Sharp Corners Research Articles

Творческие установки Л. Бакста в области журнальной графики «Мира искусства»

The work of Leo Bakst-graphic artist relates to the aesthetic position of the magazine «World of Art»: the search and free expression of «pure beauty» in the individual style of the artist. The master’s magazine graphics in all its forms – screensavers, endings, stamp, cover, title pages and frontispiece, combining elements of ancient, Asian and Christian art, are mainly plot-based; illustrating the accompanying text, Bakst designs the magazine page as a strictly perfect work of «pure art». In a single plotless screensaver, the space of the sheet is formed decoratively by the play of a thin and expressive line, symmetry, rigor of composition and elegant inscription. In theatrical and decorative screensavers, as well as title pages and frontispieces, there is strict structural stylistics of conventional theatricality and «pure» architectural and sculptural forms. At the same time, the individual style of Bakst graphics is also characterized by sensuality, which is clearly manifested in the openness, expressive prostration of the nudity of models of a number of graphic works. In some graphic works, the plot takes on an emblematic character that requires solving – this is the frontispiece of 9th volume made in the form of a triangle and the same image is like the ending of 10th volume of the magazine: the location of a massive light spot from the center to the sharp corners represents three vectors of the path: the path of the magazine, new art, the path of the artist-creator. The structure and image of L. Bakst’s magazine graphics are strictly harmonious and sensual.

Computing Medial Axis Transform with Feature Preservation via Restricted Power Diagram

We propose a novel framework for computing the medial axis transform of 3D shapes while preserving their medial features via restricted power diagram (RPD). Medial features, including external features such as the sharp edges and corners of the input mesh surface and internal features such as the seams and junctions of medial axis, are important shape descriptors both topologically and geometrically. However, existing medial axis approximation methods fail to capture and preserve them due to the fundamentally under-sampling in the vicinity of medial features, and the difficulty to build their correct connections. In this paper we use the RPD of medial spheres and its affiliated structures to help solve these challenges. The dual structure of RPD provides the connectivity of medial spheres. The surfacic restricted power cell (RPC) of each medial sphere provides the tangential surface regions that these spheres have contact with. The connected components (CC) of surfacic RPC give us the classification of each sphere, to be on a medial sheet, a seam, or a junction. They allow us to detect insufficient sphere sampling around medial features and develop necessary conditions to preserve them. Using this RPD-based framework, we are able to construct high quality medial meshes with features preserved. Compared with existing sampling-based or voxel-based methods, our method is the first one that can preserve not only external features but also internal features of medial axes.

Numerical investigation on fully-developed heat transfer augmentation and friction factor with dimple shaped intrusion and different radius of curvatures on triangular ducts

The heat transfer phenomenon is moderate in the case of triangular ducts due to the presence of sharp corners, which causes stagnant flow in the corners. Thus, this study focuses on improving heat transfer by converting one of the corners of the duct to a rounded structure having a variable curvature radius value (Rc). Rc varies from 0.67 h (maximum value) to 0.33 h (minimum value), where h is the height of the duct. Heat transfer and airflow have also been tested with dimple-shaped intrusion and rounded corners under varying ranges of relative length in the longitudinal direction (Z/e = 10–18) and relative length in the transverse direction (X/e = 10–18). Application of thermal-based boundary conditions on the turbulent flow for Re = 5600–21,000 facilitates the heat transfer analysis in a duct under steady-state. The commercial software tool, ANSYS Fluent 18.1, is used to simplify-three dimensional Reynolds averaged Navier Stokes equation with the compressible fluid flow by considering the pressure-based solver with the standard K- ε turbulence model. Compared to a typical duct, the rounded corner area shows higher velocity because of the dimple intrusions and rounded corners. Introduction of curvature to the corner opposite to the heat-conducting surface in simple triangular duct results in the increment of heat transfer by 5.71–44.37 %, 3.172–23.76 %, and 1.16–8.27 % for the values of Rc = 0.33 h, 0.49 h, and 0.56 h, respectively. Further the addition of dimple-shaped intrusion in the triangular duct with rounded corner, increases the heat transfer for Z/e = X/e = 18 as visible from the increment in average Nusselt Number by 22.9–91.52 %, 49.41–129.82 %, 31.96–89.26 % and 14.36–85 % for Rc = 0.333 h, 0.49 h, 0.56 h & 0.67 h respectively for Re spanning from 5600 to 21000.

Effect of modifications to island shape and geometrical configuration on the external aerodynamics of a generic aircraft carrier

The external aerodynamics of an aircraft carrier plays a vital role in the safe landing of aircraft during take-off and recovery. The hull, flight deck, and the island create a turbulent disturbance behind the aircraft carrier, leading to a simultaneous reduction in forward velocity and a downwash, which together create a sinking effect on the aircraft along its glideslope path. This phenomenon is known as the burble effect. It could potentially increase the pilot’s workload and strain their mental and physical faculties. Any design change that obviates or reduces the burble effect would potentially increase the probability of safely landing the aircraft on an aircraft carrier. There are only a few studies on the external aerodynamics of an aircraft carrier. The primary motivation of this study is to evaluate the effect of modifications to the island structure on the external aerodynamics of a generic aircraft carrier, especially the burble behind the carrier. The first part of the study pertains to the parametric changes to the aspect ratio of the island, that is, its length to width ratio and the consequent impact on the aerodynamics behind the carrier along the flight glide path. The second part of the study focuses on changing the geometry of the island by rounding the assumed cuboid island’s sharp corners, and evaluating its effect on the burble along the glideslope path of the aircraft. For the study, computational fluid dynamics (CFD) analysis on a generic aircraft carrier model has been carried out using the commercially available CFD solver Ansys FLUENT. The CFD studies have been validated by results of experiments conducted in a wind tunnel on the same generic aircraft carrier model. From the studies, it is seen that the aspect ratio of the island greater than one and rounding the sharp edges of the island have beneficial effects in reducing the impact of the burble behind the carrier.

Valley Hall elastic topological insulator with large Chern numbers

We present a reconfigurable electro-elastic topological insulator that produces a new valley phase with a large Chern number. This piezoelectric metamaterial comprises a hexagon-like honeycomb structure and periodic bonded piezoelectric beams. The composite piezoelectric Mindlin plate formulation in the isogeometric analysis is employed to calculate the band structure. A Dirac cone can emerge at the K point due to the C3v symmetry of the primitive element. Nontrivial topologically protected bandgaps develop after breaking mirror symmetry with the adding-on negative capacitance circuit. Additionally, we demonstrate that the topological quantity in this system arises in a large valley Chern number of one. The domain wall will exhibit two edge states between different topological microstructures according to the bulk-edge correspondence principle. The shielded transport of flexural waves is highly resistant to structural disturbances such as sharp corners or cavity flaws in the proposed metamaterial, resulting in a novel strategy for the reconfigurable electro-elastic topological insulator.

Measurement of transient liquid film and its effect on flow boiling heat transfer in non-circular microchannels

Micro liquid film plays an important role during flow boiling in microchannels. Current studies on flow boiling in microchannels have mainly focused on circular microchannels. However, microchannels with sharp corners, such as square and rectangular microchannels, are more common in practice. In the present study, flow boiling experiments were performed in square microchannels using ethanol as the working fluid. The mass flux was 26.71 kg (m−2 s−1) and heat flux ranged from 10 to 80 kW m−2. The transient liquid film thickness during flow boiling in square microchannels was measured using a laser confocal displacement meter. The pressure drop between inlet and outlet of the microchannel and the wall temperature were measured synchronously. Experimental results demonstrated that heat transfer performance depended on liquid film thickness and the thickness in square microchannels was smaller than in circular microchannels under the same capillary number. The variation of liquid film thickness during flow boiling in square microchannels was analyzed and a theoretical model was proposed for predicting liquid film thickness. According to variation in wall temperature and liquid film thickness, the flow boiling process in square microchannels was divided into liquid slug, elongated bubble, and dryout zones. The heat transfer mechanism of different zones was analyzed. In addition, the microchannel pressure drop fluctuation and backflow phenomenon were analyzed.

Numerical verification of sharp corner behavior for Giesekus and Phan-Thien–Tanner fluids

We verify numerically the theoretical stress singularities for two viscoelastic models that occur at sharp corners. The models considered are the Giesekus and Phan-Thien–Tanner (PTT), both of which are shear thinning and are able to capture realistic polymer behaviors. The theoretical asymptotic behavior of these two models at sharp corners has previously been found to involve an integrable solvent and polymer elastic stress singularity, along with narrow elastic stress boundary layers at the walls of the corner. We demonstrate here the validity of these theoretical results through numerical simulation of the classical contraction flow and analyzing the 270° corner. Numerical results are presented, verifying both the solvent and polymer stress singularities, as well as the dominant terms in the constitutive equations supporting the elastic boundary layer structures. For comparison at Weissenberg order one, we consider both the Cartesian stress formulation and the alternative natural stress formulation of the viscoelastic constitutive equations. Numerically, it is shown that the natural stress formulation gives increased accuracy and convergence behavior at the stress singularity and, moreover, encounters no upper Weissenberg number limitation in the global flow simulation for sufficiently large solvent viscosity fraction. The numerical simulations with the Cartesian stress formulation cannot reach such high Weissenberg numbers and run into convergence failure associated with the so-called high Weissenberg number problem.

CFD Analysis of Viscous Flow at the Sharp Corners of Mesh Fins

CFD Analysis of Viscous Flow at the Sharp Corners of Mesh Fins

Topological valley crystals in a photonic Su–Schrieffer–Heeger (SSH) variant

Progress on two-dimensional materials has shown that valleys, as energy extrema in a hexagonal first Brillouin zone, provide a new degree of freedom for information manipulation. Then, valley Hall topological insulators supporting such-polarized edge states on boundaries were set up accordingly. In this paper, a two-dimensional valley crystal composed of six tunable dielectric triangular pillars in each unit cell is proposed in the photonic sense of a deformed Su–Schrieffer–Heeger model. We reveal the vortex nature of valley states and establish the selection rules for valley-polarized states. Based on the valley topology, a rhombus-shaped beam splitter waveguide is designed to verify the valley-chirality selection rule above. Our numerical results entail that this topologically protected edge states still maintain robust transmission at sharp corners, thus providing a feasible idea for valley photonic devices in the THz regime.

Analysis of the topological motifs of the cellular structure of the tri-spine horseshoe crab (Tachypleus tridentatus) and its associated mechanical properties

Topological motifs in pore architecture can profoundly influence the structural properties of that architecture, such as its mass, porosity, modulus, strength, and surface permeability. Taking the irregular cellular structure of the tri-spine horseshoe crab as a research model, we present a new approach to the quantitative description and analysis of structure-property-function relationships. We employ a robust skeletonization method to construct a curve-skeleton that relies on high-resolution 3D tomographic data. The topological motifs and mechanical properties of the long-range cellular structure were investigated using the Grasshopper plugin and uniaxial compression test to identify the variation gradient. Finite element analysis was conducted for the sub-volumes to obtain the variation in effective modulus along the three principal directions. The results show that the branch length and node distribution density varied from the tip to the base of the sharp corner. These node types formed a low-connectivity network, in which the node types 3-N and 4-N tended to follow the motifs of ideal planar triangle and tetrahedral configurations, respectively, with the highest proportion of inter-branch angles in the angle ranges of 115–120° and 105–110°. In addition, mapping the mechanical gradients to topological properties indicated that narrower profiles with a given branch length gradient, preferred branch orientation, and network connectedness degree are the main factors that affect the mechanical properties. These factors suggest significant potential for designing a controllable, irregularly cellular structure in terms of both morphology and function.

Effects of heat treatment and Y addition on the microstructure and mechanical properties of as-cast Mg–Si alloys

In Mg–Si alloys, both primary and eutectic Mg2Si particles normally appear with sharp edges, which can lead to weak mechanical properties as the result of stress concentration at the sharp corners of these brittle particles. Thus, it would be of great importance to modify the morphology of these particles. In this study, microstructure modification mechanisms after 0.5 wt% Y addition and heat treatment (HT) at 420 °C for 24 h are comprehensively studied in hypo-eutectic Mg–1Si and hyper-eutectic Mg–2Si alloys. Microstructural observations were performed using optical and scanning electron microscopy equipped with electron disperse spectroscopy, while phase analysis was done by X-ray diffraction. Mechanical properties of the studied alloys were evaluated by shear punch testing technique. The obtained results indicate that 0.5% Y addition to the as-cast Mg–1Si and Mg–2Si alloys could modify morphology of the eutectic Mg2Si from coarse lamellar to very short rod-shaped. The poisoning effect of Y was the main mechanism for this modification. The ultimate shear strength (USS) increased after Y addition to the Mg–1Si and Mg–2Si alloys, due to the modified eutectic Mg2Si morphology and also formation of fine Y-containing particles. Moreover, it was observed that HT could modify the morphology of the eutectic Mg2Si phase to the punctiform or disconnected rod-shaped in the studied alloys. Another important effect of HT was observed to be rounding sharp corners of the primary Mg2Si particles and changing their morphology to some new shapes such as star-like, indicating unstable morphology of the primary Mg2Si particles in the Mg–2Si–0.5Y alloy at high temperature. The USS values were improved for the Mg–1Si and Mg–2Si alloys after HT due to the modified morphology of the Mg2Si particles.

Tunable topological edge and corner states in an all-dielectric photonic crystal.

Topological photonics has become a new and fascinating area in recent years, which enables electromagnetic waves to propagate with negligible backscattering and excellent robustness even when encountering sharp corners or defects. But the flexible tunability of edge and corner states is challenging once the topological photonic crystals (PhCs) have been fabricated. In this paper, we propose a new all-dielectric PhC with C3 symmetry constructed by hexagonal array of petal-like aperture embedded in silicon background. The proposed configuration has much wider energy gap than its triangular counterpart, and hence is suitable for wideband and high-capacity applications. When the apertures are filled with liquid crystals (LCs), the topologically-protected edge and corner states can be regulated through changing the refractive index of the LCs under different bias voltages. Moreover, the robustness of topological protection of edge and corner states is further demonstrated. This is the first demonstration of LC based tunable valley higher-order photonic topological insulator. The tunability of the proposed topological PhCs may be beneficial for development of tunable optical waveguides, reconfigurable topological microcavities, and other intelligent topological optical/terahertz devices.

A novel approach to calculate the KIII factor for a crack on a sharp corner using Green's function

This paper presents a method for determining Green's function for calculating the KIII factor for a crack initiated at the vertex of a sharp corner and coming out at different angles when the crack length is small compared to other element dimensions. A new approach to find a Green's function by means of FEM for symmetric problems and adapting it for non-symmetric problems has been applied, using the hypothesis of free released energy in combination with a special technique of building non-symmetric shapes from symmetric elements. This approach obtained approximate solutions, so special emphasis was placed on estimating the error of the obtained solutions. It was found that the high precision of the obtained Green's function is sufficient for practical use in calculating the durability and strength of structural elements under an anti-plane strain state.

Experimental and theoretical assessment of crack kinking in marble stones in the presence of a V-notch under mode I loading

Marble has been used extensively in the historical monuments as a building material. Notches and sharp corners in these buildings are potential locations for crack formation, crack extension and in some cases their eventual failure. In this study, some fracture tests are accomplished on a number of V-notched marble specimens under mode I loading condition. The specimens are in the configurations of double cantilever beam (DCB) and compact tension (CT) each embedding two various notch opening angles. It is substantiated that although both the loading conditions and geometry were symmetric, the crack initiation angle is not necessarily along the notch bisector line. It is also shown that the classical fracture criteria are not able to predict crack kinking in the tested marble specimens. Thus, the conventional strain energy density and maximum tangential stress criteria used for V-notches, V-SED and V-MTS respectively, are generalized by introducing the first non-singular term of notch stress field into the calculations. Finally, it is demonstrated that the generalized criteria, V-GSED and V-GMTS, can predict the fracture strength and the crack initiation angle of the tested marble specimens well.

Sugarcane waste based synthesized graphene like nanocarbon (GNC) for shock absorption application

We report on the synthesis, characterization, and shock absorption characteristics of Graphene like Nano Carbon (GNC) prepared by the combustion of biomass (sugarcane waste) using the Rapid Thermal Chemical Vapor Deposition (RT-CVD) technique. Post synthesis, the samples were purified by subjecting them to intercalation and annealing. The synthesised GNCs were then characterised by Raman, Infrared, and UV spectroscopy, together with microscopy. In analysis, the GNCs were observed to be rectangular in shape, thick, having sharp edges and corners, and having an area ∼50–200 μm2 with wrinkles on it. TEM images showed that GNCs exhibit smooth wrinkle contours with bits of dark showing conjugated graphene layers stacked together having multiple defects and dislocations. In Raman spectroscopy, D peak is observed at ∼1335 cm−1 and G peak is observed at ∼1591 cm−1 indicating GNC consists of sp2 and sp3 hybridised complex phases. The Crystalline Length (La), Disordered Length (LD) and Defect Density (nD) have been estimated to be 21.26 nm, 9.60 nm and 1.084 × 10−12/cm2 respectively. FTIR spectra revealed that C-C is present at ∼1420 cm−1 and C-O-C is present at 900 cm−1. In Uv measurements, no typical absorption peak was observed due to the micrometre size of GNC. The shock absorption properties of GNCs were investigated by subjecting them to pressure (~1.5 GPa) using a Split Hopkinson Pressure Bar (SHPB). The obtained mechanical parameters revealed that GNCs absorbed ∼65% of incident energy and ∼15% transmitted, demonstrating their utility in the development of armour, shock and blast mitigating blocks, defense, and space applications.

Concave gold nano-arrows (AuCNAs) for efficient catalytic reduction of 4-nitrophenol

Anisotropic gold nanostructures have attracted great attention in different fields including catalysis. Thermodynamically driven selective surface growth offers a reliable and reproducible method for anisotropic gold nanoparticle synthesis with specific morphologies. Herein, monocrystalline concave gold nano-arrows (AuCNAs) are prepared by the over-growth method using Au nanorods (AuNRs) as seeds. The as-prepared AuCNAs consist of a biconical head and four concave structures. Interestingly, silver ions (Ag+) concentration significantly affects the product morphology by tuning the peak positions of surface plasmon resonance (SPR), aspect ratio, arrow, and concave morphology of AuCNAs. The position of longitudinal SPR peaks is observed at 810, 805 and 782 nm at [Ag+]/[Au3+] molar ratios of 1:2, 1:1, and 2:1, respectively. Diameters and lengths of AuCNAs varied from 25 nm to 36 nm; 104 nm, 78 nm, and 120 nm, respectively. Additionally, the AuCNAs are applied for the catalytic reduction of 4-nitrophenol (4-NP) to 4-aminophenol (4-AP) in presence of excess NaBH4. Compared to gold nanorods (AuNRs), the prepared AuCNAs catalyst shows excellent catalytic activity, demonstrating that concave structures and sharp corners significantly enhance the catalytic activity. The value of pseudo-first-order reaction kinetic constants (kapp) increased from 0.0051 to 0.0195 s−1 with increasing catalyst valume from 7.5 to 37.5 μL. The highest normalized reaction rate constant (Knor) and turnover frequency (TOF) reach 5.84 × 104 min−1 mmol−1 and 443.47 h−1, respectively, at [Ag+]/[Au3+] ratio of 1:1 in AuCNAs catalyst. This study expands catalytic applications of anisotropic gold nanostructures and widens their potential application areas, such as surface plasmon exciton photonics, biomedical photonics, and photocatalysis.

Magnetic polycaprolactone microspheres: drug encapsulation and control

Targeted drug delivery (TDD) systems have several advantages, especially with drugs having toxic side effects such as lornoxicam (LX) which shows high hepatotoxicity and nephrotoxicity, especially with long-term use. This work represents an attempt to control magnetic microspheres encapsulating LX and magnetite nanoparticles (MNPs) for potential targeted drug delivery of LX. Superparamagnetic nanoparticles were fabricated via the co-precipitation method and together with LX were encapsulated into polycaprolactone (PCL) microspheres through an oil-in-water (O/W) emulsion solvent evaporation method. The effects of changing the amount of drug, MNPs, and volume of the aqueous phase were investigated by preparing several microsphere formulations. Increasing the amount of encapsulated MNPs increased the magnetization of the microspheres without affecting the morphology. Doubling the volume of the aqueous phase resulted in a higher encapsulation efficiency and drug loading; 83.9% and 10.7%, respectively, while increasing the amount of drug had a negative effect on both drug loading and encapsulation efficiency. Drug release from the microspheres was successfully achieved and showed a biphasic nature. A system of four planar coils was then used to magnetically control the movement of a cluster of capsules in a glycerin medium, as a simulation for the targeting process. The microspheres were successfully controlled to move in a U-turn path with sharp corners demonstrating their potential for TDD applications.

Comparative performance of novel nodal-to-edge finite elements over conventional nodal element for electromagnetic analysis

In nodal-based finite element method (FEM), degrees of freedom are associated with the nodes of the element whereas, for edge FEM, degrees of freedom are assigned to the edges of the element. Edge element is constructed based on Whitney spaces. Nodal elements impose both tangential and normal continuity of vector or scalar fields across interface boundaries. But in edge elements, only tangential continuity is imposed across interface boundaries, which is consistent with electromagnetic field problems. Therefore the required continuities in the electromagnetic analysis are directly obtained with edge elements whereas in nodal elements they are attained through potential formulations. Hence, while using edge elements, field variables are directly calculated but with nodal elements, post-processing is required to obtain the field variables from the potentials. Here, we present the finite element formulations with the edge element as well as with nodal elements. Thereafter, we have demonstrated the relative performances of different nodal and edge elements through a series of examples. All possible complexities like curved boundaries, non-convex domains, sharp corners, non-homogeneous domains have been addressed in those examples. The robustness of edge elements in predicting the singular eigen values for the domains with sharp edges and corners is evident in the analysis. A better coarse mesh accuracy has been observed for all the edge elements as compared to the respective nodal elements. Edge elements are also not susceptible to mesh distortion.

Silver particles embedded in silicon: The fabrication process and their application in surface enhanced Raman scattering (SERS)

The formation of hybrid structures for creating sensitive sensors is a difficult task. In this study, we developed a facile technique of semiconductor technology to fabricate hybrid structures based on SiO2/embeddedAg/Si and embeddedAg/Si for a surface-enhanced Raman scattering. Herein, our hybrid structures were created in one technological cycle, which consists of the reduction of silver nitrate salt from a solution on the silicon surface and subsequent high-temperature annealing at 1000 °C. In addition, it allows not only to preserve the plasmonic properties of Ag particles on the Si surface but also to protect them from further external influences by coating them with a SiO2 layer. Also, the basis for creating such hybrid structures is the performed numerical calculations of the position of a localized surface plasmon resonance as a function of the geometry of structures. Furthermore, the theoretical full-wave electromagnetic modeling of Raman scattering in an embedded Ag/Si structure showed the presence of enhancement regions “hot spots” at sharp corners with a maximum enhancement factor of 106. Finally, surface-enhanced Raman scattering spectroscopy of such structures showed reliable detection of the methyl orange from an aqueous solution at a concentration of 10-5M.

Structural behavior of an ablated reactor pressure vessel wall with external cooling

In a severe accident scenario of a nuclear power plant involving core meltdown and relocation to the lower head of the reactor pressure vessel (RPV), the vessel may undergo serious deformation and even failure due to extreme thermo-mechanical loads from the relocated core melt. Proper material models and detailed structural analysis are paramount in predicting the timing and mode of possible vessel failure.This paper presents a strain hardening creep model with optimal parameters to simulate the material behavior of the reactor steel 16MND5 under extreme thermo-mechanical loads. First, validations against two experiments, a tensile-creep test and the EU-REVISA RUPTHER #14 test, show that the proposed model is best overall compared to three previous models. Next, the creep model is implemented for the thermo-mechanical analysis of an ablated RPV under a severe accident scenario with external vessel cooling as a mitigation strategy. The effect of internal pressures from 3 to 50 bars is investigated with the assumption that the corners of the ablated part of the vessel have sharp corners. In this case, we found that the vessel fails above 40 bars. However, if we model the corners with varying smoothness or fillet sizes, we found significant delay in failure time and an increase in failure internal pressure.