Symmetric Hollow Research Articles

Euclidean and circum-Euclidean distance matrices: characterizations and interlacing property

Motivated by the inverse formula of the distance matrix of a tree and the Moore–Penrose inverse of a circum-Euclidean distance matrix (CEDM), in this paper, we study a general real square matrix M whose Moore–Penrose inverse can be expressed as the sum of a Laplacian-like matrix L and a rank one matrix. In particular, for a symmetric hollow matrix M, under an assumption, we show that M is a Euclidean distance matrix if and only if L is positive semidefinite. Based on this, we obtain a new characterization for CEDMs involving their Moore–Penrose inverses. As an application, we show that the distance matrices of block graphs and odd-cycle-clique graphs are CEDMs. Finally, we establish an interlacing property between the eigenvalues of a Euclidean distance matrix M (including the singular case) and its associated Laplacian-like matrix L, which generalizes the interlacing property proved for the distance matrices of trees.

Shear behaviour of doubly symmetric rectangular hollow flange beam with circular edge-stiffened openings

Cold-Formed Steel (CFS) sections are evolved through the last two decades compromising various aspects of construction needs. Doubly symmetric Rectangular Hollow Flange Beam (RHFB) is one of the innovative CFS sections, which was introduced to eliminate the drawbacks of conventional open CFS sections such as prone to complex buckling and torsional effects. Edge-stiffened web holes are recently recommended and available for extensive usage in the floor beams. Even though previous studies conducted researches on various kinds of stiffeners, there is no definite design equation or findings that were presented on shear behaviour. Therefore, this study focuses on the effect of edge-stiffened circular web openings on the shear capacity of doubly symmetric RHFB. Non-linear numerical models were developed using the ABAQUS software package for validation purposes and then comprehensive parametric studies were carried out for doubly symmetric RHFB with edge-stiffened openings. A total of 558 models consisting of edge-stiffeners, un-stiffened openings and plain webs were analysed in this study. Parametric results of with edge stiffeners exhibited shear capacity increment (1–90%) compared to unstiffened web openings. Hence, new design equations were proposed in the form of reduction factor and based on Direct Strength Method (DSM). Finally, optimum edge-stiffener length of 15 mm was recommended regardless of web opening size.

Adsorption of benzene on defective Pt surfaces: A DFT study

Defects occur naturally on surfaces during formation. The interaction of a benzene molecule with a defective surface of platinum is investigated using plane wave DFT. Adsorption energy, adsorbate geometry and electronic structure of benzene on defective surfaces of platinum is obtained and compared with those on a perfect platinum (111) facet. We observe that the presence of defects in the form of steps and vacancy leads to an increase in the strength of adsorption. It is found that the atop is the most stable site for adsorption on a Pt (111) surface having a vacancy defect, which agrees with the available experimental results. The terrace region, which has a symmetry similar to a perfect Pt(111) surface, gives the 3-fold symmetric fcc hollow site as energetically preferred for adsorption. The step edge has the hcp hollow as the preferred site for adsorption. Analysis of electronic structure and charge transfer at the preferred sites is performed. The presence of defects brings out major changes in adsorption process, as compared to that on perfect surfaces. Reduction in coordination of surface sites due to defects is identified as the main reason for more reactive nature of defective surfaces.

Shear behaviour and design of doubly symmetric hollow flange beam with web openings

Cold-Formed Steel (CFS) sections are extensively used in structural engineering applications replacing the conventional hot-rolled sections due to their inherent advantages. Web openings are generally placed in CFS floor joists and bearers to accommodate the building services, which leads the reduction of floor height. The web openings significantly influence the shear behaviour and reduce the shear capacity. However, very limited research studies have been conducted on hollow flange CFS beams with web openings under shear load. Therefore, this study presents a detailed Finite Element (FE) investigation of the shear behaviour of CFS doubly symmetric Rectangular Hollow Flange Beams (RHFBs) with unreinforced circular web openings. Non-linear FE models were created and validated using the laboratory shear test results. A detailed parametric study was then carried out by extending the validated FE models for doubly symmetric RHFBs with circular web openings. In total,126 FE models were investigated with different geometric parameters including section depth, thickness, material strength and web opening sizes to observe their behaviour on shear strength. The results showed that the existing shear strength design equations are either unsafe or conservative for doubly symmetric RHFBs with unreinforced circular web openings. Therefore, new Direct Strength Method (DSM) based shear design rules are proposed to estimate the shear strength of doubly symmetric RHFBs with unreinforced circular web openings in conjunction with proposed shear reduction factor (qs).

Efficiency-tunable terahertz focusing lens based on graphene metasurface

This paper proposes an efficiency-tunable terahertz focusing lens based on the graphene metasurface. The unit cell is composed of two symmetrical circular graphene hollows and an intermediate dielectric layer, wherein the hollow circular middle is connected by a rectangular graphene sheet. This structure can realize polarization conversion, for example, when an incidence with left-hand circular polarization emitted on the metasurface the polarization of the transmitted light is right-hand circular polarization. According to the principle of geometric phase, by rotating the direction of the rectangular bar, the transmitted wave will carry an additional phase and can cover the range of 2π. An THz focusing lens can be realized by properly arranging the unit structure of the graphene metasurface. The simulation results show that the conversion amplitude of circular polarized light can be adjusted by changing the Fermi level of graphene, and the focusing efficiency of the metalens can also be dynamically adjusted. Therefore, this graphene metasurface-based efficiency-tunable focusing lens can be realized by changing the Fermi level without changing the size of the unit cell, and can be widely used in terahertz applications such as energy harvesting and imaging.

Interfacially Super‐Assembled Asymmetric and H2O2 Sensitive Multilayer‐Sandwich Magnetic Mesoporous Silica Nanomotors for Detecting and Removing Heavy Metal Ions

AbstractAsymmetric hollow and magnetic mesoporous silica nanocomposites have great potential applications due to their unique structural–functional properties. Here, asymmetric multilayer‐sandwich magnetic mesoporous silica nanobottles (MMSNBs) are presented through an interfacial super‐assembly strategy. Asymmetric hollow silica nanobottles (SNBs) are first prepared, and Fe3O4 nanoparticles monolayers and mesoporous silica layers are uniformly super‐assembled on the surfaces of SNBs, respectively. The high Fe3O4 nanoparticles loading endows MMSNBs with a high magnetization (8.5 emu g−1), while the mesoporous silica layers exhibit high surface area (613.4 m2 g−1) and large pore size (3.6 nm). MMSNBs can be employed as a novel type of enzyme‐powered nanomotors by integrating catalase (Cat‐MMSNBs), which show an average speed of 7.59 µm s−1 (≈25 body lengths s−1) at 1.5 wt% H2O2. Accordingly, the water quality can be monitored by evaluating the movement speed of Cat‐MMSNBs. Moreover, MMSNBs act as a good adsorbent for removing more than 90% of the heavy metal ions with the advantage of the mesoporous structure. In addition, the good magnetic response enables the MMSNBs with precise directional control and is conducive to recycling for repeated operation. This bottom‐up interfacial super‐assembly construction strategy allows for a new understanding of the rational design and synthesis of multi‐functional nanomotors.

Mathematical model of the performance of a hopper feeding device with tangential pockets and a comb

A mathematical model and the results of the actual productivity computer simulation of an improved disk hopper feeding device with tangential profi le pockets and a toothed comb for automatic loading of ax symmetric hollow and solid elements with a conical end into assembly technological systems are considered. The results obtained can be used to evaluate the hopper feeding device actual productivity at the design stage.

Symmetry Decrease between Self‐Assembled Circular TiO4N2‐Based Helicates

A multicomponent self‐assembly reaction involving a bis‐biphenolato ligand (LH4), a 2,2'‐bipyrimidine chelate substituted by two (anthryl)vinyl moieties (bAnt) and Ti(OiPr)4 was investigated. An assembly {[Ti3(L)3(bAnt)3]}, composed of three homochiral TiO4N2 nodes, was characterized as being the thermodynamically‐end product. The crystal structure of this circular helicate highlighted an absence of symmetry for this compact compound. DOSY 1H NMR indicated that the nuclearity observed in the solid state for [Ti3(L)3(bAnt)3] was maintained in solution. An intermediate formulated as [Ti4(L)4(bAnt)4] was isolated. The structural analysis revealed that [Ti4(L)4(bAnt)4] was a symmetrical circular hollow helicate composed of four homochiral metallovertices. This study, supported by DFT calculation, brought some evidences on the sequences and the reasons leading to the symmetry decrease for this self‐assembly process.

Influence of filling properties and culvert structure parameters on the soil arching effect of upper-buried-type culverts

A high fill load may lead to several defects in culvert structures. Therefore, it is necessary to accurately calculate the earth pressure at the top of a culvert and the coefficient of earth pressure in fillings. In this paper, a numerical model is proposed to accurately calculate the earth pressure at the top of upper-buried culverts and the coefficient of earth pressure in the filling. First, indoor model tests were used to determine the earth pressure at the top of a culvert at different filling heights, and the theoretical soil arch coefficient calculation equation derived. Then, the numerical model was calibrated and its accuracy verified by comparing experimental and numerical simulation results. The effects of filling height, rock block proportion, filling Poisson's ratio, and slab thickness on the top and sides of the culvert were also analyzed. The results show that all factors will affect the earth pressure at the top and sides of the culvert. Further, the vertical earth pressure is parabolic on the top of the culvert, which can be explained by the shear lag effect of a symmetrical cantilever hollow box girder. The results of this study can be used as a reference for optimum design of culverts with high filling, and to reduce the occurrence of culvert accidents.

Current Limitations for the Axially Symmetric Hollow Electron Beam in the Drift Tubes of Millimeter-Wave Vacuum Electronic Devices

The conditions for ensuring the equilibrium steady-state of a high-density hollow electron beam transported in cylindrical drift tubes and focused by a uniform magnetic field are investigated. The results of numerical calculations of the currents limited due to the longitudinal deceleration of electrons by the space charge and the violation of equilibrium transverse magnetic focusing conditions when transporting beams of different configurations in klystron-type devices are presented. The limitations of the working length of the device associated with the excitation of diocotron instability are estimated. The calculation results were compared with the data obtained by the quasi-3D Arsenal—MSU computer code and by the approximate analytical formulas of other authors.

Electronic transport induced by asymmetric adsorption site of sulfur in molecular device

The effect of different sulfur adsorption site on right Au electrodes in molecular device is investigated by using non-equilibrium Green’s function and density functional theory. The designed devices exhibit switching behavior between hydroxychalcone and flavanone isomerization. The results indicate that the asymmetric hollow and bridge site on the Au electrodes reduces the current of device improving the switching ratio, compared with symmetric hollow and hollow adsorption, while the asymmetric hollow and top site enlarges the current of device reducing the switching ratio. And these phenomena are discussed through the transmission spectra, transmission eigenstates and molecular projected self-consistent Hamiltonian. In addition, we plot the evolution of the frontier molecular orbital and molecular projected self-consistent Hamiltonian with the increase of bias to study the electron transmission, showing different polarization effect. It suggests that asymmetric sulfur adsorption site on the Au electrode can modulate the electronic transport.

Evaluating the welding quality of longitudinal welds in a hollow profile manufactured by porthole die extrusion: Experiments and simulation

Aluminum alloy hollow profiles have wide applications in many fields, owing to their light weight and recyclability. Longitudinal welds are inevitable in hollow profiles manufactured by porthole die extrusion, and thereby their welding quality plays a critical role in the performance of profiles. In the present study, the microstructure and mechanical properties of longitudinal welds in an aluminum alloy non-fully symmetrical hollow profile was studied using chemical erosion, optical microscopy, electron backscatter diffraction, tensile tests and fracture analysis, and the welding quality of longitudinal welds was predicted by determining physical variables, flow paths, welding paths, and the geometry and location of longitudinal welds, calculating welding quality indexes, and comparing welding criteria. It was found that, the welds with micro-voids and clearly visible bonding interfaces after being chemically etched have poor welding quality and mechanical properties, and the fractures present groove structures and small dimple structures. On the contrary, the welds without any micro-void and bonding interface after being chemically etched have good welding quality and mechanical properties, and the fractures present large dimple structures. The effective strain at welds and at the inner and outer surfaces is larger than that at other locations of the profile. The distribution of the effective strain can reflect the geometry of welds, and the distribution law of the effective strain at welds is almost consistent with that of the welding quality. According to the method proposed in this study and the welding criterion considering the stress triaxiality and the effective strain, the welding quality of longitudinal welds in the aluminum alloy non-fully symmetrical hollow profile was predicted successfully, and the optimization of the extrusion die was carried out to improve the welding quality.

Evolution of ultra-relativistic hollow electron beams during their propagation in plasmas

Ultra-relativistic hollow electron beams can drive plasma wakefields (∼GV/m) suitable for positron acceleration. Stable propagation of hollow electron beams for long distances in plasmas is required to accelerate positrons to high energies by these plasma wakefields. In this work, we show by quasi-static kinetic simulations using the code WAKE that an ultra-relativistic azimuthally symmetric hollow electron beam with zero emittance propagates in a plasma by developing a fish-bone like structure and shifting its bulk, differentially along its length (rear part fastest), towards its axis due to the decrease in the betatron time period of beam electrons from the beam-front to beam-rear. Hollow electron beams with a small radius collapse into their axis due to the pull by the secondary wakefields generated by some of the beam electrons reaching the axis. Hollow beams with the radius equal to or larger than a minimum value, however, can propagate stably in plasmas for several meters. The minimum beam radius for the stable beam propagation in plasmas depends very weakly on the peak beam density with which the magnitude of the positron-accelerating electric field increases. Thus, the peak beam density can be used as a control parameter to achieve high acceleration gradients for positrons without affecting the minimum beam radius.

Application of the Monte Carlo Method for Simulation of Pattern Formation by Ion-Beam Sputtering of Amorphous Bodies

The formation of ordered structures by ion-beam sputtering of a surface of an amorphous body in the case when a strong nonlinearity has a significant effect on the morphology of the irradiated surface is studied. Three modifications of the Monte Carlo method are used for the numerical simulation of the process, and the first of them is a kind of imitational simulation. It is shown that the direct (imitating) statistical simulation of the ion bombardment of the surface of the target, which best matches the considered physical process and is widely used in other papers, has a serious disadvantage. In the case of imitational simulation, random fluctuations of the depth of the sputtering roughen the target surface to such an extent that none of the modes provided by the continuous model can be observed. It especially concerns the modes set after the long ion bombardment of the surface of the target. However, solutions of the continuous model can be investigated numerically by means of other modifications of the Monte Carlo method with decreased dispersion. Two of these modifications are developed in this paper. Applying these methods, under certain conditions, an ordered structure composed of hexagonally symmetrical hollows is obtained on the surface of the target after the target’s long-term exposure to irradiation by a normal ion beam.

Static and dynamic properties of shell-shaped condensates

Static, dynamic, and topological properties of hollow systems differ from those that are fully filled as a result of the presence of a boundary associated with an inner surface. Hollow Bose-Einstein condensates (BECs) naturally occur in various ultracold atomic systems and possibly within neutron stars but have hitherto not been experimentally realized in isolation on Earth because of gravitational sag. Motivated by the expected first realization of fully closed BEC shells in the microgravity conditions of the Cold Atomic Laboratory aboard the International Space Station, we present a comprehensive study of spherically symmetric hollow BECs as well as the hollowing transition from a filled sphere BEC into a thin shell through central density depletion. We employ complementary analytic and numerical techniques in order to study equilibrium density profiles and the collective mode structures of condensate shells hosted by a range of trapping potentials. We identify concrete and robust signatures of the evolution from filled to hollow structures and the effects of the emergence of an inner boundary, inclusive of a dip in breathing-mode-type collective mode frequencies and a restructuring of surface mode structure across the transition. By extending our analysis to a two-dimensional transition of a disk to a ring, we show that the collective mode signatures are an essential feature of hollowing, independent of the specific geometry. Finally, we relate our work to past and ongoing experimental efforts and consider the influence of gravity on thin condensate shells. We identify the conditions under which gravitational sag is highly destructive and study the mode-mixing effects of microgravity on the collective modes of these shells.

Influence of the Ovality of the Base Surfaces of Thin-Walled Extended Axially Symmetric Hollow Parts on the Error of Radial Runout Measurements in Prisms

In prisms with different cut angles, we study centering errors of long axisymmetric hollow parts during the control of the radial runout of the middle part with respect to the common axis of the extreme centering thickenings having a significant ovality. A mathematical model is developed that relates the movement of the center of the elliptic cross-section of the base surface during rotation in the prism with the geometric center of the prism. In a typical example of an oval piece, a trajectory of the relative displacement of the center of the ellipse section is determined during rotation in a prism with different cut angles (60, 90, 108, and 120°).

Thermal residual solutions of beams, plates and shells due to laminated object manufacturing with gradient cooling

Laminated object manufacturing (LOM) results in thermal residual stresses and deformations due to its material mismatch among layers and gradient cooling. The manufacturing and cooling processes in a laminated workpiece are decomposed into many turns. Through-thickness cooling gradients are considered in each layer forming turn. The thermal residual strains in each turn are deduced. The total thermal residual stresses are obtained by composing the strains in all turns. The workpieces with geometries of a beam, plate and shell are considered. For a beam or plate, the analytical solutions of the stresses and deformations in the axial and transverse directions are deduced separately and then synthesized to the total solutions. One-dimensional beams and two-dimensional plates have very similar solutions. For a symmetrical hollow cylinder or sphere, the analytical solutions of thermal residual stresses with through-thickness cooling gradients are also formulated. The numerical examples show that the assumption of synchronous cooling results in big errors and cooling gradients also induce thermal residual stresses and deformations. Four gradient cooling models are summarized according to various LOM manufacturing techniques and the thermal residual level is proportional to the cooling gradient. Processing sequence in functional gradient materials has a strong impact on thermal residual level.

Geometric and compositional influences on spin-orbit induced circulating currents in nanostructures

Circulating orbital currents, originating from the spin-orbit interaction, are calculated for semiconductor nanostructures in the shape of spheres, disks, spherical shells, and rings for the electron ground state with spin oriented along a symmetry axis. The currents and resulting orbital and spin magnetic moments, which combine to yield the effective electron $g$ factor, are calculated using a recently introduced formalism that allows the relative contributions of different regions of the nanostructure to be identified at zero magnetic field. For all these spherically or cylindrically symmetric hollow or solid nanostructures, independent of material composition and whether the boundary conditions are hard or soft, the dominant orbital current originates from intermixing of valence-band states in the electron ground state, circulates within the nanostructure, and peaks approximately halfway between the center and edge of the nanostructure in the plane perpendicular to the spin orientation. For a specific material composition and confinement character, the confinement energy and orbital moment are determined by a single size-dependent parameter for spherically symmetrical nanostructures, whereas they can be independently tuned for cylindrically symmetric nanostructures.

Heterogeneous catalytic oxidation of phenol by in situ generated hydrogen peroxide applying novel catalytic membrane reactors

This work presents a novel method for oxidation of organic matter in water solutions based on catalytic membrane reactors. The oxidant, hydrogen peroxide, is generated directly in the bulk of the liquid investigated. Commercial symmetric alumina hollow fibers have been used as a starting material thereafter introducing the active phases. It has been proven that two different catalysts are necessary in order to complete the overall reaction, as well as to generate hydrogen peroxide and a heterogeneous Fenton process. Palladium has been used for the hydrogen peroxide generation and a second active phase, transitional metal oxides or homogeneous Fe2+, has been used for the hydroxyl radical generation. An additional method for specific Pd loading to the reaction zone based on sputtering technique has been developed. All prepared catalytic membrane reactors (CMRs) are capable of generating hydrogen peroxide in amounts comparable to CMRs reported in the literature. The catalytic membrane reactors prepared by Pd impregnation show very high activity and stability in phenol oxidation reaching 40% of the generated H2O2 usage in the oxidation reaction. Despite the very high activity of the catalytic membrane reactors obtained by Pd sputtering in H2O2 production they suffer very fast deactivation. Specific reactivation including a calcination step has been found to be appropriate for the recovery of their activity. Additional experiments give new insights for better understanding of Pd deactivation especially when the metal particles are of nanometer sizes. (C) 2014 Elsevier B.V. All rights reserved.

Ceramic hollow fibres catalytic enhanced reactors for glycerol steam reforming

In this study, NiO/MgO/CeO2 catalysts with Ni content from 5% to 30% were synthetized by sol–gel method and tested in a fixed-bed reactor (FBR) in the glycerol steam reforming (GSR) reaction. The catalysts were characterized by N2 adsorption isotherms at −196°C (SBET), X-ray diffraction (XRD), H2 temperature programmed reduction (H2-TPR), transmission electron microscopy (TEM) and energy dispersive X-ray (EDX). The 20% NiO/MgO/CeO2 catalyst, which showed the highest catalytic activity in GSR reaction, was selected to be deposited in the finger-like region of the asymmetric Al2O3 hollow fibre and the sponge-like region of the symmetric Al2O3 hollow fibre in the development of the asymmetric hollow fibre reactor (AHFR) and symmetric hollow fibre reactor (SHFR), respectively. The impregnated ceramic substrates were characterized by scanning electron microscopy (SEM), EDX and TEM. The performances of the AHFR and SHFR were compared with that in a conventional FBR during the GSR reaction. Both AHFR and SHFR were operating at “dead-end” configuration at a temperature range from 250°C to 550°C, atmospheric pressure and in a reactant mixture of steam and glycerol (16:1 molar ratio). At 550°C the glycerol conversion in the AHFR and SHFR was 70% and 46%, respectively, which are 5 and 2 times higher than that obtained in the FBR. The different performances of the AHFR and SHFR could be explained due to the unlike catalyst particle size deposited in the asymmetric and symmetric substrates, 8nm and 3nm, respectively.