Elliptic Cone Research Articles

СРАВНЕНИЕ МЕТОДОВ НАЧЕРТАТЕЛЬНОЙ ГЕОМЕТРИИ И 3D КОМПЬЮТЕРНОГО ГЕОМЕТРИЧЕСКОГО МОДЕЛИРОВАНИЯ ПО ТОЧНОСТИ, СЛОЖНОСТИ И ЭФФЕКТИВНОСТИ

Urgent educational problem of inconsistency of content of the course of descriptive geometry (DG) with the trends in the development of CAD and geometric simulation is considered. While the development is aimed at expanding the scope of computer 3D geometric simulation the teaching of descriptive geometry projection methods continues despite the fact that they are in no demand in practical applications. To compare the estimations of versions of solutions in descriptive geometry and 3D five specific problems of the nomination in descriptive geometry of All-Russian Olympiad 2014 are considered. They are the construction of sphere, tangent to the paraboloid; determining the points of intersection of the ellipse defined by the axes, with a circle (without the ellipse); finding the reference points of the ellipse section and its projections; construction of a tetrahedron by one projection of its face; as well as the defining the points of intersection of the circle with an elliptical cone. The detailed versions of solutions of descriptive geometry and 3D are given for each problem. The comparison of versions of the solution according to the geometrical accuracy is done. It is offered to estimate not an abstract accuracy which corresponds to constructions made by aperfect caliper and a ruler but the real accuracy independently of methods of its achievement. It’s shown that with the computer realization of both variants their real accuracy is either equal or 3D is much better than DG. The estimation of the complexity of task solutions is given. The amount of information needed for the solution is taken as a criterion. The author makes the conclusion that generally 3D versions are easier than DG. The examples show that 3D solutions can be easily supplemented with researches of a solvable problem. Much higher visualization, accessibility and universality of 3D versions are highlighted. The author makes the conclusion about much higher general effectiveness of computer 3D variants and methods of solving the structural problems and the necessity of transfer to new training course of 3d theory. Keywords: descriptive geometry, computer graphics, 3D modeling, structural problems, geometrical accuracy, complexity and effectiveness of structural problems.

Topology Optimization of an Asymmetric Elliptical Cone Subjected to Blast Loading

This paper describes a numerical procedure for the blank shape design of thin aluminum components achieved by explosive forming. The objective is to specify the initial blank shape considering the geometry of the final product. The numerical procedure consists of three steps: At first, the forming process of an asymmetric blank in an elliptical cone die cavity and without blank holder is simulated. To rectify the wrinkles without optimization the square of the primary blank will be increased. In the next step, topology optimization is employed to obtain the optimum geometry of the blank whose diameter has been increased finally, the modified blank achieved previous step is used in the new simulation to check whether or not the wrinkles mentioned in first step has been rectified. Results show the proposed numerical procedure can provide the optimal blank shape in a few iterations.

Numerical Integration over Three-Dimensional Regions Bounded by One or More Circular Edges

A new integration method is proposed for integration of arbitrary functions over regions having circular boundaries. The method is developed using a new non-linear transformation which can transform such a region to a zero-one cube. The derivation of this formula over a circular and elliptic cylinder, cone and paraboloid is shown with numerical results.

S1910301 感温塗料を用いた高温衝撃風洞におけるHIFiRE模型の境界層遷移可視化

A visualization experiment of hypersonic boundary layer transition by Temperature-Sensitive Paint (TSP) was performed. The test facility was High-Enthalpy Shock Tunnel (HIEST) at Japan Aerospace Exploration Agency (JAXA) Kakuda Space Center. An elliptic cone model with a 2:1 aspect ratio, which is a full-scale model of HIFiRE-5, was used as the test model. This study visualized the hypersonic boundary layer transition on the side of the test model. TSP was excited by a Blue-LED and the luminescence from TSP was detected by a high-speed camera. Temperature distribution on the side of the test model was obtained by TSP. Moreover, boundary layer transition along the centerline of the model and in approximately halfway between the centerline and leading edge were visualized. The trend of temperature rise along the centerline is same in TSP and thermocouples, which is inserted on the centerline of the test model.

Centerline instabilities on the hypersonic international flight research experimentation HIFiRE-5 elliptic cone model

Linear instability of the three-dimensional boundary-layer over the Hypersonic International Flight Research Experimentation 5 (HIFiRE-5) flight test geometry, i.e. a rounded-tip 2:1 elliptic cone, is analyzed through spatial BiGlobal linear instability analysis, in an effort to understand transition and accurately predict local heat loads on this model of next-generation flight vehicles. The base flow conditions are selected for a Mach 7 flow at altitude of 33.0km and unit Reynolds number Re′=1.89×106m. The base flow is computed using the US3D solver. The three-dimensionality of the boundary-layer on the elliptic cone produces spanwise pressure gradients, inducing crossflow from the leading edge (major-axis meridian) to the centerline (minor-axis meridian) and producing lift-up of low momentum boundary-layer fluid at the centerline. The present analysis focuses on the resulting mushroom-like structure formed near the minor-axis meridian. An unstable fluid structure, which is composed of a low-velocity streak surrounded by a three-dimensional high-shear layer, is thus generated. Results show that this complex fluid structure can sustain linear growth of a number of instability modes, thus confirming earlier analyses which identified such modes without taking surface curvature of the geometry in question into consideration. These so-called centerline modes are associated with varicose or sinuous deformations of the low-velocity streak and are found to have similar growth rates in the frequency range studied, between 50 and 300kHz. Furthermore, unstable boundary-layer modes, identified as oblique second Mack modes, are unraveled in the vicinity of the centerline. At the conditions studied, Mack modes are found to be less amplified that the centerline modes.

Flume studies using 1:1 scale models of Series 2 and basal Series 3 Cambrian gogiid eocrinoids from Guizhou Province, China to determine feeding posture and mode of attachment

In Series 2 and 3 Cambrian of Guizhou Province, China, most echinoderms inhabited deeper/quieter water and were attached directly to siliciclastic substrate or biodetritus by biogluing (extrusion of extensible collagen). Feeding postures of abundant long stalked gogiids (e.g., Sinoeocrinus) from these beds were interpreted to have heeled over in the current from the thin flexible distal end of the stalk, with the brachioles streaming in a loose bundle, down current from the theca. To test these and other feeding posture assumptions, 1:1 scale models (holdfast, stalk, and theca) of three genera were carved from soft rubber and brachioles were modeled from braided fishing line. By varying current velocities long stalked flume models did not significantly heel over. Brachioles, both straight and spiraled, extended vertically from the theca in an (elliptical) cone and distally curved downstream. Disrupted flow around straight brachioles (Sinoeocrinus) kept them somewhat evenly spaced. Spiraled brachioles (Guizhoueocrinus, Globoeocrinus) are initially straight and angle outwards so that each proximal end defines a sector over the theca; this spacing keeps the brachioles free from tangling distally. Biogluing the animal to the bottom or to biodetritus seems to be correctly interpreted from the morphological evidence. Superglue was used as the proxy gluing agent for the models, success was limited. The dewatered, siliciclastic, non-bioturbated, seafloor could be only partly reconstructed and the somewhat viscous glue did not deeply penetrate the illite substrate. It is probable that bioglue had low viscosity, penetrated the sediment easily, and was able to agglutinate a large three dimensional anchoring body of sediment without (as is commonly observed) disrupting bedding.

Gel Phantom Study with High-Intensity Focused Ultrasound: Influence of Metallic Stent Containing Either Air or Fluid

We aimed to investigate whether a cylindrical structure containing either air or fluid and with or without a metallic stent affects the volume and density of cavitation produced by high-intensity focused ultrasound via a gel phantom study. Sixteen tissue-mimicking phantoms based on a polyacrylamide gel mixed with bovine serum albumin with a cylindrical hole 1 cm in diameter and 7.5 cm in length were divided into four groups of four phantoms with air in the holes (group 1), four phantoms with fluid in the holes (group 2), four phantoms with air-containing metallic stents (group 3) and four phantoms with fluid-containing metallic stents (group 4). A pulsed high-intensity focused ultrasound beam (50% duty cycle, 40-Hz pulse repetition frequency) at 75 W of acoustic power was directed perpendicularly to the longitudinal axis of the hole, with its focus at the posterior wall of the hole. The size of the cavitation on the x-, y-, and z-axes was measured, and the volumes of cavitation and coagulation were calculated using the formula for the volume of an elliptical cone. The density of cavitation was measured in the tissue phantom anterior to the hole with a 1 × 1-cm square region of interest. For statistical analysis, the Kruskal–Wallis test and Mann–Whitney U-test were used. The phantoms with air-containing holes (groups 1 and 3) developed larger and denser cavitations anterior to the focus, without unnecessary coagulation posterior to the focus, compared with the phantoms with fluid-containing holes (groups 2 and 4), regardless of the presence of stents. All of the axes and volumes of the anterior cavitations were significantly larger than those of the posterior cavitations in groups 1 and 3 (all p-values <0.05). The results of this study might be applied to maximize cavitation to enhance drug delivery into tumors.

Persistent uplift of the Lazufre volcanic complex (Central Andes): New insights from PCAIM inversion of InSAR time series and GPS data

We reanalyzed the surface displacements observed at the Lazufre volcanic complex in the Southern Andean Central Volcanic Zone using GPS measurements made between 2006 and 2008 and a large InSAR data set. We performed a detailed spatiotemporal analysis of the displacements using a principal component analysis inversion method (PCAIM). The PCAIM reveals a source with no significant changes in shape and dimension and with a remarkably linear strength increase over the whole period of observation (i.e., 2003–2010). Then we used a three-dimensional mixed boundary element method (MBEM) to invert the first component of surface displacement as obtained from PCAIM. We explored a continuum of geometries from a shallow elliptic crack to a deep massive truncated elliptical cone that could represent a sill or a large magma chamber, respectively. The best models indicate a large flat-topped source with a roof area between 40 and 670 km2 and a depth of between 2 and 14 km below ground surface. Lastly, on the basis of the limited data available for the thermomechanical structure of the crust in the Southern Andean Central Volcanic Zone, we consider some possible scenarios to explain the spatial and temporal pattern of displacements at Lazufre.

An expression for the dynamic stability of blunt slender elliptic bodies in hypersonic flow

AbstractDynamic stability data on axially symmetric pointed and blunt cones, parabolic profiles and other ogive and blunt cylindrical shapes is readily available in literature; the dynamic stability on elliptic blunt paraboloids has not been studied at any great lengths in the past. Both numerical and experimental results are scarce. The present paper uses the shock expansion method to obtain the unsteady pressure distribution on blunt elliptic conical bodies at small angles-of-attack. The resulting unsteady pressure distribution is suitably integrated over the surface of the elliptic body to obtain appropriate analytic expressions for static and dynamic stability. Owing to scarcity of meaningful numerical or measured data for elliptic bodies, the results are compared in qualitative terms against published dynamic stability data on pointed elliptical cones or other axisymmetric blunt cones.

Comparison of interplanetary CME arrival times and solar wind parameters based on the WSA‐ENLIL model with three cone types and observations

AbstractWe have made a comparison between coronal mass ejection (CME)‐associated shock propagations based on the Wang‐Sheeley‐Arge (WSA)‐ENLIL model using three cone types and in situ observations. For this we use 28 full‐halo CMEs, whose cone parameters are determined and their corresponding interplanetary shocks were observed at the Earth, from 2001 to 2002. We consider three different cone types (an asymmetric cone model, an ice cream cone model, and an elliptical cone model) to determine 3‐D CME cone parameters (radial velocity, angular width, and source location), which are the input values of the WSA‐ENLIL model. The mean absolute error of the CME‐associated shock travel times for the WSA‐ENLIL model using the ice‐cream cone model is 9.9 h, which is about 1 h smaller than those of the other models. We compare the peak values and profiles of solar wind parameters (speed and density) with in situ observations. We find that the root‐mean‐square errors of solar wind peak speed and density for the ice cream and asymmetric cone model are about 190 km/s and 24/cm3, respectively. We estimate the cross correlations between the models and observations within the time lag of ± 2 days from the shock travel time. The correlation coefficients between the solar wind speeds from the WSA‐ENLIL model using three cone types and in situ observations are approximately 0.7, which is larger than those of solar wind density (cc ∼0.6). Our preliminary investigations show that the ice cream cone model seems to be better than the other cone models in terms of the input parameters of the WSA‐ENLIL model.

Similarity Analysis of Pressure Distribution along the Wake Axis of Elliptic Cones

The Effect of freestream velocity and Ellipticity ratio on the similarity distribution of the static pressure along the wake axis of the elliptic cones is presented. A cone of elliptic cross section produces separated flow at the downstream of its base. Within the separated region the flow is observed to be opposite (reverse) to the main outer flow. To obtain the length of reverse flow region, magnitude and location of maximum reverse velocity and re attachment point knowledge of pressure distribution behind a body is essential. Experiments were carried out for three different test section freestream velocities 6m/s, 15m/s and 25 m/s (Reynolds numbers 0.16 x 105, 0.4 x 105 and 0.667 x 105 based on cone effective diameter respectively). Ellipticity ratio 1 and 3 with constant fineness and bluntness ratio of 2.75 and 0.049 respectively were considered for the experiments. A Digital Sensor Array –DSA was used for static pressure measurements. The pressure sensor has the capability of 1 PSI differential pressure range with +/- 0.12% full-scale accuracy. Good similarity in wake axis static pressure distribution is noted for different freestream velocity behind a circular cone. But, Similarity in pressure distribution is not observed along the wake axis of an elliptic cone at tested lower freestream velocity (6 m/s). Keywords: Elliptic Cone, Pressure Coefficient and Similarity Parameter, Wake Pressure

Similarity Analysis of Pressure Distribution along the Wake Axis of Elliptic Cones

The Effect of freestream velocity and Ellipticity ratio on the similarity distribution of the static pressure along the wake axis of the elliptic cones is presented. A cone of elliptic cross section produces separated flow at the downstream of its base. Within the separated region the flow is observed to be opposite (reverse) to the main outer flow. To obtain the length of reverse flow region, magnitude and location of maximum reverse velocity and re attachment point knowledge of pressure distribution behind a body is essential. Experiments were carried out for three different test section freestream velocities 6m/s, 15m/s and 25 m/s (Reynolds numbers 0.16 x 105, 0.4 x 105 and 0.667 x 105 based on cone effective diameter respectively). Ellipticity ratio 1 and 3 with constant fineness and bluntness ratio of 2.75 and 0.049 respectively were considered for the experiments. A Digital Sensor Array -DSA was used for static pressure measurements. The pressure sensor has the capability of 1 PSI differential pressure range with +/- 0.12% full-scale accuracy. Good similarity in wake axis static pressure distribution is noted for different freestream velocity behind a circular cone. But, Similarity in pressure distribution is not observed along the wake axis of an elliptic cone at tested lower freestream velocity (6 m/s).

The geometrical gear shape of a bottom trawl

An estimation of the gear shape during a bottom trawl can be achieved through geometrical modeling of the trawl system. This can be implemented by processing the field data obtained using the Scanmar system. The gear shape from the square through the bag net was assumed to be the upper and lower parts of different elliptic cones of which the cross section was an ellipse and the shape of the float rope to be of exponential function. A system of nonlinear equations was constructed to represent the gear shape of the bottom trawl net in water. When the equations were solved based on the data obtained from bottom trawl experiments with various warp lengths, the cross section of sweep and filtered volume, the eccentricity of the upper ellipse, the functional shape and inclination angle of the float rope, and the contribution of the upper side panel to the net height could be obtained in relation to towing speed and scope ratio. As the cross section of sweep at the mouth and the projected total cross section decreased a little bit with increased towing speed, the filtered volume tended to increase with increased towing speed. The gear shape at mouth of the bottom trawl was not so much changed compared to that of a mid-water trawl.

Simulation analysis of paddling motions in a single kayak: Development of a comprehensive dynamic model of a paddler, paddle and hull

The objective of this study was to develop a comprehensive dynamic model of the paddler, paddle and hull for a simulation analysis of the paddling motion in a single kayak. In the development of the model, a similar simulation model, not for the kayak, but for human swimming, was utilized. The paddler was represented as a series of 21 truncated elliptic cones. The paddle was represented as three truncated elliptic cones for the two blades and shaft. For the hull, an extension of the original simulation model to represent the detailed three-dimensional hull shape was carried out. In the extended hull model, the thin elliptic plate was replaced by a plate with a detailed cross-sectional shape. The paddler, paddle and hull in the model were connected by means of virtual springs and dampers. The geometries of the paddler, paddle and hull were acquired based on the experiments that measured them. The joint motion of the paddler was measured by means of motion analysis as well. By inputting the acquired data, simulation of the paddling motion was conducted. From the results, it was confirmed that the joint motion acquired in the experiment was successfully input into the simulation. It was also confirmed that the paddler, paddle and the hull were successfully connected by the virtual springs and dampers. In the simulation, the averaged velocity of the hull in the propulsive direction was 3.40 m/s, which was 11% lower than the actual value of 3.8 m/s.

Parametric modeling of the intervertebral disc space in 3D: Application to CT images of the lumbar spine

Gradual degeneration of intervertebral discs of the lumbar spine is one of the most common causes of low back pain. Although conservative treatment for low back pain may provide relief to most individuals, surgical intervention may be required for individuals with significant continuing symptoms, which is usually performed by replacing the degenerated intervertebral disc with an artificial implant. For designing implants with good bone contact and continuous force distribution, the morphology of the intervertebral disc space and vertebral body endplates is of considerable importance. In this study, we propose a method for parametric modeling of the intervertebral disc space in three dimensions (3D) and show its application to computed tomography (CT) images of the lumbar spine. The initial 3D model of the intervertebral disc space is generated according to the superquadric approach and therefore represented by a truncated elliptical cone, which is initialized by parameters obtained from 3D models of adjacent vertebral bodies. In an optimization procedure, the 3D model of the intervertebral disc space is incrementally deformed by adding parameters that provide a more detailed morphometric description of the observed shape, and aligned to the observed intervertebral disc space in the 3D image. By applying the proposed method to CT images of 20 lumbar spines, the shape and pose of each of the 100 intervertebral disc spaces were represented by a 3D parametric model. The resulting mean (±standard deviation) accuracy of modeling was 1.06±0.98mm in terms of radial Euclidean distance against manually defined ground truth points, with the corresponding success rate of 93% (i.e. 93 out of 100 intervertebral disc spaces were modeled successfully). As the resulting 3D models provide a description of the shape of intervertebral disc spaces in a complete parametric form, morphometric analysis was straightforwardly enabled and allowed the computation of the corresponding heights, widths and volumes, as well as of other geometric features that in detail describe the shape of intervertebral disc spaces.

Kinematics and dynamics in a bipartite-Finsler spacetime

We study some properties of a recently proposed local Lorentz-violating Finsler geometry, the so-called bipartite space. This anisotropic structure deforms the causal null surface to an elliptic cone and provides an anisotropy to the inertia. We obtain the new modified dispersion relations and the geodesic equation for a massive particle. For a weak directional-dependence we find the dynamical and interaction terms analogous to the gravitational sector of the Standard Model Extension.

Vortex expansion of the monatomic gas

We consider the one invariant solution on a three-dimensional subalgebra admitted by the equations of gas dynamics for a monatomic gas. It sets the expansion of gas into a vacuum. The motion of the particles occurs over hyperbole lying on an elliptical cone.

Proposal of a Planar Directional UWB Antenna for Any Desired Operational Bandwidth

A novel planar directional UWB antenna is proposed. The antenna design evolves from an oblique elliptic cone antenna by applying the planar-solid correspondence to two axes. Through a simple equation, this antenna can be designed, to operate at a specific lower cutoff frequency with a bandwidth larger than 10 GHz for a reflection coefficient magnitude lower than −10 dB. This characteristic provides the antenna with a good versatility. The directional radiation pattern has an average gain of 6 dBi.

A Simple Method for Calculating the Possible Habit Planes Containing One Set of Dislocations and its Applications to fcc/bct and hcp/bcc Systems

The habit planes observed in numerous alloys during phase transformation can often be explained with the condition that the interface contains a single set of dislocations. Based on the unique matching condition in the habit plane, an analytical expression of the interface orientation in a general system has been derived. The orientations of habit planes are found to be confined on an elliptic cone corresponding to a particular Burgers vector. A simple method based on a superimposed diffraction pattern in the zone axis of the Burgers vector is proposed to specify the axes and parameters of the cones. The present analytical method provides a convenient mathematical tool for a systematic investigation of possible habit planes generated from either martensitic or precipitation transformation. The applications of the method to fcc/bct and hcp/bcc systems are presented. The calculated results have been tested against data in the literature, showing full agreement.

Development of a Volumetric Horizontal-Well-Stimulation Model

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 165143, ’Development of a Volumetric Horizontal-Well-Stimulation Model,’ by Linus A. Nwoke, SPE, Shell Petroleum Development Company of Nigeria, prepared for the 2013 SPE European Formation Damage Conference and Exhibition, Noordwijk, the Netherlands, 5-7 June. The paper has not been peer reviewed. The elliptical (conical) damage profile associated with horizontal wells is well-known, but review of industry-wide applications by different operators shows no corresponding uniform correlation between the damage profile and actual treatment volumes that have been applied. This inadequacy has often led to suboptimal post-stimulation performances. Furthermore, funds spent on stimulating horizontal wells did not yield the expected rewards; the stimulation gains are mostly short-lived because of flawed volume design and application. Introduction Unlike the vertical-well-damage profile, the damage profile around a horizontal wellbore is neither radial nor distributed evenly along its entire length because of formation anisotropy that creates an elliptical damage profile normal to the wellbore. The exposure time to fluids during drilling and completion operations, or the varying magnitude of fluid flow quantities across the various segments of the drainhole length during the production and injection process, will result in a truncated elliptical cone of damage along the length of the well, representing a frustum (Fig. 1) with the base of the cone nearest to the heel (near the vertical section of the wellbore). Fluid diversion is often difficult to achieve in horizontal wells because fluids tend to take the path of least resistance, even when using mechanical diverting aids or coiled tubing. Considering the fact that large quantities of acid are required for matrix stimulation of horizontal sections, it is often desirable to assume partial damage removal, but this often results in the creation of a stimulated zone with improved permeability surrounded by a collar of damage. Notwithstanding these challenges, effective distribution of the stimulation fluid along the entire length of the well is desirable, and this is why a consideration of the nature of the damage distribution in horizontal wells is very important and key to achieving a true stimulation. In order to address this first step in horizontal-well-stimulation fluid design, a model development was carried out to simultaneously determine the acid volume required to cover the damage area of the horizontal near-wellbore region and each of the segments as desired on the basis of operational feasibilities. The required input parameters for the new model are the drainhole length, the number of desired treatment segments, average porosity, wellbore radius, and estimated damage radius at the heel. The output parameters from the model include the acid volume required to treat each segment of the drainhole, which decreases from the heel toward the toe in conformance with the established elliptical damage profile.