Search results for "ellipsoid"
showing 10 items of 46 documents
Modelling Complex Volume Shape Using Ellipsoid: Application to Pore Space Representation
2017
Natural shapes have complex volume forms that are usually difficult to model using simple analytical equations. The complexity of the representation is due to the heterogeneity of the physical environment and the variety of phenomena involved. In this study we consider the representation of the porous media. Thanks to the technological advances in Computed Topography scanners, the acquisition of images of complex shapes becomes possible. However, and unfortunately, the image data is not directly usable for simulation purposes. In this paper, we investigate the modeling of such shapes using a piece wise approximation of image data by ellipsoids. We propose to use a split-merge strategy and a…
Extended two-body problem for rotating rigid bodies
2021
A new technique that utilizes surface integrals to find the force, torque and potential energy between two non-spherical, rigid bodies is presented. The method is relatively fast, and allows us to solve the full rigid two-body problem for pairs of spheroids and ellipsoids with 12 degrees of freedom. We demonstrate the method with two dimensionless test scenarios, one where tumbling motion develops, and one where the motion of the bodies resemble spinning tops. We also test the method on the asteroid binary (66391) 1999 KW4, where both components are modelled either as spheroids or ellipsoids. The two different shape models have negligible effects on the eccentricity and semi-major axis, but…
Development of a low-alcoholic fermented beverage employing cashew apple juice and non-conventional yeasts
2019
Cashew apples are by-products in the production of cashew nuts, which are mostly left to rot in the fields. Cashew apple juice (CAJ), a highly nutritious beverage, can be produced from them. It is rich in sugars and ascorbic acid, but its high polyphenol content makes it bitter and astringent, and therefore difficult to commercialize. The kingdom of fungi contains more than 2000 yeast species, of which only a few species have been studied in relation to their potential to produce aroma compounds. The aim of this research was to develop a new low-alcoholic fermented beverage to valorize cashew apples. For this purpose, a screening was carried out employing non-conventional yeast species and …
Two-dimensional echocardiographic evaluation of left ventricular ejection fraction by the ellipsoid single-plane algorithm: a reliable method for ass…
1995
The reliability of two-dimensional (2D) echocardiographic estimation of left ventricular ejection fraction (EF) is commonly recognized, but no satisfactory data are available about the accuracy of low or very low EF values determined by 2D echocardiography (ECHO-EF). The purpose of our study was to assess the reliability of low ECHO-EF values obtained using a simple time-economical algorithm such as the ellipsoid single-plane area-length method. Radionuclide angiography (RAD-EF) was taken as the standard of comparison. We studied 59 consecutive patients (31 women and 28 men) referred to our echocardiographic laboratory. Both 2D echocardiography and radionuclide angiography were blindly perf…
The planar two-body problem for spheroids and disks
2021
We outline a new method suggested by Conway (2016) for solving the two-body problem for solid bodies of spheroidal or ellipsoidal shape. The method is based on integrating the gravitational potential of one body over the surface of the other body. When the gravitational potential can be analytically expressed (as for spheroids or ellipsoids), the gravitational force and mutual gravitational potential can be formulated as a surface integral instead of a volume integral, and solved numerically. If the two bodies are infinitely thin disks, the surface integral has an analytical solution. The method is exact as the force and mutual potential appear in closed-form expressions, and does not invol…
Experimental modeling of viscous inclusions in a circular high-strain shear rig: Implications for the interpretation of shape fabrics and deformed en…
2002
[1] Deformation experiments with initially spherical and prolate viscous inclusions suspended in a viscous Newtonian matrix in a circular high strain annular shear rig provide insights on the shape development of inclusions in high strain shear zones during progressive deformation. Inclusions with a specific viscosity ratio with respect to the matrix material show distinct types of three-dimensional shape development. For instance, at a high viscosity ratio between matrix and inclusion a pulsating ellipsoid develops, which both continuously rotates and changes its shape from a sphere to an ellipsoid and back to a sphere. The experiments show that the shape of an inclusion that has a viscosi…
Dipolar Rings of Microscopic Ellipsoids: Magnetic Manipulation and Cell Entrapment
2016
We study the formation and dynamics of dipolar rings composed by microscopic ferromagnetic ellipsoids, which self-assemble in water by switching the direction of the applied field. We show how to manipulate these fragile structures and control their shape via application of external static and oscillating magnetic fields. We introduce a theoretical framework which describes the ring deformation under an applied field, allowing to understand the underlying physical mechanism. Our microscopic rings are finally used to capture, entrap and later release a biological cell via magnetic command, i.e. performing a simple operation which can be implemented in other microfluidic devices which make us…
Structuring of polymer blends in simple shear flow
1990
A simplified model for the formation of steady state structure of discrete domains in polymer blends is established for simple shear flow. It is assumed that the domain size distribution, which results from an equilibrium between breakup processes and coalescence processes, may be divided in small and stable spherical domains and large and unstable ellipsoidal domains. Based on simplified rate balances and an expression for domain deformation rate the volume fraction of large domains and the large and small semiaxes of the ellipsoids are expressed as functions of volume fraction and shear rate/shear stress. The ability of the model to simulate actual behaviour is tested against quantitative…
Characterization of ellipsoids through an overdetermined boundary value problem of Monge–Ampère type
2014
Abstract The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non-standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In the proof we use the maximum principle applied to a suitable auxiliary function in conjunction with an entropy estimate from affine curvature flow.
Scalable Ellipsoidal Classification for Bipartite Quantum States
2008
The Separability Problem is approached from the perspective of Ellipsoidal Classification. A Density Operator of dimension N can be represented as a vector in a real vector space of dimension $N^{2}- 1$, whose components are the projections of the matrix onto some selected basis. We suggest a method to test separability, based on successive optimization programs. First, we find the Minimum Volume Covering Ellipsoid that encloses a particular set of properly vectorized bipartite separable states, and then we compute the Euclidean distance of an arbitrary vectorized bipartite Density Operator to this ellipsoid. If the vectorized Density Operator falls inside the ellipsoid, it is regarded as s…