Symmetric Point Research Articles

Charge density waves in monolayer and few-layer NbS2 and phase modulation by doping, thickness, and temperature

By carrying out first-principles calculations, we studied the charge density waves (CDWs) in monolayer/few-layer $H\text{\ensuremath{-}}{\mathrm{NbS}}_{2}$. For monolayer ${\mathrm{NbS}}_{2}$, unstable phonon modes are found to develop at the $2/3\mathrm{\ensuremath{\Gamma}}\mathrm{M}$ point and its symmetric points in the whole Brillouin zone. By displacing the atoms along the unstable mode, a new dynamically stable $3\ifmmode\times\else\texttimes\fi{}3$ structure with lower total energy is obtained, which corresponds well to the experimentally observed $3\ifmmode\times\else\texttimes\fi{}3$ CDW phase. The symmetries are broken in the $3\ifmmode\times\else\texttimes\fi{}3$ CDW phase, leading to gap opening and anisotropic properties. The $3\ifmmode\times\else\texttimes\fi{}3$ CDW phase of ${\mathrm{NbS}}_{2}$ is found to be stable with respect to small strains. In comparison with ${\mathrm{NbSe}}_{2}$, it is found that the Se atoms are much more active in vibration than the S atoms, resulting in the different CDW behaviors in these two very similar materials. We explored the CDW phase tuning by electron doping, and a sequence of CDW phase transitions from $3\ifmmode\times\else\texttimes\fi{}3$ to $2\ifmmode\times\else\texttimes\fi{}2$ and to $4\ensuremath{\surd}3\ifmmode\times\else\texttimes\fi{}4\ensuremath{\surd}3$ is found. The doping-dependent CDW phase provides insight into the inconsistent observation of CDW phases in ${\mathrm{NbS}}_{2}$/graphene and ${\mathrm{NbS}}_{2}$/Au(111) based on the difference in substrate charge doping. We further investigated the CDW phases of the bilayer and trilayer ${\mathrm{NbS}}_{2}$. With the decrease of the temperature, a series of instabilities occur in the phonon spectrum of bilayer ${\mathrm{NbS}}_{2}$, which correspond to $2\ifmmode\times\else\texttimes\fi{}2, 3\ifmmode\times\else\texttimes\fi{}3$, and $4\ifmmode\times\else\texttimes\fi{}4$ CDW phases. For trilayer ${\mathrm{NbS}}_{2}$, in contrast, only a $2\ifmmode\times\else\texttimes\fi{}2$ CDW phase is found, whereas the $3\ifmmode\times\else\texttimes\fi{}3$ CDW phase, which exists in monolayer and bilayer, is not manifested even at ultralow temperature. The layer-dependent CDW phases indicate significant effects of interlayer interactions.

On the Binary Adder Channel With Complete Feedback, With an Application to Quantitative Group Testing

We determine the exact value of the optimal symmetric rate point (r, r) in the Dueck zero-error capacity region of the binary adder channel with complete feedback. We proved that the average zero-error capacity r = h(1/2-δ) ≈ 0.78974, where h(∙) is the binary entropy function and δ = 1/(2 log2(2 + √3)). Our motivation is a problem in quantitative group testing. Given a set of n elements two of which are defective, the quantitative group testing problem asks for the identification of these two defectives through a series of tests. Each test gives the number of defectives contained in the tested subset, and the outcomes of previous tests are assumed known at the time of designing the current test. We establish that the minimum number of tests is asymptotic to (log2 n)/r as n → ∞.

Elastic anisotropy in the reduced Landau-de Gennes model.

We study the effects of elastic anisotropy on Landau–de Gennes critical points, for nematic liquid crystals, on a square domain. The elastic anisotropy is captured by a parameter, , and the critical points are described by 3 d.f. We analytically construct a symmetric critical point for all admissible values of , which is necessarily globally stable for small domains, i.e. when the square edge length, , is small enough. We perform asymptotic analyses and numerical studies to discover at least five classes of these symmetric critical points—the , , and solutions, of which the , and solutions can be stable. Furthermore, we demonstrate that the novel solution is energetically preferable for large and large , and prove associated stability results that corroborate the stabilizing effects of for reduced Landau–de Gennes critical points. We complement our analysis with numerically computed bifurcation diagrams for different values of , which illustrate the interplay of elastic anisotropy and geometry for nematic solution landscapes, at low temperatures.

Conical $3$-uniform measures: A family of new examples and characterizations

28A33, 49Q15. Uniform measures have played a fundamental role in geometric measure theory since they naturally appear as tangent objects. For instance, they were essential in the groundbreaking work of Preiss on the rectifiability of Radon measures. However, relatively little is understood about the structure of general uniform measures. Indeed, the question of whether there exist any non-flat uniform measures beside the one supported on the Kowalski–Preiss cone has been open for 30 years, ever since Kowalski and Preiss classified $n$‑uniform measures in $\mathbb{R}^{n+1}$. In this paper, we answer the question and construct an infinite family of $3$‑uniform measures in arbitrary codimension. We define a notion of distance symmetry for points and prove that every collection of $2$‑spheres whose centers are distance symmetric gives rise to a $3$‑uniform measure. We then develop a combinatorial method to systematically produce distance symmetric points. We also classify conical $3$‑uniform measures in $\mathbb{R}^5$ by proving that they all arise from distance symmetric spheres.

Complete classification of band nodal structures and massless excitations

Nodal structures (NSrs) where energy bands meet to be degenerate in the Brillouin zone (BZ) in the form of point, line or surface, received immense research interest in the past decade. However, the nearly NSrs with negligible gaps, can also own many exotic quantum responses and nontrivial topological properties and deserve a systematic investigation. Here, we provide a complete list of all symmetry-diagonalizable strictly and nearly NSrs in the 1651 magnetic space groups (MSGs) and 528 magnetic layer groups (MLGs) in both spinful and spinless settings. We first apply compatibility relations (CRs) which encode how bands split from a band node (BN) (located at a symmetric point of BZ), to obtain all NSrs (emanating from the BN). The NSrs by CRs are definitely strict and are exhaustively enumerated based on all irreducible representations of the little groups for all BNs. We then construct $k\cdot p$ models around BNs and prove that there is a cutoff $k\cdot p$ order (6 at most) for any BN which is sufficient to predict the corresponding strictly NSrs and including higher-order $k\cdot p$ terms cannot gap the NSrs. We provide all $k\cdot p$ models up to the cutoff orders around all the BNs, and comprehensively explore all the nearly NSrs by lowering the $k\cdot p$ order. Our results reveal that the same as BNs, the NSrs, especially the nearly NSrs, are also ubiquitous. For example, while strictly nodal surface can only exist in some nonsymmorphic MSGs, nearly nodal surface can occur even in many low symmetric MSGs. Moreover, we also find that for some BNs, the method of $k\cdot p$ modeling could give more strictly NSrs than CRs. With our complete list, one can conveniently obtain all possible NSrs for any two/three-dimensional and nonmagnetic/magnetic material, and given a target NSr, one can also design/search for materials realizations based on the MSGs/MLGs.

Numerical study on the effect of bifurcation vessel parameters on microwave ablation of lung tissue

ABSTRACT Background: In order to study the effect of bifurcation vessels parameters on the temperature field and coagulation zone of microwave ablation on lung tissue. Methods: The finite element method was used to establish the simulation model. The angle of bifurcation vessel model was 60°. The position of the antenna and the main blood vessel are parallel, and the distance between them was 5, 10 and 15 mm, respectively. Temperature field distribution was obtained at 2450 MHz, 50 W and 300 s. The blood flow velocity was set to 0.1 and 0.2 m/s. Results: The results showed when the antenna was 5 mm away from the bifurcation vessel and the velocity was 0.1 m/s, the position of x = 8.4 mm achieved the complete necrosis at 220 s, while the fraction of necrotic tissue at the symmetry point x = 1.6 mm was 0.2 at 300 s. For the distance was 10 mm and the velocity was 0.1 m/s, the fraction of necrotic tissue at x = 3 mm that near the bifurcation vessel was 0.53 and was 0.69 at the symmetry point x = 17 mm. When the antenna is 15 mm away from the vessel, the fraction of necrotic tissue of symmetrical points on both sides of the antenna obtained after ablation were the same. Conclusions: The distance between the antenna and the bifurcation vessel over 15 mm, the blood flow has no effect on the coagulation zone. Besides, the distance between bifurcation vessel and antenna possesses a greater influence on the temperature distribution and coagulation zone than the blood flow velocity.

Curtain-type phase unwrapping algorithm

A curtain-type phase unwrapping algorithm is proposed. First, the 2 × 2 closed curve method is used to find out the residual point of the wrapped phase to form the residual template, and the Otsu threshold method is used to binary the modulation of the deformed pattern to form the shadow template. Second, the effective phases of up-down symmetrical points about the starting point are simultaneously unwrapped in turn until all the points in the column are completed. Third, the starting point is taken as the center of left-right symmetry, the effective phases of the nearest symmetric points are simultaneously unwrapped, and the corresponding columns are unwrapped in the same way as above. Fourth, in this way, the effective phases in the corresponding symmetric columns are successively unwrapped in the form of curtain opening until the whole phases are completely unwrapped. In the previous procedure, the shadow template and residual template guide the curtain-type phase unwrapping to avoid error diffusion. Finally, the 8-neighborhood mean algorithm and the cubic b-spline algorithm are employed to unwrap the phase values of residual points and shadow areas, respectively. The proposed method realizes the whole phase unwrapping without phase error diffusion. Experimental results show that the efficiency of the proposed method is 26% higher than that of the diamond algorithm, and its accuracy is significantly improved.

A novel fast and low-cost masonry monitoring strategy and application on arches

Abstract This work proposes a novel non-destructive, vision-based measurement strategy to identify and quantify mechanical deformations between rigid blocks. First the possible motions between two rigid blocks were identified and measured, under the application of a perpendicular, parallel and symmetrical 4x4 point grid around the masonry joint line. Repeated calculations of lengths, dot products, and right triangles improved the precision of measurements through redundancy. Then, this method was verified via photographic images with defined deformation and 2D holography, showing good adaptability and precision. Finally, this strategy was performed to a video recording of an arch under tilting test until failure. With the dimensions of the points grid being the only known parameter, the mechanical joint, the type of rigid block motion, the failure point and the rotation angle were successfully determined.

Topological nodal line semimetal in an all-sp 2 monoclinic carbon

Topological nodal line semimetal is an exotic class of quantum materials featuring the continuous line of nodes inside the first Brillouin zone. Here we identify by systematical ab initio calculations a new all-sp 2 hybridized carbon allotrope with monoclinic C2/c symmetry which is termed as bcm-C16. Total energy calculations show that our proposed bcm-C16 carbon is energetically comparable to or stable than the previously proposed bco-C16, bct-C16, and oP16 carbon. Its dynamical stability has been confirmed by phonon mode calculations. Detailed analysis of the electronic properties show that bcm-C16 carbon is a topological nodal line semimetal with a single closed nodal ring around the Γ high symmetric point, protected by spatial inversion and time-reversal symmetry. When the nodal ring is projected onto the (001) surface, a topologically protected drumhead-like surface state can be seen inside or outside the nodal ring depending on the different surface terminations. Moreover, we also examined the tensile-strain robustness of the electronic properties of bcm-C16 carbon. The nodal ring is robust under a tensile-strain along the crystalline x- and z-directions up to 20%. In addition, the simulated x-ray diffraction pattern (XRD) of bcm-C16 carbon matches with the experimental pattern found in the detonation and chimney soot experiment. The present proposal has enriched the family of carbon allotropes with topological nodal lines, and pave the way for further theoretical and experimental studies.

Quasi-Hadamard Product and Partial Sums for Sakaguchi-Type Function Classes Involving q-Difference Operator

We create two Sakaguchi-type function classes that are starlike and convex with respect to their symmetric points, including a q-difference operator, which may have symmetric or assymetric properties, in the open unit disc. We first obtain sufficient coefficient bounds for these functions. In view of these bounds, we obtain quasi-Hadamard products and several partial sums for these function classes. Moreover, the special values of the parameters provided the corresponding consequences of the partial sums.

Skyrmion pinning by disk-shaped defects

High precision skyrmion pinning by an intentionally created magnetic structure is important in skyrmion manipulation. Here, we consider skyrmion pinning by various types of disks. Among other findings, we clarify that, in terms of pinning position and pinning potential landscape, one needs to distinguish thin-wall skyrmions from thick-wall skyrmions because of fundamental differences. A skyrmion wall prefers areas with a weaker exchange stiffness, a larger DMI constant, or a smaller magnetic anisotropy while a skyrmion core experiences only the magnetic anisotropy, not exchange stiffness and DMI. Depending on disk type, skyrmion type, and the relative size of the disk (to skyrmion), a skyrmion can be pinned at the symmetric (center) or asymmetric (off-center) point of a disk. In case a skyrmion is pinned by a local energy minimum, thermal agitation can depin the skyrmion, and the pinning lifetime follows an Arrhenius law. Interestingly, when the disk size is comparable to the skyrmion size, the skyrmion deforms greatly such that the skyrmion will shrink or expand to fill the whole disk. These findings should be important for skyrmion manipulations.

Nonlocal Correlation and Entanglement of Ultracold Bosons in the 2D Bose–Hubbard Lattice at Finite Temperature

AbstractThe temperature‐dependent behavior emerging in the vicinity of the superfluid (SF) to Mott‐insulator (MI) transition of interacting bosons in a 2D optical lattice, described by the Bose–Hubbard model is investigated. The equilibrium phase diagram at finite‐temperature is computed using the cluster mean‐field (CMF) theory including a finite‐cluster‐size‐scaling. The SF, MI, and normal fluid (NF) phases are characterized as well as the transition or crossover temperatures between them are estimated by computing physical quantities such as the superfluid fraction, compressibility and sound velocity using the CMF method. It is found that the nonlocal correlations included in a finite cluster, when extrapolated to infinite size, leads to quantitative agreement of the phase boundaries with quantum Monte Carlo (QMC) results as well as with experiments. Moreover, it is shown that the von Neumann entanglement entropy within a cluster corresponds to the system's entropy density and that it is enhanced near the SF–MI quantum critical point (QCP) and at the SF–NF boundary. The behavior of the transition lines near this QCP, at and away from the particle‐hole (p–h) symmetric point located at the Mott‐tip, is also discussed. The results obtained by using the CMF theory can be tested experimentally using the quantum gas microscopy method.

TMDs as a platform for spin liquid physics: A strong coupling study of twisted bilayer WSe2

The advent of twisted moiré heterostructures as a playground for strongly correlated electron physics has led to a plethora of experimental and theoretical efforts seeking to unravel the nature of the emergent superconducting and insulating states. Among these layered compositions of two-dimensional materials, transition metal dichalcogenides are now appreciated as highly tunable platforms to simulate reinforced electronic interactions in the presence of low-energy bands with almost negligible bandwidth. Here, we focus on the twisted homobilayer WSe2 and the insulating phase at half-filling of the flat bands reported therein. More specifically, we explore the possibility of realizing quantum spin liquid (QSL) physics on the basis of a strong coupling description, including up to second-nearest neighbor Heisenberg couplings J1 and J2 as well as Dzyaloshinskii–Moriya (DM) interactions. Mapping out the global phase diagram as a function of an out-of-plane displacement field, we indeed find evidence for putative QSL states, albeit only close to SU(2) symmetric points. In the presence of finite DM couplings and XXZ anisotropy, long-range order is predominantly present with a mix of both commensurate and incommensurate magnetic phases.

Morphology, Luminescence, and Optical Properties of Tb‐ and Li‐Codoped ZnO Elongated Nano‐ and Microstructures

ZnO Elongated Nano- and Microstructures The sword-like structure depicted on the cover constitutes a resonant cavity (Fabry-Perot type) for the green emission induced by the UV laser. No light escapes from the structure except through the two symmetrical exit points located at the side edges. More information can be found in article number 2100805 by Paloma Fernández and co-workers.

Experimental and Numerical Research on a Pipe Element Passing through Bulkhead with Symmetrical Elastic Installation

To reduce the transmission of vibration energy from the ship’s pipeline to the bulkhead, a novel all-metal pipe element passing through the bulkhead with symmetrical elastic installation was proposed in this paper. A metal bellow, a multi-layer thin-walled symmetrical structure, was used as an elastic element and entangled metallic wire materials (EMWM) were used as a damping element. The insertion loss was adopted to evaluate the vibration damping performance. The results show that compared with the pipe element passing through the bulkhead with rigid installation, the vibration damping performance of the pipe element passing through bulkhead with symmetrical elastic installation can significantly isolate the vibration transition, and the maximum average insertion loss in each direction can reach 25.4 dB. A thermal-vibration joint test system of the pipe element passing through the bulkhead was built. A series of comparison experiments were carried out to investigate the influence of temperature, symmetrical measure points, and exciting directions on the vibration response transmitted to the bulkhead. Therefore, the vibration damping performance was verified.

Transverse instability and universal decay of spin spiral order in the Heisenberg model

We analyze the intrinsic stability of spin spiral states in the two-dimensional Heisenberg model isolated from its environment. Our analysis reveals that the SU(2) symmetric point hosts a dynamic instability that is enabled by the existence of energetically favorable transverse deformations---both in real and spin space---of the spiral order. The instability is universal in the sense that it applies to systems with any spin number, spiral wave vector, and spiral amplitude. Unlike the Landau or modulational instabilities which require impurities or periodic potential modulation of an optical lattice, quantum fluctuations alone are sufficient to trigger the transverse instability. We analytically find the most unstable mode and its growth rate, and compare our analysis with phase-space methods. By adding an easy-plane exchange coupling that reduces the Hamiltonian symmetry from SU(2) to U(1), the stability boundary is shown to continuously interpolate between the modulational instability and the transverse instability. This suggests that the transverse instability is an intrinsic mechanism that hinders long-range phase coherence even in the presence of exchange anisotropy.

Starlike Functions of Complex Order with Respect to Symmetric Points Defined Using Higher Order Derivatives

In this paper, we introduce and study a new subclass of multivalent functions with respect to symmetric points involving higher order derivatives. In order to unify and extend various well-known results, we have defined the class subordinate to a conic region impacted by Janowski functions. We focused on conic regions when it pertained to applications of our main results. Inclusion results, subordination property and coefficient inequality of the defined class are the main results of this paper. The applications of our results which are extensions of those given in earlier works are presented here as corollaries.

Thermometry in the diagnosis of ankle injuries

Examination results on 12 patients with closed injuries of the ankle joint capsular-ligamentous system are presented. Together with the traditional clinical and roentgenologic methods, ultrasonography and thermometry were used for the assessment of the injury severity. It is shown that thermometry is the informative method for the determination of the early postinjury reactive inflammation severity in the zone of injury. The elaborated monitoring of the skin temperature changes in the symmetric points of the injured and intact extremities enabled to evaluate the markedness of metabolic disturbances, the pattern and rate of reparative processes in the zone of injury, as well as to determine the time of their completion.

Method for the generation and visualization of cross-sectional images of three-dimensional point spread functions for rotationally symmetric intraocular lenses.

Cross-sectional images of three-dimensional point spread functions of intraocular lenses are used to study their image formation. To obtain those, light sheet-based methods are established. Due to the non-negligible thicknesses of the light sheets, the image quality of the cross-sectional images is constrained. To overcome this hurdle, we present a dedicated evaluation algorithm to increase image quality in the post-processing step. Additionally, we compare the developed- with the light sheet method based on our own investigations of a multifocal diffractive intraocular lens conducted in an in-house designed optical bench. The comparative study showed the clear superiority of the newly developed method in terms of image quality, fine structure visibility, and signal-to-noise ratio compared to the light sheet based method. However, since the algorithm assumes a rotationally symmetrical point spread function, it is only suitable for all rotationally symmetrical lenses.

A DFT+U study of site dependent Fe-doped TiO2 diluted magnetic semiconductor material: Room-temperature ferromagnetism and improved semiconducting properties

This article reports the crystal structure, impurity formation energy, electronic property, magnetic property, and dopant configuration site dependence of ferromagnetic temperature Tc of anatase (Ti15FeO32, Ti14Fe2O32, and Ti13Fe3O32) by first-principles calculations based on density functional theory (DFT) with Hubbard onsite correction (DFT+U). The estimated formation energy validated the structural stability of the Fe-doped TiO2 with 2.08% (Ti15FeO32), 4.17% (Ti14Fe2O32), and 6.25% (Ti13Fe3O32) concentrations at the Ti sites. The electronic structure analysis reveals that the bandgap in the doped system changed from a wide bandgap of 3.23 eV (pristine TiO2) to slightly lower bandgaps of 3.13, 3.08, and 3.04 eV with Fe concentrations of 2.08%, 4.17%, and 6.25%, respectively. The calculated partial density of states also show the hybridization of O with 2p- and Fe 3d-orbitals near the conduction band minimum and generate the impurity energy level reducing the bandgap. Furthermore, the estimated Curie temperature (Tc) varied depending on the Fe–Fe interactions, the concentration of the Fe dopants, and doping sites. For instance, Tc is calculated to be 343.57 K for 2.08% Fe at the symmetric point of the crystal while estimated to be 323.84 and 393.297 K for 4.17% at the nearest neighbor and the next-nearest neighbor configurations. Due to the increase of the Fe concentration to 6.25%, the calculated Tc monotonically improved to 342.5 and 513.174 K at the nearest neighbor and the next-nearest neighbor of the Fe-site, respectively. These indicate that all the calculated findings estimate the ferromagnetic transition temperature Tc to above room temperature. Moreover, the system’s total magnetization reveals the augmentation of a number of unpaired electrons as a result of rise in oxygen vacancies and, hence, there could be more holes when the Fe content gets higher, perhaps generating more bound magnetic polarons that favor the critical temperature, Tc.