Symmetric Plane Research Articles

Alternating sign matrices and totally symmetric plane partitions

Alternating sign matrices and totally symmetric plane partitions

Balanced tri- and quad-band BPFs based on SIR with improved passbands selectivity

Abstract In this paper, balanced tri- and quad-band bandpass filters (BPFs) with high selectivity and controllable center frequencies and bandwidths are proposed. In the tri-band BPF design, two differential-mode (DM) passbands are formed by utilizing a stub-loaded resonator (SLR) and a uniform impedance resonator (UIR). The coupling structure of the proposed BPF realizes the third DM passband. Moreover, the center frequencies and bandwidths of the three DM passbands can be controlled by the lengths of resonators and the gaps between the resonators. In order to improve the DM selectivity further, the source-load-coupled structure is introduced. In addition, common-mode (CM) suppression is achieved by using L-shaped balanced microstrip line to slotline transition structures, achieving the independence between CM responses and DM ones. Therefore, the design procedure can be simplified greatly. In order to validate the practicability, one balanced tri-band BPF operating at 2.5, 3.5 and 4.5 GHz is designed and fabricated. Moreover, by adding a short stub to the UIR located in the symmetrical plane, one flexible resonance frequency is generated, which is used to design the balanced quad-band BPF. By manufacturing and measurement, the measurement and simulation are in good agreement.

Impact of liquid crossflow on the discharge coefficient of a gas jet hole on a flat plate

This study combines the experimental and numerical simulation methods to deeply analyze the impact of liquid crossflow on the discharge coefficient of a gas jet hole on a flat plate. Experiments were conducted to examine the influence of momentum flux ratio and theoretical momentum flux ratio on the discharge coefficient under various crossflow Reynolds numbers. It was found that the variation of the discharge coefficient with the theoretical momentum flux ratio clearly reflects the impact of the crossflow boundary layer velocity profile on the discharge coefficient. The rapid growth of velocity in the boundary layer near the wall in the direction normal to the wall surface, or the decrease in the thickness of the boundary layer, both enhance the shearing effect of the crossflow, leading to a decrease in the discharge coefficient. Analysis of the cavity morphology at the hole exit captured by high-speed camera revealed that the averaged profile of the gas–liquid boundary on the symmetrical plane of the jet below the hole can be approximated as a straight line within the scale of the hole diameter, and the sine of the angle between this line and the upper wall surface is roughly equivalent to the normalized discharge coefficient. This relationship was physically interpreted through the analysis of effective and equivalent flow cross-sectional shapes derived from numerical simulation at different crossflow Reynolds numbers and theoretical momentum flux ratios. Additionally, this paper introduces an innovative method for predicting jet flow rate based on image processing technology. A notable feature of this method is that it does not require the measurement of the pressure inside the gas chamber.

A study of conical and curved shock waves via the streamline transformation method

The axisymmetric conical and curved shock waves are studied theoretically via the streamline transformation method (STM), which integrates the differential geometries of streamlines into the conservation laws and solves the flow field geometrically. Under the condition of a straight shock wave, the governing equation is significantly simplified, from which the assumptions of the conical flow and geometric self-similarity are mathematically proved. The simplified equation is also demonstrated as equivalent to the classical Taylor–MacColl equation. The flow mechanism after a conical shock wave is discussed from a geometric perspective, where the key factor is the dimensionless lateral distance between symmetric planes. The corresponding geometric and flow parameters, e.g., the distance between streamlines, the streamline curvature, and the Mach number, are computed for the demonstration of this mechanism. In the flow field over a circular cone, the isentropic compression is modeled geometrically. Due to the isentropic compression, the conical shock wave remains approximately a Mach wave at small semi-angles and the detachment is suspended at large semi-angles. For the axisymmetric curved shock wave, the flow field is computed directly by the streamline transformation method, where both the concave and convex shock waves are considered. Along the wall streamline, an explicit proportional relation between the shock curvature and the orthogonal derivatives of flow parameters is also provided and verified numerically. These results are applicable in the theoretical analysis and inverse design of axisymmetric shock waves.

The study of ([formula omitted]01) plane in β-Ga2O3 crystal

This study confirms that the symmetric plane of (001) with respect to the twin boundary in β-Ga2O3 is the (1¯01), and it has been systematically characterized. X-ray diffraction has determined that diffraction peaks appear only at positions where the l component of the miller indices hkl is even, and these positions coincide with the diffraction peak positions of the (001) plane. The termination atomic arrangement of the (1¯01) plane is not exclusively composed of gallium or oxygen atoms, it exists in two forms with hanging bond densities of 1.614 × 1015/cm2 and 2.421 × 1015/cm2, respectively. Wet etching experiments on the (1¯01) plane reveal distinct defect morphologies compared to the (001) plane, indicating its suitability for distinguishing between these two planes. The Raman modes of (1¯01) plane coincide with other crystal planes. Through optical transmission spectra, X-ray photoelectron spectra, and Ultraviolet photoelectron spectra, its bandgap width Eg of 4.76 eV, the valence band maximum EVBM of 3.64 eV and the Schottky barrier height Φsurf of 1.12 eV were determined. Compared to studies of other crystal planes, it is believed that the (1¯01) plane also possesses similar application potential.

Production of high-purity non-diffracting optical vortex arrays with high topological charge

In this paper, we have realized the high purity non-diffracting optical vortex arrays with a high topological charge using quasi-symmetrical plane waves for the first time. The triangular vortex arrays with l = ±2 can be generated by six quasi-symmetrical plane waves, and the square vortex arrays with l = ±3 can be generated by eight quasi-symmetrical plane waves. The adjacent vortex units have opposite topological charges. We have also obtained the relations between the periods of the field formed by the six/eight quasi-symmetrical plane waves and the periods of the field formed by the three/four symmetrical plane waves. The simulation and experimental results demonstrate the feasibility of this method.

Synthesis, Structure, and Resolution of Functionalized Oxacalix[4]arenes with Planar Chirality via Dynamic SNAr Reaction

A pair of racemic oxacalix[4]arenes featuring planar chirality and a mesomer with a symmetric plane were conveniently synthesized under mild conditions via a one‐pot dynamic SNAr reaction and separated in 20% and 49% yields, respectively. X‐ray single crystal analyses confirmed their structures unambiguously. The racemic mixture could further be resolved using HPLC on a chiral column. Time‐dependent products distribution and interconversion between products with CsF as a catalyst were revealed by 1H NMR studies, convincing the dynamic nature of SNAr reaction.

Characteristics of the jet shear layer of a round elevated jet in crossflow

The present research aims at an experimental study to investigate the effect of velocity ratio (R) on the evolution of elevated round jet issued from a stack having an aspect ratio (AR) of 9.0 in a uniform crossflow at a Reynolds number of 2000. The experiments are conducted in a low-speed, recirculating water tunnel. Laser Doppler Velocimetry (LDV) is employed to characterize the water tunnel. Particle Image Velocimetry (PIV) is used to measure the flow field, and the dye visualization technique is utilized to capture the accompanying instantaneous flow structures. Depending on the velocity ratio (R = 0.16 - 1.5), distinct jet shear layer (JSL) structures are observed in the symmetric plane (XY), confirmed by both the flow visualization and PIV data. These structures include clockwise vortices, anticlockwise vortices, swing-induced mushroom vortices, and jet-like vortices. For R<0.5, entrainment of a substantial amount of jet fluid into the stack-wake region (downwash) has been observed. At R=0.5, the streak image captured in the wall parallel plane reveals the ring-like vortices that appear to wrap around the jet core while upright vortices are detected downstream on the lee side of the jet. Additionally, variations in average velocity and turbulent fluctuations in the near field, contingent on different velocity ratios, are discussed.

Some Convex Polytopes Joining Paths and Their Metric Dimension

In recent years, there is a lot of interest in the topic of conveying the groups of planar graphs with an unvarying metric dimension. A few types of planar graphs have recently had their locating number (or metric dimension) determined, and an outstanding problem concerning these graphs was brought up that: Illustrate the types of planar graphs Υ that can be generated from a graph Φ through the addition of more edges to Φ , such that d i m ( Φ ) = d i m ( Υ ) and V ( Φ ) = V ( Υ ) . While proceeding in a similar directives, we identify two families of radially identical planar graphs with unaltered metric dimension in this study: ϝ n , m and ℷ n , m . We do this by establishing that d i m ( ϝ n , m ) = d i m ( ℷ n , m ) and V ( ϝ n , m ) = V ( ℷ n , m ) , respectively. We acquire another family of a radially symmetrical plane graph (i.e., ℸ n , m ) with a constant metric dimension. We show that all the vertices of these classes of the plane graphs can potentially be identified with just three well-chosen nodes.

Small Organic Molecules with Anchoring Adsorption Enhance Corrosion Inhibition of Zinc Electrodes in ZnSO4 Medium

AbstractIn this study, trimercapto‐S‐triazine trisodium salt (TMT) with threefold rotational symmetry as a corrosion inhibitor was introduced into 2 mol ⋅ L−1 ZnSO4 medium. By electrochemical measurements, the corrosion inhibition efficiency of the zinc electrodes was 92.52 % when the concentration of TMT corrosion inhibitor was 2 mmol ⋅ L−1. Based on the microstructural characterization and theoretical analysis of Zn electrodes, it was confirmed that S and N atoms of TMT corrosion inhibitor serve as alternately zinc‐philic adsorption sites with sixfold rotational symmetry for the formation of intermolecular complexes. Adsorption energies of TMT on Zn surfaces were calculated and indicated that the bonds of Zn−N and Zn−S promoted anchoring adsorption on sixfold symmetric (002) plane of zinc. Meanwhile, TMT corrosion inhibitor can adsorb Zn2+ from the electrolyte and directionally deposit them on the surface of Zn (002), effectively avoiding the occurrence of dendrites. This study changes the common knowledge that organic corrosion inhibitors must form hydrophobic films to have corrosion inhibition performance, and provides a new approach for using small organic molecules with anchoring adsorption as metal corrosion inhibitors.

A case study of the response of support structure and stratum deformation caused by deep foundation pit excavation in soft area

Investigating the spatial distribution and evolution patterns of deformations during foundation pit excavation is crucial for safeguarding the surrounding environment. This study focuses on a deep excavation case in Nanjing and discusses the strata deformation and the response of the retaining structure through the excavation phase, informed by on-site monitoring data. A three-dimensional finite element model of the excavation was developed, with comparisons between predicted values and on-site deformation monitoring data underscoring the accuracy of the numerical simulation results. This analysis delved into the deformation spatial distribution within the retaining structure and ground surface settlement throughout the excavation. Moreover, the three-dimensional deformation patterns of the diaphragm wall at various excavation depths were scrutinized, mapping the evolution pattern and spatial distribution of ground surface settlement around the foundation pit across different excavation stages. The findings reveal a pronounced spatial effect in both the diaphragm wall deformation and ground movements behind the wall, with the greatest deformation manifesting near the symmetric plane of the excavation center and markedly less deformation near the excavation corners. Furthermore, the deformation scope broadens with increasing excavation depth. These research outcomes aim to furnish a substantive reference for practical engineering implementations.

A Kirigami Multi‐Stable Flexible Gripper with Energy‐Free Configurations Switching

Inspired by the kirigami and recombination mechanism, a kirigami flexible gripper is presented. The configuration variation behaviors are realized by recombinant kirigami segments, and thus, with only head segment actuation, the gripper slickly deforms among different configurations. Revolutionizing the conventional deployable systems, the proposed design methodology can realize configuration variation‐locking integration, and reusing of multi‐stability property. To realize rapid configuration switching with the lowest energy input, a nested origami actuation, called trigger structure, is given. Furthermore, advanced design for the trigger structure is carried out, broadening the bistable state to four‐stable geometric configurations for enhanced reachable space of the flexible gripper. By combining the design of the advanced trigger structure, the flexible gripper enables an energy‐free switching behavior between deployed and curled configurations in symmetrical and asymmetrical planes. The asymmetrical configurations, induced by the multi‐stability property of the advanced trigger structure, make the flexible gripper appropriate for various moving velocities capture. The proposed kirigami multi‐stable flexible gripper has significant capture capability for moving targets with different types and motion attitudes. Summarily, the proposed kirigami multi‐stable flexible gripper opens a new avenue for flexible robots, with potential applications in space exploration, grippers, and beyond.

Design and heat transfer numerical analysis of high-speed continuous casting mold water slot system

The water slot structure can reduce the temperature of the mold and increase the heat transfer between the mold and cooling water. It has significant impacts on high-speed continuous casting. Therefore, a three-dimensional model of heat transfer from mold to cooling water was used to analyze the influence of water slot size on the cooling capacity of a single water slot. Then, the fluid flow, heat transfer, and solidification three-dimensional models were used to analyze the temperature distribution and cooling effect of three kinds of water slot molds and non-water slot molds. Finally, the water slot mold was designed to achieve high-speed continuous casting. The results show that to make full use of the cooling water in the water slot, the width and height of a single water slot should be less than 8 mm. Compared with the conventional mold without the water slot structure, the temperature of the mold with the water slot structure significantly decreases. The final design of the mold water slot system is as follows: the water slot width and depth are 8 mm, and the number of water slots on one side of the mold is 9. The water slots have a symmetrical distribution, and the symmetrical plane is the middle plane of the mold. The high-speed continuous casting experiment was carried out, and the casting speed can reach 4–4.5 m/min. The water slot mold in this study can be applied in the high-speed continuous casting process.

Fully Complementary Higher Dimensional Partitions

AbstractWe introduce a symmetry class for higher dimensional partitions—fully complementary higher dimensional partitions (FCPs)—and prove a formula for their generating function. By studying symmetry classes of FCPs in dimension 2, we define variations of the classical symmetry classes for plane partitions. As a by-product, we obtain conjectures for three new symmetry classes of plane partitions and prove that another new symmetry class, namely quasi-transpose-complementary plane partitions, are equinumerous to symmetric plane partitions.

Optical and Electrical Properties of AlxGa1-xN/GaN Epilayers Modulated by Aluminum Content.

AlGaN-based LEDs are promising for many applications in deep ultraviolet fields, especially for water-purification projects, air sterilization, fluorescence sensing, etc. However, in order to realize these potentials, it is critical to understand the factors that influence the optical and electrical properties of the device. In this work, AlxGa1-xN (x = 0.24, 0.34, 0.47) epilayers grown on c-plane patterned sapphire substrate with GaN template by the metal organic chemical vapor deposition (MOCVD). It is demonstrated that the increase of the aluminum content leads to the deterioration of the surface morphology and crystal quality of the AlGaN epitaxial layer. The dislocation densities of AlxGa1-xN epilayers were determined from symmetric and asymmetric planes of the ω-scan rocking curve and the minimum value is 1.01 × 109 cm-2. The (101¯5) plane reciprocal space mapping was employed to measure the in-plane strain of the AlxGa1-xN layers grown on GaN. The surface barrier heights of the AlxGa1-xN samples derived from XPS are 1.57, 1.65, and 1.75 eV, respectively. The results of the bandgap obtained by PL spectroscopy are in good accordance with those of XRD. The Hall mobility and sheet electron concentration of the samples are successfully determined by preparing simple indium sphere electrodes.

Synthesis and Analysis of Plane–Space Switching Mechanisms Based on a Plane-Symmetric Eight-Bar Linkage

Abstract This paper proposes a novel synthesis method for constructing plane–space switching mechanisms based on the symmetric plane of the regular prism. First, the structure equation and motion characteristic of plane-symmetric eight-bar linkage are presented. Then, the plane-symmetric seven-bar linkage and rhombic Bricard linkage are obtained by locking the joint of the eight-bar linkage. Four types of plane–space switching mechanisms are constructed based on the synthesis method and switching linkage units. These switching mechanisms can expand completely into planar configurations and fold completely into spatial configurations. Subsequently, the kinematics of the coupled branch chain is analyzed, through which the folded and contractive characteristics of the mechanism are revealed. Then, the concept of the distributed circle of joints is proposed, and the enveloping performance of the mechanism is approximately analyzed. This paper provides a new idea and synthesis method for designing new deployable mechanisms.

Stress and Deformation Analysis of Prestressed Wound Composite Components with an Arch-Shaped Metal Liner.

The stress distribution in prestressed filament wound components plays a crucial role in determining the quality of these components during their operational lifespan. This article proposes a physical model to analyze the stress and deformation of prestressed wound composite components with arch-shaped sections. Drawing upon the principles of beam theory, we delve into the analysis of prestressed wound components with metal liners featuring arch-shaped sections. Our investigation revealed a noteworthy phenomenon termed the "additional bending moment effect" within prestressed wound components with arch-shaped sections. Furthermore, this study establishes a relationship between this additional bending moment and the external pressure. In addition, a 3D finite element (FE) model for prestressed wound components with arch-shaped sections incorporating metal liners was developed. The model's accuracy was validated through a comparison with prestressed wound experiments, showcasing an error margin of less than 2%. In comparison with prestressed wound components with circular cross-sections under identical load and dimensional parameters, it was observed that prestressed wound components with arch-shaped sections exhibit stress distributions in the arc segments akin to their circular counterparts, with differences not exceeding 5%. Notably, when the ratio of the straight segment length to the inner diameter of the arc segment inner is less than 4, the deformation on the symmetric plane of the arc segment in an arch-shaped component can be effectively considered as the summation of deformations in equivalent-sized arc and straight segments under identical loading conditions. This yields an equivalent physical model and a streamlined analysis and design methodology for describing the deformation characteristics of prestressed wound components with arch-shaped sections.

CHARACTERIZATION OF SEPARATED SHEAR LAYER OF ELEVATED JET IN CROSSFLOW AT LOW-VELOCITY RATIO

The present study reports an experimental investigation of the flow dynamics of separated shear layers of an elevated jet-in-crossflow (EJICF). The current work aims to enhance the understanding of the downwash of jet fluid into the stack-wake region, akin to plume downwash in chimney flows, particularly at a low-velocity ratio. One end of the square stack with the aspect ratio of 9.0 is kept on a flat plate while the jet emerges from the free-end open to crossflow. Flow visualization and particle image velocimetry (PIV) experiments are conducted in a recirculating, low-speed water tunnel for three Reynolds numbers, namely Re &amp;#61; 1000, 2000, and 4000, based on the side of the square stack (&lt;i&gt;D&lt;/i&gt;) and the freestream velocity (&lt;i&gt;U&lt;/i&gt;&lt;sub&gt;&amp;#8734;&lt;/sub&gt;). The study mainly focuses on the jet shear layer characteristics and the downstream wake near the free-end formed by the interaction of crossflow and the jet shear layer. The instantaneous flow behavior includes the analysis of the shedding of the jet shear layer in a symmetric plane (&lt;i&gt;z&lt;/i&gt; &amp;#61; 0) at a constant velocity ratio of &lt;i&gt;R&lt;/i&gt; &amp;#61; 0.5. On the windward side, the jet shear layer reveals the formation of small-scale vortices due to the Kelvin-Helmholtz (KH) instability for Re &amp;ge; 2000. Also, it is found that at a high Reynolds number (Re &amp;#61; 4000), an unstable vortex appears above the jet exit on the upstream side, mentioned as a hovering vortex. The mean and fluctuating flow behavior are investigated using streamline and contour plots of mean velocity and fluctuating components.

A Pipe Dream Perspective on Totally Symmetric Self-Complementary Plane Partitions

Abstract We characterize totally symmetric self-complementary plane partitions (TSSCPP) as bounded compatible sequences satisfying a Yamanouchi-like condition. As such, they are in bijection with certain pipe dreams. Using this characterization and the recent bijection of Gao–Huang between reduced pipe dreams and reduced bumpless pipe dreams, we give a bijection between alternating sign matrices and TSSCPP in the reduced, 1432-avoiding case. We also give a different bijection in the 1432- and 2143-avoiding case that preserves natural poset structures on the associated pipe dreams and bumpless pipe dreams.

Passive Focusing of Single Cells Using Microwell Arrays for High-Accuracy Image-Activated Sorting.

Sorting single cells from a population was of critical importance in areas such as cell line development and cell therapy. Image-based sorting is becoming a promising technique for the nonlabeling isolation of cells due to the capability of providing the details of cell morphology. This study reported the focusing of cells using microwell arrays and the following automatic size sorting based on the real-time recognition of cells. The simulation first demonstrated the converged streamlines to the symmetrical plane contributed to the focusing effect. Then, the influence of connecting microchannel, flowing length, particle size, and the sample flow rate on the focusing effect was experimentally analyzed. Both microspheres and cells could be aligned in a straight line at the Reynolds number (Re) of 0.027-0.187 and 0.027-0.08, respectively. The connecting channel was proved to drastically improve the focusing performance. Afterward, a tapered microwell array was utilized to focus sphere/cell spreading in a wide channel to a straight line. Finally, a custom algorithm was employed to identify and sort the size of microspheres/K562 cells with a throughput of 1 event/s and an accuracy of 97.8/97.1%. The proposed technique aligned cells to a straight line at low Reynolds numbers and greatly facilitated the image-activated sorting without the need for a high-speed camera or flow control components with high frequency. Therefore, it is of enormous application potential in the field of nonlabeled separation of single cells.