Symmetry Axis Research Articles

Position Normalization of Propellant Grain Point Clouds

Point cloud data obtained from scanning propellant grains with 3D scanning equipment exhibit positional uncertainty in space, posing significant challenges for calculating the relevant parameters of the propellant grains. Therefore, it is essential to normalize the position of each propellant grain’s point cloud. This paper proposes a normalization algorithm for propellant grain point clouds, consisting of two stages, coarse normalization and fine normalization, to achieve high-precision transformations of the point clouds. In the coarse normalization stage, a layer-by-layer feature points detection scheme based on k-dimensional trees (KD-tree) and k-means clustering (k-means) is designed to extract feature points from the propellant grain point cloud. In the fine normalization stage, a rotation angle compensation scheme is proposed to align the fitted symmetry axis of the propellant grain point cloud with the coordinate axes. Finally, comparative experiments with iterative closest point (ICP) and random sample consensus (RANSAC) validate the efficiency of the proposed normalization algorithm.

Investigation of Upper Critical Magnetic Field in 1111‐Type High‐Temperature Iron‐Based Superconductor SmFeAsO1−xFx

ABSTRACTIn this research work, we used a two‐band model to study the theoretical analysis of the upper critical magnetic field of a high‐temperature iron‐based superconductor . The graphs of the high‐temperature iron‐based superconductor's upper critical magnetic field (((T) and ) and angular dependence of the field () versus temperature were effectively plotted. The phase diagrams of the temperature‐dependent upper critical magnetic fields versus temperature were suppressed at the transitional temperature and decreased with rising temperature for both directions of the symmetry axis. Additionally, we plotted the phase diagrams and derived the Ginzburg–Landau (GL) parameters (( and ). At the superconducting critical temperature of the superconducting material, these GL parameters diverge at the transitional temperature. Furthermore, a phase diagram of GL characteristic parameter temperature dependence was plotted. By doping fluorine atoms into the parent compound Sm‐1111, the transitional temperature of this superconductor material increased, reaching a value of 54 K and above. Finally, our theoretical conclusion is consistent with the previous experimental results.

Three-Dimensional Moiré Crystal in Ultracold Atomic Gases.

The work intends to extend the moiré physics to three dimensions. Three-dimensional moiré patterns can be realized in ultracold atomic gases by coupling two spin states in spin-dependent optical lattices with a relative twist, a structure currently unachievable in solid-state materials. We give the commensurate conditions under which the three-dimensional moiré pattern features a periodic structure termed a three-dimensional moiré crystal. We emphasize a key distinction of three-dimensional moiré physics: In three dimensions, the twist operation generically does not commute with the rotational symmetry of the original lattice, unlike in two dimensions, where these two always commute. Consequently, the moiré crystal can exhibit a crystalline structure that differs from the original underlying lattice. We demonstrate that twisting a simple cubic lattice can generate various crystal structures. This capability of altering crystal structures by twisting offers a broad range of tunability for three-dimensional band structures.

Theta dependence in the presence of massless fermions

We show that, if there are conserved flavor symmetries, then some properties of a monopole can depend on θ, even when a fermion is massless. The quantized nature of global symmetries and the fractional nature of the Witten effect can lead to interesting structure. Seen from another point of view, aside from possibly breaking baryon and lepton flavor symmetries (the Callan-Rubakov effect), monopole boundary conditions can also break the axial symmetry that otherwise could have been used to remove θ from the Lagrangian. As an example, in a toy model, we calculate the θ dependence of the mass of the monopole and properties of the nonzero charge density surrounding the monopole. Published by the American Physical Society 2024

Microtubules and actin filaments direct nuclear movement during the polarisation of Marchantia spore cells.

The multicellular haploid stage of land plants develops from a single haploid cell produced by meiosis - the spore. Starting from a non-polar state, these spores develop polarity, divide asymmetrically and establish the first axis of symmetry. Here, we show that the nucleus migrates from the cell centroid to the basal pole during polarisation of the Marchantia polymorpha spore cell. A microtubule organising centre on the leading edge of the nucleus initiates a microtubule array between the nuclear surface and the cortex at the basal pole. Simultaneously, cortical microtubules disappear from the apical hemisphere but persist in the basal hemisphere. This is accompanied by the formation a dense network of fine actin filaments between the nucleus and the basal pole cortex. Experimental depolymerisation of either microtubules or actin filaments disrupts cellular asymmetry. These data demonstrate that the cytoskeleton reorganises during spore polarisation and controls the directed migration of the nucleus to the basal pole. The presence of the nucleus at the basal pole provides the cellular asymmetry for the asymmetric cell division that establishes the apical-basal axis of the plant.

INTUITIVE UNDERSTANDING OF THE VERTEX AND AXIS OF SYMMETRY OF A PARABOLA WITHOUT COMPLETING THE SQUARE

An approach towards intuitively understanding the vertex and axis of symmetry of a parabola without completing the square is presented. The main aims of this study are to help learners comprehend the following two problems: (1) the reason why the position of an axis of symmetry is essentially determined only by the coefficient of a first-order term, and (2) the reason why the positive and negative of the coefficient of the first-order term are opposite to the positive and negative of the horizontal coordinates of the axis of symmetry. The method of graphing parabolic motion is also presented as a cross-study with kinematics.

Indigenous Knowledge Content & Mathematics Curriculum

Cultural practices present opportunities for Mathematics Education to be more relevant, and effective, especially in post-colonial contexts. Despite national policies emphasising integration of Indigenous Knowledge (IK) into school curricula, there has been limited success in incorporating ethnomathematics into Mathematics teaching. We exploredgeometrical concepts inherent in traditional baskets produced by Aawambo women, an ethnic group in northern Namibia. We identified specific geometrical concepts that can be linked to the junior secondary school Mathematics syllabus. We employed ethnographic observations, interviews with local basket makers and focus group discussions with Mathematics junior secondary school teachers for triangulation. Furthermore, we adopted an interpretive paradigmusing a multi-modal method to source empirical data that demonstrated relevance to the curriculum. We explored socio-cultural perspectives of women and artefacts (baskets) to compare the subject matter from literature. The findings revealed common concepts as well as the ethnomathematical content not yet incorporated in the junior secondary school Mathematics curriculum comprising of symmetry (axial symmetry) and geometrical transformation (shear and translation). The study has implications for decolonizing western Mathematical practices through adoption ethnomathematics approaches across Africa.

On the Motion of a Point Particle on a Homogeneous Gravitating Ball with a Spherical Inclusion

A problem of motion of a point particle on a surface of a homogeneous gravitating ball with a spherical inclusion of a differing density is considered. It is assumed that the body rotates uniformly around its symmetry axis. It is supposed that "besides the gravitation force, the particle is subjected to dry friction. The gravitational properties outside the ball are described. The dependence of existence, bifurcations, and stability of relative equilibria of the point particle on the body surface on the parameters of the problem is studied. The results are represented both analytically and as numerically obtained bifurcation diagrams.

Insights into the gas-phase structure and internal dynamics of diphenylsilane: A broadband rotational spectroscopy study.

The rotational spectrum of diphenylsilane was investigated using chirped-pulse Fourier transform microwave spectroscopy in the frequency range of 2-8 GHz. The lowest energy structure of diphenylsilane has C2 point group symmetry with the C2 symmetry axis coinciding with the binertial axis of the molecule. Through the assignment of the main isotopologue as well as singly substituted heavy-atom isotopologues, including 13C, 29Si, and 30Si, we were able to obtain a comprehensive gas-phase structure of diphenylsilane. The structure of diphenylsilane was compared with its oxygen analogue, diphenylether, including a discussion of the barrier height to the large-amplitude motion of the phenyl rings. Furthermore, the structural comparison was extended to include a range of C-Si bond lengths and bond angles from other organosilicon molecules where the silicon atom is bonded to aliphatic and/or aromatic moieties.

Stokes-based analysis for the estimation of 3D dipolar emission

We provide a general description of the measurement capabilities of systems that probe the 3D state of polarization of light emitted by a dipole or a collection of dipoles. This analysis is based on a generalization of the Stokes parameters for 3D polarization, and its goal is to provide insight into what constitutes a good measurement system under specific circumstances, through the definition of appropriate merit functions. Three cases are considered: the general case of arbitrary states of 3D polarization, the special case of 3D linear full or partial polarization states, and the even more specific case of linear dipoles that wobble with rotational symmetry around a central direction. Note that the latter two cases are of interest in fluorescence microscopy. The analysis presented here is illustrated by applying it to two different approaches used commonly in orientation microscopy: PSF engineering and ratiometric measurements.

A Nonlinear Peptide Topology for Synthetic Virions.

a nonlinear de novo peptide topology for the assembly of synthetic virions is reported. The topology is a backbone cyclized amino-acid sequence in which polar l- and hydrophobic d-amino acid residues of the same-type alternate. This arrangement introduces pseudo C4 symmetries of side chains within the same cyclopeptide ring, allowing for the lateral propagation of cyclopeptides into networks with a [3/6, 4]-fold rotational symmetry closing into virus-like shells. A combination of computational and experimental approaches was used to establish that the topology forms morphologically uniform, nonaggregating and nontoxic nanoscale shells. These effectively encapsulate genetic cargo and promote its intracellular delivery and a target genetic response. The design introduces a nanotechnology inspired solution for engineering virus-like systems thereby expanding traditional molecular biology approaches used to create artificial biology to chemical space.

Magnetohydrodynamic Motions of Oldroyd-B Fluids in Infinite Circular Cylinder That Applies Longitudinal Shear Stresses to the Fluid or Rotates Around Its Axis

Two classes of magnetohydrodynamic (MHD) motions of the incompressible Oldroyd-B fluids through an infinite cylinder are analytically investigated. General expressions are firstly established for shear stress and velocity fields corresponding to the motion induced by longitudinal shear stress on the boundary. For validation, the expression of the shear stress is determined by two different methods. Using an important remark regarding the governing equations for shear stress and fluid velocity corresponding to the two different motions, this expression is then used to provide the dimensionless velocity field of the MHD motion of the same fluids generated by a cylinder that rotates around its symmetry axis. Obtained results can generate exact solutions for any motion of this kind of Oldroyd-B fluids. Consequently, both types of motions are completely solved. For illustration, some case studies are considered, and adequate velocity fields are provided. The steady-state components of these velocities are presented in different forms whose equivalence is graphically proved. The influence of the magnetic field on the fluid behavior is graphically investigated. It was found that the fluid flows slower, and a steady state is earlier reached in the presence of a magnetic field. The fluid behavior when shear stress is given on the boundary is also investigated.

Features of 2D mapping technique of non-uniform magnetic fields using self-biased magnetoelectric composites based on “bidomain LiNbO3/Ni/Metglas” structures

Magnetoelectric (ME) composites are extensively researched for their ability to detect magnetic fields but are typically characterized by their interactions with homogeneous magnetic fields. However, practical applications often involve non-uniform magnetic fields (NMFs). In this study, we developed and validated a technique for 2D mapping of NMFs using sensor based on ME composite. The primary focus was on mapping the magnetic field generated by a single wire carrying an alternating current (AC). The experimental setup included a “bidomain LiNbO3/Ni/Metglas” ME structure, which demonstrated a ME coefficient of 0.83 V/(cm⋅Oe) without external biasing at 117 Hz. The ME structure was characterized using both quasi-static and dynamic methods, with the mapping performed at a frequency of 232 Hz, chosen to ensure a linear response and minimize resonance effects. Our measurements revealed that the position of maximum magnitude of the ME signal was consistently shifted from the position of the maximum integral magnetic field intensity of the wire. This shift was attributed to the deformation of the ME structure and the redistribution of the magnetic flux along the sample due to the magnetic layers, as confirmed through modeling. Further, the measured 2D mapping of the NMF from the wire closely matched the theoretical distribution, displaying axial symmetry but with a persistent shift of 2–3 mm along the length of the ME structure. These effects were linked to the linear dimensions and clamping methods of the ME structure. Overall, our experimental results closely correlated with theoretical data and the FEM model, demonstrating that ME composites are effective for NMF detection and mapping. Future work will aim to reduce the dimensions of the ME structure using MEMS technology to minimize the observed shift effects in the measurements.

Polar and quasicrystal vortex observed in twisted-bilayer molybdenum disulfide.

We report the observation of an electric field in twisted-bilayer molybdenum disulfide (MoS2) and elucidate its correlation with local polar domains using four-dimensional scanning transmission electron microscopy (4D-STEM) and first-principles calculations. We reveal the emergence of in-plane topological vortices within the periodic moiré patterns for both commensurate structures at small twist angles and the incommensurate quasicrystal structure that occurs at a 30° twist. The large-angle twist leads to mosaic chiral vortex patterns with tunable characteristics. A twisted quasicrystal bilayer, characterized by its 12-fold rotational symmetry, hosts complex vortex patterns and can be manipulated by picometer-scale interlayer displacement. Our findings highlight that twisting 2D bilayers is a versatile strategy for tailoring local electric polar vortices.

Effects of gravity rainbow on scalar bosonic and oscillator fields in Bonnor–Melvin space-time with a cosmological constant

In this paper, we explore the relativistic quantum motion of spin-zero scalar charge-free particles influenced by rainbow gravity’s (RG’s) in Bonnor–Melvin magnetic space-time, a four-dimensional solution featuring a positive cosmological constant. We solve the Klein–Gordon equation in this scenario by using two sets of rainbow function: (i) f(χ)=1(1-βχ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\chi )=\\frac{1}{(1-\\beta \\,\\chi )}$$\\end{document}, h(χ)=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h(\\chi )=1$$\\end{document} and (ii) f(χ)=1(1-βχ)=h(χ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\chi )=\\frac{1}{(1-\\beta \\,\\chi )}=h(\\chi )$$\\end{document}, where 0<χ=|E|Ep≤1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0 < \\chi \\left( =\\frac{|E|}{E_p}\\right) \\le 1$$\\end{document} with Ep\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_p$$\\end{document} being the Planck’s energy, E is the particle’s energy, and β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document} is the rainbow parameter. Furthermore, we study the relativistic quantum oscillator through the Klein–Gordon oscillator equation in the same Bonnor–Melvin magnetic space-time under RG effects. Employing the first pair of rainbow function, we obtain an approximate eigenvalue solution of the quantum oscillator fields. Notably, we demonstrate that the relativistic energy profile of scalar and oscillator particles are influenced by the topology of the geometry and the cosmological constant which is related with the magnetic field strength lies along the symmetry axis. Additionally, we see the impact of rainbow parameter on these approximate relativistic energy profiles in both quantum systems.

Enforcing exact permutation and rotational symmetries in the application of quantum neural networks on point cloud datasets

Recent developments in the field of quantum machine learning have promoted the idea of incorporating physical symmetries in the structure of quantum circuits. A crucial milestone in this area is the realization of Sn-permutation equivariant quantum neural networks (QNNs) that are equivariant under permutations of input objects. In this paper, we focus on encoding the rotational symmetry of point cloud datasets into the QNN. The key insight of the approach is that all rotationally invariant functions with vector inputs are equivalent to a function with inputs of vector inner products. We provide a structure of the QNN that is exactly invariant to both rotations and permutations, with its efficacy demonstrated numerically in the problems of two-dimensional image classifications and identifying high-energy particle decays, produced by proton-proton collisions, with the SO(1,3) Lorentz symmetry. Published by the American Physical Society 2024

Harnessing Flex Point Symmetry to Estimate Logistic Tumor Population Growth.

The observed time evolution of a population is well approximated by a logistic growth function in many research fields, including oncology, ecology, chemistry, demography, economy, linguistics, and artificial neural networks. Initial growth is exponential, then decelerates as the population approaches its limit size, i.e., the carrying capacity. In mathematical oncology, the tumor carrying capacity has been postulated to be dynamically evolving as the tumor overcomes several evolutionary bottlenecks and, thus, to be patient specific. As the relative tumor-over-carrying capacity ratio may be predictive and prognostic for tumor growth and treatment response dynamics, it is paramount to estimate it from limited clinical data. We show that exploiting the logistic function's rotation symmetry can help estimate the population's growth rate and carry capacity from fewer data points than conventional regression approaches. We test this novel approach against published pan-cancer animal and human breast cancer data, achieving a 30% to 40% reduction in the time at which subsequent data collection is necessary to estimate the logistic growth rate and carrying capacity correctly. These results could improve tumor dynamics forecasting and augment the clinical decision-making process.

Lagrangian approach to origami vertex analysis: kinematics.

The use of origami in engineering has significantly expanded in recent years, spanning deployable structures across scales, folding robotics and mechanical metamaterials. However, finding foldable paths can be a formidable task as the kinematics are determined by a nonlinear system of equations, often with several degrees of freedom. In this article, we leverage a Lagrangian approach to derive reduced-order compatibility conditions for rigid-facet origami vertices with reflection and rotational symmetries. Then, using the reduced-order conditions, we derive exact, multi-degree of freedom solutions for degree 6 and degree 8 vertices with prescribed symmetries. The exact kinematic solutions allow us to efficiently investigate the topology of allowable kinematics, including the consideration of a self-contact constraint, and then visually interpret the role of geometric design parameters on these admissible fold paths by monitoring the change in the kinematic topology. We then introduce a procedure to construct lower-symmetry kinematic solutions by breaking symmetry of higher-order kinematic solutions in a systematic way that preserves compatibility. The multi-degree of freedom solutions discovered here should assist with building intuition of the kinematic feasibility of higher-degree origami vertices and also facilitate the development of new algorithmic procedures for origami-engineering design.This article is part of the theme issue 'Origami/Kirigami-inspired structures: from fundamentals to applications'.

Detecting and Imaging of Magnons at Nanoscale with van der Waals Quantum Sensor

AbstractMagnonic devices are extensively studied for energy‐efficient information processing. High spatial resolution and high accuracy measurement is required to characterize the excitation and distribution of magnons. Here, sensing and imaging of magnons in the magnetic insulator (YIG) is realized with negatively charged boron vacancy () spin defects in 2D hexagonal boron nitride (hBN). Thermal magnon noise is studied through spin relaxometry, illustrating the nanometers proximity of the 2D quantum sensor over a large area. The small probe‐sample standoff distance helps to detect weak signals with diffraction‐limited spatial resolution. The uniform out‐of‐plane symmetry axis of is further utilized to study perpendicular magnetic anisotropy (PMA). It effectively extracts the stray field of microwave‐excited magnons from the direct stripline field. The distributions of propagating and localized magnons in different structures are subsequently imaged and analyzed. The work provides the strategy for utilizing the distinctive advantages of the van der Waals quantum sensor in magnetic imaging. The results will promote the development of magnonic devices for diverse applications.

Computation of emitter-plasmon interactions using an axis-symmetric model for off-axis dipoles

The axis-symmetric modeling technique is based on expanding vector fields in cylindrical harmonics and computing the response on a two-dimensional cross-section separately for each azimuthal harmonic, significantly reducing computational costs. However, it has limitations when dealing with dipoles placed away from the symmetry axis due to challenges in the expansion of angular modes. To address this, we propose a reformulated axis-symmetric model based on the Fourier expansion of the delta function distribution concerning the azimuthal variable. This model is validated using standard Mie theory for off-axis dipoles and applied to study multiple-emitter-plasmon interactions. The emission properties of a non-cooperative ensemble near a plasmonic nanoparticle are observed to scale with the number of emitters considered, N. Notably, a Dicke effect-like superradiance (N2-dependence) is observed when a spatially disordered ensemble of dipoles oscillates collectively inside a plasmonic dimer gap. This kind of high-level cooperative quantum phenomenon is of high interest in fields such as quantum optics and light-harvesting.