Search Results (25)

One of the most well-known problems of dynamics is the “ladder problem”. In this paper, a theoretical model is proposed followed by the experimental validation of the predicted solution. The model refers to a rod of negligible thickness with the ends leaning frictionless on two walls. By approximating the rod as a segment, the problem is simplified, and the Lagrange equations can be applied. The experimental validation of the model had to address several challenges: the actual rod–wall contacts are singular points, friction cannot be neglected, and the rod’s motion must remain confined to the vertical plane. The physical “ladder” was designed as a cylindrical rod with two identical balls of well-controlled geometry, fixed at the ends. These spheres make contact with two half-cylinder grooves—one vertical and one horizontal—ensuring that the motion remains parallel to the vertical plane. The presence of dry friction in the sphere–groove contacts leads to a complex, strongly nonlinear differential equation of motion, requiring numerical methods of integration. A test-rig was designed and constructed for the experimental study of motion, and an aspect overlooked by the theoretical model was emphasised: the interruption of contact with the vertical wall. An excellent agreement was found between the experimental data and the theoretical results. Full article

Self-assembly of amphiphilic molecules is an important phenomenon attracting a broad range of research. In this work, we study the self-assembly of KTOF₄ sphere–rod amphiphilic molecules in mixed water–dioxane solvents. The molecules are of a T-shaped geometry, comprised of a hydrophilic spherical Keggin-type cluster attached by a flexible bridge to the center of a hydrophobic rod-like oligodialkylfluorene (OF), which consists of four OF units. Transmission electron microscopy (TEM) uncovers self-assembled spherical structures of KTOF₄ in dilute solutions. These spheres are filled with smectic-like layers of KTOF₄ separated by layers of the solution. There are two types of layer packings: (i) concentric spheres and (ii) flat layers. The concentric spheres form when the dioxane volume fraction in the solution is 35–50 vol%. The flat layers are formed when the dioxane volume fraction is either below (20 and 30 vol%.) or above (55 and 60 vol%.) the indicated range. The layered structures show no in-plane orientational order and thus resemble thermotropic smectic A liquid crystals and their lyotropic analogs. The layered packings reveal edge and screw dislocations. Evaporation of the solvent produces a bulk birefringent liquid crystal phase with textures resembling the ones of uniaxial nematic liquid crystals. These findings demonstrate that sphere–rod molecules produce a variety of self-assembled structures that are controlled by the solvent properties. Full article

The aim of this study was to assess the impact of the variability of the Yeoh model when modeling the contact of bones through cartilage in the knee in compression and flexion–extension within a hybrid knee model. Firstly, a Sobol sequence of 64 samples and four variables representing the Yeoh parameters of the cartilage of the femur and tibia was generated. Based on these samples, 2 × 64 finite element contact models of the geometry of the sphere plane were generated and solved for healthy tissue affected by osteoarthritis. The resulting indentation curves were incorporated into a multibody knee joint model. The obtained results suggested that cartilage variability severely affected the knee in compression by up to 32%. However, the same variability also affected the flexion–extension motion, although to a lesser extent, with a relative change to the range of angular displacements of almost 7%. Osteoarthritic tissue was consistently more affected by this variability, suggesting that when modeling degenerated tissue, complex joint models are necessary. Full article

We report here the synthesis of a series of nine coordinated mononuclear Ln^III complexes [LnL₁Cl₂(DMF)]Cl·2.5DMF and [LnL¹(L₂)₂]Cl·4CH₃OH (Ln^III = Gd^III, Dy^III, Er^III and Yb^III, HL₂ = 9-anthracenecarboxylic acid), where L1 is a hexadentate N₄O₂ Schiff base ligand prepared from the condensation of 1,10-phenanthroline-2,9-dicarbaldehyde and semicarbazone. The X-ray crystal structures of these complexes show the Ln^III ions to possess LnN₄O₂Cl₂ and LnN₄O₄ coordination spheres, which can be considered to be derived from a hexagonal bipyramidal geometry, with the ligand in the equatorial plane and the anions (chloride or 9-antracenecarboxylate) in axial positions, which undergo distortion after coordination of either a molecule of DMF or a bidentate coordination of the 9-anthracenecarboxxylate ligand. All these compounds exhibit field-induced slow magnetization relaxation (SMR). The absence of SMR at zero field due to QTM, as well as the processes involved in the magnetic relaxation under a field of 0.1 T, have been justified on the basis of theoretical calculations and the distortion of the respective coordination spheres. The severe discrepancy between the calculated and experimental thermal energy barriers for the Dy^III complexes seems to indicate that the relaxation occurs with the contribution of spin–vibrational coupling, which is favored by the flexibility of the ligand. Full article

In this article, we address resistance forces and torques acting onto a body with arbitrary shape moving in an unsteady Stokes flow. We start analyzing the functional form of the expressions for forces and torques, which depend on the frequency parameter and on the position of the body in the domain of the fluid, and determining the asymptotic limits for high and low frequencies. In this regard, we show that, for high frequencies (hence short times), forces and torques are obtained by the associated hydrodynamic problems considering ideal potential flows, independently of the geometry of the problem. Afterwards, with the aim of obtaining expressions for forces and torques valid in the entire range of frequencies, we extend to the unsteady case the reflection method, largely employed in the theory of the steady Stokes flows. In this way, general expressions are provided in terms of the Faxén operators of the body and the Green function associated with the geometry of the confinement, that are valid, to the leading order, at any frequency, independently of the geometry of the problem. Finally, as the application of the general expressions, explicit relations for the resistance forces acting onto a spherical body with no-slip boundary conditions near a plane wall with full-slip boundary conditions are obtained, valid over the entire frequency range, provided that the distance between the plane and the sphere is larger than one sphere radius. Full article

Starting with the most fundamental differential-geometric principles we derive here new explicit parameterizations of the Delaunay surfaces of revolution which depend on two real parameters with fixed ranges. Besides, we have proved that these parameters have very clear geometrical meanings. The first one is responsible for the size of the surface under consideration and the second one specifies its shape. Depending on the concrete ranges of these parameters any of the Delaunay surfaces which is neither a cylinder nor the plane is classified unambiguously either as a first or a second kind Delaunay surface. According to this classification spheres are Delaunay surfaces of first kind while the catenoids are Delaunay surfaces of second kind. Geometry of both classes is established meaning that the coefficients of their fundamental forms are found in explicit form. Full article

The tetrafluoroborate salt of the cationic Cu(I) complex [Cu(CHpz₃)(PPh₃)]⁺, where CHpz₃ is the tridentate N-donor ligand tris(pyrazol-1-yl)methane and PPh₃ is triphenylphosphine, was synthesized through a displacement reaction on the acetonitrile complex [Cu(NCCH₃)₄][BF₄]. The compound crystallizes in the monoclinic P2₁/c space group. The single-crystal X-ray diffraction revealed that the copper(I) centre is tetracoordinated, with a disposition of the donor atoms surrounding the metal centre quite far from the ideal tetrahedral geometry, as confirmed by continuous shape measures and by the τ₄ parameter. The intermolecular interactions at the solid state were investigated through the Hirshfeld surface analysis, which highlighted the presence of several non-classical hydrogen bonds involving the tetrafluoroborate anion. The electronic structure of the crystal was modelled using plane-wave DFT methods. The computed band gap is around 2.8 eV and separates a metal-centred valence band from a ligand-centred conduction band. NMR spectroscopy indicated the fluxional behaviour of the complex in CDCl₃ solution. The geometry of the compound in the presence of chloroform as implicit solvent was simulated by means of DFT calculations, together with possible mechanisms related to the fluxionality. The reversible dissociation of one of the pyrazole rings from the Cu(I) coordination sphere resulted in an accessible process. Full article

At microwave frequencies, radar cross-section (RCS) measurements are usually performed by placing the target in the far-field region of the antenna. The wavefront of the radiating field from the antenna can be approximated as planar, ensuring that the incident field and the power interact with the target independently of the antenna. However, for electrically large targets, the required distance becomes significant, posing challenges for implementation. Scaled-model RCS measurements offer an alternative solution. RCS measurements at terahertz and optical frequencies typically require a collimated beam as the source, where the intercepted power and RCS become dependent on the excitation. To address this dependency, researchers have proposed modifying the RCS definition to account for the intercepted power and to analytically formulate the scattering problem. However, such modifications require prior knowledge of the target’s geometry and material properties, which are often not readily available in practice. This also limits the study to only canonical targets. In this paper, we propose an alternative approach for modelling the intercepted power. The Gaussian beam is decomposed into a number of plane waves travelling to different directions using the theory of plane wave spectrum. The scattering problem is solved using the full-wave method of moment. Through theoretical proofs and numerical examples involving spheres and a non-canonical target, with a scaled-model aircraft, we demonstrate that the original RCS definition can serve as a good approximation for scaled measurements, provided that the beam waist is approximately four times the target’s dimensions. These findings provide valuable guidelines for radar engineers when performing scaled measurements using collimated beams. The results, which match those obtained from full-model measurements, enable us to predict the RCS of full-scale targets. This capability facilitates various target-related applications, such as target characterization, classification, detection, and even recognition. Full article

Two new Co(II) and Cu(II) azido complexes with 4-picoline (4-Pic) and pyridine-2-carboxaldoxime (HAld) were synthesized by self-assembly of the organic ligand and the M(II) nitrate in the presence of azide as a co-ligand. Their structures were determined to be [Co(4-Pic)₄(H₂O)(N₃)]NO₃*H₂O*4-Pic (1) and [Cu(HAld)(Ald)(N₃)] (2) using X-ray single crystal diffraction. In complex 1, the coordination geometry is a slightly distorted octahedron with a water molecule and azide ion located trans to one another. On the other hand, complex 2 has a distorted square pyramid CuN₅ coordination sphere with N-atoms of the organic ligand as a basal plane and azide ion as apical. All types of intermolecular contacts and their contributions in the molecular packing were analyzed using Hirshfeld analysis. The intermolecular contacts, H…H (53.9%), O…H (14.1%), N…H (11.0%) and H…C (18.8%) in 1, and H…H (27.4%), N…H (27.7%), O…H (14.7%) and H…C (13.6%) in 2 have the largest contributions. Of all the contacts, the O…H, N…H and C…C interactions in 2 and the O…H, N…H and H…C in 1 are apparently shorter than the van der Waals radii sum of the interacting atoms. Atoms in molecules (AIM) topological parameters explained the lower symmetry of the coordinated azide in 1 than 2. Full article

Target-based point cloud registration methods are still widely used by many laser scanning professionals due to their direct and manipulable nature. However, placing and moving multiple targets such as spheres for registration is a time-consuming and tactical process. When the number of scans gets large, the time and labor costs will accumulate to a high level. In this paper, we propose a flexible registration method that requires the installation of only a low-cost cubical target: a die-like object. The method includes virtual coordinate system construction and two error compensation techniques, in which the non-orthogonality of the scanned facets, along with the unknown sizes of the dice are estimated based on projection geometry and cubical constraints so that three pairs of conjugate points can be accurately identified along the axes of the constructed coordinate systems for the registration. No scan overlap of the facet is needed. Two different low-cost dice (with a volume of 0.125 m³ and 0.027 m³) were used for verifying the proposed method, which shows that the proposed method delivers registration accuracy (with an RMSE discrepancy of less than 0.5 mm for check planes) comparable to the traditional sphere- based method using four to six spherical targets spanning the scene. Therefore, the proposed method is particularly useful for registering point clouds in harsh scanning environments with limited target-setting space and high chances of target interruption. Full article

We present here a theory of the electronic properties of quasi two-dimensional quantum dots made of topological insulators. The topological insulator is described by either eight band $\overrightarrow{k}·\overrightarrow{p}$ Hamiltonian or by a four-band $\overrightarrow{k}·\overrightarrow{p}$ Bernevig–Hughes–Zhang (BHZ) Hamiltonian. The trivial versus topological properties of the BHZ Hamiltonian are characterized by the different topologies that arise when mapping the in-plane wavevectors through the BHZ Hamiltonian onto a Bloch sphere. In the topologically nontrivial case, edge states are formed in the disc and square geometries of the quantum dot. We account for the effects of compressive strain in topological insulator quantum dots by means of the Bir–Pikus Hamiltonian. Tuning strain allows topological phase transitions between topological and trivial phases, which results in the vanishing of edge states from the energy gap. This may enable the design of a quantum strain sensor based on strain-driven transitions in HgTe topological insulator square quantum dots. Full article

The results of an experimental investigation on pressure drop and heat transfer in spacer-filled plane channels, which are representative of Membrane Distillation units, are presented and discussed. Local and mean heat transfer coefficients were obtained by using Thermochromic Liquid Crystals and Digital Image Processing. The performances of a novel spacer geometry, consisting of spheres that are connected by cylindrical rods, and are hereafter named spheres spacers, were compared with those of more conventional woven and overlapped spacers at equal values of the Reynolds number Re (in the range ~150 to ~2500), the pitch-to-channel height ratio, the flow attack angle and the thermal boundary conditions (two-side heat transfer). For any flow rate, the novel spacer geometry provided the least friction coefficient and a mean Nusselt number intermediate between those of the overlapped and the woven spacers. For any pressure drop and for any pumping power, the novel spacer provided the highest mean Nusselt number over the whole Reynolds number range that was investigated. The influence of buoyancy was also assessed for the case of the horizontal channels. Under the experimental conditions (channel height H ≈ 1 cm, ΔT ≈ 10 °C), it was found to be large in empty (spacer-less) channels that were up to Re ≈ 1200 (corresponding to a Richardson number Ri of ~0.1), but it was much smaller and limited to the range Re < ~500 (Ri < ~0.5) in the spacer-filled channels. Full article

At the nanoscale, particle size affects the surface reactivity of anatase–water interfaces. Here, we investigate the effect of electrolyte media and particle size on the primary charging behavior of anatase nanoparticles. Macroscopic experiments, potentiometric titrations, were used to quantitatively evaluate surface charge of a suite of monodisperse nanometer sized (4, 20, and 40 nm) anatase samples in five aqueous electrolyte solutions. The electrolyte media included alkaline chloride solutions (LiCl, NaCl, KCl, and RCl) and Na-Trifluoromethanesulfonate (NaTr). Titrations were completed at 25 °C, as a function of pH (3–11) and ionic strength (from 0.005 to 0.3 m). At the molecular scale, density functional theory (DFT) simulations were used to evaluate the most stable cation surface species on the predominant (101) anatase surface. In all electrolyte media, primary charging increased with increasing particle size. At high ionic strength, the development of negative surface charge followed reverse lyotropic behavior: charge density increased in the order RbCl < KCl < NaCl < LiCl. Positive surface charge was greater in NaCl than in NaTr media. From the DFT simulations, all cations formed inner-sphere surface species, but the most stable coordination geometry varied. The specific inner-sphere adsorption geometries are dependent on the ionic radius. The experimental data were described using surface complexation modeling (SCM), constrained by the DFT results. The SCM used the charge distribution (CD) and multisite (MUSIC) models, with a two-layer (inner- and outer-Helmholtz planes) description of the electric double layer. Subtle charging differences between the smallest and larger anatase particles were the same in each electrolyte media. These results further our understanding of solid–aqueous solution interface reactivity of nanoparticles. Full article

The global demand on adipic usage in the production of plasticizers and synthetic polyamide is increasing. In line with the search for an efficient and energy-conserving way to isolate adipic acid (AA) in good yields, this paper introduces the oxidization of cyclohexanone utilizing two new coordination compounds, [Mn(2,6-pydc)₂](imi) (1) and [Co(H₂pza)₂(H₂O)₂(NO₃)].NO₃ (2), as catalysts. Compounds 1 and 2 were synthesized by room temperature and refluxing methods, and characterized by spectral analyses (IR and UV-Vis.), SEM, BET, TGA, elemental, and X-ray crystallography. The single crystal structure of compound 1 revealed that pyridinedicarboxylate (2,6-pydc) and imidazole (imi) moieties were coordinated to the Mn(II) atom through imine nitrogen and deprotonated oxygen atoms, to form an undistorted octahedral coordination geometry with the N₂O₄ donor set. The axial and equatorial planes containing O2, O4, O5, and O7 atoms were from two adjacent 2,6-pydc ligands which formed the unidendate donor ligand; imi, on the other hand, acted as a bidendate donor ligand. For compound 2, the Co(II) atom was being coordinated by two pyrazinamide (H₂pza) moieties, which acted as an unidendate donor ligand; two water molecules occupying the axial position, and one nitrate molecule occupying the apical position, were within the coordination sphere; a nitrate molecule was disordered outside the coordination sphere. The distance, 4.658 Å, between the Co1 atom and the N8 atom of the uncoordinated nitrate molecule, was within the range reported elsewhere. Cyclohexanone peroxidation experiments revealed that compound 1 exhibited unique catalytic performance by giving a 72.8% yield in adipic acid, in comparison to the 71.3% yield obtained with compound 2. The yields in AA were maintained by way of recyclability evaluation. The reaction kinetics of compound 2 gave less activation energy, E_a 2938 J mol⁻¹, while the thermodynamic parameters indicated that the chemical reactivity of cyclohexanone on the active surfaces of compounds 1 and 2 was via monolayer physisorption. Full article

Massive MIMO technology is among the most promising solutions for achieving higher gain in 5G millimeter-wave (mmWave) channel models for high-speed train (HST) communication systems. Based on stochastic geometry methods, it is fundamental to accurately develop the associated MIMO channel model to access system performance. These MIMO channel models could be extended to massive MIMO with antenna arrays in more than one plane. In this paper, the proposed MIMO 3D geometry-based stochastic model (GBSM) is composed of the line of sight component (LOS), one sphere, and multiple confocal elliptic cylinders. By considering the proposed GBSM, the local channel statistical properties are derived and investigated. The impacts of the distance between the confocal points of the elliptic cylinder, mmWave frequencies of 28 GHz and 60 GHz, and non-stationarity on channel statistics are studied. Results show that the proposed 3D simulation model closely approximates the measured results in terms of stationary time. Consequently, findings show that the proposed 3D non-wide-sense stationary (WSS) model is better for describing mmWave HST channels in an open space environment. Full article