Infinite Structure Research Articles

One-dimensional infinite chain Ag(i) complex with high quantum yield and TADF property: prepared by metal ion adjustment

The complex AgDpq exhibits excellent photophysical properties and TADF characteristics than Cu(i) complex, which is related to the unique one-dimensional infinite chain structure and the smaller contribution of metal to the excited states.

Coupled flexural and torsional vibration attenuation with locally resonant metamaterials

A metamaterial beam with coupled bending and torsional resonators for broadband flexural–torsional vibration suppression is studied. The main objective is to design and analyse the metamaterial beam for simultaneous attenuation of flexural and torsional vibration waves using FEM and the Bloch-Floquet theorem. The bandgaps of the single unit cell with an infinite periodic structure assumption are studied using Bloch-Floquet reduction with a commercial multi-physics program. Initially, the beam with a bending resonator is examined, and a high-frequency broadband vibration frequency bandgap above 10 kHz is observed. With the addition of a torsional resonator, the existing bending bandgaps are widened, and further new bandgaps are formed. Transmissibility analysis of a metamaterial beam with the above unit cells is performed using the finite element method. The FRFs show similar bandgaps observed in the dispersion curves, thereby validating unit cell analysis. It is observed that coupled bending and torsional resonators create the opportunity to widen and introduce new bandgaps compared to uncoupled resonators. These metamaterial beams with bending and coupled resonators can aid in vibration isolation and frequency filtering of structures subjected to bending and torsional impact loads.

The Ramsey theory of Henson graphs

Analogues of Ramsey’s Theorem for infinite structures such as the rationals or the Rado graph have been known for some time. In this context, one looks for optimal bounds, called degrees, for the number of colors in an isomorphic substructure rather than one color, as that is often impossible. Such theorems for Henson graphs however remained elusive, due to lack of techniques for handling forbidden cliques. Building on the author’s recent result for the triangle-free Henson graph, we prove that for each [Formula: see text], the k-clique-free Henson graph has finite big Ramsey degrees, the appropriate analogue of Ramsey’s Theorem. We develop a method for coding copies of Henson graphs into a new class of trees, called strong coding trees, and prove Ramsey theorems for these trees which are applied to deduce finite big Ramsey degrees. The approach here provides a general methodology opening further study of big Ramsey degrees for ultrahomogeneous structures. The results have bearing on topological dynamics via work of Kechris, Pestov, and Todorcevic and of Zucker.

Size effect on light propagation modulation near band edges in one-dimensional periodic structures

Periodic photonic structures can provide rich modulation in propagation of light due to well-defined band structures. Especially near band edges, light localization and the effect of near-zero refractive index have attracted wide attention. However, the practically fabricated structures can only have finite size, i.e., limited numbers of periods, leading to changes of the light propagation modulation compared with infinite structures. Here, we study the size effect on light localization and near-zero refractive-index propagation near band edges in one-dimensional periodic structures. Near edges of the band gap, as the structureʼs size shrinks, the broadening of the band gap and the weakening of the light localization are discovered. When the size is small, an added layer on the surface will perform large modulation in the group velocity. Near the degenerate point with Dirac-like dispersion, the zero-refractive-index effects like the zero-phase difference and near-unity transmittance retain as the size changes, while absolute group velocity fluctuates when the size shrinks.

A study on two unusual heterohexanuclear [CuII4LnIII2] (LnIII = LaIII and CeIII) complexes with a N2O2- and O6-donor bis(salamo)-based ligand

Two unusual heterobimetallic [Cu II 4 Ln III 2 ] complexes were constructed from a N 2 O 2 - and O 6 -donor bis(salamo)-based ligand (H 4 L), and characterized structurally. The intermolecular interactions were quantitatively analyzed by Hirshfeld surfaces, as well as, fluorescence properties have also been studied. • Two structurally novel heterobimetallic hexanuclear [Cu II 4 Ln III 2 ] complexes were prepared using a designed N 2 O 2 - and O 6 -donor bis(salamo)-based ligand. • The different natures of three-compartmental H 4 L lead to the site‐selective introduction of two various metal II/III atoms. • Quantitative analyses of intermolecular interactions were evaluated by Hirshfeld surfaces analyses. • The fluorescence properties were further discussed. Two unusual heterobimetallic [Cu II 4 Ln III 2 ] complexes, [{Cu 4 (L) 2 La 2 ( ƞ 2 -NO 3 ) 6 (EtOH)}]·2Me 2 CO ( 1 ) and [{Cu 4 (L) 2 Ce 2 ( ƞ 2 -NO 3 ) 6 (EtOH)} 2 ]·4Me 2 CO·MeOH ( 2 ) were constructed from a N 2 O 2 - and O 6 -donor bis(salamo)-based ligand (H 4 L). The structures were characterized by physical chemistry and spectroscopy methods. The two complexes 1 and 2 have similar structures, two heterotrinuclear parts with the same structure are linked by the coordination between one Cu II atom and oxime-type oxygen atoms to obtain the heterohexanuclear complexes 1 and 2 . Four penta-coordinate Cu II atoms are located at the N 2 O 2 cavities of the ligand (L) 4- units, two La III /Ce III atoms are surrounded by the open-chain 18-crown-6 (O 6 ) coordination environment. At the same time, eight bridged phenol oxygen atoms connect the six Cu II /Ln III atoms. Infinite three-dimensional supra-molecular structures are formed in complexes 1 and 2 through H-bonds. The intermolecular interactions were quantitatively analyzed by Hirshfeld surfaces, as well as, fluorescence properties have also been studied.

Incompleteness of graph neural networks for points clouds in three dimensions

Graph neural networks (GNN) are very popular methods in machine learning and have been applied very successfully to the prediction of the properties of molecules and materials. First-order GNNs are well known to be incomplete, i.e. there exist graphs that are distinct but appear identical when seen through the lens of the GNN. More complicated schemes have thus been designed to increase their resolving power. Applications to molecules (and more generally, point clouds), however, add a geometric dimension to the problem. The most straightforward and prevalent approach to construct graph representation for molecules regards atoms as vertices in a graph and draws a bond between each pair of atoms within a chosen cutoff. Bonds can be decorated with the distance between atoms, and the resulting ‘distance graph NNs’ (dGNN) have empirically demonstrated excellent resolving power and are widely used in chemical ML, with all known indistinguishable configurations being resolved in the fully-connected limit, which is equivalent to infinite or sufficiently large cutoff. Here we present a counterexample that proves that dGNNs are not complete even for the restricted case of fully-connected graphs induced by 3D atom clouds. We construct pairs of distinct point clouds whose associated graphs are, for any cutoff radius, equivalent based on a first-order Weisfeiler-Lehman (WL) test. This class of degenerate structures includes chemically-plausible configurations, both for isolated structures and for infinite structures that are periodic in 1, 2, and 3 dimensions. The existence of indistinguishable configurations sets an ultimate limit to the expressive power of some of the well-established GNN architectures for atomistic machine learning. Models that explicitly use angular or directional information in the description of atomic environments can resolve this class of degeneracies.

Finite element periodic catenary model to perform HIL pantograph tests considering non-linear dropper behaviour

In this paper, we propose a general approach to compute the dynamic response of periodic infinite structures subjected to a moving load. The method only considers one repetitive block of the structure which is modelled by the Finite Element Method. The problem is first shifted to the frequency domain where the periodicity condition is easily applied and then the temporal response is obtained. An infinite periodic catenary system has been chosen to illustrate the proposed formulation. The linear formulation is extended to include the non-linear behaviour of droppers. The efficiency and accuracy of the catenary model obtained makes it very suitable for use in Hardware in the Loop (HIL) pantograph tests. We propose to combine this catenary model with an iterative strategy to achieve the steady-state response of the coupled system and its performance is analysed in a virtual HIL simulation.

Multilayer transparent bendable broadband microwave absorber covering the frequency band near 5 GHz

A multilayer transparent microwave absorber that possesses a broadband, is bendable, and covers the frequency band near 5 GHz is proposed in this work. The absorber uses three layers of 110 Ω/sq etched patterned indium–tin–oxide-polyethylene terephthalate (ITO-PET) films as the resonant layers. The infinite cycle structure of the absorber is simulated by using the CST STUDIO SUITE. The absorber shows >90% absorption effect in the frequency band 4.16-7.48 GHz and a 99% absorption effect in the band near 5 GHz (4.98-5.83 GHz). Furthermore, by replacing the intermediate medium with polydimethylsiloxane (PDMS), the absorber obtains excellent bendability characteristics.

Recombination with plasmon emission in HgTe/CdHgTe multiple quantum well heterostructures

The work is devoted to the theoretical study of the process of recombination of nonequilibrium charge carriers with the emission of plasmons in structures with two and three quantum wells, and also in an infinite number quantum-well structure under conditions of inverse band population. The plasmon spectra in these structures have been calculated. The dependence of the average probability of electron recombination with plasmon emission on the concentration of nonequilibrium carriers for three temperatures has been found. It has been shown that an increase in the number of quantum wells leads to a slight increase in the average recombination probability.

Dynamic Analysis and Design of Metamaterial Plates With Crossed Acoustic Black Holes for Vibration Control

Abstract Acoustic black holes (ABHs) have shown great potential in vibration and noise control. Merging the ABH effect and the metamaterial can be a more efficient approach for vibration control. The aim of this article is to study the dynamics of a metamaterial plate with crossed acoustic black holes. The band gap properties of the infinite structure and the influence of the design variables are investigated by using the finite element method and the Floquet–Bloch theorem. The vibration transmission and frequency response functions of the finite structure are presented to reveal the vibration attenuation mechanism. The effect of elastic boundary conditions on the vibration properties of the metamaterial plate is also studied. Numerical results demonstrate that the vibration is remarkably weakened due to the band gap and local modes induced by the ABH effect. Then, experimental validation is given by using 3D printing techniques. Finally, we study the multi-objective optimal design problem of the ABH plate to reduce the vibration amplitude and the structural mass simultaneously. Optimization results provide more options for the trade-off design of metamaterial plates between the lightweight design and vibration suppression capability.

A novel locally resonant metastructure with soft-material rings for broadband and low frequency vibration attenuation

Metastructure has been discovered as a new and effective means of vibration suppression in recent studies. Based on the basic principle of the locally resonant (LR) metastructure, a novel two-dimensional LR metastruture is proposed in this paper. The host plate is punched out several concentric holes and filled with soft materials, with the resonator installed in the center. The band structure of an infinite structure is calculated by using Gaussian expansion method as well as the finite element method. To further evaluate the vibration attenuation performance, the vibration transmission of a finite plate is obtained by both numerical and experimental methods. Formation mechanism of band gaps (BGs) is revealed by analyzing eigenmodes at boundary frequencies. The significance of the novel design is clarified from the mechanism level, about the characteristics of generating broad band gaps in low frequencies. The influence of both geometric parameters and material damping properties on BGs are discussed, including examples of a non-periodic plate and a periodic damped plate. Because of its features and simple design, it can be expected to be widely applied in engineering.

Polyadic sets and homomorphism counting

A classical result due to Lovász (1967) shows that the isomorphism type of a graph is determined by homomorphism counts. That is, graphs G and H are isomorphic whenever the number of homomorphisms K→G is the same as the number of homomorphisms K→H for all graphs K. Variants of this result, for various classes of finite structures, have been exploited in a wide range of research fields, including graph theory and finite model theory.We provide a categorical approach to homomorphism counting based on the concept of polyadic (finite) set. The latter is a special case of the notion of polyadic space introduced by Joyal (1971) and related, via duality, to Boolean hyperdoctrines in categorical logic. We also obtain new homomorphism counting results applicable to a number of infinite structures, such as trees and profinite algebras.

Between reduced powers and ultrapowers, II.

We prove that, consistently with ZFC, no ultraproduct of countably infinite (or separable metric, non-compact) structures is isomorphic to a reduced product of countable (or separable metric) structures associated to the Fréchet filter. Since such structures are countably saturated, the Continuum Hypothesis implies that they are isomorphic when elementarily equivalent.

Distinguishing Number of Universal Homogeneous Urysohn Metric Spaces

The distinguishing number of a structure is the smallest size of a partition of its elements so that only the trivial automorphism of the structure preserves the partition. We show that for any countable subset of the positive real numbers, the corresponding countable Urysohn metric space, when it exists, has distinguishing number two or is infinite.
 While it is known that a sufficiently large finite primitive structure has distinguishing number two, unless its automorphism group is not the full symmetric group or alternating group, the infinite case is open and these countable Urysohn metric spaces provide further confirmation toward the conjecture that all primitive homogeneous countably infinite structures have distinguishing number two or else is infinite.

Elliptic K3 surfaces at infinite complex structure and their refined Kulikov models

Motivated by the Swampland Distance and the Emergent String Conjecture of Quantum Gravity, we analyse the infinite distance degenerations in the complex structure moduli space of elliptic K3 surfaces. All complex degenerations of K3 surfaces are known to be classified according to their associated Kulikov models of Type I (finite distance), Type II or Type III (infinite distance). For elliptic K3 surfaces, we characterise the underlying Weierstrass models in detail. Similarly to the known two classes of Type II Kulikov models for elliptic K3 surfaces we find that the Weierstrass models of the more elusive Type III Kulikov models can be brought into two canonical forms. We furthermore show that all infinite distance limits are related to degenerations of Weierstrass models with non-minimal singularities in codimension one or to models with degenerating generic fibers as in the Sen limit. We explicitly work out the general structure of blowups and base changes required to remove the non-minimal singularities. These results form the basis for a classification of the infinite distance limits of elliptic K3 surfaces as probed by F-theory in the companion paper [1]. The Type III limits, in particular, are (partial) decompactification limits as signalled by an emergent affine enhancement of the symmetry algebra.

Degenerated Calabi–Yau varieties with infinite components, moduli compactifications, and limit toroidal structures

For any degenerating Calabi–Yau family, we introduce a new limit space which we call galaxy, whose dense subspace is the disjoint union of countably infinite open Calabi–Yau varieties, parametrized by the rational points of the Kontsevich–Soibelman’s essential skeleton, while dominated by the Huber adification over the Puiseux series field. Other topics include: projective limits of toroidal compactifications (Sect. 3), locally modelled on limit toric varieties (Sect. 2.4), the way to attach a tropicalized family to a given Calabi–Yau family (Sect. 4), which are weakly related to each other.

Metal-organic frameworks derived from chalcone dicarboxylic acid: New topological characters and initial catalytic properties

Two metal–organic frameworks, [Ag2L(bpy)0.5]n (1) and [CoL(bpy)]n (2), were successfully assembled through mixed-ligands strategy with different metal resource. Remarkably, both MOFs manifest multi-nuclear metal units as nodes and diverse topological structures. Compound 1 is an infinite two-dimensional layer structure with unsaturated four-nuclear silver unit nodes. While compound 2 exhibits a novel three-dimensional structure. The heterogeneous catalysis efficiency of the MOFs towards cycloaddition of N-methyl propargylamine with CO2 has been explored, and compound 1 displays higher catalytic activity derived from bare Lewis acid silver active site.

Exploring dithiolate-amine binary ligand systems for the supramolecular assemblies of Ni(II) coordination compounds: Crystal structures, theoretical studies, cytotoxicity studies, and molecular docking studies

Dithiolate-amine binary ligand systems based two novel supramolecular structures of Ni(II) coordination compounds [Ni(2-ap)2(i-mnt)] (1) and [Ni2(i-mnt)2(tn)2]n (2) [where i-mnt−2: 1,1-dicyanoethylene-2,2-dithiolate, 2-ap: 2-amino pyridine, tn: 1,3-diaminopropane] have been designed, synthesized and characterized by spectroscopic techniques and X-ray crystallography. In complex 1, the N2S2 coordination kernel around Ni+2 attains distorted square planar geometry (Okuniewski parameter τ/4 = 0.17) and its supramolecular array has a dominant influence of N H···N type hydrogen bonds forming significant ring geometry of graph-set-motifR428. The i-mnt−2 adopts a diverse coordination mode in 2 contrary to 1 resulting in a binuclear one-dimensional infinite polymeric chain structure of consecutive NiS4 [square planar, S4 donor set τ/4 = 0] and NiN6 (octahedral) coordination kernels linked by i-mnt−2 that runs along [1 0 0] axis wherein N H···S, N H···N, C H···S type hydrogen bonds are believed to be crystal structure stabilizers. The Hirshfeld surface analyses (HS) at the molecular and atomic levels have been extensively studied to quantify all non-covalent interactions/contacts and the nature of ligand - metal interactions. The prominent N···H/H···N [28.1 % (1), 27.3 % (2A, NiS4), 20 % (2B, NiN6)] and S···H/H···S contacts [10.4 % (1), 32.8 % (2A), 29 % (2B)] presumably play vital role in crystal packing. The non-covalent interactions were further investigated by Molecular Electrostatic Potential (MEP) surface at PBE0-D3/def2-TZVP level and QTAIM optimizations (for 1). The MTT assay study using SW620 metastatic colon cancer cells shows a significant dose-dependent decline in cell proliferation with increasing concentration for 1 but for 2, the reverse trend is followed. A molecular docking study with the APC protein has further investigated the antiproliferative activity of 1 (MTT assay).

The positive scalar curvature cobordism category

We prove that many spaces of positive scalar curvature (psc) metrics have the homotopy type of infinite loop spaces. Our result in particular applies to the path component of the round metric inside R+(Sd) if d≥6. To achieve that goal, we study the cobordism category of manifolds with positive scalar curvature. Under suitable connectivity conditions, we can identify the homotopy fiber of the forgetful map from the psc cobordism category to the ordinary cobordism category with a delooping of spaces of psc metrics. This uses a version of Quillen’s Theorem B and instances of the Gromov–Lawson surgery theorem. We extend some of the surgery arguments by Galatius and the second-named author to the psc setting to pass between different connectivity conditions. Segal’s theory of Γ-spaces is then used to construct the claimed infinite loop space structures. The cobordism category viewpoint also illuminates the action of diffeomorphism groups on spaces of psc metrics. We show that under mild hypotheses on the manifold, the action map from the diffeomorphism group to the homotopy automorphisms of the spaces of psc metrics factors through the Madsen–Tillmann spectrum. This implies a strong rigidity theorem for the action map when the manifold has trivial rational Pontryagin classes. A delooped version of the Atiyah–Singer index theorem proved by the first-named author is, moreover, used to show that the secondary index invariant to real K-theory is an infinite loop map. These ideas also give a new proof of the main result of our previous work with Botvinnik.

Synthesis of novel 1–dimensional structure from Mo6S8 Chevrel phase of electrode for Mg batteries

The Chevrel phase (CP) (Mo6S8), which is used as an electrode material in Mg rechargeable batteries, has a capacity limit owing to ion insertion and trapping. To address this problem, we modify the wire structure of the CP. Mo6S3I6 nanowires, in which iodiene is substituted for Mo6S9 nanowires as infinite CP structures, can be synthesized in various ways. When synthesizing stoichiometrically, an unwanted secondary phase may appear. We solved these problems by reducing the synthesis time. Electrochemical analysis was performed using these nanowires as an active material in Mg batteries.