Geometrical Symmetry Research Articles

Modal Phase-Matched Bound States in the Continuum for Enhancing Third Harmonic Generation of Deep Ultraviolet Emission.

Coherent deep ultraviolet (DUV) light sources are crucial for various applications such as nanolithography, biomedical imaging, and spectroscopy. DUV light sources can be generated by using conventional nonlinear optical crystals (NLOs). However, NLOs are limited by their bulky size, inadequate transparency at the DUV regime, and stringent phase-matching requirements for harmonic generation. Recently, dielectric metasurfaces support high Q-factor resonances and offer a promising approach for efficient harmonic generation at short wavelengths. In this study, we demonstrated a crystalline silicon (c-Si) metasurface simultaneously exciting modal phase-matched bound states in the continuum (BIC) resonance at the fundamental wavelength of 840 nm with a higher degree of freedom for precise control of the BIC resonance and a plasmonic resonance at the wavelength of 280 nm in the DUV to enhance third harmonic generation (THG). We experimentally achieved a Q-factor of ∼180 owing to the relatively large refractive index of the c-Si and the geometric symmetry breaking of the structure. We realized THG at a wavelength of 280 nm with a power of 14.5 nW by using a peak power density of 15 GW/cm2 excitation. The measured THG power is 14 times higher than the state-of-the-art THG dielectric metasurfaces using the same peak power density in the DUV regime, and the maximum obtained THG power enhancement factor is up to 48. This approach relies on the significant third-order nonlinear susceptibility of c-Si, the interband plasmonic nature of the c-Si in the DUV, and the strong field confinement of BIC resonance to boost overall nonlinear conversion efficiency to 5.2 × 10-6% in the DUV regime. Our work shows the potential of c-Si BIC metasurfaces for developing efficient and ultracompact DUV light sources using high-efficacy nonlinear optical devices.

Surface and Interface Engineering for Highly Stable CsPbBr3/ZnS Core/Shell Nanocrystals.

Shelling with chalcogenides on the surface of lead halide perovskite (LHP) nanocrystals (NCs) is believed to be an effective approach to increase their stability under high-moisture/aqueous conditions, which is important for LHP NC-based optoelectronic devices. However, it is still a challenge to prepare high-quality LHP/chalcogenide core/shell NCs with moisture/aqueous stability. In this work, a surface-defect-induced strategy is carried out to facilitate the adsorption of Br- ions and subsequently Zn2+ ions to preform a bipolar surface, which reduces the energy barrier at the CsPbBr3/ZnS interface and promotes the epitaxial growth of the ZnS shell layer. The aqueous stability of the as-received NCs shows an increase of over 12 times compared to that of the original one. Likewise, Mn2+ ions are introduced to further reduce the geometric symmetry mismatch and defect density at the CsPbBr3/ZnS interface. Interestingly, aqueous stability characterizations illustrate negligible degradation even after 230 min of ultrasonication, suggesting their outstanding stability. This work proposes an effective approach to prepare high-quality LHP/chalcogenide core/shell NCs, which possess great potential in the fabrication of stable optoelectronic devices.

Multi-directional unitarity and maximal entanglement in spatially symmetric quantum states

We consider dual unitary operators and their multi-leg generalizations that have appeared at various places in the literature. These objects can be related to multi-party quantum states with special entanglement patterns: the sites are arranged in a spatially symmetric pattern and the states have maximal entanglement for all bipartitions that follow from the reflection symmetries of the given geometry. We consider those cases where the state itself is invariant with respect to the geometrical symmetry group. The simplest examples are those dual unitary operators which are also self dual and reflection invariant, but we also consider the generalizations in the hexagonal, cubic, and octahedral geometries. We provide a number of constructions and concrete examples for these objects for various local dimensions. All of our examples can be used to build quantum cellular automata in 1+1 or 2+1 dimensions, with multiple equivalent choices for the “direction of time”.

Geometrical impacts of platonic particles on nematic liquid crystal dynamics.

Platonic-solid-like particles in liquid crystals offer intriguing opportunities for engineering complex materials with tailored properties. Inspired by platonic solids' geometric simplicity and symmetry, these particles possess well-defined shapes such as cubes, tetrahedra, octahedra, dodecahedra, and icosahedra. When dispersed within nematic liquid-crystalline media, these particles interact with the surrounding medium in intricate ways, influencing the local orientational order of liquid crystal molecules. In this work, we implement continuum simulations to study how the combination of particle shape and surface anchoring gives rise to line defects that follow the edges of the particles and how they are affected by the presence of a Poiseuille flow. Platonic-solid-like particles in liquid crystals have shown promise in diverse applications ranging from photonics and metamaterials to colloidal self-assembly and responsive soft materials.

Key-Axis-based Localization of Symmetry Axes in 3D Objects Utilizing Geometry and Texture.

In pose estimation for objects with rotational symmetry, ambiguous poses may arise, and the symmetry axes of objects are crucial for eliminating such ambiguities. Currently, in pose estimation, reliance on manual settings of symmetry axes decreases the accuracy of pose estimation. To address this issue, this method proposes determining the orders of symmetry axes and angles between axes based on a given rotational symmetry type or polyhedron, reducing the need for manual settings of symmetry axes. Subsequently, two key axes with the highest orders are defined and localized, then three orthogonal axes are generated based on key axes, while each symmetry axis can be computed utilizing orthogonal axes. Compared to localizing symmetry axes one by one, the key-axis-based symmetry axis localization is more efficient. To support geometric and texture symmetry, the method utilizes the ADI metric for key axis localization in geometrically symmetric objects and proposes a novel metric, ADI-C, for objects with texture symmetry. Experimental results on the LM-O and HB datasets demonstrate a 9.80% reduction in symmetry axis localization error and a 1.64% improvement in pose estimation accuracy. Additionally, the method introduces a new dataset, DSRSTO, to illustrate its performance across seven types of geometrically and texturally symmetric objects. The GitHub link for the open-source tool based on this method is https://github.com/WangYuLin-SEU/KASAL.

Certain results on tangent bundle endowed with generalized Tanaka Webster connection (GTWC) on Kenmotsu manifolds

<p>This work studies the complete lifts of Kenmotsu manifolds associated with the generalized Tanaka-Webster connection (GTWC) in the tangent bundle. Using the GTWC, this study explores the complete lifts of various curvature tensors and geometric structures from Kenmotsu manifolds to their tangent bundles. Specifically, it examines the complete lifts of Ricci semi-symmetry, the projective curvature tensor, $ \Phi $-projectively semi-symmetric structures, the conharmonic curvature tensor, the concircular curvature tensor, and the Weyl conformal curvature tensor. Additionally, the research delves into the complete lifts of Ricci solitons on Kenmotsu manifolds with the GTWC within the tangent bundle framework, providing new insights into their geometric properties and symmetries in the lifted space. The data on the complete lifts of the Ricci soliton in Kenmotsu manifolds associated with the GTWC in the tangent bundle are also investigated. An example of the complete lifts of a $ 5 $-dimensional Kenmotsu manifold is also included.</p>

Three-dimensional covalent organic framework-based artificial interphase layer endows lithium metal anodes with high stability.

To gain a deeper understanding and address the scientific challenges of lithium dendrite growth, a robust solid-state electrolyte interface (SEI) with good mechanical properties and rapid ion conduction is crucial for the advancement of lithium metal batteries. Artificial SEI layers based on organic polymers, such as covalent organic frameworks (COF), have garnered widespread attention due to their flexible structural design and tunable functionality. In this work, a COF with 3D spatial geometric symmetry and a fully covalent dia topology was synthesized and used as artificial SEI layers. A combination of comprehensive DFT calculations and ex situ/in situ characterizations have unraveled the impact of interpenetrated chain segments and anchoring lithiophilic groups on the microscopic dynamics related to Li ion desolvation, charge transfer, migration pathways, and deposition morphology. The ultralow polarization voltage of 46 mV for 9400 hours with a symmetric Li|Li cell at a harsh current density of 10 mA cm-2, as well as the high Li+ utilization, low polarization voltage, and prolonged lifespan for 3D-COF-modified Li|S and Li|LFP full cells, unambiguously corroborate the interphase reliability. This work also aims to shed new light on the use of multi-dimensional porous polymer SEI layers to revive highly stable Li metal batteries.

The effect of co-ligands on the performance of single-molecule magnet behaviours in a family of linear trinuclear Zn-Dy-Zn complexes with a compartmental Schiff base.

We present herein magneto-structural studies of three heterometallic Zn2Dy complexes: [Zn2Dy(L)2Cl2(H2O)](ClO4)·4H2O (1), [Zn2Dy(L)2Br2(H2O)](ClO4)·4H2O (2) and [Zn2Dy(L)2(OAc)I(H2O)]I3·4H2O (3), utilizing a new Schiff base ligand, N,N'-bis(3-methoxy-5-methylsalicylidene)-1,2-diaminocyclohexane (H2L). Complexes 1 and 2 exhibit remarkable magnetic relaxation behaviour with relatively high energy barriers in zero field (Ueff: 244 K for 1 and 211 K for 2) and notable hysteresis temperatures, despite the low local geometric symmetry around the central DyIII ions. The SMM performance of these complexes is further enhanced under an applied magnetic field, with Ueff increasing to 309 K for 1 and 269 K for 2, positioning them as elite members within the Zn-Dy SMM family. These findings emphasize the substantial influence of remote modulation on ZnII beyond the first coordination sphere of DyIII ions on their dynamic magnetic relaxation properties. Ab initio studies demonstrate that the relative orientation of the phenoxo-oxygen donor atoms around the DyIII ion is critical for determining the magnetic anisotropy and relaxation dynamics in these systems. Additionally, experimental and theoretical investigations reveal that the coordination of the bridging acetate towards the hard plane, combined with significant distortion from the ideal ZnO2Dy diamond core arrangement caused by the acetate ion, results in low magnetic anisotropy in complex 3, thereby leading to field-induced SMM behaviour. Overall, this study unveils the effects of co-ligands on the SMM performance in a series of linear trinuclear Zn-Dy-Zn complexes, which exhibit low local geometric symmetry around the DyIII centres.

Cultural dimensions of symmetric pattern – an annotated bibliography of recent research

This bibliographic essay focuses on research that has explored symmetries of non-representational geometric pattern created in cultural contexts. I provide annotated discussions and full bibliographic citations of recent studies of symmetric patterns on tiling, textiles, basketry, ceramics, sculpture, architecture, and other materials. I describe studies that reveal how this focus on pattern structure as measured by geometric symmetries enhances insights into the meaning and function of symmetric pattern created on these cultural materials.

Facial symmetry perception and attractiveness ratings in body dysmorphic disorder

Facial symmetry perception and attractiveness ratings in body dysmorphic disorder

Enhanced As-COF nanochannels as a high-capacity anode for K and Ca-ion batteries.

Covalent organic frameworks can be used for next-generation rechargeable metal-ion batteries due to their controllable spatial and chemical architectures and plentiful elemental reserves. In this study, the arsenic-based covalent organic framework (As-COF) is designed by employing the geometrical symmetry of a semiconducting phosphazene-based covalent organic framework that uses p-phenylenediamine as a linker and hexachorocyclotriphosphazene as an As-containing monomer in a C3-like spatial configuration. The As-COF with engineered nanochannels demonstrates exceptional anodic behavior for potassium (K) and calcium (Ca) ion batteries. It exhibits a high storage capacity of about 914(2039) mA h g-1, low diffusion barriers of 0.12(0.26) eV, low open circuit voltage of 0.23(0.18) V, and a minimal volume expansion of 2.41(2.32)% for K (Ca) ions. These attributes collectively suggest that As-COF could significantly advance high-capacity rechargeable batteries.

STUDY OF THE CURRENT IN THE MULTIELECTRODE PLANT BATH

Active resistance heating multi-electrode ore-thermal furnaces, being in quasi-stationary and transient modes, work in the conditions of electric loop dissymmetry formed by the furnace transformers, current supply and bath caused by the action of different factors of geometric, electromagnetic, thermal and technological character. They worsen the energetic, technological and operational performances. The present methods of studying the electric processes in the furnace loop do not allow in full measure to reveal, consider and eliminate factor actions resulting in phenomena causing electrical duty dissymmetry. Unbalance of the system of currents flowing from the electrode to electrode passing the melt and unbalance of the system of currents flowing directly onto the melt influence the dissymmetry of the furnace loop electrical duty.
 
 The work objective is forming the calculated formulas for determining the resistance heating three-electrode furnace bath “star” and “triangle” currents and by means of them studying the electrode and bath geometrical parameters influence on the mentioned currents.
 
 Materials and methods. The study object is currents flowing in the resistance heating three-phase, three-electrode furnace bath. When carrying out the studies, methods of electrical technology theory and computer mathematic simulation with COMSOL Multiphysics software environment are used.
 
 Results of the study. The study novelty lies in the elaboration of procedure for constructing formulas for calculating the resistance heating three-electrode furnace bath “star” and “triangle” currents with electrode arbitrary location and dissymmetric current system feeding the bath. Influence of the round electrode embedding diameter and the diameter of their dissociation in the three-electrode furnace bath into the currents flowing from the electrode surfaces to the bottom and from the electrode to electrode passing the melt in cases of three-phase symmetric electrode current system and geometrical symmetry of electrode location in the bath is studied.
 
 Findings. Calculation procedure of the resistance heating three-electrode furnace bath “star” and ‘triangle” currents with arbitrary electrode location is developed based on the joint use of the direct admittances and difference-potential coefficients of the equivalent circuits.

An efficient end-capped engineering of pyrrole-based acceptor molecules for high-performance organic solar cells.

Various innovative molecules have been designed and explored for use in organic photovoltaics. In this study, we devised novel molecules (KZ1-KZ7) specifically for organic solar cells (OSCs). The newly formulated acceptor compounds possess a lower bandgap (Eg = 1.85-2.02), along with bathochromic shift (λmax = 713-788 nm) compared to the reference (Eg = 2.04 eV and λmax = 774 nm). Moreover, the FMO results identified the distinct charge transfer from HOMO to LUMO, which was strongly corroborated by the TDM maps. Similarly, the new designed molecules show less excitation energy (Ex = 1.31-1.54(gas)) than reference (Ex = 1.72). Likewise, all designed molecules (KZ1-KZ7) have demonstrated an analogous open circuit voltage (Voc) with the donor polymer PTB7-Th. All seven designed molecules (KZ1-KZ7) exhibited more fill factor ranging from 97.08 to 97.29 than reference 95.25 and PCE of between 8 and 20% at short circuit current densities of 9, 12, and 15 mA cm-2. Overall, the findings support that designed molecules can be potential molecules for future practical applications. Geometric calculations were conducted with Gaussian 09W software, and the findings were visualized using Gauss View software. DFT and TD-DFT were employed to evaluate various parameters for R and designed molecules (KZ1-KZ7). Firstly, four functionals including B3LYP, CAM-B3LYP, MPW1PW91, and ωB97XD with 6-31G(d,p) DFT level were applied to R to decide the best level for results. After appropriate analysis, the MPW1PW91/6-31G(d,p) was selected for further examination by comparing the experimental and DFT-based absorption graphs of R. External and internal reorganization energy are the two main factors contributing to reorganization energy. External energy refers to changes in external environment, while internal energy deals with information related to internal geometrical symmetry or the internal environment. The effect of outside factors or external reorganizational energy is omitted because it creates too little change.

Programming Anisotropic Functionality of 3D Microdenticles by Staggered-Overlapped and Multilayered Microarchitectures.

Natural sharkskin features staggered-overlapped and multilayered architectures of riblet-textured anisotropic microdenticles, exhibiting drag reduction and providing a flexible yet strong armor. However, the artificial fabrication of three-dimensional (3D) sharkskin with these unique functionalities and mechanical integrity is a challenge using conventional techniques. In this study, it is reported on the facile microfabrication of multilayered 3D sharkskin through the magnetic actuation of polymeric composites and subsequent chemical shape fixation by casting thin polymeric films. The fabricated hydrophobic sharkskin, with geometric symmetry breaking, achieves anisotropic drag reduction in frontal and backward flow directions against the riblet-textured microdenticles. For mechanical integrity, hard-on-soft multilayered mechanical properties are realized by coating the polymeric sharkskin with thin layers of zinc oxide and platinum, which have higher hardness and recovery behaviors than the polymer. This multilayered hard-on-soft sharkskin exhibits friction anisotropy, mechanical robustness, and structural recovery. Furthermore, coating the MXene nanosheets provides the fabricated sharkskin with a low electrical resistance of ≈5.3 Ω, which leads to high Joule heating (≈229.9°C at 2.75V). The proposed magnetomechanical actuation-assisted microfabrication strategy is expected to facilitate the development of devices requiring multifunctional microtextures.

Covariant canonical formulations of classical field theories

We review in simple terms the covariant approaches to the canonical formulation of classical relativistic field theories (in particular gauge field theories and general relativity) and we discuss the relationships between these approaches as well as the relation with the standard (non-covariant) Hamiltonian formulation. Particular attention is paid to conservation laws (notably related to geometric symmetries) within the different approaches. Moreover, for each of these approaches, the impact of space-time boundaries is also addressed. To make the text accessible to a wider audience, we have included an outline of Poisson and symplectic geometry for both classical mechanics and field theory.

The exotic ground state of the decorated honeycomb lattice

The study is focusing on the exploration of the magnetic properties of the frustrated decorated honeycomb lattices. The presence of geometrical frustration and C3 symmetry leads to an exotic ground state. Monte Carlo simulations and analytical calculations are used to analyze the system’s behavior. The dependence of the magnetization on the external field of the Ising model exhibits a step-like behavior, while the magnetization of the classical Heisenberg model has no plateau in the isotropic case. An efficient Hamiltonian is proposed to describe the properties of this system on the unfrustrated hexagonal lattice within the framework of the chiral Potts model. Within a specific range of fields, the state of the effective Hamiltonian aligns with that of the original Hamiltonian. The ground state configurations and degeneracy of the system are explored, revealing fractured stripe patterns separated by spins with opposite orientations. These findings contribute to the knowledge of the properties of decorated lattices, offering valuable insights for potential experimental and practical applications.

Adjustable broadband absorber based on vanadium dioxide multiple coupled diagonally sliced square ring shaped structure for THz frequency

Adjustable broadband absorber based on vanadium dioxide multiple coupled diagonally sliced square ring shaped structure for THz frequency

Thz four-beam steering using metagrating pair with angle insensitivity and tailored geometric symmetry

Thz four-beam steering using metagrating pair with angle insensitivity and tailored geometric symmetry

Modal properties of fractal trees as recursive analytical solutions

Modal properties of fractal trees as recursive analytical solutions

Nonreciprocal Transport and Optical Phenomena in Quantum Materials

In noncentrosymmetric materials, the responses (for example, electrical and optical) generally depend on the direction of the external stimuli, called nonreciprocal phenomena. In quantum materials, these nonreciprocal responses are governed by the quantum geometric properties and symmetries of the electronic states. In particular, spatial inversion ([Formula: see text]) and time-reversal ([Formula: see text]) symmetries play crucial roles, which are also relevant to the geometric Berry phase. Here, we give a comprehensive review of the nonreciprocal transport and optical responses including ( a) the magnetochiral anisotropy, i.e., the nonlinear resistivity with respect to the electric field, in semiconductors and metals, ( b) the nonreciprocal transport in superconductors such as the nonreciprocal paraconductivity and the superconducting diode effect in bulk and Josephson junctions, and ( c) the second-order nonlinear optical effects in the electric field of light, including the geometric shift current in nonmagnetic systems, magnetic systems, and superconductors.