Search

Abstract. We introduce a novel scheme based on a blending of Fourier-Motzkin elimination (FME) and adjustable robust optimization techniques to compute the maximum volume inscribed ellipsoid (MVE) in a polytopic [...]

The analysis of microheterogeneous materials exhibiting eigenstressed and/or eigenstrained phases requires an estimation of eigenstrain influence tensors. Within the framework of continuum micromechanics, we here derive these tensors from extended Eshelby-Laws matrix-inclusion problems, considering, as a new feature, an auxiliary matrix eigenstress. The auxiliary matrix eigenstress is a function of all phase eigenstresses and, hence, accounts for eigenstress interaction. If all material phases are associated with one and the same Hill tensor, the proposed method degenerates to the well-accepted transformation field analysis. Hence, the proposed concept can be interpreted as an extension of the transformation field analysis toward consideration of arbitrarily many Hill tensors, i.e., as an extension toward heterogeneous elastic media comprising inclusion phases with an arbitrary ellipsoidal shape and with arbitrary spatial orientation. This is of particular interest when studying heterogeneous media consisting of constituents with nonspherical phase shapes, e.g., cement-based materials including concrete, or bone. As for polycrystals studied by means of the self-consistent scheme, the auxiliary matrix eigenstress turns out to be equal to the eigenstresses homogenized over the representative volume element (RVE), which is analogous to the self-consistent assumption that the auxiliary stiffness is the average stiffness of the RVE. The proposed method opens the door for micromechanics-based modeling of a great variety of composite phase behaviors characterized by eigenstresses or eigenstrains, e.g., thermoelasticity, poroelasticity, drying-shrinkage, as well as general forms of inelastic behavior, damage, fatigue, and fracture. DOI: 10.1061/(ASCE)EM.1943-7889.0000138 CE Database subject headings: Micromechanics; Inelasticity; Material properties; Transformation. Author keywords: Micromechanics; Homogenization; Transformation field analysis; Generalized Eshelby problem; Thermoelastic moduli; Eigenstrain influence tensor.

This paper presents methods to model complex vasculature in three-dimensional (3-D) images using cylindroidal superellipsoids, along with robust estimation and detection algorithms for automated image analysis. This model offers an explicit, low-order parameterization, enabling joint estimation of boundary, centerlines, and local pose. It provides a geometric framework for directed vessel traversal, and extraction of topological information like branch point locations and connectivity. M-estimators provide robust region-based statistics that are used to drive the superellipsoid toward a vessel boundary. A robust likelihood ratio test is used to differentiate between noise, artifacts, and other complex unmodeled structures, thereby verifying the model estimate. The proposed methodology behaves well across scale-space, shows a high degree of insensitivity to adjacent structures and implicitly handles branching. When evaluated on synthetic imagery mimicking specific structural complexities in tumor microvasculature, it consistently produces ubvoxel accuracy estimates of centerlines and widths in the presence of closely-adjacent vessels, branch points, and noise. An edit-based validation demonstrated a precision level of 96.6% at a recall level of 95.4%. Overall, it is robust enough for large-scale application. Index Terms--Robust detection/estimation, superellipsoid, vessel detection/segmentation.

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.icarus.2006.03.006 Byline: Ishan Sharma, James T. Jenkins, Joseph A. Burns Keywords: Asteroids; rotation; Asteroids; dynamics; Geophysics; Interiors; Planetary dynamics; Rotational dynamics Abstract: We investigate planetary fly-bys of asteroids using an approximate volume-averaged method that offers a relatively simple, but very flexible, approach to study the rotational dynamics of ellipsoids. The asteroid is considered to be a deformable, prolate ellipsoid, with its interior being modeled as a rigid-granular material. Effects due to the asteroid's rotation, its self-gravity and gravitational interaction with the planet are included. Using a simplified approach allows us to explore in detail the mechanics of asteroid's deformations and disruptions during planetary encounters. We also compare our results with those obtained by Richardson et al. [Richardson, D.C., Bottke Jr., W.F., Love, S.G., 1998. Icarus 134, 47-76] who used a large numerical code. We find that many of the features reported by them can indeed be captured by our rather simple methodology, and we discuss the reasons why some of our results differ from theirs. Author Affiliation: Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA Article History: Received 10 June 2005; Revised 5 March 2006

Gas phase protein complex dissociation was modelled using ellipsoids on which discrete charges were placed in randomly chosen charge sites. A number of sizes, shapes, orientations, and types of ellipsoids were considered. For each case, charge transfer parameters and electrostatic energies were calculated as a function of the fractional surface area. It was found that to within 10-15%, the charge on product ions after dissociation is distributed according to their fractional surface area. This can imply, for example, that in experiments measuring the dissociation of homodimers, charge asymmetries of greater than 10-15% in the product ions signal that one of the ions has greatly increased its surface area, such as would occur with unfolding. This assumes that proton transfer occurs on a timescale fast enough that the dissociation products adopt the minimum electrostatic energy configuration. Calculation of this energy shows that it is minimized when one or more of the monomers is in an extended conformation. Key words: protein complex dissociation, ellipsoid charge model, charge asymmetry.

Research is presented concerning the use of analytical calculations to determine the creep rate associated with fiber reinforced composites in an effective medium approximation. Random and aligned ellipsoids are discussed.

In this paper, we discuss a fuzzy classifier with ellipsoidal regions that dynamically generates clusters. First, for the data belonging to a class we define a fuzzy rule with an ellipsoidal region. Namely, using the training data for each class, we calculate the center and the covariance matrix of the ellipsoidal region for the class. Then we tune the fuzzy rules, i.e., the slopes of the membership functions, successively until there is no improvement in the recognition rate of the training data. Then if the number of the data belonging to a class that are misclassified into another class exceeds a prescribed number, we define a new cluster to which those data belong and the associated fuzzy rule. Then we tune the newly defined fuzzy rules in the similar way as stated above, fixing the already obtained fuzzy rules. We iterate generation of clusters and tuning of the newly generated fuzzy rules until the number of the data belonging to a class that are misclassified into another class does not exceed the prescribed number. We evaluate our method using thyroid data, Japanese Hiragana data of vehicle license plates, and blood cell data. By dynamic cluster generation, the generalization ability of the classifier is improved and the recognition rate of the fuzzy classifier for the test data is the best among the neural network classifiers and other fuzzy classifiers if there are no discrete input variables. Index Terms - Blood cell data, cluster generation, fuzzy classifiers, license plate recognition, membership function, neural networks, rule extraction, thyroid data, tuning.

Ellipsoid algorithms for convexly constrained estimation and design problems were proposed. The proposed polynomial time algorithms can produce an estimate of the complete set of solutions and point estimates in the interior. Furthermore, the computationally accurate sequential algorithm can provide an estimation performance that is equal to the known polynomial time performance bound.

A fundamental equation representing invariance of ellipsoidal geodesics gives a navigational solution to the extreme latitude on great circle routes and reveals the error involved in modeling the earth as a sphere. The equation serves as a tool for formulating an algorithm that enables determination of vertex latitudes on ellipsoidal geodesics. The Sperry Marine's Voyage Management System-Vision Technology implements the algorithm using WGS-84 ellipsoid as the Earth model. Relevant concepts for spheres and great circles such as local north, unit tangent, and azimuth are presented.

A physical optics approximation based on Fresnel's laws is developed to calculate the intensity of light scattered by a three-axis ellipsoid of any orientation and any refractive index. Some results concerning totally reflecting spheres and dielectric spheroids are presented. An approach suitable for large scatterers is particularly good for small scattering angles. The angular intensities, [i.sub.1] and [i.sub.2], are then plotted versus [Theta] for large axially oriented ellipsoids of various thicknesses. Theoretical small-angle light-scattering patterns are also presented and discussed. The data from one of them correspond to red cells in a shear flow. Key words: Light scattering, physical optics approximation, ellipsoids, small-angle light-scattering patterns, red cells.

The estimation of dynamically evolving ellipsoids from noisy lower-dimensional projections is examined. In particular, this work describes a model-based approach using geometric reconstruction and recursive estimation techniques to obtain a dynamic estimate of left-ventricular ejection fraction from a gated set of planar myocardial perfusion images. The proposed approach differs from current ejection fraction estimation techniques both in the imaging modality used and in the subsequent processing which yields a dynamic ejection fraction estimate. For this work, the left ventricle is modeled as a dynamically evolving three-dimensional (3-D) ellipsoid. The left-ventricular outline observed in the myocardial perfusion images is then modeled as a dynamic, two-dimensional (2-D) ellipsoid, obtained as the projection of the former 3-D ellipsoid. This data is processed in two ways: first, as a 3-D dynamic ellipsoid reconstruction problem; second, each view is considered as a 2-D dynamic ellipse estimation problem and then the 3-D ejection fraction is obtained by combining the effective 2-D ejection fractions of each view. The approximating ellipsoids are reconstructed using a Rauch-Tung-Striebel smoothing filter, which produces an ejection fraction estimate that is more robust to noise since it is based on the entire data set; in contrast, traditional ejection fraction estimates are based only on two frames of data. Further, numerical studies of the sensitivity of this approach to unknown dynamics and projection geometry are presented, providing a rational basis for specifying system parameters. This investigation includes estimation of ejection fraction from both simulated and real data.

In this work we have obtained the fields for external points created by uniformly magnetized ellipsoids and spheroids. The problem is solved directly in rectangular coordinates, obtaining the potential created by a uniformly charged ellipsoid everywhere by a variational method, in contrast to the usual method due to Dirichlet. Using the preceding result, we calculate the potential created by a uniformly magnetized ellipsoid in any external and internal points, as a superposition of the potentials created by two uniformly charged ellipsoids, which have opposite charge densities and slightly shifted centers. Finally, we find the solutions for the potential and field in any point external to a uniformly magnetized spheroid in rectangular coordinates. The results are checked with the classical ones obtained in spheroidal coordinates, finding a complete agreement except in one case. A discussion of this discrepancy is given. Finally, we determine how the magnetic field behaves with distance from the ellipsoid boundaries, which is very useful for corrections of the stray field flux and search coil design and also for models of particulate recording media with uniaxial anisotropy.

Nondimensionalization of particle and satellite dynamics about a triaxial ellipsoid reveals that the dynamics depends on one parameter associated with mass, rotation rate and size of the ellipsoid and two parameters related to the shape of the ellipsoid. Application of Hill stability to the problem to determine the collision properties of satellites and particles reveals the presence of two types of rotating ellipsoids, one being stable and the other a highly unstable one.

The basic principles of optics and elementary mathematics are used to determine the focusing property of ellipsoids and ellipses. The determination of the focusing property involves its application to laser technology and solar energy collection. The determination of the focussing property reveals that the continuous reflection of the light ray inside an ellipse or ellipsoid flattens the path of the light ray.

Abstract: In the article, we propose a new algorithm for constructing a minimal-volume ellipsoid for a given finite collection of points in an m-dimensional Euclidean space. The algorithm is based on a construction of such ellipsoids for the most simple polyhedra. Article History: Registration Date: 23/10/2004

A study was conducted on the general rectangular prism's magnetometric demagnetizing factors. Results suggest that the square root section is the demagnetizing factor ideal for numerical calculations involving the prism. In comparing theoretical results of ellipsoid investigations, prism demagnetization should always be considered larger than ellipsoid demagnetization despite similarities in aspect ratio.

Inscribed rectangles and rectangular parallelepipeds in any general quadric with distinct semiaxes are those that have their sides parallel to the principal axes. A theorem for the general n-dimensional case not only uses linear algebra concepts including a real n by n symmetric matrix with distinct eigenvalues, but also follows it up with affine transformations. For n greater than or equal to 4, no slice of the ellipsoid by a hyperplane may be considered a sphere. A unique square may be inscribed in an ellipse wherein the circle through the vertices meets the ellipse.

We present a model calculation of the acceleration of gravity in an ellipsoidal mass with nonuniform density. Using parameters resembling that of the earth's dimensions and mass density, we are able to account for most of the observed variation of the acceleration of gravity at the pole and the equator which is not related to rotational effects. The nonuniformity of the density of mass, when considered with the ellipsoidal flattening of the earth, is one of the most important factors to be considered when explaining the difference of the acceleration of gravity at the pole and equator. A simple model of a flattened earth with a uniform mass density does not give a reasonable explanation for this variation of the gravitational acceleration.

A morphology-dependent resonance (MDR) laser emission of rhodamine-doped ellipsoidal microcavity of the poly(mthylmethacrylate) particles is reported. The elliptical particles showed different lasing properties, like the lasing threshold, intramode spectral separation, mode intensity and spectral position, when an excitation was pointed to the different locations on the particle.

The new technique to obtain the electroelastic field concentrations around ellipsoidal inhomogeneities in piezoelectric solid completely eliminates the necessity to solve complex fields outside the inhomogeneity. The electrostatic fields are determined as function of the inner electroelastic fields. This method finds applications in three-dimensional cavities and inhomogeneities, and also in the analysis of geometric and loading configurations.

The complexity of finding an O(n3/2)-rounding of a convex set C characterized by a separation oracle to O(n2 ln(nR)) oracle calls is reduced. To improve the rounding factor obtained by the volumetric barrier algorithm, or the shallow-cut ellipsoid algorithm, results of Kochol (1994) can be used. By testing O(n) points in the shallow cut oracle used by these algorithms, the rounding factor can be improved to cn (super 3/2).