Axisymmetric Objects Research Articles

Development of Scratch Inspection System for Cylindrical Products by Image Processing

Quality of products and reduction of products inspection burden are required in production. This paper describes development of automatic inspection system for cylindrical products by image processing. Since a cylindrical product is an axisymmetric object, the scratch can be detected by image processing on the difference image of the captured images. Based on this idea, we have developed the scratch detection algorithm. It has the threshold setting method where the threshold adjustment is able to be done easily by considering the threshold as image data. The availability of the developed inspection system is shown in the experimental result where actual inspection was carried out on a large quantity of cylindrical products.

Friction Drag Reduction of External Flows with Bubble and Gas Injection

The lubrication of external liquid flow with a bubbly mixture or gas layer has been the goal of engineers for many years, and this article presents the underlying principles and recent advances of this technology. It reviews the use of partial and supercavities for drag reduction of axisymmetric objects moving within a liquid. Partial cavity flows can also be used to reduce the friction drag on the nominally two-dimensional portions of a horizontal surface, and the basic flow features of two-dimensional cavities are presented. Injection of gas can lead to the creation of a bubbly mixture near the flow surface that can significantly modify the flow within the turbulent boundary layer, and there have been significant advances in the understanding of the underlying physical process of drag reduction. Moreover, with sufficient gas flux, the bubbles flowing beneath a solid surface can coalesce to form a thin drag-reducing air layer. The current applications of these techniques to underwater vehicles and surface ships are discussed.

Scattering from superspheroidal acoustic objects.

The extended boundary condition technique of Waterman [J. Acoust. Soc. Am. 45, 1417–1429 (1969)] has been used to study scattering from extended axisymmetric acoustic objects. These objects are formed using the mathematical function for a “super-ellipse” [i.e., (x/a)s + (z/b)s=1, where s=2n, n=1, 2, 3,…] and revolving around the z-axis. For s=2, the object is a spheroid with aspect ratio α=b/a. As s increases, the shape of the object approaches a right circular cylinder of radius a and length 2b. The method allows the scattered field to be accurately determined for all azimuthal angles as a function of frequency. The method is applied to the case of air-filled objects in water, which has importance for the interpretation of acoustic scattering from oceanic objects such as air-bubbles, the swim bladders of some fish, and zooplankton. It is found that the frequency increases with α, exactly as predicted using a geometrical method by Weston, and increases in a relatively minor way with $s$. In addition, the method shows that the monopole resonance, which leads to a spherically symmetric scattering distribution, continues to dominate low-frequency scattering even for cylindrically shaped, air-filled objects with an aspect ratio up to α=40 and s=32.

Investigation of the accuracy of different methods of interferogram analysis for calculation of local free convection heat transfer coefficient on axisymmetric objects

An experimental study using a Mach–Zehnder interferometer has been carried out in order to investigate the accuracy of four different methods of interferogram analysis for obtaining free convection heat transfer coefficient on heated axisymmetric objects. Different methods of reference fringe interferogram analysis can be categorized as classical and transform methods. In transform methods, a mathematical transform method is applied to solve the governing integral equation while in the classical methods the integral equation is approximated by a finite summation. Classical methods are also divided into two groups according to the equations which are based upon. Experiments have been carried out on a vertical isothermal cylinder in air with three different surface temperatures. Four methods of interferogram analysis which are three classical and a transform method have been used to calculate the temperature distributions and the local free convection heat transfer coefficients at different cross sections. In order to investigate the accuracy of the methods, experimental values of the local heat transfer coefficient have been compared with the numerical solution and the mean relative error of each method has been obtained. Results show that the transform method is the most accurate one with the shortest solution time. It is also shown that assuming more complex functions for variation of index of refraction in the classical methods could lead to more accurate results.

Experimental investigation of water impact on axisymmetric bodies

The results of an elaborate experimental investigation on bottom slamming of axisymmetric objects are presented. Drop tests have been performed on a hemisphere and two conical shapes with different deadrise angles. The test setup is designed so as to prevent small rotations of the test objects which cause scatter in the measurement data. The pressure distribution and evolution as well as the body motion parameters are measured during impact. By means of a high speed camera the water uprise is visualized and the wetting factor is determined for the cones. The results are compared with a three-dimensional asymptotic theory for axisymmetric rigid bodies with constant entry velocity. The ratio between the registered peak pressures and the asymptotic theory are in accordance with comparable experiments in the literature. The asymptotic theory, however, is found to be quite conservative, since the measured peak pressure levels appear to be approximately 50% to 75% of the theoretical levels.

Kerr-Taub-NUT spacetime with Maxwell and dilaton fields

We present an exact solution describing a stationary and axisymmetric object with electromagnetic and dilaton fields. The solution generalizes the usual Kerr-Taub-NUT (Newman-Unti-Tamburino) spacetime in general relativity and is obtained by boosting this spacetime in the fifth dimension and performing a Kaluza-Klein reduction to four dimensions. We also discuss the physical parameters of this solution and calculate its gyromagnetic ratio.

A generalized maugis model for adhesive contact of arbitrary axisymmetric elastic objects

Based on a linear combination of the solutions derived fromthe Sneddon method and the Lowengrub-Sneddon method, a general solution ofthe axisymmetric problem is obtained for the elastic half-space with mixedboundary conditions. And then, the frictionless and adhesive contact problembetween two general axisymmetric elastic objects is studied. For anarbitrary effective surface profile, i.e., the initial contact occurs at thecentral part, and an arbitrary surface adhesive interaction, a generalizedMaugis model is derived and it can be divided into two parts correspondingto the contributions of the surface profile and the surface adhesiveinteraction, respectively, and a coupling relation between the deformationand the adhesive interaction. Based on the Dugdale model for the surfaceadhesive interaction, a generalized M-D model is derived for an arbitraryeffective surface profile. Two extremes are found for this model. For ashort-range strong interaction or compliant material, its limiting form iscorresponding to the generalized JKR model. And for a long-range weakinteraction or stiff material, another limiting form is corresponding to ageneralized DMT model.

Using the Dugdale approximation to match a specific interaction in the adhesive contact of elastic objects

In the Maugis–Dugdale model of the adhesive contact of elastic spheres, the step cohesive stress σ 0 is arbitrarily chosen to be the theoretical stress σ th to match that of the Lennard-Jones potential. An alternative and more reasonable model is proposed in this paper. The Maugis model is first extended to that of arbitrary axisymmetric elastic objects with an arbitrary surface adhesive interaction and then applied to the case of a power-law shape function and a step cohesive stress. A continuous transition is found in the extended Maugis–Dugdale model for an arbitrary shape index n. A three-dimensional Johnson–Greenwood adhesion map is constructed. A relation of the identical pull-off force at the rigid limit is required for the approximate and exact models. With this requirement, the stress σ 0 is found to be k ( n ) Δ γ / z 0 , where k ( n ) is a coefficient, Δ γ the work of adhesion, and z 0 the equilibrium separation. Hence we have σ 0 ≐ 0.588 Δ γ / z 0 , especially for n = 2 . The prediction of the pull-off forces using this new value shows surprisingly better agreement with the Muller–Yushchenko–Derjaguin transition than that using σ th ≐ 1.026 Δ γ / z 0 , and this is true for other values of shape index n.

Interpreting Spectral Energy Distributions from Young Stellar Objects. I. A Grid of 200,000 YSO Model SEDs

We present a grid of radiation transfer models of axisymmetric young stellar objects (YSOs), covering a wide range of stellar masses (from 0.1Msun to 50Msun) and evolutionary stages (from the early envelope infall stage to the late disk-only stage). The grid consists of 20,000 YSO models, with spectral energy distributions (SEDs) and polarization spectra computed at ten viewing angles for each model, resulting in a total of 200,000 SEDs. [...]. These models are publicly available on a dedicated WWW server: http://www.astro.wisc.edu/protostars/ . In this paper we summarize the main features of our models, as well as the range of parameters explored. [...]. We examine the dependence of the spectral indices of the model SEDs on envelope accretion rate and disk mass. In addition, we show variations of spectral indices with stellar temperature, disk inner radius, and disk flaring power for a subset of disk-only models. We also examine how changing the wavelength range of data used to calculate spectral indices affects their values. We show sample color-color plots of the entire grid as well as simulated clusters at various distances with typical {\it Spitzer Space Telescope} sensitivities. We find that young embedded sources generally occupy a large region of color-color space due to inclination and stellar temperature effects. Disk sources occupy a smaller region of color-color space, but overlap substantially with the region occupied by embedded sources, especially in the near- and mid-IR. We identify regions in color-color space where our models indicate that only sources at a given evolutionary stage should lie. [...].

A stable boundary element method for modeling transient acoustic radiation

Transient acoustic radiation from a closed axisymmetric three-dimensional object is modeled using the time domain boundary element method. The widely reported instability problems are overcome by reformulating the integral equation to obtain a Burton and Miller type equation in the time domain. The stability of such an approach is mathematically justified and supported by subsequent numerical results. The hypersingular integrals which arise are evaluated using a method valid for any surface discretization. Numerical results for the radiation of a spherical wave are presented and compared with an exact solution. The accuracy and stability of the results are verified for several geometrically different radiating objects.

Low cost sensor for volume and surface area computation of axi-symmetric agricultural products

In this paper, a low cost sensor system has been designed to automatically compute the volume and surface area of axi-symmetric agricultural products such as eggs, lemons, limes and tamarillos. This sensor system is based on a low-cost image sensor and a low-cost programmable microcontroller. We have demonstrated that an unsupervised image-processing algorithm can generate reliable results by capturing just one image of the axi-symmetric object from a fixed projection. The volume and surface area are computed by approximating the object as a sum of elementary right conical frustums. The analytical and experimental results suggest that this automated sensor system is potentially a good alternative to manual measurements for axi-symmetric agricultural products, with an overall cost of under US$50.

Spiral galaxies as enantiomers: Chirality, an underlying feature in chemistry and astrophysics

AbstractSpiral galaxies are axisymmetric objects showing 2D chirality when projected onto a plane. Features in common with tetrahedral molecules are pointed out, in particular the existence of a preferred chiral modality for genetic galaxies as in amino acids and sugars. Environmental effects can influence the intrinsic chirality of originally isolated stellar systems so that a progressive loss of chirality is recognized in the Hubble morphological sequence of galaxies. © 2005 Wiley‐Liss, Inc. Chirality

Resonant frequency and Q factor of axisymmetric composite microwave cavities

Resonant frequency and unloaded Q factor of composite microwave cavities are computed using surface integral equations for axisymmetric objects. The equivalence principle is used to formulate the problem so that the unbounded space Green's function can be utilized. The numerical results are verified experimentally for many samples of conducting cavities and dielectric resonators inside conducting cavities. Also, cases with a sector of the rotational cavity are considered by introducing a conducting corner. The method allows the computation of the stored energy in each dielectric region and the unloaded Q factor.

Sound scattering by a hard axisymmetric object in a double layered ocean

An acoustically hard object is placed in a double layered ocean very far from a point source of acoustic waves. The object is either floating in the water layer or buried in the sediment layer. Both layers are homogenous. The size of the object is small when compared to the depth of the water channel. The free surface of the sea is assumed to be soft and the bottom is assumed to be hard. Between the two layers the classical diffraction boundary conditions are taken. The deep water approximation method is being extended to provide an approximating analytical expression of the scattered pressure field.

A Discrimination Algorithm for UXO Using Time Domain Electromagnetics

An assumption is made that the Time Domain Electromagnetic (TEM) response of a buried axisymmetric metallic object can be modelled as the sum of two dipoles centered at the midpoint of the body. The strength of the dipoles depends upon the relative orientation between the object and the source field, and also upon the shape and physical properties of the body. Upon termination of the source field, each dipole is assumed to decay as [Formula: see text]. The parameters [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] depend upon the conductivity, permeability, size and shape of the object, and these can be extracted from the measurements by using a nonlinear parametric inversion algorithm. Investigations carried out using an analytic solution for a sphere and laboratory measurements of steel and aluminum rectangular prisms, suggest the following two-step methodology: (1) The value of [Formula: see text] is first used as a diagnostic to assess whether the metallic object is non-magnetic or magnetic, (2) the ratios of [Formula: see text] and [Formula: see text] are then diagnostic indicators as to whether the geometry is plate-like (uninteresting) or rod-like (a high candidate for being a UXO). Results from the application of this algorithm to a TEM field data set acquired at the United States Army Corps of Engineers Research and Development Centre (ERDC) UXO Test Site have successfully identified a UXO to be magnetic and rod-like.

A small resistive axisymmetric object in the presence of an underwater point-source field

A small, acoustically resistive and axisymmetric object is placed in a deep homogeneous sea environment with a hard plane bottom. The size of the object is small when compared to the depth of the water channel. The free surface of the sea is assumed to be soft. The source and the receiver are placed on the same vertical line and far away from the object. Given the positions of the source and the receiver, two problems are solved: The determination of the pressure field at the receiver from the position and the shape of the object and the determination of the position and the shape of the object from the pressure field at the receiver. The special case of smooth axisymmetric objects, i.e. objects generated by the rotation of differentiable curves, is studied. I provide results for the case of a floating object and for the case of an object or a “hillock” at the bottom of the sea.

Recovery of Temperature and Species Concentration Profiles in Flames Using Low-Resolution Infrared Spectroscopy

The temperature and species distributions in semi-transparent gaseous axisymmetric objects are retrieved by carrying out the inversion of their directional low-resolution spectral transmission and/or spectral emission in the infrared by using methods based on the solution of the radiative transfer equation. The validity domains of the hypothesis on which the low resolution inversion methods are based are discussed by comparison with the corresponding exact radiative properties generated by line-by-line descriptions. A propane-air laminar premixed flame is experimentally studied. The infrared data are collected for the (ν3) band of CO2, either by a directional scanning (at a fixed frequency) or by a frequency scanning (in a fixed direction). Depending on the data acquisition methods, two different reconstruction techniques are used. For spatial scanning, a generalized Abel transformation or the regularized Murio’s method, is utilized. For spectral scanning the recovered results are carried out by the Chahine-Smith method. For both techniques, profile reconstructions are worked out accounting for a spectral data bank based on the narrow statistical band model. Finally, thermal and CO2 concentration mappings of the premixed flame are presented.

Representation of 3D surfaces by two-variable Fourier descriptors

A method for generating two-variable 3D FDs directly from a striped lighting system is developed. An iterative algorithm is proposed to compute the two-variable 3D FDs for both axisymmetric and nonaxisymmetric objects and a formula for convergence test is derived. Experiments conducted for a set of 3D objects show that the iterative algorithm converges very quickly and the two-variable 3D FD representations are attained accurately.

Coupled-mode modeling of acoustic scattering from three-dimensional, axisymmetric objects

In this paper a coupled-mode method for computing the wave field scattered by three-dimensional, axisymmetric fluid objects is presented. The method provides a unified approach to solving three-dimensional scattering problems for axisymmetric objects in free space, in a waveguide, or partially or fully buried in a basement. Numerical computations of scattering from finite cylinders in free space and embedded between two half-spaces are presented. Also, the method is used to compute the scattering from an infinitely long cylinder for which analytical results are available.

Distribution of large Pacific seamounts from Geosat/ERS‐1: Implications for the history of intraplate volcanism

We characterize the seamount distribution on the Pacific Plate using the gridded vertical gravity gradient (VGG, or geoid curvature) derived from Geosat and ERS‐1 satellite altimetry. The VGG amplifies short‐wavelength information and suppresses longer wavelength components, making it suitable for seamount detection purposes. Furthermore, the VGG over seamounts has a much more pronounced zero crossing than that of the free‐air anomaly (FAA); the distance to the zero crossing can be used as a proxy for seamount radius. After removing a regional field obtained by robust median filtering we identify seamount amplitudes and locations from local maxima in the VGG grid. The radius of a seamount is more difficult to estimate since seamounts tend to cluster and overprint each other's signals. Individual seamounts are modeled as Gaussian, axisymmetric objects loading an elastic lithosphere; the VGG over such features can be approximated by a simple analytical expression which we use to determine the zero‐crossing distances for overlapping seamounts. By using the VGG the maximum amplitude and distance to the zero crossing become largely independent of the elastic plate thickness and infill density. We do forward modeling of Gaussian seamounts and their gravimetric response and create a look up table that relates seamount FAA (in milligals), VGG (in Eötvös), and zero‐crossing distance (in kilometers) to actual height and radius (in kilometers). The frequency‐size distribution of these predicted seamount heights follows a power law for heights between 2 and 8 km. The seamount density (number of seamounts per area) is greatest in the central Pacific. We confirm earlier results suggesting that the majority of large seamounts are located in the western region of the Pacific Plate, on older crust. As crustal age increases, so does seamount density, peaking on 100–130 m.y. crust, supporting suggestions of high magmatism in the Cretaceous. We demonstrate that there may be an empirical relationship between the seamount VGG amplitude and the age of the lithosphere at the time of seamount formation and invert this relationship to predict seamount ages from VGG amplitudes. These pseudo ages have large uncertainties but, nevertheless, may be used to investigate temporal fluctuations in Pacific intraplate volcanism. Our results indicate that seamount intraplate volcanism attained a maximum level in the mid‐Cretaceous to Late Cretaceous, about 70–120 Ma, apparently contemporaneous with the formation of large oceanic plateaus in the Pacific.