Symmetry Axis Research Articles

Island myriads in periodic potentials.

A phenomenon of emergence of stability islands in phase space is reported for two periodic potentials with tiling symmetries, one square and the other hexagonal, inspired by bidimensional Hamiltonian models of optical lattices. The structures found, here termed as island myriads, resemble web-tori with notable fractality and arise at energy levels reaching that of unstable equilibria. In general, the myriad is an arrangement of concentric island chains with properties relying on the translational and rotational symmetries of the potential functions. In the square system, orbits within the myriad come in isochronous pairs and can have different periodic closure, either returning to their initial position or jumping to identical sites in neighbor cells of the lattice, therefore impacting transport properties. As seen when compared to a more generic case, i.e., the rectangular lattice, the breaking of square symmetry disrupts the myriad even for small deviations from its equilateral configuration. For the hexagonal case, the myriad was found but in attenuated form, mostly due to extra instabilities in the potential surface that prevent the stabilization of orbits forming the chains.

Enhanced viscous dissipation of sound in phononic supercrystal

Sound wave propagating in a homogeneous viscous medium decays due viscous losses with decay coefficient γ;0∼ηω2, where η is shear viscosity. Presence of a hard wall strongly increases viscous losses which now occurs mainly within a narrow boundary layer δ. Viscous losses in a 2D phononic crystal are analytically calculated in the low-frequency limit for arbitrary Bravais lattice. The decay coefficient is expressed through series over reciprocal lattice vectors. If the phononic crystal possesses less than 3-fold rotational symmetry it behaves as anisotropic viscous medium. Otherwise, the decay coefficient is isotropic. Depending on the crystal structure and the filling fraction of solid cylinders the decay coefficient γ;ph may exceed γ;0 by two-four orders of magnitude. The decay coefficient may be further enhanced in a supercrystal – a structure with doubly periodicity. The supercrystal is a 2D structure of two sets of aluminum cylinders in air. A periodic set of larger cylinders is imbedded in another set of smaller cylinders arranged in a lattice with smaller period. We present analytical, numerical, and experimental results for decay of sound in a hexagonal supercrystal of aluminum cylinders in air. [This work is supported by the NSF under EFRI Grant No. 1741677.]

Spectroscopic observation and ab initio calculations of a new isomer of the CS2 trimer

We report spectroscopic observation and theoretical calculations of a new isomer of (CS2)3 as observed in the regions of the ν3 fundamental band of CS2 (6.5 μm) and the ν1 + ν3 combination band (4.5 μm), using tunable laser sources and a pulsed supersonic slit-jet. The previously observed CS2 trimer has a barrel-shaped structure with three equivalent monomers and D3 symmetry. The new isomer consists of a staggered parallel “dimer pair” of equivalent CS2 monomers with a third CS2 monomer sitting “on top”, similar to the known non-cyclic CO2 trimer. This structure has C2 rotational symmetry corresponding to the b inertial axis of the trimer, as proven by observed nuclear spin statistics. Ab initio calculations correctly give the two observed isomer structures and indicate that they lie very close in binding energy.

Cn -symmetric quasi-periodic Chern insulators

Chern insulators have been recently extended to quasicrystal systems, namely the quasi-periodic Chern insulators (QCIs). Here we study the topological properties and topological response of QCIs on two-dimensional singular surfaces. Such singular QCIs with arbitrary n− fold rotational symmetry (i.e. C n -symmetric QCIs) can be constructed by ‘cutting and gluing’ unit sectors on the Dürer’s pentagonal tiling. Chiral edge states and real-space Chern number can well characterize the topological properties of C n -symmetric QCIs. Intriguingly, we numerically identify the emergence of charge fractionalization in unit of e/10 around the singular center in Cn -symmetric QCIs though their bulk densities are inhomogeneous. In addition, we explore the phase transitions of these C n -symmetric QCIs.

Multifunctional metasurface for ultrafast all-optical efficient modulation of terahertz wave

Metasurfaces have been widely used to terahertz (THz) modulators due to their unique electromagnetic (EM) modulation properties. However, to realize ultrafast and efficient control of the active metasurfaces remains a critical challenge. Herein, we first demonstrate a multifunctional metasurface modulator based on metal square rings, which have central rotational symmetry with local asymmetry. The former captures more EM energy to achieve strong enhancement of the local EM responses, and the latter generates high quality factor (Q-factor) Fano resonance. By scaling the unit structure, the resonant frequency shifts in an ultra-wideband range of ∼0.29-10 THz, which shows a linear relation between the Q-factor and the scaling factor, and an exponential variation between the full width at half maximum (FWHM) and the scaling factor. The results provide an effective approach to predict the frequency selection characteristics of the modulators in the THz regime. More importantly, by embedding the silicon into the specific position of the metasurface, external optical control results in the unit structure is constructed from meta-atom to molecularization model, the shifting of resonant frequency and the multi-level modulation of amplitude are realized, and the maximum modulation depth (MD) reaches ∼100 %. By systematically studying the dynamics of frequency and amplitude regulation, benefiting from the ultra-short relaxation time of the photo-carriers in silicon bridge, an ultrafast full recovery time of 2000 ps is achieved. Combined with the local field characteristics, the scaled unit structure achieves efficient modulation of the resonant frequency and amplitude under optical pumping, which provides a promising approach for the development of active metasurface modulator suitable for the whole THz band. This work demonstrates the viability of optical control molecularization of specific meta-atoms is applicable to the entire THz band, which has great potential use for future state-of-the-art THz modulators.

Model matematyczny procesu pracy układu wyrzutowego podczas obrotu pompy strumieniowej w otworze

A mathematical model of an above-bit jet pump has been developed for the conditions of its rotation in a well, based on the use of hydrodynamic functions of a complex variable. These functions take the form of a sum of partial solutions of differential equations describing the potential motion of radial, circulation and homogeneous flows. The working flow is considered as a leak for a stationary jet pump or as a vortex in the case of rotation. The injected flow corresponds to a homogeneous one. The mixed flow is assessed in accordance with the principle of superposition by summing the complex potentials of elementary flows. The complex potential of the total flow determines the velocity field in the mixing chamber of the jet pump and allows us to set the configuration of the zero flow line, which separates the working and injected flows. In the process of integrating the velocity profile, the coefficient of uneven distribution of kinematic parameters is assessed, the value of which is included in the structure of the equation for the pressure characteristic of the jet pump and determines the effect of circulation flows on the working process of the ejection system. It has been established that the maximum velocity of the symmetrical rotation of the jet pump in the well increases the generated pressure and efficiency by 7.79% and 9.57%, respectively. Using the experimental head characteristic of the jet pump, obtained for the case of simultaneous swirling of the working and injected flows by the guide elements, the value of the relative head corresponding to the same rotation velocity of the mixed media has been assessed. The investigated values of the relative head pressure are used to verify the adequacy of the developed mathematical model of the ejection system for the rotation of the jet pump in the well. The maximum discrepancy between the theoretical and experimental values of the relative head pressure of the jet pump is 3.64%.

Two split rings resonator-based perfect metamaterial absorbers with the incident and polarization angle independent for sensing applications

The perfect metamaterial absorber (PMA) optimized for high-performance absorbers to find the multiple sensing application. The structural composition of the PMA consists of two split ring resonators with six split gaps configured in an exhibit symmetry of rotation. The fundamental component of the design has three distinct layers: (1) the top and bottom layers, composed of a metallic substance with copper dielectric substrate with a thickness of 0.035 mm that exhibits lossy metal; (2) the middle layer, made of a lossy dielectric material referred to as Rogers RT5870 dielectric substrate with a thickness of 1.575 mm. The findings reveal that the absorber achieves a broad absorption spectrum, with simulated results from the CST Microwave Studio simulator indicating absorption peaks at 5.88, 9.20, and 15.88 GHz. whereas the strong absorbance is 99.91, 99.99, and 99.97 % with a good quality factor (Q) 29.40, 9.20, 13.23, respectively. The structural dimensions (7 × 7 mm2) are designed to deliver remarkable performance. The tri-band PMA exhibits polarization independent at various angles, including 0, 45, 90, 135, and 180° for both transverse magnetic (TM) and transverse electric (TE) modes. It has excellent absorption capabilities across multiple angles of incidence from 0 to 80°, including the whole operational spectrum. A comparative investigation of the circuit indicates the enhanced performance of the PMA, demonstrating its potential for exceptional functionality inside the advanced design system (ADS) software. Furthermore, the structures under consideration, which were simulated using the High-Frequency Structure Simulator (HFSS), demonstrate a strong agreement with the highest level of absorption seen at each resonance peak in the CST simulation outcomes. This paper introduces an alternative protocol, expressed in terms of the TE and TM modes, for use with the restricted symmetric structure to find multiple sensing application. The proposed study highlights the exceptional properties of PMA provides several practical advantages, including its high absorption capacity, in multiple sensing application, insensitivity to incident and polarization angles, satellite technology, raw satellite feeds, and radars owing to these performance features.

Mechanical properties and failure modes of additively-manufactured chiral metamaterials based on Euclidean tessellations: an experimental and finite element study

PurposeThe “chiralisation” of Euclidean polygonal tessellations is a novel, recent method which has been used to design new auxetic metamaterials with complex topologies and improved geometric versatility over traditional chiral honeycombs. This paper aims to design and manufacture chiral honeycombs representative of four distinct classes of 2D Euclidean tessellations with hexagonal rotational symmetry using fused-deposition additive manufacturing and experimentally analysed the mechanical properties and failure modes of these metamaterials.Design/methodology/approachFinite Element simulations were also used to study the high-strain compressive performance of these systems under both periodic boundary conditions and realistic, finite conditions. Experimental uniaxial compressive loading tests were applied to additively manufactured prototypes and digital image correlation was used to measure the Poisson’s ratio and analyse the deformation behaviour of these systems.FindingsThe results obtained demonstrate that these systems have the ability to exhibit a wide range of Poisson’s ratios (positive, quasi-zero and negative values) and stiffnesses as well as unusual failure modes characterised by a sequential layer-by-layer collapse of specific, non-adjacent ligaments. These findings provide useful insights on the mechanical properties and deformation behaviours of this new class of metamaterials and indicate that these chiral honeycombs could potentially possess anomalous characteristics which are not commonly found in traditional chiral metamaterials based on regular monohedral tilings.Originality/valueTo the best of the authors’ knowledge, the authors have analysed for the first time the high strain behaviour and failure modes of chiral metamaterials based on Euclidean multi-polygonal tessellations.

Explaining supernova remnant G352.7-0.1 as a peculiar type Ia supernova inside a planetary nebula

I identify a point-symmetric morphology of the supernova remnant (SNR) G352.7-0.1 and propose that the outer axially-symmetric structure is the remnant of a common envelope evolution (CEE) of the progenitor system, while the inner structure is the ejecta of a thermonuclear explosion triggered by the merger of a white dwarf (WD) and the core of an asymptotic giant branch (AGB) star. The main radio structure of SNR G352.7-0.1 forms an outer (large) ellipse. The bright X-ray emitting gas forms a smaller ellipse with a symmetry axis inclined to the symmetry axis of the large radio ellipse. The high abundance of iron and the energy of its X-ray lines suggest a type Ia supernova (SN Ia). The massive swept-up gas suggests a relatively massive progenitor system. I propose a scenario with progenitors of initial masses of MZAMS,1≃5–7M⊙ and MZAMS,2≃4–5M⊙. At a later phase, the WD remnant of the primary star and the AGB secondary star experience a CEE that ejects the circumstellar material that swept up more ISM to form the large elliptical radio structure. An explosion during the merger of the WD with the core of the AGB star triggered a super-Chandrasekhar thermonuclear explosion that formed the inner structure that is bright in X-ray. A tertiary star in the system caused the misalignment of the two symmetry axes. This study adds to the wide variety of evolutionary routes within the scenarios of normal and peculiar SNe Ia.

Emergence of the isotropic Kitaev honeycomb lattice α− RuCl3 and its magnetic properties

We present a comprehensive investigation of the crystal and magnetic structures of the van der Waals antiferromagnet α− RuCl3 using single crystal x-ray and neutron diffraction. The crystal structure at room temperature is a monoclinic ( C2/m ). However, with decreasing temperature, a remarkable first-order structural phase transition is observed, leading to the emergence of a rhombohedral ( R3ˉ ) structure characterized by three-fold rotational symmetry forming an isotropic honeycomb lattice. On further cooling, a zigzag-type antiferromagnetic order develops below TN=6∼6.6 K. The critical exponent of the magnetic order parameter was determined to be β=0.11(1) , which is close to the two-dimensional Ising model. Additionally, the angular dependence of the magnetic critical field of the zigzag antiferromagnetic order for the polarized ferromagnetic phase reveals a six-fold rotational symmetry within the ab− plane. These findingsreflect the symmetry associated with the Ising-like bond-dependent Kitaev spin interactions and underscore the universality of the Kitaev interaction-dominated antiferromagnetic system.

Structure and Synthesis of Vindolicine and Derivatives.

This article describes the reaction of vindoline with formaldehyde and trimethyl orthoformate to prepare vindolicine, tris-vindolicinyl methane and higher molecular weight homologues. The synthesis of 10-formyl vindoline as an intermediate allowed further exploration of its chemistry, in particular the reaction with acetone which yielded a symmetrical dimer, which was further reacted with vindoline to give molecules containing three and four vindoline units. These molecules were characterized by NMR and for some of them (vindolicine, 10-formyl vindoline, 10-(1'-(but-1'-en-3'-one))-vindoline) by X-ray crystallography. Depending on the substitution and on the absence of axes of symmetry, the NMR spectra displayed non-equivalent spin systems for the vindoline moieties. The dimer formed from the double condensation of 10-formyl vindoline with acetone showed cytotoxic activity in the micromolar range.

Fermions at finite density in the path integral approach

We study relativistic fermionic systems in 3 + 1 spacetime dimensions at finite chemical potential and zero temperature, from a path-integral point of view. We show how to properly account for the iε term that projects on the finite density ground state, and compute the path integral analytically for free fermions in homogeneous external backgrounds, using complex analysis techniques. As an application, we show that the U(1) symmetry is always linearly realized for free fermions at finite charge density, differently from scalars. We study various aspects of finite density QED in a homogeneous magnetic background. We compute the free energy density, non-perturbatively in the electromagnetic coupling and the external magnetic field, obtaining the finite density generalization of classic results of Euler-Heisenberg and Schwinger. We also obtain analytically the magnetic susceptibility of a relativistic Fermi gas at finite density, reproducing the de Haas-van Alphen effect. Finally, we consider a (generalized) Gross-Neveu model for N interacting fermions at finite density. We compute its non-perturbative effective potential in the large-N limit, and discuss the fate of the U(1) vector and ℤ2A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathbb{Z}}_2^A $$\\end{document} axial symmetries.

Pure optical twist with zero net torque.

In photonic systems, bilayer or multilayer systems exhibit numerous exciting phenomena induced by twisting. Thus, it is highly desired to explore the twisting effect by engineering the light-matter interactions. Optical torque, an important means in optical micromanipulation, can rotate micro-objects in various ways, enabling a wide range of promising applications. In this study, we present an interesting phenomenon called "pure optical twist" (POT), which emerges when a bilayer structure with specific symmetry is illuminated by counter-propagating lights with opposite spin and/or orbital angular momentum. Remarkably, this leads to zero net optical torque but yet possesses an interesting mechanical effect of bilayer system twisting. The crucial determinant of this phenomenon is the rotational symmetries of each layer, which govern the allowed azimuthal channels of the scattered wave. When the rotational symmetries do not allow these channels to overlap, no resultant torque is observed. Our work will encourage further exploration of the twisting effect through engineered light-matter interactions. This opens up the possibility of creating twisted bilayer systems using optical means, and constructing a stable bilayer optical motor that maintains identical rotation frequencies for both layers.

Learning fast, accurate, and stable closures of a kinetic theory of an active fluid

Important classes of active matter systems can be modeled using kinetic theories. However, kinetic theories can be high dimensional and challenging to simulate. Reduced-order representations based on tracking only low-order moments of the kinetic model serve as an efficient alternative, but typically require closure assumptions to model unrepresented higher-order moments. In this study, we present a learning framework based on neural networks that exploits rotational symmetries in the closure terms to learn accurate closure models directly from kinetic simulations. The data-driven closures demonstrate excellent a-priori predictions comparable to the state-of-the-art Bingham closure. We provide a systematic comparison between different neural network architectures and demonstrate that nonlocal effects can be safely ignored to model the closure terms. We develop an active learning strategy that enables accurate prediction of the closure terms across the entire parameter space using a single neural network without the need for retraining. We also propose a data-efficient training procedure based on time-stepping constraints and a differentiable pseudo-spectral solver, which enables the learning of stable closures suitable for a-posteriori inference. The coarse-grained simulations equipped with data-driven closure models faithfully reproduce the mean velocity statistics, scalar order parameters, and velocity power spectra observed in simulations of the kinetic theory. Our differentiable framework also facilitates the estimation of parameters in coarse-grained descriptions conditioned on data.

Angle-resolved transport non-reciprocity and spontaneous symmetry breaking in twisted trilayer graphene.

The identification and characterization of spontaneous symmetry breaking is central to our understanding of strongly correlated two-dimensional materials. In this work, we utilize the angle-resolved measurements of transport non-reciprocity to investigate spontaneous symmetry breaking in twisted trilayer graphene. By analysing the angular dependence of non-reciprocity in both longitudinal and transverse channels, we are able to identify the symmetry axis associated with the underlying electronic order. We report that a hysteretic rotation in the mirror axis can be induced by thermal cycles and a large current bias, supporting the spontaneous breaking of rotational symmetry. Moreover, the onset of non-reciprocity with decreasing temperature coincides with the emergence of orbital ferromagnetism. Combined with the angular dependence of the superconducting diode effect, our findings uncover a direct link between rotational and time-reversal symmetry breaking. These symmetry requirements point towards exchange-driven instabilities in momentum space as a possible origin for transport non-reciprocity in twisted trilayer graphene.

Effect of eccentricity on electromagnetic logging signals with LWD and VEMKZ instruments (numerical simulation results from some publications)

During drilling, formation fluids are pushed aside by mud filtrate. As a result, the electrophysical properties of rocks near the borehole wall change. Sounding methods are used to determine the resistivity of the part of the reservoir that is remote from the well and unchanged during drilling. Among these methods, electromagnetic logging has the best spatial resolution. However, when analyzing the practical data of electromagnetic sounding, "wrong" ratios of signals from probes of different lengths are often observed, including those showing penetration in impermeable rocks. One of the reasons may be the influence of the shift of the device from the axis of symmetry of the medium. The paper considers the results of numerical simulation of signals from decentralized probes of LWD and VEMKZ instruments in some models.

Crystal-Structure Matches in Solid-Solid Phase Transitions.

The exploration of solid-solid phase transition suffers from the uncertainty of how atoms in two crystal structures match. We devised a theoretical framework to describe and classify crystal-structure matches (CSM). Such description fully exploits the translational and rotational symmetries and is independent of the choice of supercells. This is enabled by the use of the Hermite normal form, an analog of reduced echelon form for integer matrices. With its help, exhausting all CSMs is made possible, which goes beyond the conventional optimization schemes. In an example study of the martensitic transformation of steel, our enumeration algorithm finds many candidate CSMs with lower strains than known mechanisms. Two long-sought CSMs accounting for the most commonly observed Kurdjumov-Sachs orientation relationship and the Nishiyama-Wassermann orientation relationship are unveiled. Given the comprehensiveness and efficiency, our enumeration scheme provide a promising strategy for solid-solid phase transition mechanism research.

Assessment of stability of earth dams based on construction pace by fuzzy inference logic

This study aims to evaluate the earth dam stability fuzzy model based on the pace of construction by way of influential parameters, including the dam construction time (embankment consolidation time) in the stability analysis of earth dams. A fuzzy inference system based on the Sugeno inference engine was developed, and 620 if-then rules in plane strain and axial symmetry (Plaxis) were used to train the fuzzy system. The input parameters included the dam height, crest width, dam slope, cohesion, friction angle, elasticity modulus, Poisson’s ratio, unsaturated unit weight, consolidation (construction) time and permeability coefficient, with the factor of safety output. To develop the fuzzy inference system, a triangular membership function was employed, calculating the influential parameters over five periods in Matrix laboratory (Matlab) software. The fuzzy model results were compared with the results of numerical Plaxis and fast Lagrangian analysis of continua models. High coefficients of determination (R2) suggest good agreement between the fuzzy and numerical models, and it can be assumed that the proposed fuzzy model is efficient and effective for the stability analysis, and hence assessment of factors of safety, of earth dams.

Synthesis and Dynamic Behavior of Ce(IV) Double-Decker Complexes of Sterically Hindered Phthalocyanines.

Phthalocyanines and their double-decker complexes are interesting in designing rotative molecular machines, which are crucial for the development of molecular motors and gears. This study explores the design and synthesis of three bulky phthalocyanine ligands functionalized at the α-positions with phenothiazine or carbazole fragments, aiming to investigate dynamic rotational motions in these sterically hindered molecular complexes. Homoleptic and heteroleptic double-decker complexes were synthesized through the complexation of these ligands with Ce(IV). Notably, CeIV(Pc2)2 and CeIV(Pc3)2, both homoleptic complexes, exhibited blocked rotational motions even at high temperatures. The heteroleptic CeIV(Pc)(Pc3) complex, designed to lower symmetry, demonstrated switchable rotation along the pseudo-C4 symmetry axis upon heating the solution. Variable-temperature 1H-NMR studies revealed distinct dynamic behaviors in these complexes. This study provides insights into the rotational dynamics of sterically hindered double-decker complexes, paving the way for their use in the field of rotative molecular machines.

Relative variation between γ coordinate and the potential of the Bohr Hamiltonian producing X(4) from Z(4)

In this paper, four degree of freedom γ-rigid solutions of the Bohr Hamiltonian at γ 0 = π/6 are obtained. The relative variation between γ and the potential of the Hamiltonian is employed to retrieve X(4) from Z(4). γ is varied in the interval 0 ≤ γ 0 ≤ π/6 while the potential minimum, β 0, is varied in the interval 0 ≤ β 0 ≤ ∞ . Very small value of β 0 yields Z(4) while a large value of β 0 produces X(4) and SU(3) is realized at β 0 ≈ ∞ . The solutions at γ 0 = 0 correspond to X(4) while the solutions at γ 0 = π/6 yield Z(4): a dynamic link between Z(4) and X(4) critical point symmetries (CPSs) has been provided. The fact that γ and β 0 of the potential play the same role in the dynamical link between Z(4) and X(4) shows that β 0 also measures the departure from axial symmetry to other shapes as γ does. In the experimental realization of the model, the conformation of 192Pt and 194Pt isotopes to the present Z(4) model shows that the present model can be employed in the description of triaxial rotors and γ-soft isotopes. 194Pt is shown to be the best choice for triaxial rigid rotor candidacy. 130Xe, a critical point isotope, which belongs to the class of γ-soft nuclei, reproduces this present model very well in all the states. Consequently, this present model can serve as a critical point model. 40,0 − β 0 distribution for Z(4) and X(4) candidate isotopes shows a significant interval between the two models where the T(4) CPS lies.