Oblate Ellipsoids Research Articles

Submicroscopic voids in glassy carbon

Small angle X-ray scattering by glassy carbon was used to establish the characteristic of submicroscopic porosity. A monochromatized linear beam was used and corrections were made to obtain the scattering curve free of aberration. From analysis of the scattering curve, the voids were deduced to be oblate ellipsoids of revolution. Using the two-density theory, the geometrical parameters and concentration of the voids were determined. Fluctuations of atomic density in the carbon matrix were detected and their magnitude evaluated.

The geometric effects of volume change during deformation processes

Measurement of finite and of total strain in rocks deformed by natural tectonic processes indicates that specific types of strain fields are associated with certain zones of orogenic belts. Rocks which have slaty cleavage generally have oblate deformation ellipsoids (1 > K > 0) of an apparent flattening type of deformation. Deformation of this type can occur under conditions of plane strain where there is a reduction in volume during deformation. Deformation paths arising from tectonic deformation with progressive volume loss superposed on previously compacted material are computed, and these lead to predicted deformation fields which accord well with much of the data available on natural deformation fields.

Comparison of equivalent spherical volume and aerodynamic diameters for irregularly shaped particles.

Airborne particles are often classified according to their equivalent volume diameter using (he Coulter counter. Recently enacted regulatory health standards required that airborne particulate matter be classified according to their aerodynamic size. The relationship between these two different size parameters was determined for coal, limestone, and mica particles by comparing respective aerodynamic diameters (Stokes' diameter, ds) and equivalent spherical volume diameters (dv) measured with the Couliter counter. The dv/ds relationships derived were approximately equal to 1.0 for the coal and limestone and 1.3 for the mica particles. These results indicate that with the coal and limestone particles investigated, dv is a good measure of ds. The platelet mica particles, representing the case of extreme particle shape, were associated with disparity of 30% between dv and ds; however, this was in close agreement with an experimentally determined and theoretically verified shape factor for oblate ellipsoids.

The isolation and characterization of IgD from dysgammaglobulinemic serum

IgD has been isolated in homogeneous form from a dysgammaglobulinemic plasma. This preparation of IgD represents the first pure preparation isolated from a plasma having a titer of IgD approaching that of normal plasma rather than from a plasma having a high titer such as myeloma plasma. The isolation procedure was developed from the solubility properties of IgD in solutions of (NH 4) 2SO 4, Zn-acetate, Rivanol, etc. Final purification involved gel filtration on Sephadex G-200, batch adsorption on DEAE Sephadex A-50, chromatography on DE-52 microgranular cellulose, and immunoadsorption. The procedure permitted the isolation of IgD from large volumes of plasma and yielded enriched fractions of albumin, IgM and IgG. The physicochemical properties of IgD were determined. The electrophoretic mobility in veronal buffer, pH 8.6, Γ/2-0.1 was 2.52 × 10 −5 cm 2/V sec. The isoelectric point determined by electrophoresis in phosphate buffers, Γ/2-0.1 was 5.85. The sedimentation coefficient extrapolated to zero concentration in water was 6.92S. Molecular weight by osmotic pressure was 183,000, by sedimentation equilibrium was 178,800, and by a combination of sedimentation, viscosity, and partial specific volume data was from 128,500 to 175,700. The weight intrinsic viscosity was 0.094, and the partial specific volume was 0.717. Molecular dimensions were calculated by assuming prolate and oblate ellipsoids of revolution. The IgD was homogeneous by electrophoresis, sedimentation and by antigenicity.

A model for grain dispersion and magnetic anisotropy in sedimentary rocks

This paper is concerned with deriving the susceptibility ellipsoids for aggregates of small anisotropic magnetic grains dispersed thinly in a nonmagnetic matrix, given the individual grain susceptibilities. The statistical orientation of the magnetic grains is assumed to be represented by a Boltzmann distribution of their individual magnetic moments in thermal equilibrium with the earth‘s ambient magnetic field. This argument is similar to that used to describe a classical paramagnetic gas, in which it is assumed that magnetic grain interactions are negligible. Once the equilibrium distribution is reached, the aggregate is assumed to be cemented, and the anisotropy of the aggregate is calculated from the susceptibility parallel to and perpendicular to the preferred direction. Two types of grains are considered, grains with prolate and oblate susceptibility ellipsoids. The aggregate susceptibility is found to be prolate with both types of grains. The conclusion reached is that this should always be so unless factors other than thermodynamic equilibrium in the earth’s field affect individual magnetic grains during the accumulation and lithification of a sedimentary rock.

The relative motion of two spheroidal rigid bodies, II

We consider two spheroidal rigid bodies of comparable size constituting the components of an isolated binary system. We assume that (1) the bodies are homogeneous oblate ellipsoids of revolution, and (2) the meridional eccentricities of both components are small parameters.

Singularities of spheroidal metrics

An analysis is made of the singularities of Weyl gravitational fields in the spheroidal coordinates of oblate and prolate ellipsoids of revolution. Analysis of the Kretschmann scalars calculated shows them to be directional, so the singularities have a non-Schwarzschild topology. These singularities are accompanied by the appearance of “conjugate” regions, whose physical interpretation is that the active mass of the singularity changes its sign to that opposite the sign of the mass of a test particle which enters the conjugate region. These singular objects are designated as being of types PO and OP; they have images OP* and PO*, respectively, in the conjugate regions. The images of such objects, which attract matter into the conjugate region, act as explosive sources of matter and radiation in our region of space.

Growth of children with thalassaemia: effect of different transfusion regimens.

<h3>Abstract</h3> Oxygen plays a central role in cellular metabolism, in both healthy and tumour tissue. The presence and concentration of molecular oxygen in tumours has a substantial effect on both radiotherapy response and tumour evolution, and as a result the oxygen micro-environment is an area of intense research interest. Multicellular tumour spheroids closely mimic real avascular tumours, and in particular they exhibit physiologically relevant heterogeneous oxygen distribution. This property has made them a vital part of in vitro experimentation. For ideal spheroids, their heterogeneous oxygen distributions can be predicted from theory, allowing determination of cellular oxygen consumption rate (OCR) and anoxic extent. However, experimental tumour spheroids often depart markedly from perfect sphericity. There has been little consideration of this reality. To date, the question of how far an ellipsoid can diverge from perfect sphericity before spherical assumptions breakdown remains unanswered. In this work we derive equations governing oxygen distribution (and more generally, nutrient and drug distribution) in both prolate and oblate tumour ellipsoids, and quantify the theoretical limits of the assumption that the spheroid is a perfect sphere. Results of this analysis yield new methods for quantifying OCR in ellipsoidal spheroids, and how this can be applied to markedly increase experimental throughput and quality. <h3>Author summary</h3> Multicellular tumour spheroids (MCTS) are an increasingly important tool in cancer research, exhibiting non-homogeneous oxygen distributions and central necrosis. These are more similar to <i>in situ</i> avascular tumours than conventional 2D biology, rendering them exceptionally useful experimental models. Analysis of spheroids can yield vital information about cellular oxygen consumption rates, and the heterogeneous oxygen contribution. However, such analysis pivots on the assumption of perfect sphericity, when in reality spheroids often depart from such an ideal. In this work, we construct a theoretical oxygen diffusion model for ellipsoidal tumour spheroids in both prolate and oblate geometries. With these models established, we quantify the limits of the spherical assumption, and illustrate the effect of this assumption breaking down. Methods of circumventing this breakdown are also presented, and the analysis here suggests new methods for expanding experimental throughput to also include ellipsoidal data.

Effect of shape upon the settling vellocity of regular convex geometric particles

ABSTRACT H, a measure of the effect of shape upon the settling velocity of a regular rigid convex particle, is synthesized here from two geometric components, a form component and a surface area component, plus a third non-geometric parameter which is a function of Rs, the Reynolds number of the flow surrounding a sphere with the same volume and density as the particle and settling in the same fluid. Two expressions for the Reynolds number are found, one for the Stokes regime and beyond, through Rs = 4.0, and the other for flow conditions represented by 4.0<=Rs<2,900. These expressions are based upon the published data of several authors for smooth spheres, prolate and oblate ellipsoids, disks, rectangular parallelepipeds, ight circular cylinders, right circular cones base-to-base, and right rectangular pyramids base-to-base. The standard error of estimate for the low velocity regime is about 4 per cent (n = 100); for the high velocity regime it is about 5.5 per cent (n = 112).

The velocity of rise of distorted gas bubbles in a liquid of small viscosity

The terminal velocity of rise of small, distorted gas bubbles in a liquid of small viscosity is calculated. Small viscosity means that the dimensionless group gμ4/ρT3 where g is the acceleration of gravity, μ the viscosity, ρ the density and T the surface tension, is less than 10−8. It is assumed—and the numerical accuracy of the assumption is discussed—that the distorted bubbles are oblate ellipsoids of revolution. The drag coefficient is found by extending the theory given recently (Moore 1963) for the boundary layer on a spherical gas bubble. The results are in reasonable quantitative agreement with the experimental data.

Calculation of the Intensity of Small-Angle X-Ray Scattering at Relatively Large Scattering Angles

Since the small-angle x-ray scattering intensity can be expressed as a Fourier integral, the techniques of asymptotic expansion of Fourier integrals can be used to calculate the small-angle x-ray scattering at relatively large scattering angles. Some asymptotic expansion techniques which are often useful are described. The relation between the scattered intensity at relatively large angles and the characteristic function and its derivatives is discussed. The scattered intensity for both prolate and oblate ellipsoids of revolution is calculated to provide examples of asymptotic expansion methods, and the resulting expressions are evaluated numerically. The behavior of the scattered intensity at relatively large scattering angles for platelet particles of negligible thickness is described.

Microwave Absorption and Molecular Structure in Liquids. XXVI. The Dielectric Relazation Times of Two Large Oblate Ellipsoidal Molecules in Benzene Solution

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTMicrowave Absorption and Molecular Structure in Liquids. XXVI. The Dielectric Relazation Times of Two Large Oblate Ellipsoidal Molecules in Benzene SolutionDonald A. Pitt and Charles P. SmythCite this: J. Phys. Chem. 1959, 63, 4, 582–587Publication Date (Print):April 1, 1959Publication History Published online1 May 2002Published inissue 1 April 1959https://doi.org/10.1021/j150574a032RIGHTS & PERMISSIONSArticle Views39Altmetric-Citations19LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (756 KB) Get e-Alerts

THE SIZE, SHAPE AND HYDRATION OF LOBSTER HEMOCYANIN

1. The sedimentation coefficient of lobster hemocyanin corrected to water at 20° and extrapolated to zero concentration has been found to be 24.5 x 10-13 cgs units.2. The intrinsic viscosity has been found to be 4.85 ml./ml.3. From the variation of the sedimentation rate of hemocyanin in sucrose solutions of different densities and from the partial specific volume, the hydration of hemocyanin was calculated to be 0.15 ml. of water per gram of dry protein.4. The specific refractive increment was determined to be 0.00193 ml. per 10-2 g.5. From the above parameters and others taken from the literature, lobster hemocyanin molecules were calculated to have a molecular weight of 825,000, corresponding to oblate ellipsoids of revolution with hydrated diameter of 32.2 mµ and hydrated thickness of 7.8 mµ.6. Electron micrographs are consistent with the assumption that the molecules are plate-like ellipsoids of revolution 33 mµ in diameter and 7.5 mµ in thickness in the dried state.