Dual Lattice Research Articles

Heterointerface of Monodispersed Ultrathin-MnO2@Amorphous Carbon to Attain Durable Lattice Oxygen Redox Chemistry through Creation of Dual Lattice Oxygens.

Lattice oxygen (OL) redox chemistry is a key to alleviating the energy and environmental crisis, but it faces challenges in activating the OL while ensuring structural stability. We disclosed herein that engineering a heterogeneous interface between ultrathin oxide and amorphous carbon can attain the durable OL redox chemistry without introducing catalytically impure sites. To this end, we proposed a green strategy to grow ∼3.9 nm-thickness wrinkled δ-MnO2 nanosheets that are rich in defects and are vertically aligned on amorphous carbon spheres. Experiments and calculations reveal that the electrons can easily migrate from the amorphous carbon to MnO2 at the δ-MnO2@C heterointerface. The heterogeneous interfaces can not only regulate the Mn-O bond and create oxygen defects in δ-MnO2 but also introduce lattice oxygen with varying reactivities. Specifically, the δ-MnO2@C structure carries more activated lattice oxygen that contributes to the enhanced activity on catalytic oxidation of bioderived 5-hydroxymethylfurfural (HMF) to 2,5-furandicarboxylic acid (FDCA), with a high FDCA formation rate of 1759 μmol gcat-1 h-1 and a high selectivity of 95%. The heterogeneous interface of MnO2@C also brings inert lattice oxygen, so that it manifests high structural stability during the oxidation reactions. This work deepens the fundamental understandings in the engineering of lattice oxygen for durable lattice oxygen redox chemistry and showcases an effective interface technique in creating advanced catalysts for clean sustainable energy.

Study on mechanical response control of metal-ceramic dual phase hybrid lattice structure

Different from the previous trial-and-error and empirical development process of new materials, the failure and deformation of meso-structure of lattice structures are considered as a means to customize the mechanical response in this paper. Based on this, we propose a novel metal-ceramic dual-phase hybrid lattice structure (DPHLS) that exhibits both high peak stress and a prolonged plateau stage in its mechanical response. This design aims to meet the complex mechanical response requirements of impact target materials in hard target penetration research. The DPHLS is composed of a ceramic-based SC plate lattice structure and a metal-based FCC plate lattice structure, allowing for a broad range of mechanical properties control. Besides, by combining the advantages of both ceramic and metal, the DPHLS exhibits seemingly conflicting properties of load-bearing capacity and energy absorption. In the present work, the contribution of failure and deformation behavior to the mechanical response of the structure is deeply analyzed at the mesoscopic level using theoretical analysis and numerical simulation. The quantitative relationship between the geometrical parameters of the structure and the mechanical response is established actively. The results show that the three dimensionless geometric parameters, which characterize the geometry of DPHLS, can effectively regulate its mechanical response. This study not only provides a reliable theoretical basis for the design of mesostructures in DPHLS, but also proposes a novel strategy for the customization of mechanical response.

Ultrabroadband mid-infrared emission and gas sensing of cobalt-doped chalcogenide glass ceramics.

Mid-infrared (MIR) gain materials are of great significance for the development of MIR tunable fiber lasers. Herein, for the first time, to the best of our knowledge, it is found that Ga2Se3 nanocrystals distributed in chalcogenide glass ceramics can provide new tetrahedral-coordinated sites that can be used to activate ultrabroadband MIR emissions of divalent transition metal ions, such as Co2+. Under the excitation of a 1550 nm diode laser, the transparent Ge-Ga-Se glass ceramic embedded with Co2+: Ga2Se3 nanocrystals shows an intense 2.5-5.5 µm ultrabroadband emission. The peak wavelength is located at ∼4.2 µm and the full width at half maximum exceeds 2 µm. Such emission properties, originating from the dual lattice sites of Ga3+ ions, are superior to those of transparent chalcogenide glass ceramics embedded with Co2+: ZnSe nanocrystals. Moreover, the gas detection system built based on the glass ceramic shows a sensitivity of 45.9 ppm for butane gas. Therefore, the chalcogenide glass ceramics embedded with active Co2+: Ga2Se3 nanocrystals have great potential in MIR tunable fiber lasers and gas sensing.

Representations of quantum lattice vertex algebras

Let Q be a non-degenerate even lattice, let VQ be the lattice vertex algebra associated to Q, and let VQη be a quantum lattice vertex algebra ([10]). In this paper, we prove that every VQη-module is completely reducible, and the set of simple VQη-modules are in one-to-one correspondence with the set of cosets of Q in its dual lattice.

Moiré photonic superlattice-induced transparency at commensurate angle in a terahertz metasurface composed of triple layer square lattices

The control of the speed of terahertz waves is always a challenge since the bandgap of most optical materials is much larger beyond meV with subtle nonlinear susceptibility. Moiré metasurfaces are shown to exhibit wide tunable optical properties and extraordinary physical phenomena at specific commensurate angles. These can be achieved by a careful design of the metasurface to manipulate terahertz slow light. Herein, we demonstrate a triple layer Moiré metasurface with a distinct electromagnetically induced transparency (EIT) phenomenon at commensurate angles. The proposed metasurface is composed of an intrinsic square lattice embedded into another Moiré photonic superlattice made of twisted square lattice at commensurate angles of 10.39° and 7.63°. The coupling between adjacent meta-atoms on the combined metasurface leads to destructive interference of dual trapped lattice modes, which results in a transparency window at the terahertz band. A maximum group delay of 9.76 ps is found at the transparent window of 0.84 THz when the commensurate angle is 10.39°. When the commensurate angle reduces to 7.63°, the transparency window shifts to 0.57 THz with a 5.96 ps group delay. The coupled Lorentz oscillator model indicates that the nonlinear optical susceptibility at transparency windows is above zero. Our results create an approach to tune the EIT as well as slow light in the terahertz band. Our device can have potential applications in terahertz signal processing and storage.

On trilinear and quadrilinear equations associated with the lattice Gel’fand–Dikii hierarchy

Introduced in Zhang et al. (2012), the trilinear Boussinesq equation is the natural form of the equation for the τ-function of the lattice Boussinesq system. In this paper we study various aspects of this equation: its highly nontrivial derivation from the bilinear lattice AKP equation under dimensional reduction, a quadrilinear dual lattice equation, conservation laws, and periodic reductions leading to higher-dimensional integrable maps and their Laurent property. Furthermore, we consider a higher Gel’fand–Dikii lattice system, its periodic reductions and Laurent property. As a special application, from both a trilinear Boussinesq recurrence as well as a higher Gel’fand–Dikii system of three bilinear recurrences, we establish Somos-like integer sequences.

Dual Polyanion Mechanism for Superionic Transport in BH4‐Based Argyrodites

AbstractPolyanion rotations are often linked to cation diffusion, but the study of multiple polyanion systems is scarce due to the complexities in experimentally determining their dynamic interactions. This work focuses on BH4‐based argyrodites, synthesized to achieve a high conductivity of 11 mS cm−1. Advanced tools, including high‐resolution X‐ray diffraction, neutron pair distribution function analysis, and mutinuclear magic‐angle‐spinning nuclear magnetic resonance (NMR) spectroscopy and relaxometry, along with theoretical calculations, are employed to unravel the dynamic intricacies among the dual polyanion lattice and active charge carriers. The findings reveal that the anion sublattice of Li5.07PS4.07(BH4)1.93 affords an even temporal distribution of Li among PS43− and BH4−, suggesting minimal trapping of the charge carriers. Moreover, the NMR relaxometry unveils rapid BH4− rotation on the order of ∼GHz, affecting the slower rotation of neighboring PS43− at ∼100 MHz. The PS43− rotation synchronizes with Li+ motion and drives superionic transport. Thus, the PS43− and BH4− polyanions act as two‐staged dual motors, facilitating rapid Li+ diffusion.

Dual digraphs of finite meet-distributive and modular lattices

We describe the digraphs that are dual representations of finite lattices satisfying conditions related to meet-distributivity and modularity. This is done using the dual digraph representation of finite lattices by Craig, Gouveia and Haviar (2015). These digraphs, known as TiRS digraphs, have their origins in the dual representations of lattices by Urquhart (1978) and Ploščica (1995). We describe two properties of finite lattices which are weakenings of (upper) semimodularity and lower semimodularity respectively, and then show how these properties have a simple description in the dual digraphs. Combined with previous work in this journal on dual digraphs of semidistributive lattices (2022), it leads to a dual representation of finite meet-distributive lattices. This provides a natural link to finite convex geometries. In addition, we present two sufficient conditions on a finite TiRS digraph for its dual lattice to be modular. We close by posing three open problems.

Three-dimensional numerical modeling of the temporal evolution of backward erosion piping

Backward erosion piping (BEP) is a complex degradation mechanism in geotechnical flood protection infrastructure (GFPI) that is still relatively less understood, particularly when considering its time-dependent features. This manuscript presents a novel dual random lattice modeling approach for three-dimensional simulation of BEP, with a focus on its evolution over time. The key novelty of this presented framework is twofold: (1) we propose and incorporate a novel constitutive relationship for computation of time-dependent soil erosion based on the theory of rate processes, and (2) we devise an algorithm for calculation of coupled degradation of the dual lattices for accurate computation of 3-D hydraulic gradients. The constitutive relationship was developed from fundamental granular physics, and brings the potential to provide deeper fundamental physical understanding of the phenomenon. The capabilities of the modeling framework are investigated by comparison with available laboratory experiments which illustrates good agreement in the spatial advancement of piping erosion, pipe progression speeds, as well as the evolution of local gradients. To the best knowledge of the authors, the presented model is the first to be able to capture all of the aforementioned features when simulating BEP.

Higher categorical symmetries and gauging in two-dimensional spin systems

We present a framework to systematically investigate higher categorical symmetries in two-dimensional spin systems. Though exotic, such generalised symmetries have been shown to naturally arise as dual symmetries upon gauging invertible symmetries. Our framework relies on an approach to dualities whereby dual quantum lattice models only differ in a choice of module 2-category over some input fusion 2-category. Given an arbitrary two-dimensional spin system with an ordinary symmetry, we explain how to perform the (twisted) gauging of any of its sub-symmetries. We then demonstrate that the resulting model has a symmetry structure encoded into the Morita dual of the input fusion 2-category with respect to the corresponding module 2-category. We exemplify this approach by specialising to certain finite group generalisations of the transverse-field Ising model, for which we explicitly define lattice symmetry operators organised into fusion 2-categories of higher representations of higher groups.

Ising model on the aperiodic Smith hat

Smith et al discovered an aperiodic monotile of 13 sided shape in 2023. It is called the ‘Smith hat’ and consists of eight kites. We deal with the statistical physics of the lattice of the kites, which we call the ‘Smith-kite lattice’. We studied the Ising model on the aperiodic Smith-kite lattice and the dual Smith-kite lattice using Monte Carlo simulations. We combined the Swendsen–Wang multi-cluster algorithm and the replica exchange method. We simulated systems up to the total spin number 939201 . Using the finite-size scaling (FSS) analysis, we estimated the critical temperature on the Smith-kite lattice as Tc/J=2.405±0.0005 and that of the dual Smith-kite lattice as Tc∗/J=2.143±0.0005 . Moreover, we confirmed the duality relation between the critical temperatures on the dual pair of aperiodic lattices, sinh(2J/Tc)sinh(2J/Tc∗)=1.000±0.001 . We also checked the duality relation for the nearest-neighbor correlation at the critical temperature, essentially the energy, ϵ(Tc)/coth(2J/Tc)+ϵ(Tc∗)/coth(2J/Tc∗)=1.000±0.001 .

Trimer quantum spin liquid in a honeycomb array of Rydberg atoms

Quantum spin liquids are elusive but paradigmatic examples of strongly correlated quantum states that are characterized by long-range quantum entanglement. Recently, signatures of a gapped topological Z2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\mathbb{Z}}}_{2}$$\\end{document} spin liquid have been observed in a system of Rydberg atoms; however, the full capability of these platforms to realize quantum spin liquids extends far beyond this state alone. Here, we propose the realization of a different class of spin liquids in a honeycomb array of Rydberg atoms. Exploring the system’s quantum phase diagram using density-matrix renormalization group and exact diagonalization calculations, we identify several density-wave-ordered phases and a trimer spin liquid ground state with an emergent U(1) × U(1) local symmetry. This liquid state originates from superpositions of classical trimer configurations on the dual triangular lattice in the regime where third-nearest-neighbor atoms lie within the Rydberg blockade radius. Finally, we discuss the conditions to enhance the preparation fidelity of this state by a general Rydberg-blockade-based projection mechanism, test the robustness of the trimer spin liquid phase in a range of realistic parameters, and outline methods for its experimental detection.

Bosonic flux ladder considering the next nearest neighbor kinetic tunneling

We investigate interacting bosons in a two-leg lattice, which is subject to an uniform artificial magnetic field. Its Hamiltonian takes into account the next nearest neighbor kinetic tunneling term, along the principal diagonal direction. With the help of an inhomogeneous dynamical Gutzwiller mean-field theory, we figure out four novel quantum phases of the system site by site, three of which are the dual vortex lattice, the triplet vortex lattice, and the composite vortex lattice. They particularly present parallelogram vortical particle currents, inside those conventional rectangular vortical currents, due to the import of next nearest neighbor kinetic tunneling. Under certain parameters, we further identify the crossed circulation lattice featuring alternating sequences on local currents and occupancies, whose minimal periods are determined by the value of flux quanta.

Free dual spaces and free Banach lattices

The relation between the free Banach lattice generated by a Banach space and free dual spaces is clarified. In particular, it is shown that for every Banach space E the free p-convex Banach lattice generated by E⁎⁎, denoted FBL(p)[E⁎⁎], admits a canonical isometric lattice embedding into FBL(p)[E]⁎⁎ and FBL(p)[E⁎⁎] is lattice finitely representable in FBL(p)[E]. Moreover, we also show that for p>1, FBL(p)[E]⁎⁎ can actually be considered as the free dual p-convex Banach lattice generated by E, whereas for p=1 this happens precisely when E does not contain complemented copies of ℓ1.

Systems of Precision: Coherent Probabilities on Pre-Dynkin Systems and Coherent Previsions on Linear Subspaces.

In the literature on imprecise probability, little attention is paid to the fact that imprecise probabilities are precise on a set of events. We call these sets systems of precision. We show that, under mild assumptions, the system of precision of a lower and upper probability form a so-called (pre-)Dynkin system. Interestingly, there are several settings, ranging from machine learning on partial data over frequential probability theory to quantum probability theory and decision making under uncertainty, in which, a priori, the probabilities are only desired to be precise on a specific underlying set system. Here, (pre-)Dynkin systems have been adopted as systems of precision, too. We show that, under extendability conditions, those pre-Dynkin systems equipped with probabilities can be embedded into algebras of sets. Surprisingly, the extendability conditions elaborated in a strand of work in quantum probability are equivalent to coherence from the imprecise probability literature. On this basis, we spell out a lattice duality which relates systems of precision to credal sets of probabilities. We conclude the presentation with a generalization of the framework to expectation-type counterparts of imprecise probabilities. The analogue of pre-Dynkin systems turns out to be (sets of) linear subspaces in the space of bounded, real-valued functions. We introduce partial expectations, natural generalizations of probabilities defined on pre-Dynkin systems. Again, coherence and extendability are equivalent. A related but more general lattice duality preserves the relation between systems of precision and credal sets of probabilities.

Field-driven design and performance evaluation of dual functionally graded triply periodic minimal surface structures for additive manufacturing

Triply periodic minimal surface (TPMS) structures prepared by additive manufacturing (AM) have been widely used in aerospace and thermal management systems due to their functional advantages such as high specific strength and excellent heat transfer coefficient. However, lattices with uniform or simple gradients cannot match the regional diversity needs of functional advantages in service. This study proposed a field-driven AM data processing framework for dual functionally graded TPMS lattices. For unified data processing, mathematical functions, simulated outcomes, and geometric models were transformed into fields. I-WP and Diamond units were selected as the primitive and filling structures of Ti-6Al-4V lattices, respectively. According to the functional requirements, the gradient distribution design guided by the simulated stress field is completed through the proposed framework. The results illustrate that the field-driven dual graded lattices present superior compressive mechanical response. At almost equal volume fractions, their compressive strength is approximately 100% more than that of primitive lattices and 69% greater than that of dual uniform lattices. Furthermore, the dual lattices have larger specific surface areas than the primitive lattices, making them better at heat insulation and heat dissipation. This field-driven digital framework will show enormous potential in the matching design of functionally graded lattices.

Mechanical Properties and Energy Absorption of Soft–Hard Dual Phase Lattice Structures Manufactured via Selective Laser Melting

Mechanical Properties and Energy Absorption of Soft–Hard Dual Phase Lattice Structures Manufactured via Selective Laser Melting

Lifts for Voronoi Cells of Lattices

Many polytopes arising in polyhedral combinatorics are linear projections of higher-dimensional polytopes with significantly fewer facets. Such lifts may yield compressed representations of polytopes, which are typically used to construct small-size linear programs. Motivated by algorithmic implications for the closest vector problem, we study lifts of Voronoi cells of lattices. We construct an explicit d-dimensional lattice such that every lift of the respective Voronoi cell has 2^{Omega (d/{log d})} facets. On the positive side, we show that Voronoi cells of d-dimensional root lattices and their dual lattices have lifts with {{mathcal {O}}}(d) and {{mathcal {O}}}(d log d) facets, respectively. We obtain similar results for spectrahedral lifts.

Magnetic operators in 2D compact scalar field theories on the lattice

Abstract In lattice compact gauge theories, we must impose the admissibility condition to have well-defined topological sectors. The admissibility condition, however, usually forbids the presence of magnetic operators, and it is not so trivial if one can study the physics of magnetic objects that depends on the topological term, such as the Witten effect, on the lattice. In this paper, we address this question in the case of 2D compact scalars as it would be one of the simplest examples having analogues of the monopole and the topological term. To define the magnetic operator, we propose the “excision method,” which consists of excising lattice links (or bonds) in an appropriate region containing the magnetic operator and defining the dual lattice in a particular way. The size of the excised region is O(1) in lattice units so that the magnetic operator becomes point-like in the continuum limit. We give the lattice derivation of the ’t Hooft anomalies between the electric and magnetic symmetries and also derive the higher-group-like structure related to the Witten effect.

Quantum Particle on Dual Weight Lattice in Even Weyl Alcove

Even subgroups of affine Weyl groups corresponding to irreducible crystallographic root systems characterize families of single-particle quantum systems. Induced by primary and secondary sign homomorphisms of the Weyl groups, free propagations of the quantum particle on the refined dual weight lattices inside the rescaled even Weyl alcoves are determined by Hamiltonians of tight-binding types. Described by even hopping functions, amplitudes of the particle’s jumps to the lattice neighbours are together with diverse boundary conditions incorporated through even hopping operators into the resulting even dual-weight Hamiltonians. Expressing the eigenenergies via weighted sums of the even Weyl orbit functions, the associated time-independent Schrödinger equations are exactly solved by applying the discrete even Fourier–Weyl transforms. Matrices of the even Hamiltonians together with specifications of the complementary boundary conditions are detailed for the C2 and G2 even dual-weight models.