Ellipticity Of Ellipse Research Articles

Morphometric analysis of in vitro human crystalline lenses using digital shadow photogrammetry

There is a great need for accurate biometric data on human lenses. To meet this, a compact tabletop optical comparator, the minishadowgraph, was built for measuring isolated eye lens shape and dimensions while the lens was fully immersed in supporting medium. The instrument was based around a specially designed cell and an illumination system which permitted image recording in both sagittal and equatorial (coronal) directions. Data were acquired with a digital camera and analyzed using a specially written MATLAB program as well as by manual measurements in image analysis software. The possible effect of lens orientation and gravity on the dimensions was examined by measuring dimensions with anterior or posterior surfaces up and by measuring lenses with calipers after removal from the minishadowgraph cell.Dimensions, curvatures and shape factors were obtained for 134 fully accommodated lenses ranging in age from birth to 88 years postnatal. Of these, 41 were from donors aged under 20 years, ages which are generally of limited availability. Thickness and diameter showed the same age-related trends described in previous studies but, for the lenses measured in air, age-dependent differences were observed in thickness (−5 to 0%) and diameter (+5 to 0%), consistent with gravitational sag. Anterior and posterior radii of curvature of the central 3 or 6 mm, depending on lens diameter, increase with age, with the anterior increase greater than the posterior. The anterior surface shape of the neonatal lens is that of a prolate ellipse and the posterior, an oblate ellipse. Both surfaces become hyperbolic after age 20.The data presented here on dimensions, shape and sagging will be of great value in assessing age-related changes in the optical and mechanical performance of the lens. In particular, the comprehensive data set from donors aged under 20 years provides a unique and valuable insight to the changes in size and shape during the early dynamic growth period of the lens.

Effect of morphology of nanoparticles on performance of transparent display

Nanoparticles based transparent display is one of the most successful methods to realize transparent monitors. Also, an array of nanoparticles, especially aperiodic arrangements, plays an important role in this case. Normally, when one talks about nanoparticles, the spherical morphology appears in mind, in which it is possible to implement different morphology for nanoparticles. In this paper, six different classes of morphologies with various arrangements, such as periodic array and deterministic aperiodic arrays, have been investigated to propose a high-performance transparent display. We compare different morphologies of Si–SiO2 nanoparticles at RGB (Red, Green, Blue) wavelengths in different types of arrays to find the highest scattering cross-section. Our calculations and figure of merit depending on the optical properties of nanoparticles, such as the resonance wavelength, the extinction, scattering and absorption cross-section, and the scattering to absorption ratio (SAR). We will show that in the proposed structures, there are suitable parameters to provide higher scattering cross-section as well as narrow bandwidth in which that is equivalent to introduce the maximum transparency and contrast ratio of transparent monitor. We use the Finite-Difference Time-Domain (FDTD) numerical method to simulate and calculate the deterministic aperiodic and periodic arrays of nanoparticles. Finally, we obtain the absorption and scattering cross-sections for six classes of nanoparticles: Cube, Sphere, Disk, Oblate ellipse, Prolate ellipse, and Pyramid into aperiodic and periodic arrays.

Polymorphic calcium alginate microfibers assembled using a programmable microfluidic field for cell regulation.

Effectively guiding and accurately controlling cell adhesion and growth on the surfaces of specific morphological materials are key issues and hot research topics for optimizing biomaterials. Herein, novel polymorphic alginate microfibers formed through microfluidic spinning technology in a single microchip are presented. Through programming the flow and reaction kinetics in microchannels, other than self-modified micromorphic channel geometry, polymorphic microfibers with precisely tuned curvature-adjustable morphology can be obtained. Finite element (FE) simulations of the flow field (unidirectional fluid-solid coupling) proved the efficacy of the proposed control strategy. Moreover, the specific disordered-ordered cell arrangements showed a linear relationship between bioinspired alginate microfibers with different curvatures and the orientation angle of L929 cells, and diversified growth morphologies, including oblate ellipse, star, tree and strip shapes, occurred on the customizable interface curvature of the calcium alginate microfibers, providing a paradigm for using specific structured natural biomedical materials for cell regulation. This work represents a new design concept for manufacturing polymorphic fibrous biomedical materials through a unique marriage of the fields of green chemistry, hydromechanics, and biomaterials, which should be very useful for guiding the controllable construction of alginate materials for use in structural materials for biomedical and engineering purposes.

An approximation of geodesic circle passing through three points on an ellipsoid

Abstract In this paper we present an approximation method for a geodesic circle passing through three points on an oblate ellipsoid. Our method uses a prolate ellipsoid passing through the three points, and the new approximation curve is the intersection of the oblate and prolate ellipsoids, which can be obtained algebraically without iterations. The advantage of our approximation method is that it yields a significantly smaller approximation error. Compared to the plane section curve passing through the three points on the oblate ellipse, our method reduces the approximation error by at least 98 % 98\hspace{0.1667em}\% when the radii of geodesic circles are 100 km∼1000 km on the surface of the Earth. We illustrate the results using numerical examples.

Electrohydrodynamics of a liquid jet in transverse AC electric fields

The behavior of a liquid jet in a transverse AC electric field is investigated. The governing electrohydrodynamic equations are solved analytically for Newtonian and immiscible fluids in the framework of leaky-dielectric model and in the limit of small electric field and fluid inertia. It is shown that ratios of electric conductivity and permittivity of the constituting fluids along with a nondimensional frequency (i.e., the time scale of the electric field oscillation over the time scale of charge relaxation from the bulk of the ambient fluid to the jet surface) are the key parameters that determine the mean and the time-periodic behavior of the jet, and that on the basis of these parameters the fluids can be categorized into three different classes in terms of their impact on the mean behavior of the jet. In the first class, the jet elongates in the direction of or perpendicular to the field, becoming a prolate or an oblate ellipse, respectively, depending on the field frequency, and the mean deformation increases with an increase in the frequency of the field. In the second class, the jet deforms to a prolate and the mean deformation increases with an increase in the frequency. In the third class, the jet deforms to a prolate and the mean deformation decreases with an increase in the frequency. It is shown that for the first class of the fluids a critical frequency exists at which the jet remains circular regardless of the strength of the electric field. Concerning the time-periodic behavior, it is shown that the jet surface oscillates with a frequency that is twice that of the imposed electric field, and the time-periodic deformation has a time lag with respect to the imposed electric field. The evolution of the flow field with time is studied and it is shows that the flow structure is determined by the interplay of the net interfacial tangential and normal electric forces, and that depending on the relative importance of these two parameters the flow will consist of closed vortices or open-ended streamlines (open vortices). The frequency of oscillation of the flow field is twice that of the external electric field, and it has a time lag with respect to the imposed electric field.

Detection of shape manufacturing defects of flat fan-pattern nozzle orifices using elliptic fourier descriptors

Shape defects originating from the manufacture in the orifice openings of the flat fan-pattern nozzles may result in deteriorating the spray pattern. This study has been conducted with the aim of detecting the manufacturing defects of the fan-pattern nozzle orifices in terms of shape uniformity using the elliptic Fourier descriptors (EFDs), and revealing the shape differences among the nozzle orifices made in polyacetal for various nominal sizes ranging from 01 to 06. At first, descriptive data describing dimensions (major and minor length, projected area, etc.) and shapes (shape factor, elongation and roundness) of the nozzle orifices were obtained using an image processing method. The next process, to evaluate the nozzles’ orifice shape using elliptic Fourier analysis (EFA), the progresses of generating the orifice’s contour data, derivation of EFDs, principal component analysis (PCA) of EFDs and visualization of shape variations estimated by the principal component scores (PCs) were followed respectively. Although the shape differences of the orifice outlines could be visually distinguished, the descriptive shape data were not able to discriminate the contour differences. The EFDs determined for each orifice size could individually detect the nozzle orifices with shape defect originating from the manufacture and they could be explicitly distinguished from the scatter plots. The results of the Hotelling’s pairwise comparison test showed that the nozzle orifices in shape were significantly different from each other. Linear discriminant analysis demonstrated that the group centroids of the orifices of 03, 04 and 06 were found close-range to each other. The orifice of 01 which is rectangular in shape had an extraordinary attribute compared to the other orifices. The orifice outline of 015 with a smooth shape was in appearance of an oblate ellipse in shape. The contour of the nozzle orifice of 02 size was explicitly found different from the others. It was concluded that the EF method can be used intended for the manufacturers inspect and improve the quality of nozzle orifices.

Shape of the Posterior Vitreous Chamber in Human Emmetropia and Myopia

To compare posterior vitreous chamber shape in myopia to that in emmetropia. Both eyes of 55 adult subjects were studied, 27 with emmetropia (mean spherical error [MSE] ≥ -0.55; <+0.75 D; mean +0.09 ± 0.36 D) and 28 with myopia (MSE -5.87 ± 2.31 D). Cycloplegic refraction was measured with a Shin Nippon autorefractor and anterior chamber depth and axial length with a Zeiss IOLMaster. Posterior vitreous chamber shapes were determined from T2-weighted magnetic resonance imaging (3.0-T) using procedures previously reported by our laboratory. Three-dimensional surface model coordinates were assigned to nasal, temporal, superior, and inferior quadrants and plotted in two dimensions to illustrate the composite shape of respective quadrants posterior to the second nodal point. Spherical analogues of chamber shape were constructed to compare relative sphericity between refractive groups and quadrants. Differences in shape occurred in the region posterior to points of maximum globe width and were thus in general accord with an equatorial model of myopic expansion. Shape in emmetropia is categorized distinctly as that of an oblate ellipse and in myopia as an oblate ellipse of significantly less degree such that it approximates to a sphere. There was concordance between shape and retinotopic projection of respective quadrants into right, left, superior, and inferior visual fields. Prolate ellipse posterior chamber shapes were rarely found in myopia, and we propose that spherical shape in myopia may constitute a biomechanical limitation on further axial elongation. Synchronization of quadrant shapes with retinotopic projection suggests that binocular growth is coordinated by processes that operate beyond the optic chiasm.

Study of the size and morphology of aggregates formed by pentaethylene glycol monooctyl ether (C8EO5) in n-heptane

The size and morphology adopted by aggregates formed by a non-ionic surfactant, pentaethylene glycol monooctyl ether (C8EO5) in deuterated heptane were studied in detail. Self-diffusion coefficients were estimated by means of 1H-NMR DOSY measurements. Considerable differences in the diffusion coefficients were found for samples with concentrations below and above the critical aggregate concentration – CAC – of the surfactant. The difference is attributed to the presence of aggregates. No significant change in the diffusion coefficient was observed by increasing surfactant concentration; therefore the aggregates exhibit a homogeneous size distribution. Through the diffusion coefficient, a study of the possible size and shape of these aggregates was made. Four different structures were considered: prolate and oblate ellipse, sphere and cylinder, for which structural parameters were calculated using the general Stokes–Einstein equation. The results allow delimiting the size for the possible configurations that C8EO5 aggregates exhibit in heptane.

A contraction model for the flattening and equatorial ridge of Iapetus

Others have explained the excess flattening of Iapetus by a model in which the moon formed at a high spin rate, achieved isostatic equilibrium by very rapid interior heating caused by short-lived radioactive isotopes (SLRI), and subsequently cooled, locking in the excess flattening with respect to an equilibrium shape at its present spin rate. Here we propose an alternate model that does not require an unusually high initial spin rate or the SLRI. The initial formation of Iapetus results in a slightly oblate spheroid with porosity >10%. Radioactive heating by long-lived isotopes warms the interior to about 200 K, at which point it becomes ductile and the interior compacts by 10%, while the 120 km-thick exterior shell remains strong. The shell must deform to match the reduced volume of the ductile interior, and we propose that this deformation occurs along the equator, perhaps focused by a thinner equatorial shell. The final shape of the collapsed sphere matches the observed shape of Iapetus today, described as an oblate ellipse, except along the equator where strain concentration forms a broad ridge. To maintain this non-equilibrium shape, the thickness of the shell must exceed 120 km. Testing the equatorial focusing hypothesis will require a model that includes non-linear processes to account for the finite yield strength of the thick lithosphere. Nevertheless, we show that the stress in the lithosphere generated by the contraction of the interior is about 3 times greater than the stress needed to deform the lithosphere, so some type of lithospheric deformation is expected.

Path Instabilities of Bubble Rising in Polymer Solutions of Hele–Shaw Cell

The buoyancy-driven path instabilities of an air bubble rising in a Hele–Shaw cell filled with pure water and aqueous poly( N -isopropyl acrylamide) (PNIPAM) solutions are examined as a function of the Eotvos number ( Eo ) by measuring changes in the bubble shape, the trajectory, and the peripheral length of a bubble ( L ) as well as the visualization of the wake structures behind the bubble. The instabilities can be categorized into four regimes: (1) an oblate ellipse bubble accompanied with a vibrational trajectory, no changes in L , and a Karman vortex street for the wake structure, (2) a comma-shaped bubble with a vibrational motion of both path and L , together with a vortex street different from a Karman one, and (3) changes in the bubble shape, such as a comma-shaped bubble and a jellyfish one with a vibration of both path and L accompanied with a vortex street different from a Karman one, and (4) changes in the bubble shape, such as a bird flapping its wings bubble and a jellyfish one with a strai...

Buckling of imperfect elastic elliptic toroidal shells subjected to uniform external pressure

The effects of axisymmetric initial geometric imperfections on the buckling pressures of externally pressurized steel elastic toroidal shells of elliptical cross-section are studied in this paper. The shapes of the axisymmetric localized imperfections are increased-radius circular ‘flat spots’ and smooth dimples. In most cases, the locations of the imperfections are at the north (Φ = 180°) and south (Φ = 0°) poles of the cross-section. The main shells investigated are prolate ellipses having k(≡ a/ b) = 1.5, R/ b = 4 and 10 and b/ t = 50, 100 and 500. Some studies of shells with k = 2.0 and 2.5 and k = 0.833 (an oblate ellipse) are also included.

Molecular Dynamics Study of the Dependence of Water Solvation Free Energy on Solute Curvature and Surface Area

We have investigated changes in water properties when deforming an initially spherical cavity into an oblate ellipsoid of equal volume in liquid water. The purely hydrophobic cavity has an initial thermal radius of 6.45 A and is flattened out to an oblate ellipse with a thickness corresponding to one layer of methane molecules. The water-solute interactions are modeled by a repulsive, single-site Gay-Beme potential that preserves the volume of the solute; water-water interactions are modeled using a pairwise additive potential. The Gibbs free energy change, AG, of the aqueous solution was calculated using thermodynamic perturbation theory. Comparison with the process of radially expanding a sphere shows that the free energy change cannot consistently be interpreted as being solely proportional to an exposed solute area but contains terms involving the curvature of the solute. As the meanings of exposed surface area and molecular curvature are not welldefined concepts on the microscopic length scale, these terms have to be defined to yield a consistent interpretation of the free energy data. The microscopic origin of the curvature dependence of the free energy is traced back to changes in water-water interactions in the region immediately surrounding the solute. The process of deforming the liquid around the hydrophobic pocket was found to be dominated by entropic contributions. The free energy values do not contain any contributions arising from the deformation of the hydrophobic solute itself nor any attractive solute-solvent term and thus cannot be compared directly with hydrocarbon-water surface tension data.