to the Verlinde formula, thus answering the question that motivated the paper.
Electrochemiluminescence (ECL) plays a key role in analysis and sensing because of its high sensitivity and low background. Its wide applications are however limited by a lack of highly tunable ECL ...luminophores. Here we develop a scalable method to design ECL emitters of covalent organic frameworks (COFs) in aqueous medium by simultaneously restricting the donor and acceptor to the COFs' tight electron configurations and constructing high-speed charge transport networks through olefin linkages. This design allows efficient intramolecular charge transfer for strong ECL, and no exogenous poisonous co-reactants are needed. Olefin-linked donor-acceptor conjugated COFs, systematically synthesized by combining non-ECL active monomers with C
or C
symmetry, exhibit strong ECL signals, which can be boosted by increasing the chain length and conjugation of monomers. The present concept demonstrates that the highly efficient COF-based ECL luminophores can be precisely designed, providing a promising direction toward COF-based ECL phosphors.
SnS2 nanoplatelet electrodes can offer an exceptionally high pseudocapacitance in an organic Na+ ion electrolyte system, but their underlying mechanisms are still largely unexplored, hindering the ...practical applications of pseudocapacitive SnS2 anodes in Na‐ion batteries (SIBs) and Na hybrid capacitors (SHCs). Herein, SnS2 nanoplatelets are grown directly on SnO2/C composites to synthesize SnS2/graphene‐carbon nanotube aerogel (SnS2/GCA) by pressurized sulfidation where the original morphology of carbon framework is preserved. The composite electrode possessing a large surface area delivers a remarkable specific capacity of 600.3 mA h g−1 at 0.2 A g−1 and 304.8 mA h g−1 at an ultrahigh current density of 10 A g−1 in SIBs. SHCs comprising a SnS2/GCA composite anode and an activated carbon cathode present exceptional energy densities of 108.3 and 26.9 W h kg−1 at power densities of 130 and 6053 W kg−1, respectively. The in situ transmission electron microscopy and the density functional theory calculations reveal that the excellent pseudocapacitance originates from the combination of Na adsorption on the surface/Sn edge of SnS2 nanoplatelets and ultrafast Na+ ion intercalation into the SnS2 layers.
Metal dichalcogenide SnS2 nanoplatelets are synthesized by pressurized sulfidation and are anchored on graphene‐carbon nanotube aerogels as anodes for Na‐ion batteries and Na hybrid capacitors. The composite anode delivers an ultrahigh pseudocapacitance which originates from both Na+ ion intercalation into the SnS2 layers and adsorption of Na on the surface/Sn edge of SnS2 nanoplatelets.
Following our previous proposal, we construct a class of good "lattice cross sections" (LCSs), from which we can study the partonic structure of hadrons from ab initio lattice QCD calculations. These ...good LCSs, on the one hand, can be calculated directly in lattice QCD, and on the other hand, can be factorized into parton distribution functions (PDFs) with calculable coefficients, in the same way as QCD factorization for factorizable hadronic cross sections. PDFs could be extracted from QCD global analysis of the lattice QCD generated data of LCSs. We also show that the proposed functions for lattice QCD calculation of PDFs in the literature are special cases of these good LCSs.
Parton distribution functions (PDFs) are nonperturbative quantities describing the relation between a hadron and the quarks and gluons within it. We propose to extract PDFs from QCD global analysis ...of “data” generated by lattice QCD calculations of good “lattice cross sections,” which are basically single-hadron matrix elements that are lattice QCD calculable and perturbative QCD factorizable into the PDFs. To demonstrate the existence of good “lattice cross sections,” we take quasiquark distribution introduced by Ji Phys. Rev. Lett. 110, 262002 (2013) as a case study to show that it could be factorized into the PDFs to all orders in perturbation theory if it can be multiplicatively renormalized. We calculate the factorized coefficients at the next-to-leading order in αs.
Uranium is a key resource for the development of the nuclear industry, and extracting uranium from the natural seawater is one of the most promising ways to address the shortage of uranium resources. ...Herein, a semiconducting covalent organic framework (named NDA‐TN‐AO) with excellent photocatalytic and photoelectric activities was synthesized. The excellent photocatalytic effect endowed NDA‐TN‐AO with a high anti‐biofouling activity by generating biotoxic reactive oxygen species and promoting photoelectrons to reduce the adsorbed UVI to insoluble UIV, thereby increasing the uranium extraction capacity. Owing to the photoinduced effect, the adsorption capacity of NDA‐TN‐AO to uranium in seawater reaches 6.07 mg g−1, which is 1.33 times of that in dark. The NDA‐TN‐AO with enhanced adsorption capacity is a promising material for extracting uranium from the natural seawater.
Photoelectric and photocatalytic effects endow the covalent organic framework NDA‐TN‐AO with good anti‐biofouling activity. This occurs by generating biotoxic reactive oxygen species and promoting photoelectrons to reduce the adsorbed UVI to insoluble UIV, thereby improving the uranium adsorption capacity.
Generalized parton distributions (GPDs) are important nonperturbative functions that provide tomographic images of partonic structures of hadrons. We introduce a type of exclusive processes, to be ...referred to as single diffractive hard exclusive processes (SDHEPs). We discuss the necessary and sufficient conditions for SDHEPs to be factorized into GPDs. We demonstrate that the SDHEP is not only sufficiently generic to cover all known processes for extracting GPDs, but is also well motivated for the search of new processes for the study of GPDs. We examine the sensitivity of the SDHEP to the parton momentum fraction x dependence of GPDs.
Quasiparton distribution functions have received a lot of attention in both the perturbative QCD and lattice QCD communities in recent years because they not only carry good information on the parton ...distribution functions but also could be evaluated by lattice QCD simulations. However, unlike the parton distribution functions, the quasiparton distribution functions have perturbative ultraviolet power divergences because they are not defined by twist-2 operators. In this paper, we identify all sources of ultraviolet divergences for the quasiparton distribution functions in coordinate space and demonstrate that power divergences as well as all logarithmic divergences can be renormalized multiplicatively to all orders in QCD perturbation theory.
The emergence of flexible and wearable electronic devices with shape amenability and high mobility has stimulated the development of flexible power sources to bring revolutionary changes to daily ...lives. The conventional rechargeable batteries with fixed geometries and sizes have limited their functionalities in wearable applications. The first‐ever graphene‐based fibrous rechargeable batteries are reported in this work. Ultralight composite fibers consisting of reduced graphene oxide/carbon nanotube filled with a large amount of sulfur (rGO/CNT/S) are prepared by a facile, one‐pot wet‐spinning method. The liquid crystalline behavior of high concentration GO sheets facilitates the alignment of rGO/CNT/S composites, enabling rational assembly into flexible and conductive fibers as lithium–sulfur battery electrodes. The ultralight fiber electrodes with scalable linear densities ranging from 0.028 to 0.13 mg cm−1 deliver a high initial capacity of 1255 mAh g−1 and an areal capacity of 2.49 mAh cm−2 at C/20. A shape‐conformable cable battery prototype demonstrates a stable discharge characteristic after 30 bending cycles.
A freestanding and ultralight reduced graphene oxide (rGO)/carbon nanotube (CNT)/sulfur composite fibers are prepared by wet‐spinning as the cathode for lithium–sulfur batteries (LSBs). The liquid crystallinity of high concentration GO sheets enables rational assembly of rGO/CNT/S as flexible, conductive fibers. A cable LSB prototype comprising rGO/CNT/S cathode and lithium wire anode demonstrates excellent flexibility and stable static discharge performance.
2D covalent organic frameworks (2D COFs) have been recognized as a novel class of photoactive materials owing to their extended π‐electron conjugation and high chemical stabilities. Herein, a new ...covalent organic framework (Tph‐BDP) is facilely synthesized by using a porphyrin derivative and an organic dye BODIPY derivative (5,5‐difluoro‐2,8‐diformyl‐1,3,7,9‐tetramethyl‐10‐phenyl‐5H‐dipyrrolo1,2‐c:2′,1′‐f1,3,2diazabori‐nin‐4‐ium‐5‐uide) as monomers for the first time, and their unique photosensitive properties endow them excellent simulated oxidase activity under 635 nm laser irradiation that can catalyze the oxidation of 3,3′,5,5′‐tetramethylbenzidine (TMB). Further findings demonstrate that the presence of uranium (UO22+) can coordinate with imines of the oxidation products of TMB, thus modulating the charge transfer process of the colored products accompanied with intensive aggregation and remarkable color fading. This research provides a preparation strategy for COFs with excellent photocatalytic properties and nanozyme activity, and broadens the applications of the simple colorimetric methods for sensitive and selective radionuclide detection.
A new covalent organic framework is facilely synthesized and its unique photosensitive property endows excellent simulated oxidase activity that can catalyze the oxidation of 3,3′,5,5′‐tetramethylbenzidine (TMB). The presence of uranium can coordinate with imines of the oxidation products of TMB, thus modulating the charge transfer process of the colored products accompanied with intensive aggregation and remarkable color fading.
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