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Topic: Prolate

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	Error analysis using ellipsoids. Three-dimensional mathematical analysis of particle shape using x-ray tomography and ...
		By this is meant ellipsoids with axes in the ratio of 1:1:5, and 5:5:1.
		Figure 10 shows the volume and surface area for a 5:1 prolate ellipsoid as a function of the number of spherical harmonic coefficients used (in terms of N), for an ellipsoid that now has axis dimensions, in terms of voxels, of 11:11:55.
		For an aspect ratio of 20, the oblate ratio is 1.085, and the prolate ratio is 1.371.
	ciks.cbt.nist.gov /~garbocz/paper134/node5.html (1565 words)

	[No title] (Site not responding. Last check: 2007-09-20)
		A method of ablating a cornea into a prolate shape in accordance with still another aspect of the present invention comprises determining a desired ablation pattern to form a prolate shaped ellipsoid on a surface of the cornea.
		An eccentricity of the prolate shaped ellipsoid is adjusted to intentionally leave approximately 10% astigmatism on an ablated surface of the cornea to cancel an astigmatic condition on a posterior side of the cornea and any contribution from lenticular astigmatism.
		Prolate ablation using ellipsoidal modeling with three (3) degrees of freedom in accordance with the principles of the present invention is best used with regular astigmatism.
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=01/24728.010412&ELEMENT_SET=DECL (5199 words)

	Glossary of Pollen and Spore Terminology - Part 4 (P-R) (Site not responding. Last check: 2007-09-20)
		prolate, prolate spheroidal, shape classes, spheroidal, suboblate, subprolate, subspheroidal.
		In this system prolate is defined as a ratio between the polar axis and the equatorial diameter of 1.33-2.00.
		Describing the shape of a pollen grain or spore in which the ratio between the polar axis and the equatorial diameter is 1.00-1.14.
	www.bio.uu.nl /~palaeo/glossary/glos-p4.htm (2071 words)

	LaserMyEye :: Encyclopedia :: Prolate
		Flatter in the middle - like your cornea after laser eye surgery (if you are near/shortsighted).
		In the last couple of years there has been increasing attention paid to the potential drawbacks to vision quality when the natural prolate shape of the eye is disturbed.
		Some of the newest developments have been to try to maintain the prolate shape while reshaping the cornea.
	www.lasermyeye.org /encyclopedia/prolate.html (104 words)

	Radiofrequency Radiation Dosimetry Handbook - Illustrations (Site not responding. Last check: 2007-09-20)
		Relative absorption cross section in prolate spheroidal models of an average man, a rabbit, and a medium-sized rat--as a function of frequency for E polarization
		Calculated average SAR in a prolate spheroidal model of an average man irradiated by the near fields of a short electric dipole, as a function of the dipole-to-body spacing, d
		Calculated average SAR in a prolate spheroidal model of an average man irradiated by the near fields of a small magnetic dipole, as a function of the dipole-to-body spacing, d
	www.brooks.af.mil /AFRL/HED/hedr/reports/handbook/illus.htm (3577 words)

	Fluent NEWS - Spring 2005 - The Prolate Spheroid Separates Turbulence Models
		Contours of the normalized invariant of the deformation tensor in a cross-flow plane toward the rear of the spheroid; the RSTM-2 model was used with an incidence angle of 20°
		Despite its simple geometry, the flow around a prolate spheroid at incidence offers a rich gallery of complex three-dimensional turbulent shear flows, featuring stagnation flow, a highly three-dimensional boundary layer under the influence of strong pressure gradients and streamline curvature, cross-flow separation, and the formation and evolution of free-vortex sheets and stream-wise vortices.
		For slender bodies like prolate spheroids, there is a nonlinear increase of lift with incidence angle, due to the low pressure near the cores of vortices that is impressed upon the nearby body surface.
	www.fluent.com /about/news/newsletters/05v14i1/a4.htm (1227 words)

	Fluctuations of Prolate Vesicles
		, vesicles exhibit pronounced pear-like fluctuations as the upper limit of meta-stability of the prolate phase is approached [2].
		Near this spinodal line, prolate vesicles with a sufficiently large volume-to-area ratio spontaneously expel a bud to assume a shape consisting of two spheres.
		A vesicle is seen to change its shape from a prolate with the mean symmetry axis within the focal plane to an oblate with the mean symmetry axis perpendicular to the focal plane and vice versa.
	www.mpikg-golm.mpg.de /th/work/Prolate (379 words)

	Clarkson U. \| CRCD \| ME 537 \| Viscous Flows
		The motion of a rigid prolate spheroid parallel to its axis of revolution as shown in Figure 4 is studied in this section.
		Schematic of a prolate spheroids in creeping flow motion.
		The stream function for a prolate spheroid translating with velocity U in the positive z-direction parallel to its axis of revolution is given as
	www.clarkson.edu /projects/crcd/me537/notes/viscous_flows/viscous_flows_page37.html (127 words)

	Study of a dissipative particle dynamics based approach for modeling suspensions
		Accompanying the nematic phase was an apparent reduction in the rate of increase of the relative viscosity.
		Note that at φ≈ 0.1 of rate of increase of relative viscosity with φ for the oblate spheroid decreases, indicative of the onset of an apparent nematic phase.
		A nematic phase for the prolate spheroids occurs at somewhat higher φ.
	ciks.cbt.nist.gov /~garbocz/dynamics_suspensions_files/node13.htm (597 words)

	Energy Citations Database (ECD) - Energy and Energy-Related Bibliographic Citations
		Prolate spheroidal wavefunctions as an alternative to Chebyshev and Legendre polynomials for spectral element and pseudospectral algorithms
		Prolate spheroidal functions of order zero are generalizations of Legendre polynomials which, when the 'bandwidth parameter' c>0, oscillate more uniformly on x is a member of [-1,1] than either Chebyshev or Legendre polynomials.
		The timestep can be lengthened by several times, but not by a factor that grows rapidly with N. The prolate basis is not likely to radically expand the range of problems that can be done on a workstation.
	www.osti.gov /energycitations/product.biblio.jsp?osti_id=20558397 (329 words)

	Radiofrequency Radiation Dosimetry Handbook - Chapter 6 (Site not responding. Last check: 2007-09-20)
		Calculated planewave average SAR in a prolate spheroidal model of a medium rat irradiated by a circularly polarized wave for two orientations; a = 0.1 m, b = 0.0276 m, V = 3.2 x 10
		Calculated planewave average SAR in a prolate spheroidal model of a sitting rhesus monkey irradiated by an elliptically polarized wave, for,two orientations; a = 0.2 m, b = 0.0646 m, V = 3.5 x 10
		Calculated planewave average SAR in a prolate spheroidal model of a medium rat irradiated by an elliptically polarized wave, for two orientations; a = 0.1 m, b = 0.0276 m, V = 3.2 x 10
	www.brooks.af.mil /AFRL/HED/hedr/reports/handbook/chp6-1-1.htm (1334 words)

	Spheroid - Wikipedia, the free encyclopedia
		If the ellipse is rotated about its major axis, the surface is called a prolate spheroid (similar to the shape of a rugby ball or cigar).
		A spheroid can also be characterised as an ellipsoid having two equal semi-axes, as represented by the equation
		A prolate spheroid has one semiaxis longer than the other two, (b > a); an oblate spheroid has one semiaxis shorter than the other two (b < a) and can resemble a disk.
	en.wikipedia.org /wiki/Spheroid (171 words)

	Morphology, swimming performance and propulsive mode of six co-occurring hydromedusae -- Colin and Costello 205 (3): ...
		Performance variables (maximum velocity and maximum acceleration) and velar aperture ratios of individual medusae are described as a function of both bell diameter and fineness.
		for the prolate hydromedusae (Aglantha digitale, Sarsia sp.
		and velar aperture ratios of the prolate medusae (Fig.
	jeb.biologists.org /cgi/content/full/205/3/427 (4208 words)

	Chapter Prohibiter <i>to</i> Proll of P by Webster's Dictionary (1913 Edition)
		Stretched out; extended; especially, elongated in the direction of a line joining the poles; as, a prolate spheroid; — opposed to oblate.
		The act of prolating or pronouncing; utterance; pronunciation.
		A mediæval method of determining of the proportionate duration of semibreves and minims.
	www.bibliomania.com /2/3/257/1207/23687/3.html (273 words)

	Analytical Description of Transmembrane Voltage Induced by Electric Fields on Spheroidal Cells -- Kotnik and Miklavcic ...
		of transmembrane voltage induced on prolate and oblate spheroidal
		With a nonconductive membrane surrounding a prolate spheroid, the induced transmembrane voltage is the opposite of the electric
		As with a prolate spheroid, two parameters are needed to characterize an oblate spheroid, and this can be accomplished either
	www.biophysj.org /cgi/content/full/79/2/670 (3465 words)

	The -deformation and -softness.
		parameters, deformed nuclei can be subdivided into prolate, oblate and triaxial deformed nuclei.
		Figure: The prolate and oblate axes for deformed nuclei and the unique region which contains all shapes uniquely.
		In this case, the nucleus is sensitive to the shape-polarizing effects of specific multi-quasiparticle configurations and the nuclear shape may drive from prolate to oblate or viceversa.
	www.pa.uky.edu /~jnorce/deformation/node5.html (121 words)

	Rhombic polyhedra
		From dissection of the cube to space filling with prolate rhombohedra and rhombic dodecahedra of the second kind
		There is a family of isohedral rhombic polyhedra that consists of prolate and obtuse rhombohedron, (rhombic) dodecahedron of the second kind, discovered by Bilinski in 1960, rhombic icosahedron, discovered by Fedorov in 1885 and triacontahedron, discovered by Kepler in 1611 [1, p.156].
		So the cube can be decomposed into 8 prolate rhombohedra, 12 quarters and 6 halfs of the dodecahedron (so 6 dodecahedra all together).
	members.tripod.com /vismath8/hafner4/SFVisual.html (374 words)

	ACM TOMS: Bibliographic record for `Boyd:2005:ACG' (Site not responding. Last check: 2007-09-20)
		In this article, we explain the practicalities of computing all the numbers needed to switch bases: the grid points $x_j$, the quadrature weights $w_j$, and the values of the prolate functions and their derivatives at the grid points.
		The prolate functions themselves are computed by a Legendre-Galerkin discretization of the prolate differential equation;this yields a symmetric tridiagonal matrix.
		The prolate functions are then de ned by Legendre series whose coefficients are the eigenfunctions of the matrix eigenproblem.
	math.nist.gov /toms/cgi-bin/TOMSbibget?Boyd:2005:ACG (181 words)

	The Prolate Solar Chromosphere
		In summary, 1) prolateness is evident in the K3CaII line with a value ~ 1.5"; 2) prolateness is not evident in the 1083 nm HeI line.
		Hence, it is considered likely that the prolateness is, to a small extent, a function of the solar cycle.
		It is speculated that differences in scale height largely account for the different prolateness values obtained for the lines measured.
	www.noao.edu /noao/noaonews/dec98/node5.html (528 words)

	Fusor and/or General Fusion Theory - Re: Prolate spheroid (Site not responding. Last check: 2007-09-20)
		So the prolate is actually an ellipsoid and remains so with two focii.
		So, it looks like there is no way to genrate a prolate sphere from a sphere.
		Bottom line appears that, like the ellipse, the prolate has two focii.
	fusor.net /board/view.php?site=fusor&bn=fusor_theory&key=1062080005 (228 words)

	Character of 'prolate' galaxies
		The prototype 'prolate' galaxy NGC2685 has a rapid observed stellar rotation rate around the projected minor axis.
		We show here that a steady figure, exactly prolate model can have no such rotation, and that a nearly prolate model fails by a factor of 7.
		We suggest that the galaxy is oblate and that the gas disk is the wreck of a dwarf companion.
	www.nature.com /cgi-taf/DynaPage.taf?file=/nature/journal/v298/n5876/abs/298728a0.html (133 words)

	Prolate in Zeiss MEL-80
		Zeiss MEL-80 lasers the eye so, that the shape of the eye will be prolate as illustrated in this brochure for example http://www.grane.cz/pdf/MEL80%20brochure.pdf.
		My understanding is, that spherical aberration correction is based on the curvature of the lens.
		How is it possible, that prolate (MEL-80) and oblate (others like Zyoptix etc.) will produce the same refractive correction?
	www.talkaboutsupport.com /group/alt.lasik-eyes/messages/42180.html (127 words)

	Flometrics - Computed Flow around Prolate Spheroid
		The flow around a prolate spheroid is similar to the flow around a submarine or aircraft fuselage.
		The paths were visualized using a custom algorithm which give the paths thickness and then shades them.
		The flow around the prolate spheroid models was simulated using a commercial finite element code, FIDAP.
	www.flometrics.com /services/CFD/comprslt.htm (195 words)

	In praise of the prolate spheroid \| csmonitor.com
		When it's jarred loose we are reminded that the football may be symmetrical, but it is far from spherical.
		The unusual shape, known as a prolate spheroid, means that this ball bounces with more maddening unpredictability than any other in sports.
		By the mid-1870s, a rugby ball had become the ball of choice, but it wasn't until 1911 that the rules specified use of a prolate spheroid.
	www.csmonitor.com /2003/1119/p18s03-hfes.html?entryBottomStory (1431 words)

	College Football Encyclopedia - Introduction
		Through the 1920s various restrictions continued to discourage some coaches from utilizing a passing attack, but by the 1930s the rules had changed sufficiently (including a slight size modification of the ball to make it easier to grip) to make the pass an important factor in most offensive schemes.
		A prolate spheroid had been required for the football's shape as early as 1896, but specific measurements did not go into effect until 1912.
		Further specifications in the 1929-1941 period not only led to narrower, more bullet-shaped balls, but allowed the use of white or other-colored balls for night games.
	www.footballencyclopedia.com /cfeintro.htm (2391 words)

	OVDs and Modified Prolate IOLs
		Healon (Advanced Medical Optics [AMO], Santa Ana, Calif.) was the first ophthalmic viscosurgical device (OVD) available to surgeons with Healon5 (AMO) the latest evolution in a new generation of OVDs known as the viscoadaptives.
		The Tecnis Z9000 IOL (AMO) is the first modified prolate anterior surface IOL to be approved in the United States by the Food and Drug Administration.
		Together, these products represent firsts in their technology and deserve close attention as ophthalmologists enter the next generation of cataract procedures.
	www.asiteforeyes.com /PhysicianResource/OVDsandModifiedProlateIOLs.htm (972 words)

	Search Results for prolate - Encyclopædia Britannica
		Typically, these nuclei have a prolate distortion, meaning that they have an elongated...
		Several models have been used to describe nuclei and their properties.
		The nucleus exhibits some properties that reflect the collective motion of all its constituent nucleons as a unit, as well as other properties that are dependent on the motion and state of the...
	www.britannica.com /search?query=prolate&submit=Find&source=MWTEXT (312 words)

	Numerical Prediction of Flow over a Prolate Spheroid Undergoing a Pitchup Maneuver
		Accurate numerical prediction of truly unsteady, high excursion, high-Reynolds number separated flows is of great interest in aeronautics and naval hydrodynamics.
		Prediction of the time-dependent flow around a 6:1 prolate spheroid undergoing a pitchup maneuver was obtained using Detached-Eddy Simulation (DES).
		DES is a hybrid formulation which attempts to capitalize on the often adequate performance of Reynolds-Averaged Navier-Stokes (RANS) models in predicting boundary layer growth and separation, and to use Large-Eddy Simulation (LES) away from solid surfaces to model the typically geometry-dependent and unsteady scales of motion in separated regions.
	home.gwu.edu /~rupesh/spheroid.html (436 words)

	(WO 01/24728) PROLATE SHAPED CORNEAL RESHAPING (Site not responding. Last check: 2007-09-20)
		A desired prolate shaped ablation profile is determined based on a desired prolate ellipsoidal shape.
		In accordance with the principles of the present invention, the spheroequivalent ellipsoid model has only three degrees of freedom (not four as in a conventional biconic technique) to define a desired ablation profile, providing extremely accurate and predictable long term vision correction.
		value replaces two degrees of freedom (i.e., eccentricities) in an otherwise conventional biconic modeling system, leaving only three (3) variables to determine for a best fit ellipsoid to a corneal surface, to make accurate prolate ellipsoidal modeling of a cornea possible, and to limit results to regular astigmatism that can be corrected with optical spherocylinders.
	wipo.int /cgi-pct/guest/getbykey5?KEY=01/24728.010412&ELEMENT_SET=DECL (274 words)

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