Symmetry Axis Research Articles

The coalescence and oscillation of eutectic gallium indium alloy droplets

The coalescence and oscillation of eutectic gallium indium alloy droplets

Symmetry breaking induced asymmetric dislocation-planar fault interactions in ordered intermetallic alloys

In this study, we present the first comprehensive examination of symmetry breaking in the interactions between dislocation and superlattice planar faults, including anti-phase boundary (APB), complex stacking fault (CSF), superlattice intrinsic stacking fault (SISF), to reveal the underlying asymmetric dislocation reaction mechanisms depending on the sense of applied stress, employing both large-scale atomistic simulations and continuum dislocation theory. Four ordered intermetallic alloy systems including γ−Ni/γ′−Ni3Al and γ−Ni/γ′−Ni3Fe, γ−Al/γ−TiAl, and α−Ti/α2−Ti3Al were selected as the representative model systems, with two primary symmetry breaking effects, i.e., translational and three-fold rotational symmetry breaking considered. Detailed atomic steps of asymmetrical dislocation reactions and the corresponding asymmetrical dislocation bypassing mechanisms of precipitation have been elucidated, shown to be highly dependent on the geometrical configuration of the precipitate and the relative magnitudes of APB, CSF and SISF fault energies. A continuum model framework was then developed, which, for the first time, provides accurate and quantitative predictions of the threshold conditions triggering critical asymmetrical dislocation slips, verified to be in good agreement with the simulation results. Our study also successfully reproduced the experimentally observed dislocation-induced APB-SISF transformation, with a new dislocation reaction mechanism proposed to explain the transformation process. The findings are expected to be a key enabling stepstone for future innovation in intermetallic alloys strengthened through ordered phases for advanced applications in aeronautic and automotive industries.

Strain in Hybrid Organic-Inorganic Metal Halide Perovskites Microstructures by Numerical Simulations.

Hybrid organic-inorganic metal halide perovskites (HOIPs) are promising materials for optoelectronics applications. Their optical and electrical properties can be controlled by strain engineering, that results from application of local elastic deformation or deposition on pre-patterned substrates acquiring a conformal 3D shape. Most interesting, their mechanical properties depend on their crystal structure, composition and dimensionality. We explore by numerical simulations the deformation of a selection of HOIPs comprising a broad range of elastic properties. We consider an axial symmetry with the formation of microdomes on flakes. Radial and vertical forces are considered, finding that the radial force is more effective to obtain large deformation. Large vertical displacement and strain is obtained for HOIPs with low stiffness. The layered nature of HOIPs, that are formed by inorganic layers of different thickness and organic spacers, is also investigated, revealing a non-monotonous trend with the proportion of inorganic to organic part.

Modal approach to the dynamics of string instruments over the audible range

The present theoretical analysis addresses the dynamics of the bow instruments in the whole audible range of frequencies. Several scenarios are considered for the string-bridge-soundbox system: natural vibrations and frequency spectrum, external periodic excitation on some bridge point, and vibration induced by the bow rubbing. The single parts of the musical artifact are conveniently modelled and the bridge interfacing between the strings and the top plate of the soundbox is studied considering two possible vibrating modes of the bridge: a translational mode along its symmetry axis and a rotational mode around the waist centre. The bridge mechanical model is thus definable from both the kinematical and the dynamical aspects, and the relations between the forces and displacements of the strings and the sound box are formulated.The coupled natural modes of vibration are obtained in non-dissipative conditions, finding that the whole frequency spectrum is roughly given by the union of the uncoupled spectra, of the strings and the harmonic box. Then, introducing some level of dissipation, the frequency response to a transverse harmonic excitation on an arbitrary bridge point and the admittance on another arbitrary point of the instrument are studied, obtaining a useful tool to identify or verify the mechanical characteristics of the system. At last, the response to the bow excitation is analysed introducing an appropriate model for the nonlinear stick-slip contact between the bow and the strings and solving the motion equations by modal decomposition.

Improved effective dipole moment model for axially symmetric [formula omitted] molecules: Parallel [formula omitted] bands

The new improved effective dipole moment model is derived for molecules of the axial C3v symmetry. The obtained result is, on the one hand, of the same order of efficiency but much simpler and clearer in applications in comparison with previous models derived on the basis of the irreducible tensorial sets theory and, on the other hand, mathematically more correct in comparison with concepts like the Herman–Walles function. Symmetric ro–vibrational bands of the mentioned molecule types are considered in the present study with taking into account the fourth order centrifugal corrections to the main effective dipole moment operator both for”allowed“ and ”forbidden“ transitions.

Noncollinear Electric Dipoles in a Polar Chiral Phase of CsSnBr3 Perovskite.

Polar and chiral crystal symmetries confer a variety of potentially useful functionalities upon solids by coupling otherwise noninteracting mechanical, electronic, optical, and magnetic degrees of freedom. We describe two phases of the 3D perovskite, CsSnBr3, which emerge below 85 K due to the formation of Sn(II) lone pairs and their interaction with extant octahedral tilts. Phase II (77 K < T < 85 K, space group P21/m) exhibits ferroaxial order driven by a noncollinear pattern of lone pair-driven distortions within the plane normal to the unique octahedral tilt axis, preserving the inversion symmetry observed at higher temperatures. Phase I (T < 77 K, space group P21) additionally exhibits ferroelectric order due to distortions along the unique tilt axis, breaking both inversion and mirror symmetries. This polar and chiral phase exhibits second harmonic generation from the bulk and pronounced electrostriction and negative thermal expansion along the polar axis (Q22 ≈ 1.1 m4 C-2; αb = -7.8 × 10-5 K-1) through the onset of polarization. The structures of phases I and II were predicted by recursively following harmonic phonon instabilities to generate a tree of candidate structures and subsequently corroborated by synchrotron X-ray powder diffraction and polarized Raman and 81Br nuclear quadrupole resonance spectroscopies. Preliminary attempts to suppress unintentional hole doping to allow for ferroelectric switching are described. Together, the polar symmetry, small band gap, large spin-orbit splitting of Sn 5p orbitals, and predicted strain sensitivity of the symmetry-breaking distortions suggest bulk samples and epitaxial films of CsSnBr3 or its neighboring solid solutions as candidates for bulk Rashba effects.

The nematic susceptibility of the ferroquadrupolar metal TmAg2 measured via the elastocaloric effect

Elastocaloric measurements of the ferroquadrupolar/nematic rare-earth intermetallic TmAg2 are presented. TmAg2 undergoes a cooperative Jahn-Teller-like ferroquadrupolar phase transition at 5K, in which the Tm3+ ion’s local 4f electronic ground state doublet spontaneously splits and develops an electric quadrupole moment which breaks the rotational symmetry of the tetragonal lattice. The elastocaloric effect, which is the temperature change in the sample induced by adiabatic strains the sample experiences, is sensitive to quadrupolar fluctuations in the paranematic phase which couple to the induced strain. We show that elastocaloric measurements of this material reveal a Curie-Weiss like nematic susceptibility with a Weiss temperature of T* ≈ 2.7K, in agreement with previous elastic constant measurements. Furthermore, we establish that a magnetic field along the c-axis acts as an effective transverse field for the quadrupole moments.

Weak (non)conservation and stochastic dynamics of angular momentum

Angular momentum conservation influences equilibrium statistical mechanics, leading to a generalized microcanonical density for an isolated system and a generalized Gibbs density for a weakly coupled system. We study the stochastic decay of angular momentum due to the weakly imperfect rotational symmetry of the external potential that confines the isolated many-particle system. We present a mesoscopic description of the system, deriving Langevin and Fokker–Planck equations, which are consistent with equilibrium statistical mechanics when rotational symmetry is maintained. When the symmetry is weakly violated, we formulate a coarse-grained stochastic differential equation governing the decay of total angular momentum over time. To validate our analytical predictions, we conduct numerical simulations of the microcanonical ensemble, an isolated system undergoing thermalization due to weak two-body interactions. Our coarse-grained Langevin equation accurately characterizes both the decay of the angular momentum and its fluctuations in a steady state. Furthermore, we estimate the parameters of our mesoscopic model directly from simulations, providing insights into the dissipative phenomenological coefficients, such as friction. More generally, this study contributes to a deeper understanding of the behavior of the integrals of motion when the corresponding symmetry is weakly violated.

Evaluating aliphatic CF, CF2, and CF3 groups as vibrational Stark effect reporters.

Given the extensive use of fluorination in molecular design, it is imperative to understand the solvation properties of fluorinated compounds and the impact of the C-F bond on electrostatic interactions. Vibrational spectroscopy can provide direct insights into these interactions by using the C-F bond stretching [v(C-F)] as an electric field probe through the vibrational Stark effect (VSE). In this work, we explore the VSE of the three basic patterns of aliphatic fluorination, i.e., mono-, di-, and trifluorination in CF, CF2, and CF3 groups, respectively, and compare their response to the well-studied aromatic v(C-F). Magnitudes (i.e., Stark tuning rates) and orientations of the difference dipole vectors of the v(C-F)-containing normal modes were determined using density functional theory and a molecular dynamics (MD)-assisted solvatochromic analysis of model compounds in solvents of varying polarity. We obtain Stark tuning rates of 0.2-0.8cm-1/(MV/cm), with smallest and largest electric field sensitivities for CFaliphatic and CF3,aliphatic, respectively. While average electric fields of solvation were oriented along the main symmetry axis of the CFn, and thus along its static dipole, the Stark tuning rate vectors were tilted by up to 87° potentially enabling to map electrostatics in multiple dimensions. We discuss the influence of conformational heterogeneity on spectral shifts and point out the importance of multipolar and/or polarizable MD force fields to describe the electrostatics of fluorinated molecules. The implications of this work are of direct relevance for studies of fluorinated molecules as found in pharmaceuticals, fluorinated peptides, and proteins.

Identification of nonlinear effects of background asymmetry on solitary oscillations in a cylindrical plasma

A symmetry-breaking in rotational spatial pattern of quasi-periodic solitary oscillations is revealed with tomography measurement of plasma emission, simultaneously with background asymmetry in stationary plasma structure. Although the oscillatory pattern deformation is a natural course in the presence of asymmetry, elaborate analyses identify existence unfeatured nonlinear effects of the background asymmetry, i.e., its nonlinear couplings with harmonic modes of rotational symmetry, to produce non-harmonic mode to break the symmetry and cause the oscillatory pattern to be chaotic. The findings suggest the unrecognized fundamental process for plasmas to be turbulent.

Nondestructive global corrosion measurement using guided wavefield data

Metallic structures often face degradation, and corrosion ranks among the most prevalent forms of deterioration. Accurate quantification of corrosion is crucial, especially for structures exposed to harsh environmental conditions, such as marine vessels and offshore installations. Because the traditional measurement methods based on scanning by ultrasonic gauge are time-consuming and provide only rough information on the thickness variability, there is a need to develop new robust and accurate diagnostics methods. This paper aims to investigate the corrosion monitoring of metal plates using guided wave propagation. Guided waves propagate within the entire volume of the specimen. If it is undamaged and isotropic, the velocity in all directions is the same, and the spreading wavefront takes a circular shape. The primary assumption presented in this paper is that the potential damage caused by corrosion leads to disturbance of this symmetry. The study shows Bilateral and Rotational Corrosion Symmetry Degree (BCSD and RCSD) functions, demonstrating a consistent decrease in symmetry values with increasing degree of degradation (DoD) caused by the corrosion process. The main aim of the study was to test the possibility of corrosion monitoring by using variable number of sensors comprising the transducer network. Also, the influence of the distance between the sensors affecting the size of the monitored area on the corrosion monitoring procedure was investigated. The paper contains the results of numerical and experimental campaigns conducted for corroded plates characterized by variable DoD and monitored using nine different transducers configurations. It is the first step in developing a novel measurement procedure specially designed for the ship and offshore industry. Therefore, because of the initial stage of the study, the last part of the paper discusses the limitations and drawbacks of the presented wave symmetry-based approach.

Robustness and Tunability of Symmetric‐Protected Bound States in the Continuums and Quasi‐Bound States in the Continuums in Terahertz Metasurfaces

Symmetry‐protected bound states in the continuum (BICs), emerging at the point in the Brillouin zone of periodic lattices of scatters, are robust optical modes under modifications in the lattice if the C2 symmetry (two fold rotational symmetry) is preserved. In this study, the manipulation of these symmetry‐protected BIC and quasi‐BIC modes in a system comprising two metallic rods per unit cell by adjusting their lateral separation and displacement is focused on. With non‐symmetric systems under 180° rotation, two distinct coupling mechanisms resulting from changes in the lateral separation are investigated: the coupling of two half‐wavelength (λ/2) resonances and the coupling of two surface lattice resonances (SLRs). Notably, symmetric structures with minimal lateral separation cannot sustain BIC modes owing to the near‐field coupling between the rods. However, when the lateral separation is sufficiently large, the existence of a BIC mode supported by an SLR remains robust even with positional shifts. Furthermore, increasing the lateral separation and the shift displacement between the rods in asymmetric systems induces a redshift and a blueshift in the quasi‐BIC mode, respectively. This shift is attributed to the near‐field coupling effect between two rods, enabling the tunability of the resonance frequency with a high‐quality factor.

Temperature-Driven Rotation Symmetry-Breaking States in an Atomic Kagome Metal KV3Sb5.

Kagome lattice AV3Sb5 has attracted tremendous interest because it hosts correlated and topological physics. However, an in-depth understanding of the temperature-driven electronic states in AV3Sb5 is elusive. Here we use scanning tunneling microscopy to directly capture the rotational symmetry-breaking effect in KV3Sb5. Through both topography and spectroscopic imaging of defect-free KV3Sb5, we observe a charge density wave (CDW) phase transition from an a0 × a0 atomic lattice to a robust 2a0 × 2a0 superlattice upon cooling the sample to 60 K. An individual Sb-atom vacancy in KV3Sb5 further gives rise to the local Friedel oscillation (FO), visible as periodic charge modulations in spectroscopic maps. The rotational symmetry of the FO tends to break at the temperature lower than 40 K. Moreover, the FO intensity shows an obvious competition against the intensity of the CDW. Our results reveal a tantalizing electronic nematicity in KV3Sb5, highlighting the multiorbital correlation in the kagome lattice framework.

Synthetic gauge field and exotic vortex phase with spin-orbital-angular-momentum coupling

Abstract Ultracold atoms endowed with tunable spin-orbital-angular-momentum coupling (SOAMC) represent a promising avenue for delving into exotic quantum phenomena. Building on recent experimental advancements, we propose the generation of synthetic gauge fields and including exotic vortex phases within spinor Bose-Einstein condensates, employing a combination of a running wave and Laguerre-Gaussian laser fields. We investigate the ground-state characteristics of the SOAMC condensate, revealing the emergence of exotic vortex states with controllable orbital angular momenta. It is shown that the interplay of the SOAMC and conventional spin-linear-momentum coupling (SLMC) induced by the running wave beam, leads to the formation of vortex state exhibiting phase stripe hosting single multiply quantized singularity. The phase of the ground state will undergo the phase transition phase corresponding to the breaking of rotational symmetry while preserving the mirror symmetry. Importantly, the observed density distribution of ground state wavefunction, exhibiting broken rotational symmetry can be well characterized by the synthetic magnetic field generated through light interaction with the dressed spin state. Our findings pave the way for further exploration into the rotational properties of stable, exotic vortices with higher orbital angular momenta against splitting in the presence of synthetic gauge fields in ultracold quantum gases.

High Q chiroptical responses with maximum chirality in all-dielectric metasurfaces driven by quasi-bound states in the continuum

Chiral metasurfaces have attracted considerable attention because of their immense potential for diverse applications requiring chiral light-matter interactions. Recently, boosted by a mechanism based on the concept of bound states in the continuum (BICs), high Q factor chiroptical resonances have been exhibited by breaking the inversion symmetries of planar metasurfaces. However, the optical chirality of these chiral metasurfaces is generally intolerable with respect to the structural geometries, especially the geometric asymmetry. Here, we present a novel chiral quasi-BIC with strong optical chirality in an all-dielectric metasurface. By simultaneously breaking the in-plane C2 rotational and mirror symmetries, the chiral metasurface shows enhanced chiroptical resonances with near-unity CD (∼0.996) and high Q factors (∼2274) at terahertz frequencies. Further analyses based on numerical simulations reveal that the CD of the chiroptical resonance depicts exceptional remarkable tolerableness to the geometry asymmetry δ when δ are present in a broad range, while the corresponding Q factor is modulated accordingly. The results may develop a novel approach to manipulating the advanced optical chirality for potential applications requiring strong CD with enhanced light-matter interactions.

Corrosion damage identification based on the symmetry of propagating wavefield measured by a circular array of piezoelectric transducers: Theoretical, experimental and numerical studies

The article investigates the results obtained from numerical simulations and experimental tests concerning the propagation of guided waves in corroded steel plates. Developing innovative methodologies for assessing corrosion-induced degradation is crucial for accurately diagnosing offshore and ship structures exposed to harsh environmental conditions. The main aim of the research is to analyze how surface irregularities affect wave propagation characteristics. An investigation was conducted for antisymmetric fundamental mode A0. Specifically, the study examines the asymmetrical wavefronts generated by nonuniform thickness in damaged specimens. Initially, numerical analysis explores the impact of thickness variation on wave field symmetry. Corroded plates with varying levels of degradation are modeled using the random fields approach, with degradation levels ranging from 0 % to 60 %. Subsequently, the research investigates how the standard deviation of thickness distribution (from 5 % to 20 % of the initial thickness) and excitation frequency (from 50 to 150 kHz) influence recorded signals and the shape of reconstructed wavefronts. Each scenario compares wavefront symmetry levels estimated using rotational and bilateral symmetry degrees as indicative parameters. The numerical simulations are complemented by experimental tests conducted on plates with three different degradation levels. The results demonstrate the efficacy of the proposed wave field analysis approach for assessing structural integrity, as evidenced by the agreement between numerical predictions and experimental observations.

A two stage pipeline architecture for hardware implementation of multi-level decomposition of 1-D framelet transform

In this paper a two stage pipeline architecture for computation of multilevel decomposition of framelet transform is proposed. To handle the problem of perfect reconstruction, an area efficient symmetric extension router is used that duplicates the appropriate number of data samples of input signal at the boundary followed by reflection about the symmetry axis. In addition, to reduce the period and number of clock cycles required for computing the framelet transform, the inter-stage and intrastage pipeline of the computational units is maximized. The inter-stage pipelining is obtained by distributing the various levels of decomposition among the computational units of two stages, and a synchronization mechanism is adopted to reduce the total number of clock cycles. Similarly, the intrastage pipelining is achieved by using the pipeline registers such that the clock period is limited to the delay of multiplier and accumulator (MAC) circuit of the finite-impulse response (FIR) filter. To validate the feasibility and functionality of the proposed hardware architecture, the design is implemented on Artix7 XC7A100TCSG324-1 field-programmable gate array (FPGA) for the case of framelet transform with one low-pass and two high-pass filters. The proposed architecture is able to operate at a maximum clock frequency of 112 MHz.

A network model for can-annular combustors using a multidimensional transfer matrix based on the mode matching method

Heavy-duty land-based gas turbines with can-annular combustors typically exhibit a set of thermoacoustic modes with similar frequencies, due to their rotational symmetry and the weak coupling between neighbouring cans. The Bloch boundary condition is often used to simplify these combustors. Because the widely used (quasi-)one-dimensional model cannot naturally consider high-order modal components in the three-dimensional acoustic field, it is valid only when the frequency is sufficiently low and the length of the can-to-can interaction gap is sufficiently short. In this paper, we present a theoretical model using the mode-matching method to consider high-order modal components. A reflection coefficient matrix is used to accurately describe the acoustic characteristics of the gap area. This reflection coefficient matrix is found to depend on the nondimensional cross-sectional area ratio, the Helmholtz number based on the length of the gap area, and the Bloch number. To facilitate a full low-order network modelling of the high-frequency thermoacoustic modes in can-annular combustors, a flame transfer matrix is also used to describe the modal coupling effect across the flame. Based on this model, the thermoacoustic problem of a four-flame can-annular combustor is studied as an example. It is shown that the frequency and growth rate of the thermoacoustic modes can be predicted accurately using the reflection coefficient matrix and flame transfer matrix. The effects of high-order modal components across the flame and in the gap areas are studied separately. The results show that the model containing both of the two coupling effects has the widest range of validity. These couplings can be ignored if only low-frequency plane acoustic waves are considered but need to be carefully considered for higher frequency modes. Moreover, when multiple flames are considered, asymmetric flame distributions are found to more easily lead to modal coupling compared to symmetric flame distributions. All results are validated by comparing with the numerical solutions of the full two-dimensional Helmholtz equation using the finite element method.

Driven generalized quantum Rayleigh-van der Pol oscillators: Phase localization and spectral response.

Driven classical self-sustained oscillators have been studied extensively in the context of synchronization. Using the master equation, this work considers the classically driven generalized quantum Rayleigh-van der Pol oscillator, which is characterized by linear dissipative gain and loss terms as well as three nonlinear dissipative terms. Since two of the nonlinear terms break the rotational phase space symmetry, the Wigner distribution of the quantum mechanical limit cycle state of the undriven system is, in general, not rotationally symmetric. The impact of the symmetry-breaking dissipators on the long-time dynamics of the driven system are analyzed as functions of the drive strength and detuning, covering the deep quantum to near-classical regimes. Phase localization and frequency entrainment, which are required for synchronization, are discussed in detail. We identify a large parameter space where the oscillators exhibit appreciable phase localization but only weak or no entrainment, indicating the absence of synchronization. Several observables are found to exhibit the analog of the celebrated classical Arnold tongue; in some cases, the Arnold tongue is found to be asymmetric with respect to vanishing detuning between the external drive and the natural oscillator frequency.

An approach to describe the twinning and detwinning processes of the martensitic structure in ferromagnetic alloy with shape memory in magnetic and force fields

In the article, based on the theory of micromagnetism, a special case of the moment theory of elasticity for an anisotropic material and the Hadamard compatibility condition for deformations, a microstructural model of the behavior of the Heusler alloy with shape memory in magnetic and force fields is constructed. The dynamics of the magnetic process is described by the Landau-Lifshitz-Gilbert equation. Using the Galerkin procedure, variational equations corresponding to the differential relations of the magnetic problem are written out and the finite element method is used for numerical realization of these equations. Considering the problems of the moment theory of elasticity we come to a special case of this theory in which, under the action of force and magnetic fields, the tensor of moment stresses initiated only by the magnetic field is zero. Using this result, the general expression for the state equation is constructed that describes, within the framework of small deformations, the behavior of an anisotropic material under force and magnetic influences. The stress tensor in this equation consists of a symmetric part and a skew-symmetric part, depending only on the magnetic field. For the problem of deformable solid mechanics with such a state equation, the Lagrange variational equation was constructed, which made it possible to reduce the requirements for the smoothness of the desired solution by an order of magnitude. The general expression for the state equation has been concretized for an anisotropic material having one axis of symmetry of the fourth order and two axes of symmetry of the second order. The solution of the Hadamard compatibility equation for deformations made it possible to determine the sliding surfaces and sliding directions in a tetragonal crystal cell of a ferromagnetic material in the martensitic state, along which a shift occurs, leading to the appearance and dissipation of a twinned structure. The microstructural model, constructed using all these positions, is used to describe experimental results on the combined action of magnetic and force fields on the Heusler alloy.