Quadratic Geometry Research Articles

Static Performance Measurements and Model Predictions of Gas Foil Thrust Bearing with Curved Incline Geometry

Gas foil thrust bearings (GFTBs) have been successfully used to support the axial load of oil-free microturbomachinery with low drag friction due to the low viscosity of gas or air used as a bearing lubricant. However, the widespread use of GFTBs in various high-power turbomachinery still needs reliable test data and an accurate predictive model. This research measures the height profile of a test GFTB to determine its actual incline geometry and estimate the drag torque of the GFTB. The measured GFTB height profile demonstrates that the incline geometry is closer to a quadratic curve than a line, which has been conventionally used to model GFTBs mathematically. The newly developed GFTB test rig is used to measure the lift-off speed, drag torque, and maximum load capacity of the test GFTB. A series of rotor speed-up tests estimate that the lift-off speeds of the GFTB increase with the increase in preloads. The maximum load capacity is determined by increasing the static load on the GFTB until a sudden sharp peak in the drag torque appears. The new GFTB model using quadratic incline geometry is in suitable agreement with the measured height profile of the GFTB incline and measured drag torque during the load capacity test. In addition, a comparison of the predicted GFTB performances reveals that the quadratic incline geometry model predicts a higher load capacity than the linear model.

C1-smooth isogeometric spline functions of general degree over planar mixed meshes: The case of two quadratic mesh elements

Splines over triangulations and splines over quadrangulations (tensor product splines) are two common ways to extend bivariate polynomials to splines. However, combination of both approaches leads to splines defined over mixed triangle and quadrilateral meshes using the isogeometric approach. Mixed meshes are especially useful for representing complicated geometries obtained e.g. from trimming. As (bi-)linearly parameterized mesh elements are not flexible enough to cover smooth domains, we focus in this work on the case of planar mixed meshes parameterized by (bi-)quadratic geometry mappings. In particular we study in detail the space of C1-smooth isogeometric spline functions of general polynomial degree over two such mixed mesh elements. We present the theoretical framework to analyze the smoothness conditions over the common interface for all possible configurations of mesh elements. This comprises the investigation of the dimension as well as the construction of a basis of the corresponding C1-smooth isogeometric spline space over the domain described by two elements. Several examples of interest are presented in detail.

The influence of aspect ratio on the determination of tearing energy in mode I fracture tests

The energy for tearing is a classical measure of fracture toughness for elastic materials at finite strains. The prominent approach to quantify the tearing energy utilizes a tensile test on edge-cut thin rectangular specimens with low height-to-width ratio to determine the critical stretch at which a crack propagates from the tip of the cut. The analysis of the experiment, proposed by Rivlin and Thomas (1953), relies on the assumption that a large portion of the test piece is in a state of plane strain, and that the change of the total elastic energy is equal to the energy release due to the formation of new crack surfaces. While these assumptions are well justified for test pieces with sufficiently low height-to-width ratio, limitations in the availability and homogeneity of various sample materials have enforced the use of specimens with higher height-to-width ratios. In order to analyse the applicability of the classical theory and the corresponding errors, we investigate in the present work the influence of the sample’s height-to-width ratio on the estimation of the tearing energy in mode I fracture tests. Exemplified with experiments and simulations for the elastomer Ecoflex 1:1, we show that reliable measurements can be obtained even for a quadratic sample geometry. For tough materials, however, significant overestimation of the tearing energy is expected already for a height-to-width ratio larger than 1/2. Surprisingly, in very brittle materials the tearing energy is vice-versa prone to be underestimated by up to 10% for ratios up to 1. The error also depends on the non-linear stress–strain characteristics, as illustrated by the use of different constitutive models. While a generally valid geometrical criterion cannot be defined based on the present results, our results suggest that the error hardly exceeds 10% for height-to-width ratios of up to 1/2.

Biomechanical analysis of novel leaflet geometries for bioprosthetic valves

ObjectivesAlthough bioprosthetic valves have excellent hemodynamic properties and can eliminate the need for lifelong anticoagulation therapy, these devices are associated with high rates of reoperation and limited durability. Although there are many distinct bioprosthesis designs, all bioprosthetic valves have historically featured a trileaflet pattern. This in silico study examines the biomechanical effect of modulating the number of leaflets in a bioprosthetic valve. MethodsBioprosthetic valves with 2 to 6 leaflets were designed in Fusion 360 using quadratic spline geometry. Leaflets were modeled with standard mechanical parameters for fixed bovine pericardial tissue. A mesh of each design was structurally evaluated using finite element analysis software Abaqus CAE. Maximum von Mises stresses during valve closure were assessed for each leaflet geometry in both the aortic and mitral position. ResultsComputational analysis demonstrated that increasing the number of leaflets is associated with reduction in leaflet stresses. Compared with the standard trileaflet design, a quadrileaflet pattern reduces leaflet maximum von Mises stresses by 36% in the aortic position and 38% in the mitral position. Maximum stress was inversely proportional to the square of the leaflet quantity. Surface area increased linearly and central leakage increased quadratically with leaflet quantity. ConclusionsA quadrileaflet pattern was found to reduce leaflet stresses while limiting increases in central leakage and surface area. These findings suggest that modulating the number of leaflets can allow for optimization of the current bioprosthetic valve design, which may translate to more durable valve replacement bioprostheses.

Efficiency Enhancement of CMOS Power Amplifier for RF Applications

This paper presented a new structure for the CMOS power amplifiers as a more effective trend to amplify radio frequency (RF) signals compared to polar power amplifiers PA's by using envelope removal and restoration (EER) technique. Polar PA offers high-efficiency RF-modulated linear signal amplification. However, these amplifiers need high uniformity between the amplitude and phase of the modulated signals. The last translates promptly into higher energy consumption. Rather than deconstructing the quadrature signals into the combination of phase and amplitude signals, it is suggested that the CMOS quadrature power amplifier (QPA's) technique had been used to amplify RF signals immediately. The linearity, bandwidth, efficiency, and power consumption of the QPA's has been improved by separate amplitude and phase quadrature signals. The quadratic geometry architecture contains two bridges from modulated PA's that are able to treat negative or positive voltages, modulation, and RF-power bundling. The design of the new structure is compared with respect to parameters such as fundamental frequency, power gain, PAE, output power, technology or fabrication process, and number of stage transistors. Simulation results for PA's design using CMOS process show an effective quadrature model by a power-added-efficiency (PAE) of 78.413% at a maximum output power of 21.619dBm. The third intermodulation IDM3 is -49.2dBc at output power driven at frequency 2.4 GHz and input power greater than 20dBm. The amplitude and phase distortion has been obtained of 1.4 and 0.26 ᵒ/dB respectively at 50MHz of bandwidth for modulated signals.

Copper(II) complexes derived from furfurylamine and thiophenyl ligands: cytotoxicity, antioxidant properties, and molecular docking assessments

This manuscript describes the synthesis, structural analysis, antioxidant evaluation, cytotoxicity, interaction with DNA, and molecular docking modeling of copper(II) complexes derived from aromatic aldehydes and amines containing furyl and thiophene fragments (C1-C5). All compounds were tested as catalytic mimetics of superoxide dismutase (SOD) using the NBT photoreduction method in a pH 7.8 buffer solution, and structural analysis revealed that all complexes had a quadratic geometry. However, there were important differences in the evaluations with CT-DNA interaction, antioxidant activity, and cytotoxic characteristics. The main interest was to correlate the structure obtained by X-ray diffraction with the tested activities, adding relevant information for future and even deeper applications.

Visual Detection of Adenosine Triphosphate by Taylor Rising: A Simple Point-of-Care Testing Method Based on Rolling Circle Amplification.

Rapid and sensitive point-of-care testing (POCT) is an extremely critical mission in practical applications, especially for rigorous military medicine, home health care, and in the third world. Here, we report a visual POCT method for adenosine triphosphate (ATP) detection based on Taylor rising in the corner of quadratic geometries between two rod surfaces. We discuss the principle of Taylor rising, demonstrating that it is significantly influenced by contact angle, surface tension, and density of the sample, which are controlled by ATP-dependent rolling circle amplification (RCA). In the presence of ATP, RCA reaction effectively suppresses Taylor-rising behavior, due to the increased contact angle, density, and decreased surface tension. Without addition of ATP, untriggered RCA reaction is favorable for Taylor rising, resulting in a significant height. With this proposed method, visual sensitive detection of ATP without the aid of other instruments is realized with only a 5 μL droplet, which has good selectivity and a low detection limit (17 nM). Importantly, this visual method provides a promising POCT tool for user-friendly molecular diagnostics.

A mixed lubrication analysis of a flat‐land thrust bearing with a surface optimisation method

AbstractThrust bearings are widely used in many rotary industrial applications. In this work, a thrust bearing surface under the mixed lubrication regime is analysed and then optimised with aim for use in an injection moulded polymer bearing. A model which couples the mechanical deformation, boundary lubrication and solid contact is developed to investigate the behaviour of the thrust bearing under the load balance condition. This model provides the predictions of important quantities such as load carrying capacity from fluid and solid contact, minimum film thickness and contact pressure. More important, the large‐scale surface geometry is optimised using a quadratic geometry and this large‐scale surface is superimposed with the small‐scale roughness from measured surface to form an optimised surface. This large‐scale geometry might be controlled in the injection moulding process of polymer thrust bearings, whereas it is more difficult to control the roughness. The fluid load carrying capacity for the optimised surface has more than doubled compared to the fluid load carrying capacity for the measured surface.

Coordination of Zn(II), Pd(II) and Pt(II) with ligands derived from diformylpyridine and thiosemicarbazide: Synthesis, structural characterization, DNA/BSA binding properties and molecular docking analysis

Synthesis of three novel inorganic complexes (Zn(II), Pd(II), and Pt(II) – [Zn(H2L)](NO3)2, [Pd(L)], and [Pt(L)], respectively) based on 2,6-diformylpyridine-bis-(4-phenyl) thiosemicarbazone (H2L) was obtained under reflux medium, yielded in the range of 67% and 86%. Characterization of each compound was done via X-ray diffraction and spectroscopic methods. Structural analysis revealed the formation of complexes with pentagonal and quadratic bipyramidal geometry. Electronic absorption spectra for the ligand and inorganic complexes exhibited π → π* and n → π* transitions in the UV region, however, [Pd(L)] and [Pt(L)] showed other less energetic bands attributed to ligand-to-metal charge transfer (LMCT). The interaction between each compound and two macromolecules: calf-thymus DNA (CT-DNA) and bovine serum albumin (BSA) was conducted by spectroscopic techniques combined to molecular docking calculation. For CT-DNA interaction, [Zn(H2L)](NO3)2 is the weakest intercalate compound and the increasing order of Kb values follows [Zn(H2L)](NO3)2 < H2L < [Pd(L)] ≈ [Pt(L)]. Molecular docking results suggested van der Waals interactions as the main intermolecular force involved in the interaction process between DNA and each derivative. For BSA, experimental results indicated weak (H2L and [Zn(H2L)](NO3)2) and moderate ([Pd(L)] and [Pt(L)]) interaction in the ground-state, in the proportion 1:1 (n ~ 1.0). Molecular docking results suggested Trp-212 containing binding site as the main protein pocket for H2L, [Zn(H2L)](NO3)2, [Pd(L)], and [Pt(L)].

Technical Note: Harmonic analysis applied to MR image distortion fields specific to arbitrarily shaped volumes.

Magnetic resonance imaging is expected to play a more important role in radiation therapy given the recent developments in MR-guided technologies. MR images need to consistently show high spatial accuracy to facilitate RT-specific tasks such as treatment planning and in-room guidance. The present study investigates a new harmonic analysis method for the characterization of complex three-dimensional (3D) fields derived from MR images affected by system-related distortions. An interior Dirichlet problem based on solving the Laplace equationwith boundary conditions (BCs) was formulated for the case of a 3D distortion field. The second-order boundary value problem (BVP) was solved using a finite elements method (FEM) for several quadratic geometries - that is, sphere, cylinder, cuboid, D-shaped, and ellipsoid. To stress-test the method and generalize it, the BVP was also solved for more complex surfaces such as a Reuleaux 9-gon and the MR imaging volume of a scanner featuring a high degree of surface irregularities. The BCs were formatted from reference experimental data collected with a linearity phantom featuring a volumetric grid structure. The method was validated by comparing the harmonic analysis results with the corresponding experimental reference fields. The harmonic fields were found to be in good agreement with the baseline experimental data for all geometries investigated. In the case of quadratic domains, the percentage of sampling points with residual values larger than 1mm was 0.5% and 0.2% for the axial components and vector magnitude, respectively. For the general case of a domain defined by the available MR imaging field of view, the reference data showed a peak distortion of about 1mm and 79% of the sampling points carried a distortion magnitude larger than 1mm (tolerance intrinsic to the experimental data). The upper limits of the residual values after comparison with the harmonic fields showed max and mean of 1.4 and 0.25mm, respectively, with only 1.5% of sampling points exceeding 1mm. A novel harmonic analysis approach relying on finite element methods was introduced and validated for multiple volumes with surface shape functions ranging from simple to highly complex. Since a boundary value problem is solved the method requires input data from only the surface of the desired domain of interest. It is believed that the harmonic method will facilitate (a) the design of new phantoms dedicated for the quantitation of MR image distortions in large volumes and (b) an integrative approach of combining multiple imaging tests specific to radiotherapy into a single test object for routine imaging quality control.

Computing the Distance between Two Finite Element Solutions Defined on Different 3D Meshes on a GPU

This article introduces a new method to efficiently compute the distance (i.e., $L^p$ norm of the difference) between two functions supported by two different meshes of the same 3D domain. The functions that we consider are typically finite element solutions discretized in different function spaces supported by meshes that are potentially completely unrelated. Our method computes an approximation of the distance by resampling both fields over a set of parallel 2D regular grids. By leveraging the parallel horse power of computer graphics hardware (graphics processing unit (GPU)), our method can efficiently compute distances between meshes with multimillion elements in seconds. We demonstrate our method applied to different problems (distance between known functions, Poisson solutions, and linear elasticity solutions) using different function spaces (Lagrange polynomials from order one to seven) and different meshes (tetrahedral and hexahedral, with linear or quadratic geometry).

Inorganic and organic structures as interleavers among [bis(1-methyl-3-(p-carboxylatephenyl)triazenide 1-oxide)Ni(II)] complexes to form supramolecular arrangements

Alternative compounds to capture metal ions are triazenes 1-oxide since they are basic compounds O(N) with negative charge in the deprotonated form. The proximity of both coordination sites (O and N) enables these compounds to have good chelating ability and a tendency to stabilize in the formation of rings with soft and hard transition metal ions. The structure analysis by single crystal X-ray diffraction of compounds (1) and (2) demonstrate the formation of 3D supramolecular arrangements through ion-ion, ion-dipolo and dipolo-dipolo interactions. In one of them, there are [(H2O)2(CH3CH3SO)K2]2+ as linkers of polymerization and, in another complex, there are [(H2O)(CH3CH3SO)Ni(H2O)6]2+ as a linker of polymerization. These linkers act in the polymerization of the novel mononuclear complex [bis(1-methyl (p-carboxylatephenyl) triazenide 1-oxide) NiII] (3). The crystallography analysis of (1) and (2) showed distorted quadratic geometry for Ni (II), thus, there are two axial positions available in Ni (II) to be used in catalysis studies and as sensor or biosensor. In addition, this study shows the support of this novel mononuclear complex of Ni (II) (3) on protonated chitosan chains (4). The compounds (3) and (4) were characterized by spectroscopic analysis, infrared (IR) and energy dispersive X-ray detector (EDS), and by differential scanning calorimetry analysis (DSC). The specificity of ligand 1-methyl (p-carboxyphenyl) triazene 1-oxide to capture potassium and nickel ions will be tested at different pH values, as well as the capacity of the triazenide 1-oxide of Ni (II) complex, supported on chitosan polymer, or not, to act as a catalyst for organic reactions and biomimetic organic reactions.

Characters, bilinear forms and solvable groups

We prove a number of results about the ordinary and Brauer characters of finite solvable groups in characteristic 2, by defining and using the concept of the extended nucleus of a real irreducible character. In particular we show that the Isaacs canonical lift of a real irreducible Brauer character has Frobenius–Schur indicator +1. We also show that the principal indecomposable module corresponding to a real irreducible Brauer character affords a quadratic geometry if and only if each extended nucleus is a split extension of a nucleus.

Möbius Maps and Periodic Continued Fractions

SummaryWe describe some of the relationships that exist between quadratic irrationals, continued fractions, Möbius maps, and hyperbolic geometry, and we illustrate these by giving a simple geometric proof of Galois' result on dual continued fractions.

Interface problems with quadratic X-FEM: design of a stable multiplier space and error analysis

SUMMARY The aim of this paper is to propose a procedure to accurately compute curved interfaces problems within the extended finite element method and with quadratic elements. It is dedicated to gradient discontinuous problems, which cover the case of bimaterials as the main application. We focus on the use of Lagrange multipliers to enforce adherence at the interface, which makes this strategy applicable to cohesive laws or unilateral contact. Convergence then occurs under the condition that a discrete inf-sup condition is passed. A dedicated P1 multiplier space intended for use with P2 displacements is introduced. Analytical proof that it passes the inf-sup condition is presented in the two-dimensional case. Under the assumption that this inf-sup condition holds, a priori error estimates are derived for linear or quadratic elements as functions of the curved interface resolution and of the interpolation properties of the discrete Lagrange multipliers space. The estimates are successfully checked against several numerical experiments: disparities, when they occur, are explained in the literature. Besides, the new multiplier space is able to produce quadratic convergence from P2 displacements and quadratic geometry resolution. Copyright © 2014 John Wiley & Sons, Ltd.

Synthesis, Characterization, Crystal Structure and Antimicrobial Evaluation of a Novel –M–X–M–X– Type Infinite Chain 1D Cu(II) Complex with Eflornithine Hydrochloride Hydrate as Ligand

A novel –M–X–M–X– type infinite chain 1D copper(II) complex of Eflornithine, Dichloro-[2-amino-5-ammonio-2-(difluoromethyl)pentanoate]copper(II) hydrate, [Cu(C6H12F2N2O2)Cl2]·H2O 1 has been synthesized and characterized by elemental analysis, spectroscopic techniques (UV/Vis and FT-IR), TGA and X-ray diffraction. Single-crystal X-ray diffraction analysis of the complex 1 showed the structure to be monoclinic with space group Cc, a = 13.1295(15) A, b = 12.1859(14) A, c = 8.1927(9) A, β = 118.359(3) A, V = 1153.5(2) A3, Z = 4. The complex exhibits a quadratic planar coordination of the Cu-atom. The Cu(II) centre is coordinated by two chloride atoms, an oxygen atom of the carboxyl- and a nitrogen atom of the amino-group, respectively, forming a quadratic planar geometry. The terminal amino group of the ligand is protonated to form NH3+ while the carboxylic moiety is deprotonated to form Zwitterionic eflornithine ligand, with the coordination of the metal at the nitrogen atom of the second amino group. The compound has –M–X–M–X– infinite 1D chain polymeric structure. Two neigbouring Cu(EFL)Cl chain units are bridged by an Cl− ion, forming a –Cu–Cl–Cu–Cl– linear chain structure along C-axis. The antibacterial activities of the complex on Escherichia coli (E. coli), Staphylococcus aureus (S. aureus) and Pseudomonas aeruginosa (P. aeruginosa) were investigated and found to be active at higher concentration than the parent ligand.

Optimal geometry design of double coat-hanger die for melt blowing process

Design of the wide coat-hanger die is of significant importance for melt blowing system because the die plays a key role in the uniformity wider nonwoven webs. In this article, a mathematical method combining finite element and numerical simulation is used to optimize double coat-hanger die with uniform outlet velocity. A numerical approach is developed for design of double coat-hanger die with quadratic geometry manifold. The results indicate that melt flow direction in the manifold is along its lengthwise direction and the CV value of outlet velocity is decreased obviously. In addition, a 40:3 elliptic rate of ellipse cavity is inserted in the double coat-hanger die slot. It shows that the ellipse cavity and slot act together to improve flow distribution and pressure drop. The result of outlet velocity CV value is under 1 % for 3.4 meter width of double coat-hanger die. The current study provides a simple method to obtain wider coat-hanger die suitable for melt blowing commercial production.

Characterization of tissue magnetic susceptibility‐induced distortions for MRIgRT

MR image geometric integrity is one of the building blocks of MRI-guided radiotherapy. In particular, tissue magnetic susceptibility-induced effects are patient-dependent and their behavior is difficult to assess and predict. In this study, the authors investigated in detail the characteristics of susceptibility (χ) distortions in the context of MRIgRT, including the case of two common MR-linac system configurations. The magnetic field distortions were numerically simulated for several imaging parameters and anatomical sites, i.e., brain, lung, pelvis (with air pockets), and prostate. The simulation process consisted of (a) segmentation of patient CT data into susceptibility relevant anatomical volumes (i.e., soft-tissue, bone and air∕lung), (b) conversion of CT data into susceptibility masks by assigning bulk χ values to the structures defined at (a), (c) numerical computations of the local magnetic fields by using a finite difference algorithm, and (d) generation of the geometric distortion maps from the magnetic field distributions. For each patient anatomy, the distortions were quantified at the interfaces of anatomical structures with significantly different χ values. The analysis was performed for two specific orientations of the external main magnetic field (B(0)) characteristic to the MR-linac systems, specifically along the z-axis for a bore MR scanner and in the (x,y)-plane for a biplanner magnet. The magnetic field local perturbations were reported in ppm. The metrics used to quantify the geometric distortions were the maximum, mean, and range of distortions. The numerical simulation algorithm was validated using phantom data measurements. Susceptibility-induced distortions were determined for both quadratic and patient specific geometries. The numerical simulations showed a good agreement with the experimental data. The measurements were acquired at 1.5 and 3 T and with an encoding gradient varying between 3 and 20 mT∕m by using an annular phantom mimicking the water-air and water-oil χ interfaces. For quadratic geometries, the magnitude of field distortion increased rapidly with the size of the inhomogeneity up to about 10 mm and then tended to plateau. This trend became more evident for materials with a larger Δχ relative to water. The simulations showed only a slight increase in the maximum distortion values when the B(0) orientation was varied with regard to the shape of the χ inhomogeneity. In the case of patient anatomy, the largest distortion values arose at the air-soft-tissue interface. Considering the two MR-linac system configurations and comparing the field distortion values corresponding to all organ structures, the distortions tended to be larger for the biplanar magnet. The authors provide a reference table with ppm values which can be used to easily evaluate the geometric distortions for patient data as a function of B(0) and the strength of the encoding gradient. The susceptibility distortions were quantified as a function of multiple parameters such as the χ inhomogeneity size and shape, the magnitude of B(0) and the readout gradient, and the orientation of B(0) with respect to the sample geometry. The analysis was performed for several anatomical sites and corresponding to two B(0) orientations as featured by MR-linac systems.

An integrated experimental and theoretical investigation of the vibrational modes and molecular structure of a new Cu(II)–phosphocreatine complex

A new complex of Cu(II) of stoichiometry [Cu(PCr)(H 2O)] was prepared from aqueous solution at pH 6. Its synthesis, characterization, thermogravimetric, vibrational spectroscopy, and electron paramagnetic resonance analyses were described and suggest that phosphocreatine (PCr) in solid state is acting as a tridentate ligand (the nitrogen atom of the guanidine group and the oxygen atoms of the phosphate group and the carboxylate group being the donor atoms). The fourth position is occupied by a water molecule. These results were confirmed through computational calculations (DFT/B3LYP:6-311G theoretical procedure). The tetra coordination of Cu(II) arranged in a quadratic planar geometry was found to be more stable in the DFT calculations. The calculated vibrational spectrum agrees well with the FT-IR experimental spectrum.

Projective indecomposable modules, Scott modules and the Frobenius–Schur indicator

Let Φ be a principal indecomposable character of a finite group G in characteristic 2. The Frobenius–Schur indicator ν ( Φ ) of Φ is shown to equal the rank of a bilinear form defined on the span of the involutions in G. Moreover, if the principal indecomposable module corresponding to Φ affords a quadratic geometry, then ν ( Φ ) > 0 . This result is used to prove a more precise form of a theorem of Benson and Carlson on the existence of Scott components in the endomorphism ring of an indecomposable G-module, in case the module affords a G-invariant symmetric form.