Perfect Geometries Research Articles

Topology Prediction of Gas-Separating Metal-Organic Frameworks with Low Symmetry Vertices.

Topology serves as a blueprint for the construction of reticular structures such as metal-organic frameworks, especially for those based on building blocks with highly symmetrical shapes. However, it remains a challenge to predict the topology of the frameworks from less symmetrical units, because their corresponding vertex figures are largely deformed from the perfect geometries with no "default" net embedding. Furthermore, vertices involving flexible units may have multiple shape choices, and the competition among their designated topologies makes the structure prediction in large uncertainty. Herein, the deformation index is proposed to characterize the symmetry loss of the vertex figure by comparing it with its ideal geometry. The mathematical index is employed to predict the shapes of two in situ formed Co-based metalloligands (pseudo-tetrahedron and pseudo-square), which further dictate the framework topology (flu and scu) when they are joined with the [Zr6O8]-based cuboid units. The two frameworks with very similar constituents provide an ideal platform to investigate how the pore shapes and interconnectivity influence the gas separation. The net with cylindrical channels outperforms the other with discreate cages in C3H8/C2H6/CH4 separation, benefiting from the facile accessibility of its interaction sites to the guests imposed by the specific framework topology.

Incorporation of Defects in Finite Elements to Model Effective Mechanical Properties of Metamaterial Cells Printed by Selective Laser Melting

Additively printed mechanical metamaterial structures optimize material, energy and waste, producing more sustainable products. Their introduction in the production workflow depends on having proper tools for accurately predicting their performance. However, the additive manufacturing process incorporates significant defects which result in an important change of the effective properties of the metamaterial cell. Finite element predictions using perfect geometries and nominal base material properties result in important errors which may require excessive uncertainty-related safety design margins. This work presents a methodology to introduce the effect of the most common defects in finite element models to compute the effective mechanical response of different metamaterials printed by Selective Laser Melting. It is shown that even at elastic infinitesimal strains, the defects produce an important change in the effective mechanical capabilities of the metamaterial, which also depend on the type of the metamaterial cell studied and on the type and magnitude of defects. With the proposed methodology, which incorporates the distribution of defects in the finite element model, the predicted mechanical properties of the metamaterial better match the experimental ones. It is shown that the initial discrepancies in the order of 100% are reduced to an order of 5%.

Performance analysis and precoder design for IRS-assisted MIMO system with non-linear power amplifiers

In this work, a point-to-point intelligent-reflecting-surface (IRS) assisted single input single output (SISO) model is first developed and later modified to the multiple-input multiple-output (MIMO) case. For the SISO case, the transmitter or the access point (AP) is assumed to be equipped with a non-linear memory-less power amplifier (PA). A PA is assumed to be present for each data stream at the AP or base station (BS) side for the MIMO case. For both cases, three different types of PAs (A) Soft envelope limiter (SEL), (B) Solid-state power amplifier (SSPA), and (C) Travelling wave tube amplifier (TWTA) are considered. A Bussgang decomposition of the transmitted signal is then utilized for further analysis. A modified channel model is conceived for the AP-IRS-User equipment (UE) link based on the reflecting IRS elements’ radar cross-section (RCS). For the SISO system, both perfect and imperfect geometries of IRS elements with uniformly distributed element size errors are considered. An approximate closed-form expression for the upper bound on the above system’s spectral efficiency (SE) with ideal IRS elements is derived. The expression of the SE for two special cases of (A) Infinitely large IRS and (B) Ideal PA is deduced. Approximate closed-form expressions of various quality parameters for the IRS-assisted MIMO system with ideal and non-ideal PAs are also derived and verified numerically. Maximum ratio transmission (MRT) based precoder for this system is designed assuming that the information about the BS-UE link, BS-IRS-UE link, and the non-linear PA statistics is available at the BS. A closed-form expression for the SE of this system with this precoder is then derived and verified for various parametric situations.

On the buckling of mechanically lined pipes under combined tension and bending

During the installation of offshore pipelines, the pipe often encounters the joint action of bending and tension over a rigid curved surface. For example, in the S-lay installation, when the pipe passes over a stinger, it experiences the combined bending, tension, and the reactions from the support. In the case of a mechanically lined pipe, this combined loading tends to ovalize both tubes severely and separate the liner from the outer pipe, leading to flattening and even collapse. The paper deals with the buckling response of bi-material pipes bent over a rigid surface with tension, aiming to understand the extent to which lined pipes can be loaded before the buckling occurs. A custom numerical framework, including the quasi-two-dimensional and three-dimensional models, is presented. Two loading histories of bending and tension, namely κ→T and T→κ, are examined with lined pipes of perfect and imperfect geometries. The results show that tension, either applied before or after bending, affects the growth of ovalization and liner collapse, the extent of which depends on the load path followed. It is also demonstrated that bending with modest levels of internal pressure delays the onset of liner collapse, but the threshold pressure varies for different load paths.

Impact of Geometrical Imperfections on Estimation of Buckling and Limit Loads in a Silo Segment Using the Vibration Correlation Technique.

The paper examines effectiveness of the vibration correlation technique which allows determining the buckling or limit loads by means of measured natural frequencies of structures. A steel silo segment with a corrugated wall, stiffened with cold-formed channel section columns was analysed. The investigations included numerical analyses of: linear buckling, dynamic eigenvalue and geometrically static non-linear problems. Both perfect and imperfect geometries were considered. Initial geometrical imperfections included first and second buckling and vibration mode shapes with three amplitudes. The vibration correlation technique proved to be useful in estimating limit or buckling loads. It was very efficient in the case of small and medium imperfection magnitudes. The significant deviations between the predicted and calculated buckling and limit loads occurred when large imperfections were considered.

Modelling imperfections in unreinforced masonry structures: Discrete element simulations and scale model experiments of a pavilion vault

The structural assessment of doubly-curved vaulted masonry structures, such as pavilion vaults, poses challenges specific to their high degree of indeterminacy. Two-dimensional equilibrium analysis methods may provide a lower bound of load or displacement capacity, but they do not accurately describe the three-dimensional (3D) behaviour of these structures, particularly when shear deformation (e.g. sliding) is important. Therefore, discrete element modelling (DEM) methods, which can effectively simulate 3D load re-distribution, have been used to investigate support displacement capacity and corresponding 3D collapse mechanisms. DEM analyses are usually conducted on perfect digital geometries. Meanwhile, both real structures and small-scale physical models have implicit assembly and fabrication imperfections, which may significantly alter their response. The present paper aims to investigate the influence of geometrical and mechanical imperfections by comparing DEM analyses with the results obtained from tests on a scale model. In particular, a new method to simulate imperfections within the DEM framework is proposed, and a DEM parametric analysis is compared to the measured behaviour of a 3D-printed scale model of a pavilion (or cloister) vault on spreading supports. The influence of both mechanical imperfections andgeometrical imperfections, due to element geometry deviations or imprecision of the assembly process, have been investigated. Based on these analyses, the three-dimensional behaviour of a pavilion vault subjected to horizontal displacement of the supports is described, and the variability of results due to imperfections is demonstrated. A good agreement between DEM analyses and 3D-printed scale model tests is achieved, in terms of crack patterns and mechanisms. Geometrical imperfections did change the load paths within the vault, as expected, and also influenced the displacement capacity.

Adaptation of the iterative Marchenko scheme for imperfectly sampled data

SUMMARY The Marchenko method retrieves the responses to virtual sources in the Earth’s subsurface from reflection data at the surface, accounting for all orders of multiple reflections. The method is based on two integral representations for focusing- and Green’s functions. In discretized form, these integrals are represented by finite summations over the acquisition geometry. Consequently, the method requires ideal geometries of regularly sampled and colocated sources and receivers. Recently new representations were derived, which handle imperfectly sampled data. These new representations use point spread functions (PSFs) that reconstruct results as if they were acquired using a perfect geometry. Here, the iterative Marchenko scheme is adapted, using these new representations, to account for imperfect sampling. This new methodology is tested on a 2-D numerical data example. The results show clear improvement of the proposed scheme over the standard iterative scheme. By removing the requirement for perfect geometries, the Marchenko method can be more widely applied to field data.

Interactive buckling in prestressed stayed beam-columns

The instability of beam-columns with crossarms and externally prestressed cable stays is studied analytically, where the combination of bending and compression is assumed to be derived from the system self-weight acting orthogonally to the applied axial load. A nonlinear analytical model for prestressed stayed beam-columns with doubly-symmetric and mono-symmetric configurations, based on the Rayleigh–Ritz method, is presented that captures modal interactions for perfect geometries explicitly for the first time. It is demonstrated that the theoretical compressive strength enhancements under certain configurations can only be obtained at the expense of triggering a sequence of destabilizing bifurcations. This can give rise to severely unstable interactive post-buckling behaviour including the so-called ‘mode jumping’ phenomenon. Moreover, for mono-symmetric stayed beam-columns, it is shown that the varying levels of prestress within the stays can lead to different buckling modes which all have their own characteristic post-buckling responses. The analytical model is verified using a nonlinear finite element model formulated within the commercial code ABAQUS and excellent comparisons are obtained.

Non-fullerene Acceptors with a Thieno[3,4-c]pyrrole-4,6-dione (TPD) Core for Efficient Organic Solar Cells

To achieve the red-shifted absorptions and appropriate energy levels of A-D-A type non-fullerene acceptors (NFAs), in this work, we design and synthesize two new NFAs, named TPDCIC and TPDCNC, whose electron-donating (D) unit is constructed by a thieno[3,4-c]pyrrole-4,6-dione (TPD) core attached to two cyclopentadithiophene (CPDT) moieties at both sides, and the electron-accepting (A) end-groups are 2-(3-oxo-2,3-dihydroinden-1-ylidene)malononitrile (IC) and 2-(3-oxo-2,3-dihydro-1H-cyclopenta[b] naphthalen-1-ylidene)malononitrile (NC), respectively. Benefiting from TPD core, which easily forms quinoid structure and O⋯H or O⋯S intramolecular noncovalent interactions, TPDCIC and TPDCNC show more delocalization of π-electrons and perfect planar molecular geometries, giving the absorption ranges extended to 822 and 852 nm, respectively. Furthermore, the highest occupied molecular orbital (HOMO) levels of TPDCIC and TPDCNC remain relatively low-lying due to the electronegativity of the carbonyl groups on TPD core. Considering that the absorptions and energy levels of the two NFAs match well with those of a widely used polymer donor, PBDB-T, we fabricate two kinds of organic solar cells (OSCs) based on the PBDB-T:TPDCIC and PBDB-T:TPDCNC blended films, respectively. Through a series of optimizations, the TPDCIC-based devices yield an impressing power conversion efficiency (PCE) of 10.12% with a large short-circuit current density (JSC) of 18.16 mA·cm−2, and the TPDCNC-based ones exhibit a comparable PCE of 9.80% with a JSC of 17.40 mA·cm−2. Our work is the first report of the TPD-core-based A-D-A type NFAs, providing a good reference for the molecular design of high-performance NFAs.

Experimental and numerical collapse properties of externally pressurized egg-shaped shells under local geometrical imperfections

The present investigation is devoted to the nonlinear elastic collapse properties of externally pressurized egg-shaped shells under local geometrical imperfections. The shells have nominal major axis, nominal minor axis, and nominal wall thickness of 256 mm, 180 mm, and 2 mm, respectively. Nine resin egg-shaped shells are manufactured, measured accurately, tested hydrostatically, and analysed numerically. Of these, three each have nominally identical perfect geometries, nominally identical geometries with local flat imperfections, and local dimple imperfections. Furthermore, the effect of local and eigenmode imperfection depths on the collapse pressures of egg-shaped shells are studied numerically using nonlinear elastic buckling analysis. Both experimental and numerical data are presented and compared through graphs and tables.

Structural characterizations, spectroscopic, electrochemical properties, and antibacterial activities of copper (II) and cobalt (II) complexes containing imidazole ring

Two two‐dimensional and three‐dimensional supramolecular complexes [M (L)2] (NO3)2·2CH3OH (M = Cu(1) and Co(2), L = 2‐(4‐imidazolyl)‐4‐methyl‐1,2‐quinazoline‐N3‐oxide), were synthesized and characterized by FT‐IR and UV–Vis spectroscopy, as well as elemental analysis. The spectroscopic data of both complexes were compared with the ligand L. Both complexes were determined by X‐ray single‐crystal diffraction and display similar coordination geometry and have a 2:1 ligand‐to‐metal ratio. All the central M (II) atoms are hexa‐coordinated with perfect octahedral geometries. In the crystal structures, complexes 1 and 2 form an infinite 1‐D chain‐like and 2‐D, 3‐D supramolecular frameworks. X‐ray photoelectron spectrum (XPS) and thermal stability of 2 was investigated. Moreover, electrochemical properties and antimicrobial activities of both complexes were also studied.

“Stonehenge in the Mind” and “Stonehenge on the Ground”:

In Stone-Heng Restored (1655), Inigo Jones, the father of English neoclassicism, used drawings, histories, and questionable logic to argue that Stonehenge was built by the ancient Romans and that it originally exhibited perfect Platonic geometries. This argument was never given much credence, but by 1725 the subject matter and the architect had received enough attention that two book-length responses (a challenge and a defense) were published, and both were then republished in a single volume alongside Jones's original text. While most Jones scholars have neglected this work because of its logical and historical shortcomings, Ryan Roark argues in “Stonehenge in the Mind” and “Stonehenge on the Ground”: Reader, Viewer, and Object in Inigo Jones's Stone-Heng Restored (1655) that it was in fact exemplary of what made Jones, for many, a protomodern architect and scholar. Rather than viewing Jones's book as an earnest attempt to prove a historical inaccuracy, Roark considers it as an exercise in formal analysis, one that set the precedent for the contemporary pedagogical trend of using geometric simplifications of existing structures as a first step in new design. Jones's idiosyncratic reading of Stonehenge belied the idea that such analysis could be anything but intensely reliant on the subjectivity of both architect and viewer.

THREE-DIMENSIONAL DIGITAL DOCUMENTATION OF HERITAGE SITES USING TERRESTRIAL LASER SCANNING AND UNMANNED AERIAL VEHICLE PHOTOGRAMMETRY

Abstract. Three-dimensional digital documentation is an important technique for the maintenance and monitoring of cultural heritage sites. This study focuses on the three-dimensional digital documentation of the Magoksa Temple, Republic of Korea, using a combination of terrestrial laser scanning and unmanned aerial vehicle (UAV) photogrammetry. Terrestrial laser scanning mostly acquired the vertical geometry of the buildings. In addition, the digital orthoimage produced by UAV photogrammetry had higher horizontal data acquisition rate than that produced by terrestrial laser scanning. Thus, the scanning and UAV photogrammetry were merged by matching 20 corresponding points and an absolute coordinate system was established using seven ground control points. The final, complete threedimensional shape had perfect horizontal and vertical geometries. This study demonstrates the potential of integrating terrestrial laser scanning and UAV photogrammetry for three-dimensional digital documentation. This new technique is expected to contribute to the three-dimensional digital documentation and spatial analysis of cultural heritage sites.

Unusual C–N Coupling Reactivity of Thiopyridazines: Efficient Synthesis of Iron Diorganotrisulfide Complexes

The reaction of iron(II) triflate with 6-tert-butyl-3-thiopyridazine (PnH) and 4-methyl-6-tert-butyl-3-thiopyridazine (MePnH) respectively led to iron bis(diorganotrisulfide) complexes [Fe(RPnS3PnR)2](OTf)2 [R = H (1a) and Me (2a)]. The corresponding perchlorate complexes were prepared by using the iron(II) chloride precursor and the subsequent addition of 2 equiv of NaClO4, giving [Fe(RPnS3PnR)2](ClO4)2 [R = H (1b) and Me (2b)]. The compounds were fully characterized including single-crystal X-ray diffraction analysis. All four compounds exhibit nearly perfect octahedral geometries with an iron center coordinated by four nitrogen atoms from two RPnS3PnR ligands and by two sulfur atoms of the central atom in the S3 unit. The diamagnetic complexes exhibit unusually high redox potentials for the Fe2+/3+ couple at E1/2 = 1.15 V (for 1a and 1b) and 1.08 V (for 2a and 2b) versus Fc/Fc+, respectively, as determined by cyclic voltammetry. Furthermore, the source of the extra sulfur atom within the S3 unit was elucidated by isolation of C-N-coupled pyridazinylthiopyridazine products.

Honeytubes: Hollow lattice truss reinforced honeycombs for crushing protection

Lattice truss reinforced honeycombs (LTRHs), termed honeytubes, were developed based on a hybrid design of micro-lattice truss and square honeycomb topologies. Carbon fiber reinforced composite and polymer LTRHs were fabricated using different manufacturing approaches. Out-of-plane compression tests were performed on the LTRHs, and the properties were compared with the conventional square honeycombs. The stiffness and strength values of composite LTRHs didn’t surpass those of composite square honeycombs due to the manually induced defects. On the other hand, polymeric LTRHs with perfect geometries were stiffer and stronger than the corresponding polymeric square honeycombs. A parametric study of the buckling resistance was carried out via finite element analysis, and the results indicated that hollow lattice stiffens honeycombs and increases the resistance to buckling, while the specific properties of honeytubes depend on their geometrical parameters. Moreover, the crush force efficiency and specific energy absorption were greater than those of square honeycombs and hollow lattice. This work demonstrates that hybrid designs that capitalize on micro-topologies can populate vacant regions in mechanical property charts, and provide increased energy absorption as crushing protection structures.

Mode interaction in triple-bay prestressed stayed columns

Prestressed stayed columns are an innovative type of structural system where the compressive load-carrying capacity can be enhanced through prestressed external cable stays. A nonlinear analytical model for prestressed stayed columns with multiple crossarm systems along the column length, based on the Rayleigh–Ritz method, is presented that captures modal interactions for perfect geometries explicitly for the first time. It is demonstrated that the theoretical compressive strength enhancements under certain configurations can only be obtained at the expense of triggering a sequence of destabilizing bifurcations. This can give rise to dangerously unstable interactive post-buckling behaviour including so-called ‘mode jumping’ and ‘snaking’ phenomena. Parametric spaces where the system is most susceptible to the modal interactions are identified and it is for those configurations that the system is likely to be highly sensitive to initial imperfections. The model is validated using a nonlinear finite element model formulated within the commercial code ABAQUS and excellent comparisons are obtained.

Crystal structures of a copper(II) and the isotypic nickel(II) and palladium(II) complexes of the ligand (E)-1-[(2,4,6-tri-bromo-phen-yl)diazen-yl]naphthalen-2-ol.

In the copper(II) complex, bis-{(E)-1-[(2,4,6-tri-bromo-phen-yl)diazen-yl]naph-thalen-2-olato}copper(II), [Cu(C16H8Br3N2O)2], (I), the metal cation is coord-inated by two N atoms and two O atoms from two bidentate (E)-1-[(2,4,6-tri-bromo-phen-yl)diazen-yl]naphthalen-2-olate ligands, forming a slightly distorted square-planar environment. In one of the ligands, the tri-bromo-benzene ring is inclined to the naphthalene ring system by 37.4 (5)°, creating a weak intra-molecular Cu⋯Br inter-action [3.134 (2) Å], while in the other ligand, the tri-bromo-benzene ring is inclined to the naphthalene ring system by 72.1 (6)°. In the isotypic nickel(II) and palladium(II) complexes, namely bis-{(E)-1-[(2,4,6-tri-bromo-phen-yl)diazen-yl]naphthalen-2-olato}nickel(II), [Ni(C16H8Br3N2O)2], (II), and bis-{(E)-1-[(2,4,6-tri-bromo-phen-yl)diazen-yl]naphthalen-2-olato}palladium(II), [Pd(C16H8Br3N2O)2], (III), respectively, the metal atoms are located on centres of inversion, hence the metal coordination spheres have perfect square-planar geometries. The tri-bromo-benzene rings are inclined to the naphthalene ring systems by 80.79 (18)° in (II) and by 80.8 (3)° in (III). In the crystal of (I), mol-ecules are linked by C-H⋯Br hydrogen bonds, forming chains along [010]. The chains are linked by C-H⋯π inter-actions, forming sheets parallel to (011). In the crystals of (II) and (III), mol-ecules are linked by C-H⋯π inter-actions, forming slabs parallel to (10-1). For the copper(II) complex (I), a region of disordered electron density was corrected for using the SQUEEZE routine in PLATON [Spek (2015 ▸). Acta Cryst. C71, 9-18]. The formula mass and unit-cell characteristics of the disordered solvent mol-ecules were not taken into account during refinement.

Near-infrared luminescent Sn(IV) complexes of N-confused tetraphenylporphyrin: Effect of axial anion coordination

Novel tin(IV) halo complexes of an N-confused tetraphenylporphyrin with different axial ligands have been synthesized and characterized by various spectroscopic methods including X-ray crystallographic analysis. The molecular structures of the dichloro and dibromo derivatives possess perfect octahedral geometries, which are nearly comparable to the corresponding regular porphyrin complexes. In contrast, the iodide/triiodide complex obtained by a same reaction manner, demonstrated that the tin(IV) cation is slightly displaced towards axially coordinated iodide anion, giving rise to the different electronic structure due to the tautomeric form of N-confused porphyrin ligand. These structural differences reflected to the distinct photophysical and electrochemical properties. The Sn(IV) complexes are near IR luminescent, however the unsymmetrical axial coordination of iodide and triiodide anions in the tin(IV) N-confused porphyrin complex allows, in particular, the longer emission lifetimes and a smaller singlet-triplet energy gap, which were investigated by steady-state and time-resolved spectroscopies as well as theoretical calculations.

Quantitative Angle-Resolved Small-Spot Reflectance Measurements on Plasmonic Perfect Absorbers: Impedance Matching and Disorder Effects

Plasmonic devices with absorbance close to unity have emerged as essential building blocks for a multitude of technological applications ranging from trace gas detection to infrared imaging. A crucial requirement for such elements is the angle independence of the absorptive performance. In this work, we develop theoretically and verify experimentally a quantitative model for the angular behavior of plasmonic perfect absorber structures based on an optical impedance matching picture. To achieve this, we utilize a simple and elegant k-space measurement technique to record quantitative angle-resolved reflectance measurements on various perfect absorber structures. Particularly, this method allows quantitative reflectance measurements on samples where only small areas have been nanostructured, for example, by electron-beam lithography. Combining these results with extensive numerical modeling, we find that matching of both the real and imaginary parts of the optical impedance is crucial to obtain perfect absorption over a large angular range. Furthermore, we successfully apply our model to the angular dispersion of perfect absorber geometries with disordered plasmonic elements as a favorable alternative to current array-based designs.

Robust Optimization of Cylindrical Gear Tooth Surface Modifications Within Ranges of Torque and Misalignments

Tooth surface modifications are small, micron-level intentional deviations from perfect involute geometries of spur and helical gears. Such modifications are aimed at improving contact pressure distribution, while minimizing the motion transmission error to reduce noise excitations. In actual practice, optimal modification requirements vary with the operating torque level, misalignments, and manufacturing variance. However, most gear literature has been concerned with determining optimal flank form modifications at a single design point, represented by fixed, single load and misalignment values. A new approach to the design of tooth surface modifications is proposed to handle such conditions. The problem is formulated as a robust design optimization problem, and it is solved, in conjunction with an efficient gear contact solver (Load Distribution Program (LDP)), by a direct search, global optimization algorithm aimed at guaranteeing global optimality of the obtained microgeometry solutions. Several tooth surface modifications can be used as microgeometry design variables, including profile, lead, and bias modifications. Depending on the contact solver capabilities, multiple performance metrics can be considered. The proposed method includes the capability of simultaneously and robustly handling several conflicting design objectives. In the present paper, peak contact stress and loaded transmission error amplitude are used as objective functions (to be minimized). At the end, two example optimizations are presented to demonstrate the effectiveness of the proposed method.