Constant Axial Ratio Research Articles

Analysis of elliptical structures with constant axial ratio by Body-of-Revolution Finite Element Method and Transformation Optics

AbstractThis paper describes a method to analyze open or closed elliptical structures with constant axial ratio by a Body-of-Revolution (BoR) Finite Element Method (FEM). The method is based on Transformation Optics, a coordinate transformation that maps the elliptical shape to a circular shape, for which BoR-FEM represents a greatly efficient tool for the analysis.

Experimental study of the flow across an elliptic cylinder at subcritical Reynolds number

In this work, an incompressible flow across an elliptic cylinder with an axial ratio of 0.5 was experimentally studied in a low-turbulence horizontal wind tunnel at two Reynolds numbers: $ 1.5\times 10^4$ and $ 3.0\times 10^4$ . Hot-wire anemometry measurements were carried out in the cylinder wake to obtain turbulence intensity, average stream-wise velocity, higher-order central moments of velocity signals (i.e. skewness and flatness), and dimensionless vortex shedding frequency for the two Reynolds numbers. The obtained results showed that, the turbulence intensity profiles in the wake become broader as one moves toward downstream and peak turbulence intensities occur at points of high velocity gradient along the velocity profile. With increasing the Reynolds number, lower turbulence intensity and velocity defect parameters were observed within the near-wake zone. It was further observed that, upon the increase in Reynolds number at constant axial ratio, the wake became narrower with its Strouhal number (associated with the Karman vortex) remaining constant. In addition, the drag coefficient decreased with increasing the Reynolds number. When it came to the drag coefficient, the results of the present research were in good agreement with other experimental works.

Mass, shape and thermal properties of Abell 1689 using a multiwavelength X-ray, lensing and Sunyaev–Zel'dovich analysis

Knowledge of mass and concentration of galaxy clusters is crucial to understand their formation and evolution. Unbiased estimates require the understanding of the shape and orientation of the halo as well as its equilibrium status. We propose a novel method to determine the intrinsic properties of galaxy clusters from a multi-wavelength data set spanning from X-ray spectroscopic and photometric data to gravitational lensing to the Sunyaev-Zel'dovich effect (SZe). The method relies on two quite non informative geometrical assumptions: the distributions of total matter or gas are approximately ellipsoidal and co-aligned; they have different, constant axial ratios but share the same degree of triaxiality. Weak and strong lensing probe the features of the total mass distribution in the plane of the sky. X-ray data measure size and orientation of the gas in the plane of the sky. Comparison with the SZ amplitude fixes the elongation of the gas along the line of sight. These constraints are deprojected thanks to Bayesian inference. The mass distribution is described as a Navarro-Frenk-White halo with arbitrary orientation, gas density and temperature are modelled with parametric profiles. We applied the method to Abell 1689. Independently of the priors, the cluster is massive, M_{200}=(1.3+-0.2)*10^{15}M_sun, and over-concentrated, c_{200}=8+-1, but still consistent with theoretical predictions. The total matter is triaxial (minor to major axis ratio ~0.5+-0.1 exploiting priors from N-body simulations) with the major axis nearly orientated along the line of sight. The gas is rounder (minor to major axis ratio ~0.6+-0.1) and deviates from hydrostatic equilibrium. The contribution of non-thermal pressure is ~20-50 per cent in inner regions, <~ 300 kpc, and ~25+-5 per cent at ~1.5 Mpc.

Orbital structure of self-consistent triaxial stellar systems

We used a multipolar code to create, through the dissipationless collapses of systems of 1,000,000 particles, three self-consistent triaxial stellar systems with axial ratios corresponding to those of E4, E5 and E6 galaxies. The E5 and E6 models have small, but significant, rotational velocities although their total angular momenta are zero, that is, they exhibit figure rotation; the rotational velocity decreases with decreasing flattening of the models and for the E4 model it is essentially zero. Except for minor changes, probably caused by unavoidable relaxation effects, the systems are highly stable. The potential of each system was subsequently approximated with interpolating formulae yielding smooth potentials, stationary for the non-rotating model and stationary in the rotating frame for the rotating ones. The Lyapunov exponents could then be computed for randomly selected samples of the bodies that make up the different systems, allowing the recognition of regular and partially and fully chaotic orbits. Finally, the regular orbits were Fourier analyzed and classified using their locations on the frequency map. As it could be expected, the percentages of chaotic orbits increase with the flattening of the system. As one goes from E6 through E4, the fraction of partially chaotic orbits relative to that of fully chaotic ones increases, with the former surpassing the latter in model E4; the likely cause of this behavior is that triaxiality diminishes from E6 through E4, the latter system being almost axially symmetric. We especulate that some of the partially chaotic orbits may obey a global integral akin to the long axis component of angular momentum. Our results show that is perfectly possible to have highly stable triaxial models with large fractions of chaotic orbits, but such systems cannot have constant axial ratios from center to border: a slightly flattened reservoir of highly chaotic orbits seems to be mandatory for those systems.

Conduction-limited crystallite melting

High-purity pivalic acid (PVA) dendrites were observed growing under convection-free conditions during the isothermal dendritic growth experiment (IDGE) flown on NASA's space shuttle Columbia on STS-87. The IDGE was part of the complement of primary scientific experiments designated as the United States Microgravity Payload Mission (USMP4) launched late in 1997. The IDGE video data show that PVA dendrites may be melted without exhibiting any detectable relative motion with respect to the surrounding quiescent melt phase. Thus, melting occurs by heat conduction alone. When a small fixed superheating is imposed on pre-existing dendritic fragments, they melt steadily toward extinction. Individual fragments steadily decrease in size according to a square-root of time dependence predicted using quasi-static conduction-limited theory. Agreement between analytic melting theory and microgravity experiments was found originally if the melting process occurs under the restriction of shape-preserving conditions, where needle-like crystal fragments may be approximated as ellipsoids with a constant axial ratio. Among the new results reported here is the influence of capillarity effects on melting in needle-like crystallites, observed as a dramatic change in their axial ratio, when the size scale of a crystallite decreases below a critical value. In microgravity melting experiments, the axial ratio of individual crystallites does not remain constant, because of interactions with neighboring fragments within the mushy zone. The kinetic data were then “sectorized” to divide the total melting process into a series of short intervals. Each melting sector for a crystallite could then be approximated by a constant average value of the axial ratio. Sectorization also allows accurate prediction of melting kinetics by applying quasi-static heat conduction theory, despite the suspected presence of capillarity and the occurrence of fragmentation. These additional processes that accompany the melting of slender crystallites currently lie outside conventional melting theory. The data presented show that melting kinetics of small crystallites remains dominated by heat conduction from the surrounding melt, which is modified by the appearance of additional heat fluxes. These additional heat fluxes flow within the crystallites. They arise from capillary effects induced by steep interfacial curvature gradients that accompany the small crystallite size scales prior to their extinction.

Hexacyanoferrate(III) Transport in Coated Montmorillonite Clay Films. Effects of Water-Soluble Polymers

Hexacyanoferrate(III) Fe(CN)63-, transport through coated montmorillonite clay films at a platinum electrode is studied with the cyclic voltammetric method. Experimental conditions are first established guaranteeing voltammetric detection based on a linear diffusion in the clay film. The square of the ratio (R2) of current intensities obtained at the clay modifed electrode (CME) and the bare Pt electrode measures the relative variation of the Fe(CN)63-, diffusion coefficient in the clay film. Thus, the effects of bathing electrolyte concentrations on R2 are investigated and related to the swelling properties of the montmorillonite clay characterized by X-ray diffraction and sedimentation volume results. According to an applied model for the electric conductivity of montmorillonite clay solution, a relationship between the formation factor F = 1/R2, the shape factor (α), and the clay film effective porosity (Φe) is established. The shape factor (α) includes orientation and axial ratio (the ratio (A/B) of the major axis (A) to the minor axis (B)) parameters which characterize the arrangement of montmorillonite particles in the clay film. The determination of Φe is based on relative variations of the sedimentation volumes. In a salt concentration range from 0.02 to 1 M NaCl, it can be thus proposed that an interparticle Fe(CN)63- transport in the clay film is limited by occluded montmorillonite particles with a constant axial ratio. The effects of water-soluble polymers on the shape factor (α), of montmorillonite particles are investigated. At polymer concentrations ≤5% (polymer to montmorillonite, w/w), nonionic poly(vinylpyrrolidone) (PVP) decreases Fe(CN)63- transport in CME while interactions with a low-molecular-weight poly(acrylic acid) (PAA) increases it. The polymer modifications of the clay film can be thus modeled. An aggregation with PVP favors a lateral formation of a band-type network with an increase of the particle axial ratio, i.e., lengthening of the interparticle transport pathway in the clay film. In the case of low-molecular-weight PAA, a specific adsorption at the edge of montmorillonite platelets induces an apparent decrease of the particle axial ratio. This can be related to an electrostatic stabilization of clay platelets stacked in a column model, which shortens the interparticle transport pathway in the clay film.

Inversion of stellar statistics equation for the Galactic bulge

A method based on Lucy's iterative algorithm is developed to invert the equation of stellar statistics for the Galactic bulge and is then applied to the K-band star counts from the Two-Micron Galactic Survey in a number of off-plane regions (10°>|b|>2°, |l|<15°). The top end of the K-band luminosity function is derived and the morphology of the stellar density function is fitted to triaxial ellipsoids, assuming a non-variable luminosity function within the bulge. The results, which have already been outlined by López-Corredoira et al., are shown in this paper with a full explanation of the steps of the inversion: the luminosity function shows a sharp decrease brighter than MK=−8.0 mag when compared with the disc population; the bulge fits triaxial ellipsoids with the major axis in the Galactic plane at an angle with the line of sight to the Galactic centre of 12° in the first quadrant; the axial ratios are 1:0.54:0.33, and the distance of the Sun from the centre of the triaxial ellipsoid is 7860 pc. The major-minor axial ratio of the ellipsoids is found not to be constant, the best fit to the gradient being Kz=(8.4±1.7)×exp(−t/(2000±920) pc), where t is the distance along the major axis of the ellipsoid in parsecs. However, the interpretation of this is controversial. An eccentricity of the true density-ellipsoid gradient and a population gradient are two possible explanations. The best fit for the stellar density, for 1300 pc<t<3000 pc, is calculated for both cases, assuming an ellipsoidal distribution with constant axial ratios, and when Kz is allowed to vary. From these, the total number of bulge stars is ∼3×1010 or ∼4×1010, respectively.

Lattice spacing variations in some intra,-rare-earth alloy systems

The room temperature lattice spacing variations across the intra-rare-earth alloy systems, Ce-Ho, Pr-Ho and Nd-Sm have been determined. Certain common characteristics of these variations have been identified such as a constant axial ratio c a within the composition ranges of the double hexagonal alloys. Extrapolation of the spacings of the double hexagonal Nd-Sm alloys gave the spacings of a double hexagonal form of samarium; these show excellent agreement with the spacings of a recently reported double hexagonal form of this metal. The compositional variations of the a and c spacings of a number of cerium intra-rare-earth alloys have been correlated with the mean atomic number Z m of the alloy.

Elliptical markers and non-coaxial strain increments

A succession of geologically observed, non-coaxial strain increments is applied homogeneously to two models: 1. (1) a suite of randomly oriented ellipses with constant axial ratio, 2. (2) a suite of ellipses with variable axial ratio and semi-planar long axis orientation. In the first model the final ellipses lie on an Rf/ φ curve that gives an estimate of the finite strain state that is correct in both axial ratio and orientation. In the deformed state the second model results in a tectonically imbricated shape fabric and it is shown that an attempt to estimate the finite strain by the “unstraining Rf/ φ” technique gives an incorrect axial ratio.

Dimensional analysis of phases having the ThMn12, CaCu5 and MgZn2 structures: study of the influence of Kagomé nets of atoms

Abstract The cell dimensions of phases having the ThMn12, CaCu5 and MgZn2, MNx structures are analysed as a function of the CN-12 diameters of the component atoms M and N, which avoids the usual problems of effective coordination numbers and appropriate atomic sizes, since the equations obtained are independent there of, except for a constant term. In the ThMn12 structure the intersecting Kagomé nets of N atoms about (100) and (010) planes, control the cell dimensions and lead to the constant axial ratio, except for MMn12 phases where M is a rare-earth atom, or Th. The Kagomé net of N atoms in the (0001) plane controls the a dimension of phases with the CaCu5 structure except for phases of Co, Ni, Cu (and Fe) with the rare earths, but it does not control the a dimension of phases with the MgZn2 structure. Contacts between rare-earth metals and transition metals of the first long period, can not be compressed greatly, so arrays of atoms involving M–N contacts control the a and c dimensions of MMn12 phases and the a dimension of MCo5, MNi5 and MCu5 phases. Lines of trigonal bipyramids of N atoms along [001] control the c dimension of all phases with the CaCu5 structure.

The Th2Zn17 structure: accounting for the constant axial ratio of the hexagonal cell

The Th₂Zn₁₇ structure: accounting for the constant axial ratio of the hexagonal cell

Reduced electric dipole moments and polarizabilities of rigid colloids from electric birefringence data

Values of the electric dipole moments and polarizabilities of macromolecules and colloids vary with particle size. Determinations of “reduced” or size independent values of these parameters are often hampered owing to the finite polydispersity of practical systems. A method is proposed, whereby the electric birefringence data can be used simultaneously to yield the distribution of particle sizes (for monomodal, two parameter distributions) and reduced values of the permanent dipole moments and polarizabilities of the material. Theory is developed for rods and disks of constant thickness and ellipsoids of constant axial ratio. The theory embraces bulk and surface origins for each of the electrical parameters and for all three particle geometries. By way of an example, the theory is utilized for the interpretation of birefringence data of the rod-like clay mineral sepiolite.

Particle size distribution from transient electric birefringence data: III. polydisperse ellipsoids by two-parameter distribution functions

The decay of the electrically induced transient birefringence, for a dilute polydisperse suspension of ellipsoidally shaped particles of constant axial ratio, is analysed. It is shown that, for the decay process, the initial slopes of the natural logarithm of the normalised birefringence versus time curves for transients obtained under two discrete experimental conditions provide sufficient data to describe the spread in particle size in terms of two-parameter distribution functions. The procedure is described for three common skew distributions and two symmetric ones. A simple procedure for identifying the most appropriate distribution function is given.

Particle size distributions from transient electric birefringence data: II. polydisperse discs by two-parameter distribution functions

Abstract The decay of the electrically induced transient birefringence, for a dilute polydisperse suspension of ellipsoidally shaped particles of constant axial ratio, is analysed. It is shown that, for the decay process, the initial slopes of the natural logarithm of the normalised birefringence versus time curves for transients obtained under two discrete experimental conditions provide sufficient data to describe the spread in particle size in terms of two-parameter distribution functions. The procedure is described for three common skew distributions and two symmetric ones. A simple procedure for identifying the most appropriate distribution function is given.

A low temperature X-ray investigation of technetium and the TcMo A-15 compound

X-ray investigation between 4.2 and 298 K have shown (a) that technetium maintains its hcp structure down to 4.2 K with a nearly constant axial ratio, and (b) that no tetragonal distortion occurs in this temperature range in a Tc-40 at.% Mo alloy which is an A-15 Type II superconductor.