Twisted Surfaces Research Articles

Integrating Sulfur Doping with a Multi-Heterointerface Fe7S8/NiS@C Composite for Wideband Microwave Absorption.

Heterointerface engineering is presently considered a valuable strategy for enhancing the microwave absorption (MA) properties of materials via compositional modification and structural design. In this study, a sulfur-doped multi-interfacial composite (Fe7S8/NiS@C) coated with NiFe-layered double hydroxides (LDHs) is successfully prepared using a hydrothermal method and post-high-temperature vulcanization. When assembled into twisted surfaces, the NiFe-LDH nanosheets exhibit porous morphologies, improving impedance matching, and microwave scattering. Sulfur doping in composites generates heterointerfaces, numerous sulfur vacancies, and lattice defects, which facilitate the polarization process to enhance MA. Owing to the controllable heterointerface design, the unique porous structure induced multiple heterointerfaces, numerous vacancies, and defects, endowing the Fe7S8/NiS@C composite with an enhanced MA capability. In particular, the minimum reflection loss (RLmin) value reached -58.1dB at 15.8GHz at a thickness of 2.1mm, and a broad effective absorption bandwidth (EAB) value of 7.3GHz is achieved at 2.5mm. Therefore, the Fe7S8/NiS@C composite exhibits remarkable potential as a high-efficiency MA material owing to the synergistic effects of the polarization processes, multiple scatterings, porous structures, and impedance matching.

Twisted Surfaces in Semi-Euclidean $4$-Space with Index $2$

In this paper, we consider the twisted surfaces in semi-Euclidean 4-space with index 2.We classify the twisted surface with respect to their spine curve which are non-null or null curves. So, we study the geometric properties of these surfaces. Also we obtain the family of some special surfaces such as flat surfaces, marginally trapped surfaces.

2D surfaces twisted to enhance electron freedom toward efficient advanced oxidation processes

Two-dimensional (2D)-interface engineering for designing effective electron-rich catalyst center is pivotal in manipulating the catalytic behaviors and activity, but still challenging. Here, we’ve successfully twisted the surfaces of the 2D layered FeOCl, fulfilling the targeted fine-tuning of its Fe sites. The obtained new catalyst can boost peroxymonosulfate activation for reactive species with much lower energy barriers and efficiently oxidized target organic with almost 41 orders of magnitude faster reaction kinetics than pristine FeOCl. The increased degree of freedom of electron around Fe site has been identified as the key driver. The distorted geometry structure around Fe has led to an increased polarization of charge distribution, associating with less symmetric electron valence cloud and higher electron mobility. Thus, the twisted surfaces enable a much enhanced interfacial charge transfer between Fe site and the electron-deficient peroxymonosulfate. This work highlights the concept of twisted surface construction toward efficient advanced oxidation catalyst design.

L^p bounds for singular integral operators along twisted surfaces

L^p bounds for singular integral operators along twisted surfaces

Twisted Surfaces Family in Euclidean 3-Space

In this study, we examine a distinct set of twisted surfaces in the three-dimensional Euclidean space E3. Our focus lies in the investigation of the differential geometry of this surface family, including the determination of their curvatures. Furthermore, we establish the essential conditions for minimal surfaces within this framework. Additionally, we calculate the Laplace−Beltrami operator for this particular surface family and provide an illustrative example.

The Conchoidal Twisted Surfaces Constructed by Anti-Symmetric Rotation Matrix in Euclidean 3-Space

A twisted surface is a type of mathematical surface that has a nontrivial topology, meaning that it cannot be smoothly deformed into a flat surface without tearing or cutting. Twisted surfaces are often described as having a twisted or Möbius-like structure, which gives them their name. Twisted surfaces have many interesting mathematical properties and applications, and are studied in fields such as topology, geometry, and physics. In this study, a conchoidal twisted surface is formed by the synchronized anti-symmetric rotation matrix of a planar conchoidal curve in its support plane and this support plane is about an axis in Euclidean 3-space. In addition, some examples of the conchoidal twisted surface are given and the graphs of the surfaces are presented. The Gaussian and mean curvatures of this conchoidal twisted surface are calculated. Afterward, the conchoidal twisted surface formed by an involute curve and the conchoidal twisted surface formed by a Bertrand curve pair are given. Thanks to the results obtained in our study, we have added a new type of surface to the literature.

Loxodromes On Twisted Surfaces in Euclidean 3-Space

In the present paper, loxodromes, which cut all meridians and parallels of twisted surfaces (that can be considered as a generalization of rotational surfaces) at a constant angle, have been studied in Euclidean 3-space and also some examples have been constructed to visualize and support our theory.

Loxodromes on twisted surfaces in Lorentz–Minkowski 3-space

In this paper, first, we give the general formulas according to first fundamental form of a surface for different types of loxodromes, meridians and surfaces in [Formula: see text]. After that, we obtain the differential equations of loxodromes on Type-I, Type-II and Type-III twisted surfaces in [Formula: see text] and also, we state a theorem which generalizes the differential equations of different types of loxodromes on the twisted surfaces for a special case. Finally, we provide several examples for visualizing our obtained results and draw our loxodromes and meridians on twisted surfaces with the aid of Mathematica.

Lifts of Twisted K3 Surfaces to Characteristic 0

Abstract Deligne [9] showed that every K3 surface over an algebraically closed field of positive characteristic admits a lift to characteristic 0. We show the same is true for a twisted K3 surface. To do this, we study the versal deformation spaces of twisted K3 surfaces, which are particularly interesting when the characteristic divides the order of the Brauer class. We also give an algebraic construction of certain moduli spaces of twisted K3 surfaces over ${\operatorname {Spec}}\ \textbf {Z}$ and apply our deformation theory to study their geometry. As an application of our results, we show that every derived equivalence between twisted K3 surfaces in positive characteristic is orientation preserving.

Singular integral operators on product domains along twisted surfaces

We introduce a class of singular integral operators on product domains along twisted surfaces. We prove that the operators are bounded on Lp provided that the kernels satisfy weak conditions.

Activating Lattice Oxygen at the Twisted Surface in a Mesoporous CeO2Single Crystal for Efficient and Durable Catalytic CO Oxidation

AbstractActivating lattice oxygen linked to active sites at surface remains a fundamental challenge in many catalytic reactions. Here we create well‐defined surface by directly growing porous CeO2single crystals at 2 cm scale and confining Pt in lattice to construct isolated Pt1/CeO2sites at a continuously twisted surface in a monolith. We demonstrate significantly enhanced activation of lattice oxygen linked to Pt ions in contrast to Ce ions in local structures. We show complete CO oxidation with air at 67 °C without degradation being observed after operation of 300 hours. The isolated Pt1/CeO2sites at twisted surfaces not only contribute to the chemisorption of CO but also effectively activate the lattice oxygen linked to Pt ion for CO oxidation. The current work would open a new route to activate lattice oxygen by incorporating well‐defined active structures confined at the surfaces.

Activating Lattice Oxygen at the Twisted Surface in a Mesoporous CeO2 Single Crystal for Efficient and Durable Catalytic CO Oxidation.

Activating lattice oxygen linked to active sites at surface remains a fundamental challenge in many catalytic reactions. Here we create well-defined surface by directly growing porous CeO2 single crystals at 2 cm scale and confining Pt in lattice to construct isolated Pt1 /CeO2 sites at a continuously twisted surface in a monolith. We demonstrate significantly enhanced activation of lattice oxygen linked to Pt ions in contrast to Ce ions in local structures. We show complete CO oxidation with air at 67 °C without degradation being observed after operation of 300 hours. The isolated Pt1 /CeO2 sites at twisted surfaces not only contribute to the chemisorption of CO but also effectively activate the lattice oxygen linked to Pt ion for CO oxidation. The current work would open a new route to activate lattice oxygen by incorporating well-defined active structures confined at the surfaces.

Derived equivalences of twisted supersingular K3 surfaces

We study the derived categories of twisted supersingular K3 surfaces. We prove a derived crystalline Torelli theorem for twisted supersingular K3 surfaces, characterizing Fourier-Mukai equivalences in terms of the twisted K3 crystals introduced in [2]. This is a positive characteristic analog of the Hodge-theoretic derived Torelli theorem of Orlov [23] and its extension to twisted K3 surfaces by Huybrechts and Stellari [9,10]. We give applications to various questions concerning Fourier-Mukai partners, extending results of Căldăraru [5] and Huybrechts and Stellari [9]. We also give an exact formula for the number of twisted Fourier-Mukai partners of a twisted supersingular K3 surface.

Surface Engineering in Mesoporous Single Crystal to Enhance Pseudocapacitance

AbstractMesoporous single crystals combining the ordering of crystal lattice and the disordering of interconnected pores would create well‐defined structures confined at continuously twisted surfaces that are kinetically trapped. Here, mesoporous WN single crystal at 2 cm scale is grown to create and engineer the well‐defined surface structures. The unsaturated coordination structures including W–N1/2, W–N1/3, and W–N1/6 confined at twisted surfaces account for the chemisorption of H in acidic electrolyte and deliver a record high areal capacitance of ≈250 F cm−2 without degradation being observed even after 15 000 cycles. The engineering of well‐defined coordination structures at twisted surfaces would open an alternative to create active surfaces in the wealth of other single‐crystalline materials.

Twisted Surfaces in Porous Single Crystals to Deliver Enhanced Catalytic Activity and Stability

AbstractPorous single crystals which combine ordered lattice structures and disordered inter‐connected pores would provide an alternative to create twisted surface in porous microstructures. Now, transition‐metal nitride Nb4N5 and MoN single crystals are grown on a 2 cm scale to create well‐defined active structures at twisted surfaces. High catalytic activity and stability toward non‐oxidative dehydrogenation of ethane to ethylene is observed. Unsaturated metal–nitrogen coordination structures including Nb‐N1/5, Nb‐N2/5, Mo‐N1/3, and Mo‐N1/6 at the twisted surface mainly account for the C−H activation with chemisorption of H in molecular ethane at the twisted surface, which not only improves dehydrogenation performance but also avoids the deep cracking of ethane to enhance coking resistance. 11–25 % ethane conversion and 98–99 % ethylene selectivity is demonstrated without degradation being observed even after the operation of 50 hours.

Twisted Surfaces in Porous Single Crystals to Deliver Enhanced Catalytic Activity and Stability

Porous single crystals which combine ordered lattice structures and disordered inter-connected pores would provide an alternative to create twisted surface in porous microstructures. Now, transition-metal nitride Nb4 N5 and MoN single crystals are grown on a 2 cm scale to create well-defined active structures at twisted surfaces. High catalytic activity and stability toward non-oxidative dehydrogenation of ethane to ethylene is observed. Unsaturated metal-nitrogen coordination structures including Nb-N1/5 , Nb-N2/5 , Mo-N1/3 , and Mo-N1/6 at the twisted surface mainly account for the C-H activation with chemisorption of H in molecular ethane at the twisted surface, which not only improves dehydrogenation performance but also avoids the deep cracking of ethane to enhance coking resistance. 11-25 % ethane conversion and 98-99 % ethylene selectivity is demonstrated without degradation being observed even after the operation of 50 hours.

Moduli spaces of twisted K3 surfaces and cubic fourfolds

Motivated by the relation between (twisted) K3 surfaces and special cubic fourfolds, we construct moduli spaces of polarized twisted K3 surfaces of any fixed degree and order. We do this by mimicking the construction of the moduli space of untwisted polarized K3 surfaces as a quotient of a bounded symmetric domain.

Coordinatively Unsaturated Metal-Nitrogen Active Sites at Twisted Surfaces in Metallic Porous Nitride Single Crystals Delivering Enhanced Electrocatalysis Activity.

To create active sites on surfaces, the identification of structural features that could confine the local-defect structure in the lattice is required. Porous nitride single crystals, combining the advantages of porosity and structural coherence, provide the possibility to create coordinatively unsaturated metal-nitrogen active sites confined on surfaces. For the first time, ordered active sites and tailor the atomically resolved Fe-N and Co-N local structures are created through control of the unsaturated nitrogen coordination at twisted surfaces in porous single-crystalline Fen N (n=2-4) and Con N (n=1-3) nanocubes. The precise tailoring of the electronic structures of these coordinatively unsaturated active sites therefore engineer the catalytic activity. Optimum electrocatalysis performances are observed with the porous Fe4 N and Co3 N nanocubes with highly unsaturated nitrogen coordination for selective nitrate reduction to ammonia and nitrobenzene amination to aminobenzene, while the structural coherence of these porous nitride single crystals delivers excellent durability.

Metallic porous nitride single crystals at two-centimeter scale delivering enhanced pseudocapacitance

Pseudocapacitors that originate from chemisorption contain redox active sites mainly composed of transition metal ions with unsaturated coordination in lattice on the electrode surface. The capacitance is generally dictated by the synergy of the porous microstructure, electronic conduction and active sites in the porous electrode. Here we grow metallic porous nitride single crystals at 2-cm scale to enhance pseudocapacitance through the combination of large surface area with porous microstructure, high conductivity with metallic states and ordered active sites with unsaturated coordination at twisted surfaces. We show the enhanced gravimetric and areal pseudocapacitance and excellent cycling stability both in acidic and alkaline electrolyte with porous MoN, Ta5N6 and TiN single crystals. The long-range ordering of active metal-nitrogen sites account for the fast redox reactions in chemisorption while the high conductivity together with porous microstructure facilitate the charge transfer and species diffusion in electrodes.

Singlet superconductivity enhanced by charge order in nested twisted bilayer graphene Fermi surfaces

Using the continuum model for low energy non-interacting electronic structure of moiré van der Waals heterostructures developed by Bistritzer and MacDonald [1], we study the competition between spin, charge, and superconducting order in twisted bilayer graphene. Surprisingly, we find that for a range of small angles inclusive of the so-called magic angle, this model features robust Fermi pockets that preclude any Mott insulating phase at weak coupling. However, a Fermi surface reconstruction at θ ≳ 1.2° gives emergent van Hove singularities without any Fermi pockets. Using a hot-spot model for Fermi surface patches around these emergent saddle points, we develop a random-phase approximation from which we obtain a phase diagram very similar to that obtained recently by Isobe, Yuan, and Fu using the parquet renormalization group [2] but with additional insights. For example, our model shows strong nesting around time-reversal symmetric points at a moderate doping of ∼2 × 1011 cm−2 away from the van Hove singularity. When this nesting dominates, we predict that charge-order enhances singlet superconductivity, while spin-order suppresses superconductivity. Our theory also provides additional possibilities for the case of unnested Fermi surfaces.