Symmetry Properties Research Articles

Bioinspired Nanolayered Structure Tuned by Extensional Stress: A Scalable Way to High-Performance Biodegradable Polyesters.

The nacre-inspired multi-nanolayer structure offers a unique combination of advanced mechanical properties, such as strength and crack tolerance, making them highly versatile for various applications. Nevertheless, a significant challenge lies in the current fabrication methods, which is difficult to create a scalable manufacturing process with precise control of hierarchical structure. In this work, a novel strategy is presented to regulate nacre-like multi-nanolayer films with the balance mechanical properties of stiffness and toughness. By utilizing a co-continuous phase structure and an extensional stress field, the hierarchical nanolayers is successfully constructed with tunable sizes using a scalable processing technique. This strategic modification allows the robust phase to function as nacre-like platelets, while the soft phase acts as a ductile connection layer, resulting in exceptional comprehensive properties. The nanolayer-structured films demonstrate excellent isotropic properties, including a tensile strength of 113.5MPa in the machine direction and 106.3MPa in a transverse direction. More interestingly, these films unprecedentedly exhibit a remarkable puncture resistance at the same time, up to 324.8Nmm-1, surpassing the performance of other biodegradable films. The scalable fabrication strategy holds significant promise in designing advanced bioinspired materials for diverse applications.

Axial Symmetry in Primary School Through a Milieu Based on Visual Programming

AbstractThis paper outlines the design and application of a didactic sequence aimed at facilitating primary students’ understanding of axial symmetry, utilizing a combination of digital artefacts and paper tasks. We wondered to what extent the designed didactic sequence is able to make primary school students formulate and validate effective programming strategies to construct symmetrical images with respect to an axis and identify the key properties of axial symmetry. Data analysis from a study carried out with fifth-grade students shows a link between the evolution of students’ programming strategies and the construction of mathematical knowledge related to the definition of axial symmetry. The digital artefact and the paper tasks were effective in bringing out programming strategies and some of the key properties of axial symmetry. However, the designed didactic sequence was not enough to allow students to identify all properties related to axial symmetry, and a subsequent intervention by the teacher was necessary. The results of the experimentation led us to expand the paper tasks with additional questions for students.

Deep Ultraviolet Optical Anisotropy of β-Gallium Oxide Thin Films.

β-Crystalline phase gallium oxide (β-Ga2O3) is an ultrawide bandgap material with prospective applications in electronics and deep ultraviolet (DUV) optoelectronics and optics. The monoclinic crystal structure of β-Ga2O3 results in optical anisotropy to incident light with different polarization states. This attribute can lead to different optical applications in the DUV. In this article, we investigated the optical properties of β-Ga2O3 thin films grown by pulsed laser deposition technique on sapphire substrates with different crystallographic orientations. Marked in-plane polarization anisotropy, determined by reflectance and Raman spectroscopy, was observed for β-Ga2O3 films deposited on an r-cut sapphire substrate. In contrast, isotropic optical properties were observed in β-Ga2O3 films deposited on a c-cut sapphire substrate.

Effective elastic properties of novel aperiodic monotile-based lattice metamaterials

Two-dimensional aperiodic lattices emerge as remarkably isotropic metamaterials with potentially unconventional mechanical behavior. This study investigates numerically estimating the effective elastic properties, as a function of relative density, of novel two-dimensional aperiodic lattice metamaterials derived from the recently discovered aperiodic monotiles, known as the “Hat,” “Turtle,” and “Spectre” tiles. Furthermore, several classes of the Hat-based lattices; namely Hexagon (H), Triangle (T), Parallelogram (P), and Fan (F), are also investigated. The results show that these aperiodic lattices have isotropic elastic properties independent of relative density. The Hat-based and Turtle lattices exhibit larger elastic moduli, gradually converging to the Spectre-based lattices as relative density increases. A distinctive feature of the Hat-based lattices is their directional auxetic behaviour with an anisotropic Poisson’s ratio, whereas the Turtle lattices show an auxetic behaviour only at lower relative densities. Despite anisotropic Poisson’s ratios, the current aperiodic lattices maintain elastic isotropy, offering a unique blend of anisotropic auxetic behavior and isotropic elastic moduli. This study contributes to a better understanding of the elastic properties of aperiodic monotile lattice metamaterials and their potential for engineering their mechanical behavior for certain applications.

Flavor-spin symmetry of the PψN/HΩcccN and PψsΛ/HΩcccsΛ molecular states

Based on a contact Lagrangian that incorporates the SU(3) flavor and SU(2) spin symmetries, we discuss the symmetry properties of the interactions among the heavy flavor meson-baryon PψN, PψsΛ (with quark components [nc¯][nnc], [sc¯][nnc], or [nc¯][nsc]) systems and dibaryon HΩcccN, HΩcccsΛ (with quark components [nnc][ncc], [nnc][scc], or [nsc][ncc]) systems (n=u, d). The light quark components of the PψN (PψsΛ) and HΩcccN (HΩcccsΛ) systems have identical flavors, the interactions generated from the exchanges of light mesons in the PψN (PψsΛ) systems should be very similar to that of the HΩcccN (HΩcccsΛ) systems. We perform the single-channel and multichannel calculations on the PψN/PψsΛ/HΩcccN/HΩcccsΛ systems and introduce the SU(3) breaking effect to identify the different mass spectra among the PψN (HΩcccN) and PψsΛ (HΩcccsΛ) systems. We suggest two kinds of evidences for the existence of the flavor-spin symmetry among the heavy flavor PψN/HΩcccN/PψsΛ/HΩcccsΛ molecule community, i.e., the mass arrangements of the PψN/HΩcccN/PψsΛ/HΩcccsΛ mass spectra and the binding energies of the heavy flavor meson-baryon (dibaryon) systems attributed to the same contact potentials. Published by the American Physical Society 2024

Chiral photoelectron spectroscopy using unpolarized light

This Letter studies the symmetry properties of general vector correlations resulting from one-photon excitation of chiral molecules. We show that the parity-odd second rank tensor is nonzero for molecules in all chiral point groups Cn, Dn, T, O, and I. This chirality-sensitive tensor is nonzero even for chiral isotopomers excited by linearly polarized or even unpolarized light. We develop an irreducible tensor theory based on Curie's limiting groups. As an example of vector correlations, recoil-frame photoelectron angular distributions (RFPADs) are calculated for methyloxirane and CHFCl35Cl37. The difference in the RFPAD between a chiral molecule and its mirror image reaches ±35% of the maximum value for the RFPAD for unpolarized light and ±55% of the value for linearly polarized light. Chiral sensitivity in vector correlation is a quite general phenomenon arising from one-photon excitation by unpolarized and linearly polarized light, and we expect it to be of great importance in time-resolved spectroscopy of ultrafast chemical reactions. Published by the American Physical Society 2024

Resonance behaviour of magnetoelectric (PSLZT multilayer - NZFO) layered composites: A comprehensive theory – Experimental perspective

In recent years, compact antenna and miniaturized power transfer devices are among the interesting applications of magnetoelectric (ME) composites in low frequency (LF) / very low frequency (VLF) range. Here we elucidate, in general, analytical calculations used to understand, the vibrational modes and resonance frequencies of the layered ME composite and; Finite Element Analyses (FEM) with isotropic and anisotropic properties to accurately predict the resonance frequencies pertaining to the axisymmetric and asymmetric mode of vibrations with respect to significant ME response. Further, ME coefficient of the composite with Longitudinal - Transverse (L-T) configuration based on the interface coupling model were utilized to completely study the ME composites. The configuration optimized through the design was in particular corroborated experimentally with a representative PSLZT multilayer on NZFO based ME layered composite system. The PSLZT multilayer on NZFO based ME composite was fabricated by tape casting the constituent thick films and co-sintering process which are further analysed for their ME responses at their resonance frequencies. ME voltage spectrum showed a maximum of 7.74 V/cm.Oe at its axisymmetric resonance mode at 30.6 kHz. Various peaks at different resonance frequencies with respect to axisymmetric and asymmetric modes of vibrations agree well and validates the above modeling studies. Overall, the complete study provides a systematic design guideline for optimizing the ME composite configuration suitable for specific application with required resonance frequency.

Influence of Mechanical Loading on the Process of Tribochemical Action on Physicochemical and Biopharmaceutical Properties of Substances, Using Lacosamide as an Example: From Micronisation to Mechanical Activation.

Many physical and chemical properties of solids, such as strength, plasticity, dispersibility, solubility and dissolution are determined by defects in the crystal structure. The aim of this work is to study in situ dynamic, dispersion, chemical, biological and surface properties of lacosamide powder after a complete cycle of mechanical loading by laser scattering, electron microscopy, FR-IR and biopharmaceutical approaches. The SLS method demonstrated the spontaneous tendency toward surface-energy reduction due to aggregation during micronisation. DLS analysis showed conformational changes of colloidal particles as supramolecular complexes depending on the loading time on the solid. SEM analysis demonstrated the conglomeration of needle-like lacosamide particles after 60 min of milling time and the transition to a glassy state with isotropy of properties by the end of the tribochemistry cycle. The following dynamic properties of lacosamide were established: elastic and plastic deformation boundaries, region of inhomogeneous deformation and fracture point. The ratio of dissolution-rate constants in water of samples before and after a full cycle of loading was 2.4. The lacosamide sample, which underwent a full cycle of mechanical loading, showed improved kinetics of API release via analysis of dissolution profiles in 0.1 M HCl medium. The observed activation-energy values of the cell-death biosensor process in aqueous solutions of the lacosamide samples before and after the complete tribochemical cycle were 207 kJmol-1 and 145 kJmol-1, respectively. The equilibrium time of dissolution and activation of cell-biosensor death corresponding to 20 min of mechanical loading on a solid was determined. The current study may have important practical significance for the transformation and management of the properties of drug substances in solid form and in solutions and for increasing the strength of drug matrices by pre-strain hardening via structural rearrangements during mechanical loading.

The mechanism for the superior isotropic mechanical properties attained in a cross rolling TiNb alloy

In the present study, the Ti–41Nb (wt.%) alloy featuring a microstructure composed of β and α″ phases have been prepared through the application of the Cross Rolling (CSR) technique to achieve a near-isotropic superior mechanical behavior. The experimental findings revealed that the CSR sample exhibits a uniform β matrix, randomly dispersed α″ martensite and a high density of dislocations and grain boundaries. Subsequent experiments unveiled that the CSR sample displays an almost isotropic mechanical response across three typical directions, Rolling Direction (RD), a 45° deviation from RD, and Transverse Direction (TD), evidenced by comparable stress-strain curve profiles and ultimate tensile strength (UTS) values. Due to the randomly distributed textures and high density of dislocations and grain boundaries, the stress-induced martensitic (SIM) transformation exhibits a similar characteristic in three typical directions, that is, the SIM transformation took place homogeneously and continuously. Consequently, the CSR sample can achieve a near-isotropic and outstanding mechanical performance due to the similar characteristics of martensitic phase transformation and the strengthening effect brought by the high density of dislocations and grain boundaries.

A non-hierarchical multi-layer multi-configurational time-dependent Hartree approach for quantum dynamics on general potential energy surfaces.

The correlation discrete variable representation (CDVR) enables multi-layer multi-configurational time-dependent Hartree (MCTDH) quantum dynamics simulations on general potential energy surfaces. In a recent study [R. Ellerbrock and U. Manthe, J. Chem. Phys. 156, 134107 (2022)], an improved CDVR that can account for the symmetry properties of a tree-shaped wavefunction representation has been introduced. This non-hierarchical CDVR drastically reduces the number of grid points required in the time-dependent quadrature used to evaluate all potential energy matrix elements. While the first studies on the non-hierarchical CDVR approach have been restricted to single-layer calculations, here the complete theory required for the implementation of the non-hierarchical CDVR approach in the multi-layer MCTDH context will be presented. Detailed equations facilitating the efficient recursive computation of all matrix elements are derived, and a new notation adapted to the symmetry properties of the tree-shaped representation is introduced. Calculations studying the non-adiabatic quantum dynamics of photoexcited pyrazine in 24 dimensions illustrate the properties of the non-hierarchical multi-layer CDVR.

BaCu, a Two-Dimensional Electride with Cu Anions.

The electron-rich characteristic and low work function endow electrides with excellent performance in (opto)electronics and catalytic applications; these two features are closely related to the structural topology, constituents, and valence electron concentration of electrides. However, the synthesized electrides, especially two-dimensional (2D) electrides, are limited to specific structural prototypes and anionic p-block elements. Here we synthesize and identify a distinct 2D electride of BaCu with delocalized anionic electrons confined to the interlayer spaces of the BaCu framework. The bonding between Cu and Ba atoms exhibits ionic characteristics, and the adjacent Cu anions form a planar honeycomb structure with metallic Cu-Cu bonding. The negatively charged Cu ions are revealed by the theoretical calculations and experimental X-ray absorption near-edge structure. Physical property measurements reveal that BaCu electride has a high electronic conductivity (ρ = 3.20 μΩ cm) and a low work function (2.5 eV), attributed to the metallic Cu-Cu bonding and delocalized anionic electrons. In contrast to typical ionic 2D electrides with p-block anions, density functional theory calculations find that the orbital hybridization between the delocalized anionic electrons and BaCu framework leads to unique isotropic physical properties, such as mechanical properties, and work function. The freestanding BaCu monolayer with half-metal conductivity exhibits low exfoliation energy (0.84 J/m2) and high mechanical/thermal stability, suggesting the potential to achieve low-dimensional BaCu from the bulk. Our results expand the space for the structure and attributes of 2D electrides, facilitating the discovery and potential application of novel 2D electrides with transition metal anions.

Extremal functions for a fractional Morrey inequality: Symmetry properties and limit at infinity

In a series of articles, Hynd and Seuffert have studied extremal functions for the Morrey inequality. Building upon their work, we study the extremals of a Morrey-type inequality for fractional Sobolev spaces. We verify a few of the results in the spirit of Hynd and Seuffert concerning the symmetry of extremals and their limit at infinity.

Analytic solution for two dimensional beam problems: Pure displacement boundary conditions

The present manuscript delineates the derivation of strong solutions for the linear elasticity problem in a two dimensional rectangular beam. The materials under consideration can exhibit either isotropic or orthotropic properties. Additionally, the analysis is not restricted to slender beams because the ratio between the length and the height of the beam can be arbitrary. The boundary conditions fall into the Dirichlet category, implying that both horizontal and vertical displacements are specified on all four surfaces. The sole requirement is that these surface displacements are continuous functions, although they may not necessarily be smooth. Since the displacements at the surfaces can be arbitrary, there is no need to consider approximations, such as those concerning local (small) boundaries in slender beams. Nonetheless, it is demonstrated that an equivalent principle to the Saint-Venant principle exists for pure displacement boundary conditions. The partial differential equations are solved through the separation of variables method, leading to the identification of two solution types, encompassing both cosine and sine Fourier series. Particular emphasis is placed on evaluating the convergence of these solutions. For two distinct and general examples, it is confirmed that the solutions indeed exist.

Superconducting Diode Effect in a Constricted Nanowire

AbstractDue to isotropic superconducting properties and the lack of breaking of inversion symmetry for conventional s‐wave superconductors, a nonreciprocal superconducting diode effect is absent. Recently, a series of superconducting structures, including superconducting superlattice, and quantum‐material‐based superconducting Josephson junction, have exhibited a superconducting diode effect in terms of polarity‐dependent critical current. However, due to complex structures, these composite systems are not able to construct large‐scale integrated superconducting circuits. Here, it is demonstrated that the minimal superconducting electric component‐superconducting nanowire‐based diode with a nonreciprocal transport effect under a perpendicular magnetic field, in which the superconducting to normal metallic phase transition relies on the polarity and amplitude of the bias current. These nanowire diodes can be reliably operated near at all temperatures below the critical temperature, and the rectification efficiency at 2 K can be more than 24%. Moreover, the superconducting nanowire diode is able to rectify both square wave and sine wave signals. Combining the superconducting nanowire‐based diodes and transistors, superconducting nanowires hold the possibility to construct novel low‐dissipation superconducting integrated circuits.

A Synthesis Approach of XYZ Compliant Parallel Mechanisms Toward Motion Decoupling With Isotropic Property and Simplified Manufacturing

Abstract Decoupled compliant parallel mechanisms with isotropic legs possess many excellent performances, including ease of actuation, control, manufacture and mathematical analysis, as well as effective error compensation. Despite the advent of numerous isotropic compliant parallel mechanisms, their synthesis process predominantly relies on the empirical knowledge of engineers, with an absence of dedicated synthesis methodologies. This paper proposes the constraint algebra method, a novel synthesis method capable of autonomously exploring feasible constraint space for the synthesis. This method involves algebraic formulation of the constraints for the compliant modules, followed by solving constraint equations to find the feasible constraints and orientations, thereby facilitating the synthesis with intended performance characteristics. The multiplicity of solutions to the constraint equations enables the generation of diverse designs, including innovative configurations that are challenging to obtain via other methods and experience. Furthermore, by the consideration of machinability in several steps of synthesis, the optimal configuration can be selected for simplified manufacture. A design case has been monolithically prototyped and experimentally tested. The proposed methodology holds promise for potential extension to the synthesis of other types of compliant mechanisms.

Spatiotemporally distinct responses to mechanical forces shape the developing seed of Arabidopsis

Organ morphogenesis depends on mechanical interactions between cells and tissues. These interactions generate forces that can be sensed by cells and affect key cellular processes. However, how mechanical forces, together with biochemical signals, contribute to the shaping of complex organs is still largely unclear. We address this question using the seed of Arabidopsis as a model system. We show that seeds first experience a phase of rapid anisotropic growth that is dependent on the response of cortical microtubule (CMT) to forces, which guide cellulose deposition according to shape-driven stresses in the outermost layer of the seed coat. However, at later stages of development, we show that seed growth is isotropic and depends on the properties of an inner layer of the seed coat that stiffens its walls in response to tension but has isotropic material properties. Finally, we show that the transition from anisotropic to isotropic growth is due to the dampening of cortical microtubule responses to shape-driven stresses. Altogether, our work supports a model in which spatiotemporally distinct mechanical responses control the shape of developing seeds in Arabidopsis.

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

The Effect of Implant Length and Bone Quality on the Biomechanical Responses of Dental Implant and Surrounding Bone – A Three-Dimensional Finite Element Analysis

The robustness of dental implant systems in the context of occlusal restoration relies significantly on biomechanical factors associated with the imposition of excessive loads. These factors encompass the macro geometries of the implants, bone qualities, parafunctional oral habits, and specific materials employed. The choice of different implant lengths in different bone qualities may give rise to distinct effects on the way loads are distributed across the interface between the implant and the adjacent bone. As of now, the influence of implant length and bone quality on the surrounding tissues and the stability of implant structure continues to be a matter of debate and uncertainty, particularly in situations involving the possibility of implant failure. This study employed three-dimensional finite element analysis to investigate five distinct implant lengths (4, 6, 10, 13, and 15 mm) in two types of bone quality (type II and III). The bone tissues were characterized through the utilization of computed tomography image datasets and then underwent processing within the SolidWorks software. All geometric configurations were transformed into finite element models, which were subjected to analysis within the ANSYS software. Anisotropic and isotropic properties were attributed to the bone and implant models, respectively. A dynamic occlusal loading quantified at 300 N was applied to the implant body, accompanied by a pre-tension force of 20 N on the screw component. The longer implants exhibited decreased stress magnitudes in type II bone (87.86 – 36.66 MPa) and increased stress magnitudes in type III bone (80.5 – 2128.9 MPa) within the surrounding bone tissue, in comparison to the shorter implants. However, stress within the implant body was generally elevated with the use of longer implants in both bone types (type II: 505.32 – 625.35 MPa; type III: 500.45 – 2186.7 MPa). Irrespective of bone quality, the longer implants predominantly led to lower bone strain levels (type II: 0.006828 – 0.003328; type III: 0.054250 – 0.021678) and overall deformation of the implant-abutment assembly (type II: 0.1458 – 0.1348 μm; type III: 0.1754 – 0.1492 μm) compared to their shorter counterparts. Among all the assessed findings, type III bone displayed a more pronounced adverse impact on the biomechanical responses of the dental implant and neighbouring bone except for the implant stresses under the applied physiological loading.

From cavitation to astrophysics: Explicit solution of the spherical collapse equation.

Differential equationsof the form R[over ̈]=-kR^{γ}, with a positive constant k and real parameter γ, are fundamental in describing phenomena such as the spherical gravitational collapse (γ=-2), the implosion of cavitation bubbles (γ=-4), and the orbital decay in binary black holes (γ=-7). While explicit elemental solutions exist for select integer values of γ, more comprehensive solutions encompassing larger subsets of γ have been independently developed in hydrostatics (see Lane-Emden equation) and hydrodynamics (see Rayleigh-Plesset equation). I here present a universal explicit solution for all real γ, invoking the beta distribution. Although standard numerical ordinary differential equationsolvers can readily evaluate more general second-order differential equations, this explicit solution reveals a hidden connection between collapse motions and probability theory that enables further analytical manipulations, it conceptually unifies distinct fields, and it offers insights into symmetry properties, thereby enhancing our understanding of these pervasive differential equations.

Advanced Excitation Symmetry Analysis Method (ESAM) for improved automated ultrasonic testing of polished materials

One of the strategic plans of the international NDT community is to define standards for developing advanced and digitalized non-destructive testing for automated set-up in mass production [1,2]. Excitation Symmetry Analysis Method (ESAM) are new coded signal processing tools exploring symmetry properties [3]. ESAM method aims to extract the nonlinearity from an ultrasound output by studying the property of symmetry of the transfer function. More precisely, the extraction of nonlinearity is done using basis function associated to a group which is associated to an a priori transfer function. As soon as the linear tomography uses the invariant properties of amplitude dependence, nonlinear tomography should exploit the invariance properties (or symmetry properties) of the complex system. Consequently, the invariance of the stationary properties of a complex medium would be supposed to be associated to a signature of the degradation, that will be extracted with advanced signal processing tools. The idea remains the same: studying the symmetry and more precisely the time reversal one and the inversion. A signal processing is used to measure discrepancies in the autocorrelation function (output signal called chirp coda) for two inputs: a signal and its inversion (pulse inversion). The experiments were done on different sample with and without cracks. It has been shown that when the nonlinearities are extracted from the chirp coda amplitude are non- negligible in crack area and nonlinearities are out of phase. Then, mixing symmetries like time reversal and pulse inversion enable the detection of defect that are difficult to detect with conventional ultrasound method. Indeed, for such crack a destructive mechanical analysis called Jomini is done where the material is polished and examined with microscope. The sensitivity improvement of chirp-coded signal processing has been validated in various domains. Coded excitation techniques, used in communication systems such as radar and sonar provide improved SNR without increasing the amplitude of excitation. The typical test equipment consists of a preamplifier Juvitek TRA-02 (0.02 - 5 MHz) connected to a computer, an amplifier ENI model A150 (55 dB at 0.3-35 MHz), a shear wave transducer Technisonic (2.25 MHz), and a longitudinal wave transducer Panametrics V155 (5 MHz). The experimental device was tested with the V3 calibration block, improved, and specially scaled in order to access to a wide range of multivalued parameters: mechanical properties, ultrasonic parameters (celerity and attenuation) and local geometric data.