Conical Model Research Articles

Investigation of Relationship between Instrumented Indentation Nominal Hardness and Reduced Elastic Modulus with Large Apex Angle Indenter

Based on dimensional analysis, finite element numerical calculation is undertaken on elastic–plastic solids to investigate the relationship between instrumented indentation nominal hardness Hn and reduced elastic modulus Er for three different apex angle indenters. The half-included angles of axisymetric conical indenter models are 62.9°, 70.3°and 85.566° which are corresponding to the real indenters of cube corner indenter with 60° face angle, Berkovich indenter with 65.27° face angle and cube corner indenter with 85° face angle, respectively. The relationship between a nominal hardness/reduced elastic modulus (Hn/Er) and elastic work/total indentation work (We/Wt) is established with a sixth-order polynomial form for each apex angle indenter. For rigid indenter of instrumented indentation model, reduced elastic modulus Er=1/[(1+v2)/E], where E and v are elastic modulus and Poisson’s ratio of the indented material. Therefore, Hn/Er–We/Wt relationship can be used to give estimates of E. Accuracy estimation for the each relationship of each half-included angle indenter shows that the large half-included angle of 85.566° gives better Er measurement error of +11.56% for a low yield strength material(e.g., materials for which σy=100MPa, n=0 and E=200GPa), while for the smaller half-included angle of 62.9° or 70.3° indenter, the measurement error is > ±12.74%. The research in this paper confirms that Hn/Er–We/Wt relationship of large apex angle indenter such as 85.566° half-included angle is recommended to be used for estimating the elastic modulus E of indented material.

Thermo-mechanical modeling of dendrite deformation in continuous casting of steel

In the field of modern steelmaking, continuous casting has become the major manufacturing process to handle a wide range of steel grades. An important criterion characterizing the quality of semi-finished cast products is the macrosegregation forming at the centre of these products during solidification. The deformation induced interdendritic melt flow has been identified as the key mechanism for the formation of centreline segregation. Bulging of the solidified strand shell causes deformation of the solidifying dendrites at the casting's centre. Hence, a fundamental knowledge about the solid phase motion during casting processes is crucial to examine segregation phenomena in detail. To investigate dendritic deformation particularly at the strand centre, a thermo-mechanical Finite Element (FE) simulation model is built in the commercial software package ABAQUS. The complex dendritic shape is approximated with a conical model geometry. Varying this geometry allows considering the influence of different centreline solid fractions on the dendrite deformation. A sinusoidal load profile is used to describe bulging of the solid which deforms the dendrites. Based on the strain rates obtained in the FE simulations the dendrite deformation velocity perpendicular to the casting direction is calculated. The velocity presented for different conditions is used as input parameter for computational fluid dynamics (CFD) simulations to investigate macrosegregation formation inside of a continuous casting strand using the commercial software package FLUENT.

Three-Dimensional Surface Profile Measurement of Microlenses Using the Shack–Hartmann Wavefront Sensor

We present a 3-D surface profiling method for microlenses that utilizes a Shack-Hartmann wavefront sensor. This method applies to both solid microlenses and liquid-liquid interfaces in liquid microlenses. The wavefront at the aperture stop of a microlens is measured by a Shack-Hartmann wavefront sensor and is then used to calculate the 3-D surface profile of the microlens. Three types of microlenses-a photoresist microlens, a hydrogel-driven tunable liquid lens, and an electrowetting-driven tunable liquid lens-were fabricated and measured. The variable-focus liquid lenses were tested within a wide focal length range. The obtained surface profiles were fitted to spherical and conical surface models to study their geometrical properties. The photoresist microlens was found to be approximately spherical. For the hydrogel-driven microlens, the profile was smooth and nearly spherical at the center but became steep and linear at the aperture edges. The electrowetting-driven liquid lens was also fitted better with the conical model, and its conic constant was determined. The obtained surface profiles were used to estimate the optical properties of microlenses in an optical analysis software package. The comparison between the simulation and experiment results indicated that the accuracy of the estimation is rough and the error could be due to the wavefront measurement and surface fitting approximation.

Synchrotron and inverse-Compton emission from blazar jets - I. A uniform conical jet model

In the first of a series of papers investigating emission from blazar jets from radio to high-energy {\gamma}-rays, we revisit the class of models where the jet has a uniform conical ballistic structure. We argue that by using simple developments of these models, in the context of new multi-frequency data extending to gamma-ray energies, valuable insights may be obtained into the properties that fully realistic models must ultimately have. In this paper we consider the synchrotron and synchrotron-self-Compton emission from the jet, modelling the recent simultaneous multi-wavelength observations of BL Lac. This is the first time these components have been fitted simultaneously for a blazar using a conical jet model. In the model we evolve the electron population dynamically along the jet taking into account the synchrotron and inverse-Compton losses. The inverse-Compton emission is calculated using the Klein-Nishina cross section and a relativistic transformation into the jet frame, and we explicitly show the seed photon population. We integrate synchrotron opacity along the line of sight through the jet plasma, taking into account the emission and opacity of each section of the jet. In agreement with previous studies of radio emission, we find that a conical jet model which conserves magnetic energy produces the characteristic blazar flat radio spectrum, however, we do not require any fine-tuning of the model to achieve this. Of particular note, in our model fit to BL Lac--which at ~10^37W is a relatively low jet-power source--we find no requirement for significant re-acceleration within the jet to explain the observed spectrum.

Research on Complex Channel Characteristic for Hypersonic Vehicles

Hypersonic vehicles experience complex and bad communication environment including high dynamic Doppler and unique plasma sheath. Characteristics of the complex channel environment, which is divided into two distinguished channel part, will be discussed. The atmospheric propagation part of the complex channel is modeled as frequency-selective fast fading channel based on analysis of its coherence time and coherence bandwidth. The plasma sheath channel transmission (attenuation) and phase shift characteristics when radio wave pass through it is obtained by the scatter matrix method and FDTD algorithm. Finally a typical blunt conical hypersonic vehicle model is simulated to evaluate plasma sheath channel transmission and phase shift features, results show that communications might completely interrupted under high speed above 16 Mach because of small transmission coefficient and large phase shift.

Set-valued risk measures for conical market models

Set-valued risk measures on $${L^p_d}$$ with 0 ≤ p ≤ ∞ for conical market models are defined, primal and dual representation results are given. The collection of initial endowments which allow to super-hedge a multivariate claim are shown to form the values of a set-valued sublinear (coherent) risk measure. Scalar risk measures with multiple eligible assets also turn out to be a special case within the set-valued framework.

Experimental investigation of bounce phenomenon

During the entry of objects into water, several fluid dynamics phenomena, such as air and vapor cavities and jet formation, occur that contribute to the bouncing behavior of the body. In this study, experimental tests are carried out to investigate these effects. In these tests, the consequences of speed and entry angle changes along with different model nose shapes, on bounce phenomenon, are explored. Two models, with different lengths, including hemispherical and conical nose shapes, are also designed, prepared and tested in a test tank, equipped with a high speed movie camera and launching system. As the muzzle velocity increases and the water entry angle decreases, it is observed that the hemispherical nose model has no essential orientation change, while the conical nose model bears an orientation change that is quite large and which may end up in the bounce of the model. This is mainly related to the extent of the separation and jet formation on the nose surface, which is discussed in this paper. A numerical model of the experiment also predicts the same behavior.

An evaluation of the conical approximation as a generic model for estimating stem volume, biomass and nutrient content in young Eucalyptus plantations

Accurately and non-destructively quantifying the volume, mass or nutrient content of tree components is fundamental for assessing the impact of site, treatment, and climate on biomass, carbon sequestration, and nutrient uptake of a growing plantation. Typically, this has involved the application of allometric equations utilising diameter and height, but for accurate results, these equations are often specific to species, site, and silvicultural treatment. In this study, we assessed the value of incorporating a third piece of information: the height of diameter measurement. We derived a more general volume equation, based on the conical approximation, using a diameter projected to the base of the tree. Common equations were developed which allowed an accurate estimate of stem volume, dry weight and nutrient content across two key plantation grown eucalypt species, Eucalyptus grandis W. Hill ex Maiden and Eucalyptus globulus (Labill.). The conical model was developed with plantation-grown E. grandis trees ranging from 0.28 to 15.85 m in height (1.05 g to 80.3 kg stem wood dry weight), and E. globulus trees ranging from 0.10 to 34.4 m in height (stem wood dry weight from 0.48 g to 652 kg), grown under a range of contrasting cultural treatments, including spacing (E. grandis), site (E. globulus) and fertilization (nitrogen and phosphorus) for both species. With log transformed data the conical function (Vcon) was closely related to stem sectional volume over bark and stem weight (R2 = 0.996 and 0.990, respectively) for both E. grandis and E. globulus, and the same regressions can be applied to both species. Back transformed data compared with the original data yielded modelling efficiencies of 0.99 and 0.97, respectively. Relationships between Vcon and bark dry weight differed for the two species, reflecting differing bark characteristics. Young trees with juvenile foliage had a different form of relationship to older trees with intermediate or adult foliage, the change of slope corresponding to heights about 1.5 m for E. grandis and age 1 year for E. globulus. The Vcon model proved to be robust, and unlike conventional models, does not need additional parameters for estimating biomass under different cultural treatments. More than 99% of the statistical variance of the logarithm of biomass was accounted for in the model. Vcon captures most of the change in stem taper associated with cultural treatments and some of the change in stem form that occurs after the crown base has lifted appreciably. Fertilization increased N and P concentrations in stem wood and bark, and regressions to estimate N and P contents (the products of biomass and concentration) were dependent on treatment. For instance, there was a large growth response to N fertilization in E. globulus corresponding with a change (P < 0.05) in the intercept of the regression to estimate N content.

Dynamic Response of Rocket Swirl Injectors, Part II: Nonlinear Dynamic Response

of a classic swirl (simplex) injector. The abrupt convergence resonance model (ACRM) describes the magnitude of injector mass flow response assuming a radial step contraction, while the conical convergence resonance model (CCRM) treats the contraction from the vortex chamber to the nozzle using an arbitrary number of small radial steps. In this second part of the study, numerical calculations are performed to assess nonlinear dynamic response and to compare results with ACRM and CCRM predictions. The vehicle for these computations is a boundary element method (BEM) that preserves surface shapes with high accuracy.

Methodological approach to the 3D ultrasound reconstruction of human fetal thymus: a preliminary study

The aim of this preliminary study is to propose a new methodological approach to the study of thymic morphology and volume in human fetus by ultrasound, using mathematical three-dimensional (3D) models and comparing them to the volumes obtained by Virtual Organ Computer-aided (VOCAL). Thymic volume and morphology of two fetuses at 21 and at 28 weeks of gestational age were reconstructed using VOCAL system and two different 3D models of fetal thymus were created with a CAD 3D software by an addition of geometrical solids: a conical model for the 21 weeks thymus; an elliptical model for the 28 weeks thymus. We believe that dysmorphism, volume and involution of fetal thymus should be investigated by this method during pregnancy. The relationship between the volumes obtained by VOCAL and those obtained with 3D models should be confirmed by further studies.

Methodological approach to the 3D ultrasound reconstruction of human fetal thymus: a preliminary study

The aim of this preliminary study is to propose a new methodological approach to the study of thymic morphology and volume in human fetus by ultrasound, using mathematical three-dimensional (3D) models and comparing them to the volumes obtained by Virtual Organ Computer-aided (VOCAL). Thymic volume and morphology of two fetuses at 21 and at 28 weeks of gestational age were reconstructed using VOCAL system and two different 3D models of fetal thymus were created with a CAD 3D software by an addition of geometrical solids: a conical model for the 21 weeks thymus; an elliptical model for the 28 weeks thymus. We believe that dysmorphism, volume and involution of fetal thymus should be investigated by this method during pregnancy. The relationship between the volumes obtained by VOCAL and those obtained with 3D models should be confirmed by further studies.

A Capillary Model for Gasesas Coolant and Lubricant in Metal Cutting

The gases of nitrogen, oxygen, argon and carbon dioxide were employed as coolant and lubricant in metal cutting. Therefore, the smaller kinetic diameter of gas, the lower cutting forces can be obtained. A conical capillary model is proposed, based on the experimental results and the theory analysis of stress distributions at the tool-chip interface. According to the boundary-layer theory, the kinetics equations of gas flow were solute. The velocity and flux of gas molecule are presented. In the capillary, the adsorption of tool-chip interface results in boundary lubricating film; the conical shape of capillary limits the depth of coolant and lubricant penetrating; and the negative press is the motility for coolant and lubricant penetrating. The study results show the molecule size of the coolant and lubricant could effect on its performances, and the coolant and lubricant with a relatively small molecule may have the particularly effective nature, in metal cutting.

Understanding structure-property relationship of resistive switching oxide thin films using a conical filament model

The relations between the reset current IR, room temperature filament resistance R0, and third harmonic coefficient B0 were evaluated by a conical filament model. It was found that IR∼1/R0 when the filament is either very weak, where the filament is more conical, or quite strong, where the filament is more cylindrical. The physical implication of the B0 was also understood from the materials properties. The coherence between the model expectations for the bulkier conical filaments, typically found in TiO2, and the more random-network like filaments, typically found in NiO, suggests a common switching mechanism works in both materials.

Distributed actuation characteristics of clamped-free conical shells using diagonalpiezoelectric actuators

In spacecraft, severe vibrations induced by the launch vehicle may cause damage to theprecision payload. Therefore active adapters with vibration suspending characteristics areneeded. This paper presents theoretical studies of the active vibration controlcharacteristics of conical shells with laminated piezoelectric actuators. A diagonalpiezoelectric actuator is proposed to control the axial, lateral and transverse vibrations ofthe conical shell. Modal functions are designed to represent the free vibrations of theconical shell with clamped-free boundary conditions. General formulae of the modal controlforce and corresponding components are derived based on the converse piezoelectriceffects and then specified for the diagonal actuators. By using an open-loop controlmethod, the modal control characteristics of diagonal actuator segments at differentlocations are investigated and compared, and the axial, lateral and transversevibrations of two conical shell models are evaluated. The optimal locations ofactuator segments for the control of different natural modes are also investigated.

Linear Stability Analysis of a Conical Liquid Sheet

A linear instability analysis method has been used to investigate the breakup of a conical liquid sheet under the combined influence of sinuous and varicose modes of disturbances at the liquid―gas interfaces. The maximum disturbance wave growth rate of two disturbance modes has been worked out by solving the dispersion equation of a conical liquid sheet, and the corresponding angular frequencies and dominant wave numbers have been obtained. A modified model to predict the breakup length of the conical liquid sheet was adopted. Furthermore, the surface deformation curves, which can estimate how long time the breakup process will take, have been plotted by solving the surface deformation equation. For both modes, the maximum disturbances growth rate and the dominant wave number increase as the pressure drop increase, while the breakup length and breakup time decrease with the increase of the pressure drop. Although the whole conical liquid sheet presents the varicose shape when the breakup takes place, the sinuous mode dominates the breakup process. With the increase of the geometrical characteristic parameter, the breakup length and breakup time decrease. The phase angle between the two modes affects the breakup slightly. To validate the conical sheet breakup model, the experiments were performed with the injectors of different geometry characteristics parameters and a high-speed dynamic measurement system was used to grab the detailed information of the liquid sheet breakup process. Comparison with experimental results shows that the calculation results coincide with the experiments, and the present analysis provides a good starting point for predicting unstable, wave-type behavior of the conical liquid sheet.

REVISING THE KINEMATICS OF 12 GHz CH3OH MASERS TOWARD W3(OH)

We derive accurate proper motions of the CH3OH 12 GHz masers toward the W3(OH) ultra-compact (UC) H ii region, employing seven epochs of VLBA observations spanning a time interval of about 10 yr. The achieved velocity accuracy is of the order of 0.1 km s−1, adequate to precisely measure the relative velocities of most of the 12 GHz masers in W3(OH), with amplitude varying in the range 0.3–3 km s−1. Toward W3(OH), the most intense 12 GHz masers concentrate in a small area toward the north (the northern clump) of the UC H ii region. We have compared the proper motions of the CH3OH 12 GHz masers with those (derived from literature data) of the OH 6035 MHz masers, emitting from the same region of the methanol masers. In the northern clump, the two maser emissions emerge from nearby (but likely distinct) cloudlets of masing gas with, in general, a rather smooth variation of line-of-sight and sky-projected velocities, which suggests some connection of the environments and kinematics traced by both maser types. The conical outflow model, previously proposed to account for the 12 GHz maser kinematics in the northern clump, does not reproduce the new, accurate measurements of 12 GHz maser proper motions and has to be rejected. We focus on the subset of 12 GHz masers of the northern clump belonging to the "linear structure at P.A. = 130°–140°," whose regular variation of LSR velocities with position presents evidence for some ordered motion. We show that the three-dimensional velocities of this "linear distribution" of 12 GHz masers can be well fitted considering a flat, rotating disk, seen almost edge-on.

Multifrequency emission analysis of TeV blazars H 2356–309 and 1ES 1218+304

The multiband nonthermal emissions in radio, X-ray, and very high-energy (VHE) γ-ray bands from two distant blazars, H 2356–309 and 1ES 1218+304, have been detected, and, especially from recent observations with the Suzaku, MAGIC and VERITAS telescopes, clearly reveal nonthermal power-law spectra. We study the broadband nonthermal spectra of the two sources by using a combination of a one-zone homogeneous synchrotron self-Compton (SSC) model and an inhomogeneous conical jet model, where the new external background light (EBL) model is taken into account. The results show that (1) the nonthermal emissions of the two blazars, ranging from X-rays to VHE γ-rays, are from the homogeneous zone whereas the emissions in the radio bands can be explained as the radiation from the inhomogeneous conical jet; (2) a strict lower-limit EBL model can be used to explain their observed spectra well.

Velocity Distribution of CMEs After Projection Correction

The observed CME (coronal mass ejection) is its projection on the sky plane, and this leads to certain discrepancies between the observational and true parameters of the CME. For example, the observed velocity is generally smaller than the true velocity. The method of making projection correction for the CME velocity based on the conical model is utilized to analyze the velocity distributions of the 1691 CMEs which are only correlated to flares (called the class FL CMEs for short) and the 610 CMEs which are only correlated to filament eruptions (called the class FE CMEs for short) before and after the projection correction. These CMEs were observed with the Large Angle and Spectrometric Coronograph on the Solar and Heliospheric Observatory from September 1996 to September 2007 (close to a solar cycle). The obtained results are as follows: (1) before and after the projection correction the velocity distribution of FL CMEs is quite similar to that of FE CMEs, and before and after the projection correction the mean velocities of the two classes of CMEs are almost the same; (2) before and after the projection correction, the natural logarithm distribution of the FL CME velocities is also very similar to that of the FE CME velocities.

Hedging of Claims with Physical Delivery under Convex Transaction Costs

We study superhedging of contingent claims with physical delivery in a discrete-time market model with convex transaction costs. Our model extends Kabanov's currency market model by allowing for nonlinear illiquidity effects. We show that an appropriate generalization of Schachermayer's robust no-arbitrage condition implies that the set of claims hedgeable with zero cost is closed in probability. Combined with classical techniques of convex analysis, the closedness yields a dual characterization of premium processes that are sufficient to superhedge a given claim process. We also extend the fundamental theorem of asset pricing for general conical models.

Structural Convergence between Cryo-EM and NMR Reveals Intersubunit Interactions Critical for HIV-1 Capsid Function

Mature HIV-1 particles contain conical-shaped capsids that enclose the viral RNA genome and perform essential functions in the virus life cycle. Previous structural analysis of two- and three-dimensional arrays of the capsid protein (CA) hexamer revealed three interfaces. Here, we present a cryoEM study of a tubular assembly of CA and a high-resolution NMR structure of the CA C-terminal domain (CTD) dimer. In the solution dimer structure, the monomers exhibit different relative orientations compared to previous X-ray structures. The solution structure fits well into the EM density map, suggesting that the dimer interface is retained in the assembled CA. We also identified a CTD-CTD interface at the local three-fold axis in the cryoEM map and confirmed its functional importance by mutagenesis. In the tubular assembly, CA intermolecular interfaces vary slightly, accommodating the asymmetry present in tubes. This provides the necessary plasticity to allow for controlled virus capsid dis/assembly.