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52 results for “Ellipsoids”
Equilibrium ellipsoids
<p>Equilibrium rubble pile ellipsoids. The models are obtained through numerical N-body simulations, using the GRAINS software. Simulations are performed using non-spherical particles, mutually interacting under contact/collisions and self-gravity. See Ferrari & Tanga 2020 (doi: 10.1016/j.icarus.2020.113871) for analysis and discussion of results. See Ferrari et al 2020 (doi: 10.1093/mnras/stz3458), Ferrari et al 2016 (doi: 10.1007/s11044-016-9547-2) for further details on the numerical model.</p>
15000 Ellipsoidal Binary Candidates in TESS: Associated Tables
<p>A catalogue of 15779 candidate ellipsoidal binary systems, identified from the first two years of TESS full-frame images.</p> <p>Table 2 contains the 'BEER' score applied to approximately 8,000,000 input TESS targets.</p> <p>Table 3 contains the details of the 15779 selected candidates.</p> <p>Full details of both tables, and the selection process, can be found in the associated paper.</p> <p>https://arxiv.org/abs/2211.06194</p>
Test set of geodesics on a triaxial ellipsoid
<p>This is a set of 500000 shortest geodesics on a triaxial ellipsoid. The ellipsoid is defined by</p> <p>$$\frac{X^2}{a^2} + \frac{Y^2}{b^2} + \frac{Z^2}{c^2} - 1 = 0,$$</p> <p>with \(a = \sqrt2\), \(b = 1\), \(c = 1/\sqrt2\) (measured in arbitrary units). (This ellipsoid was studied by A. Cayley, <em>On the geodesic lines on an ellipsoid</em>, Mem. Roy. Astron. Soc. <strong>39</strong>, 31-53, 1872.) Each line of the test set consists of 10 space-delimited numbers</p> <ul> <li>the latitude at point 1, \(\beta_1\) (\(^\circ\), exact)</li> <li>the longitude at point 1, \(\omega_1\) (\(^\circ\), exact)</li> <li>the azimuth at point 1, \(\alpha_1\) (\(^\circ\), accurate to \(10^{-18}{}^\circ\))</li> <li>the latitude at point 2, \(\beta_2\) (\(^\circ\), exact)</li> <li>the longitude at point 2, \(\omega_2\) (\(^\circ\), exact)</li> <li>the azimuth at point 2, \(\alpha_2\) (\(^\circ\), accurate to \(10^{-18}{}^\circ\))</li> <li>the geodesic distance from 1 to 2, \(s_{12}\) (units, accurate to \(10^{-20}\))</li> <li>the reduced length of the geodesic, \(m_{12}\) (units, accurate to \(10^{-20}\))</li> <li>the geodesic scale, \(M_{12}\) (accurate to \(10^{-20}\))</li> <li>the geodesic scale, \(M_{21}\) (accurate to \(10^{-20}\))</li> </ul> <p>Here \(\beta\), \(\omega\), and \(\alpha\), are the <em>ellipsoidal</em> latitude, longitude, and azimuth. For a given \((\beta, \omega)\), the Cartesian coordinates of a point are</p> <p>$$\begin{align}<br> X &= a \cos\omega<br> \frac{\sqrt{a^2 - b^2\sin^2\beta - c^2\cos^2\beta}}<br> {\sqrt{a^2 - c^2}}, \\<br> Y &= b \cos\beta \sin\omega, \\<br> Z &= c \sin\beta<br> \frac{\sqrt{a^2\sin^2\omega + b^2\cos^2\omega - c^2}}<br> {\sqrt{a^2 - c^2}}.<br>\end{align}$$</p> <p>Lines of constant \(\beta\) and \(\omega\) are orthogonal. The azimuth \(\alpha\) of a geodesic is the direction measured clockwise from North (defined as \(\beta\) increasing at constant \(\omega\)). The coordinates are singular at the four <em>umbilical</em> points \(\cos\beta = \sin\omega = 0\). The azimuth of a geodesic jumps by \(\pm\frac12\pi\) on passage through such points and the value for such points is the azimuth on <em>leaving</em> the umbilical point.</p> <p>The geodesics are computed using high-precision inverse calculations with the exact <em>integer</em> values for \((\beta_1, \omega_1)\) and \((\beta_2, \omega_1)\). Any of the other entries reported as an integer is also exact.</p> <p>For most pairs of points, there is a unique shortest geodesic. However</p> <ul> <li>for opposite umbilical points, \(\alpha_1\) and \(\alpha_2\) can take on arbitrary values provided that the ratio \(\tan\alpha_1/\tan\alpha_2\) is maintained;</li> <li>if \(\beta_1 + \beta_2 = 0\) and if \(\cos\alpha_1\) and \(\cos\alpha_2\) have opposite signs, then there is another shortest geodesic with azimuths \(\pi - \alpha_1\) and \(\pi - \alpha_2\).</li> </ul> <p>For a particular \((\beta_1, \omega_1)\) and \((\beta_2, \omega_2)\), additional geodesics of the same length can be trivially generated by swapping the points or by reflecting them in any of the coordinate planes. A non-trivial symmetry is given by swapping <em>just</em> the longitude coordinates; this also results in a geodesic of the same length. The data set has had any such redundant geodesics removed.</p> <p>The data set is sorted according to whether either point</p> <ul> <li>is an umbilical point</li> <li>lies on the middle principal ellipse, with \(\sin\omega = 0\)</li> <li>lies on the middle principal ellipse, with \(\cos\beta = 0\)</li> <li>lies on the major principal ellipse, \(Z = 0\)</li> <li>lies on the minor principal ellipse, \(X = 0\)</li> <li>is near an umbilical point</li> <li>is general (all other points)</li> </ul> <p>Approximately 85% of the entries are with two general points. If only a small set of random test cases is needed, select a random subset with, e.g.,</p> <p> <code>shuf Geod3Test.txt | head -1000 > Geod3Test-samp.txt</code></p> <p> </p>
Reference data for the Perram and Wertheim (1985) contact function of ellipsoids
<p>Reference data for the Perram and Wertheim (1985) contact function of ellipsoids</p> <p>This dataset provides reference values of the contact function of two ellipsoids, as defined by Perram and Wertheim (Perram, J. W., & Wertheim, M. S. (1985). Statistical mechanics of hard ellipsoids. I. Overlap algorithm and the contact function. Journal of Computational Physics, 58(3), 409–416. <a href="https://doi.org/10.1016/0021-9991(85)90171-8">DOI:10.1016/0021-9991(85)90171-8</a>). This paper will be referred to as PW85 in what follows.</p> <p>Reference values of the <code>F</code> function</p> <p>The data is shared as a HDF5 file <code>pw85_ref_data-YYYYMMDD.h5</code>, which contains the following datasets (to be described below)</p> <ul> <li><code>directions</code>: a 12×3 array,</li> <li><code>F</code>: a 108×108×12×9 array,</li> <li><code>lambdas</code>: a length-9 array,</li> <li><code>radii</code>: a length-3 array,</li> <li><code>spheroids</code>: a 108×6 array.</li> </ul> <p>The attached Python script <code>pw85_gen_ref_data.py</code> was used to generate the data; it uses the <a href="http://mpmath.org/">mpmath</a> library.</p> <p>Mathematical definition of the contact function</p> <p>The contact function is defined in PW85 as the maximum over <code>(0, 1)</code> of the <code>F</code> function which is defined as follows [see Eq. (3.7) in PW85, with slightly different notations]</p> <pre><code>F(λ) = λ(1-λ)r₁₂ᵀ⋅Q⁻¹⋅r₁₂,</code></pre> <p>where <code>0 ≤ λ ≤ 1</code> is a scalar, <code>r₁₂</code> is the center-to-center vector. <code>Q</code> is the matrix defined as follows</p> <pre><code>Q = (1-λ)Q₁ + λQ₂,</code></pre> <p>where <code>Qᵢ</code> is the symmetric, positive definite matrix that defines ellipsoid <code>Ωᵢ</code> through</p> <pre><code>m ∈ Ωᵢ iff (m-cᵢ)ᵀ⋅Qᵢ⁻¹⋅(m-cᵢ) ≤ 1,</code></pre> <p>where <code>cᵢ</code> is the center of <code>Ωᵢ</code>. Then, the contact function <code>F₁₂</code> is defined as the maximum of <code>F</code> [see Eq. (3.8) in PW85]</p> <pre><code>F₁₂(r₁₂, Q₁, Q₂) = max{ F(λ), 0 ≤ λ ≤ 1 }.</code></pre> <p>Parametrization</p> <p>The reference data is restricted to spheroids (equatorial radius: <code>aᵢ</code>; polar radius: <code>cᵢ</code>; direction of axis of revolution: <code>nᵢ</code>)</p> <pre><code>Qᵢ = aᵢ²I + (cᵢ²-aᵢ²)nᵢᵀ⋅nᵢ,</code></pre> <p>(<code>I</code>: identity matrix). The radii take the following values</p> <pre><code>aᵢ, cᵢ ∈ {0.01999, 1.999, 9.999}.</code></pre> <p>These values of the radii are stored in the <code>radii</code> dataset of the HDF5 file. The orientations <code>nᵢ</code> coincide with the vertices of an icosahedron</p> <pre><code>nᵢ = [0, ±u, ±v]ᵀ or nᵢ = [±v, 0, ±u]ᵀ or nᵢ = [±u, ±v, 0]ᵀ,</code></pre> <p>where</p> <pre><code> 1 φ 1+√5 u = ───────, v = ─────── and φ = ────. √(1+φ²) √(1+φ²) 2</code></pre> <p>The orientations are stored in the <code>directions</code> dataset as a 12×3 array. The matrices <code>Qᵢ</code> are precomputed and stored in the <code>spheroids</code> dataset as a 108×6 array (note: 108 = 12 orientations × 3 equatorial radii × 3 polar radii). <code>spheroids[i, :]</code> stores the upper triangular part of the corresponding matrix in row-major order</p> <pre><code>⎡ spheroids[i, 0] spheroids[i, 1] spheroids[i, 2] ⎤ ⎢ spheroids[i, 3] spheroids[i, 4] ⎥. ⎣ sym. spheroids[i, 5] ⎦</code></pre> <p>The scalar <code>λ</code> takes tabulated values (see the <code>lambdas</code> dataset)</p> <pre><code>λ ∈ {0.1, 0.2, …, 0.9}.</code></pre> <p>Note that <code>λ = 0.0</code> and <code>λ = 1.0</code> are excluded, since <code>F</code> is uniformly 0 in that case.</p> <p>Reference values of the <code>F</code> function</p> <p>The reference values of the function <code>F</code> are stored in the <code>F</code> dataset, which is a 108×108×12×9, such that <code>F[i, j, h, k]</code> is the value of <code>F</code> for</p> <pre><code>Q₁ = spheroids[i], Q₂ = spheroids[j], r₁₂ = directions[h] and λ = lambdas[k].</code></pre> <p>Note that the <code>r₁₂</code> vector takes values in the <code>directions</code> dataset. In other words, only unit-length center-to-center vectors are considered here. Indeed, <code>F</code> trivially depends on the norm of <code>r₁₂</code>, which is therefore not considered here in order to reduce the size of the dataset.</p> <p>Reference values of the contact function</p> <p>Note: the following is <em>not</em> implemented yet, as reference values of the contact function were not deemed useful. Indeed, once <code>F</code> is validated, it is straightforward to check that the implementation of <code>F₁₂</code> to be tested indeed maximizes <code>F</code>.</p> <blockquote> <p>The reference values of the contact function <code>F₁₂</code> are stored in the <code>contact_function</code> dataset, which is a 108×108×12×3 array, such that <code>contact_function[i, j, h, k]</code> is the value of <code>F₁₂</code> for</p> <pre><code>Q₁ = spheroids[i], Q₂ = spheroids[j] and r₁₂ = radii[h] * directions[k].</code></pre> <p>Note that the <code>r₁₂</code> vector is not normed, here.</p> </blockquote>
Ellipsoidal Harmonic Forward Model derived from Earth2014 topographies up to d/o 7200: EHFM_Earth_7200
<p>The model named EHFM_Earth_7200 was derived by layer-based forward modeling technique in ellipsoidal harmonics, the maximum degree of this model reaches 7200. The relief information was provided by Earth2014 relief model. EHFM_Earth_7200 provides very detailed (~3 km) information for the Earth’s short-scale gravity field, and it is expected to be able to augment or refine existing global gravity models. To meet the existing standard, here we provide spherical harmonic coefficients, which are transformed from original ellipsoidal harmonic coefficients.</p>
Text-fig. 4. Scanning electron micrographs (a, c, e–k) and X-ray microtomographic orthoslices (b, d) of capsular fruits compose of five carpels from Zliv-Řídká Blana locality. a–d: Taxon 4, a – fruit elliptical in shape, no. NM-F 3188, b – young fruit with reminisce of free styles at top and showing central placentation of seeds, no. NM-F 3188, c – pentacarpellate capsules in apical view, no. NM-F 3188, d – fruit with five locules, no. NM-F 3235; e, f: Taxon 6, e – elongated fruit in lateral view, the persistent perianth at the base of the fruit (arrowhead), no. NM-F 3194, f – fruit in apical view, no. NM-F 3194; g, h: Taxon 5, g – elongated fruit in lateral view, no. NM-F 3193, h – fruit showing remains of a persistent calyx in the basal part (arrowhead), no. NM-F 3193; i–k: Taxon 7, i – pentacarpellate capsules of broadly elliptical shape, no. NM-F 4091, j – fruit, apical view, no. NM-F 4091, k – fruit with five seeds (arrowheads) ellipsoidal or triangular in outline and with a thick seed coat, no. NM-F 4091. in Plant Mesofossils From The Late Cretaceous Klikov Formation, The Czech Republic
Text-fig. 4. Scanning electron micrographs (a, c, e–k) and X-ray microtomographic orthoslices (b, d) of capsular fruits compose of five carpels from Zliv-Řídká Blana locality. a–d: Taxon 4, a – fruit elliptical in shape, no. NM-F 3188, b – young fruit with reminisce of free styles at top and showing central placentation of seeds, no. NM-F 3188, c – pentacarpellate capsules in apical view, no. NM-F 3188, d – fruit with five locules, no. NM-F 3235; e, f: Taxon 6, e – elongated fruit in lateral view, the persistent perianth at the base of the fruit (arrowhead), no. NM-F 3194, f – fruit in apical view, no. NM-F 3194; g, h: Taxon 5, g – elongated fruit in lateral view, no. NM-F 3193, h – fruit showing remains of a persistent calyx in the basal part (arrowhead), no. NM-F 3193; i–k: Taxon 7, i – pentacarpellate capsules of broadly elliptical shape, no. NM-F 4091, j – fruit, apical view, no. NM-F 4091, k – fruit with five seeds (arrowheads) ellipsoidal or triangular in outline and with a thick seed coat, no. NM-F 4091.
Routine to reproduce the figures from "Experimental study of the flows in a non-axisymmetric ellipsoid under precession"" JFM, 2022
<p>The Zip file contains the python notebook and all necessary datasets to reproduce the figures from the publication:</p> <ol> <li>Burmann, F. and <strong>Noir, J</strong>., 2022. Experimental study of the flows in a non-axisymmetric ellipsoid under precession. <em>Journal of Fluid</em> <em>Mechanics</em>, <em>932</em>,<a href="https://doi.org/10.1017/jfm.2021.932">https://doi.org/10.1017/jfm.2021.932</a></li> </ol> <p>The data are saved in .npz format, the structure of the data is explained in the header of the python jupyter notebook. </p>
Observation of liquid glass in suspensions of ellipsoidal colloid
<p>While all analyzed correlation functions are in the manuscript and supporting information, here, original particle trajectories from experiment and simulations are stored which are analyzed in the Publication</p> <p>"Observation of liquid glass in suspensions of ellipsoidal colloids"</p> <p>by J. Roller, A. Laganapan, J.-M. Meijer, M. Fuchs, and A. Zumbusch</p>
Prolate ellipsoid of revolution
* The ellipse is rotated about its longer axis; the resulting surface is known as a prolate spheroid or prolate ellipsoid of revolution. The model shows the behaviour of geodesic lines of a three-axial ellipsoid passing through its umbilical points. * Эллипс вращается вокруг своей длинной оси; полученная поверхность известна как вытянутый сфероид или вытянутый эллипсоид вращения. * (метка Р7)* Source: Objaverse 1.0 / Sketchfab
Prolate ellipsoid of revolution
* The ellipse is rotated about its longer axis; the resulting surface is known as a prolate spheroid or prolate ellipsoid of revolution. no label * Эллипс вращается вокруг своей длинной оси; полученная поверхность известна как вытянутый сфероид или вытянутый эллипсоид вращения. * *(метка Р94)* Source: Objaverse 1.0 / Sketchfab
Ellipsoid / эллипсоид
* This white plaster model shows a wave surface of a negative uniaxial crystal. It is an ellipsoid, cut away in one quadrant to reveal a portion of a sphere. * *(метка 19)* Source: Objaverse 1.0 / Sketchfab
Model for String Construction of Ellipsoids
* This white plaster model shows an ellipsoid and a hyperboloid. The visible part of the ellipsoid is the thickening around the hyperboloid. There are thin metal rods extending from the lower right and the underside of the upper left. The model was manufactured by the Darmstadt publishing company of Ludwig Brill. The model is listed in Brill's 1892 catalog as "Model of Staude's string construction of the ellipse from two confocal second order surfaces." * Гисовая модель изображает эллипсоид и гиперболоид. Видимая часть эллипсоида - утолщение вокруг гиперболоида. Из поверхности выступают два тонких металлических стержня с проушинами на концах, предназначенные для натягивания нити вокруг модели. Присутствует бирка (Modelle fur Fadenconstructionen des Ellipsoids. Verl. v. L. Brill. 10. Ser. 1. Nachtr. Nr. 2b.), которая позволяет предположить, что модель была изготовлена дармштадтским издательством Людвига Брилла под руководством немецкого математика Отто Штауде. * *(метка Р67)* Source: Objaverse 1.0 / Sketchfab
Semi-empirical error ellipsoid clustering for identifying the second-order structural features from a laboratory AE source location cloud—method, validation, and application to a hydraulic fracturing test [DATA]
<p>Data and metadata for the publication "Semi-empirical error ellipsoid clustering for identifying the second-order structural features from a laboratory AE source location cloud—method, validation, and application to a hydraulic fracturing test", published in Earth and Space Science.</p>
FR065, Late Archaic, Ellipsoidal Bar Weight
Ellipsoidal Bar Weight Late Archaic Glacial Kame Catalog #: P469 Uploaded by Carson Wright Suggested Data Citation: Thompson, Christine, Erin Powers, Carson Wright, and Kevin C. Nolan, 2021. FRHS_FR065, 3D Model .ply file. Digital Exhibit of Fort Recovery Historical Society's Precontact Collection, Fort Recovery Historical Society and Applied Anthropology Laboratories, Ball State University. Source: Objaverse 1.0 / Sketchfab
Ellipsoid / Эллипсоид
* It represents a rotational ellipsoid that can be unwound on the surface of a screw. A grid of lines is indicated. * *(метка Р109)* Source: Objaverse 1.0 / Sketchfab
2. Files with parameters of anisotropy of thermoremanent magnetization and file with modulus of TRM intensity recalculated into direction of remanent magnetization according to the shape of ATRM ellipsoid
<p>Files with parameters of anisotropy of thermoremanent magnetization and file with modulus of TRM intensity recalculated into direction of remanent magnetization according to the shape of ATRM ellipsoid</p> <p>Data supporting manuscript entitled “Archaeomagnetic studies of bricks from ancient buildings sampled in SE Poland (Central Europe)” by J. Nawrocki, K. Standzikowski, M. Chadima, T. Werner, M. Łanczont, J. Gancarski, Z. Gil submitted to Journal of Archaeological Science: Reports (JASREP-D-23-00078).</p>
Three-axial ellipsoid
* Models has the second version with the (orthogonal) net of curvature lines. Model also show locations of umbilical points - singular points of such nets.The surface that can be represented by the equation **x2/a2 + y2/ b2 + z2/c2 = 1**. Sections parallel to any of the axes are ellipses. * Гипсовая модель изображает эллипсоид, поверхность, которую можно представить уравнением x2/a2 + y2/b2 + z2/c2 = 1. Сечения, параллельные любой из осей, представляют собой эллипсы. На модели показана сетка перпендикулярных линий кривизны, а также показывает расположение особых точек таких сетей. * *(метка 39)* Source: Objaverse 1.0 / Sketchfab
Prolate ellipsoid of revolution
* This series of models was designed at the technical high school in Munich under the direction of Alexander Brill. The surface is known as a prolate spheroid or prolate ellipsoid of revolution. * Эллипс вращается вокруг своей длинной оси; полученная поверхность известна как вытянутый сфероид или вытянутый эллипсоид вращения. * *(метка Р92)* Source: Objaverse 1.0 / Sketchfab
Collective dynamics and pair-distribution function of active Brownian ellipsoids
<p>Supplemental data for the following manuscript: Stephan Bröker, Michael te Vrugt, Raphael Wittkowski,</p> <p>"Collective dynamics and pair-distribution function of active Brownian ellipsoids"</p>
FIGURES – 0. Shape and position of pseudocyphellae in several Ramalina species. 6. orbicular pseudocyphellae and laminal soralia (R. chiguarensis), scale = 1.3 mm. 7. Orbicular pseudocyphellae (R. cochlearis), scale = 0.4 mm. 8. Ellipsoid pseudocyphellae (R. santanensis), scale = 0.3 mm. 9. Linear pseudocyphellae (R. tenuissima), scale = 0.6 mm. 10. Flattened pseudocyphellae (R. maegdefraui), scale = 61.5 µm. in The genus Ramalina Acharius (Ascomycota, Lecanoromycetes, Ramalinaceae) in northern South America
FIGURES – 0. Shape and position of pseudocyphellae in several Ramalina species. 6. orbicular pseudocyphellae and laminal soralia (R. chiguarensis), scale = 1.3 mm. 7. Orbicular pseudocyphellae (R. cochlearis), scale = 0.4 mm. 8. Ellipsoid pseudocyphellae (R. santanensis), scale = 0.3 mm. 9. Linear pseudocyphellae (R. tenuissima), scale = 0.6 mm. 10. Flattened pseudocyphellae (R. maegdefraui), scale = 61.5 µm.
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Allen Brain Atlas
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Annotated Behaviour and Observability Dataset (ABODe)
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DANDI Archive for NWB datasets
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International Brain Laboratory public data
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OpenNeuro
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