Oblate Spheroidal Shape Research Articles

Palinologia de espécies da tribo Eupatorieae (Compositae Giseke) ocorrentes na Restinga de Carapebus, Carapebus, Rio de Janeiro

Foram estudados os graos de polen de sete taxons pertencentes a tribo Eupatorieae, ocorrentes na Restinga de Carapebus, Carapebus, Estado do Rio de Janeiro. Sao eles: Barrosoa atlantica King & Robins., B. betonicaeformis (DC.) King & Robins., Mikania belemii King & Robins., M. cordifolia Willd., M. glomerata Spreng., M. micrantha H.B.K., M. trinervis Hook & Arn. e Trichogoniopsis podocarpa (DC.) King & Robins. A tribo apresentou em comum, graos de polen pequenos a medios, oblato-esferoidais a prolato-esferoidais, tricolporados, sexina espinhosa e cavada. Os taxons puderam ser separados quando foram consideradas a forma polinica, as dimensoes do espinho e a distância entre eles. Assim, foi possivel formar dois conjuntos de especies identificados pela forma polinica: o primeiro, com forma oblato-esferoidal, composto por Barrosoa atlantica, Mikania micrantha e M. trinervis e o segundo, com forma prolato-esferoidal, composto por Barrosoa betonicaeformis, Mikania belemii, M. cordifolia, M. glomerata e Trichogoniopsis podocarpa. Os resultados obtidos, em comparacao a literatura corrente, permitem concluir que a tribo Eupatorieae e, palinologicamente, homogenea, porem algumas especies podem ser separadas pelo grao de polen, exceto M. glomerata de T. podocarpa e M. belemii de M. cordifolia.

Quantitative Evaluation of Void Distributions within a Plasma‐Sprayed Ceramic

The size–shape distribution of voids, which includes cracks and pores, was determined using quantitative stereological analysis. The analysis was performed on a water‐stabilized plasma‐spray‐formed Al2O3–13 wt% TiO2. The individual voids were assumed to have an oblate spheroidal shape, which could simulate shapes ranging from spherical pores to cracks. The cracks were generally intralamellar or translamellar, and the pores were interlamellar. The information obtained from two‐dimensional plane sections was unfolded to three‐dimensional information using stereological analysis. The quantitative information of voids was acquired in terms of shape and size.

Stability of a charged drop having the form of a triaxial ellipsoid

The stability of a highly charged, isolated conductive drop is analyzed within the principle of minimum potential energy of a closed system. A treatment of the stability of drops of ellipsoidal shape shows that both spherical drops and drops having an oblate spheroidal shape experience instability at sufficiently large charges according to a single scheme, i.e., they deform to a prolate spheroid.

Collapse and Fragmentation Models of Prolate Molecular Cloud Cores. II. Initial Differential Rotation

The prevalence of companions to pre-main-sequence stars and the emerging observational evidence for binary and multiple protostellar condensations suggest that fragmentation during protostellar collapse is a mechanism that may occur frequently in the star formation process. Here a second-order accurate hydrodynamic code has been used to investigate the gravitational (postmagnetic) collapse and fragmentation of low-mass (~1 M☉), small (~0.05 pc) molecular cloud cores, starting from moderately centrally condensed (Gaussian), prolate (2:1 and 4:1 axial ratios) configurations with varying thermal energies (α) and degrees of differential rotation (ν = 1/3 and 2/3). To facilitate comparisons with previous collapse calculations of uniformly rotating prolate cloud cores (Sigalotti & Klapp), all the models were made to start with a ratio of rotational to gravitational energy of β ≈ 0.036. The results indicate that prolate clouds are highly susceptible to binary fragmentation and that with respect to uniformly rotating initial conditions, differential rotation plays no role in either determining or enhancing fragmentation in initially slowly rotating clouds. In contrast to the fragmentation criteria previously established by Boss and Myhill, the results also indicate that clouds with α = 0.56 and varied prolateness collapse in a similar fashion, producing intermediate central condensations of oblate spheroidal shape before fragmenting into either a binary (2:1 clouds) or multiple protostellar core (4:1 clouds). The models with α ≤ 0.45 all produced binary systems after having formed intermediate central condensations, which might be of prolate ellipsoidal (2:1 clouds) or narrow cylindrical (4:1 clouds) shape. The mass and separation of the binary fragments increase with decreasing α and with an increase of both the degree of differential rotation and the cloud elongation. The results imply that for initial low β, the degree of cloud prolateness has a greater effect on the outcome than does differential rotation.

Rainbow scattering by a cylinder with a nearly elliptical cross section

We both theoretically and experimentally examine the behavior of the first- and the second-order rainbows produced by a normally illuminated glass rod, which has a nearly elliptical cross section, as it is rotated about its major axis. We decompose the measured rainbow angle, taken as a function of the rod's rotation angle, into a Fourier series and find that the rod's refractive index, average ellipticity, and deviation from ellipticity are encoded primarily in the m = 0, 2, 3 Fourier coefficients, respectively. We determine these parameters for our glass rod and, where possible, compare them with independent measurements. We find that the average ellipticity of the rod agrees well with direct measurements, but that the rod's diameter inferred from the spacing of the supernumeraries of the first-order rainbow is significantly larger than that obtained by direct measurement. We also determine the conditions under which the deviation of falling water droplets from an oblate spheroidal shape permits the first few supernumeraries of the second-order rainbow to be observed in a rain shower.

Numerical solutions for shape evolution of a particle growing in axisymmetric flows of supersaturated solution

Numerical studies are performed to investigate the growth behaviors of a precipitate particle in the well-defined flows of supersaturated solution with consideration of the isotropic and the anisotropic interfacial free energies. For the well-defined flows, three types of axisymmetric flows are considered: uniform streaming flow, uniaxial straining flow, and biaxial straining flow. The numerical solutions are obtained on the numerically generated orthogonal curvilinear coordinate system, which is automatically adjusted to fit the boundary shape at any time. The initial value problem of particle growth is solved using a fully implicit first-order backward time differencing in order to ensure the numerical stability. The numerical solutions show that the convection effect results in higher local growth rate near the surface where the flow is incoming and lower local growth rate near the surface where the flow is outgoing. Due to the difference in local growth rate, an initially spherical particle evolves into a peach-like shape in the uniform streaming flow, an oblate spheroidal shape in the uniaxial straining flow, and a prolate barrel-like shape in the biaxial straining flow.

Osmotic de-swelling of polystyrene microgel particles

The effects of added free polymer on the swelling and stability of polystyrene microgel particles dispersed in ethylbenzene have been investigated. The microgel particles were characterized by photon correlation spectroscopy (PCS), transmission electron microscopy (TEM), and scanning electron microscopy (SEM) measurements. TEM measurements showed that particles deposited on grids from ethylbenzene (a good solvent for polystyrene) were invariably larger than the same particles deposited from water. SEM data revealed that removal of ethylbenzene favoured the collapse of the particles to a deformed oblate spheroid shape. The stability of the microgel particles in the presence of free (i.e. non-adsorbing) polystyrene was investigated by turbidity — wavelength measurements, and the stability thresholds established. Osmotic de-swelling of the swollen particles was observed in the presence of free polystyrene using PCS. The extent of de-swelling increased with an increase of the molecular weight and concentration of the free polystyrene. A thermo-dynamic model, based on Flory’s theory of network swelling, is presented which, in the presence of excluded free polystyrene, provides a qualitative description of the deswelling of the microgel particles. The results are also compared to the predictions of scaling theory.

Aspects of the mechanics of lobed liposomes.

Hotani has studied, by means of dark-field light microscopy, morphological transformations which unilamellar liposomes undergo when their interior volume decreases steadily with time as a consequence of osmosis. In a previous paper, we made a theoretical study of the initial buckling of an originally spherical vesicle into the observed oblate spheroidal shape; and we argued that some in-plane shear elastic stiffness is required-in addition to the well-known flexural stiffness of the lipid bilayer-in order to explain the observed phenomena. In the present paper, we consider a later stage in the chain of morphological transitions observed by Hotani, when a series of cudgel-shaped lobes have sprung out of a previously axisymmetric, biconcave-shaped vesicle. Specifically, we compare the observed shapes of such lobes with half of a series of "peanut"-shaped vesicles that are an equilibrium conformation of an initially spherical liposome under reduced internal volume. We find that the shapes do not match well. On the other hand, the observed lobe forms do match satisfactorily portions of "undulating tube" shapes which evolve from a hypothetical cylindrical vesicle, according to some simple calculations. In view of this agreement, we are led to propose that the formation of cudgel-shaped lobes requires some sliding of one lipid monolayer over another. This conflicts, of course, with the Love-Kirchhoff hypothesis which is normally invoked at the outset of analyses of lipid vesicles by means of classical thin-shell theory; but it is in accord with previous suggestions in the context of more obviously severe distortion of the lipid bilayer.

Comparison of experimental velocity measurements with theoretical results in a solid‐solid composite material

Two‐phase composite media were constructed of aluminum powder inclusions embedded randomly in a clear resin matrix. The shapes of the inclusions are elongate, with aspect ratios ranging from 0.1 to 1.0, averaging about 0.25. The effective velocities of ultrasonic elastic waves in the bulk media were measured for these composite materials, and the observed data were compared to the theoretical values calculated using five different numerical models. The observed velocities agree with the theoretical values calculated using a dynamic model under the assumption that the inclusions have an oblate spheroidal shape.

Thermal and osmotic deswelling of poly(NIPAM) microgel particles

The effects of temperature and added free polymer on the swelling of poly(NIPAM)(NIPAM =N-isopropylacrylamide) microgel particles cross-linked with N,N′-methylene bisacrylamide have been investigated. The microgel particles were characterized by photocorrelation spectroscopy (PCS), TEM and SEM measurements. Particle sizes determined by TEM were invariably larger than those measured at 50 °C by PCS. SEM data suggest that dried particles have an oblate spheroid shape. The rate at which poly(NIPAM) particles collapse and swell in response to cycling of the temperature between 28 and 60 °C was examined and some hysteresis was observed. Excluded free polymer [PEG, where PEG = poly(ethyleneglycol)] also caused deswelling of the poly(NIPAM) particles at 25 °C due to osmotic pressure effects. Osmotic deswelling occurred in the presence of monodisperse PEG when the molecular weight of the latter was 1470 g mol–1. Higher molecular weight PEG polymers caused a general decrease in the extent of deswelling (at a fixed concentration of PEG).

Light scattering by polydispersions of randomly oriented spheroids with sizes comparable to wavelengths of observation

We report the results of an extensive study of the scattering of light by size and size-shape distributions of randomly oriented prolate and oblate spheroids with the index of refraction 1.5 + 0.02i typical of some mineral terrestrial aerosols. The scattering calculations have been carried out with Waterman's T-matrix approach, as developed recently by Mishchenko [J. Opt. Soc. Am. A 8, 871 (1991); Appl. Opt. 32, 4562 (1993)]. Our main interest is in light scattering by polydisperse models of nonspherical particles because averaging over sizes provides more realistic modeling of natural ensembles of scattering particles and washes out the interference structure and ripple typical of monodisperse scattering patterns, thus enabling us to derive meaningful conclusions about the effects of particle nonsphericity on light scattering. Following Hansen and Travis [Space Sci. Rev. 16, 527 (1974)], we show that scattering properties of most physically plausible size distributions of randomly orientednonspherical part cles depend primarily on the effective equivalent-sphere radius and effective variance of the distribution, the actual shape of the distribution having a minor influence. To minimize the computational burden, we have adopted a computationally convenient power law distribution of particle equivalent-sphere radii n(r) α r(-3),r(1) ≤ r≤r(2). The effective variance of the size distribution is fixed at 0.1, and the effective size parameter continuously varies from 0 to 15. We present results of computer calculations for 24 prolate and oblate spheroidal shapes with aspect ratios from 1.1 to 2.2. The elements of the scattering matrix for the whole range of size parameters and scattering angles are displayed in the form of contour plots. Computational results are compared with analogous calculations for surface-equivalent spheres, and the effects of particle shape on light scattering are discussed in detail.

Lamellar structure in a thin polymer blend film

We have fully characterized the three-dimensional morphology of thin films of mixtures of polystyrene and polybutadiene cast from a toluene solution, using nuclear reaction analysis, neutron reflectometry and transmission electron microscopy. Polystyrene-rich phases wet both the air and substrate interfaces and are separated by a polybutadiene-rich phase; these layers are very well defined and the interfaces between them are sharp (down to <20 Å). Within the polybutadiene-rich central layer, lateral phase separation is also evident, with polystyrene-rich domains of oblate spheroidal shape. Under certain circumstances thin polystyrene-rich layers exist within the polybutadiene-rich phase. We discuss possible mechanisms for this unusual morphology in terms of surface effects on the mechanism of phase separation in the ternary polymer-solvent system from which the films are cast.

Effect of Initial Void Shape on the Occurrence of Cavitation Instabilities in Elastic-Plastic Solids

A void in an infinite elastic-plastic material grows without bound when a cavitation stress limit is reached. Such unstable void expansion, driven by the elastic energy stored in the surrounding material, has been studied for the relatively simple case of spherically symmetric conditions and also for a spherical void in an axisymmetric remote stress field. The analyses are here extended to consider the effect of a void with an initially prolate or oblate spheroidal shape. Numerical unit cell analyses are carried out for a power-hardening elastic-plastic material subject to various axisymmetric remote stress states. For the range of void shapes analyzed it is found that the critical cavitation stress state shows very little influence of the initial void shape.

Self-propulsion of general deformable shapes in a perfect fluid

We consider the hydrodynamical problem of a general three-dimensional smooth deformable body moving in a perfect fluid, which undergoes arbitrary continuous temporal variations in its shape. Special attention is payed to the phenomena of selfpropulsion (translation and rotation) of such a shape and reference is made to the dynamics of non-spherical deformable bubbles, cavities and drops. Some distinctive cases, in which the method can be applied to impulsively started highly-vibrating rigid surfaces, are also presented. The Lagally theorem for deformable surfaces, is applied to determine the induced velocity of self-propulsion. The general deformation is assumed to consist of a large scale volume-mode and superposed small scale shapemodes. The time-averaging procedure is introduced and the effect of persistent self-propulsion is shown to be generated as a result of nonlinear interactions between these modes, which must preserve certain skew-symmetric and phase-difference properties. It is proven that, as a result of perfect symmetry, a spherical shape is a degenerate and an inefficient self-propulsor. The results are demonstrated for prolate (oblate) spheroidal shapes and simplified expressions are obtained as limiting cases for spherical, rod-like (slender) and circular disc shapes.

The structure of hydrogenated fullerene (C60H36)

Electron and X-ray diffraction techniques have been used to study the structure of polycrystalline C[sub 60]H[sub 36] with 10-15% C[sub 70]H[sub 36]. X-ray diffraction has shown that the molecular packing is body-centered cubic. Electron diffraction data were converted to a reduced density function by Fourier transformation. Comparison of the reduced density functions for three molecular models shows that C[sub 60]H[sub 36] is best described by a structure having D[sub 3d] symmetry. These results are consistent with recent solid-state [sup 13]C nuclear magnetic resonance and infrared spectroscopy studies. The D[sub 3d] structure has an oblate spheroidal shape for which we show body-centered cubic packing to be more efficient than the face-centered cubic packing of C[sub 60]. 10 refs., 6 figs., 2 tab.

Magnetic resonance imaging for quantitation of right ventricular volume in patients with pulmonary hypertension.

Evaluation of right ventricular function in patients with right-sided heart failure is difficult because of the complex anatomy of the right ventricle; the distinct geometry of the dilating, failing right ventricle; its variance from the typical oblate spheroid shape used to model the left ventricle; associated cardiac lesions in patients with right ventricular failure (including tricuspid and pulmonary regurgitation); and the inherent risk of conventional contrast ventriculography. With magnetic resonance techniques, tomographic images of the heart may be obtained at multiple points in the cardiac cycle without the use of intravascular contrast agents. From the end-diastolic and end-systolic images, chamber volume may then be determined directly without any modeling assumptions as to the geometry of the ventricular chamber.

Scalar space-time waves in their spectral-domain first- and second-order Thiele approximations

For the simple case of the scalar wave motion generated by a point source in an unbounded homogeneous medium, it is investigated what the consequences of the first- and second-order Thiele approximations in the spectral domain are in the space-time domain. To this end, the corresponding spectral domain Green's function is transformed back to the space-time domain with the aid of the modified Cagniard method. The exact solution to the problem is a spherical wave with the same wave shape as the source signature and a single wave front. The first-order Thiele, or parabolic, approximation has a wave front in the shape of a double oblate spheroid, combined with a head-wave like precursor having a cylindrical wave front. The second-order Thiele approximation contains two wave fronts, one associated with a fast body wave and the other with a slow body wave, in combination with a head-wave-like precursor, the latter again having a cylindrical wave front. From the results, it can be concluded in which regions below or above the source the approximations have sufficient accuracy for application in inversion and “true amplitude” depth migration procedures in geophysical prospecting.

THERMOCAPILLARY MIGRATION OF SLIGHTLY DEFORMED DROPLETS

ABSTRACT A small viscous droplet which is suspended in an immiscible liquid in a zero-gravity environment can be made to migrate by subjecting the system to an external temperature gradient. This so-called thermocapillary migration occurs since the surface tension of the interface is a function of temperature. If inertial effects are negligible and the interface is clean, the shape of the migrating droplet remains spherical. However, when inertial effects are significant or when surfactants are present at the interface, the droplet assumes a prolate or oblate spheroidal shape. In this work we calculate the change in the net migration velocity of the droplet which results from such a deformation. This is done by solving the requisite viscous flow problem in the deformed geometry by perturbation, in conjunction with a generalization of the so-called Lorentz reciprocal theorem which simplifies the calculations. It is found that the migration velocity could increase, decrease or remain unchanged depending on ...

Structure and growth of bis(2-ethylhexyl) sulfosuccinate micelles in aqueous solutions

The structure and growth of micelles formed by anionic surfactant sodium bis(2-ethylhexyl) sulfosuccinate (AOT) in aqueous solutions have been studied by small angle neutron scattering (SANS). They used the contrast variation technique to determine the aggregation number, the effective charge, and two molecular parameters of the micelles in solutions of 0.8 g/dL surfactant concentration. They then used these two molecular parameters to analyze micellar solutions at other concentrations. Two micellar parameters, the mean aggregation number n and the effective charge z0, have been extracted from experimental data for solutions with surfactant concentrations ranging from 0.2 to 1.0 g/dL. The minimum micellar aggregation number is predicted to be 15 at the critical micellar concentration (cmc) and the structure is a compact spherical aggregate having well-defined hydrophobic and hydrophilic regions. The micelles grow moderately as the surfactant concentration increases, transforming from a spherical to an oblate spheroidal shape in a manner describable by the ladder model.

Mass Transport from Single Droplets in Imposed Electric Fields

Abstract The influence of electric charge phenomena on mass transfer in systems involving droplets in a continuous medium is of increasing importance. The enhanced transport behavior of droplets in imposed fields on mass transfer and the influence of naturally occurring charges on droplets, particularly in the atmosphere, are both subjects of current interest. The objective of this study is to elucidate the hydrodynamic and mass transfer effect of imposed fields on charged single droplets. Investigations of both static and pulsed electric fields are reported. The experimental approach is based on the suspension of single droplets in a precisely machined expanding channel. A stationary, saturated water droplet is fluidized by the upflow of 2-ethylhexanol. This arrangement allows precise photographic monitoring of droplet size and shape as well as the hydrodynamics of both phases in the region of the interface. Baseline continuous-phase mass transfer studies with internally circulating droplets corroborate earlier studies with the same system. The effect of the accumulation of unavoidable surfactant on droplet circulation and mass transport rate at long exposure times is reported. The imposition of a static electric field in the axial direction caused distortion of droplets into prolate spheroidal shape. An electric field pulsed at a tuned frequency is observed to cause oscillation of droplets between prolate-and oblate-spheroidal shapes. In addition to frequency and field amplitude, the interfacial properties of the fluid system as well as viscosities and densities of the two phases influence the oscillation. The effect of the pulsation of the field on mass transfer to the continuous phase is reported. These data are compared with results for both nonoscillating mass transfer and theoretical models.