Elliptical Annulus Research Articles

Effect of opposed eccentricity on free convective heat transfer through elliptical annulus enclosures in blunt and slender orientations

This paper presents an experimental investigation for the effect of opposed lateral and vertical eccentricities on free convective heat transfer through elliptical annulus enclosures in blunt and slender orientations. Three test specimens of elliptical cylinders having an equal radius ratio and an equal length were prepared. The surface area of the inner cylinder is the same for each specimen as well as the area of the outer cylinder. Different elliptical ratios of 0.662, 0.866 and 0.968 were investigated. Experimental tests were done by maintaining constant heat flux on the inner cylinder and the outer one was exposed to approximately constant temperature of the closed laboratory. Both annuals ends of the annular elliptical cylinders were closed by cork to form the annular enclosure space. The experimental tests monitored Rayleigh number (1.642 × 103 ≤ Ra* ≤ 3.849 × 106). The effects of both opposed vertical and lateral eccentricities for both blunt and slender orientations were investigated. The experimental results were fitted by correlations. Considerable agreement was found in the comparison among the results of present and previous works. Opposed eccentricity enhances free convective heat transfer by about 40 % from concentric. Slender orientation results in more enhancements in free convection than blunt one.

Eigenproblems of two-dimensional acoustic cavities with smoothly varying boundaries by using the generalized multipole method

This paper presents a semi-analytical approach to solve the eigenproblem of a two-dimensional acoustic cavity with smoothly varying boundaries. The multipole expansion for the acoustic pressure is formulated in terms of Bessel and Hankel functions to satisfy the Helmholtz equation in the polar coordinate system. Rather than using the addition theorem, the multipole method and directional derivative are both combined to propose a generalized multipole method in which the acoustic pressure and its normal derivative with respect to non-local polar coordinates can be calculated. The boundary conditions are satisfied by uniformly collocating points on the boundaries. By truncating the multipole expansion, a finite linear algebraic system is acquired. The direct searching approach is applied to identify the natural frequencies using the singular value decomposition technique. Several numerical examples are presented, including those of an annulus cavity, a confocal elliptical annulus cavity and an arbitrarily shaped cavity with an inner elliptical boundary. The accuracy and numerical convergence of the proposed method are validated by comparison with results of the available analytical method and the commercial finite-element code ABAQUS. No spurious eigensolutions are found in the proposed formulation. Due to its semi-analytical character, excellent accuracy and fast rate of convergence are the main features of the proposed method.

Tuning the focusing spot of plasmonic nanolens by aspect ratio under linear polarization

A new plasmonic nanolens that can be tuned by varying the circular structure into an elliptical annulus and the aspect ratio from 1 to 0.1 and 1 to 2, respectively, is proposed. Using the rigorous finite-difference and time-domain algorithm, we find that when the aspect ratio ranges from 1 to 0.1, a good linear relationship exists between the aspect ratio and focusing spot size at the full-width at half-maximum in the x- and y-directions, respectively. The corresponding calculated FWHM ranges from 96 × 126 (nm) to 15 \times 52 (nm) (Full Width at Half Maximum).

Acoustic eigenproblems of elliptical cylindrical cavities with multiple elliptical cylinders by using the collocation multipole method

Abstract Acoustic eigenproblems of 3-D elliptical cylindrical cavities having multiple elliptical cylinders are solved by means of a 3-D semi-analytical formulation based on a multipole expansion, directional derivative, collocation technique and singular value decomposition (SVD). The multipole expansion for the acoustic pressure is formulated in terms of angular and radial Mathieu functions due to elliptical boundaries considered here. The boundary conditions are satisfied by uniformly collocating points along the boundaries. When considering sound-hard or Neumann boundary conditions, the normal derivative of acoustic pressure with respect to non-local elliptic coordinates is derived using the directional derivative for multiply-connected domain problems. By truncating the multipole expansion, a finite linear algebraic system is acquired. The direct searching approach is applied to identify the natural frequencies by using the SVD. Several numerical examples are examined, including those of an elliptical cylindrical cavity, a confocal elliptical annulus cylindrical cavity and an elliptical cylindrical cavity with two elliptical cylinders. Convergence and comparison studies are done to demonstrate the validation and accuracy of the present method. No spurious eigensolutions are found in the proposed formulation. Excellent accuracy and fast rate of convergence are the main features of the present method thanks to its semi-analytical character.

Reproducibility of SD-OCT–Based Ganglion Cell–Layer Thickness in Glaucoma Using Two Different Segmentation Algorithms

To compare the reproducibility of spectral-domain optical coherence tomography (SD-OCT)-based ganglion cell-layer-plus-inner plexiform-layer (GCL+IPL) thickness measurements for glaucoma patients obtained using both a publicly available and a commercially available algorithm. Macula SD-OCT volumes (200 × 200 × 1024 voxels, 6 × 6 × 2 mm(3)) were obtained prospectively from both eyes of patients with open-angle glaucoma or with suspected glaucoma on two separate visits within 4 months. The combined GCL+IPL thickness was computed for each SD-OCT volume within an elliptical annulus centered at the fovea, based on two algorithms: (1) a previously published graph-theoretical layer segmentation approach developed at the University of Iowa, and (2) a ganglion cell analysis module of version 6 of Cirrus software. The mean overall thickness of the elliptical annulus was computed as was the thickness within six sectors. For statistical analyses, eyes with an SD-OCT volume with low signal strength (<6), image acquisition errors, or errors in performing the commercial GCL+IPL analysis in at least one of the repeated acquisitions were excluded. Using 104 eyes (from 56 patients) with repeated measurements, we found the intraclass correlation coefficient for the overall elliptical annular GCL+IPL thickness to be 0.98 (95% confidence interval [CI]: 0.97-0.99) with the Iowa algorithm and 0.95 (95% CI: 0.93-0.97) with the Cirrus algorithm; the intervisit SDs were 1.55 μm (Iowa) and 2.45 μm (Cirrus); and the coefficients of variation were 2.2% (Iowa) and 3.5% (Cirrus), P < 0.0001. SD-OCT-based GCL+IPL thickness measurements in patients with early glaucoma are highly reproducible.

The effect of adiabatic obstacles on natural convection inside a horizontal elliptical porous annulus

This study numerically examines the influence of installing two identical radial adiabatic obstacles on natural convection within a porous layer of constant thickness. This porous layer surrounds an isothermal hot elliptical cylinder and is surrounded by an isothermal cold one. The obstacles' length, angular position and radial position were changed in various amounts. A non-orthogonal curvilinear coordinate system is adopted, in order to treat the presence of the obstacles inside a two dimensional elliptical annulus. Consequently, Finite Differences Techniques and ADI with Relaxation Method were used to approximate the computational regime of the non-Darcian-Boussinesq equation, governing the flow inside the computational porous domain. An efficient code of high accuracy was constructed to solve the approximated governing equations. The results showed that the installation of long obstacles in the meeting place of two convection cells causes an increase in heat transfer rates by up to 16%. Whereas the installation of short obstacles in a place lying close to the center of the major convection cell causes a reduction in heat transfer by up to 19% .

Transcatheter aortic valve implantation for patients with elliptical aortic annulus

Purpose: The purpose of this study was to elucidate impact of annulus ellipticity on clinical outcomes after transcatheter aortic valve implantation (TAVI). Methods: Of 548 patients included in our TAVI database with either of the Edwards or CoreValve (October 2006 to June 2012), 305 consecutive patients undergoing pre-procedural multidetector computed tomography (MDCT) were analyzed. Ellipticity was defined as MDCT-measured diameter ratio>1.20. We compared clinical outcomes in patients with (n = 155) vs. without (n = 150) ellipticity. Results: Patients were 83.2±6.6 years old and EuroSCORE was 19.9±12.0%. The ellipticity group was similar to the non-ellipticity group except for coronary disease (49.0 vs. 64.0%, P = 0.01). Despite no significant difference in mean MDCT-measured diameter (23.7±2.1 vs. 23.8±2.1mm, P = 0.47), ellipticity was associated with decreased short-axis (21.3±2.0 vs. 22.5±2.0mm, P <0.01) and increased long-axis diameter (27.0±2.5 vs. 25.7±2.5mm, P <0.01) resulting in increased long/short-axis diameter ratio (1.27±0.07 vs. 1.14±0.06mm, P <0.01). Ellipticity group tended to have increased incidence of bicuspid valve (12.3% vs. 6.0%, P = 0.06). The CoreValve was used similarly (21.3% vs. 22.0%, P = 0.88). There was no significant difference in device success (94.2% vs. 93.3%, P = 0.76), risk of annulus rupture (1.3% vs. 0.7%, P = 0.51) or valve migration (0 vs. 2.0%, P = 0.12) between 2 groups. Post-procedural mean gradient (10.1±6.1 vs. 9.7±3.7mmHg, P = 0.52), aortic regurgitation ≥2/4 (15.5% vs 17.3%, P = 0.66), 30-day mortality (5.8% vs. 10.0%, P = 0.17) and 30-day combined safety point (14.2% vs. 14.7%, P = 0.91) were also similar in both groups. Conclusions: In patients with ellipticity, TAVI is associated with equally high rates of success, low complication rates, similar efficacy and acceptable outcomes as in non-ellipticity patients.

Solution of a problem of ℝ-linear conjugation for confocal elliptical annulus in the class of piecewise meromorphic functions

We consider the problem of disturbance of a complex potential after insertion of a foreign inclusion in the form of a two-phase confocal elliptical annulus into a homogeneous medium. We investigate the cases of an arbitrary distribution of singularities.

Localization of Laplacian Eigenfunctions in Circular, Spherical, and Elliptical Domains

We consider Laplacian eigenfunctions in circular, spherical and elliptical domains in order to discuss three kinds of high-frequency localization: whispering gallery modes, bouncing ball modes, and focusing modes. Although the existence of these modes was known for a class of convex domains, the separation of variables for above domains helps to better understand the "mechanism" of localization, i.e. how an eigenfunction is getting distributed in a small region of the domain, and decays rapidly outside this region. Using the properties of Bessel and Mathieu functions, we derive the inequalities which imply and clearly illustrate localization. Moreover, we provide an example of a non-convex domain (an elliptical annulus) for which the high-frequency localized modes are still present. At the same time, we show that there is no localization in most of rectangle-like domains. This observation leads us to formulating an open problem of localization in polygonal domains and, more generally, in piecewise smooth convex domains.

The Shape of the Ganglion Cell plus Inner Plexiform Layers of the Normal Human Macula

To use surfaces generated by two-dimensional penalized splines (2D P-splines) to characterize the shape of the macular ganglion cell plus inner plexiform layers (GCL+IPL) in a group of normal humans. Macular images of the right eyes of 23 normal subjects ranging in age from 18 to 75 years were obtained with spectral-domain optical coherence tomography (SD-OCT). The thickness of GCL+IPL was determined by manual segmentation, areas with blood vessels were removed, and the resulting maps were fit by smooth surfaces in polar coordinates centered on the fovea. Smooth surfaces based on 2D P-splines could precisely represent GCL+IPL thickness data, with errors comparable to the axial resolution of the SD-OCT instrument. Metrics were developed for the size, shape, and slope of the edge of the foveal depression and size and shape of the surrounding macular ridge. The slope of the foveal edge was negatively correlated with foveal size (r = -0.60). The size of the macular ridge was positively correlated with foveal size (r = 0.75), with a slope near unity (0.90 ± 0.18). The centroids of the foveal edge and macular ridge clustered near the foveal center. The foveal edge and macular ridge were well fit by ellipses. The mean GCL+IPL thickness formed an elliptical annulus elongated by approximately 30% in the horizontal direction. The methods developed here provide precise characterization of retinal layers for the study of glaucoma, foveal development, and other applications.

A Novel Method to Detect Local Ganglion Cell Loss in Early Glaucoma Using Spectral-Domain Optical Coherence Tomography

To test the glaucoma-discriminating ability of a new method for detecting local ganglion cell loss using spectral-domain optical coherence tomography (OCT). This study included 58 glaucomatous and 48 healthy eyes from Japanese subjects. Combined thickness of the ganglion cell layer and inner plexus layer (GCIPL) was measured on a macular cube scan in Cirrus HD-OCT. Average GCIPL thickness within a macular elliptical annulus and minimum GCIPL thickness on 360 spokes extending from the inner to the outer radius of the elliptical annulus were calculated. Area under the receiver operating characteristic curve (AROC) to discriminate between healthy eyes and early (mean deviation [MD], ≥-6 dB)/advanced (MD, <-6 dB) glaucomatous were compared between parameters. Forty-three were normal-tension glaucoma, and 15 were high-tension glaucoma. The mean minimum GCIPL thickness was 77.0 μm in healthy eyes and 60.6 μm in glaucomatous eyes (P < 0.001). For the intersession repeatability, the coefficients of variation for average GCIPL and minimum GCIPL were 0.98 and 1.85 in glaucomatous eyes, and 0.89 and 1.85 in healthy eyes, respectively. Minimum GCIPL thickness AROC (0.896) was significantly higher (P = 0.0062) than average GCIPL thickness (0.821) for early glaucoma, whereas minimum GCIPL AROC (0.991) was comparable (P = 0.103) to average GCIPL (0.964) for advanced glaucoma. The minimum GCIPL thickness AROC was comparable (P = 0.861) to average circumpapillary retinal nerve fiber layer (cpRNFL) thickness (0.890) for early glaucoma. In Japanese patients with 74.1% of normal-tension glaucoma, the minimum GCIPL on spokes may be useful for detecting early glaucoma.

Variance Reduction in a Dataset of Normal Macular Ganglion Cell Plus Inner Plexiform Layer Thickness Maps with Application to Glaucoma Diagnosis

To examine the similarities and differences in the shape of the macular ganglion cell plus inner plexiform layers (GCL+IPL) in a healthy human population, and seek methods to reduce population variance and improve discriminating power. Macular images of the right eyes of 23 healthy subjects were obtained with spectral domain optical coherence tomography. The thickness of GCL+IPL was determined by manual segmentation, areas with blood vessels were removed, and the resulting maps were fit by smooth surfaces in polar coordinates centered on the fovea. The mean GCL+IPL thickness formed a horizontal elliptical annulus. The variance increased toward the center and was highest near the foveal edge. Individual maps differed in foveal size and overall GCL+IPL thickness. Foveal size correction by radially shifting individual maps to the same foveal size as the mean map reduced perifoveal variance. Thickness alignment by shifting individual maps axially, then radially, to match the mean map reduced overall variance. These transformations had very little effect on the population mean. Simple transformations of individual GCL+IPL thickness maps to a canonical form can considerably reduce the population variance in a sample of normal eyes, likely improving the ability to discriminate abnormal maps. The transformations considered here preserve the local geometry of the thickness maps. When used on a patient's map, they can produce a deviation map that provides a meaningful measurement of the size of local thickness deviations and allows estimation of the number of ganglion cells lost in a glaucomatous defect.

Accurate measurement of mitral annular area by using single and biplane linear measurements: comparison of conventional methods with the three-dimensional planimetric method

The planimetry method using three-dimensional (3D) echocardiography is useful for providing an accurate mitral annulus area (MAA) value. However, this method is relatively unavailable. Therefore, we evaluated the accuracy of conventional methods for MAA measurement compared with that of 3D planimetry. Two-dimensional (2D) and 3D transoesophageal echocardiography (TEE) were performed in 70 patients. The mitral annulus diameter (MAD) was measured using four standard TEE imaging planes: four-chamber (4Ch), two-chamber (2Ch), anterior-posterior (LAX), and commissure-commissure (CC). MAA was calculated using a single diameter based on that of a circle and using two diameters based on that of an ellipse. MAA measurements using the single 4Ch MAD method (r = 0.84, P < 0.001), and two anatomically orthogonal MAD method in 4Ch/2Ch (r = 0.93, P < 0.001) and LAX/CC (r = 0.97, P < 0.001) planes correlated with 3D planimetric MAA measurements. Further analysis with Bland-Altman plots revealed that the LAX/CC MAD measurement exhibited the closest limits of agreement with the 3D planimetric MAA measurement. Notably, in patients showing an elliptical annulus shape, only LAX/CC MAD, but not 4Ch or 4Ch/2Ch MAD, provided results comparable with those of 3D planimetric MAA measurements. However, in patients with a circular annulus shape, reliable MAA measurements can be achieved using either single 4Ch MAD or any biplane MAD. Conventional LAX/CC MAD can be recommended for MAA measurements in a diverse patient population. This method is applicable as an alternative to the 3D planimetric method, regardless of the mitral annulus shape.

Natural mode analysis of an acoustic cavity with multiple elliptical boundaries by using the collocation multipole method

This paper presents a semi-analytical approach to solve the eigenproblem of an acoustic cavity with multiple elliptical boundaries. To satisfy the Helmholtz equation in the elliptical coordinate system, the multipole expansion for the acoustic pressure is formulated in terms of angular and radial Mathieu functions. The boundary conditions are satisfied by uniformly collocating points on the boundaries. The acoustic pressure at each point is directly calculated in each elliptical coordinate system. In different coordinate systems, the normal derivative of the acoustic pressure is calculated by using the appropriate directional derivative, an alternative to the addition theorem. By truncating the multipole expansion, a finite linear algebraic system is derived. The direct searching approach is employed to determine the natural frequencies by using the singular value decomposition (SVD). Numerical results are widely discussed for several examples including an elliptical cavity, a confocal elliptical annulus cavity and an elliptical cavity with two elliptical cylinders. The accuracy and numerical convergence of the presented method is validated by comparison with available results from the analytical method and the commercial finite-element code ABAQUS. No spurious eigensolutions are found in the proposed formulation. Excellent accuracy and fast rate of convergence are the key features of the present method thanks to its semi-analytical feature.

Scatter correction method for x‐ray CT using primary modulation: Phantom studies

Scatter correction is a major challenge in x-ray imaging using large area detectors. Recently, the authors proposed a promising scatter correction method for x-ray computed tomography (CT) using primary modulation. Proof of concept was previously illustrated by Monte Carlo simulations and physical experiments on a small phantom with a simple geometry. In this work, the authors provide a quantitative evaluation of the primary modulation technique and demonstrate its performance in applications where scatter correction is more challenging. The authors first analyze the potential errors of the estimated scatter in the primary modulation method. On two tabletop CT systems, the method is investigated using three phantoms: A Catphan 600 phantom, an anthropomorphic chest phantom, and the Catphan 600 phantom with two annuli. Two different primary modulators are also designed to show the impact of the modulator parameters on the scatter correction efficiency. The first is an aluminum modulator with a weak modulation and a low modulation frequency, and the second is a copper modulator with a strong modulation and a high modulation frequency. On the Catphan 600 phantom in the first study, the method reduces the error of the CT number in the selected regions of interest (ROIs) from 371.4 to 21.9 Hounsfield units (HU); the contrast to noise ratio also increases from 10.9 to 19.2. On the anthropomorphic chest phantom in the second study, which represents a more difficult case due to the high scatter signals and object heterogeneity, the method reduces the error of the CT number from 327 to 19 HU in the selected ROIs and from 31.4% to 5.7% on the overall average. The third study is to investigate the impact of object size on the efficiency of our method. The scatter-to-primary ratio estimation error on the Catphan 600 phantom without any annulus (20 cm in diameter) is at the level of 0.04, it rises to 0.07 and 0.1 on the phantom with an elliptical annulus (30 cm in the minor axis and 38 cm in the major axis) and with a circular annulus (38 cm in diameter). On the three phantom studies, good scatter correction performance of the proposed method has been demonstrated using both image comparisons and quantitative analysis. The theory and experiments demonstrate that a strong primary modulation that possesses a low transmission factor and a high modulation frequency is preferred for high scatter correction accuracy.

Heat Convection Between Two Confocal Elliptic Tubes Placed at Different Orientations

In this paper, transient and steady natural convection heat transfer in an elliptical annulus has been investigated. The annulus occupies the space between two horizontal concentric tubes of elliptic cross-section. The resulting velocity and thermal fields are predicted at different annulus orientations assuming isothermal surfaces. The full governing equations of mass, momentum and energy are solved numerically using the Fourier Spectral method. The heat convection process between the two tubes depends on Rayleigh number, Prandtl number, angle of inclination of tube axes and the geometry and dimensions of both tubes. The Prandtl number and inner tube axis ratio are fixed at 0.7 and 0.5, respectively. The problem is solved for the two Rayleigh numbers of 104 and 105 considering a ratio between the two major axes up to 3 while the angle of orientation of the minor axes varies from 0 to 90◦. The results for local and average Nusselt numbers are obtained and discussed together with the details of both flow and thermal fields. For isothermal heating conditions, the study has shown an optimum value for major axes ratio that minimizes the rate of heat transfer between the two tubes. Another important aspect of this paper is to prove the successful use of the Fourier Spectral Method in solving confined flow and heat convection problems. AMS subject classifications: 80A20, 35Q80

Nonlinear optical catastrophe from a smooth initial beam

We observed an optical cusp diffraction catastrophe with an initially smooth but elongated Gaussian beam with an aspect ratio of 2:1. Nonlinear and linear diffraction regimes account for the near-field elliptical annulus and the far-field spatially complex astroid.

NGC 3081: Surface Photometry and Kinematics of a Classic Resonance Ring Barred Galaxy

This paper presents a detailed photometric and kinematic study of the well-known Seyfert 2 galaxy NGC 3081, one of the best examples of a resonance ring barred galaxy in the sky. Improved optical images compared to previous studies reveal that NGC 3081 is a classic R1R galaxy, a type that shows a distinctive outer ring/pseudoring pattern at large radii that can be linked to orbit families at the outer Lindblad resonance (OLR). Together with an exceptionally strong inner ring and a blue nuclear ring, NGC 3081 has the rare distinction of having all four of the main types of resonance rings that have been predicted by test-particle models of barred spirals. Near-infrared imaging of NGC 3081 reveals clear old rings connected to the inner ring and the R1 outer ring. Objective comparison of the B- and H-band positions of the inner ring indicates no significant difference in shape, major-axis position angle, or major-axis radius between the two passbands, in spite of the different stellar populations each band emphasizes. Imaging Fabry-Perot interferometry provides an intriguing picture of star formation in the galaxy and of the dynamics of the system. Hα emission is strong in the inner ring and is confined to a bounded elliptical annulus of diffuse emission whose ellipticity increases from the inner edge to the outer edge. A few H II regions are connected to the strong R1-type outer ring, particularly just off the major axis of the inner ring where dimples, typical of the R1 morphology, are found. There is bright emission in an oval zone in the inner 10'' radius, but no enhancement of emission is associated with the blue-light nuclear ring. Since most of the emission is connected with the intrinsically oval inner ring and the bright center, the global dynamics of the galaxy are uncertain. Nevertheless, using a combination of the gravitational potential derived from the H-band light distribution and a simple halo model, we estimate the pattern speed and the location of all major resonances in the disk of NGC 3081. We find that NGC 3081 fits extremely well into recent ideas of barred galaxy dynamics.

Standardization of tibial fractures in the rat

The influence of the fracture level on the biomechanical properties of healing rat tibial fractures has not been investigated so far, despite the widespread use of rats in fracture healing studies. Fractures were produced in four different zones in the right rat tibia and immobilized with a K-wire. A fifth group of rats was not fractured. After 40 days of healing the fractures and the non-fractured bones were tested in three-point bending. A distinct correlation was found between fracture level and mechanical parameters: maximum load, maximum stiffness and maximum stress decreased the more distal the fracture was located. In the non-fractured bones, maximum load and maximum stress were constant in all four zones tested, whereas energy absorption increased in the distal part of the tibia. No influence of the healing fracture was found on the contralateral, non-fractured tibia, compared with the animals left undisturbed and the mechanical properties of the right and the left tibia were found to be symmetrical in terms of mean values. Four different methods of determining the area moment of inertia were investigated and the simple method of approximating the cross section to an elliptical annulus was found to correlate well with the area moment of inertia, determined from computer tracings of bone slices prepared from the test specimens after the bending test. The computer tracings were corrected for the compression of the specimens caused by the mechanical test.

Outward-Dipping Ring-Fault Structure at Rabaul Caldera as Shown by Earthquake Locations

The locations of a large number of earthquakes recorded at Rabaul caldera in Papua New Guinea from late 1983 to mid-1985 have produced a picture of this active caldera's structural boundary. The earthquake epicenters form an elliptical annulus about 10 kilometers long by 4 kilometers wide, centered in the southern part of the Rabaul volcanic complex. A set of events with well-constrained depth determinations shows a ring-fault structure that extends from the surface to a depth of about 4 kilometers and slopes steeply outward from the center of the caldera. This is the first geophysical data set that clearly outlines the orientation of an active caldera's bounding faults. This orientation, however, conflicts with the configuration of many other calderas and is not in keeping with currently preferred models of caldera formation.