Symmetry Axis Research Articles

Moving mirrors and event horizons in non-flat background geometry

Moving mirrors have been used for a long time as simple models for studying various properties of black hole radiation, such as the thermal spectrum and entanglement entropy. These models are typically constructed to mimic the collapse of a spherically symmetric distribution of matter in the Minkowski background. We generalize this correspondence to the case of non-trivial background geometry and consider two examples, the Schwarzschild—de Sitter black hole and the Bañados–Teitelboim–Zanelli (BTZ) black hole. In the BTZ case we were also able to show that this approach works for the spinning black hole which has only axial symmetry.

Analysis of the features of the shielding system of polymer insulation structures of high voltage electrical equipment

In the article, the authors analysed the existing shielding systems of insulating structures of high-voltage devices together with electrodes under high potential. At the same time, the possibilities of using toroidal screens of various designs and the conditions of their installation in gas-filled equipment structures (gas-filled current and voltage measuring transformers, arresters, etc.) using polymer insulating materials are considered. Based on the analysis of literary sources, the most effective method of estimating the electric load parameters for determining the electric field strength distribution along the continuous insulating structure of gas-filled high-voltage devices with axial symmetry is proposed. This design is a support-insulating shell filled with SF6 as an internal insulating medium. Methodical materials are recommended that allow you to estimate the electrical load parameters (voltage and field strength) depending on the design features of the device and the shielding system used to level the electric field. Based on them, it is possible to evaluate the effectiveness of the calculation coefficients of the shielding system of gas-filled high-voltage equipment in the design process and during the improvement of individual design solutions. The results of the analytical evaluation by such methods are in good agreement with the data of experimental studies and statistical information obtained as a result of monitoring the work of insulating structures, taking into account real operating conditions and the influence of external factors. The introduction of the obtained materials allows you to take into account the influence of external factors and operational characteristics inherent in measuring transformers and overvoltage limiters. To explain the results of the analysis of methodical materials carried out in the article, as an example, the results of calculations of the support-insulation shell of the gas-filled current transformer of the TOG series, which was the most affected during operation, are given. in adverse conditions, given under such conditions as external pollution, humidity and their combination, as well as under conditions of overvoltage of various origins, etc. On the basis of the presented materials, it is possible to more accurately determine the effectiveness of various screenings. system, as well as how to predict the field strength distribution parameters under the influence of the shielding system, taking into account its design features. In addition, on the basis of the conclusions formed in the work, it is possible to plan and conduct an additional series of calculations and experimental tests taking into account the features of specific structures. Thus, the obtained results can be used to evaluate the external insulation parameters of both gas-filled measuring transformers and similar high-voltage equipment of distribution devices and transformer substations.

Spontaneous symmetry breaking in plasmon lattice lasers.

Spontaneous symmetry breaking (SSB) is key for our understanding of phase transitions and the spontaneous emergence of order. In this work, we report that, for a two-dimensional (2D) periodic metasurface with gain, SSB occurs in the lasing transition. We study diffractive hexagonal plasmon nanoparticle lattices, where the K-points in momentum space provide two modes that are degenerate in frequency and identically distributed in space. Using femtosecond pulses to energize the gain medium, we simultaneously capture single-shot real-space and Fourier-space images of laser emission. By combining Fourier and real space, we resolve the two order parameters for which symmetry breaking simultaneously occurs: spatial parity and U(1) (rotational) symmetry breaking, evident respectively as random relative mode amplitude and phase. The methodology reported in this work is generally applicable to 2D plasmonic and dielectric metasurfaces and opens numerous opportunities for the study of SSB and the emergence of spatial coherence in metaphotonics.

Comparative analysis of molecular dynamics and method of moments in two-dimensional concentric circular layers

In this manuscript, we undertake an examination of a classical plasma deployed on two finite co-planar surfaces: a circular region Ωin into an annular region Ωout with a gap in between. It is studied both from the point of view of statistical mechanics and the electrostatics of continua media. We employ a dual perspective: the first one is by using molecular dynamics (MD) simulations to find the system’s positional correlation functions and velocity distributions. That by modeling the system as a classical two-dimensional Coulomb plasma of point-like charged particles q 1 and q 2 on the layers Ωin and Ωout respectively with no background density. The second one corresponds to a finite Surface Electrode (SE) composed of planar metallic layers displayed on the regions Ωin , Ωout at constant voltages Vin , Vout considering axial symmetry. The surface charge density is calculated by the Method of Moments (MoM) under the electrostatic approximation. Point-like and differential charges elements interact via a 1/r —electric potential in both cases. The thermodynamic averages of the number density, and electric potential due to the plasma depend on the coupling and the charge ratio ξ=q1/q2 once the geometry of the layers is fixed. On the other hand, the fields due to the SE depend on the layer’s geometry and their voltage. In the document, is defined a protocol to properly compare the systems. We show that there are values of the coupling parameter, where the thermodynamic averages computed via MD agree with the results of MoM for attractive ξ=−1 and repulsive layers ξ = 1.

High-NA multi-foci metalenses based on deformed metagratings

Nonlocal engineering, as an extension of the local design of the metasurface, provides a new scheme to precisely tune the electromagnetic response through diffraction of the constitutive supercells. It has shown great potential in large-gradient wavefront shaping, but just limited to one-dimensional or rotation-symmetric two-dimensional applications. In this study, we extend the nonlocal method to design large-gradient metasurfaces without rotation symmetry, through the optimization of the metagratings and their deformation along the isophase contour path. The effectiveness of the method is verified by the three-foci metalenses with NA of 0.89 and NA of 0.97. Consistent simulation and experimental results are obtained at 140 GHz. Obvious advances are observed in this method especially when the spatial phase gradient is increased.

P-038 Sperm head morphometric reference values of 1856 sperms in fertile Asian males

Abstract Study question To explore comprehensive normal sperm morphometric reference values by measuring 1856 sperms in fertile males using artificial intelligence (AI) technique. Summary answer Four novel describing parameters of sperm head (size, shape, area, and uniformity) and 14 other features for normal sperm head were extracted and characterized. What is known already Sperm head morphology is crucial for male factor infertility diagnosis and assessment of male reproductive potential. The human spermatozoon is one of the most diverse cell types known. However, most assessment criteria have only 3 morphometric parameters (Length, width, and length/width ratio) for sperm head morphometric measurement. We detailed the features of sperm head by defining and characterizing 14 parameters based on AI. Study design, size, duration This is a prospective observational study. The study included 1856 normal sperm images from 23152 stained sperm acquired by an Automated Sperm Morphology Analysis (ASMA) system. The measured sperm morphometry data were acquired from May 2020 to December 2021. Participants/materials, setting, methods All participants (54 fertile males) had fathered a child naturally during the past year. The measured sperm morphometry data were acquired from candidate donors of the Sichuan Province Human Sperm Bank (SPHSB, Chengdu, China). Images of 23,152 stained sperm captured by ASMA. All sperm images were assessed by three experienced technicians. Finally, we concluded 14 morphometric data from normal sperm by measuring sizes in pixels. Main results and the role of chance (1) Characteristics of sperm head size and shape: We present eight sperm head size and shape parameters for the 1856 visually normal spermatozoa. The median head size parameters included head length of 4.02 (95% CI: 4.01–4.05) μm, head width of 2.52 (95% CI: 2.52–2.54) μm, length to width ratio of 1.59 (95% CI: 1.59–1.62), and head girth of 11.18 (95% CI: 11.17–11.25) μm. The median head symmetry parameters included short axis symmetry (SAS) of 92.1% (95% CI: 88.3%–89.2%) and the long axis symmetry (LAS) of 94.3% (95% CI: 91.6%–92.3%). The median head shape parameters included median of ellipse intersection over union (EIoU) of 88.9% (95% CI: 85.4%–86.3%) and girth intersection over union (GIoU) of 102.4% (95% CI: 102.4%–102.5%). (2) Characteristics of sperm head area and acrosome uniformity: Descriptive analysis of the sperm head area characteristics included a median sperm head area of 7.72 (95% CI: 7.74–7.85) μm2, acrosome area of 3.67 (95% CI: 3.77–3.88) μm2, acrosome area ratio of 48.2% (95% CI: 47.8%–48.6%), post-acrosomal area of 3.95 (95% CI: 3.95–4.00) μm2, acrosome uniformity of 88.6% (95% CI: 88.6%–89.1%), and nuclear uniformity of 100.0% (95% CI: 99.8%–99.9%). Limitations, reasons for caution This study had several limitations that should be noted. The use of samples from a single center, covering relatively young participants from only seven provinces in China, could limit the usage of our findings. The use of only three technicians to assess the samples may have introduced a subjective bias. Wider implications of the findings The measurement technique was accurate, objective, and highly informative by AI. The data provide extremely detailed information for reference studies and comparison of sperm head parameters among different male groups. These new parameters can be applied in routine semen analysis when assessing sperm morphology and male fertility potential. Trial registration number not applicable

Parsing Dynamics of Protein Backbone NH and Side-Chain Methyl Groups using Molecular Dynamics Simulations.

Experimental NMR spectroscopy and theoretical molecular dynamics (MD) simulations provide complementary insights into protein conformational dynamics and hence into biological function. The present work describes an extensive set of backbone NH and side-chain methyl group generalized order parameters for the Escherichia coli ribonuclease HI (RNH) enzyme derived from 2-μs microsecond MD simulations using the OPLS4 and AMBER-FF19SB force fields. The simulated generalized order parameters are compared with values derived from NMR 15N and 13CH2D spin relaxation measurements. The squares of the generalized order parameters, S2 for the N-H bond vector and Saxis2 for the methyl group symmetry axis, characterize the equilibrium distribution of vector orientations in a molecular frame of reference. Optimal agreement between simulated and experimental results was obtained by averaging S2 or Saxis2 calculated by dividing the simulated trajectories into 50 ns blocks (∼five times the rotational diffusion correlation time for RNH). With this procedure, the median absolute deviations (MAD) between experimental and simulated values of S2 and Saxis2 are 0.030 (NH) and 0.061 (CH3) for OPLS4 and 0.041 (NH) and 0.078 (CH3) for AMBER-FF19SB. The MAD between OPLS4 and AMBER-FF19SB are 0.021 (NH) and 0.072 (CH3). The generalized order parameters for the methyl group symmetry axis can be decomposed into contributions from backbone fluctuations, between-rotamer dihedral angle transitions, and within-rotamer dihedral angle fluctuations. Analysis of the simulation trajectories shows that (i) backbone and side chain conformational fluctuations exhibit little correlation and that (ii) fluctuations within rotamers are limited and highly uniform with values that depend on the number of dihedral angles considered. Low values of Saxis2, indicative of enhanced side-chain flexibility, result from between-rotamer transitions that can be enhanced by increased local backbone flexibility.

Approximate analytical solution using power series method for the propagation of blast waves in a rotational axisymmetric non-ideal gas

In this paper, the propagation of the blast (shock) waves in non-ideal gas atmosphere in rotational medium is studied using a power series method in cylindrical geometry. The flow variables are assumed to be varying according to the power law in the undisturbed medium with distance from the axis of symmetry. To obtain the similarity solution, the initial density is considered as constant in the undisturbed medium. Approximate analytical solutions are obtained using Sakurai’s method by extending the power series of the flow variables in power of a0U2, where U and a0 are the shock velocity and speed of sound, respectively, in undisturbed fluid. The strong shock wave is considered for the ratio a0U2 which is considered to be a small quantity. With the aid of that method, the closed-form solutions for the zeroth-order approximation is given as well as first-order approximate solutions are discussed. Also, with the help of graphs behind the blast wave for the zeroth-order, a comparison between the numerical solution and the approximate analytical solution are shown. The distributions of flow variables such as density, radial velocity, pressure and azimuthal velocity are analyzed. The results for the rotationally axisymmetric non-ideal gas environment are compared to those for the ideal gas atmosphere. The velocity-distance and time-distance curves are also shown to analyze the decaying characteristic of a blast wave.

3D reverse-time migration for pure P-wave in orthorhombic media

Compared with the transverse isotropic (TI) medium, the orthorhombic anisotropic medium has both horizontal and vertical symmetry axes and it can be approximated as a set of vertical fissures developed in a group of horizontal strata. Although the full-elastic orthorhombic anisotropic wave equation can accurately simulate seismic wave propagation in the underground media, a huge computational cost is required in seismic modeling, migration, and inversion. The conventional coupled pseudo-acoustic wave equations based on acoustic approximation can be used to significantly reduce the cost of calculation. However, these equations usually suffer from unwanted shear wave artifacts during wave propagation, and the presence of these artifacts can significantly degrade the imaging quality. To solve these problems, we derived a new pure P-wave equation for orthorhombic media that eliminates shear wave artifacts while compromising computational efficiency and accuracy. In addition, the derived equation involves pseudo-differential operators and it must be solved by 3D FFT algorithms. In order to reduce the number of 3D FFT, we utilized the finite difference and pseudo-spectral methods to conduct 3D forward modeling. Furthermore, we simplified the equation by using elliptic approximation and implemented 3D reverse-time migration (RTM). Forward modeling tests on several homogeneous and heterogeneous models confirm that the accuracy of the new equation is better than that of conventional methods. 3D RTM imaging tests on three-layer and SEG/EAGE 3D salt models confirm that the ORT media have better imaging quality.

A group theory based topology optimization scheme for the design of inhomogeneous waveguides with dihedral group symmetries

In this paper, we introduce a novel topology optimization scheme dedicated to designing waveguides with inhomogeneities holding rotation and reflection symmetries. To fully exploit the symmetry features of the guide, we build the scheme by first developing a new computational algorithm that combines the Finite Element Method (FEM) with the group representation theory (GRT), i.e., the GRT – FEM algorithm. This combination allows the decomposition of the eigenvalue problem in a classic FEM to orthogonal (decoupled) subproblems. The subproblems are of much smaller sizes and can be treated in parallel, which therefore leads to an improved solver efficiency by an order of magnitude. For a targeted mode profile, the involvement of the GRT does not only enable a pre-selection of the subproblems that are to be optimized, which further improves the computational speed, but also completely avoids potential mode degeneracies, which adversely affects the convergence of the optimization. To validate, the GRT – FEM algorithm is first tested against the results from a full FEM simulation for a guide with inhomogeneities with six-fold rotation and reflection symmetries. Then, as an illustration, the entire scheme is applied to achieve a desired eigenmode with a targeted propagation constant. The proposed scheme does not only provide an efficient design tool for exploiting interesting wave phenomena in waveguiding structures possessing rotation and reflection symmetries, but also lays down a theoretical foundation for systematically integrating symmetries with classic Computational Electromagnetics (CEM) algorithms.

Unusual Janus Bi2TeSe2 Topological Insulators Displaying Second-Harmonic Generation, Linear-in-Temperature Resistivity, and Weak Antilocalization.

Well-established knowledge about inversion-symmetric Bi2TexSe3-x topological insulators characterizes the promising new-generation quantum device. Noticeably, the inversion asymmetric phase containing different surface electronic structures may create an extra topological phenomenon pointing to a new device paradigm. Herein, Janus Bi2TeSe2 single-crystal nanosheets with an unconventional stacking sequence of Se-Bi-Se-Bi-Te are realized via chemical vapor deposition growth, which is clarified by atomically resolved AC-STEM and elemental mapping. An obvious polarization-dependent second-harmonic generation with a representative 6-fold rotational symmetry is detected due to the broken out-of-plane mirror symmetry in this system. Low-temperature transport measurements display a strange metal-like linear-in-temperature resistivity. Anomalous conductance peaks under low magnetic fields induced by the weak antilocalization effect of topological surface states and the two-dimensional transport-dominated anisotropic magnetoresistance are revealed. These findings correlate the Janus Bi2TeSe2 phase with emerging physics topics, which would inspire fresh thoughts in well-developed Bi3TexSe3-x topological insulators and open up opportunities for exploring hybrid nonlinear optoelectronic topological devices.

Novel numerical analysis of electric fields in the near field of very‐low‐frequency antennas based on the charge simulation method

AbstractVery‐low‐frequency (VLF) transmitting antennas have a crucial influence on the nearby electromagnetic environment. Commercial software packages, such as CST Studio Suite (CST) or Altair FEKO (FEKO), are always utilised to calculate the electric fields of VLF antennas, which consume considerable computing resources and time. The classical method of electric field calculation, the charge simulation method (CSM), is first applied to the calculation of electric field near the VLF transmitting antenna. The distribution characteristics of three‐dimensional electric fields were analysed. The electric field surrounding the antenna exhibited axial symmetry. The highest electric field strength was at the top of the antenna, and as the distance from the antenna increased, the electric field strength exponentially decreased. The comparisons are performed between the results of the CSM and those of commercial software, the average relative errors of CSM on two observation paths are very small, 2.20% and 2.21%, respectively. Meanwhile, the CSM shows considerable advantages in saving calculation resources and improving efficiency. Additionally, the comparison between CSM calculation and the measured data is carried out. The results show that this method can accurately calculate the electric field near VLF transmitting antenna and offer valuable insights and a new solution.

Differentiating dilatons from the axions by their mixing with photons

The quanta of scalar fields like the dilaton (ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document}) of scale symmetry origin and those of pseudoscalar fields like the axion (ϕ′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi '$$\\end{document}) of Peccei–Quinn symmetry origin couple to di-photons through dimension-5 operators. In a magnetized medium (MM), they in principle can interact with the two transverse (A‖,⊥\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_{\\parallel ,\\perp }$$\\end{document}) and one longitudinal (AL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_{L}$$\\end{document}) degree of freedom of photons (γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma $$\\end{document}) as long as the total spin is conserved. However, of ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} and ϕ′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi '$$\\end{document}, only one interacts with AL\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$A_{L}$$\\end{document}. We found that the ambient external magnetic field B and media break the intrinsic Lorentz symmetry of the system affecting the dispersion relation of the propagating modes. The boost and the rotational symmetry along and around B are however the ones that are preserved. Invoking C, P, and T symmetries, we analyze the mixing dynamics of ϕγ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi \\gamma $$\\end{document} and ϕ′γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi '\\gamma $$\\end{document} systems and the structural difference in their mixing pattern. It is noted that while the ϕγ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi \\gamma $$\\end{document} mixing matrix is 3×3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3\ imes 3$$\\end{document}, the ϕ′γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi ^{\\prime }\\gamma $$\\end{document} is governed by a 4×4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$4\ imes 4$$\\end{document} mixing matrix. Using the exact solutions of both systems in MM, we estimate the strength of the electromagnetic (EM) signals available due to these interactions, which are found to be different in strength. We conclude by commenting on (a) the possibility of detecting this difference in polarimetric observables of the EM signal, (b) the implications of these different mixing patterns with respect to the minimum detectable signal for astrophysical observations, and (c) the variation in the energy of the dispersed photons of different polarization with the variation in B.

Crystalline finite-size topology

Topological phases stabilized by crystalline point group symmetry protection are a large class of symmetry-protected topological phases subjected to considerable experimental scrutiny. Here, we show that the canonical three-dimensional (3D) crystalline topological insulator protected by time-reversal symmetry T and fourfold rotation symmetry C4 individually or the product symmetry C4T, generically realizes finite-size crystalline topological phases in thin film geometry [a quasi-(3−1)-dimensional, or q(3−1)D, geometry]: response signatures of the 3D bulk topology coexist with topologically protected, quasi-(3−2)D, and quasi-(3−3)D boundary modes within the energy gap resulting from strong hybridization of the Dirac cone surface states of the underlying 3D crystalline topological phase. Importantly, we find qualitative distinctions between these gapless boundary modes and those of strictly 2D crystalline topological states with the same symmetry protection and develop a low-energy, analytical theory of the finite-size topological magnetoelectric response. Published by the American Physical Society 2024

Understanding the physics of eigenvalue-eigenfunction problems: Rotating beam problem

Eigenvalue-eigenfunction problems frequently appear in many physical areas. Some mathematical experience is needed to identify whether the differential system is an eigenvalue-eigenfunction problem or not. Apart from the mathematical nature of the problem, the eigenvalue-eigenfunction solutions have physical interpretations which have to be addressed properly for real problems. The rotating beam problem is treated to exploit the mathematical and physical nature of such problems and the conditions to divert from the eigenvalue-eigenfunction problem. The rotation of a beam about its symmetry axis along its length and about another axis parallel to its symmetry axis changes the nature of the problem. While the former is an eigenvalue-eigenfunction problem, the latter is not. The interpretations of the physical consequences of the solutions are discussed in detail. The problem can be used as supplementary material in undergraduate courses such as differential equations, mechanics and dynamics.

A stargate mechanism of Microviridae genome delivery unveiled by cryogenic electron tomography.

Single-stranded DNA bacteriophages of the Microviridae family are major components of the global virosphere. Microviruses are highly abundant in aquatic ecosystems and are prominent members of the mammalian gut microbiome, where their diversity has been linked to various chronic health disorders. Despite the clear importance of microviruses, little is known about the molecular mechanism of host infection. Here, we have characterized an exceptionally large microvirus, Ebor, and provide crucial insights into long-standing mechanistic questions. Cryogenic electron microscopy of Ebor revealed a capsid with trimeric protrusions that recognise lipopolysaccharides on the host surface. Cryogenic electron tomography of the host cell colonized with virus particles demonstrated that the virus initially attaches to the cell via five such protrusions, located at the corners of a single pentamer. This interaction triggers a stargate mechanism of capsid opening along the 5-fold symmetry axis, enabling delivery of the virus genome. Despite variations in specific virus-host interactions among different Microviridae family viruses, structural data indicate that the stargate mechanism of infection is universally employed by all members of the family. Startlingly, our data reveal a mechanistic link for the opening of relatively small capsids made out of a single jelly-roll fold with the structurally unrelated giant viruses.

Uniaxial Symmetry Breaking in Bacteriorhodopsin at the Thermal Phase Transition of Lipids of Purple Membranes.

The article correlates between symmetry breaking and phase transition. An analogy, extending from physics to biology, is known to exist between these two topics. Bacteriorhodopsin (bR) as a paradigm of membrane proteins has been used as a case study in the present work. The bR, as the sole protein embedded in what is called a purple membrane (PM), has attracted widespread interest in bionanotechnological applications. The lipids of PM have a crucial role in maintaining the crystal lattice of bR inside PM. For this reason, the present work has been concerned with elucidating the thermal phase transition properties of the PM lipids in orthogonal directions. The results indicated that the axial symmetry of bR exhibits considerable changes occurring at the thermal phase transition of lipids. These changes are brought by an anomaly observed in the time course of orthogonal electric responses during the application of thermal fields on PM. The observed anomaly may bear on symmetry breaking in bR occurring at the phase transition of lipids based on such analogy found between symmetry breaking and phase transition. Lipid-protein interactions may underlie the broken axial symmetry of bR at such lipid thermal transition of PM. Accordingly, thermally perturbed axial symmetry of bR may be of biological relevance relying on the essence of the crystal lattice of bR. Most importantly, a question has to be raised in the present study: Can bR, as a helical protein with broken axial symmetry, affect the symmetry breaking of helical light? This may be of potential technical applications based on a recent discovery that bR breaks the symmetry of helical light.

Microscopic Model for Fractional Quantum Hall Nematics.

Geometric fluctuations of the density mode in a fractional quantum Hall (FQH) state can give rise to a nematic FQH phase, a topological state with a spontaneously broken rotational symmetry. While experiments on FQH states in the second Landau level have reported signatures of putative FQH nematics in anisotropic transport, a realistic model for this state has been lacking. We show that the standard model of particles in the lowest Landau level interacting via the Coulomb potential realizes the FQH nematic transition, which is reached by a progressive reduction of the strength of the shortest-range Haldane pseudopotential. Using exact diagonalization and variational wave functions, we demonstrate that the FQH nematic transition occurs when the system's neutral gap closes in the long-wavelength limit while the charge gap remains open. We confirm the symmetry-breaking nature of the transition by demonstrating the existence of a "circular moat" potential in the manifold of states with broken rotational symmetry, while its geometric character is revealed through the strong fluctuations of the nematic susceptibility and Hall viscosity.

Dynamic and magnetic properties of excited magnons in tetragonal fcc [formula omitted]/SiO multilayer alloys

In this paper, we investigate by numerical lattice simulations the magnetic and dynamic properties of excited magnons in d transition metal alloys FexPt1−x/SiO using Green functions and second quantification techniques. The sandwich structure consists of magnetic (FePt) and non-magnetic (SiO) layers. The corresponding quantum Heisenberg Hamiltonian includes exchange interactions, magnetocrystalline anisotropy, surface anisotropy and magnetic field. The existence of the surface magnons is demonstrated by the surface creation factor η, which is in good agreement with the measured lifetime data. Surface magnons are characterized by their excitation spectrum, susceptibility of creation, creation gap, permitted band for creation, and lifetime, which are different from volume magnons properties. The susceptibility of creation analysis is compatible with experimental values, and the calculated lifetimes are in the order of femtoseconds (fs) reproducing the analytical behavior of the measured values along the lattice symmetry axis. The surface magnons are found to be more confined in time and space than those excited in volume, indicating the presence of short-range spin correlations. Magnetization per spin versus temperature is also calculated for different iron concentrations x and found to be in excellent agreement with the measured values. Also, the response of the system to an external magnetic field is shown for xFe=0.29 with various temperature values, and it agrees well with the experience.

Origin of symmetry breaking in the grasshopper model

The planar grasshopper problem, originally introduced by Goulko and Kent [], is a striking example of a model with long-range isotropic interactions whose ground states break rotational symmetry. In this paper we analyze and explain the nature of this symmetry breaking with emphasis on the importance of dimensionality. Interestingly, rotational symmetry is recovered in three dimensions for small jumps, which correspond to the nonisotropic cogwheel regime of the two-dimensional problem. We discuss simplified models that reproduce the symmetry properties of the original system in N dimensions. For the full grasshopper model in two dimensions we obtain quantitative predictions for optimal perturbations of the disk. Our analytical results are confirmed by numerical simulations. Published by the American Physical Society 2024