Geometrical Symmetry Research Articles

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

A broadband absorber with multiple coupled diagonally sliced square rings at terahertz frequency using vanadium dioxide is proposed. The proposed structure exhibits more than 90 % absorption in the frequency range of 2.85–7.51 THz, with a relative bandwidth of 89.96 % and an absorption bandwidth of 4.66 THz. The absorptivity curve increases as vanadium dioxide conductivity rises from 200 S/m to 200,000 S/m, giving a wide range of tunability from 1.62 % to 100 % at 3.4 THz. Due to its geometrical symmetry, the proposed structure is independent of the polarization angle under normal incident plane waves. The proposed structure works for different incident angles for transverse electric (TE) mode and transverse magnetic (TM) mode with oblique incidence plane waves. The results demonstrate the broad bandwidth compared to the state-of-the-art designs within the same frequency band with potential applications in sensors, switches, tuning, and modulation in the terahertz range.

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

Dynamic multi-beam steering is highly desired in target tracking and networking, with faster speed and larger flexibility as compared to single-beam steering. Here, instead of actively controlling meta-atoms in phased array metasurfaces, four beams are simultaneously scanned by cascaded diffraction of a pair of rotating metagratings. By tailoring the rotation symmetry and azimuth-angle-insensitive diffraction of the metagratings, multiple tangential wave vectors in the two layers are one-to-one added vectorially in order to govern the output four-beam direction. By combining a four-beam splitter metagrating with a beam deflector, we experimentally demonstrate THz four-beam steering with symmetric or asymmetric trajectories. The asymmetric steering shows ± 60° field of view with average efficiency of 41 % by tuning the relative orientation of the two metagratings, and the symmetric steering shows ± 22° field of view with the potential for further increasing the coverage. The efficiency fluctuation of the four beams is less than 4 %. This dynamic multi-beam steering strategy shows great potential for flexible signal transmission and processing in the THz band.

Modal properties of fractal trees as recursive analytical solutions

This study analyzes the modal properties of two-dimensional fractal trees under the assumptions of linear-elastic vibrations and axially inextensible branches. The examined fractal trees are of a generalized sympodial architecture with possibly non-zero and non-uniform branching angles. The study first presents the construction of tree geometry via iterated functions and then formulates the trees’ dynamic matrices from a renormalization viewpoint. The study proposes a novel recursive analytical solution to capture the trees’ modal properties. The proposed solution perceives the modal analysis of the fractal trees as an equivalent static analysis of trees with a modified configuration. These “modified” trees are made from the original trees but with all branches connected to the ground via negative stiffness springs. The analysis shows that identifying the lateral trunk displacements of the modified trees (under a static unit force) is associated with the recursive construction of a new family of functions that are introduced in the study, called the auxiliary P-functions. The results reveal that the modal frequencies of the original fractal trees are given by the roots of all auxiliary P-functions. Crucially, these auxiliary P-functions allow the graphical construction of the trees’ mode shapes. Illustrative examples demonstrate how the proposed recursive analytical solutions can be used to determine the trees’ modal properties. Lastly, the study concludes that the repetition of branches, even without geometrical symmetry, is a necessary condition for the existence of a unique vibration mitigation mechanism in fractal trees, namely the self-similar modes.

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.

Multi-polarization selective absorber based on terahertz metasurface

Tunable absorbers attract much attention due to their wide applications, such as integrated optical sensors, multiplexing far-field imaging and so on. In this paper, we design a multi-polarization selective absorber based on terahertz metasurface, whose geometric symmetry is tunable to satisfy the requirements of linear and circular polarization selective absorbers. At the ON state, the metasurface selectively absorbs y-polarized wave at 1.0 THz, with the linear dichroism of 0.84. At the OFF state, the metasurface selectively absorbs left circularly polarized wave at 1.16 THz, with the circular dichroism of 0.81. The physical mechanism of the metasurface is explained by the Jones calculus and the electromagnetic field distributions. In addition, the multi-polarization selective behavior is insensitive to the incident angle. Finally, we design a sample to verify the potential application of the metasurface absorber, which displays multiplexing imaging of ‘C’, ‘mirrored C’, ‘O’ and blurred images under different polarized incidences at different states. Such a metasurface, switching between linear polarization selective absorber and circular polarization selective absorber, may achieve stable applications in multifunction integrated absorbers, detectors, and image encryptions.

Harnessing local flow in buckling pores for low-frequency attenuation

While attenuation at low frequencies remains highly desirable for industrial applications such as multistory buildings or spacecraft propellant tanks, fluid-filled rocks can achieve this goal naturally by so-called local flow in their heterogeneous pore structure. The present work aims at combining this natural phenomenon with controlled instabilities in light-weight structures. Buckling of their pores is harnessed to break local geometric symmetry and maximize the local-flow effect. A prototype structure with elliptical pores is analyzed numerically. It does not show local flow or attenuation for the starting geometry, but reversibly switches into an attenuating structure by imposing a critical buckling strain. The simulations reach inverse quality factors larger than 0.3 around 5Hz for material properties of air-filled silicone rubber. A key to high attenuation is a tradeoff between the unstable structure and the pore fluid. If the solid is too soft, the fluid-filled pores are not compressed and buckling is not triggered. If the solid is too stiff, most energy is stored elastically and not dissipated by fluid flow. The proposed, fluid-filled structure allows for a scalable, light-weight material exhibiting significant low-frequency attenuation.

Peptide-dendrimer-reinforced bioinks for 3D bioprinting of heterogeneous and biomimetic in vitro models.

Despite 3D bioprinting having emerged as an advanced method for fabricating complex in vitro models, developing suitable bioinks that fulfill the opposing requirements for the biofabrication window still remains challenging. Although naturally derived hydrogels can better mimic the extracellular matrix (ECM) of numerous tissues, their weak mechanical properties usually result in architecturally simple shapes and patchy functions of in vitro models. Here, this limitation is addressed by a peptide-dendrimer-reinforced bioink (HC-PDN) which contained the peptide-dendrimer branched PEG with end-grafted norbornene (PDN) and the cysteamine-modified HA (HC). The extensive introduction of ethylene end-groups facilitates the grafting of sufficient moieties and enhances thiol-ene-induced crosslinking, making HC-PDN exhibits improved mechanical and rheological properties, as well as a significant reduction in reactive oxygen species (ROS) accumulation than that of methacrylated hyaluronic acid (HAMA). In addition, HC-PDN can be applied for the bioprinting of numerous complex structures with superior shape fidelity and soft matrix microenvironment. A heterogeneous and biomimetic hepatic tissue is concretely constructed in this work. The HepG2-C3As, LX-2s, and EA.hy.926s utilized with HC-PDN and assisted GelMA bioinks closely resemble the parenchymal and non-parenchymal counterparts of the native liver. The bioprinted models show the endothelium barrier function, hepatic functions, as well as increased activity of drug-metabolizing enzymes, which are essential functions of liver tissue in vivo. All these properties make HC-PDN a promising bioink to open numerous opportunities for in vitro model biofabrication. STATEMENT OF SIGNIFICANCE: In this manuscript, we introduced a peptide dendrimer system, which belongs to the family of hyperbranched 3D nanosized macromolecules that exhibit high molecular structure regularity and various biological advantages. Specifically, norbornene-modified peptide dendrimer was grafted onto PEG, and hyaluronic acid (HA) was selected as a base material for bioink formulation because it is a component of the ECM. Peptide dendrimers confer the following advantages to bioinks: (a) Geometric symmetry can facilitate construction of bioinks with homogeneous networks; (b) abundant surface functional groups allow for abundant crosslinking points; (c) the biological origin can promote biocompatibility. This study shows conceptualization to application of a peptide-dendrimer bioink to extend the Biofabrication Window of natural bioinks and will expand use of 3D bioprinting of in vitro models.

A morphological study of fivefold Islamic geometric patterns using formal grammar for computer-aided design applications

This paper presents a morphological study of Islamic geometric patterns (IGP) and their role in application of formal grammar in computational modeling of IGPs. Through a comprehensive literature review and data collection, we analyze the morphological properties of these patterns using techniques such as geometric transformations, pattern classification, and symmetry analysis. Based on our findings, we explore how these properties can be used in constructing a formal grammar through string rewriting system for a CAD application. Building on a study on the potential of a string rewriting system for modeling IGPs, the current research suggests an update to the previous system and introduces a new morphological structure for IGPs. The new method has an expanded sample set and is tested on a class of 5-fold star patterns with 12 members and demonstrates successful development. The results are implemented in a Grasshopper add-on, providing a flexible platform to generate the patterns through strings and to control their parameters. This tool opens up new possibilities to bridge traditional patterns with contemporary technologies and make them more accessible. Furthermore, it contributes to the preservation of IGPs as a significant cultural and architectural heritage, while also advancing the evolution of these patterns to a new and contemporary generation.

Structural Expansion of Catalytic RNA Nanostructures through Oligomerization of a Cyclic Trimer of Engineered Ribozymes.

The multimolecular assembly of three-dimensionally structured proteins forms their quaternary structures, some of which have high geometric symmetry. The size and complexity of protein quaternary structures often increase in a hierarchical manner, with simpler, smaller structures serving as units for larger quaternary structures. In this study, we exploited oligomerization of a ribozyme cyclic trimer to achieve larger ribozyme-based RNA assembly. By installing kissing loop (KL) interacting units to one-, two-, or three-unit RNA molecules in the ribozyme trimer, we constructed dimers, open-chain oligomers, and branched oligomers of ribozyme trimer units. One type of open-chain oligomer preferentially formed a closed tetramer containing 12 component RNAs to provide 12 ribozyme units. We also observed large assembly of ribozyme trimers, which reached 1000 nm in size.

Enhancing the Goos–Hänchen shift based on quasi-bound states in the continuum through material asymmetric dielectric compound gratings

Quasi-bound state in the continuum (QBIC) resonance is gradually attracting attention and being applied in Goos–Hänchen (GH) shift enhancement due to its high quality (Q) factor and superior optical confinement. Currently, symmetry-protected QBIC resonance is often achieved by breaking the geometric symmetry, but few cases are achieved by breaking the material symmetry. This paper proposes a dielectric compound grating to achieve a high Q factor and high-reflection symmetry-protectede QBIC resonance based on material asymmetry. Theoretical calculations show that the symmetry-protected QBIC resonance achieved by material asymmetry can significantly increase the GH shift up to −980 times the resonance wavelength, and the maximum GH shift is located at the reflection peak with unity reflectance. This paper provides a theoretical basis for designing and fabricating high-performance GH shift tunable metasurfaces/dielectric gratings in the future.

Identifying the geometric symmetry role of single-atom chlorine evolution electrocatalyst

Identifying the geometric symmetry role of single-atom chlorine evolution electrocatalyst

Chlorine-Coordinated Unsaturated Ni-N2 Sites for Efficient Electrochemical Carbon Dioxide Reduction.

Heteroatom-doping is an effective method for modifying the geometric symmetry of metal-nitrogen-carbon (M-N-C) single-atom catalysts and thereby tuning the electronic structure. Up to now, most of the current reports have concentrated on introducing heteroatoms into the highly symmetrical M-N4 structure. The coordination-unsaturated M-N2 structure is more sterically favorable for the insertion of alien atoms to optimize the electronic structure. Herein, a Ni-N2 catalyst with out-of-plane coordinated chlorine(Cl) atoms (Ni-N2 Cl/C) is successfully constructed on chlorine-functionalized carbon supports (C-Cl) for an efficient carbon dioxide reduction reaction (CO2 RR). Density functional theory calculations demonstrate that the prepared Ni-N2 Cl/C catalyst exhibits a higher capability in balancing COOH* formation and CO* desorption. In addition, in situ Raman spectra confirm that the lower CO binding energy on the Ni-N2 Cl/C facilitates CO escape, leading to excellent CO2 RR performance. A high CO Faradaic efficiency (FECO ) of more than 80% is achieved from -0.6 to -1.2V versus reversible hydrogen electrode on the Ni-N2 Cl/C and it exhibits negligible FECO and current declination over a 40-h stability test. Furthermore, a high turnover frequency (TOF) value of 15 808 h-1 is obtained, which is more than ten times that of Ni-N2 /C (1476 h-1 ) without coordinated Cl atoms.

Three-dimensional critical points and flow patterns in pulmonary alveoli with rhythmic wall motion

The dynamics of airflow in the pulmonary acini are of broad interest in understanding respiratory diseases and the fate of inhaled particles. This study investigates the three-dimensional (3d) alveolar flows with rhythmic cavity wall motion, using a finite element method based computational fluid dynamics. This study reports the new research findings on the critical points and associated flow patterns. The locations of critical points are found based on the Brouwer degree theory and Broyden’s method. The phase portrait is used to evaluate the flow patterns around the critical points and the stability (repelling/attracting property) of the critical points on the symmetry plane of the alveolus. Based on the Poincare–Bendixson theorem, the closed orbits on the symmetry plane are found which have the capability to alter the spiral direction of the spiral streamlines. In the 3d space, the alveolar flow is symmetric about the geometric symmetry plane of the alveolus. Different types of 3d critical points, including saddle, spiral, and spiral saddle, are revealed. There are only one saddle point and at least one spiral point or spiral saddle in the alveolar flow. Spiral points and spiral saddles are located on the vortex core line and their number is dependent on the Reynolds number and varies with time. The study of critical points and their evolution helps us to understand the mechanism of irreversible transport of particle tracers from a new perspective.

Semianalytical findings for the dynamics of the charged particle in the Störmer problem

In this semianalytical research, we present a new ansatz in solving the Störmer problem with numerical findings in graphical representations of solutions where dynamics of the charged particle in the classical dipole magnetic field (here, Earth's magnetic field) was investigated in detail. We have fully solved the Störmer problem for partial class of the charged particle's motion close to the equatorial plane of Earth; this result is the main important theoretical finding presented here with prescribed symmetry. Aforementioned motions, determined by Lorentz force in nonrelativistic case, thereby are explored in polar coordinates to present them in a quasi‐periodic motions in a general case (in equatorial plane of Earth). Thus, the system of momentum equations has been successfully solved numerically or semianalytically in each case and the resulting semianalytical solving algorithm can clarify the quasi‐periodic structure of such family of solutions (with reduction of their geometric symmetry around the Earth in an equatorial plane).

Exploratory study of a multifrequency EIT-based method for detecting intracranial abnormalities.

The purpose of this paper is to compare the differences in the features of multifrequency electrical impedance tomography (MFEIT) images of human heads between healthy subjects and patients with brain diseases and to explore the possibility of applying MFEIT to intracranial abnormality detection. Sixteen healthy volunteers and 8 patients with brain diseases were recruited as subjects, and the cerebral MFEIT data of 9 frequencies in the range of 21 kHz - 100 kHz of all subjects were acquired with an MFEIT system. MFEIT image sequences were obtained according to certain imaging algorithms, and the area ratio of the ROI (AR_ROI) and the mean value of the reconstructed resistivity change of the ROI (MVRRC_ROI) on both the left and right sides of these images were extracted. The geometric asymmetry index (GAI) and intensity asymmetry index (IAI) were further proposed to characterize the symmetry of MFEIT images based on the extracted indices and to statistically compare and analyze the differences between the two groups of subjects on MFEIT images. There were no significant differences in either the AR_ROI or the MVRRC_ROI between the two sides of the brains of healthy volunteers (p > 0.05); some of the MFEIT images mainly in the range of 30 kHz - 60 kHz of patients with brain diseases showed stronger resistivity distributions (larger area or stronger signal) that were approximately symmetric with the location of the lesions. However, statistical analysis showed that the AR_ROI and the MVRRC_ROI on the healthy sides of MFEIT images of patients with unilateral brain disease were not significantly different from those on the affected side (p > 0.05). The GAI and IAI were higher in all patients with brain diseases than in healthy volunteers except for 80 kHz (p < 0.05). There were significant differences in the geometric symmetry and the signal intensity symmetry of the reconstructed targets in the MFEIT images between healthy volunteers and patients with brain diseases, and the above findings provide a reference for the rapid detection of intracranial abnormalities using MFEIT images and may provide a basis for further exploration of MFEIT for the detection of brain diseases.