Lattice Form Research Articles

Characterization of entropy measures with connection number based indices of boric acid hydrogen-bonded 2D lattice sheets.

The cut method is a computational approach utilized to predict the fundamental activities of physicochemical properties of chemical networks, also called topological indices. The connection number is a new idea, that gives interesting and good results of the topological indices (TIs) and entropy measures (EMs) for structural representation of chemical compounds and networks. The physical density of chemical networks is characterized by these indices. In this paper, we determined the computational results for indices based on connection numbers for a two-dimensional lattice sheet of hydrogen-bonded boric acid. Boric acid, an inorganic compound, is not very harmful when applied to the skin or consumed. Finally, graphical and numerical comparisons of topological numbers including the number of borate hydrogen-bonded double lattice forms are also included in this study.

Rapidly rotating quantum droplets confined in a harmonic potential

We consider a “symmetric” quantum droplet in two spatial dimensions, which rotates in a harmonic potential, focusing mostly on the limit of “rapid” rotation. We examine this problem using a purely numerical approach, as well as a semianalytic Wigner-Seitz approximation (first developed by Baym, Pethick, and their co-workers) for the description of the state with a vortex lattice. Within this approximation we assume that each vortex occupies a cylindrical cell, with the vortex-core size treated as a variational parameter. Working with a fixed angular momentum, as the angular momentum increases and depending on the atom number, the droplet accommodates none, few, or many vortices, before it turns to center-of-mass excitation. For the case of a “large” droplet, working with a fixed rotational frequency of the trap Ω, as Ω approaches the trap frequency ω, a vortex lattice forms, the number of vortices increases, the mean spacing between them decreases, while the “size” of each vortex increases as compared to the size of each cell. In contrast to the well-known problem of contact interactions, where we have melting of the vortex lattice and highly correlated many-body states, here no melting of the vortex lattice is present, even when Ω=ω. This difference is due to the fact that the droplet is self-bound. For Ω=ω, the “smoothed” density distribution becomes a flat top, very much like the static unconfined droplet. When Ω exceeds ω, the droplet maintains its shape and escapes to infinity, via center-of-mass motion. Published by the American Physical Society 2024

Porous structural battery composite for coordinated integration of mechanical and electrical functionalities

AbstractStructural battery composites (SBCs) represent an emerging multifunctional technology in which materials functionalized with energy storage capabilities are used to build load‐bearing structural components. However, due to the liquid electrolyte contamination in structural battery electrolyte (SBE) and the large volume expansion of active battery materials, the poor interlayer interfacial in multilayer SBCs often causes difficulties in practical use. In this study, a new porous LiFePO4‐graphite SBC is designed and fabricated by independently distributing battery materials and resin matrix on carbon fiber fabric in pattern lattice form to prepare electrodes prepreg. The cured porous composite framework supports the load‐bearing function while limiting the electrochemical reaction in liquid electrolyte within lattices. The electrodes show reversible electric resistance after 3000 bending cycles with radius as small as 10 mm. The mechanical properties enhance significantly with tensile strength of 486.1 MPa and Young's modulus of 9.1 GPa compared to that with a liquid–solid biphasic mixed SBE structure. The SBC also exhibits a favorable capacity of 27.8 mAh/g at 0.1C. This straightforward integration path of mechanical and electrical functionalities is compatible with the manufacturing process of aerospace composite structures, which will provide an efficient and convenient energy supply solution for distributed electronics.Highlights A porous full‐cell structural battery composite (SBC) was designed and fabricated with prepregs. A suspension deposition and volatilization method was developed for robust battery material coating. Electrodes layer exhibited reversible electric resistance after 3000 tensile/bending cycles. The tensile strength and modulus increased significantly compared to the SBC with liquid–solid biphasic mixed structural battery electrolyte. Coordinated integration path was completely compatible with the manufacturing process of aerospace composite structures.

Stability and deformation of a vacancy defect in skyrmion crystal under external magnetic and temperature fields

Skyrmion, a local bubble-like topological magnetization structure, can collectively emergent in magnets in a lattice form skyrmion crystal (SkX). SkX has great application potential in functional devices because it can manipulate material properties via coupling with atomic lattices. The lattice defects such as vacancy widely exist in the SkX as well, and they have rich dynamic behaviors and have great implications for the host material. However, although the nature of ideal SkX is well studied, the characteristics of SkX defects are relatively underdeveloped. Here, we deeply studied the structural properties of a vacancy defect in the SkX by a thermodynamic phase-field simulation. We found that the higher external magnetic and temperature fields favor rigid skyrmions (crystal), in which the SkX vacancy is less deformed, while the lower fields favor softer skyrmions where the SkX vacancy structure is considerably deformed. Such unique deformation and stability of the SkX vacancy are mainly the results of the competition between free energies in the view of thermodynamics. Our study demonstrated that the external field-controlled static properties of SkX vacancy highly depend on the quasiparticle nature of skyrmions. This indicates the properties of SkX defects can be controlled by the SkX features under different fields, which should open an avenue for the study and design of smart materials and advanced devices by engineering skyrmion crystals.

Infiltrated electroless deposition of gold nanoparticles on porous Prussian blue-Fe2O3 hetero-microstructures for environmental remediation applications: A novel infiltration strategy to form 3-D nano-catalytic networks

Metal and metal oxide nanocomposites are promising candidates for heterogeneous catalytic applications. In this regard, most of the metal oxide inner core volume remains as a dead volume, not participating in the catalysis, only the metal/metal oxide hetero-junctions available at the surfaces are involved in the catalysis. Herein, we report a novel strategy for the infiltration of gold nanoparticles into the inner core of 3D-porous Prussian blue/Fe2O3 hetero-microstructures (PBFHM-Au) beyond its outer surface to form an advanced heterogeneous catalyst for the environmental remediation applications. The porosity of the Prussian blue microstructures is thermally tuned for the infiltration of gold ion precursor into the inner core volume of Prussian blue/Fe2O3 hetero-microstructures to facilitate the galvanic displacement reaction between Fe and Au to enlarge the lattice shell and form Au nanoparticle 3D networks throughout the PBFHM. Notably, the resulting PBFHM-Au2 shows enhanced structural stability electron transfer kinetics and catalytic activity in comparison with the only surface-attached Au/Fe2O3 composite. The obtained PBFHM-Au2 catalyst demonstrates remarkable catalytic activity for Rhodamine-B dye degradation with rate constant (k = 3.47 × 10−2 s−1) and p-nitrophenol reduction reactions with rate constant (k = 1.199 × 10−1 s−1).

Real-Space Imaging of Intrinsic Symmetry-Breaking Spin Textures in a Kagome Lattice.

The electronic orders in kagome materials have emerged as a fertile platform for studying exotic quantum states, and their intertwining with the unique kagome lattice geometry remains elusive. While various unconventional charge orders with broken symmetry is observed, the influence of kagome symmetry on magnetic order has so far not been directly observed. Here, using a high-resolution magnetic force microscopy, it is, for the first time, observed a new lattice form of noncollinear spin textures in the kagome ferromagnet in zero magnetic field. Under the influence of the sixfold rotational symmetry of the kagome lattice, the spin textures are hexagonal in shape and can further form a honeycomb lattice structure. Subsequent thermal cycling measurements reveal that these spin textures transform into a non-uniform in-plane ferromagnetic ground state at low temperatures and can fully rebuild at elevated temperatures, showing a strong second-order phase transition feature. Moreover, some out-of-plane magnetic moments persist at low temperatures, supporting the Kane-Mele scenario in explaining the emergence of the Dirac gap. The observations establish that the electronic properties, including both charge and spin orders, are strongly coupled with the kagome lattices.

A Formal Concept Analysis approach to hierarchical description of malware threats

The problem of intelligent malware detection has become increasingly relevant in the industry, as there has been an explosion in the diversity of threats and attacks that affect not only small users, but also large organisations and governments. One of the problems in this field is the lack of homogenisation or standardisation in the nomenclature used by different antivirus programs for different malware threats. The lack of a clear definition of what a category is and how it relates to individual threats makes it difficult to share data and extract common information from multiple antivirus programs. Therefore, efforts to create a common naming convention and hierarchy for malware are important to improve collaboration and information sharing in this field.Our approach uses as a tool the methods of Formal Concept Analysis (FCA) to model and attempt to solve this problem. FCA is an algebraic framework able to discover useful knowledge in the form of a concept lattice and implications relating to the detection and diagnosis of suspicious files and threats. The knowledge extracted using this mathematical tool illustrates how formal methods can help prevent new threats and attacks. We will show the results of applying the proposed methodology to the identification of hierarchical relationships between malware.

Cairo lattice with time-reversal non-invariant vertex couplings

We analyze the spectrum of a periodic quantum graph of the Cairo lattice form. The used vertex coupling violates the time reversal invariance and its high-energy behavior depends on the vertex degree parity; in the considered example both odd and even parities are involved. The presence of the former implies that the spectrum is dominated by gaps. In addition, we discuss two modifications of the model in which this is not the case, the zero limit of the length parameter in the coupling, and the sign switch of the coupling matrix at the vertices of degree three; while different they both yield the same probability that a randomly chosen positive energy lies in the spectrum.

Barrier-free subwavelength multi-channel topological acoustic interlayer under direct resonance induction

In this paper, a new topological acoustic interlayer is proposed, which is formed by combining multi-order resonators in the form of the triangular lattice in the normal direction of the acoustic interlayer. Through the strong resonance of the resonator, the distribution of modes in the acoustic interlayer is directly induced to form a combination of modes with different topological states to support the subwavelength multi-channel lossless directional acoustic transmission in barrier-free space. Since there are no scatterers, not only can the required frequency band be directly achieved through the resonance frequency of the resonator alone, but also the background medium space in which the acoustic wave transmitting is a uniform medium, so the transmission is secret and the structure is ventilated. More importantly, there is more space in the normal direction of the barrier-free interlayer for design sub-wavelength multi-channel transmission. Furthermore, the random obstacles in interlayer do not affect the transmission under the pseudo spin modes. Finally, experimental verification is carried out. This research paves the way for the engineering application of multi-band acoustic antennas, covert communication, ventilated devices and other multi-functional devices, and will bring new enlightenment to the fields of elastic wave, light wave and electromagnetic wave.

In-in correlators and scattering amplitudes on a causal set

Causal set theory is an approach to quantum gravity in which spacetime is fundamentally discrete at the Planck scale and takes the form of an irregular Lorentzian lattice, or “causal set,” from which continuum spacetime emerges in a large-scale (low-energy) approximation. In this work, we present new developments in the framework of interacting quantum field theory on causal sets. We derive a diagrammatic expansion for in-in correlators in local scalar field theories with finite polynomial interactions. We outline how these same correlators can be computed using the double-path integral, which acts as a generating functional for the in-in correlators. We modify the in-in generating functional to obtain a generating functional for in-out correlators. We define a notion of scattering amplitudes on causal sets with noninteracting past and future regions and verify that they are given by S-matrix elements (matrix elements of the time-evolution operator). We describe how these formal developments can be implemented to compute early Universe observables under the assumption that spacetime is fundamentally discrete. Published by the American Physical Society 2024

On the modulo p zeros of modular forms congruent to theta series

For a prime p larger than 7, the Eisenstein series of weight p−1 has some remarkable congruence properties modulo p. Those imply, for example, that the j-invariants of its zeros (which are known to be real algebraic numbers in the interval [0,1728]), are at most quadratic over the field with p elements and are congruent modulo p to the zeros of a certain truncated hypergeometric series. In this paper we introduce “theta modular forms” of weight k≥4 for the full modular group as the modular forms for which the first dim⁡(Mk) Fourier coefficients are identical to certain theta series. We consider these theta modular forms for both the Jacobi theta series and the theta series of the hexagonal lattice. We show that the j-invariant of the zeros of the theta modular forms for the Jacobi theta series are modulo p all in the ground field with p elements. For the theta modular form of the hexagonal lattice we show that its zeros are at most quadratic over the ground field with p elements. Furthermore, we show that these zeros in both cases are congruent to the zeros of certain truncated hypergeometric functions.

Elasto-dynamic characterization of material extrusion infills using homogenization methods

Dynamic properties of additively-manufactured materials are generally under-characterized compared to static properties. Material extrusion (MEX) is the most readily available and economical method of 3D printing available. In order to reduce weight and material costs, most commercial MEX slicing software utilizes a concept called infill, often in the form of lattices, which fills the 3D space with a computer-generated design. In this study, finite element modeling of representative volume elements is utilized to predict the speed of sound for a polylactic acid–based structure with varying infill percentages. Experimental validation of the sound speeds for a subset of infill percentages are measured using an underwater acoustic through-transmission technique at frequency ranges which correspond to the assumptions used in the modeling approach. Significant anisotropy in elasto-dynamic response was observed numerically and experimentally. Insertion loss of the printed panels was also measured as part of general discussion of the effectiveness of the underwater acoustic method for air-filled samples. This work provides a framework for both characterization and design of MEX-printed parts for acoustic applications.

Wave Manipulation in Intelligent Metamaterials: Recent Progress and Prospects

AbstractMetamaterials (MMs), which include phononic crystals (PCs) as a particular type, exhibit anomalous wave propagation properties through artificial design of topologies or lattice forms of unit‐cells. Recent advancements in MMs signify an ascendant research trend, providing promising design ideas and means for unprecedented wave propagation properties. The imperative for on‐demand, real‐time active control of wave propagation underscores the significance of tunable manipulation of acoustic/elastic waves, promoting the design and development of tunable MMs. Furthermore, the versatility of intelligent materials and their ongoing development and innovation contribute significantly to the emergence of diverse intelligent MMs. This comprehensive survey provides an overview of recent advancements and current research trends in the interdisciplinary field of intelligent MMs with electro‐/magneto‐mechanical couplings. The primary objective of the review is to emphasize significant progress in agile manipulation of acoustic/elastic waves in electro‐/magneto‐mechanical coupled MMs, followed by an in‐depth exploration of intelligent metasurfaces, topological MMs, non‐Hermitian parity‐time symmetric wave systems, odd elastic MMs, and spatiotemporally modulated MMs. Special emphasis is given to multi‐field coupling effects. The review concludes with a summary and outlines potential prospects, offering a timely and informative guide for future studies on actively tunable PCs and MMs in practical engineering applications.

Investigation on the elastic flexural stiffness of dot-by-dot wire-and-arc additively manufactured stainless steel bars

Among different metal additive manufacturing (AM) technologies, arc-based Directed Energy Deposition, also known as Wire-and-Arc Additive Manufacturing (WAAM), is considered the most suitable for large-scale structural components production. In particular, the WAAM printing strategy referred to as “dot-by-dot” allows the realization of complex 3D lattice forms at the scale of structural steel parts, composed of unitary cells made of slender bars. Nonetheless, the outcomes of this process are still to be properly investigated in terms of their mechanical behavior under various loading conditions. To assess the buckling behavior of WAAM-produced slender bars, extensive effort is requested to properly characterize the main driving aspects, namely the flexural stiffness possibly influenced by mechanical anisotropy induced by the printing process and the influence of the geometrical imperfections. The present work reports the first results of experimental bending tests conducted on vertically printed (i.e. with a fixed build angle equal to 0°) straight dot-by-dot WAAM stainless steel bars, as an initial investigation towards a more comprehensive analysis of the buckling behavior of WAAM slender elements. The results are then interpreted by introducing three approaches of increasing complexity, including two analytical approaches based on a simplified idealization of the real geometry of the bar, and a third approach based on the reconstruction of the real geometry of the bar using advanced numerical simulations and 3D scanning. The three approaches lead to a different appraisal of the influence of the geometrical irregularities on the flexural stiffness of the specimens. The main results of the present study could be utilized to interpret the results of future experimental compressive tests on WAAM slender elements and to develop ad-hoc buckling curves for structural design purposes.

Backscattering-free edge states below all bands in two-dimensional auxetic media

Unidirectional and backscattering-free propagation of sound waves is of fundamental interest in physics and highly sought-after in engineering. Current strategies utilize topologically protected chiral edge modes in bandgaps or complex mechanisms involving active constituents or nonlinearity. Here, we propose a new class of passive, linear, one-way edge states based on spin-momentum locking of Rayleigh waves in two-dimensional media in the limit of vanishing bulk modulus, which provides 100% unidirectional and backscattering-free edge propagation immune to any edge roughness at a broad range of frequencies instead of residing in gaps between bulk bands. We further show that such modes are characterized by a new topological winding number that is analogous to discrete angular momentum eigenvalues in quantum mechanics. These passive and backscattering-free edge waves have the potential to enable a new class of phononic devices in the form of lattices or continua that work in previously inaccessible frequency ranges.

Plasticity in nonlinear elastic metamaterials: Low-order dynamic modeling

Nonlinear elastic metamaterials have been shown to admit a variety of rich, dynamical features that can be leveraged to tailor the propagation of mechanical waves. Since these materials derive their properties from intricate, subwavelength geometries, direct numerical simulations are often prohibitively expensive at scales of interest. To overcome this limitation, reduced-order models, typically in the form of effective continua or discrete lattices that capture the essential features of the material at sufficiently long wavelengths, have been developed. While many prior studies have implemented these models successfully, the vast majority have considered only recoverable elastic deformations with linear damping and neglected history-dependent effects, such as plasticity and friction. In this presentation, we introduce an effective lattice modeling framework for nonlinear elastic metamaterials undergoing plastic deformation. Due to the history-dependent nature of plasticity, this framework generally yields a system of differential-algebraic equations whose computational cost is significantly greater than a purely elastic system of similar size. We apply the method to several examples of interest and explore means to obtain phenomenological elastic-plastic models for general material architectures.

Electron-Assisted Generation and Straight Movement of Skyrmion Bubble in Kagome TbMn6Sn6.

Topological magnetic textures are promising candidates as binary data units for the next-generation memory device. The precise generation and convenient control of nontrivial spin topology at zero field near room temperature endows the critical advantages in skyrmionic devices but is not simultaneously integrated into one material. Here, in the Kagome plane of quantum TbMn6Sn6, the expedient generation of the skyrmion bubbles in versatile forms of lattice, chain, and isolated one by converging the electron beam, where the electron intensity gradient contributes to the dynamic generation from local anisotropy variation near spin reorientation transition (SRT) is reported. Encouragingly, by utilizing the dynamic shift of the SRT domain interface, the straight movement is actualized with the skyrmion bubble slave to the SRT domain interface forming an elastic composite object, avoiding the usual deflection from the skyrmion Hall effect. The critical contribution of the SRT domain interface via conveniently electron-assisted heating is further theoretically validated in micromagnetic simulation, highlighting the compatible application possibility in advanced devices.

Manipulating metastability: Quenched control of topological defects in multiferroics

The topological properties of quasiparticles, such as skyrmions and vortices, have the potential to offer extraordinary metastability through topological protection, and drive motion with minimal electrical current excitation. This has promising implications for future applications in spintronics. Skyrmions frequently appear either in lattice form or as separate, isolated quasiparticles [Y. Tokura and N. Kanazawa, Chemical Reviews 121, 2857–2897 (2021)]. Magnetic ferroelectrics, a subset of multiferroics that exhibit magnetically induced ferroelectricity, possess intriguing characteristics like magnetic (electric) field-controlled ferroelectric (magnetic) responses. Previous research based on Landau theory indicated the potential to stabilize metastable phases in multiferroic barium hexaferrite [Karpov et al., Phys. Rev. B 100, 054432 (2019)]. We have successfully stabilized these meta-stable phases through magnetic quenching of hexaferrite nanoparticles, leading to the creation of compelling topological structures. The structural changes in individual BaFe12O19 nanocrystals were scrutinized using Bragg coherent diffractive imaging, granting us insight into the emergent topological structures in field-quenched multiferroics. Additionally, we explored why these structures are energetically preferable for the formation of metastable topological structures [Karpov et al., Nature Communications 8, 280 (2017) and Karpov et al., Phys. Rev. B 100, 054432 (2019)].

Extension of topological structures using lattices and rough sets

<abstract><p>This paper explores the application of rough set theory in analyzing ambiguous data within complete information systems. The study extends topological structures using equivalence relations, establishing an extension of topological lattice within lattices. Various relations on topological spaces generate different forms of exact and rough lattices. Building on Zhou's work, the research investigates rough sets within the extension topological lattice and explores the isomorphism between topology and its extension. Additionally, the paper investigates the integration of lattices and rough sets, essential mathematical tools widely used in problem-solving. Focusing on computer science's prominent lattices and Pawlak's rough sets, the study introduces extension lattices, emphasizing lower and upper extension approximations' adaptability for practical applications. These approximations enhance pattern recognition and model uncertain data with finer granularity. While acknowledging the benefits, the paper stresses the importance of empirical validations for domain-specific efficacy. It also highlights the isomorphism between topology and its extension, revealing implications for data representation, decision-making, and computational efficiency. This isomorphism facilitates accurate data representations and streamlines computations, contributing to improved efficiency. The study enhances the understanding of integrating lattices and rough sets, offering potential applications in data analysis, decision support systems, and computational modeling.</p></abstract>

Theoretical insights into dopamine photochemistry adsorbed on graphene-type nanostructures.

The equilibrium geometry structures and light absorption properties of the dopamine (DA) and dopamine-o-quinone (DAQ) adsorbed on the graphene surface have been investigated using the ground state and linear-response time-dependent density functional theories. Two types of graphene systems were considered, a rectangular form of hexagonal lattice with optimized C-C bond length as the model system for graphene nanoparticles (GrNP) and a similar system but with fixed C-C bond length (1.42 Å) as the model system for graphene 2D sheet (GrS). The analysis of the vertical excitations showed that three types of electronic transitions are possible, namely, localized on graphene, localized on the DA or DAQ, and charge transfer (CT). In the case of the graphene-DA complex, the charge transfer excitations were characterized by the molecule-to-surface (MSCT) character, whereas the graphene-DAQ was characterized by the reverse, i.e. surface-to-molecule (SMCT). The difference between the two cases is given by the presence of an energetically low-lying unoccupied orbital (LUMO+1) that allows charge transfer from the surface to the molecule in the case of DAQ. However, it was also shown that the fingerprints of excited electronic states associated with the adsorbed molecules cannot be seen in the spectrum, as they are mostly suppressed by the characteristic spectral shape of graphene.