Symmetric Point Research Articles

Size-dependent fracture analysis of Centrally-Cracked nanobeam using Stress-Driven Two-Phase Local/Nonlocal integral model with discontinuity and symmetrical conditions

A novel mathematical formulation is presented to deal with stress-driven two-phase local/nonlocal integral model (SD-TPNIM) with discontinuity and symmetrical conditions, which is transformed equivalently into the differential form together with four constitutive constraints. Compare with classic SD-TPNIM, two extra constitutive continuity conditions are introduced, and a few integral items are introduced to constitutive discontinuity conditions and constitutive boundary conditions at symmetrical point. SD-TPNIM with symmetrical or anti-symmetrical conditions is applied to formulate the size-dependent fracture behavior of simply-supported and clamped–clamped centrally-cracked nanobeams subjected to uniformly distributed load (UDL) or middle point force (MPF) along opposite (Mode I crack) or same (Mode II crack) directions. The bending deflections are deduced and expressed in explicit form for different boundary and loading conditions. Accordingly, one can calculate the work done by external loads and energy release rate for both mode I and II crack problems. In addition, the asymptotic solutions for energy release rate are deduced for small nonlocal length parameter. The influence of nonlocal parameters on the size-dependent fracture behaviors including external work and energy release rate as well as the accuracy of asymptotic solutions for energy release rate is investigated numerically. The size-dependent fracture behavior can explain the superior fracture performance of nanomaterial to some extent.

Moments and power corrections of longitudinal and transverse proton structure functions from lattice QCD

We present a simultaneous extraction of the moments of ${F}_{2}$ and ${F}_{L}$ structure functions of the proton for a range of photon virtuality, ${Q}^{2}$. This is achieved by computing the forward Compton amplitude on the lattice utilizing the second-order Feynman-Hellmann theorem. Our calculations are performed on configurations with two different lattice spacings and volumes, all at the $SU(3)$ symmetric point. We find the moments of ${F}_{2}$ and ${F}_{L}$ in good agreement with experiment. Power corrections turn out to be significant. This is the first time the ${Q}^{2}$ dependence of the lowest moment of ${F}_{2}$ has been quantified.

Worldsheet computation of heavy-light correlators

We compute a large collection of string worldsheet correlators describing light probes interacting with heavy black hole microstates. The heavy states consist of NS5 branes carrying momentum and/or fundamental string charge. In the fivebrane decoupling limit, worldsheet string theory on a family of such backgrounds is given by exactly solvable null-gauged WZW models. We construct physical vertex operators in these cosets, including all massless fluctuations. We compute a large class of novel heavy-light-light-heavy correlators in the AdS3 limit, where the light operators include those dual to chiral primaries of the holographically dual CFT. We compare a subset of these correlators to the holographic CFT at the symmetric product orbifold point, and find precise agreement in all cases, including for light operators in twisted sectors of the orbifold CFT. The agreement is highly non-trivial, and includes amplitudes that describe the analogue of Hawking radiation for these microstates. We further derive a formula for worldsheet correlators consisting of n light insertions on these backgrounds, and discuss which subset of these correlators are likely to be protected. As a test, we compute a heavy-light five-point function, obtaining precisely the same result both from the worldsheet and the symmetric orbifold CFT. This paper is a companion to and extension of [1].

Critical phenomena around the SU(3) symmetric tricritical point of a spin-1 chain

We investigate critical phenomena of a spin-1 chain in the vicinity of the SU(3) symmetric critical point, which we already specified in a previous study [Mashiko and Nomura, Phys. Rev. B 104, 155405 (2021)]. We numerically diagonalize a Hamiltonian combining the bilinear-biquadratic Hamiltonian with the trimer Hamiltonian. We then discuss the numerical results based on the conformal field theory and the renormalization group. As a result, we first verify that the critical point found in our previous study is the tricritical point among the Haldane phase, the trimer phase, and the the trimer-liquid (TL) phase. Second, with regard to the TL-trimer transition and the TL-Haldane transition, we find that the critical phenomena around this tricritical point belong to the Berezinskii-Kosterlitz-Thouless-like universality class. Third, we find the boundary between the Haldane phase and the trimer phase, which is illustrated by the massive self-dual sine-Gordon model.

First Principles Computation of New Topological B2X2Zn (X = Ir, Rh, Co) Compounds

Recent attempts at searching for new materials have revealed a large class of materials that show topological behaviors with unusual physical properties and potential applications leading to enthralling discoveries both theoretically and experimentally. We computationally predict new three-dimensional topological compounds of space group 139(I/4mmm). After conducting a full volume optimization process by allowing the rearrangement of atomic positions and lattice parameters, the first-principles calculation with a generalized gradient approximation is utilized to identify multiple Dirac-type crossings around X and P symmetric points near Fermi energy. Importantly, the band inversion at point P is recognized. Further, we investigate the compound for topological crystalline insulating behavior by conducting surface state calculation and by investigating gapping behavior by increasing lattice parameters. Additionally, we perform formation energy, elastic properties, and phonon modes calculations to verify the structural, mechanical, and dynamical stability of the compounds. Therefore, we suggest compounds for further investigation and experimental realization.

A grasp planning algorithm under uneven contact point distribution scenario for space non-cooperative target capture

The contact point configuration should be carefully chosen to ensure a stable capture, especially for the non-cooperative target capture mission using multi-armed spacecraft. In this work scenario, the contact points on the base and on the arms are distributed on the opposite side of the target. Otherwise, large forces will be needed. To cope with this problem, an uneven-oriented distribution union criterion is proposed. The union criterion contains a virtual symmetrical criterion and a geometry criterion. The virtual symmetrical contact point criterion is derived from the proof of the force closure principle using computational geometry to ensure a stable grasp, and the geometry criterion is calculated by the volume of the minimum polyhedron formed by the contact points to get a wide-range distribution. To further accelerate the optimization rate and enhance the global search ability, a line array modeling method and a continuous-discrete global search algorithm are proposed. The line array modeling method reduces the workload of calculating the descent direction and the gradient available, while the continuous-discrete global search algorithm reducing the optimization dimension. Then a highly efficient grasping is achieved and the corresponding contact point is calculated. Finally, an exhaustive verification is conducted to numerically analyze the disturbance resistance ability, and simulation results demonstrate the effectiveness of the proposed algorithms.

Complete classification on center of cubic planar systems symmetric with respect to a straight line

In this paper, we study bi-center and bi-isochronous center problems in cubic planar systems which are symmetric with respect to a straight line. These systems can be transformed to ones which are symmetric with respect to the y-axis and have two symmetric singular points at (±1,0), which can be classified as elementary and nilpotent singular points. A complete classification is given on the centers, including nine conditions for elementary singular points and four conditions for nilpotent singular points. Moreover, seven bi-isochronous center conditions are obtained for the elementary singular points.

Self-Assembly of Glycerol-Amphiphilic Janus Dendrimers Amplifies and Indicates Principles for the Selection of Stereochemistry by Biological Membranes.

The principles for the selection of the stereochemistry of phospholipids of biological membranes remain unclear and continue to be debated. Therefore, any new experiments on this topic may help progress in this field. To address this question, three libraries of constitutional isomeric glycerol-amphiphilic Janus dendrimers (JDs) with nonsymmetric homochiral, racemic, and symmetric achiral branching points were synthesized by an orthogonal-modular-convergent methodology. These JDs amplify self-assembly, and therefore, monodisperse vesicles known as dendrimersomes (DSs) with predictable dimensions programmed by JD concentration were assembled by rapid injection of their ethanol solution into water. DSs of homochiral JD enantiomers, racemic, including mixtures of different enantiomers, and achiral exhibited similar DS size-concentration dependence. However, the number of bilayers of DSs assembled from homochiral, achiral, and racemic JDs determined by cryo-TEM were different. Statistical analysis of the number of bilayers and coarse-grained molecular dynamics simulations demonstrated that homochiral JDs formed predominantly unilamellar DSs. Symmetric achiral JDs assembled only unilamellar DSs while racemic JDs favored multilamellar DSs. Since cell membranes are unilamellar, these results indicate a new rationale for nonsymmetric homochiral vs racemic selection. Simultaneously, these experiments imply that the symmetric achiral lipids forming more stable membrane, probably had been the preferable assemblies of prebiotic cell membranes.

Certain subclasses of $$\lambda $$-pseudo bi-univalent functions with respect to symmetric points associated with the Gegenbauer polynomial

Certain subclasses of $$\lambda $$-pseudo bi-univalent functions with respect to symmetric points associated with the Gegenbauer polynomial

Spectral flow and string correlators in AdS3× S3× T4

We consider three-point correlation functions for superstrings propagating in AdS3 × S3 × T4. In the RNS formalism, these generically involve correlators with current insertions. When vertex operators with non-trivial spectral flow charges are present, their complicated OPEs with the currents imply that standard methods can not be used to compute such correlators. Here we develop techniques for computing all m-basis correlators of the supersymmetric model. We then show how, in some cases, these results can be translated to the x-basis. We obtain a new family of holographic three-point functions involving spacetime chiral primaries living in spectrally flowed sectors of the worldsheet CFT. These match precisely the predictions from the holographic dual at the symmetric product orbifold point. Finally, we also consider long strings and compute the probability amplitude associated with the process describing the emission/absorption of fundamental string quanta.

On the Second Hankel Determinant of Logarithmic Coefficients for Certain Univalent Functions

In this paper, we investigate the sharp bounds of the second Hankel determinant of Logarithmic coefficients for the starlike and convex functions with respect to symmetric points in the open unit disk.

Some properties of a new subclass of tilted star-like functions with respect to symmetric conjugate points

<abstract><p>In this paper, we introduced a new subclass $ S_{SC}^*\left({\alpha, \delta, A, B} \right) $ of tilted star-like functions with respect to symmetric conjugate points in an open unit disk and obtained some of its basic properties. The estimation of the Taylor-Maclaurin coefficients, the Hankel determinant, Fekete-Szegö inequality, and distortion and growth bounds for functions in this new subclass were investigated. A number of new or known results were presented to follow upon specializing in the parameters involved in our main results.</p></abstract>

Probing the physical properties of M2LiCeF6 (M = Rb and Cs) double perovskite compounds for prospective high-energy applications employing the DFT framework.

Herein, the optoelectronic, structural, thermoelectric, and elastic characteristics of M2LiCeF6 (M = Rb and Cs) double perovskite compounds were investigated using ab initio modeling in the DFT framework. The Birch-Murnaghan fitting curve used for the optimization showed that these two compounds are structurally stable. The elastic properties of the M2LiCeF6 (M = Rb and Cs) double perovskite compounds were examined using the IRelast code. The results showed that these two compounds possess mechanical stability, anisotropy, and toughness, and offer resistance to plastic deformation. The precise and accurate determination of their electronic properties was achieved via the Trans-Blaha-modified Becke-Johnson (TB-mBJ) approximation. The Rb2LiCeF6 and Cs2LiCeF6 compounds are narrow band gap semiconductors with band gaps of 0.6 eV and 0.8 eV at the high symmetrical points from (Γ-M), respectively, exhibiting an indirect nature. To further understand how the various states contribute to the different band structures, total and partial density of state (DOS) computations were performed. The optical properties in the energy range of 0-40 eV for Rb2LiCeF6 and Cs2LiCeF6 were explored. The selected materials show transparency in the low incident photon energy range and have large light absorption and transmission at higher photon energies. Thus, it can be concluded that Rb2LiCeF6 and Cs2LiCeF6 can be used in high-frequency UV devices based on their optical characteristics. Both materials exhibit high electrical conductivity, power factors, and figures of merit (ZT) and act as effective thermoelectric resources. To the best of our knowledge, this is the first theoretical research on the optoelectronic, structural, thermoelectric, and elastic features of M2LiCeF6 (M = Rb and Cs).

Study of the structural and electronic properties of semimetallic InBi: first-principles calculation of compound with peculiarities of the electronic structure

The electronic properties as well as the structural characteristics and their pressure dependence of the semi-metallic B10-structured compound InBi were investigated. It is found that the structural values of InBi calculated in the first-principles calculations reproduce the experimental values worse than those for other heavy III-V pnictides, which are characterized by cubic B3 and B2 structures, as well as for IV-VI compounds SnO and PbO having the same B10 structure. The low accuracy of the first-principles calculations is a consequence of the peculiarities of the band structure inherent to InBi and not observed in all the other above-mentioned compounds. To improve the agreement with the experiment, it is proposed to take into account the distortion of the compensated half-metal condition at the highly symmetric points of the Brillouin zone, where the electronic and hole pockets are located.

METHOD OF DESIGNING ANTENNAS BY SYNTHESIS OF A BAND FILTER

A novel antenna design technique is proposed, which offers bandwidth enhancement up to the limits defined by element radiation efficiency. The employed technique is referred as frequency pulling (FP) as it mimics the insertion loss design methodology of bandpass filters. This is essentially a wideband matching approach pushing the antenna efficiency to the limits set up by radiation efficiency. There are three options towards this trend: (1) first to enhance a single element bandwidth (compact element) exploiting its possibly multiple symmetrical feeding points as distinct resonator ports, (2) frequency pulled array as to design a small antenna array (less than about 10 elements) where eachelement acts as a resonator and (3) second order frequency-pulled array as to build a small array using compact elements of category (1). Similar to the band-pass filter design, all antennas or distinct-port circuits resonate at the same resonant frequency when isolated, cascading two or more of them; FP yields to multiple-overlapping successive resonances in their overall response. Although the proposed technique is general within this first effort, it is applied to simple patch antenna elements exhibiting multiple symmetrical feeding points, namely two-for rectangular, four-for square and five-for pentagonal. The third option is applied to an array of three compact 4-feeding point square elements offering triple bandwidth with respect to the already wideband single element. However, this is achieved at the expense of a significant beam squint. Thus, in general, these wideband compact elements should be used within a classical array design. Further bandwidth enhancement using FP to antenna elements with inherent multiple resonances as patches with slots or truncated edges constitutes our next task. Their inherent wider bandwidth in radiation efficiency is expected to allow multiply higher bandwidths when exploited with our FP technique.

A Generalized Bohr–Rogosinski Phenomenon

In this paper, we study a generalized Bohr–Rogosinski sum for the Ma-Minda classes of starlike and convex functions. The phenomenon is also explored for the classes of starlike functions with respect to symmetric and conjugate points along with their convex cases. Further, the connection between the derived results and the known ones are established with the suitable examples.

Upper bound to second Hankel determinant for a family of bi-univalent functions

In the current investigation, we study a certain family of analytic and bi-univalent functions with respect to symmetric conjugate points defined in the open unit disk $U$ and find an upper bounds for the second Hankel determinant $H_{2}(2)$ of the functions belongs to this class.

Quark and lepton flavor structure in magnetized orbifold models at residual modular symmetric points

We study quark and lepton mass matrices derived from magnetized $T^2/\mathbb{Z}_2$ orbifold models. Quark and lepton masses have a large hierarchy. In addition, mixing angles are large in the lepton sector, while those are small in the quark sector. We find that this structure can be realized in certain flavor models, which are identified by the zero points of the zero-mode wave functions of fermions and Higgs modes. We classify such realistic flavor models. Fixed points $\tau=i$, $e^{2\pi i/3}$ and $i\infty$ of the modulus $\tau$ play a role in realizing a large mass hierarchy through our scenario, where residual $S$, $ST$, and $T$ symmetries remain and the lightest Higgs modes can correspond to eigenstates of residual symmetries at the leading order. As a result, we find that there are 24 flavor models in total which can be realistic in a vicinity of $S$-symmetric vacuum but no flavor models for $ST$ and $T$-symmetric vacua.

Lithium-ion insertion properties of one-dimensional layered rhenium phosphide

Metal phosphides have aroused great interest among the electrochemical community due to their stunning performance, including good electrical conductivity, high theoretical capacity, and considerable cycling stability. In this work, we synthesized and utilized Re6P13 for the first time as a promising anode material for lithium-ion batteries (LIBs). High-purity Re6P13 needle-like crystals were successfully grown by a chemical vapor transport method. Surface modification of Re6P13 by conductive carbon results in Re6P13 @C composite electrode, exhibiting a high specific capacity of 1265 mAh g−1 at 0.1 A g−1. The calculated band structure of Re6P13 reveals a highly symmetric point path that is beneficial for achieving high electrical conductivity and good structural flexibility. These features further empower the Re6P13 @C composite anodes with good cycling life (775 mAh g−1 at 1 A g−1 after 100 cycles) and rate performance (558 mAh g−1 at 20 A g−1). This work suggests that Re6P13 compounds with needle-like structures are promising anode materials for LIBs.

Deformation and Simulation of the Cellular Structure of Foamed Polypropylene Composites.

Foamed Polymer is an important polymer material, which is one of the most widely used polymer materials and plays a very important role in the polymer industry. In this work, foamed polypropylene (PP) composites are prepared by injection molding, and the cell deformation process within them is studied by combining visualization technology and COMSOL software simulation. The results shows that the deformation of isolated cells depends in temperature, and there is no macroscopic deformation. There was no significant difference between the stress around adjacent cells at different temperatures, but the stress at different positions around the adjacent cells has obvious changes, and the maximum stress at the center of the adjacent cells was 224.18 N·m-2, which was easy to cause a lateral deformation of the cells. With the increase in temperature, the displacement around the adjacent cell gradually increased, the maximum displacement of the upper and lower symmetrical points of the cell was 14.62 μm, which is most likely to cause longitudinal deformation of the cell; the deviation of the cell deformation parameter gradually increased, which led to deformation during the growth of the cell easily. The simulation results were consistent with the visualized cell deformation behaviors of the foamed PP composites.