Elliptical Axis Research Articles

Experimental study on convective heat transfer in alternating elliptical axis tubes

Experiments are carried out on the convection inside a novel alternating elliptical axis tube. The unified correlations of heat transfer and flow resistance for 500 < Re < 5 × 10 4 are obtained from the experimental results. The experiments show that the heat transfer can be greatly enhanced with less flow resistance increment compared with other enhanced elements. Analyses indicate that the mechanism for heat transfer enhancement is mainly due to the effect of the multi-longitudinal vortices induced by the cross-sectional change in the alternating elliptical axis tubes.

Numerical Study on Low Reynolds Number Convection in Alternate Elliptical Axis Tube

Numerical Study on Low Reynolds Number Convection in Alternate Elliptical Axis Tube

Experimental and theoretical study of the transient rotation of isotropic transparent microparticles in astigmatic optical tweezers

Micrometer-sized rod-like non-birefringent transparent particles trapped by an astigmatic laser beam having elliptical intensity profile spontaneously rotate until they become aligned with the major axis of the beam cross-section. The observed rotation confirms a simple picture based on orbital angular momentum transfer from the light beam to the trapped particle. A model which regards the particle as a thin cylindrical lens with effective focal lengths f 1 and f 2 has allowed to calculate the applied optical torque and, hence, the time law governing the particle alignment. The time evolution of the particle alignment is studied for different rod-like particles by analysing the sequence of frames recorded by a CCD camera. The time evolution of the angle α formed between the main axes of the body and the laser shape results in good agreement with the theory for bodies fully immersed in the spot size of the laser. Discrepancies observed for rod-like particles longer than the minor elliptical axis of the beam cross-section, were removed by developing a more general model taking into account the partial overlapping between the body and the laser profile.

Elliptical Descriptors: Some Simplified Morphometric Parameters for the Quantification of Complex Outlines

Among morphometric methods, a method called Elliptical Fourier Analysis, has been developed to decompose complex outlines into Fourier series. This elliptical Fourier formulation has been rarely applied to date, which is probably explainable because of the mathematical complexity and the difficulty of translating the Fourier coefficients into simple geometrical concepts. Utilizing elliptical analysis, a simplified geometrical approach to the Fourier decomposition is proposed in this study. We showed that the geometrical locus of the points associated with each harmonic used in the Fourier decomposition is an ellipse. The contribution of each harmonic was then characterized with four new geometrical parameters called elliptical descriptors. These are: the half-length of the major axis (L A j ), the half-length of the minor axis (L B j ), the orientation of the major axis, and the phase angle. These descriptors, in contrast to classical Fourier coefficients, possess geometrical significance, and allow for an estimate of each ellipse consisting of: (1) the size of the ellipse (proportional to the product L A B⋅ L B j), (2) the anisotropy of the ellipse (characterized by the ratio L A B/LB j ), and (3) the orientation of the ellipse given by the orientation of the elliptical axes. These parameters completely define the geometry of the ellipse associated with each harmonic, and provide an evaluation of the importance of the harmonic contribution in the description of the form studied. Using these elliptical descriptors, an outline can be described, as well as reconstructed. A methodology is then proposed to characterize and to compare complex outlines using these elliptical descriptors. This new methodology allows the quantification of any form, regardless of their degree of complexity, and allows the translation of the morphological differences into simple geometrical concepts, a procedure difficult to carry out with conventional Fourier coefficients.

Superfluorescence polarization: Signature of collisional redistribution

We have studied effects of magnetic sublevel degeneracy on the polarization of superfluorescent pulses generated on the Ca 4s4p 1 P 1 -3d4s 1 D 2 transition at 5.5 μm. These pulses were generated from a cell of length 50 cm by optically pumping calcium vapor on the 4s 2 1 S 0 -4s4p 1 P 1 transition in the presence of Ar gas. The axis of ellipticity of superfluorescence (SF) polarization is oriented parallel to the axis of the pump-laser polarization at large detunings, and undergoes an abrupt rotation through 90° for detunings close to resonance. The distribution of populations in the magnetic sublevels of the 1 P 1 state can be estimated using a simple model based on previously calculated cross sections for collisionally aided absorption in the presence of an intense (pump) field. For large detunings, these estimates are consistent with the polarized SF intensity measured in the experiment. A direct measurement of the populations of the 1 P 1 magnetic sublevels also supports the collisional redistribution predicted by the calculated cross sections. We therefore suggest that SF polarization can be a useful signature of collisional redistribution. However, the change in ellipticity is unexpected, and probable causes for this effect are discussed.

Observation of Mesoscopic Structures in NdBa2Cu3O7-δ by Small-Angle Neutron Scattering

In order to clarify the origin of the high critical current density (Jc) of NdBa2Cu3O7-δ (Nd123), we investigated the inhomogeneities in this material by small-angle neutron scattering (SANS) experiments. As a result of numerical calculations, it was found that the anisotropic scattering patterns and radial intensity profiles can be explained by the existence of elliptic cylindrical objects of which the cylindrical axis is parallel to the crystallographic c-axis. Long and short elliptic axis lengths and the height of the elliptic cylinders in the high-Jc sample are about 400, 200 and 100 nm, and those of the low-Jc sample are about 200, 100 and 50 nm. Since these two samples have been heat-treated in different manners, it is suggested that sizes of the elliptic cylinders are affected by the heat treatments and this change in scale, as a result, increases or decreases the Jc characteristics of the samples.

Generation and characterization of polarization-shaped femtosecond laser pulses

We demonstrate the generation and complete characterization of femtosecond laser pulses which change their intensity, frequency, and light polarization almost arbitrarily within a single pulse employing the new technique of femtosecond polarization pulse shaping. Specifically, the degree of polarization ellipticity as well as the orientation of the elliptical principal axes can be varied as a function of time in a completely controllable manner, using a 128-pixel, two-layer, liquid-crystal display (LCD) inside a zero-dispersion compressor. A mathematical formalism is presented with which polarization-shaped pulse parameters can be calculated and used to generate intuitive quasi-three-dimensional electric field representations. However, laboratory realization requires accurate and complete experimental pulse characterization methods. For this purpose, the technique of dual-channel spectral interferometry is employed. Furthermore, Jones calculus for polarization-shaped pulses with experimentally determined Jones matrices is developed. It can be used to predict and account for all pulse-shape modifications occurring in various optical elements of the pulse shaper and the experimental setup.

Electron Delocalization in Acyclic andN-Heterocyclic Carbenes and Their Complexes: A Combined Experimental and Theoretical Charge-Density Study

Combined experimental and theoretical charge-density studies on free and metal-coordinated N-heterocyclic carbenes have been performed to investigate the extent of electron delocalization in these remarkable species. Tracing the orientation of the major axis of the bond ellipticity (the least negative curvature in the electron density distribution) along the complete bond paths distinguishes unambiguously between fully delocalized systems and those with interrupted cyclic electron delocalization. Evaluation of charge-density-based properties such as atomic quadrupole moments serves as a direct and quantitative measure of the extent of pi-electron delocalization and reveals consistency between theory and experiment. A detailed topological analysis of theoretical charge densities for two benchmark carbene systems, viz., 1,2-dimethylpyrazol-3-ylidene 1a and 1,3-dimethylimidazol-2-ylidene 2a, and their corresponding stable chromium pentacarbonyl complexes 1 and 2, highlights the advantages of charge-density-based criteria to analyze such complex electronic situations. Thus, 1a and 2a display a different extent of electron delocalization; yet nearly identical p(pi) occupations at the carbene center are computed for 1a and 2a. However, atomic quadrupoles Q(zz) - the charge-density analogues of p(pi) occupation - reveal faithfully the electronic differences in 1a and 2a and demonstrate the sensitivity of charge-density-based properties to the bonding situation. The acyclic aminocarbene (iPr(2)N)(2)CCr(CO)(4) has also been studied, and the high barrier to rotation about the C-N bond is shown not to arise solely from p(pi)-p(pi) bonding.

Femtosecond polarization pulse shaping

We report computer-controlled femtosecond polarization pulse shaping where intensity, momentary frequency, and light polarization are varied as functions of time. For the first time to our knowledge, a pulse shaper is used to modulate the degree of ellipticity as well as the orientation of the elliptical principal axes within a single laser pulse by use of a 256-pixel two-layer liquid-crystal display inside a zero-dispersion compressor. Interferometric stability of the setup is not required. Complete pulse characterization is achieved by dual-channel spectral interferometry. This technology has a large range of applications, especially in the field of quantum control.

A Subarcsecond Resolution Near‐Infrared Study of Seyfert and “Normal” Galaxies. II. Morphology

We present a detailed study of the bar fraction in the CfA sample of Seyfert galaxies, and in a carefully selected control sample of non-active galaxies, to investigate the relation between the presence of bars and of nuclear activity. To avoid the problems related to bar classification in the RC3, e.g., subjectivity, low resolution and contamination by dust, we have developed an objective bar classification method, which we conservatively apply to our new sub-arcsecond resolution near-infrared imaging data set (Peletier et al. 1999). We are able to use stringent criteria based on radial profiles of ellipticity and major axis position angle to determine the presence of a bar and its axial ratio. Concentrating on non-interacting galaxies in our sample for which morphological information can be obtained, we find that Seyfert hosts are barred more often (79% +/- 7.5%) than the non-active galaxies in our control sample (59% +/- 9%), a result which is at the 2.5 sigma significance level. The fraction of non-axisymmetric hosts becomes even larger when interacting galaxies are taken into account. We discuss the implications of this result for the fueling of central activity by large-scale bars. This paper improves on previous work by means of imaging at higher spatial resolution and by the use of a set of stringent criteria for bar presence, and confirms that the use of NIR is superior to optical imaging for detection of bars in disk galaxies.

Frequency analysis of echo texture in tendon

A texture discriminant based on spatial frequencies is proposed for characterizing B-scans of Achilles’ tendon. The anisotropic echo texture of normal tendon has an ellipsoidal spatial spectrum that can be quantified by the ratio of the major-to–minor axis and by the direction of the major axis. Applying a moving window to the B-scan, a corresponding tissue elliptical axis ratio (TEAR) image is derived that segments out tendon. The algorithm was applied to B-scan images taken from 13 volunteers, 6 of whom had tendon abnormalities: tendon rupture (n = 3) or cholesterol deposits (xanthomas) in patients with heterozygous familial hypercholesterolemia (n = 3). The average TEAR value was 1.75 ± 0.17 for normal tendon, 1.04 ± 0.06 for torn tendon, and 1.31 ± 0.16 for tendons with xanthomas. The dispersion of the directionality vectors was used to further differentiate tendons with xanthomas from normal tendons. This technique appears to be useful for characterizing both diffuse and focal tendon abnormalities.

Elliptical Modeling of the Sagittal Lumbar Lordosis and Segmental Rotation Angles as a Method to Discriminate Between Normal and Low Back Pain Subjects

Clinical significance of lumbar lordosis has not been agreed on. Our purpose is to compare lordotic measurements of normal and pain subjects and to test the validity of a new anthropometric model of lumbar curvatures. Digitized radiographic points (body corners) from standing lateral lumbar radiographs were modeled with ellipses in a least-squares method and were used to create segmental angles, a global angle at L1-L5, a Cobb angle from T12 to S1, Ferguson's sacral base angle, and an angle of pelvic tilt. Fifty normal subjects were matched in age, sex, weight, and height with 50 acute pain subjects, 50 chronic pain subjects, and 24 pain subjects with radiographic abnormalities. Of 11 angles, 2 distances, and 2 ratios, statistical analysis was significantly different across groups for 12 of these measurements, with the alternative hypotheses accepted for the other 3 measurements. The lordosis of both normal and low back pain subjects can be successfully modeled with a portion (approximately 86 degrees) of an ellipse, but with different major and minor axis ratios. The normal group's average elliptic lordosis has the smallest least-squares error, approximately 1 mm per digitized point, with (minor axis)/(major axis) ratio = 0.39, L1-L5 global angle = 40 degrees, and Cobb angle = 65 degrees. The chronic and radiographic abnormalities pain groups have an elongated ellipse with hypolordosis, reduced L1-L5 global angle = 29.6-35 degrees, reduced Cobb angle = 57-58 degrees, and elliptic axis ratio = 0.27-0.30. The acute pain group is hyperlordotic with the largest L1-L5 global angle, largest Cobb angle = 70 degrees, largest Ferguson's angle, and largest pelvic tilt angle.

Dynamic model of anisotropic x-ray refraction

General mechanisms of anisotropic x-ray refraction at the resonance energy are investigated on the basis of dynamic-scattering theory. The deductions show that x rays within the crystals that have anisotropic susceptibility are completely polarized and have two elliptical polarization states. Analytical expressions of the elliptical axes, refractive indices, and absorption coefficients for these two types of polarized waves are obtained in terms of the anisotropic components of the susceptibility tensor. Anisotropic birefringence and dichroism effects associated with the polarization properties of the x-ray waves are also illustrated theoretically.

SYMMETRICALLY OSCILLATING VISCOUS FLOW OVER AN ELLIPTIC CYLINDER

The paper deals with the problem of two-dimensional oscillating viscous flow past an elliptic cylinder. The flow is considered incompressible and two-dimensional, and the free-stream oscillations are harmonic. These oscillations are only allowed in the magnitude of the free-stream velocity, which is always parallel to one of the elliptic section axes. The resulting flow field is symmetrical about either the major or minor axis of the ellipse. The parameters involved are the cylinder axis ratio. Reynolds number and the oscillation frequency. The major-minor axis ratio of the elliptic cylinder ranges between 0·5 and 0·8, the Reynolds number ranges between 500 and 103, and the frequency parameter ranges betweenπ/4 andπ/2. Present calculations are performed within the range of sufficiently large oscillation amplitude to induce separation. The time variation of the flow field is presented in the form of streamline patterns as well as the surface pressure distribution. The time variation of the drag coefficients is also presented and compared with the inviscid flow solution. The results show that the force coefficient predicted for the case of viscous flow approaches that of potential flow as the Reynolds number and frequency increase.

NdBa2Cu3O7 − δ single crystal growth by the traveling-solvent floating-zone method

We have succeeded in growing large size NdBa 2 Cu 3 O 7 − δ crystals (the cross-section was elliptical, the major and minor axes were about 4.5 and 3.5 mm, respectively, and the length about 30–60 mm that depended on the length of the feed rod) by improving the traveling-solvent floating-zone method. A typical one of these crystals has been proved to be of single crystal from X-ray Laue diffraction measurements. These crystals show superconducting properties throughout the crystal length, whose transition temperature T C (onset) is 94 K and transition width ΔT C is about 5 K. The success of growing these single crystals was achieved by selecting the optimum solvent composition, increasing the density of the feed rod, interchanging the crystal growing direction, setting up the temperature gradient for the region of the solvent and finding the appropriate growing rate for the crystal growth in the TSFZ method. The compositions of grown crystals deviate slightly from the stoichiometric ratio, Nd : Ba : Cu = 1 : 2 : 3. It seems that there are regions in the crystals in which Nd atoms substitute for the Ba-site. Therefore, these crystals have broad ΔT C compared to stoichiometric crystals.

Arithmeticity, discreteness and volume

We give an arithmetic criterion which is sufficient to imply the discreteness of various two-generator subgroups of $PSL(2,{\bold C})$. We then examine certain two-generator groups which arise as extremals in various geometric problems in the theory of Kleinian groups, in particular those encountered in efforts to determine the smallest co-volume, the Margulis constant and the minimal distance between elliptic axes. We establish the discreteness and arithmeticity of a number of these extremal groups, the associated minimal volume arithmetic group in the commensurability class and we study whether or not the axis of a generator is simple.

Semi-Serial Electron-Micrographic Reconstruction of Putative Transducer Sites in Pacinian Corpuscles

The Pacinian corpuscle (PC) is composed of an afferent neurite surrounded by an accessory capsule formed by concentric layers of lamellae. Projecting from the neurite, which is elliptical in cross-section, are "filopodia" or axonal, spike-like extensions. These filopodia are the putative sites of transduction. It has been proposed that two populations of filopodia organized in morphofunctional opposition exist, and that this arrangement is responsible for the bidirectional sensitivity of PCs as seen in receptor potential recordings. In order to explore this possibility, PCs obtained from cat mesentery were processed for electron microscopy, and semiserial reconstructions were made. We evaluated the extensions' (n > 110) locations, inclusions, shapes, and sizes. The filopodia were found to project along the major elliptical axis of the neurite, their density being approximately 2.8 per micron. The filopodia were found to contain filaments, vesicles, and amorphous ground substance, and dense accumulations of mitochondria were found at their bases. Measurements of their size (i.e., length, width, and height) suggest that there are two different types of filopodia. No other obvious relations among filopodial type, location along the neurite, and landmarks for transduction were found. The presence of the two filopodial types may be the basis for the bidirectional sensitivity of the PC.

A new method to calculate k1 for semi-elliptical surface cracks in finite plates

Irwin's solution of the stress intensity factor K I for an embedded elliptical cracks was extended to solve for K I for semi-elliptical surface cracks in finite plates. A double series was set up to express the displacement of the crack surface, and the unknown coefficients of the series were determined by the crack surface displacements of two dimensional edge cracks and center cracks. The maximum displacement was determined with an energy method. The results reflected the influence of both the relative crack depth a t and the relative crack length c W . The cases in which elliptical axis ratio a c > 1 were also included.

Stellar populations as a function of radius in giant elliptical galaxies

Accurate surface photometry has been obtained inJ andK for 12 giant elliptical galaxies. Ellipses have been fitted, to obtain luminosity, ellipticity, and major axis position angle profiles. The results have been combined with visual profiles from CCD observations. We find that elliptical galaxies become bluer inV - K on the average by 0.3 (mag/sq″ xre) going outward from the nucleus. Radial colour gradients inV - K correlate strongly with those inU - V andB - V. By modelling, using theoretical isochrones, it is found that the observed colour gradients can be explained by a gradient in metallicity, if in addition the proportion of hot stars rises very rapidly with decreasing metallicity.

Correlation of process parameters with morphology and magnetic properties of Co-based amorphous, soft, thin films

The in-plane, dipolar anisotropy of a soft magnetic thin film with columnar growth features is thought to result from the alignment and eccentricity of the column cross sections. This anisotropy can be reduced either by randomizing the alignment of the elliptic axes or by reducing the eccentricity. To determine the origin of the reductions produced by processing variations, we image processed micrographs from transmission electron microscope (TEM) of sequentially sputtered, amorphous CoB alloy thin films, and correlated their in-plane magnetic anisotropies with the statistics of the nanoscale features in their morphologies. The results confirmed that the in-plane anisotropies were dominated by correlations in the alignment of the major axes of the anisotropic growth features. Reduced anisotropies were observed in obliquely deposited films grown under the influence of a substrate bias, even though the eccentricity in their growth features was significantly increased. The effect of the increased eccentricity was apparently overcompensated by a randomization in the orientation of the features of the relaxed film structures.