Symmetric Unit Research Articles

X Wave Radiator Implemented With 3-D Printed Metamaterials

A radiator is presented, capable of generating paraxial X waves over a 50% fractional bandwidth (7.5–12.5 GHz) in its radiative near-field. X waves are localized pulses formed by the superposition of Bessel beams with a common cone angle. Quasiconformal transformation optics, a 2-D variant of transformation optics, is employed to find the inhomogeneous, isotropic dielectric constant profile needed to convert the radiation of a monopole into a paraxial Bessel beam. An impedance matching layer is applied to reduce reflections at the air-dielectric interface of the device. The transformation and impedance matching regions are implemented using rotationally symmetric metamaterial unit cells that yield a spatially varying effective dielectric constant. The resulting design is fabricated through 3-D printing, by combining parts made from three low-loss dielectric filaments. The device is experimentally measured, and shows good agreement with simulations. Its ability to generate paraxial X waves when excited by a broadband pulse is verified.

Coverage‐Controlled Superstructures of C3‐Symmetric Molecules: Honeycomb versus Hexagonal Tiling

The competition between honeycomb and hexagonal tiling of molecular units can lead to large honeycomb superstructures on surfaces. Such superstructures exhibit pores that may be used as 2D templates for functional guest molecules. Honeycomb superstructures of molecules that comprise a C3 symmetric platform on Au(111) and Ag(111) surfaces are presented. The superstructures cover nearly mesoscopic areas with unit cells containing up to 3000 molecules, more than an order of magnitude larger than previously reported. The unit cell size may be controlled by the coverage. A fairly general model was developed to describe the energetics of honeycomb superstructures built from C 3 symmetric units. Based on three parameters that characterize two competing bonding arrangements, the model is consistent with the present experimental data and also reproduces various published results. The model identifies the relevant driving force, mostly related to geometric aspects, of the pattern formation.

Coverage‐Controlled Superstructures of C3‐Symmetric Molecules: Honeycomb versus Hexagonal Tiling

AbstractThe competition between honeycomb and hexagonal tiling of molecular units can lead to large honeycomb superstructures on surfaces. Such superstructures exhibit pores that may be used as 2D templates for functional guest molecules. Honeycomb superstructures of molecules that comprise a C3 symmetric platform on Au(111) and Ag(111) surfaces are presented. The superstructures cover nearly mesoscopic areas with unit cells containing up to 3000 molecules, more than an order of magnitude larger than previously reported. The unit cell size may be controlled by the coverage. A fairly general model was developed to describe the energetics of honeycomb superstructures built from C3 symmetric units. Based on three parameters that characterize two competing bonding arrangements, the model is consistent with the present experimental data and also reproduces various published results. The model identifies the relevant driving force, mostly related to geometric aspects, of the pattern formation.

RETRACTED: The effect of n–π* electronic transitions on the N2 photofixation ability of phosphorus doped g-C3N4 synthesized by microwave treatment

Abstract Light harvest is an important part of the photocatalysis process. In this work, phosphorus doped g-C3N4 with outstanding N2 photofixation ability was prepared via microwave treatment. XRD, N2 adsorption, UV–Vis, SEM, XPS, ESR and PL were used to characterize the as-prepared catalysts. Combining the P doping with microwave treatment, the planar and symmetric heptazine units in g-C3N4 was destroyed. This causes that the n-π* electronic transition becomes allowed. The remarkable red shift of absorption edge from 465 nm to near 600 nm was observed, leading to the obviously promoted visible light absorption. The synergy effect of P doping and microwave treatment also enhances the surface area and separation efficiency of electron-hole pairs. The as-prepared catalyst displays the highest NH4+ concentration of 6.5 mg·L−1·gcat−1, over 13.5 times higher than that of neat g-C3N4, as well as the excellent photocatalytic stability.

Dynamically tunable multi-channel and polarization-independent electromagnetically induced transparency in terahertz metasurfaces

Switchable multi-channel electromagnetic induced transparency (EIT) is achieved in designed terahertz metasurfaces. The underlying physics of the EIT effect is analyzed. The influence of structure parameters on the EIT effect is investigated. A metasurface with a symmetrical unit cell is proposed, by which polarization-independent EIT is achieved. In addition, photosensitive silicon is integrated into the metal layer aiming for active modulation. Tunable EIT with adjustable peak frequency and amplitude is obtained. Moreover, the dynamic control is not limited to a single EIT transparency window. We show that the number of EIT transparency windows can be tailored, and switchable multi-channel EIT are successively realized. The results would provide significant guidance in multifunctional active devices, such as modulators and switches in nanophotonics optics.

Crystal Structure and Computational Study on Methyl-3-Aminothiophene-2-Carboxylate

Methyl-3-aminothiophene-2-carboxylate (matc) is a key intermediate in organic synthesis, medicine, dyes, and pesticides. Single crystal X-ray diffraction analysis reveals that matc crystallizes in the monoclinic crystal system P21/c space group. Three matc molecules in the symmetric unit are crystallographically different and further linked through the N–H⋯O and N–H⋯N hydrogen bond interactions along with weak C–H⋯S and C–H⋯Cg interactions, which is verified by the three-dimensional Hirshfeld surface, two-dimensional fingerprint plot, and reduced density gradient (RDG) analysis. The interaction energies within crystal packing are visualized through dispersion, electrostatic, and total energies using three-dimensional energy-framework analyses. The dispersion energy dominates in crystal packing. To better understand the properties of matc, electrostatic potential (ESP) and frontier molecular orbitals (FMO) were also calculated and discussed. Experimental and calculation results suggested that amino and carboxyl groups can participate in various inter- and intra-interactions.

Dynamic Phasor Modeling of Various Multipulse Rectifiers and a VSI Fed by 18-Pulse Asymmetrical Autotransformer Rectifier Unit for Fast Transient Analysis

To study the fast modelling of dynamic characteristics caused by power electronic switching, the dynamic phasor (DP) theory based on the time-varying Fourier decomposition and frequency shifting is firstly applied to the modelling of various multipulse rectifiers. The DP model for symmetrical 12-pulse phase-shifting reactor rectifier unit (PSR-RU) is derived with model order reduction, relations between ac and dc terminals, and Taylor series expansion. The DP model of asymmetrical 18-pulse autotransformer rectifier unit (AT-RU) is proposed based on the switching functions expressed in the DP domain. Meanwhile, the DP model of voltage source inverter (VSI) fed by asymmetrical 18-pulse AT-RU is built with the harmonic state-space (HSS) equations. Under both balanced and unbalanced conditions, the good calculation accuracy and rapid simulation speed of the developed DP models are validated by the detailed time-domain (TD) simulation.

Analysis of periodicity-induced attenuation effect in a nonlinear waveguide by means of the method of polynomial system resultants

This paper addresses the application of the novel method of polynomial system resultants for solving two problems governed by systems of cubic equations. Both problems emerge in analysis of stationary dynamics of a periodic waveguide, which consists of linearly elastic continuous rods with nonlinear springs between them. The first one is the classical problem of finding “backbone curves” for free nonlinear vibrations of a symmetric unit periodicity cell of the waveguide. The second one is the problem of finding the Insertion Losses for a semi-infinite waveguide with several periodicity cells. Similarly to the canonical linear case, a very good agreement between boundaries of high attenuation frequency ranges and eigenfrequencies of a unit cell is demonstrated.

Design of 3D broad-band and wide-angle absorber based on resistive metamaterial and magnetic absorbing material

A 3D broad-band and wide-angle absorber (3D BWA) was designed through a 3D resistive metamaterial in which a traditional magnetic absorbing material was added on top of the metallic backplane. Owing to the better magnetic loss performance of the magnetic absorber at lower frequencies and superior impedance matching effect and ohmic loss property of the resistive films at higher frequencies, the absorption can be extended to a wider band through their combination. Simulation result shows that the absorption of the 3D BWA is more than 90% in the frequency range of 3.7–40 GHz at normal incidence, and it is in accordance with the experimental result. The absorption performance for each part of the 3D BWA was analyzed using electric field and magnetic field distributions, surface current distributions and Smith chart. For TE polarized waves of 3.7–40 GHz, the absorption with the incident angles of 0°–60° is more than 77%. The absorption higher than 80% can be achieved under TM polarized waves of 4.2–40 GHz as the incident angle changes from 0° to 60°. When the incident angle is 70°, the absorption is greater than 85% in the frequency range of 5.7–40 GHz. Owing to the four-fold rotationally symmetric unit cell structure, the absorption spectrum under different polarization angles remains unchanged. These two characteristics make the designed absorber a good candidate in stealth applications.

Surface acoustic waves in one-dimensional piezoelectric phononic crystals with symmetric unit cell

The paper studies the existence of surface acoustic waves in half-infinite one-dimensional piezoelectric phononic crystals consisting of perfectly bonded layers, which are arranged so that the unit cell is symmetric, i.e., is invariant with respect to inversion about its midplane. An example is a bilayered structure with exterior layer being half thinner than the interior layers of the same material. The layers may be generally anisotropic. The maximum possible number of surface acoustoelectric waves referred to a fixed wave number and a given full stop band is established for different types of electric boundary conditions at the mechanically free or clamped surface. In particular, it is proved that the phononic crystal-vacuum interface can support two surface waves in any full stop band. The same statement holds true in the case of a metallized surface of the crystal. This number is greater than that in a purely elastic case. In the presence of crystallographic symmetry, which decouples the sagittally and horizontally polarized surface waves, their separate admissible numbers are obtained. It is shown that the propagation along the normal to the surface is a special case, where the maximum number of surface waves is less than that along oblique directions.

Interfacial acoustic waves in one-dimensional anisotropic phononic bicrystals with a symmetric unit cell.

The paper is concerned with the interfacial acoustic waves localized at the internal boundary of two different perfectly bonded semi-infinite one-dimensional phononic crystals represented by periodically layered or functionally graded elastic structures. The unit cell is assumed symmetric relative to its midplane, whereas the constituent materials may be of arbitrary anisotropy. The issue of the maximum possible number of interfacial waves per full stop band of a phononic bicrystal is investigated. It is proved that, given a fixed tangential wavenumber, the lowest stop band admits at most one interfacial wave, while an upper stop band admits up to three interfacial waves. The results obtained for the case of generally anisotropic bicrystals are specialized for the case of a symmetric sagittal plane.

Modeling of Nanomolecular and Reticular Architectures with 6-fold Grooved, Programmable Interlocking Disks

Single-type, 6-fold symmetrically grooved, and commercially accessible interlocking disks (ILDs) have been used for modeling of sp2 hybridized carbon-based nanoarchitectures and complex polyhedral and reticular material models. In the case of the carbon-based nanoarchitectures, we showcase that the primary ILDs can be directly used for representing individual atoms and bonds. Further on, the spatial connectivity of the primary ILDs can be extended by assembly of symmetrical secondary building units (SBUs). The constructed (deci)meter scale models are robust, light, scalable, and suitable for classroom demonstrations. The ILD technique is also suitable for use in workshops for facile discovery-based learning of nanomolecular structure, showing promise for wider use in the chemistry curriculum.

QM-sym, a symmetrized quantum chemistry database of 135 kilo molecules

Applying deep learning methods in materials science research is an important way of solving the time-consuming problems of typical ab initio quantum chemistry methodology, but due to the size of large molecules, large and uncharted fields still exist. Implementing symmetry information can significantly reduce the calculation complexity of structures, as they can be simplified to the minimum symmetric units. Because there are few quantum chemistry databases that include symmetry information, we constructed a new one, named QM-sym, by designing an algorithm to generate 135k organic molecules with the Cnh symmetry composite. Those generated molecules were optimized to a stable state using Gaussian 09. The geometric, electronic, energetic, and thermodynamic properties of the molecules were calculated, including their orbital degeneracy states and orbital symmetry around the HOMO-LUMO. The basic symmetric units were also included. This database p rovides consistent and comprehensive quantum chemical properties for structures with Cnh symmetries. QM-sym can be used as a benchmark for machine learning models in quantum chemistry or as a dataset for training new symmetry-based models.

A Low-Profile Design of Polarization Rotation Reflective Surface for Wideband RCS Reduction

A novel compact ultrawideband polarization rotation reflective surface (PRRS) with a high polarization conversion ratio (PCR) is proposed. The 90° polarization rotation (PR) is achieved by employing a PRRS-based diagonally symmetric unit cell including two L-shaped strips with two vias and a centered via-less square patch. The air-based substrate of the structure and its overall dimensions equal to 6 × 6 × 3.3 mm3 (i.e., $0.128{\boldsymbol{\lambda \times 0.128{\boldsymbol{\lambda \times 0.07{\boldsymbol{\lambda }_0} $ based on the lowest frequency of the band) provide a low-profile PRRS with a considerable reduction in thickness. The PR bandwidth of the proposed PRRS is 111% with a PCR over 90%. This PRRS is also applied for radar cross section reduction (RCSR), which provides a measured 10 dB RCSR in an ultrawide bandwidth of about 114.4% (6.4∼23.5 GHz, covering C-, X-, Ku-, and K-bands). A good agreement between the simulated and measured results and a fair comparison with the state-of-the-art approaches prove the accuracy and efficiency of the proposed design.

Lattice model for fast diffusion equation

We obtain a fast diffusion equation (FDE) as scaling limit of a sequence of zero-range process with symmetric unit rate. Fast diffusion effect comes from the fact that the diffusion coefficient goes to infinity as the density goes to zero. In order to capture this fast diffusion effect from a microscopic point of view we are led to consider a proper rescaling of a model with a typically high number of particles per site. Furthermore, we obtain some results on the convergence for the method of lines for FDE.

Topological design of 3D phononic crystals for ultra-wide omnidirectional bandgaps

As a unique kind of artificial periodic composite materials, phononic crystals have attracted the wide attention in recent years. Unremitting efforts have been made to investigate the potential existence of phononic bandgaps, which can be used to manipulate the propagation of acoustic/elastic waves. This paper proposes a new topology optimization algorithm to achieve the optimised bandgap structures of 3D phononic crystals based on fixed-grid finite element method (FEM) and evolutionary procedure. The maximum normalised gap ratio obtained is as large as 97% between the 12th and 13th order of bands, with the optimised structure of tungsten carbide spheres embraced in epoxy matrix. Symmetric unit cells for simple cubic (SC) lattice are presented for the specified bandgaps to validate the effectiveness of the proposed optimization algorithm for designing 3D phononic bandgap crystals. Meanwhile, the proposed topology optimization represents structures with clear topologies and smooth boundaries.

Compact microstrip low‐pass filtering power divider with wide harmonic suppression

A compact, low-cost Wilkinson power divider (WPD) of 1.3 GHz (f 0 ) operating frequency, with a low-pass filtering response, is presented in this study. Power division and low-pass filtering responses are both achieved by using two symmetrical units of interdigital line resonators (ILRs). Each square unit of ILR exhibits a low-pass filtering response, with a minimum insertion loss of 0.3 dB. The dumbbell-shaped, defected ground structures are introduced for widening the attenuation band by suppressing the harmonics up to 14 GHz (up to 10.76 f 0 ) and also for miniaturising the circuit. An isolation resistor of 100 Ω is placed between two output ports of the WPD for obtaining good isolation. The operating frequency of the low-pass filter is 2 GHz with an attenuation of -17 dB up to 20 GHz. The proposed structure is fabricated using low-cost substrate material FR4. Both the low-pass filter and the power divider are fabricated and measured. The electromagnetic-simulated and measurement results are experimentally verified.

A Novel Method for Constructing Multimode Deployable Polyhedron Mechanisms Using Symmetric Spatial Compositional Units

A novel construction method is proposed to construct multimode deployable polyhedron mechanisms (DPMs) using symmetric spatial RRR compositional units, a serial kinematic chain in which the axes of the first and the third revolute (R) joints are perpendicular to the axis of the second R joint. Single-loop deployable linkages are first constructed using RRR units and are then assembled into polyhedron mechanisms by connecting the single-loop linkages using RRR units. The proposed mechanisms are over-constrained and can be deployed. The prism mechanism constructed using two Bricard linkages and six RRR chains has one degree-of-freedom (DOF). When removing three of the RRR chains, the mechanism will have one additional 1-DOF motion mode. The DPMs based on 8R and 10R linkages also have multiple modes, and several mechanisms have variable-DOF. The DPMs can switch among different motion modes through transition positions. Prototypes are 3D-printed to verify the feasibility of the mechanisms.

Unitary and Symmetric Units of a Commutative Group Algebra

AbstractLetFbe a field of characteristic two andGa finite abelian 2-group with an involutory automorphismη. IfG=H×Dwith non-trivial subgroupsHandDofGsuch that η inverts the elements ofH(Hwithout a direct factor of order 2) and fixesDelement-wise, then the linear extension ofηto the group algebraFGis called anice involution. This determines the groups of unitary and symmetric normalized units ofFG. We calculate the orders and the invariants of these subgroups.

How to stabilize the HOMO levels and to improve the charge transport properties of hole-transporting materials? Introducing a symmetrical core unit

Designed with a symmetrical core naphthatetrathiophene (NTT) and diphenylamine (DPA)-based side arms, a series of novel organic small molecule hole-transporting materials are simulated for perovskite solar cells (PSCs) by using density functional theory (DFT) and Marcus theory of electron transfer. As a fundamental understanding, the energy level alignments and the charge transport properties are explored for their potential applications. Our results show that, by introducing a symmetrical NTT core and regulating the terminal groups, the highest occupied molecular orbital (HOMO) levels of new predicted molecules are obviously down-shifted from -4.96 eV to -5.25 eV, which is beneficial for enlarging the open circuit voltage of PSCs. Moreover, we also find that rigidifying the core structure can make the HOMO down-shift and the lowest unoccupied molecular orbital (LUMO) up-shift simultaneously. On the other hand, the quasi-planar molecular architecture and the delocalized frontier molecular orbitals can effectively enhance the electronic coupling between adjacent molecules, and coupled with the lower reorganization energies, the hole mobilities of molecules 3–5 are clearly increased with the extension of the π-conjugated core. In summary, through systemic investigations, several potential candidates are proposed toward more efficient PSCs, and we hope that our work could provide some new clues for the rational design of organic small molecule materials.