Dual Lattice Research Articles

Dual narrow surface lattice resonances in Si/SiO2 nanopillar dimer arrays

Si/SiO2 nanopillar dimer arrays are proposed to form two narrow surface lattice resonances (SLRs). One (named SLR1) mainly comes from the coupling between single Si/SiO2 nanopillar dimers’ electric dipole resonance and arrays’ diffraction waves. Another (named SLR2) mainly comes from the coupling between single Si/SiO2 nanopillar dimers’ magnetic dipole resonance and arrays’ diffraction waves. In the array, Si nanopillar dimers are on SiO2 nanopillar dimers, and SiO2 nanopillar dimers are on a quartz substrate. The simulated results reveal that the two SLRs’ linewidths can be as small as 2.6 nm. However, for the Si/SiO2 nanopillar array without dimers, only one SLR can be formed. Compared to the SLR of the Si/SiO2 nanopillar array, the SLRs’ intensity of the Si/SiO2 nanopillar dimer array is stronger and the SLRs’ linewidth of the Si/SiO2 nanopillar dimer array is smaller. The Si/SiO2 nanopillar dimers’ height and diameter, the gap of dimers, and the arrays’ period are all important to regulate the two SLRs. This work is important to the design of micro–nano photonic devices based on multiple SLRs.

Duality for normal lattice expansions and sorted residuated frames with relations

We revisit the problem of Stone duality for lattices with quasioperators, presenting a fresh duality result. The new result is an improvement over that of our previous work in two important respects. First, the axiomatization of frames is now simplified, partly by incorporating Gehrke’s proposal of section stability for relations. Second, morphisms are redefined so as to preserve Galois stable (and co-stable) sets and we rely for this, partly again, on Goldblatt’s recently proposed definition of bounded morphisms for polarities. In studying the dual algebraic structures associated to polarities with relations we demonstrate that stable/co-stable set operators result as the Galois closure of the restriction of classical (though sorted) image operators generated by the frame relations to Galois stable/co-stable sets. This provides a proof, at the representation level, that non-distributive logics can be regarded as fragments of sorted residuated (poly)modal logics, a research direction recently initiated by this author.

Dual lattice oxygens in amorphous Zr-doped manganese oxide for highly efficient aerobic oxidation of 5-hydroxymethylfurfural to 2,5-furandicarboxylic acid

One hurdle in developing transition metal oxide (TMO) catalysts for aerobic oxidation reactions is their need for a low binding energy of the lattice oxygen (OL) to create active OL and a high OL binding energy to maintain structural stability during catalysis. In this work, we prepared amorphous Zr-doped manganese oxide (amor-Zr:MnOx) catalysts carrying dual lattice oxygens that can address such conflicting objectives in catalyst development. In the aerobic oxidation of 5-(hydroxymethyl)furfural (HMF), the amor-Zr0.2MnOx catalyst gave 99% selectivity for 2,5-furandicarboxylic acid (FDCA) and a high FDCA formation rate of 3600 µmolFDCA gcat−1 h−1 in 1 h. To the best of our knowledge, the aerobic oxidation performance of the amor-Zr0.2MnOx catalyst is superior to those of most Mn-based and related TMO-based catalysts under comparable conditions. Experimental and theoretical studies show that the OL in amor-Zr: MnOx can be divided into two groups. One group includes the more stable OL that strengthens the catalyst structure and prevents phase transition, while the other group includes the more reactive OL that improves catalyst activity through the strong adsorption/activation of O2 and helps regenerate OL during catalysis.

Guest Editorial: Selected papers from the 24th International Conference on Information Security and Cryptology (ICISC 2021)

Guest Editorial: Selected papers from the 24th International Conference on Information Security and Cryptology (ICISC 2021)

Lattice Chern-Simons model for FQHE

Motivated by [60][61] and using topological invariance and cycle homology, we construct an effective gauge invariant lattice Chern-Simons (CS) model for the fractional quantum Hall effect (FQHE) with applications to (i) the Laughlin state on 3D crystals, (ii) Haldane hierarchy, and (iii) composite fermions. First, we give a new derivation of the lattice CS action and demonstrate its gauge symmetry and invariance under lattice duality. Then, we use this lattice construction to study the filling factors of the above mentioned QH states. We show amongst others that the νlattL of Laughlin state on lattice is given by the ratio Φ0/ΦWL with ΦWL designating the flux of CS link variables through Wilson loops WL. For composite fermions, we use the adb formalism to show that the factor νlattCF is given by the charge Qb of the dumbbell field under the dual gauge link variables. Our model gives explicitly the effective filling fraction of composite fermions on the lattice as νlatt⁎=νlattCF/(1−2nνlattCF) with νlattCF being the bare lattice filling factor in agreement with the continuum limit result.

A dual-lattice hydrodynamic-thermal MRT-LBM model implemented on GPU for DNS calculations of turbulent thermal flows

PurposeThe purpose of this paper is to present a fast and bare bones implementation of a numerical method for quickly simulating turbulent thermal flows on GPUs. The work also validates earlier research showing that the lattice Boltzmann method (LBM) method is suitable for complex thermal flows.Design/methodology/approachA dual lattice hydrodynamic (D3Q27) thermal (D3Q7) multiple-relaxation time LBM model capable of thermal DNS calculations is implemented in CUDA.FindingsThe model has the same computational performance compared to earlier publications of similar LBM solvers. The solver is validated against three benchmark cases for turbulent thermal flow with available data and is shown to be in excellent agreement.Originality/valueThe combination of a D3Q27 and D3Q7 stencil for a multiple relaxation time -LBM has, to the authors’ knowledge, not been used for simulations of thermal flows. The code is made available in a public repository under a free license.

Frozen Deconfined Quantum Criticality

There is a number of contradictory findings with regard to whether the theory describing easy-plane quantum antiferromagnets undergoes a second-order phase transition. The traditional Landau-Ginzburg-Wilson approach suggests a first-order phase transition, as there are two different competing order parameters. On the other hand, it is known that the theory has the property of self-duality which has been connected to the existence of a deconfined quantum critical point (DQCP). The latter regime suggests that order parameters are not the elementary building blocks of the theory, but rather consist of fractionalized particles that are confined in both phases of the transition and only appear-deconfine-at the critical point. Nevertheless, many numerical MonteCarlo simulations disagree with the claim of a DQCP in the system, indicating instead a first-order phase transition. Here we establish from exact lattice duality transformations and renormalization group analysis that the easy-plane CP^{1} antiferromagnet does feature a DQCP. We uncover the criticality starting from a regime analogous to the zero temperature limit of a certain classical statistical mechanics system which we therefore dub frozen. At criticality our bosonic theory is dual to a fermionic one with two massless Dirac fermions, which thus undergoes a second-order phase transition as well.

Classical vertex model dualities in a family of two-dimensional frustrated quantum antiferromagnets

We study a general class of easy-axis spin models on a lattice of corner sharing even-sided polygons with all-to-all interactions within a plaquette. The low energy description corresponds to a quantum dimer model on a dual lattice of even coordination number with a multi dimer constraint. At an appropriately constructed frustration-free Rokhsar-Kivelson (RK) point, the ground state wavefunction can be exactly mapped onto a classical vertex model on the dual lattice. When the dual lattice is bipartite, the vertex models are bonded and are self dual under Wegner's duality, with the self dual point corresponding to the RK point of the original multi-dimer model. We argue that the self dual point is a critical point based on known exact solutions to some of the vertex models. When the dual lattice is non-bipartite, the vertex model is arrowed, and we use numerical methods to argue that there is no phase transition as a function of the vertex weights. Motivated by these wavefunction dualities, we construct two other distinct families of frustration-free Hamiltonians whose ground states can be mapped onto these vertex models. Many of these RK Hamiltonians provably host $\mathbb{Z}_2$ topologically ordered phases.

Polarization-controlled dual resonant lattice Kerker effects

Polarization-controlled dual resonant lattice Kerker effects

Localization in a non-Hermitian flat band lattice with nonlinearity

In this article, we aim to report the competing role of non-Hermiticity and nonlinearity introduced in the flat band lattice. For this, we initially examine the dynamics of a non-Hermitian single chain diamond network and show a pure imaginary flat band between the complex dispersive bands. The presence of a pure imaginary flat band leads to light propagation either with amplification or attenuation in a confined manner. With this information, we shift to exploiting the non-Hermitian dual chain diamond lattice which shows PT-symmetric nature in a particular situation. In the linear case, the model has two flat bands in its spectrum, whereas its nature depends on the system parameters. This gives rise to the distinct nature of localized light propagation in the system with controllable intensity. Interestingly, in the case of a pure real flat band with broad-site excitation, large-site stable oscillations appear in the system and exist for a long propagation distance. Finally, we study the dual chain lattice with on-site cubic nonlinearity which shows transient localized propagation for initially localized excitation and stationary kovaton like localization for broad-site excitation. Our results reveal the possibility of controlling transport dynamics in non-Hermitian systems with nonlinearity. Our system also acts as a candidate for optical applications, as in the long-distance diffraction-less transmission of information.

On generation and enumeration of orthogonal Chebyshev-Frolov lattices

We discuss orthogonal Chebyshev-Frolov lattices, their generating matrices and their use in Frolov cubature formula. We give a detailed account on coordinate-permuted systems that lead to fast computation and enumeration of such lattices. In particular, we explain the recurrences identified in (K. Suzuki and T. Yoshiki, Hiroshima Math. J., 49(1):139–159, 2019) via a plain constructive approach exhibiting a new hierarchical basis of polynomials. Dual Chebyshev-Frolov lattices and their generating matrices are also studied. Lattices enumeration in axis-parallel boxes is discussed.

The Minor Order of Homomorphisms via Natural Dualities

We study the minor relation for algebra homomorphims in finitely generated quasivarieties that admit a logarithmic natural duality. We characterize the minor homomorphism posets of finite algebras in terms of disjoint unions of dual partition lattices and investigate reconstruction problems for homomorphisms.

A separation lemma on sub-lattices

Abstract We prove that Bourgain’s separation lemma [J. Bourgain, Green’s Function Estimates for Lattice Schrödinger Operators and Applications, Ann. of Math. Stud. 158, Princeton University, Princeton, 2005] holds at fixed frequencies and their neighborhoods, on sub-lattices, sub-modules of the dual lattice associated with a quasi-periodic Fourier series in two dimensions. And, by extension, it holds on the affine spaces. Previously Bourgain’s lemma was not deterministic, and it is valid only for a set of frequencies of positive measure. The new separation lemma generalizes classical lattice partition-type results to the hyperbolic Lorentzian setting, with signature ( 1 , - 1 , - 1 ) {(1,-1,-1)} , and could be of independent interest. Combined with the method in [W.-M. Wang, Quasi-periodic solutions to a nonlinear Klein–Gordon equation with a decaying nonlinear term, preprint 2021, https://arxiv.org/abs/1609.00309], this should lead to the existence of quasi-periodic solutions to the nonlinear Klein–Gordon equation with the usual polynomial nonlinear term u p + 1 {u^{p+1}} .

Mechanical properties and energy absorption performance of bio-inspired dual architecture phase lattice structures

In this paper, a novel dual architecture phase lattice (DPL) structure consisting with hard and soft phases is proposed, and their mechanical properties as well as the deformation features under compression are investigated. Firstly, two different types of basic cubic cells are selected as the constitution phases, and the DPLs with different arrangements are then constructed by additive manufacturing. Quasi-static compression tests and numerical simulations are performed to explore the deformation patterns and stress-strain responses. The compressive strength, plateau stress and the specific energy absorption of the DPLs are characterized. The effects of base material fracture, rod diameter and the cell arrangements on the mechanical responses are explored. Results show that the deformation and failure initiate in the matrix phase and trigger the embedding of the reinforcing phase into the crushed regions. The fracture of the rods results in a lower stress level and more serious fluctuations in the stress-strain responses. Increasing the rod diameter is an effective approach for enhancing the compressive strength and specific energy absorption. Introducing appropriate agreements of reinforcement phases can result in 112% and 37% increments for the compression strength and specific energy absorption, respectively. The findings of this work can facilitate the designs of lattice structures with outstanding mechanical properties and energy absorption performances.

Assembling Metal Organic Layer Composites for High‐Performance Electrocatalytic CO2 Reduction to Formate

Abstract2D metal–organic‐framework (MOF) based composites have emerged as promising candidates for electrocatalysis due to their high structural flexibility and fully exposed active sites. Herein, a freestanding metal–organic layer (MOL) with a 2D kgd (kagome dual) lattice was constructed with abundant surface oxygenate groups serving as anchoring sites to immobilize diverse guests. Taking Bi as an example, tetragonal Bi2O3 nanowires can be uniformly grown on MOLs after solvothermal treatment, the structural evolution of which was followed by ex situ electron microscopy. The as‐prepared Bi2O3/MOL exhibits excellent CO2 electroreduction activity towards formate reaching a specific current of 2.3 A mgBi−1 and Faradaic efficiencies of over 85 % with a wide potential range from −0.87 to −1.17 V, far surpassing Bi2O3/UiO (a 3D Zr6‐oxo based MOF) and Bi2O3/AB (Acetylene Black). Such a post‐synthetic modification strategy can be flexibly extended to develop versatile MOL composites, highlighting the superiority of optimizing MOL‐based composites for electrocatalysis.

Assembling Metal Organic Layer Composites for High-Performance Electrocatalytic CO2 Reduction to Formate.

2D metal–organic‐framework (MOF) based composites have emerged as promising candidates for electrocatalysis due to their high structural flexibility and fully exposed active sites. Herein, a freestanding metal–organic layer (MOL) with a 2D kgd (kagome dual) lattice was constructed with abundant surface oxygenate groups serving as anchoring sites to immobilize diverse guests. Taking Bi as an example, tetragonal Bi2O3 nanowires can be uniformly grown on MOLs after solvothermal treatment, the structural evolution of which was followed by ex situ electron microscopy. The as‐prepared Bi2O3/MOL exhibits excellent CO2 electroreduction activity towards formate reaching a specific current of 2.3 A mgBi −1 and Faradaic efficiencies of over 85 % with a wide potential range from −0.87 to −1.17 V, far surpassing Bi2O3/UiO (a 3D Zr6‐oxo based MOF) and Bi2O3/AB (Acetylene Black). Such a post‐synthetic modification strategy can be flexibly extended to develop versatile MOL composites, highlighting the superiority of optimizing MOL‐based composites for electrocatalysis.

Abelian Chern-Simons gauge theory on the lattice

The Abelian Chern-Simons gauge theory is constructed on the three-dimensional spacetime lattice. This proposal introduces both lattice and dual lattice, and the gauge field on the dual lattice is expressed in terms of the gauge field on the original lattice. This treatment circumvents the issue of forward/backward difference, which is the common problem that many previous proposals have, and also avoids the duplication problem, which prevents people from introducing the dual lattice. The form of the lattice action is very simple, and is symmetric with respect to the three spacetime dimensions. These features make it straightforward to calculate the expectation values of Wilson loops, and the results agree with the topological field theory in continuous spacetime. Generalizations to multiple types of lattices are also discussed.

Modelling of capillary water absorption in sound and cracked concrete using a dual-lattice approach: Computational aspects

Lattice models have been used to simulate mass transport to predict durability of cementitious materials. In particular, the use of dual lattice meshes allows for the coupling of fracture and transport processes, which commonly occur at the same time in these materials. Literature has shown good agreement between simulations and experimental results. Nevertheless, work regarding relevant computational aspects of the numerical model are scarce. In this study, a Voronoi-discretized lattice model is used to simulate unsaturated moisture transport in cement-base materials through the Richards equation. First, investigations regarding the choice of elemental volume approximation, time-stepping procedure and quadrature are evaluated . After validation of the approximations, simulated moisture transport in sound concrete was compared to experiments and mesh and time step sensitivity were discussed. A new approach to model capillary absorption of water in cracked concrete was also proposed and its advantages with respect to existing approaches are discussed by comparing to experimental measurements. The results confirm that the model can accurately predict the transport processes for the earlier stage of capillary absorption. Furthermore, moisture ingress in cracked concrete is simulated for different crack configurations and the use of different approaches is suggested accordingly. Finally, guidelines regarding the approximations used for optimization of the computations are presented.

A unidirectional certificateless proxy re‐signature scheme based on lattice

AbstractAs a kind of special digital signature, proxy re‐signature is becoming more and more important in transparent certification and management of group signatures. But most existing proxy re‐signature schemes cannot resist collusion attack. So we construct a scheme by using dual modulus technology and lattice structure. Dual modulus technology can ensure that our solution can resist various collusion attacks. Lattice structure can ensure that our scheme is secure in the postquantum era. Compared with the previous scheme, our scheme is unidirectional and certificateless, is secure in the post‐quantum era, does not require key escrow, can prevent man‐in‐the‐middle attacks, and can resist collusion attacks of proxy and delegatee as well as proxy and delegator. Moreover, our scheme is unidirectional and has better privacy. Furthermore, under the random oracle model, we prove that our scheme is strong nonforgeability against external attackers and the internal key generation center.

On Combinatorics of Voronoi Polytopes for Perturbations of the Dual Root Lattices

The Voronoi conjecture on parallelohedra claims that for every convex polytope P that tiles Euclidean d-dimensional space with translations there exists a d-dimensional lattice such that P and the Voronoi polytope of this lattice are affinely equivalent. The Voronoi conjecture is still open for the general case but it is known that some combinatorial restrictions for the face structure of P ensure that the Voronoi conjecture holds for P. In this article, we prove that if P is the Voronoi polytope of one of the dual root lattices or or their small perturbations, then every parallelohedron combinatorially equivalent to P in strong sense satisfies the Voronoi conjecture.