Symmetry Axis Research Articles

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.

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.

Experimental study on the rock breaking effect of different tooth shapes of inserted teeth in a hobbing-cone hybrid PDC bit under complex stress environment

The hobbing-cone hybrid PDC bit has emerged with the increasing exploitation of deep oil and gas resources. As an important component of new bits, studying the mechanism of toothed fracturing of deep rocks is crucial for improving rock-breaking efficiency. In this paper, the spherical teeth and conical teeth were used to intrude sandstone under different confining pressures, and the brittleness index (BIm), specific energy (SE), and average fragment size (dm) were used to analyze the rock-breaking effect. The 3D contour scanner quantitatively analyzed the crushing pit area. Finally, the in-situ CT scanning and discrete element numerical simulation were used to summarize the crack propagation law. The results show that with the increase of confining pressure, the BIm of inserted teeth increases continuously, and the growth rate of conical teeth increases, while that of spherical teeth decreases. The SE and dm exhibit a symmetrical distribution with a confining pressure of 10MPa as the axis of symmetry. When the difference in principal stress is 5MPa, the SE is the lowest point, the rock-breaking efficiency is the highest, and the corresponding dm is at the highest point, but the curve trend is the opposite. When the stress difference is 5MPa, it is conducive to propagating surface cracks, thus forming a larger crushing area and the highest rock-breaking efficiency. Based on CT results, the dense particle core is formed near the inserted teeth, and that of the spherical teeth is located below. In contrast, that of the conical teeth is located on the side, which is also the reason for the difference in crack propagation between different tooth shapes.

2D mechanical representation of superconducting magnets: A comparative study of plane stress and plane strain

When approaching the mechanical design of a superconducting magnet, whenever possible the starting model is a 2D approximation. If rotational symmetry (solenoid-like winding) is present, the 2D representation is unique and contains no approximations. If, on the other hand, a non-axisymmetric system is opted for, the 2D representation is not unique and there are main options available, as plane stress, plane stress with thickness, plane strain and generalized plane strain. Considering z as the direction normal to the 2D plane, the plane stress option defines a stress state in which no normal or shear stresses perpendicular to the xy plane can occur (σz=σxz=σyz=0). In this option, deformation can occur in the thickness direction of the element, which will become thinner when stretched and thicker when compressed; it is generally used for objects with limited depth (thin objects).In contrast, plane strain refers to the fact that deformation can only occur in plane, which means that no out-of-plane deformation will occur (ϵz=ϵxz=ϵyz=0). The plane strain option is generally appropriate for structures of nearly infinite length, relative to their cross section, that exhibit negligible length changes under load. The “generalized plane strain” option imposes the axial strain equal to a constant value; this condition does not reproduce the real operating condition of the magnet and is therefore excluded. The “plane stress with thickness” uses the same equations as the plane stress option but, output quantities are given per unit length defined with thickness; therefore, it is again excluded from the comparison. Superconducting magnets, such as dipoles, do not fit neatly into any of the above options: they are far from thin but deform longitudinally under load. This work reports a comparative study of plane stress and plane strain in the specific case study of a dipole magnet.

Effect of a longitudinal magnetic field on streamer propagation in air: Numerical simulation

Two-dimensional numerical simulation of the negative streamer propagation in external electric and magnetic fields is performed for the case when applied electric and magnetic field vectors are parallel to the symmetry axis of the problem. The calculations are performed for air (a mixture of 80% N2 and 20% O2) with a concentration of gas molecules equal to Loshmidt's number. It is shown that the presence of a longitudinal field leads to a noticeable increase in the streamer propagation velocity associated with a decrease in its radius, which agrees with the known analytical estimates.

Rotation Equivariant Proximal Operator for Deep Unfolding Methods in Image Restoration.

The deep unfolding approach has attracted significant attention in computer vision tasks, which well connects conventional image processing modeling manners with more recent deep learning techniques. Specifically, by establishing a direct correspondence between algorithm operators at each implementation step and network modules within each layer, one can rationally construct an almost "white box" network architecture with high interpretability. In this architecture, only the predefined component of the proximal operator, known as a proximal network, needs manual configuration, enabling the network to automatically extract intrinsic image priors in a data-driven manner. In current deep unfolding methods, such a proximal network is generally designed as a CNN architecture, whose necessity has been proven by a recent theory. That is, CNN structure substantially delivers the translational symmetry image prior, which is the most universally possessed structural prior across various types of images. However, standard CNN-based proximal networks have essential limitations in capturing the rotation symmetry prior, another universal structural prior underlying general images. This leaves a large room for further performance improvement in deep unfolding approaches. To address this issue, this study makes efforts to suggest a high-accuracy rotation equivariant proximal network that effectively embeds rotation symmetry priors into the deep unfolding framework. Especially, we deduce, for the first time, the theoretical equivariant error for such a designed proximal network with arbitrary layers under arbitrary rotation degrees. This analysis should be the most refined theoretical conclusion for such error evaluation to date and is also indispensable for supporting the rationale behind such networks with intrinsic interpretability requirements. Through experimental validation on different vision tasks, including blind image super-resolution, medical image reconstruction, and image de-raining, the proposed method is validated to be capable of directly replacing the proximal network in current deep unfolding architecture and readily enhancing their state-of-the-art performance. This indicates its potential usability in general vision tasks.

On Boundary Discontinuity in Angle Regression Based Arbitrary Oriented Object Detection.

With vigorous development e.g., in autonomous driving and remote sensing, oriented object detection has gradually been featured. The majority of existing methods directly perform regression on the rotation angle, which we argue has fundamental limitations of boundary discontinuity (even if using Gaussian or RotatedIoU-based losses). In this paper, a novel angle coder named phase-shifting coder (PSC) is proposed to address this issue. Different from another well-explored alternative i.e., angle classification, PSC achieves boundary-discontinuity-free in a continuous and differentiable manner and thus can work together with Gaussian or RotatedIoU-based methods to further boost their performance. Moreover, by rethinking the boundary discontinuity of elongated and square-like objects as rotational symmetry of different cycles, a dual-frequency version (PSCD) is proposed to accurately predict the orientation of both types of objects. Visual analysis and extensive experiments on several popular backbone detectors and datasets demonstrate the effectiveness and the potentiality of our approach. When facing scenarios requiring high-quality bounding boxes, the proposed methods are expected to give a competitive performance.

Torque-driven superhydrophobic cylinders swim in circles

A superhydrophobic cylinder is a circular cylinder with a boundary pattern of alternating shear-free menisci and solid portions. This article derives analytical solutions for the torque-driven Stokes flow around a superhydrophobic cylinder that is free to move, or ‘swim’, subject to the constraint that it is free of net force. The mathematical approach is a natural generalization of one used to solve for transverse shear flow over a superhydrophobic surface comprising a periodic array of no-shear slots (Crowdy 2011 Phys. Fluids 23 (doi: 10.1063/1.3605575 )). First, the torque-driven Stokes flow around a superhydrophobic cylinder with two unequal no-shear menisci and two equal solid portions is solved in detail. It is then shown how that analysis generalizes, in a natural way, to a cylinder with M no-shear menisci between M solid portions with full exposition given of the case of M = 3 equal solid portions. A further generalization to flow around a superhydrophobic cylinder with an N -fold rotationally symmetric patterning with M menisci in each 2 π / N sector is made. Torque-driven superhydrophobic cylinders with a no-shear pattern devoid of any rotational symmetry are shown to swim on circular trajectories with formulas for the radius and cylinder angular velocity on these trajectories derived here as functions of the no-shear pattern geometry. The M = 1 case of a ‘Janus’ superhydrophobic cylinder having one meniscus and one solid portion can be solved completely explicitly.

Transport through a monolayer-tube junction: Sheet-to-tube spin current

We develop a method to calculate the electron flow between an arbitrary atomic monolayer sheet and an arbitrary tube by expressing the corresponding sheet-tube tunneling matrix elements with those between sheets. We use this method to calculate the spin current from a monolayer silicene sheet with sublattice-staggered current-induced spin polarization to a silicene tube. The calculated sheet-to-tube spin current exhibits an oscillation as a function of the tube circumferential length because the Fermi points in the tube cross the Fermi circle in the sheet. Furthermore, the spin current with spin in the out-of-plane direction, which is absent in the sheet-sheet junction (including twisted sheets) with C3 rotational symmetry, appears in an oscillating form in the tube-sheet junction due to the broken C3 rotational symmetry. This is an example of the symmetry manipulation which realizes switching a particular component of the spin current.

Pentagonal Symmetry in Aperiodic Cyclic Multiply Twinned Nano- and Mesodiamonds.

This Review provides the first comprehensive overview of the structure and properties of exotic sp3-crystalline aperiodic cyclic multiply twinned nano- (10-100 nm) and meso- (up to 1 mm) diamond particles (MTPs) exhibiting pentagonal symmetry. It spans their independent experimental discoveries (1963, 1964, 1972, and 1983) and theoretical structural insights (1993) to recent advancements. The Review focuses on high-symmetry MTPs formed by the fusion of multiple cubic diamond fragments through [111] facets. The sp3 diamond lattice of individual fragments offers a vast range of MTP varieties. These particles are shown to be a special case of aperiodic crystalline solids with limited dimensions and rotational symmetry, leading to a breakdown of translational invariance. Detailed mathematical analysis of the MTPs' lattices highlights the crucial role of central cores in determining the symmetry and effective dimensions of these structures. Both structural and kinetic aspects of the formation mechanisms of pentagonal diamond particles are considered, revealing the main role of embryo seeds (low fullerenes, polyhexacyclo[5.5.1.12,6.18,12.03,11.05,9]pentadecane (C15), and polyheptacyclo[5.5.1.12,7.19,14.03,13.06,11]octadecane (C18)) in determining the MTPs' symmetry and structure. The effective dimensions of multiply twinned diamonds are shown to be limited by structural stress caused by the mismatch of perfect pentagonal and tetrahedral dihedral angles. The extraordinary mechanical and electronic properties of multiply twinned diamonds are discussed, highlighting that hexagonal interfaces between cubic diamond fragments may determine exceptional ultrahard and quantum characteristics. The MTP X-ray diffraction spectra reveal clear pentagonal patterns with single (diamond decahedrons or dodecahedrons) or ten (diamond icosahedra) central 5-fold axes. A comparative analysis of experimental structural data and simulations at different theoretical levels demonstrates a perfect correspondence of theoretical models with crystalline lattices.

Remarks on Soft Ball Packings in Dimensions 2 and 3

We study translative arrangements of centrally symmetric convex domains in the plane (resp., of congruent balls in the Euclidean 3-space) that neither pack nor cover. We define their soft density depending on a soft parameter and prove that the largest soft density for soft translative packings of a centrally symmetric convex domain with 3-fold rotational symmetry and given soft parameter is obtained for a proper soft lattice packing. Furthermore, we show that among the soft lattice packings of congruent soft balls with given soft parameter the soft density is locally maximal for the corresponding face centered cubic (FCC) lattice.