Symmetric generalized binomial distributions
Bergeron, H.; Curado, E. M. F.; Gazeau, J. P.; Rodrigues, Ligia M. C. S. E-mail: evaldo@cbpf.br E-mail: ligia@cbpf.br
2013-12-15
In two recent articles, we have examined a generalization of the binomial distribution associated with a sequence of positive numbers, involving asymmetric expressions of probabilities that break the symmetry win-loss. We present in this article another generalization (always associated with a sequence of positive numbers) that preserves the symmetry win-loss. This approach is also based on generating functions and presents constraints of non-negativeness, similar to those encountered in our previous articles.
Prior Distributions on Symmetric Groups
ERIC Educational Resources Information Center
Gupta, Jayanti; Damien, Paul
2005-01-01
Fully and partially ranked data arise in a variety of contexts. From a Bayesian perspective, attention has focused on distance-based models; in particular, the Mallows model and extensions thereof. In this paper, a class of prior distributions, the "Binary Tree," is developed on the symmetric group. The attractive features of the class are: it…
Novel species and expanded distribution of ellipsoidal multicellular magnetotactic prokaryotes.
Chen, Yi-ran; Zhang, Wen-yan; Zhou, Ke; Pan, Hong-miao; Du, Hai-jian; Xu, Cong; Xu, Jian-hong; Pradel, Nathalie; Santini, Claire-Lise; Li, Jin-hua; Huang, Hui; Pan, Yong-xin; Xiao, Tian; Wu, Long-fei
2016-04-01
Multicellular magnetotactic prokaryotes (MMPs) are a peculiar group of magnetotactic bacteria, each comprising approximately 10-100 cells of the same phylotype. Two morphotypes of MMP have been identified, including several species of globally distributed spherical mulberry-like MMPs (s-MMPs), and two species of ellipsoidal pineapple-like MMPs (e-MMPs) from China (Qingdao and Rongcheng cities). We recently collected e-MMPs from Mediterranean Sea sediments (Six-Fours-les-Plages) and Drummond Island, in the South China Sea. Phylogenetic analysis revealed that the MMPs from Six-Fours-les-Plages and the previously reported e-MMP Candidatus Magnetananas rongchenensis have 98.5% sequence identity and are the same species, while the MMPs from Drummond Island appear to be a novel species, having > 7.1% sequence divergence from the most closely related e-MMP, Candidatus Magnetananas tsingtaoensis. Identification of the novel species expands the distribution of e-MMPs to Tropical Zone. Comparison of nine physical and chemical parameters revealed that sand grain size and the content of inorganic nitrogen (nitrate, ammonium and nitrite) in the sediments from Rongcheng City and Six-Fours-les-Plages were similar, and lower than found for sediments from the other two sampling sites. The results of the study reveal broad diversity and wide distribution of e-MMPs. PMID:26711721
Modeling free molecular plume flow and impingement by an ellipsoidal distribution function
NASA Astrophysics Data System (ADS)
Legge, Hubert
Modeling frozen plume flow is outlined using a freezing surface and an ellipsoidal distribution function beyond a freezing surface. Formulas are given for the number flux, pressure, shear stress, and heat-transfer on a surface element in free molecular flow with an ellipsoidal distribution function. To demonstrate the accuracy of the modeling, the method is applied to the totally frozen Knudsen effusion, for which the flow quantities are given. For the given example, the accuracy is better than 2.5 percent.
NASA Technical Reports Server (NTRS)
Munk, Max M.
1979-01-01
The pressure distribution over ellipsoids when in translatory motion through a perfect fluid is calculated. A method to determine the magnitude of the velocity and of the pressure at each point of the surface of an ellipsoid of rotation is described.
The pressure distribution on the surface of an ellipsoid in inviscid flow
NASA Astrophysics Data System (ADS)
Band, E. G. U.; Payne, P. R.
1980-02-01
The classic equations for inviscid flow about an ellipsoid are employed to compute the corresponding static pressure distribution which can then be applied to a number of practical problems. The tension in the skin of a dirigible, the gross pressure distribution around a man in an open ejection seat, the aerodynamic lift on an air cushion vehicle, automobile or high speed boat, the 'squatting' of a ship, are all examples of practical applications. A remarkable result from the theory is that the lowest pressure, that around the equator normal to the flow, is always constant around the equator, no matter how much disparity there is between the semi-axes b and c.
NASA Technical Reports Server (NTRS)
Munk, Max M
1924-01-01
This note, prepared for the National Advisory Committee for Aeronautics, contains a discussion of the pressure distribution over ellipsoids when in translatory motion through a perfect fluid. An easy and convenient way to determine the magnitude of the velocity and of the pressure at each point of the surface of an ellipsoid of rotation is described. The knowledge of such pressure distribution is of great practical value for the airship designer. The pressure distribution over the nose of an airship hull is known to be in such good agreement with the theoretical distribution as to permit basing the computation of the nose stiffening structure on the theoretical distribution of pressure.
Cooperative Lamb shift in an ellipsoid
Friedberg, Richard; Manassah, Jamal T.
2010-06-15
It has been long known that the global cooperative Lamb shift (CLS) in a large superradiantly emitting sphere has equal magnitude but opposite sign to that of a slab. This result was obtained from QED in 1973 for samples of uniform density. This change of sign holds as well for a Gaussian density distribution. The same result is also obtained for either density in the scalar simplification of QED now in frequent use. Since the CLS must be a continuous function of shape, and the slab resembles a limiting case of oblate ellipsoid, there must be some shape of ellipsoid for which the CLS is zero. We report a calculation of CLS for a Gaussian distribution of general azimuthally symmetric ellipsoidal shape. The CLS is found to vanish when the mean square radius is twice as great transversely as longitudinally.
Yang, Jaw-Yen; Yan, Chih-Yuan; Diaz, Manuel; Huang, Juan-Chen; Li, Zhihui; Zhang, Hanxin
2014-01-01
The ideal quantum gas dynamics as manifested by the semiclassical ellipsoidal-statistical (ES) equilibrium distribution derived in Wu et al. (Wu et al. 2012 Proc. R. Soc. A 468, 1799–1823 (doi:10.1098/rspa.2011.0673)) is numerically studied for particles of three statistics. This anisotropic ES equilibrium distribution was derived using the maximum entropy principle and conserves the mass, momentum and energy, but differs from the standard Fermi–Dirac or Bose–Einstein distribution. The present numerical method combines the discrete velocity (or momentum) ordinate method in momentum space and the high-resolution shock-capturing method in physical space. A decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. Computations of two-dimensional Riemann problems are presented, and various contours of the quantities unique to this ES model are illustrated. The main flow features, such as shock waves, expansion waves and slip lines and their complex nonlinear interactions, are depicted and found to be consistent with existing calculations for a classical gas. PMID:24399919
Canonical distributions on Riemannian homogeneous k-symmetric spaces
NASA Astrophysics Data System (ADS)
Balashchenko, Vitaly V.
2015-01-01
It is known that distributions generated by almost product structures are applicable, in particular, to some problems in the theory of Monge-Ampère equations. In this paper, we characterize canonical distributions defined by canonical almost product structures on Riemannian homogeneous k-symmetric spaces in the sense of types AF (anti-foliation), F (foliation), TGF (totally geodesic foliation). Algebraic criteria for all these types on k-symmetric spaces of orders k = 4, 5, 6 were obtained. Note that canonical distributions on homogeneous k-symmetric spaces are closely related to special canonical almost complex structures and f-structures, which were recently applied by I. Khemar to studying elliptic integrable systems.
Error diffusion with a more symmetric error distribution
NASA Astrophysics Data System (ADS)
Fan, Zhigang
1994-05-01
In this paper a new error diffusion algorithm is presented that effectively eliminates the `worm' artifacts appearing in the standard methods. The new algorithm processes each scanline of the image in two passes, a forward pass followed by a backward one. This enables the error made at one pixel to be propagated to all the `future' pixels. A much more symmetric error distribution is achieved than that of the standard methods. The frequency response of the noise shaping filter associated with the new algorithm is mirror-symmetric in magnitude.
Implications of the Cosmological Constant for Spherically Symmetric Mass Distributions
NASA Astrophysics Data System (ADS)
Zubairi, Omair; Weber, Fridolin
2013-04-01
In recent years, scientists have made the discovery that the expansion rate of the Universe is increasing rather than decreasing. This acceleration leads to an additional term in Albert Einstein's field equations which describe general relativity and is known as the cosmological constant. This work explores the aftermath of a non-vanishing cosmological constant for relativistic spherically symmetric mass distributions, which are susceptible to change against Einstein's field equations. We introduce a stellar structure equation known as the Tolman-Oppenhiemer-Volkoff (TOV) equation modified for a cosmological constant, which is derived from Einstein's modified field equations. We solve this modified TOV equation for these spherically symmetric mass distributions and obtain stellar properties such as mass and radius and investigate changes that may occur depending on the value of the cosmological constant.
Nagel, Thomas; Kelly, Daniel J
2012-05-01
Continuous fibre distribution models can be applied to a variety of biological tissues with both charged and neutral extracellular matrices. In particular, ellipsoidal models have been used to describe the complex material behaviour of tissues such as articular cartilage and their engineered tissue equivalents. The choice of material parameters is more difficult than in classical anisotropic models and the impact that changes to these parameters can have on the predictions of such models are poorly understood. The objective of this study is to demonstrate the apparent behaviour of this class of materials over a range of material parameters. We further introduce a scaling approach to overcome certain counter-intuitive aspects related to the choice of anisotropy parameters and outline the integration method used in our implementations. User material codes for the commercial FE software packages Abaqus and MSC Marc are provided for use by other investigators. Cross-validation of our code against similar implementations in FEBio is also presented. PMID:22498290
Salzman, Gary C.; Mullaney, Paul F.
1976-01-01
The disclosure relates to a system incorporating an ellipsoidal flow chamber having light reflective walls for low level light detection in practicing cellular analysis. The system increases signal-to-noise ratio by a factor of ten over prior art systems. In operation, laser light passes through the primary focus of the ellipsoid. A controlled flow of cells simultaneously passes through this focus so that the laser light impinges on the cells and is modulated by the cells. The reflective walls of the ellipsoid reflect the cell-modulated light to the secondary focus of the ellipsoid. A tapered light guide at the secondary focus picks up a substantial portion of modulated reflective light and directs it onto a light detector to produce a signal. The signal is processed to obtain the intensity distribution of the modulated light and hence sought after characteristics of the cells. In addition, cells may be dyed so as to fluoresce in response to the laser light and their fluorescence may be processed as cell-modulated light above described. A light discriminating filter would be used to distinguish reflected modulated laser light from reflected fluorescent light.
Norris, Jodi R.; Jackson, Stephen T.; Betancourt, Julio L.
2006-01-01
Aim? Ponderosa pine (Pinus ponderosa Douglas ex Lawson & C. Lawson) is an economically and ecologically important conifer that has a wide geographic range in the western USA, but is mostly absent from the geographic centre of its distribution - the Great Basin and adjoining mountain ranges. Much of its modern range was achieved by migration of geographically distinct Sierra Nevada (P. ponderosa var. ponderosa) and Rocky Mountain (P. ponderosa var. scopulorum) varieties in the last 10,000 years. Previous research has confirmed genetic differences between the two varieties, and measurable genetic exchange occurs where their ranges now overlap in western Montana. A variety of approaches in bioclimatic modelling is required to explore the ecological differences between these varieties and their implications for historical biogeography and impending changes in western landscapes. Location? Western USA. Methods? We used a classification tree analysis and a minimum-volume ellipsoid as models to explain the broad patterns of distribution of ponderosa pine in modern environments using climatic and edaphic variables. Most biogeographical modelling assumes that the target group represents a single, ecologically uniform taxonomic population. Classification tree analysis does not require this assumption because it allows the creation of pathways that predict multiple positive and negative outcomes. Thus, classification tree analysis can be used to test the ecological uniformity of the species. In addition, a multidimensional ellipsoid was constructed to describe the niche of each variety of ponderosa pine, and distances from the niche were calculated and mapped on a 4-km grid for each ecological variable. Results? The resulting classification tree identified three dominant pathways predicting ponderosa pine presence. Two of these three pathways correspond roughly to the distribution of var. ponderosa, and the third pathway generally corresponds to the distribution of var
Hierarchical Molecular Modelling with Ellipsoids
Max, N
2004-03-29
Protein and DNA structures are represented at varying levels of details using ellipsoidal RGBA textured splats. The splat texture at each level is generated by rendering its children in a hierarchical model, from a distribution of viewing directions, and averaging the result. For rendering, the ellipsoids to be used are chosen adaptively, depending on the distance to the viewpoint. This technique is applied to visualize DNA coiling around nucleosomes in chromosomes.
Technology Transfer Automated Retrieval System (TEKTRAN)
The ability to simulate the surface energy balance and microclimate within a plant canopy is contingent upon accurate simulation of radiation exchange within the canopy. Accurate radiation simulations require some assumption of leaf angle distribution to compute transmissivity, reflection and scatte...
Finite key analysis for symmetric attacks in quantum key distribution
Meyer, Tim; Kampermann, Hermann; Kleinmann, Matthias; Bruss, Dagmar
2006-10-15
We introduce a constructive method to calculate the achievable secret key rate for a generic class of quantum key distribution protocols, when only a finite number n of signals is given. Our approach is applicable to all scenarios in which the quantum state shared by Alice and Bob is known. In particular, we consider the six state protocol with symmetric eavesdropping attacks, and show that for a small number of signals, i.e., below n{approx}10{sup 4}, the finite key rate differs significantly from the asymptotic value for n{yields}{infinity}. However, for larger n, a good approximation of the asymptotic value is found. We also study secret key rates for protocols using higher-dimensional quantum systems.
Circularly symmetric distributed feedback semiconductor laser: An analysis
Erdogan, T.; Hall, D.G.
1990-08-15
We analyze the near-threshold behavior of a circularly symmetric distributed feedback laser by developing a coupled-mode theory analysis for all azimuthal modes. We show that the equations that describes the low-order azimuthal modes are, to a very good approximation, the same as those for the one-dimensional (linear) distributed feedback laser. We examine the behavior of higher-order azimuthal modes by numerically solving the exact coupled-mode equations. We find that while a significant amount of mode discrimination exists among radial (longitudinal) modes, as in the one-dimensional distributed feedback laser, there is a much smaller degree of discrimination among azimuthal modes, indicating probability of multimode operation. Despite the multimode behavior, we find the frequency bandwidth associated with modes that do lase ought to be smaller than the spacing between Fabry-Perot modes of a typical semiconductor laser. This laser is an excellent candidate for a surface-emitting laser-it should have a superb quality output beam and is well-suited for array operation.
Circularly symmetric distributed feedback semiconductor laser: An analysis
Erdogan, T.; Hall, D.G. )
1990-08-15
We analyze the near-threshold behavior of a circularly symmetric distributed feedback laser by developing a coupled-mode theory analysis for all azimuthal modes. We show that the equations that describe the low-order azimuthal modes are, to a very good approximation, the same as those for the one-dimensional (linear) distributed feedback laser. We examine the behavior of higher-order azimuthal modes by numerically solving the exact coupled-mode equations. We find that while a significant amount of mode discrimination exists among radial (longitudinal) modes, as in the one-dimensional distributed feedback laser, there is a much smaller degree of discrimination among azimuthal modes, indicating probability of multimode operation. Despite the multimode behavior, we find that the frequency bandwidth associated with modes that do lase ought to be smaller than the spacing between Fabry-Perot modes of a typical semiconductor laser. This laser is an excellent candidate for a surface-emitting laser---it should have a superb quality output beam and is well-suited for array operation.
Low energy ion distribution measurements in Madison Symmetric Torus plasmas
Titus, J. B. Mezonlin, E. D.; Johnson, J. A.
2014-06-15
Charge-exchange neutrals contain information about the contents of a plasma and can be detected as they escape confinement. The Florida A and M University compact neutral particle analyzer (CNPA), used to measure the contents of neutral particle flux, has been reconfigured, calibrated, and installed on the Madison Symmetric Torus (MST) for high temperature deuterium plasmas. The energy range of the CNPA has been extended to cover 0.34–5.2 keV through an upgrade of the 25 detection channels. The CNPA has been used on all types of MST plasmas at a rate of 20 kHz throughout the entire discharge (∼70 ms). Plasma parameter scans show that the ion distribution is most dependent on the plasma current. Magnetic reconnection events throughout these scans produce stronger poloidal electric fields, stronger global magnetic modes, and larger changes in magnetic energy all of which heavily influence the non-Maxwellian part of the ion distribution (the fast ion tail)
Bisnovatyi-Kogan, Gennady S.
2009-09-20
We construct numerical models of spherically symmetric Newtonian stellar clusters with anisotropic distribution functions. These models generalize solutions obtained earlier for isotropic Maxwellian distribution functions with an energy cutoff and take into account distributions with different levels of anisotropy.
Tunable unidirectional scattering of ellipsoidal single nanoparticle
NASA Astrophysics Data System (ADS)
Reena, Kalra, Yogita; Kumar, Ajeet; Sinha, R. K.
2016-06-01
We report unidirectional scattering by tri-axial single ellipsoidal dielectric nanoparticle, which is applicable in the design and development of tunable, low-loss and ultra-compact nanoantennas. Based on the orientation and rotation of the ellipsoidal nanoparticle, three types of modes, one longitudinal mode and two transverse modes, have been excited. Electric and magnetic dipoles have been optically induced in the nanoparticle. Generalized Kerker's conditions have been applied at the interference of optically induced electric and magnetic dipoles. Azimuthally symmetric forward scattering with complete suppression of backward scattering using first Generalized Kerker's condition has been achieved at three different wavelengths for the allowed longitudinal mode and transverse modes in the optical region using single ellipsoidal nanoparticle. Due to 3-fold symmetry, forward scattering can be tuned at different wavelengths, using single ellipsoidal nanoparticle just by changing the direction of the incident electric field.
Wigner distribution and fractional Fourier transform for two-dimensional symmetric optical beams.
Alieva, T; Bastiaans, M J
2000-12-01
A useful relationship between the fractional Fourier transform power spectra of a two-dimensional symmetric optical beam, on the one hand, and its Wigner distribution, on the other, is established. This relationship allows a significant simplification of the standard procedure for the reconstruction of the Wigner distribution from the field intensity distributions in the fractional Fourier domains. The Wigner distribution of a symmetric optical beam is analyzed, both in the coherent and in the partially coherent case. PMID:11140492
Ellipsoid flowed around by a harmonic vector field
NASA Astrophysics Data System (ADS)
Savchenko, A. O.; Savchenko, O. Ya.
2012-03-01
We consider the screening of an external magnetic field in which a superconducting ellipsoid is inserted and a change in the velocity distribution in an ideal liquid flowing around an ellipsoid inserted in it. In both cases, the solution is given by a harmonic vector field parallel to the surface near the ellipsoid.
A GENERALIZED FAMILY OF POST-NEWTONIAN DEDEKIND ELLIPSOIDS
Gürlebeck, Norman; Petroff, David E-mail: david.petroff@zks.uni-leipzig.de
2013-11-01
We derive a family of post-Newtonian (PN) Dedekind ellipsoids to first order. They describe non-axially symmetric, homogeneous, and rotating figures of equilibrium. The sequence of the Newtonian Dedekind ellipsoids allows for an axially symmetric limit in which a uniformly rotating Maclaurin spheroid is recovered. However, the approach taken by Chandrasekhar and Elbert to find the PN Dedekind ellipsoids excludes such a limit. In a previous work, we considered an extension to their work that permits a limit of 1 PN Maclaurin ellipsoids. Here we further detail the sequence and demonstrate that a choice of parameters exists with which the singularity formerly found by Chandrasekhar and Elbert along the sequence of PN Dedekind ellipsoids is removed.
Charged line segments and ellipsoidal equipotentials
NASA Astrophysics Data System (ADS)
Curtright, T. L.; Aden, N. M.; Chen, X.; Haddad, M. J.; Karayev, S.; Khadka, D. B.; Li, J.
2016-05-01
This is a survey of the electrostatic potentials produced by charged straight-line segments, in various numbers of spatial dimensions, with comparisons between uniformly charged segments and those having non-uniform linear charge distributions that give rise to ellipsoidal equipotentials surrounding the segments. A uniform linear distribution of charge is compatible with ellipsoidal equipotentials only for three-dimensions. In higher dimensions, the linear charge density giving rise to ellipsoidal equipotentials is counter-intuitive—the charge distribution has a maximum at the centre of the segment and vanishes at the ends of the segment. Only in two-dimensions is the continuous charge distribution intuitive—for that one case of ellipsoidal equipotentials, the charge is peaked at the ends of the segment and minimised at the centre.
Reference Ellipsoid and Geoid in Chronometric Geodesy
NASA Astrophysics Data System (ADS)
Kopeikin, Sergei M.
2016-02-01
Chronometric geodesy applies general relativity to study the problem of the shape of celestial bodies including the earth, and their gravitational field. The present paper discusses the relativistic problem of construction of a background geometric manifold that is used for describing a reference ellipsoid, geoid, the normal gravity field of the earth and for calculating geoid's undulation (height). We choose the perfect fluid with an ellipsoidal mass distribution uniformly rotating around a fixed axis as a source of matter generating the geometry of the background manifold through the Einstein equations. We formulate the post-Newtonian hydrodynamic equations of the rotating fluid to find out the set of algebraic equations defining the equipotential surface of the gravity field. In order to solve these equations we explicitly perform all integrals characterizing the interior gravitational potentials in terms of elementary functions depending on the parameters defining the shape of the body and the mass distribution. We employ the coordinate freedom of the equations to choose these parameters to make the shape of the rotating fluid configuration to be an ellipsoid of rotation. We derive expressions of the post-Newtonian mass and angular momentum of the rotating fluid as functions of the rotational velocity and the parameters of the ellipsoid including its bare density, eccentricity and semi-major axes. We formulate the post-Newtonian Pizzetti and Clairaut theorems that are used in geodesy to connect the parameters of the reference ellipsoid to the polar and equatorial values of force of gravity. We expand the post-Newtonian geodetic equations characterizing the reference ellipsoid into the Taylor series with respect to the eccentricity of the ellipsoid, and discuss the small-eccentricity approximation. Finally, we introduce the concept of relativistic geoid and its undulation with respect to the reference ellipsoid, and discuss how to calculate it in chronometric
Distributed Hypothesis Testing With Social Learning and Symmetric Fusion
NASA Astrophysics Data System (ADS)
Rhim, Joong Bum; Goyal, Vivek K.
2014-12-01
We study the utility of social learning in a distributed detection model with agents sharing the same goal: a collective decision that optimizes an agreed upon criterion. We show that social learning is helpful in some cases but is provably futile (and thus essentially a distraction) in other cases. Specifically, we consider Bayesian binary hypothesis testing performed by a distributed detection and fusion system, where all decision-making agents have binary votes that carry equal weight. Decision-making agents in the team sequentially make local decisions based on their own private signals and all precedent local decisions. It is shown that the optimal decision rule is not affected by precedent local decisions when all agents observe conditionally independent and identically distributed private signals. Perfect Bayesian reasoning will cancel out all effects of social learning. When the agents observe private signals with different signal-to-noise ratios, social learning is again futile if the team decision is only approved by unanimity. Otherwise, social learning can strictly improve the team performance. Furthermore, the order in which agents make their decisions affects the team decision.
NASA Astrophysics Data System (ADS)
Yadav, R. B. S.; Prasad, U.
1993-05-01
The nonstatic conformally flat spherically symmetric perfect fluid distribution in Einstein-Cartan theory is considered, and the field equations and their general solution are obtained using Hehl's approach (1974). Particular attention is given to the solution in co-moving coordinates and the explicit expressions for pressure, density, expansion, rotation, and shear and nonzero components of flow vector.
Conformally flat static spherically symmetric perfect-fluid distribution in Einstein-Cartan theory
NASA Astrophysics Data System (ADS)
Kalyanshetti, S. B.; Waghmode, B. B.
1983-06-01
We consider the static, conformally flat spherically symmetric perfect-fluid distribution in Einstein-Cartan theory and obtain the field equations. These field equations are solved by adopting Hehl's approach with the assumption that the spins of the particles composing the fluid are all aligned in the radial direction only and the reality conditions are discussed.
Approximating conductive ellipsoid inductive responses using static quadrupole moments
Smith, J. Torquil
2008-10-01
Smith and Morrison (2006) developed an approximation for the inductive response of conducting magnetic (permeable) spheroids (e.g., steel spheroids) based on the inductive response of conducting magnetic spheres of related dimensions. Spheroids are axially symmetric objects with elliptical cross-sections along the axis of symmetry and circular cross sections perpendicular to the axis of symmetry. Spheroids are useful as an approximation to the shapes of unexploded ordnance (UXO) for approximating their responses. Ellipsoids are more general objects with three orthogonal principal axes, with elliptical cross sections along planes normal to the axes. Ellipsoids reduce to spheroids in the limiting case of ellipsoids with cross-sections that are in fact circles along planes normal to one axis. Parametrizing the inductive response of unknown objects in terms of the response of an ellipsoid is useful as it allows fitting responses of objects with no axis of symmetry, in addition to fitting the responses of axially symmetric objects. It is thus more appropriate for fitting the responses of metal scrap to be distinguished electromagnetically from unexploded ordnance. Here the method of Smith and Morrison (2006) is generalized to the case of conductive magnetic ellipsoids, and a simplified form used to parametrize the inductive response of isolated objects. The simplified form is developed for the case of non-uniform source fields, for the first eight terms in an ellipsoidal harmonic decomposition of the source fields, allowing limited corrections for source field geometry beyond the common assumption of uniform source fields.
NASA Astrophysics Data System (ADS)
Wang, Qiong; He, Zhi; Yao, Chun-Mei; Li, Wen-Juan
2016-08-01
We propose a physical realization of robust symmetric telecloning scheme for spin quantum states by employing the weak measurement and reversal (WMR) operation. Using proper WMR, the ultrahigh telecloning fidelity and long distance of quantum state transfer with certain success probability can be achieved. More interestingly, the lowest average telecloning fidelity can attain 80 %, which is almost independent of the spin chain length. We also study the properties of entanglement distribution via the spin chain for arbitrary two-qubit entangled pure states as inputs and find that the WMR operation indeed helps for protecting distributed entanglement.
Geometric Modeling of Inclusions as Ellipsoids
NASA Technical Reports Server (NTRS)
Bonacuse, Peter J.
2008-01-01
Nonmetallic inclusions in gas turbine disk alloys can have a significant detrimental impact on fatigue life. Because large inclusions that lead to anomalously low lives occur infrequently, probabilistic approaches can be utilized to avoid the excessively conservative assumption of lifing to a large inclusion in a high stress location. A prerequisite to modeling the impact of inclusions on the fatigue life distribution is a characterization of the inclusion occurrence rate and size distribution. To help facilitate this process, a geometric simulation of the inclusions was devised. To make the simulation problem tractable, the irregularly sized and shaped inclusions were modeled as arbitrarily oriented, three independent dimensioned, ellipsoids. Random orientation of the ellipsoid is accomplished through a series of three orthogonal rotations of axes. In this report, a set of mathematical models for the following parameters are described: the intercepted area of a randomly sectioned ellipsoid, the dimensions and orientation of the intercepted ellipse, the area of a randomly oriented sectioned ellipse, the depth and width of a randomly oriented sectioned ellipse, and the projected area of a randomly oriented ellipsoid. These parameters are necessary to determine an inclusion s potential to develop a propagating fatigue crack. Without these mathematical models, computationally expensive search algorithms would be required to compute these parameters.
Moments of the Wigner distribution of rotationally symmetric partially coherent light.
Bastiaans, Martin J; Alieva, Tatiana
2003-12-15
The Wigner distribution of rotationally symmetric partially coherent light is considered, and the constraints for its moments are derived. Although all odd-order moments vanish, these constraints lead to a drastic reduction in the number of parameters that we need to describe all even-order moments: whereas in general we have (N + 1)(N + 2)(N + 3)/6 different moments of order N, this number reduces to (1 + N/2)2 in the case of rotational symmetry. A way to measure the moments as intensity moments in the output planes of (generally anamorphic) fractional Fourier-transform systems is presented. PMID:14690109
Oryspayev, Dossay; Aktulga, Hasan Metin; Sosonkina, Masha; Maris, Pieter; Vary, James P.
2015-07-14
In this article, sparse matrix vector multiply (SpMVM) is an important kernel that frequently arises in high performance computing applications. Due to its low arithmetic intensity, several approaches have been proposed in literature to improve its scalability and efficiency in large scale computations. In this paper, our target systems are high end multi-core architectures and we use messaging passing interface + open multiprocessing hybrid programming model for parallelism. We analyze the performance of recently proposed implementation of the distributed symmetric SpMVM, originally developed for large sparse symmetric matrices arising in ab initio nuclear structure calculations. We also study important features of this implementation and compare with previously reported implementations that do not exploit underlying symmetry. Our SpMVM implementations leverage the hybrid paradigm to efficiently overlap expensive communications with computations. Our main comparison criterion is the "CPU core hours" metric, which is the main measure of resource usage on supercomputers. We analyze the effects of topology-aware mapping heuristic using simplified network load model. Furthermore, we have tested the different SpMVM implementations on two large clusters with 3D Torus and Dragonfly topology. Our results show that the distributed SpMVM implementation that exploits matrix symmetry and hides communication yields the best value for the "CPU core hours" metric and significantly reduces data movement overheads.
Oryspayev, Dossay; Aktulga, Hasan Metin; Sosonkina, Masha; Maris, Pieter; Vary, James P.
2015-07-14
In this article, sparse matrix vector multiply (SpMVM) is an important kernel that frequently arises in high performance computing applications. Due to its low arithmetic intensity, several approaches have been proposed in literature to improve its scalability and efficiency in large scale computations. In this paper, our target systems are high end multi-core architectures and we use messaging passing interface + open multiprocessing hybrid programming model for parallelism. We analyze the performance of recently proposed implementation of the distributed symmetric SpMVM, originally developed for large sparse symmetric matrices arising in ab initio nuclear structure calculations. We also study important featuresmore » of this implementation and compare with previously reported implementations that do not exploit underlying symmetry. Our SpMVM implementations leverage the hybrid paradigm to efficiently overlap expensive communications with computations. Our main comparison criterion is the "CPU core hours" metric, which is the main measure of resource usage on supercomputers. We analyze the effects of topology-aware mapping heuristic using simplified network load model. Furthermore, we have tested the different SpMVM implementations on two large clusters with 3D Torus and Dragonfly topology. Our results show that the distributed SpMVM implementation that exploits matrix symmetry and hides communication yields the best value for the "CPU core hours" metric and significantly reduces data movement overheads.« less
On the Maxwellian distribution, symmetric form, and entropy conservation for the Euler equations
NASA Technical Reports Server (NTRS)
Deshpande, S. M.
1986-01-01
The Euler equations of gas dynamics have some very interesting properties in that the flux vector is a homogeneous function of the unknowns and the equations can be cast in symmetric hyperbolic form and satisfy the entropy conservation. The Euler equations are the moments of the Boltzmann equation of the kinetic theory of gases when the velocity distribution function is a Maxwellian. The present paper shows the relationship between the symmetrizability and the Maxwellian velocity distribution. The entropy conservation is in terms of the H-function, which is a slight modification of the H-function first introduced by Boltzmann in his famous H-theorem. In view of the H-theorem, it is suggested that the development of total H-diminishing (THD) numerical methods may be more profitable than the usual total variation diminishing (TVD) methods for obtaining wiggle-free solutions.
Stokes flow in ellipsoidal geometry
NASA Astrophysics Data System (ADS)
Vafeas, Panayiotis; Dassios, George
2006-09-01
Particle-in-cell models for Stokes flow through a relatively homogeneous swarm of particles are of substantial practical interest, because they provide a relatively simple platform for the analytical or semianalytical solution of heat and mass transport problems. Despite the fact that many practical applications involve relatively small particles (inorganic, organic, biological) with axisymmetric shapes, the general consideration consists of rigid particles of arbitrary shape. The present work is concerned with some interesting aspects of the theoretical analysis of creeping flow in ellipsoidal, hence nonaxisymmetric domains. More specifically, the low Reynolds number flow of a swarm of ellipsoidal particles in an otherwise quiescent Newtonian fluid, that move with constant uniform velocity in an arbitrary direction and rotate with an arbitrary constant angular velocity, is analyzed with an ellipsoid-in-cell model. The solid internal ellipsoid represents a particle of the swarm. The external ellipsoid contains the ellipsoidal particle and the amount of fluid required to match the fluid volume fraction of the swarm. The nonslip flow condition on the surface of the solid ellipsoid is supplemented by the boundary conditions on the external ellipsoidal surface which are similar to those of the sphere-in-cell model of Happel (self-sufficient in mechanical energy). This model requires zero normal velocity component and shear stress. The boundary value problem is solved with the aim of the potential representation theory. In particular, the Papkovich-Neuber complete differential representation of Stokes flow, valid for nonaxisymmetric geometries, is considered here, which provides the velocity and total pressure fields in terms of harmonic ellipsoidal eigenfunctions. The flexibility of the particular representation is demonstrated by imposing some conditions, which made the calculations possible. It turns out that the velocity of first degree, which represents the leading
Orientation statistics and settling velocity of ellipsoids in decaying turbulence
NASA Astrophysics Data System (ADS)
Siewert, C.; Kunnen, R. P. J.; Meinke, M.; Schröder, W.
2014-06-01
Motivated by applications in technology as well as in other disciplines where the motion of particles in a turbulent flow field is important, the orientation and settling velocity of ellipsoidal particles in a spatially decaying isotropic turbulent flow are numerically investigated. With respect to cloud microphysics ellipsoidal particles of various shapes are interpreted as archetypes of regular ice crystals, i.e., plates and columns approximated by oblate and prolate ellipsoids. The motion of 19 million small and heavy ellipsoidal particles is tracked by a Lagrangian point-particle model based on Stokes flow conditions. Five types of ellipsoids of revolution such as prolates, spheres, and oblates are considered. The orientation and settling velocity statistics are gathered at six turbulence intensities characterized by the turbulent kinetic energy dissipation rate ranging from 30 to 250 cm2s- 3. It is shown that the preferential orientation of ellipsoids is disturbed by the turbulent fluctuations of the fluid forces and moments. As the turbulence intensity increases the orientation probability distribution becomes more and more uniform. That is, the settling velocity of the ellipsoids is influenced by the turbulence level since the drag force is dependent on the orientation. The effect is more pronounced, the longer the prolate or the flatter the oblate is. The theoretical settling velocity based on the orientation probability of the non-spherical particles is smaller than that found in the simulation. The results show the existence of the preferential sweeping phenomenon also for non-spherical particles. These two effects of turbulence on the motion of ellipsoids change the settling velocity and as such the swept volume, that is expected to result in modified collision probabilities of ellipsoid-shaped particles.
Calculation of the fast ion tail distribution for a spherically symmetric hot spot
McDevitt, C. J.; Tang, X.-Z.; Guo, Z.; Berk, H. L.
2014-10-15
The fast ion tail for a spherically symmetric hot spot is computed via the solution of a simplified Fokker-Planck collision operator. Emphasis is placed on describing the energy scaling of the fast ion distribution function in the hot spot as well as the surrounding cold plasma throughout a broad range of collisionalities and temperatures. It is found that while the fast ion tail inside the hot spot is significantly depleted, leading to a reduction of the fusion yield in this region, a surplus of fast ions is observed in the neighboring cold plasma region. The presence of this surplus of fast ions in the neighboring cold region is shown to result in a partial recovery of the fusion yield lost in the hot spot.
NASA Astrophysics Data System (ADS)
Bergeron, H.; Curado, E. M. F.; Gazeau, J. P.; Rodrigues, Ligia M. C. S.
2016-02-01
Asymptotic behavior (with respect to the number of trials) of symmetric generalizations of binomial distributions and their related entropies is studied through three examples. The first one has the q-exponential as the generating function, the second one involves the modified Abel polynomials, and the third one has Hermite polynomials. We prove analytically that the Rényi entropy is extensive for these three cases, i.e., it is proportional (asymptotically) to the number n of events and that q-exponential and Hermite cases have also extensive Boltzmann-Gibbs. The Abel case is exceptional in the sense that its Boltzmann-Gibbs entropy is not extensive and behaves asymptotically as the square root of n. This result is obtained numerically and also confirmed analytically, under reasonable assumptions, by using a regularization of the beta function and its derivative. Probabilistic urn and genetic models are presented for illustrating this remarkable case.
Calculation of the fast ion tail distribution for a spherically symmetric hot spot
NASA Astrophysics Data System (ADS)
McDevitt, C. J.; Tang, X.-Z.; Guo, Z.; Berk, H. L.
2014-10-01
The fast ion tail for a spherically symmetric hot spot is computed via the solution of a simplified Fokker-Planck collision operator. Emphasis is placed on describing the energy scaling of the fast ion distribution function in the hot spot as well as the surrounding cold plasma throughout a broad range of collisionalities and temperatures. It is found that while the fast ion tail inside the hot spot is significantly depleted, leading to a reduction of the fusion yield in this region, a surplus of fast ions is observed in the neighboring cold plasma region. The presence of this surplus of fast ions in the neighboring cold region is shown to result in a partial recovery of the fusion yield lost in the hot spot.
Revisiting the phase diagram of hard ellipsoids.
Odriozola, Gerardo
2012-04-01
In this work, the well-known Frenkel-Mulder phase diagram of hard ellipsoids of revolution [D. Frenkel and B. M. Mulder, Mol. Phys. 55, 1171 (1985)] is revisited by means of replica exchange Monte Carlo simulations. The method provides good sampling of dense systems and so, solid phases can be accessed without the need of imposing a given structure. At high densities, we found plastic solids and fcc-like crystals for semi-spherical ellipsoids (prolates and oblates), and SM2 structures [P. Pfleiderer and T. Schilling, Phys. Rev. E 75, 020402 (2007)] for x : 1-prolates and 1 : x-oblates with x ≥ 3. The revised fluid-crystal and isotropic-nematic transitions reasonably agree with those presented in the Frenkel-Mulder diagram. An interesting result is that, for small system sizes (100 particles), we obtained 2:1- and 1.5:1-prolate equations of state without transitions, while some order is developed at large densities. Furthermore, the symmetric oblate cases are also reluctant to form ordered phases. PMID:22482570
Revisiting the phase diagram of hard ellipsoids
NASA Astrophysics Data System (ADS)
Odriozola, Gerardo
2012-04-01
In this work, the well-known Frenkel-Mulder phase diagram of hard ellipsoids of revolution [D. Frenkel and B. M. Mulder, Mol. Phys. 55, 1171 (1985), 10.1080/00268978500101971] is revisited by means of replica exchange Monte Carlo simulations. The method provides good sampling of dense systems and so, solid phases can be accessed without the need of imposing a given structure. At high densities, we found plastic solids and fcc-like crystals for semi-spherical ellipsoids (prolates and oblates), and SM2 structures [P. Pfleiderer and T. Schilling, Phys. Rev. E 75, 020402 (2007)] for x : 1-prolates and 1 : x-oblates with x ≥ 3. The revised fluid-crystal and isotropic-nematic transitions reasonably agree with those presented in the Frenkel-Mulder diagram. An interesting result is that, for small system sizes (100 particles), we obtained 2:1- and 1.5:1-prolate equations of state without transitions, while some order is developed at large densities. Furthermore, the symmetric oblate cases are also reluctant to form ordered phases.
A calculation model for primary intensity distributions from cylindrically symmetric x-ray lenses
NASA Astrophysics Data System (ADS)
Hristov, Dimitre; Maltz, Jonathan
2008-02-01
A calculation model for the quantitative prediction of primary intensity fluence distributions obtained by the Bragg diffraction focusing of kilovoltage radiation by cylindrical x-ray lenses is presented. The mathematical formalism describes primary intensity distributions from cylindrically-symmetric x-ray lenses, with a planar isotropic radiation source located in a plane perpendicular to the lens axis. The presence of attenuating medium inserted between the lens and the lens focus is accounted for by energy-dependent attenuation. The influence of radiation scattered within the media is ignored. Intensity patterns are modeled under the assumption that photons that are not interacting with the lens are blocked out at any point of interest. The main characteristics of the proposed calculation procedure are that (i) the application of vector formalism allows universal treatment of all cylindrical lenses without the need of explicit geometric constructs; (ii) intensity distributions resulting from x-ray diffraction are described by a 3D generalization of the mosaic spread concept; (iii) the calculation model can be immediately coupled to x-ray diffraction simulation packages such as XOP and Shadow. Numerical simulations based on this model are to facilitate the design of focused orthovoltage treatment (FOT) systems employing cylindrical x-ray lenses, by providing insight about the influence of the x-ray source and lens parameters on quantities of dosimetric interest to radiation therapy.
Rubio, Francisco J; Genton, Marc G
2016-06-30
We study Bayesian linear regression models with skew-symmetric scale mixtures of normal error distributions. These kinds of models can be used to capture departures from the usual assumption of normality of the errors in terms of heavy tails and asymmetry. We propose a general noninformative prior structure for these regression models and show that the corresponding posterior distribution is proper under mild conditions. We extend these propriety results to cases where the response variables are censored. The latter scenario is of interest in the context of accelerated failure time models, which are relevant in survival analysis. We present a simulation study that demonstrates good frequentist properties of the posterior credible intervals associated with the proposed priors. This study also sheds some light on the trade-off between increased model flexibility and the risk of over-fitting. We illustrate the performance of the proposed models with real data. Although we focus on models with univariate response variables, we also present some extensions to the multivariate case in the Supporting Information. Copyright © 2016 John Wiley & Sons, Ltd. PMID:26856806
Disk Galaxy Stellar Velocity Ellipsoids
NASA Astrophysics Data System (ADS)
Westfall, Kyle B.; Bershady, M. A.; Verheijen, M. A. W.; Andersen, D. R.; Swaters, R. A.
2007-12-01
We have measured the disk stellar velocity ellipsoids in a subset of spiral galaxies observed for the Disk-Mass Survey, which provide information on disk stability and secular heating mechanisms. Our methodology invokes our 2D ionized gas and stellar kinematics and a suite of dynamical assumptions based on the Jeans' equations. When combined with orthogonal axes from our 2D data, either the epicycle approximation (EA) or asymmetric drift (AD) equation may close the necessary equation set, individually. We have isolated large observational and inherent systematic effects via EA-only, AD-only, and EA+AD ellipsoid decomposition methodologies. In an attempt to minimize these effects and generate robust ellipsoid measurements we explore constraints provided by higher order expansions of the Jeans' equations and direct orbital integrations. We compare our best ellipsoid axial ratio estimates to similar measurements made by, e.g., van der Kruit & de Grijs (1999, A&A, 352, 129) and Shapiro et al. (2003, AJ, 126, 2707). Finally, we discuss possibilities for the measurement of vertical velocity dispersions in low-surface-brightness galaxies by applying the characterization of the stellar velocity ellipsoid in late-type galaxies. This work is supported by the National Science Foundation (AST-0607516).
Elastic Flows Of Ellipsoidal Particles
NASA Astrophysics Data System (ADS)
Campbell, Charles S.
2009-06-01
Granular flow rheology can be divided into two global regimes, the Elastic, which is dominated by force chains and the inertial which are nearly free of force chains. The propensity of a material to form force chains is strongly influenced by particle shape. This paper is an attempt to assess the effect of particle shape on flow regime transitions, through computer simulations of shear flow of ellipsoidal particles. On one hand, the results show that at a given concentration, ellipsoidal particles generate smaller quasistatic stress than spheres, likely a result of their ability to form denser static packings. But at the same time, large aspect ratio ellipsoids more readily form force chains and demonstrate Elastic behavior at smaller concentrations than spheres.
The optics of ellipsoidal domes
NASA Astrophysics Data System (ADS)
Ellis, Kenneth Scott
An ellipsoidal dome is a conformal optical element used to replace a hemispherical dome on a missile to enhance its performance by reducing its aerodynamic drag. Conformal optics are a general class of optical systems in which the optical elements are shaped to optimize something other than image quality, such as aerodynamics. An ellipsoidal dome has lower aerodynamic drag than a comparably sized hemispherical dome. On a missile, lower drag improves its aerodynamic performance by increasing its range and fuel efficiency but degrades the quality of the transmitted wavefront. In particular, an ellipsoidal dome introduces a varying aberration component that depends on the orientation of the aperture stop, which is pivoted about a fixed axis inside the dome. The transmitted ray bundle is incident only on a portion of the dome surface, and the included area lacks axial symmetry. To better understand the imaging characteristics of an ellipsoidal dome in this application, the first- and third-order optical properties of a constant thickness dome are investigated. Particular emphasis is placed on the geometry and symmetry of an ellipse, which impose certain constraints on the form of the aberration coefficients. The geometry is defined in terms of the aerodynamic fineness ratio, outer diameter, and center thickness of the dome. Emphasis is placed on third-order astigmatism and coma, which are shown to be the dominant aberration terms. The effects of varying the fineness ratio, thickness, and index of refraction of a dome are also investigated.
General Theorems about Homogeneous Ellipsoidal Inclusions
ERIC Educational Resources Information Center
Korringa, J.; And Others
1978-01-01
Mathematical theorems about the properties of ellipsoids are developed. Included are Poisson's theorem concerning the magnetization of a homogeneous body of ellipsoidal shape, the polarization of a dielectric, the transport of heat or electricity through an ellipsoid, and other problems. (BB)
Davies, Gary B; Botto, Lorenzo
2015-10-28
Capillary interactions have emerged as a tool for the directed assembly of particles adsorbed at fluid-fluid interfaces, and play a role in controlling the mechanical properties of emulsions and foams. In this paper, following Davies et al. [Adv. Mater., 2014, 26, 6715] investigation into the assembly of ellipsoidal particles at interfaces interacting via dipolar capillary interactions, we numerically investigate the interaction between tilted ellipsoidal particles adsorbed at a fluid-fluid interface as their aspect ratio, tilt angle, bond angle, and separation vary. High-resolution Surface Evolver simulations of ellipsoidal particle pairs in contact reveal an energy barrier between a metastable tip-tip configuration and a stable side-side configuration. The side-side configuration is the global energy minimum for all parameters we investigated. Lattice Boltzmann simulations of clusters of up to 12 ellipsoidal particles show novel highly symmetric flower-like and ring-like arrangements. PMID:26323324
Point Relay Scanner Utilizing Ellipsoidal Mirrors
NASA Technical Reports Server (NTRS)
Manhart, Paul K. (Inventor); Pagano, Robert J. (Inventor)
1997-01-01
A scanning system uses a polygonal mirror assembly with each facet of the polygon having an ellipsoidal mirror located thereon. One focal point of each ellipsoidal mirror is located at a common point on the axis of rotation of the polygonal mirror assembly. As the mirror assembly rotates. a second focal point of the ellipsoidal mirrors traces out a scan line. The scanner can be utilized for scanned output display of information or for scanning information to be detected.
An ellipsoidal representation of human hand anthropometry
NASA Technical Reports Server (NTRS)
Buchholz, Bryan; Armstrong, Thomas J.
1991-01-01
Anthropometric data concerning the heometry of the hand's surface are presently modeled as a function of gross external hand measurements; an effort is made to evaluate the accuracy with which ellipsoids describe the geometry of the hand segments. Graphical comparisons indicate that differences between the ellipsoidal approximations and the breadth and depth measurements were greatest near the joints. On the bases of the present data, a set of overlapping ellipsoids could furnish a more accurate representation of hand geometry for adaptation to ellipsoid segment-geometry employing biomechanical models.
Symmetrizing the symmetrization postulate
NASA Astrophysics Data System (ADS)
York, Michael
2000-11-01
Reasonable requirements of (a) physical invariance under particle permutation and (b) physical completeness of state descriptions [1], enable us to deduce a Symmetric Permutation Rule(SPR): that by taking care with our state descriptions, it is always possible to construct state vectors (or wave functions) that are purely symmetric under pure permutation for all particles, regardless of type distinguishability or spin. The conventional exchange antisymmetry for two identical half-integer spin particles is shown to be due to a subtle interdependence in the individual state descriptions arising from an inherent geometrical asymmetry. For three or more such particles, however, antisymmetrization of the state vector for all pairs simultaneously is shown to be impossible and the SPR makes observably different predictions, although the usual pairwise exclusion rules are maintained. The usual caveat of fermion antisymmetrization—that composite integer spin particles (with fermionic constituents) behave only approximately like bosons—is no longer necessary.
Non-universal Voronoi cell shapes in amorphous ellipsoid packs
NASA Astrophysics Data System (ADS)
Schaller, Fabian M.; Kapfer, Sebastian C.; Hilton, James E.; Cleary, Paul W.; Mecke, Klaus; De Michele, Cristiano; Schilling, Tanja; Saadatfar, Mohammad; Schröter, Matthias; Delaney, Gary W.; Schröder-Turk, Gerd E.
2015-07-01
In particulate systems with short-range interactions, such as granular matter or simple fluids, local structure determines the macroscopic physical properties. We analyse local structure metrics derived from the Voronoi diagram of oblate ellipsoids, for various aspect ratios α and global packing fractions φ\\text{g} . We focus on jammed static configurations of frictional ellipsoids, obtained by tomographic imaging and by discrete element method simulations. The rescaled distribution of local packing fractions φ\\text{l} , defined as the ratio of particle volume and its Voronoi cell volume, is found to be independent of the particle aspect ratio, and coincide with results for sphere packs. By contrast, the typical Voronoi cell shape, quantified by the Minkowski tensor anisotropy index β=β_02,0 , points towards a difference between random packings of spheres and those of oblate ellipsoids. While the average cell shape β of all cells with a given value of φ\\text{l} is similar in dense and loose jammed sphere packings, the structure of dense and loose ellipsoid packings differs substantially such that this does not hold true.
Harnessing Multivariate Statistics for Ellipsoidal Data in Structural Geology
NASA Astrophysics Data System (ADS)
Roberts, N.; Davis, J. R.; Titus, S.; Tikoff, B.
2015-12-01
Most structural geology articles do not state significance levels, report confidence intervals, or perform regressions to find trends. This is, in part, because structural data tend to include directions, orientations, ellipsoids, and tensors, which are not treatable by elementary statistics. We describe a full procedural methodology for the statistical treatment of ellipsoidal data. We use a reconstructed dataset of deformed ooids in Maryland from Cloos (1947) to illustrate the process. Normalized ellipsoids have five degrees of freedom and can be represented by a second order tensor. This tensor can be permuted into a five dimensional vector that belongs to a vector space and can be treated with standard multivariate statistics. Cloos made several claims about the distribution of deformation in the South Mountain fold, Maryland, and we reexamine two particular claims using hypothesis testing: 1) octahedral shear strain increases towards the axial plane of the fold; 2) finite strain orientation varies systematically along the trend of the axial trace as it bends with the Appalachian orogen. We then test the null hypothesis that the southern segment of South Mountain is the same as the northern segment. This test illustrates the application of ellipsoidal statistics, which combine both orientation and shape. We report confidence intervals for each test, and graphically display our results with novel plots. This poster illustrates the importance of statistics in structural geology, especially when working with noisy or small datasets.
Ellipsoidal Relaxation of Deformed Vesicles
NASA Astrophysics Data System (ADS)
Yu, Miao; Lira, Rafael B.; Riske, Karin A.; Dimova, Rumiana; Lin, Hao
2015-09-01
Theoretical analysis and experimental quantification on the ellipsoidal relaxation of vesicles are presented. The current work reveals the simplicity and universal aspects of this process. The Helfrich formula is shown to apply to the dynamic relaxation of moderate-to-high tension membranes, and a closed-form solution is derived which predicts the vesicle aspect ratio as a function of time. Scattered data are unified by a time scale, which leads to a similarity behavior, governed by a distinctive solution for each vesicle type. Two separate regimes in the relaxation are identified, namely, the "entropic" and the "constant-tension" regimes. The bending rigidity and the initial membrane tension can be simultaneously extracted from the data analysis, posing the current approach as an effective means for the mechanical analysis of biomembranes.
Characterization of an Ellipsoidal Radiometer
Murthy, Annageri V.; Wetterlund, Ingrid; DeWitt, David P.
2003-01-01
An ellipsoidal radiometer has been characterized using a 25 mm variable-temperature blackbody as a radiant source. This radiometer is intended for separating radiation from convection effects in fire test methods. The characterization included angular response, responsivity, and purge-gas flow effect studies. The angular response measurements showed that the reflection from the radiometer cavity was higher on one of the cavity halves relative to the other half. Further development work may be necessary to improve the angular response. The responsivity measured with reference to a transfer-standard electrical-substitution radiometer showed dependence on the distance of the radiometer from the blackbody cavity. The purge-gas had the effect of reducing the signal output nearly linearly with flow rate.
Deformed ellipsoidal diffraction grating blank
NASA Technical Reports Server (NTRS)
Decew, Alan E., Jr.
1994-01-01
The Deformed Ellipsoidal Grating Blank (DEGB) is the primary component in an ultraviolet spectrometer. Since one of the major concerns for these instruments is throughput, significant efforts are made to reduce the number of components and subsequently reflections. Each reflection results in losses through absorption and scattering. It is these two sources of photon loss that dictated the requirements for the DEGB. The first goal is to shape the DEGB in such a way that the energy at the entrance slit is focused as well as possible on the exit slit. The second goal is to produce a surface smooth enough to minimize the photon loss due to scattering. The program was accomplished in three phases. The first phase was the fabrication planning. The second phase was the actual fabrication and initial testing. The last phase was the final testing of the completed DEGB.
Generalization of symmetric α-stable Lévy distributions for q >1
NASA Astrophysics Data System (ADS)
Umarov, Sabir; Tsallis, Constantino; Gell-Mann, Murray; Steinberg, Stanly
2010-03-01
The α-stable distributions introduced by Lévy play an important role in probabilistic theoretical studies and their various applications, e.g., in statistical physics, life sciences, and economics. In the present paper we study sequences of long-range dependent random variables whose distributions have asymptotic power-law decay, and which are called (q,α)-stable distributions. These sequences are generalizations of independent and identically distributed α-stable distributions and have not been previously studied. Long-range dependent (q,α)-stable distributions might arise in the description of anomalous processes in nonextensive statistical mechanics, cell biology, finance. The parameter q controls dependence. If q =1 then they are classical independent and identically distributed with α-stable Lévy distributions. In the present paper we establish basic properties of (q,α)-stable distributions and generalize the result of Umarov et al. [Milan J. Math. 76, 307 (2008)], where the particular case α =2,qɛ[1,3) was considered, to the whole range of stability and nonextensivity parameters α ɛ(0,2] and q ɛ[1,3), respectively. We also discuss possible further extensions of the results that we obtain and formulate some conjectures.
Generalization of symmetric α-stable Lévy distributions for q>1
Umarov, Sabir; Tsallis, Constantino; Gell-Mann, Murray; Steinberg, Stanly
2010-01-01
The α-stable distributions introduced by Lévy play an important role in probabilistic theoretical studies and their various applications, e.g., in statistical physics, life sciences, and economics. In the present paper we study sequences of long-range dependent random variables whose distributions have asymptotic power-law decay, and which are called (q,α)-stable distributions. These sequences are generalizations of independent and identically distributed α-stable distributions and have not been previously studied. Long-range dependent (q,α)-stable distributions might arise in the description of anomalous processes in nonextensive statistical mechanics, cell biology, finance. The parameter q controls dependence. If q=1 then they are classical independent and identically distributed with α-stable Lévy distributions. In the present paper we establish basic properties of (q,α)-stable distributions and generalize the result of Umarov et al. [Milan J. Math. 76, 307 (2008)], where the particular case α=2,q∊[1,3) was considered, to the whole range of stability and nonextensivity parameters α∊(0,2] and q∊[1,3), respectively. We also discuss possible further extensions of the results that we obtain and formulate some conjectures. PMID:20596232
Latitudinal Libration in a Triaxial Ellipsoid
NASA Astrophysics Data System (ADS)
Cebron, D.; Vantieghem, S.; Noir, J.
2014-12-01
As a consequence of gravitational coupling with their orbital partners, the rotational dynamics of planets and moons exhibits periodic variations in time, such as precession, libration and nutation. Moreover, most planets are subject to tidal forces, which in combination with the planet's rotation, result in a departure from a purely spherically symmetric object. In this theoretical-numerical study, we investigate the flows driven by latitudinal libration (i.e. an oscillation of the figure axis with respect to the mean rotation axis) within liquid cores of triaxial ellipsoidal shape. We first derive a uniform-vorticity solution for the equations of motion, and find that it can resonate with the spin-over inertial mode. Using a reduced model of viscosity (J. Noir and D. Cébron, J. Fluid Mech., vol. 737 (2013)), we deduce that the amplitude of the flow at resonance diverges as the inverse square-root of the Ekman number. Our results are consistent with previous studies in a spheroidal geometry (K. Zhang et al., J. Fluid Mech., vol. 696 (2012)). In a following step, we address the dynamical stability of this uniform-vorticity flow. We show that it is prone to inertial instabilities arising from a parametric resonance between two free inertial modes and the base flow. We also show that the vigor of the instability is governed by the frequency and two parameters that capture the dependence on the libration amplitude and geometry. The resonant nature of these phenomena suggests that libration in latitude, despite its small amplitude, may drive strong flows within planetary cores with possibly major implications for heat transport, dissipation and magnetic field generation/induction. This is discussed at planetary settings for the cores of the Moon, Io and Mercury, and the ancient lunar core.
NASA Astrophysics Data System (ADS)
Ma, John Zhen Guo; Ma, John Zhen Guo; St-Maurice, Jean-Pierre
Because of the strong ambient magnetic field, particularly at ionospheric altitudes, the auroral regions are flush with cylindrical structures covering an impressive range of scales which include lower hybrid cavities on decameter scales, auroral rays on km scales and vortices on tens to hundreds of km scales. In addition, a plethora of in-situ magnetic field and electric field observations and groundbased radar observations strongly suggests that very large parallel current densities are triggered in the upper ionosphere. These observations and just simple geometric considerations have motivated us to study the ion velocity distributions that would accompany strong perpendicular electric fields in a cylindrically symmetric geometry. The applications of the work have to do with the transport coefficients in such regions as well as with local instrumental observations of distribution functions with particle detectors. We have evolved a kinetic theoretical framework in which we have obtained analytical solutions for a number of important limits. We have also developed a semi-numerical method by which to obtain the ion velocity distribution under more general conditions for which analytical solutions are not possible. Our presentation will focus strongly on collision-free results, which stem from the following assumptions: (1) a perpendicular electric field is introduced initially on a time scale that is fast compared to the local ion gyrofrequency (but slow compared to electron plasma and gyrofrequencies); (2) the ion collision frequency is much smaller than the ion gyrofrequency, so that we can calculate meaningful collisionfree solutions. We will present analytical solutions for the distribution functions and their velocity moments inside regions for which the electric field can be assumed to increase linearly with distance from the axis of the cylindrical region, this for a number of initial cylindrically symmetric density distributions. We will also present our
Ellipsoidal relaxation of electrodeformed vesicles
NASA Astrophysics Data System (ADS)
Yu, Miao; Lin, Hao; Lira, Rafael; Dimova, Rumiana; Riske, Karin
2015-11-01
Electrodeformation has been extensively applied to investigate the mechanical behavior of vesicles and cells. While the deformation process often exhibits complex behavior and reveals interesting physics, the relaxation process post-pulsation is equally intriguing yet less frequently studied. In this work theoretical analysis and experimental quantification on the ellipsoidal relaxation of vesicles are presented, which reveal the simplicity and universal aspects of this process. The Helfrich formula, which is derived only for equilibrated shapes, is shown to be applicable to dynamic situations such as in relaxation. A closed-form solution is derived which predicts the vesicle aspect ratio as a function of time. Scattered data are unified by a timescale, which leads to a similarity behavior, governed by a distinctive solution for each vesicle type. Two separate regimes in the relaxation are identified, namely, the ``entropic'' and the ``constant-tension'' regime. The bending rigidity and the initial membrane tension can be simultaneously extracted from the data/model analysis, posing the current approach as an effective means for the mechanical analysis of biomembranes.
A nonspherically symmetric model for the peculiar A star Alpha-2
NASA Technical Reports Server (NTRS)
Bohm-Vitense, Erika; Van Dyk, Schuyler D.
1987-01-01
Observations show that in the optical region the peculiar A star Alpha-2 CVn has a flatter energy distribution during maximum light than during minimum light. This indicates that during maximum light a lower-temperature region, but necessarily larger surface area, than during minimum light is seen. This suggests a nonspherically symmetric star, which is oblate with respect to the magnetic axis and which is cooler at the magnetic poles than at the magnetic equator. The light variations of such nonspherically symmetric oblique rotator models have been studied. It is found that, for an oblate ellipsoid with an axial ratio of 0.92 and a temperature difference of about 1000 K between the poles and the equator, the overall variations of the optical and the ultraviolet energy distributions can be well understood.
The ellipsoidal universe in the Planck satellite era
NASA Astrophysics Data System (ADS)
Cea, Paolo
2014-06-01
Recent Planck data confirm that the cosmic microwave background displays the quadrupole power suppression together with large-scale anomalies. Progressing from previous results, that focused on the quadrupole anomaly, we strengthen the proposal that the slightly anisotropic ellipsoidal universe may account for these anomalies. We solved at large scales the Boltzmann equation for the photon distribution functions by taking into account both the effects of the inflation produced primordial scalar perturbations and the anisotropy of the geometry in the ellipsoidal universe. We showed that the low quadrupole temperature correlations allowed us to fix the eccentricity at decoupling, edec = (0.86 ± 0.14) 10-2, and to constraint the direction of the symmetry axis. We found that the anisotropy of the geometry of the universe contributes only to the large-scale temperature anisotropies without affecting the higher multipoles of the angular power spectrum. Moreover, we showed that the ellipsoidal geometry of the universe induces sizeable polarization signal at large scales without invoking the reionization scenario. We explicitly evaluated the quadrupole TE and EE correlations. We found an average large-scale polarization ΔTpol = (1.20 ± 0.38) μK. We point out that great care is needed in the experimental determination of the large-scale polarization correlations since the average temperature polarization could be misinterpreted as foreground emission leading, thereby, to a considerable underestimate of the cosmic microwave background polarization signal.
Petersen, A.
1986-04-01
Results of inclusive charged particle distribution for gluon jets using nearly 3-fold symmetric 3-jet events taken at center of mass energies of 29 GeV in e/sup +/e/sup -/ annihilation are presented. The charged particle spectrum for these jets is observed to be softer than that of quark jets with the same jet energy.
Asteroid lightcurve inversion using Lommel-Seeliger ellipsoids
NASA Astrophysics Data System (ADS)
Muinonen, K.; Wilkman, O.; Wang, X.; Cellino, A.
2014-07-01
The rotational period, pole orientation, and convex three-dimensional shape of an asteroid can be derived from photometric lightcurves observed in a number of apparitions with varying illumination and observation geometries (e.g., Kaasalainen et al. 2001, Torppa et al. 2008, Durech et al. 2009). It is customary to estimate the rotational period with a simplified shape model and a small number of trial pole orientations. Once the period is available, the pole orientation can be refined with a general convex shape model represented by the spherical harmonics expansion for the Gaussian surface density. Once the Gaussian surface density is available, the actual convex shape is constructed as a solution of the Minkowski problem. We focus on the initial derivation of the rotational period and pole orientation with the help of the Lommel-Seeliger ellipsoid (LS-ellipsoid), a triaxial ellipsoid with a Lommel-Seeliger surface scattering law. The disk-integrated photometric brightness for the LS-ellipsoid is available in a closed form (Muinonen and Lumme, in preparation), warranting efficient direct computation of lightcurves. With modern computers and the LS-ellipsoid, the rotation period, pole orientation, and ellipsoidal shape can be derived, in principle, simultaneously (see Cellino et al., present meeting). However, here we choose to proceed systematically as follows. First, the rotation period is scanned systematically across its relevant range with a resolution of P_0^2/2T dictated by a tentative period estimate P_0 and the time interval spanned by the photometric data T. This is typically carried out for a small number of pole orientations distributed uniformly on a unit sphere. For each pole orientation, the ellipsoid pole orientation, rotational phase, and axial ratios are optimized with the help of the Nelder-Mead downhill simplex method. Although the shape optimization can suffer from getting stuck in local minima, overall, the rotation period is fairly accurately
Diffusion of Ellipsoids in Bacterial Suspensions.
Peng, Yi; Lai, Lipeng; Tai, Yi-Shu; Zhang, Kechun; Xu, Xinliang; Cheng, Xiang
2016-02-12
Active fluids such as swarming bacteria and motile colloids exhibit exotic properties different from conventional equilibrium materials. As a peculiar example, a spherical tracer immersed inside active fluids shows an enhanced translational diffusion, orders of magnitude stronger than its intrinsic Brownian motion. Here, rather than spherical tracers, we investigate the diffusion of isolated ellipsoids in a quasi-two-dimensional bacterial bath. Our study shows a nonlinear enhancement of both translational and rotational diffusions of ellipsoids. More importantly, we uncover an anomalous coupling between particles' translation and rotation that is strictly prohibited in Brownian diffusion. The coupling reveals a counterintuitive anisotropic particle diffusion, where an ellipsoid diffuses fastest along its minor axis in its body frame. Combining experiments with theoretical modeling, we show that such an anomalous diffusive behavior arises from the generic straining flow of swimming bacteria. Our work illustrates an unexpected feature of active fluids and deepens our understanding of transport processes in microbiological systems. PMID:26919019
Diffusion of Ellipsoids in Bacterial Suspensions
NASA Astrophysics Data System (ADS)
Peng, Yi; Lai, Lipeng; Tai, Yi-Shu; Zhang, Kechun; Xu, Xinliang; Cheng, Xiang
2016-02-01
Active fluids such as swarming bacteria and motile colloids exhibit exotic properties different from conventional equilibrium materials. As a peculiar example, a spherical tracer immersed inside active fluids shows an enhanced translational diffusion, orders of magnitude stronger than its intrinsic Brownian motion. Here, rather than spherical tracers, we investigate the diffusion of isolated ellipsoids in a quasi-two-dimensional bacterial bath. Our study shows a nonlinear enhancement of both translational and rotational diffusions of ellipsoids. More importantly, we uncover an anomalous coupling between particles' translation and rotation that is strictly prohibited in Brownian diffusion. The coupling reveals a counterintuitive anisotropic particle diffusion, where an ellipsoid diffuses fastest along its minor axis in its body frame. Combining experiments with theoretical modeling, we show that such an anomalous diffusive behavior arises from the generic straining flow of swimming bacteria. Our work illustrates an unexpected feature of active fluids and deepens our understanding of transport processes in microbiological systems.
NASA Technical Reports Server (NTRS)
Froessling, Nils
1958-01-01
The fundamental boundary layer equations for the flow, temperature and concentration fields are presented. Two dimensional symmetrical and unsymmetrical and rotationally symmetrical steady boundary layer flows are treated as well as the transfer boundary layer. Approximation methods for the calculation of the transfer layer are discussed and a brief survey of an investigation into the validity of the law that the Nusselt number is proportional to the cube root of the Prandtl number is presented.
Paramagnetic ellipsoidal microswimmer in a magnetic field
NASA Astrophysics Data System (ADS)
Sandoval, Mario; Fan, Louis; Pak, On Shun
We study the two-dimensional Brownian dynamics of an ellipsoidal paramagnetic microswimmer moving at low-Reynolds-number and subject to a magnetic field. Its corresponding mean-square displacement tensor showing the effect of particles's shape, activity and magnetic field, on the microswimmer's diffusion is analytically obtained. A comparison among analytical and computational results is also made and we obtain excellent agreement.
AirMSPI Ellipsoid File Explanation
Atmospheric Science Data Center
2014-05-02
AirMSPI Ellipsoid-projected File Name Explanation The file name structure is as follows: ... observation tttt: Target name aaa: Mean viewing angle (reported to the nearest ...
Ramond, P. . Dept. of Physics)
1993-01-01
The Wolfenstein parametrization is extended to the quark masses in the deep ultraviolet, and an algorithm to derive symmetric textures which are compatible with existing data is developed. It is found that there are only five such textures.
Ramond, P.
1993-04-01
The Wolfenstein parametrization is extended to the quark masses in the deep ultraviolet, and an algorithm to derive symmetric textures which are compatible with existing data is developed. It is found that there are only five such textures.
Ferroelectric order in liquid crystal phases of polar disk-shaped ellipsoids
NASA Astrophysics Data System (ADS)
Bose, Tushar Kanti; Saha, Jayashree
2014-05-01
The demonstration of a spontaneous macroscopic ferroelectric order in liquid phases in the absence of any long range positional order is considered an outstanding problem of both fundamental and technological interest. Recently, we reported that a system of polar achiral disklike ellipsoids can spontaneously exhibit a long searched ferroelectric nematic phase and a ferroelectric columnar phase with strong axial polarization. The major role is played by the dipolar interactions. The model system of interest consists of attractive-repulsive Gay-Berne oblate ellipsoids embedded with two parallel point dipoles positioned symmetrically on the equatorial plane of the ellipsoids. In the present work, we investigate in detail the profound effects of changing the separation between the two symmetrically placed dipoles and the strength of the dipoles upon the existence of different ferroelectric discotic liquid crystal phases via extensive off-lattice N-P-T Monte Carlo simulations. Ferroelectric biaxial phases are exhibited in addition to the uniaxial ferroelectric fluids where the phase biaxiality results from the dipolar interactions. The structures of all the ferroelectric configurations of interest are presented in detail. Simple phase diagrams are determined which include different polar and apolar discotic fluids generated by the system.
Ferroelectric order in liquid crystal phases of polar disk-shaped ellipsoids.
Bose, Tushar Kanti; Saha, Jayashree
2014-05-01
The demonstration of a spontaneous macroscopic ferroelectric order in liquid phases in the absence of any long range positional order is considered an outstanding problem of both fundamental and technological interest. Recently, we reported that a system of polar achiral disklike ellipsoids can spontaneously exhibit a long searched ferroelectric nematic phase and a ferroelectric columnar phase with strong axial polarization. The major role is played by the dipolar interactions. The model system of interest consists of attractive-repulsive Gay-Berne oblate ellipsoids embedded with two parallel point dipoles positioned symmetrically on the equatorial plane of the ellipsoids. In the present work, we investigate in detail the profound effects of changing the separation between the two symmetrically placed dipoles and the strength of the dipoles upon the existence of different ferroelectric discotic liquid crystal phases via extensive off-lattice N-P-T Monte Carlo simulations. Ferroelectric biaxial phases are exhibited in addition to the uniaxial ferroelectric fluids where the phase biaxiality results from the dipolar interactions. The structures of all the ferroelectric configurations of interest are presented in detail. Simple phase diagrams are determined which include different polar and apolar discotic fluids generated by the system. PMID:25353817
Ellipsoids and lightcurves. [for deduction of physical properties of asteroids
NASA Technical Reports Server (NTRS)
Connelly, R.; Ostro, S. J.
1984-01-01
The determination of the light curve (LC) of a geometrically scattering ellipsoid is considered in relation to the problem of investigating the physical properties of asteroids. A simple concise formula is derived for the area of a projection of an ellipsoid, and this expression is used to obtain a general formula for the projected, visible, illuminated area of a triaxial ellipsoid for arbitrary sun-earth-asteroid geometry. It is found that the LC of an ellipsoid has special properties that can be exploited to test the hypothesis that a given optical or radar LC could be due to a geometrically scattering ellipsoid.
Inertial modes in a rotating triaxial ellipsoid
Vantieghem, S.
2014-01-01
In this work, we present an algorithm that enables computation of inertial modes and their corresponding frequencies in a rotating triaxial ellipsoid. The method consists of projecting the inertial mode equation onto finite-dimensional bases of polynomial vector fields. It is shown that this leads to a well-posed eigenvalue problem, and hence, that eigenmodes are of polynomial form. Furthermore, these results shed new light onto the question whether the eigenmodes form a complete basis, i.e. whether any arbitrary velocity field can be expanded in a sum of inertial modes. Finally, we prove that two intriguing integral properties of inertial modes in rotating spheres and spheroids also extend to triaxial ellipsoids. PMID:25104908
ABJM on ellipsoid and topological strings
NASA Astrophysics Data System (ADS)
Hatsuda, Yasuyuki
2016-07-01
It is known that the large N expansion of the partition function in ABJM theory on a three-sphere is completely determined by the topological string on local Hirzebruch surface {F}_0 . In this note, we investigate the ABJM partition function on an ellipsoid, which has a conventional deformation parameter b. Using 3d mirror symmetry, we find a remarkable relation between the ellipsoid partition function for b 2 = 3 (or b 2 = 1 /3) in ABJM theory at k = 1 and a matrix model for the topological string on another CalabiYau threefold, known as local {P}^2 . As in the case of b = 1, we can compute the full large N expansion of the partition function in this case. This is the first example of the complete large N solution in ABJM theory on the squashed sphere. Using the obtained results, we also analyze the supersymmetric Rényi entropy.
NASA Astrophysics Data System (ADS)
Hu, Xuanyu
2016-06-01
The spherical and ellipsoidal harmonic series of the external gravitational potential for a given mass distribution are equivalent in their mutual region of uniform convergence. In an instructive case, the equality of the two series on the common coordinate surface of an infinitely large sphere reveals the exact correspondence between the spherical and ellipsoidal harmonic coefficients. The transformation between the two sets of coefficients can be accomplished via the numerical methods by Walter (Celest Mech 2:389-397, 1970) and Dechambre and Scheeres (Astron Astrophys 387:1114-1122, 2002), respectively. On the other hand, the harmonic coefficients are defined by the integrals of mass density moments in terms of the respective solid harmonics. This paper presents general algebraic formulas for expressing the solid ellipsoidal harmonics as a linear combination of the corresponding solid spherical harmonics. An exact transformation from spherical to ellipsoidal harmonic coefficients is found by incorporating these connecting expressions into the density integral. A computational procedure is proposed for the transformation. Numerical results based on the nearly ellipsoidal Martian moon, Phobos, are presented for validation of the method.
Aberrations of ellipsoidal reflectors for unit magnification.
Mielenz, K D
1974-12-01
Ellipsoidal reflectors are useful for the 1:1 imaging of small objects without spherical and chromatic aberration. The magnitude of the off-axis aberrations of such reflectors is computed by application of Fermat's principle to the Hamiltonian point characteristic. The limiting form of the mirror aperture for which these aberrations do not exceed a set tolerance is an ellipse whose semiaxes depend on object size and angle of incidence. PMID:20134811
Resonant response of electromagnetic scattering from ellipsoid
NASA Astrophysics Data System (ADS)
Gavriloaia, Mihai-Bogdan; Vizireanu, Constantin-Radu; Neamtu, Catalin; Preda, Radu; Achimescu, Emanuel; Halunga, Simona
2015-02-01
Modern radars must provide in a very short time: existence, mobility and shape of objects evolving in airspace. Evaluation of the object shapes through active research by using synthetic aperture radar is limited in time, resolution, and cost. A new way of processing non-stationary signals is presented in this article. Signals are obtained from the reflection of the electromagnetic field by objects with complex shape when they are irradiated with linear frequency modulated signals. The amplitude of reflected signal is variable on the radio-impulse duration depending on object shape, causing a certain electromagnetic signature. This phenomenon is caused by specific electromagnetic resonance. The reflected signal has maximum amplitude when the frequency of the incident wave is the same with the resonant frequency of the investigated object. The structure of an radar target can be decomposed into simple geometric shapes such as spheres, ellipsoids, prisms, and so on. Using resonant effect that ensures pattern recognition is exemplified by an object with an aerodynamic profile accepted in many component elements of the aircraft, namely - an ellipsoid. It is a geometric shape used extensively in aviation, because it has a very low aerodynamic resistance. The resonant response of ellipsoid is evaluated in a decade frequency band, but the pattern recognition of this shape is enough for an octave band. The resonant response is assessed for cross polarization of incident electromagnetic field, as well. As a result, the radio-impulse shape can be used in a data base for pattern recognition.
Elastic granular flows of ellipsoidal particles
NASA Astrophysics Data System (ADS)
Campbell, Charles S.
2011-01-01
Granular flow rheology can be divided into two global regimes: the elastic, which is dominated by force chains, and the inertial, which is nearly free of force chains. As the propensity of a material to form force chains should be strongly influenced by particle shape, this paper is an attempt to assess the effects of shape on flow regime transitions through computer simulations of shear flow of ellipsoidal particles. On one hand, the results show that at a given concentration, ellipsoidal particles generate smaller quasistatic stress than spheres, likely a result of their ability to form denser packings. But at the same time, large aspect ratio ellipsoids more readily form force chains and demonstrate elastic behavior at smaller concentrations than spheres. This is shown to be due to a tradeoff between a shear-induced particle alignment that tends to minimize the interference of the particles and the shear flow, and the particle surface friction, which works to rotate the particles into the flow.
A contour calculation method for rapid freeform reflector construction with ellipsoid patches
NASA Astrophysics Data System (ADS)
Zhuang, Zhenfeng; Yu, Feihong
2014-03-01
This paper presents a contour calculation method (CCM) for the freeform reflector design. Conservation of energy relates the light flux from a Lambertian-type point source to a desired irradiance and a discrete spot distribution on a target plane. This relationship determines the edges of the reflector patches, thus, enabling the design of a non-imaging freeform reflector based on a series of ellipsoid patches modeled as NURBS curves in Rhinoceros. As an example, we present a freeform reflector design composed of 6400 ellipsoid patches to illuminate a surface with 94% uniformity. A computer calculation takes 18.5 s.
Impingement of Water Droplets on an Ellipsoid with Fineness Ratio 5 in Axisymmetric Flow
NASA Technical Reports Server (NTRS)
Dorsch, Robert G.; Brun, Rinaldo J.; Gregg, John L.
1954-01-01
The presence of radomes and instruments that are sensitive to water films or ice formations in the nose section of all-weather aircraft and missiles necessitates a knowledge of the droplet impingement characteristics of bodies of revolution. Because it is possible to approximate many of these bodies with an ellipsoid of revolution, droplet trajectories about an ellipsoid of revolution with a fineness ratio of 5 were computed for incompressible axisymmetric air flow. From the computed droplet trajectories, the following impingement characteristics of the ellipsoid surface were obtained and are presented in terms of dimensionless parameters: (1) total rate of water impingement, (2) extent of droplet impingement zone, (3) distribution of impinging water, and (4) local rate of water impingement.
Polymer translocation into and out of an ellipsoidal cavity.
Polson, James M
2015-05-01
Monte Carlo simulations are used to study the translocation of a polymer into and out of an ellipsoidal cavity through a narrow pore. We measure the polymer free energy F as a function of a translocation coordinate, s, defined to be the number of bonds that have entered the cavity. To study polymer insertion, we consider the case of a driving force acting on monomers inside the pore, as well as monomer attraction to the cavity wall. We examine the changes to F(s) upon variation in the shape anisometry and volume of the cavity, the polymer length, and the strength of the interactions driving the insertion. For athermal systems, the free energy functions are analyzed using a scaling approach, where we treat the confined portion of the polymer to be in the semi-dilute regime. The free energy functions are used with the Fokker-Planck (FP) equation to calculate mean translocation times, as well as translocation time distributions. We find that both polymer ejection and insertion are faster for ellipsoidal cavities than for spherical cavities. The results are in qualitative agreement with those of a Langevin dynamics study in the case of ejection but not for insertion. The discrepancy is likely due to out-of-equilibrium conformational behaviour that is not accounted for in the FP approach. PMID:25956116
Ellipsoidal nested sampling, expression of the model uncertainty and measurement
NASA Astrophysics Data System (ADS)
Palmisano, C.; Mana, G.; Gervino, G.
2015-07-01
The measurand value, the conclusions, and the decisions inferred from measurements may depend on the models used to explain and to analyze the results. In this paper, the problems of identifying the most appropriate model and of assessing the model contribution to the uncertainty are formulated and solved in terms of Bayesian model selection and model averaging. As computational cost of this approach increases with the dimensionality of the problem, a numerical strategy, based on multimodal ellipsoidal nested sampling, to integrate over the nuisance parameters and to compute the measurand post-data distribution is outlined. In order to illustrate the numerical strategy, by use of MATHEMATICA an elementary example concerning a bimodal, two-dimensional distribution has also been studied.
Angle amplifying optics using plane and ellipsoidal reflectors
Glass, Alexander J.
1977-01-01
An optical system for providing a wide angle input beam into ellipsoidal laser fusion target illumination systems. The optical system comprises one or more pairs of centrally apertured plane and ellipsoidal mirrors disposed to accept the light input from a conventional lens of modest focal length and thickness, to increase the angular divergence thereof to a value equivalent to that of fast lenses, and to direct the light into the ellipsoidal target illumination system.
Internal ellipsoidal estimates of reachable set of impulsive control systems
Matviychuk, Oksana G.
2014-11-18
A problem of estimating reachable sets of linear impulsive control system with uncertainty in initial data is considered. The impulsive controls in the dynamical system belong to the intersection of a special cone with a generalized ellipsoid both taken in the space of functions of bounded variation. Assume that an ellipsoidal state constraints are imposed. The algorithms for constructing internal ellipsoidal estimates of reachable sets for such control systems and numerical simulation results are given.
All-around convergent view acquisition system using ellipsoidal mirrors
NASA Astrophysics Data System (ADS)
Takeda, Gentaro; Yendo, Tomohiro; Tehrani, Mehrdad Panahpour; Fujii, Toshiaki; Tanimoto, Masayuki
2010-04-01
In this paper, we present a new image acquisition system for FTV (Free-viewpoint TV). The proposed system can capture the dynamic scene from all-around views. The proposed system consists of two ellipsoidal mirrors, a high-speed camera, and a rotating aslope mirror. As for two ellipsoidal mirrors, the size and the ellipticity are mutually different. The object is set in the focus of ellipsoidal mirror. The size of this system is smaller than that of early system since ellipsoidal mirrors can reduce virtual images. High-speed camera can acquire multi viewpoint images by mirror scanning. Here, we simulated this system with ray tracing and confirmed the principle.
Irrotational and zero angular momentum ellipsoids in the Dirichlet problem
NASA Astrophysics Data System (ADS)
Kondratev, B. P.
1986-05-01
Two classes of new exact solutions are found in the Dirichlet problem of the oscillations of a self-gravitating fluid ellipsoidal mass with linear velocity field. These solutions describe irrotational ellipsoids and ellipsoids with zero angular momentum (which are adjoint in the sense of a theorem due to Dedekind). For elliposoids with stationary boundary surface it is established that irrotational and zero angular momentum figures exist not only when the ellipsoids rotate around the central symmetry axis (Chandrasekhar considered this special case) but also for an inclined position of the rotation axis.
Point cloud uncertainty analysis for laser radar measurement system based on error ellipsoid model
NASA Astrophysics Data System (ADS)
Zhengchun, Du; Zhaoyong, Wu; Jianguo, Yang
2016-04-01
Three-dimensional laser scanning has become an increasingly popular measurement method in industrial fields as it provides a non-contact means of measuring large objects, whereas the conventional methods are contact-based. However, the data acquisition process is subject to many interference factors, which inevitably cause errors. Therefore, it is necessary to precisely evaluate the accuracy of the measurement results. In this study, an error-ellipsoid-based uncertainty model was applied to 3D laser radar measurement system (LRMS) data. First, a spatial point uncertainty distribution map was constructed according to the error ellipsoid attributes. The single-point uncertainty ellipsoid model was then extended to point-point, point-plane, and plane-plane situations, and the corresponding distance uncertainty models were derived. Finally, verification experiments were performed by using an LRMS to measure the height of a cubic object, and the measurement accuracies were evaluated. The results show that the plane-plane distance uncertainties determined based on the ellipsoid model are comparable to those obtained by actual distance measurements. Thus, this model offers solid theoretical support to enable further LRMS measurement accuracy improvement.
An Application Using Triaxial Ellipsoids to Model Martian Dust at the Phoenix Landing Site
NASA Astrophysics Data System (ADS)
Mason, E. L.; Lemmon, M. T.
2014-12-01
Martian atmospheric dust is not spherical and contains irregular shaped particles. This irregularity adds complexity to models determining radiative heating of the atmosphere. Particle size has been studied extensively with remote sensing, but particle shape is still poorly understood. Bi et al. show that an assortment of triaxial ellipsoids provides a good analog for the scattering properties of terrestrial dust aerosols. In addition Z. Meng et al. (2010) have developed a database containing single-scattering properties of irregularly shaped dust particles with pre-defined microphysical and optical parameters. The tabulation allows quick and efficient use of the results from time-consuming models and can be applied to the Martian atmosphere. The landing site for Phoenix was in a region that fell within the northern seasonal ice cap and was active during a period of large dust upwelling. The lander's Surface Stereo Imager performed several cross-sky brightness surveys to constrain the size distribution and scattering and absorption properties of the airborne dust in the Martian northern polar environment. Using the database, single scattering properties adapted to the Martian atmosphere can be used to determine bulk scattering properties of the medium at the Phoenix landing site. We will present a comparison of triaxial ellipsoids with spheroidal models using Phoenix spectrophotometric data and show that triaxial ellipsoid properties can produce a good fit to the observed data. In addition we will provide initial results of polarization to test the triaxial ellipsoid hypothesis.
Granular gas of ellipsoids: analytical collision detection implemented on GPUs
NASA Astrophysics Data System (ADS)
Rubio-Largo, S. M.; Lind, P. G.; Maza, D.; Hidalgo, R. C.
2015-06-01
We present a hybrid GPU-CPU implementation of an accurate discrete element model for a system of ellipsoids. The ellipsoids have three translational degrees of freedom, their rotational motion being described through quaternions and the contact interaction between two ellipsoids is described by a force which accounts for the elastic and dissipative interactions. Further we combine the exact derivation of contact points between ellipsoids (Wang et al. in Computing 72(1-2):235-246, 2004) with the advantages of the GPU-NVIDIA parallelization strategy (Owens et al. in Comput Graph Forum 26:80-113, 2007). This novelty makes the analytical algorithm computationally feasible when dealing with several thousands of particles. As a benchmark, we simulate a granular gas of frictionless ellipsoids identifying a classical homogeneous cooling state for ellipsoids. For low dissipative systems, the behavior of the granular temperature indicates that the cooling dynamics is governed by the elongation of the ellipsoids and the restitution coefficient. Our outcomes comply with the statistical mechanical laws and the results are in agreement with previous findings for hard ellipsoids (Bereolos et al. in J Chem Phys 99:6087, 1993; Villemot and Talbot in Granul Matter 14:91-97, 2012). Additionally, new insight is provided namely suggesting that the mean field description of the cooling dynamics of elongated particles is conditioned by the particle shape and the degree of energy equipartition.
Design considerations regarding ellipsoidal mirror based reflectometers.
Benson, Michael R; Marciniak, Michael A
2013-11-18
Hemi-ellipsoidal mirrors are used in reflection-based measurements due to their ability to collect light scattered from one focal point at the other. In this paper, a radiometric model of this energy transfer is derived for arbitrary mirror and detector geometries. This model is used to examine the imaging characteristics of the mirror away from focus for both diffuse and specular light. The radiometric model is applied to several detector geometries for measuring the Directional Hemispherical Reflectance for both diffuse and specular samples. The angular absorption characteristics of the detector are then applied to the measurement to address measurement accuracy for diffuse and specular samples. Examining different detector configurations shows the effectiveness of flat detectors at angles ranging from normal to 50°, and that multifaceted detectors can function from normal incidence to grazing angles. PMID:24514271
Quantum steering ellipsoids, extremal physical states and monogamy
NASA Astrophysics Data System (ADS)
Milne, Antony; Jevtic, Sania; Jennings, David; Wiseman, Howard; Rudolph, Terry
2014-08-01
Any two-qubit state can be faithfully represented by a steering ellipsoid inside the Bloch sphere, but not every ellipsoid inside the Bloch sphere corresponds to a two-qubit state. We give necessary and sufficient conditions for when the geometric data describe a physical state and investigate maximal volume ellipsoids lying on the physical-unphysical boundary. We derive monogamy relations for steering that are strictly stronger than the Coffman-Kundu-Wootters (CKW) inequality for monogamy of concurrence. The CKW result is thus found to follow from the simple perspective of steering ellipsoid geometry. Remarkably, we can also use steering ellipsoids to derive non-trivial results in classical Euclidean geometry, extending Euler's inequality for the circumradius and inradius of a triangle.
Post-Newtonian reference ellipsoid for relativistic geodesy
NASA Astrophysics Data System (ADS)
Kopeikin, Sergei; Han, Wenbiao; Mazurova, Elena
2016-02-01
We apply general relativity to construct the post-Newtonian background manifold that serves as a reference spacetime in relativistic geodesy for conducting a relativistic calculation of the geoid's undulation and the deflection of the plumb line from the vertical. We chose an axisymmetric ellipsoidal body made up of a perfect homogeneous fluid uniformly rotating around a fixed axis, as a source generating the reference geometry of the background manifold through Einstein's equations. We then reformulate and extend hydrodynamic calculations of rotating fluids done by a number of previous researchers for astrophysical applications to the realm of relativistic geodesy to set up algebraic equations defining the shape of the post-Newtonian reference ellipsoid. To complete this task, we explicitly perform all integrals characterizing gravitational field potentials inside the fluid body and represent them in terms of the elementary functions depending on the eccentricity of the ellipsoid. We fully explore the coordinate (gauge) freedom of the equations describing the post-Newtonian ellipsoid and demonstrate that the fractional deviation of the post-Newtonian level surface from the Maclaurin ellipsoid can be made much smaller than the previously anticipated estimate based on the astrophysical application of the coordinate gauge advocated by Bardeen and Chandrasekhar. We also derive the gauge-invariant relations of the post-Newtonian mass and the constant angular velocity of the rotating fluid with the parameters characterizing the shape of the post-Newtonian ellipsoid including its eccentricity, a semiminor axis, and a semimajor axis. We formulate the post-Newtonian theorems of Pizzetti and Clairaut that are used in geodesy to connect the geometric parameters of the reference ellipsoid to the physically measurable force of gravity at the pole and equator of the ellipsoid. Finally, we expand the post-Newtonian geodetic equations describing the post-Newtonian ellipsoid to
Jiang, Jun; Mitroy, J.; Cheng, Yongjun; Bromley, M.W.J.
2015-01-15
Effective oscillator strength distributions are systematically generated and tabulated for the alkali atoms, the alkaline-earth atoms, the alkaline-earth ions, the rare gases and some miscellaneous atoms. These effective distributions are used to compute the dipole, quadrupole and octupole static polarizabilities, and are then applied to the calculation of the dynamic polarizabilities at imaginary frequencies. These polarizabilities can be used to determine the long-range C{sub 6}, C{sub 8} and C{sub 10} atom–atom interactions for the dimers formed from any of these atoms and ions, and we present tables covering all of these combinations.
ERIC Educational Resources Information Center
Lee, Sik-Yum; Xia, Ye-Mao
2006-01-01
By means of more than a dozen user friendly packages, structural equation models (SEMs) are widely used in behavioral, education, social, and psychological research. As the underlying theory and methods in these packages are vulnerable to outliers and distributions with longer-than-normal tails, a fundamental problem in the field is the…
Shape and gravitational field of the ellipsoidal satellites
NASA Astrophysics Data System (ADS)
Gao, BuXi; Huang, Yong
2014-10-01
The shape and gravitational field of ellipsoidal satellites are studied by using the tidal theory. For ellipsoidal satellites, the following conclusions were obtained: Firstly, in the early stage of the satellite formation, strong tidal friction allowed the satellites move in a synchronous orbit and evolve into a triaxial ellipsoidal shape. Because the tidal potential from the associated primary and the centrifugal potential from the satellite spin are nearly fixed at the surface, the early satellites are the viscoelastic celestial body, and their surfaces are nearly in the hydrostatic equilibrium state. The deformation is fixed in the surface of the satellite. By using the related parameters of primary and satellite, the tidal height and the theoretical lengths of three primary radii of the ellipsoidal satellite are calculated. Secondly, the current ellipsoidal satellites nearly maintain their ellipsoidal shape from solidification, which happened a few billion years ago. According to the satellite shape, we estimated the orbital period and spinning angular velocity, and then determined the evolution of the orbit. Lastly, assuming an ellipsoidal satellite originated in the hydrostatic equilibrium state, the surface shape could be determined by tidal, rotation, and additional potentials. However, the shape of the satellite's geoid differs from its surface shape. The relationship between these shapes is discussed and a formula for the gravitational harmonic coefficients is presented.
Heterogeneous nucleation on surfaces of the ellipsoid of rotation
NASA Astrophysics Data System (ADS)
Li, Xiang-Ming; Liu, Qing-Hui
2016-08-01
This paper focusses on the heterogeneous nucleation on the surface with the non-constant curvature. The formation of a spherical nucleus on the ellipsoid of rotation is considered. Following the classical nucleation theory, the work of formation of a critical nucleus on the ellipsoid of rotation has been given, and the effects of geometry sizes and the material properties of the ellipsoid of rotation on the work of formation of a critical nucleus have been obtained. When the geometry size of the substrate is about value of the critical nucleus radius, there may exist twice nucleation on the ellipsoid of rotation for the case of the smaller value of λ and ϕ < π / 2. As the work of formation of a nucleus has only one extremum (the maximum), the nucleation on the oblate rotational ellipsoid is more easy than on the spherical surface, while nucleation on the prolate ellipsoid of rotation is more difficult than on the spherical surface. Furthermore, if the particles of the ellipsoid are added into the parent phase as nucleation agents or catalysts, for some geometry sizes, they would not have the effects on the heterogeneous nucleation.
Achromatic axially symmetric wave plate.
Wakayama, Toshitaka; Komaki, Kazuki; Otani, Yukitoshi; Yoshizawa, Toru
2012-12-31
An achromatic axially symmetric wave plate (AAS-WP) is proposed that is based on Fresnel reflections. The wave plate does not introduce spatial dispersion. It provides retardation in the wavelength domain with an axially symmetric azimuthal angle. The optical configuration, a numerical simulation, and the optical properties of the AAS-WP are described. It is composed of PMMA. A pair of them is manufactured on a lathe. In the numerical simulation, the achromatic angle is estimated and is used to design the devices. They generate an axially symmetric polarized beam. The birefringence distribution is measured in order to evaluate the AAS-WPs. PMID:23388751
Chaotic Mixing around a Quasigeostrophic Ellipsoidal Vortex
NASA Astrophysics Data System (ADS)
Miyazaki, T.; Yamamoto, M.
2002-05-01
In geophysical flows, coherent vortex structures persist for long time and they dominate both the dynamics and the scalar transport of geophysical turbulence. Meacham et al.1,2) obtained a series of exact unsteady solution of the quasigeostrophic equation, which represents a uniform ellipsoidal vortex patch embedded in a uniform 3D shear field. These solutions are natural extension of the well known 2D Kirchhoff-Moore & Saffman-Kida elliptical vortices. The motion of fluid particles around a 2D elliptical vortex patch in an external shear flow has been investigated both numerically by Polvani & Wisdom3) and Dahleh4) and analytically by Kawakami & Funakoshi5). Chaotic mixing occurs in the regions near the heteroclinic orbits of the Poincare map of particle locations after every vortex rotation period and the chaotic region expands wider and wider as the strain increases. In this paper, the motion of fluid particle around an ellipsoidal vortex (almost a tilted spheroid) in an external 3D shear flow is examined analytically and numerically. When a spheroidal vortex is embedded in an otherwise quiescent fluid, it rotates rigidly with a constant angular velocity Ω 0, which is a function of the aspect ratio. A fluid particle moves along a streamline in the coordinate system rotating with the spheroid. There are two saddles and heteroclinic orbits connecting them on the horizontal plane z=0 including the vortex center. The heteroclinic orbits change into homoclinic orbits on the horizontal plane slightly off center (z>0). One saddle becomes a node as z increases but the other remains to be a saddle with homoclinic orbits on the horizontal plane which intersects the vortex. We impose such perturbations as, 1) deformation to slightly non-spheroidal ellipsoid, 2) uniform horizontal strain and 3) uniform vertical shear on the tilted spheroidal vortex. In order to show the appearance of the chaotic motion analytically, we apply Melnikov's method to the perturbed system. The
NASA Technical Reports Server (NTRS)
Bilharz, Herbert; Hoelder, Ernst
1947-01-01
The present report concerns a method of computing the velocity and pressure distributions on bodies of revolution in axially symmetrical flow in the subsonic range. The differential equation for the velocity potential Phi of a compressible fluid motion is linearized tn the conventional manner, and then put in the form Delta(Phi) = 0 by affine transformation. The quantity Phi represents the velocity potential of a fictitious incompressible flow, for which a constant superposition of sources by sections is secured by a method patterned after von Karman which must comply with the boundary condition delta(phi)/delta(n) = 0 at the originally specified contour. This requirement yields for the "pseudo-stream function" psi a differential equation which must be fulfilled for as many points on the contour as source lengths are assumed. In this manner, the problem of defining the still unknown source intensities is reduced to the solution of an inhomogeneous equation system. The pressure distribution is then determined with the aid of Bernoulli's equation and adiabatic equation of state. Lastly, the pressure distributions in compressible and incompressible medium are compared on a model problem.
Stitching interferometry for ellipsoidal x-ray mirrors.
Yumoto, Hirokatsu; Koyama, Takahisa; Matsuyama, Satoshi; Yamauchi, Kazuto; Ohashi, Haruhiko
2016-05-01
Ellipsoidal mirrors, which can efficiently produce a two-dimensional focusing beam with a single mirror, are superior x-ray focusing optics, especially when compared to elliptical-cylinder mirrors in the Kirkpatrick-Baez geometry. However, nano-focusing ellipsoidal mirrors are not commonly used for x-ray optics because achieving the accuracy required for the surface metrology of nano-focusing ellipsoidal mirrors is difficult due to their small radius of curvature along the short ellipsoidal axis. Here, we developed a surface metrology system for nano-focusing ellipsoidal mirrors using stitching interferometric techniques. The developed system simultaneously measures sub-aperture shapes with a microscopic interferometer and the tilt angles of the sub-aperture shapes with a large Fizeau interferometer. After correcting the systematic errors included in the sub-aperture shapes, the entire mirror shape is calculated by stitching the sub-aperture shapes based on the obtained relative angles between partially overlapped sub-apertures. In this study, we developed correction methods for systematic errors in sub-aperture shapes that originated from off-axis aberrations produced in the optics of the microscopic interferometer. The systematic errors on an ellipsoidal mirror were estimated by measuring a series of tilted plane substrates and the ellipsoidal substrate. From measurements of an ellipsoidal mirror with a 3.6-mm radius of curvature at the mirror center, we obtained a measurement repeatability of 0.51 nm (root-mean-square) in an assessment area of 0.5 mm × 99.18 mm. This value satisfies the requirements for surface metrology of nano-focusing x-ray mirrors. Thus, the developed metrology system should be applicable for fabricating nano-focusing ellipsoidal mirrors. PMID:27250377
Elliptical instability of compressible flow in ellipsoids
NASA Astrophysics Data System (ADS)
Clausen, N.; Tilgner, A.
2014-02-01
Context. Elliptical instability is due to a parametric resonance of two inertial modes in a fluid velocity field with elliptical streamlines. This flow is a simple model of the motion in a tidally deformed, rotating body. Elliptical instability typically leads to three-dimensional turbulence. The associated turbulent dissipation together with the dissipation of the large scale mode may be important for the synchronization process in stellar and planetary binary systems. Aims: In order to determine the influence of the compressibility on the stability limits of tidal flows in stars or planets, we calculate the growth rates of perturbations in flows with elliptical streamlines within ellipsoidal boundaries of small ellipticity. In addition, the influence of the orbiting frequency of the tidal perturber ΩP and the viscosity of the fluid are taken into account. Methods: We studied the linear stability of the flow to determine the growth rates. We solved the Euler equation and the continuity equation. The viscosity was introduced heuristically in our calculations. We assumed a power law for the radial dependence of the background density. Together with the use of the anelastic approximation, this enabled us to use semi-analytical methods to solve the equations. Results: It is found that the growth rate of a certain mode combination depends on the compressibility. However, the influence of the compressibility is negligible for the growth rate maximized over all possible modes if viscous bulk damping effects can be neglected. The growth rate maximized over all possible modes determines the stability of the flow. The stability limit for the compressible fluid confined to an ellipsoid is the same as for incompressible fluid in an unbounded domain. Depending on the ratio ΩP/ΩF, with ΩF the spin rate of the central object in the frame of the rotating tidal perturber, certain pairs of modes resonate with each other. The size of the bulk damping term depends on the modes
Anisotropic materials appearance analysis using ellipsoidal mirror
NASA Astrophysics Data System (ADS)
Filip, Jiří; Vávra, Radomír.
2015-03-01
Many real-world materials exhibit significant changes in appearance when rotated along a surface normal. The presence of this behavior is often referred to as visual anisotropy. Anisotropic appearance of spatially homogeneous materials is commonly characterized by a four-dimensional BRDF. Unfortunately, due to simplicity most past research has been devoted to three dimensional isotropic BRDFs. In this paper, we introduce an innovative, fast, and inexpensive image-based approach to detect the extent of anisotropy, its main axes and width of corresponding anisotropic highlights. The method does not rely on any moving parts and uses only an off-the-shelf ellipsoidal reflector with a compact camera. We analyze our findings with a material microgeometry scan, and present how results correspond to the microstructure of individual threads in a particular fabric. We show that knowledge of a material's anisotropic behavior can be effectively used in order to design a material-dependent sampling pattern so as the material's BRDF could be measured much more precisely in the same amount of time using a common gonioreflectometer.
Computational study of the optical trapping of ellipsoidal particles
Simpson, Stephen H.; Hanna, Simon
2011-11-15
Ellipsoidal dielectric particles may be trapped in a linearly polarized Gaussian beam such that they are harmonically bound with respect to each of their rotational and translational degrees of freedom. The ellipsoid belongs to the highest symmetry class for which this is possible. Typically, the longest axis of the ellipsoid aligns itself with the incident beam axis and the second longest with the polarization direction. We investigate this special property by evaluating the trap stiffness matrix for dielectric ellipsoids with aspect ratios (largest:smallest dimension) in the range 1-10, using the discrete dipole approximation. The results are interpreted using a simple phenomenological model and conclusions are drawn concerning optimization of the trap stiffness for specific applications.
Cartesian to geodetic coordinates conversion on a triaxial ellipsoid
NASA Astrophysics Data System (ADS)
Ligas, Marcin
2012-04-01
A new method of transforming Cartesian to geodetic (or planetographic) coordinates on a triaxial ellipsoid is presented. The method is based on simple reasoning coming from essentials of vector calculus. The reasoning results in solving a nonlinear system of equations for coordinates of the point being the projection of a point located outside or inside a triaxial ellipsoid along the normal to the ellipsoid. The presented method has been compared to a vector method of Feltens (J Geod 83:129-137, 2009) who claims that no other methods are available in the literature. Generally, our method turns out to be more accurate, faster and applicable to celestial bodies characterized by different geometric parameters. The presented method also fits to the classical problem of converting Cartesian to geodetic coordinates on the ellipsoid of revolution.
AirMSPI PODEX Big Sur Ellipsoid Images
Atmospheric Science Data Center
2013-12-11
... AirMSPI Browse Images from the PODEX 2013 Campaign Big Sur target 02/03/2013 Ellipsoid-projected Select ... Version number For more information, see the Data Product Specifications (DPS) ...
Automated composite ellipsoid modelling for high frequency GTD analysis
NASA Technical Reports Server (NTRS)
Sze, K. Y.; Rojas, R. G.; Klevenow, F. T.; Scheick, J. T.
1991-01-01
The preliminary results of a scheme currently being developed to fit a composite ellipsoid to the fuselage of a helicopter in the vicinity of the antenna location are discussed under the assumption that the antenna is mounted on the fuselage. The parameters of the close-fit composite ellipsoid would then be utilized as inputs into NEWAIR3, a code programmed in FORTRAN 77 for high frequency Geometrical Theory of Diffraction (GTD) Analysis of the radiation of airborne antennas.
NASA Astrophysics Data System (ADS)
Ma, Chi-Tang; Chou, Kao-Hsu; Chen, Yi-Yung; Whang, Allen Jong-Woei; Chen, Kuan-Yu
2010-05-01
Due to the energy crisis, the issue about how to improve the efficiency of lighting gains popularity. Many researches focus on using LED to be the light source of car lamps because LED has the advantages, such as low power consumption, adjustable luminous intensity, high color rendering index, long lifetime, and short reaction time, and the car lamps will become smaller and lighter. In our design, the LED headlamp consists three parts: a double ellipsoidal reflector, an aspherical lens, and a baffle. The double ellipsoidal reflector can improve the luminous flux in front of the headlamp and provide adequate illumination; the aspherical lens can eliminate spherical aberration; and the designed location of baffle can solve the glare problems. According to the optical simulation, the design successfully fits the request of intensity distribution in the ECE regulation.
NASA Technical Reports Server (NTRS)
Fu, L. S. W.
1982-01-01
The scattering of a single ellipsoidal inhomogeneity is studied via an eigenstrain approach. The displacement field is given in terms of volume integrals that involve eigenstrains that are related to mismatch in mass density and that in elastic moduli. The governing equations for these unknown eigenstrains are derived. Agreement with other approaches for the scattering problem is shown. The formulation is general and both the inhomogeneity and the host medium can be anisotrophic. The axisymmetric scattering of an ellipsoidal inhomogeneity in a linear elastic isotropic medium is given as an example. The angular and frequency dependence of the scattered displacement field, the differential and total cross sections are formally given in series expansions for the case of uniformly distributed eigenstrains.
Wave-optical assessment of alignment tolerances in nano-focusing with ellipsoidal mirror
NASA Astrophysics Data System (ADS)
Yumoto, Hirokatsu; Koyama, Takahisa; Matsuyama, Satoshi; Yamauchi, Kazuto; Ohashi, Haruhiko
2016-01-01
High-precision ellipsoidal mirrors, which can efficiently focus X-rays to the nanometer dimension with a mirror, have not been realized because of the difficulties in the fabrication process. The purpose of our study was to develop nano-focusing ellipsoidal mirrors in the hard X-ray region. We developed a wave-optical focusing simulator for investigating alignment tolerances in nano-focusing with a designed ellipsoidal mirror, which produce a diffraction-limited focus size of 30 × 35 nm2 in full width at half maximum at an X-ray energy of 7 keV. The simulator can calculate focusing intensity distributions around the focal point under conditions of misalignment. The wave-optical simulator enabled the calculation of interference intensity distributions, which cannot be predicted by the conventional ray-trace method. The alignment conditions with a focal length error of ≲ ±10 µm, incident angle error of ≲ ±0.5 µrad, and in-plane rotation angle error of ≲ ±0.25 µrad must be satisfied for nano-focusing.
Numerical study on dielectrophoretic chaining of two ellipsoidal particles.
House, Dustin L; Luo, Haoxiang; Chang, Siyuan
2012-05-15
Electric field-induced assembly of biological and synthetic particles has proven useful in two- and three-dimensional fabrication of composite materials, microwires, photonic crystals, artificial tissues, and more. Biological particles are typically irregularly shaped, and using non-spherical synthetic particles has the ability to expand current applications. However, there is much to be understood about the dielectrophoretic (DEP) interaction that takes place between particles of general shape. In this work, we numerically study the DEP interaction between two prolate spheroid particles suspended in an unbounded fluid. The boundary-element method (BEM) is applied to solve the coupled electric field, Stokes flow, and particle motion, and the DEP forces are obtained by integrating the Maxwell stress tensor over the particle surfaces. Effects of the initial configuration and aspect ratio are investigated. Results show that the particles go through a self-rotation process, that is, electro-orientation, while translating slowly to form a chain pair. The final formation resembles the chaining pattern observed previously in experiments using densely distributed ellipsoidal particles. Thus, the transient behavior and particle-particle interaction exhibited in the current study could be used as the fundamental mechanism to explain the phenomenon in the experiment. PMID:22340950
NASA Astrophysics Data System (ADS)
Cattabiani, Alessandro; Barbarulo, Andrea; Riou, Hervé; Ladevèze, Pierre
2015-12-01
Recently, interest of aerospace and automotive industries on medium-frequency vibrational behavior of composite shell structures has grown due to their high specific stiffness and fatigue resistance. Conventional methods such as the finite element method and the statistical energy analysis are not suitable for the medium-frequency bandwidth. Conversely, the variational theory of complex rays (VTCR) is taking place as an ad-hoc technique to tackle such frequency band. It is a Trefftz method based on a weak variational formulation. Equilibrium equations are met using exact solutions as shape functions. The variational problem imposes boundary conditions in weak form. The present paper extends VTCR to orthotropic shell structures. Moreover, several new enhancements are introduced. Now, we use a quasi-symmetric ray distribution which can greatly reduce computational costs, and addresses in-plane inertia which was neglected in previous works. Some relevant numerical examples are presented to show the strategy and results are compared with a FEM reference to study performances.
Symmetric Novikov superalgebras
Ayadi, Imen; Benayadi, Saied
2010-02-15
We study Novikov superalgebras with nondegenerate associative supersymmetric bilinear forms which are called symmetric Novikov superalgebras. We show that Novikov symmetric superalgebras are associative superalgebras with additional condition. Several examples of symmetric Novikov superalgebras are included, in particular, examples of symmetric Novikov superalgebras which are not 2-nilpotent. Finally, we introduce some notions of double extensions in order to give inductive descriptions of symmetric Novikov superalgebras.
Self-Assembly of Diblock Copolymers in Half-Ellipsoid-Shape Confinements
NASA Astrophysics Data System (ADS)
Park, So Jung; Kim, Myong-Hyun; Lee, Dagam; Kim, Jin Kon; Kim, Jaeup
2014-03-01
AB block copolymers can assemble into various nanoscale morphologies such as lamella, cylinder, sphere and gyroid depending on their composition and the interaction strength. In this work, we theoretically study various block copolymer morphologies in hemispherical and ellipsoidal shape confinements and compare the results with experiments. In the experiment, PS-PMMA block copolymers are physically confined by air and surface of nanobowl which interacts preferentially or randomly depending on the coating of the nanobowl. Our theoretical modeling uses self-consistent field theory (SCFT) which calculates the mean field density distribution of AB block copolymers in this confined geometry. The key parameters for the morphology determination are the size and shape of the container and the surface tension between components. For example, when the container wall is coated with PS polymers, onion-shape lamellar phase with PS at the bottom is observed rather than the parallel lamella r phase. It is also found that preferential air-polymer surface interaction promotes the alignment of domains. Our versatile method allows us to model ellipsoid-shaped confinements, and other interesting morphologies are found depending on the eccentricity of the ellipsoid. This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (no. 2012R1A1A2043633).
A Model with Ellipsoidal Scatterers for Polarimetric Remote Sensing of Anisotropic Layered Media
NASA Technical Reports Server (NTRS)
Nghiem, S. V.; Kwok, R.; Kong, J. A.; Shin, R. T.
1993-01-01
This paper presents a model with ellipsoidal scatterers for applications to polarimetric remote sensing of anisotropic layered media at microwave frequencies. The physical configuration includes an isotropic layer covering an anisotropic layer above a homogeneous half space. The isotropic layer consists of randomly oriented spheroids. The anisotropic layer contains ellipsoidal scatterers with a preferential vertical alignment and random azimuthal orientations. Effective permittivities of the scattering media are calculated with the strong fluctuation theory extended to account for the nonspherical shapes and the scatterer orientation distributions. On the basis of the analytic wave theory, dyadic Green's functions for layered media are used to derive polarimetric backscattering coefficients under the distorted Born approximation. The ellipsoidal shape of the scatterers gives rise to nonzero cross-polarized returns from the untilted anisotropic medium in the first-order approximation. Effects of rough interfaces are estimated by an incoherent addition method. Theoretical results and experimental data are matched at 9 GHz for thick first-year sea ice with a bare surface and with a snow cover at Point Barrow, Alaska. The model is then used to study the sensitivity of polarimetric backscattering coefficients with respect to correlation lengths representing the geometry of brine inclusions. Polarimetric signatures of bare and snow-covered sea ice are also simulated based on the model to investigate effects of different scattering mechanisms.
NASA Astrophysics Data System (ADS)
Wang, Yuan; Wu, Linhui; Jia, Mengyu; Liu, Lingling; Zhao, Huijuan; Gao, Feng
2013-03-01
As a new non-invasive medical imaging technology, diffuse optical tomography (DOT) has received considerable attention that can provide vast quantities of functional information of tissues. The reconstruction problem of DOT is highly ill-posed, meaning that a small error in the measurement data can bring about drastic errors of the reconstruction optical properties. In this paper, the shape-based image reconstruction algorithm of DOT is proposed for reducing the ill-poseness under the assumption that the optical properties of target region distribute uniformly. Since some human organs and tumors can be simplified as an ellipsoid, in this paper, the shape of the inhomogeneity is described as an ellipsoid. In the forward problem, the boundary element method (BEM) is implemented to solve the continuous wave diffusion equation (DE). By the use of the ellipsoid parametric method, the description of the shape, location and optical properties of the inhomogeneity, and the value of the background could be realized with only a small number of parameters. In the inverse calculation, a Levenberg-Marquardt algorithm with line searching is implemented to solve the underlying nonlinear least-squares problem. Simulation results show that the algorithm developed in this paper is effective in reducing the ill-poseness and robust to the noise.
Ellipsoids beat Spheres: Experiments with Candies, Colloids and Crystals
NASA Astrophysics Data System (ADS)
Chaikin, Paul
2006-04-01
How many gumballs fit in the glass sphere of a gumball machine? Scientists have been puzzling over problems like this since the Ancient Greeks. Yet it was only recently proven that the standard way of stacking oranges at a grocery store--with one orange on top of each set of three below--is the densist packing for spheres, with a packing fraction φ˜ 0.74. Random (amorphous) packings of spheres have a lower density, with φ ˜0.64. The density of crystalline and random packings of atoms is intimately related to the melting transition in matter. We have studied the crystal-liquid transition in spherical colloidal systems on earth and in microgravity. The simplest objects to study after spheres are squashed spheres -- ellipsoids. Surprisingly we find that ellipsoids can randomly pack more densely than spheres, up to φ˜0.68 - 0.71 for a shape close to that of M&M's^ Candies, and even approach φ˜0.75 for general ellipsoids. The higher density relates directly to the higher number of neighbors needed to prevent the more asymetric ellipsoid from rotating. We have also found the ellipsoids can be packed in a crystalline array to a density, φ˜.7707 which exceeds the highest previous packing. Our findings provide insights into granular materials, rigidity, crystals and glasses, and they may lead to higher quality ceramic materials.
Dispersions of ellipsoidal particles in a nematic liquid crystal.
Tasinkevych, Mykola; Mondiot, Frédéric; Mondain-Monval, Olivier; Loudet, Jean-Christophe
2014-03-28
Colloidal particles dispersed in a partially ordered medium, such as a liquid crystal (LC) phase, disturb its alignment and are subject to elastic forces. These forces are long-ranged, anisotropic and tunable through temperature or external fields, making them a valuable asset to control colloidal assembly. The latter is very sensitive to the particle geometry since it alters the interactions between the colloids. We here present a detailed numerical analysis of the energetics of elongated objects, namely prolate ellipsoids, immersed in a nematic host. The results, complemented with qualitative experiments, reveal novel LC configurations with peculiar topological properties around the ellipsoids, depending on their aspect ratio and the boundary conditions imposed on the nematic order parameter. The latter also determine the preferred orientation of ellipsoids in the nematic field, because of elastic torques, as well as the morphology of particle aggregates. PMID:24651907
Microscopic analysis of Hopper flow with ellipsoidal particles
NASA Astrophysics Data System (ADS)
Liu, Sida; Zhou, Zongyan; Zou, Ruiping; Pinson, David; Yu, Aibing
2013-06-01
Hoppers are widely used in process industries. With such widespread application, difficulties in achieving desired operational behaviors have led to extensive experimental and mathematical studies in the past decades. Particularly, the discrete element method has become one of the most important simulation tools for design and analysis. So far, most studies are on spherical particles for computational convenience. In this work, ellipsoidal particles are used as they can represent a large variation of particle shapes. Hopper flow with ellipsoidal particles is presented highlighting the effect of particle shape on the microscopic properties.
Force-coupling method for flows with ellipsoidal particles
NASA Astrophysics Data System (ADS)
Liu, D.; Keaveny, E. E.; Maxey, M. R.; Karniadakis, G. E.
2009-06-01
The force-coupling method, previously developed for spherical particles suspended in a liquid flow, is extended to ellipsoidal particles. In the limit of Stokes flow, there is an exact correspondence with known analytical results for isolated particles. More generally, the method is shown to provide good approximate results for the particle motion and the flow field both in viscous Stokes flow and at finite Reynolds number. This is demonstrated through comparison between fully resolved direct numerical simulations and results from the numerical implementation of the force-coupling method with a spectral/hp element scheme. The motion of settling ellipsoidal particles and neutrally buoyant particles in a Poiseuille flow are discussed.
The generalized Mollweide projection of the biaxial ellipsoid
NASA Astrophysics Data System (ADS)
Grafarend, E.; Heidenreich, A.
1995-09-01
The standard Mollweide projection of the sphere S{/R 2} which is of type pseudocylindrical — equiareal is generalized to the biaxial ellipsoid E {/A,B 2}. Within the class of pseudocylindrical mapping equations (1.8) of E {/A,B 2} (semimajor axis A, semiminor axis B) it is shown by solving the general eigenvalue problem (Tissot analysis) that only equiareal mappings, no conformal mappings exist. The mapping equations (2.1) which generalize those from S{/R 2} to E {/A,B 2} lead under the equiareal postulate to a generalized Kepler equation (2.21) which is solved by Newton iteration, for instance (Table 1). Two variants of the ellipsoidal Mollweide projection in particular (2.16), (2.17) versus (2.19), (2.20) are presented which guarantee that parallel circles (coordinate lines of constant ellipsoidal latitude) are mapped onto straight lines in the plane while meridians (coordinate lines of constant ellipsoidal longitude) are mapped onto ellipses of variable axes. The theorem collects the basic results. Six computer graphical examples illustrate the first pseudocylindrical map projection of E {/A,B 2} of generalized Mollweide type.
Olivares, Alberto; Ruiz-Garcia, Gonzalo; Olivares, Gonzalo; Górriz, Juan Manuel; Ramirez, Javier
2013-01-01
Ellipsoid fitting algorithms are widely used to calibrate Magnetic Angular Rate and Gravity (MARG) sensors. These algorithms are based on the minimization of an error function that optimizes the parameters of a mathematical sensor model that is subsequently applied to calibrate the raw data. The convergence of this kind of algorithms to a correct solution is very sensitive to input data. Input calibration datasets must be properly distributed in space so data can be accurately fitted to the theoretical ellipsoid model. Gathering a well distributed set is not an easy task as it is difficult for the operator carrying out the maneuvers to keep a visual record of all the positions that have already been covered, as well as the remaining ones. It would be then desirable to have a system that gives feedback to the operator when the dataset is ready, or to enable the calibration process in auto-calibrated systems. In this work, we propose two different algorithms that analyze the goodness of the distributions by computing four different indicators. The first approach is based on a thresholding algorithm that uses only one indicator as its input and the second one is based on a Fuzzy Logic System (FLS) that estimates the calibration error for a given calibration set using a weighted combination of two indicators. Very accurate classification between valid and invalid datasets is achieved with average Area Under Curve (AUC) of up to 0.98. PMID:24013490
Translational viscous drags of an ellipsoid straddling an interface between two fluids.
Boniello, Giuseppe; Stocco, Antonio; Gross, Michel; In, Martin; Blanc, Christophe; Nobili, Maurizio
2016-07-01
We study the dynamics of individual polystyrene ellipsoids of different aspect ratios trapped at the air-water interface. Using particle tracking and in situ vertical scanning interferometry techniques we are able to measure translational drags and the protrusion in air of the ellipsoids. We report that translational drags on the ellipsoid are unexpectedly enhanced: despite the fact that a noticeable part of the ellipsoid is in air, drags are found larger than the bulk one in water. PMID:27575174
Translational viscous drags of an ellipsoid straddling an interface between two fluids
NASA Astrophysics Data System (ADS)
Boniello, Giuseppe; Stocco, Antonio; Gross, Michel; In, Martin; Blanc, Christophe; Nobili, Maurizio
2016-07-01
We study the dynamics of individual polystyrene ellipsoids of different aspect ratios trapped at the air-water interface. Using particle tracking and in situ vertical scanning interferometry techniques we are able to measure translational drags and the protrusion in air of the ellipsoids. We report that translational drags on the ellipsoid are unexpectedly enhanced: despite the fact that a noticeable part of the ellipsoid is in air, drags are found larger than the bulk one in water.
Intensity-symmetric Airy beams.
Vaveliuk, P; Lencina, Alberto; Rodrigo, Jose A; Martnez-Matos, Ó
2015-03-01
Theoretical, numerical, and experimental research on a novel family of Airy beams in rectangular coordinates having a symmetric transverse pattern of light intensity is presented. The intensity-symmetric Airy beams include both the symmetric Airy beam whose field amplitude is an even function of the transverse coordinates and the antisymmetric Airy beam whose field amplitude is an odd function of such coordinates. The theoretical foundations are based on the relationship of the symmetries of the spectral phase with the cosine and sine Fourier transforms. These beams are analyzed in a propagation range also including the region preceding the Fourier plane. These beams exhibit autofocusing, collapse, self-bending, and reversal propagation. Moreover, the intensity distribution is strongly asymmetric with respect to the Fourier plane. All these peculiar features were not reported for other classes of paraxial beams in a rectangular frame. The experimental generation of intensity-symmetric Airy beams is demonstrated supporting the theoretical predictions. Possible applications in planar waveguide writing and optical trapping are also discussed. PMID:26366655
Volume integrals of ellipsoids associated with the inhomogeneous Helmholtz equation
NASA Technical Reports Server (NTRS)
Fu, L. S.; Mura, T.
1982-01-01
Problems of wave phenomena in the fields of acoustics, electromagnetics and elasticity are often reduced to an integration of the inhomogeneous Helmholtz equation. Results are presented for volume integrals associated with the inhomogeneous Helmholtz equation, for an ellipsoidal region. By using appropriate Taylor series expansions and the multinomial theorem, these volume integrals are obtained in series form for regions r greater than r-prime and r less than r-prime, where r and r-prime are the distances from the origin to the point of observation and the source. Derivatives of these integrals are easily evaluated. When the wavenumber approaches zero the results reduce directly to the potentials of ellipsoids of variable densities.
Actuation of shape-memory colloidal fibres of Janus ellipsoids
NASA Astrophysics Data System (ADS)
Shah, Aayush A.; Schultz, Benjamin; Zhang, Wenjia; Glotzer, Sharon C.; Solomon, Michael J.
2015-01-01
Many natural micrometre-scale assemblies can be actuated to control their optical, transport and mechanical properties, yet such functionality is lacking in colloidal structures synthesized thus far. Here, we show with experiments and computer simulations that Janus ellipsoids can self-assemble into self-limiting one-dimensional fibres with shape-memory properties, and that the fibrillar assemblies can be actuated on application of an external alternating-current electric field. Actuation of the fibres occurs through a sliding mechanism that permits the rapid and reversible elongation and contraction of the Janus-ellipsoid chains by ~36% and that on long timescales leads to the generation of long, uniform self-assembled fibres. Colloidal-scale actuation might be useful in microrobotics and in applications of shape-memory materials.
Transport of active ellipsoidal particles in ratchet potentials
Ai, Bao-Quan Wu, Jian-Chun
2014-03-07
Rectified transport of active ellipsoidal particles is numerically investigated in a two-dimensional asymmetric potential. The out-of-equilibrium condition for the active particle is an intrinsic property, which can break thermodynamical equilibrium and induce the directed transport. It is found that the perfect sphere particle can facilitate the rectification, while the needlelike particle destroys the directed transport. There exist optimized values of the parameters (the self-propelled velocity, the torque acting on the body) at which the average velocity takes its maximal value. For the ellipsoidal particle with not large asymmetric parameter, the average velocity decreases with increasing the rotational diffusion rate, while for the needlelike particle (very large asymmetric parameter), the average velocity is a peaked function of the rotational diffusion rate. By introducing a finite load, particles with different shapes (or different self-propelled velocities) will move to the opposite directions, which is able to separate particles of different shapes (or different self-propelled velocities)
Dish antenna having switchable beamwidth. [with truncated concave ellipsoid subreflector
NASA Technical Reports Server (NTRS)
Schmidt, R. F. (Inventor)
1975-01-01
A switchable beamwidth antenna includes a concave parabolic main reflecting dish which has a central circular region and a surrounding coaxial annular region. A feed means selectively excites only the central region of the main dish via a truncated subreflector for wide beamwidth or substantially the entire main dish for narrow beamwidth. In one embodiment, the feed means comprises a truncated concave ellipsoid subreflector and separate feed terminations located at two foci of the ellipsoid. One feed termination directly views all of the main dish while the other feed termination, exciting the main dish via the subreflector, excites only the central region because of the subreflector truncation. In the another embodiment, the feed means comprises one feed termination and a convex hyperboloid subreflector via which the feed excites the main dish.
Numerical simulation of laminar hypersonic flows about an ellipsoid
NASA Astrophysics Data System (ADS)
Riedelbauch, S.; Mueller, B.
The laminar hypersonic flow about a double ellipsoid, which idealizes the nose and cockpit of a spacecraft, were numerically simulated. The calculation method solves the three dimensional thin layer Navier-Stokes equations in a conservative formulation on a surface oriented calculation grid using an implicit/explicit finite difference technique. The conservative formulation allows the correct calculation of embedded compression shocks, while the head wave was treated with a shock-fitting procedure. The calculated flow fields about the ellipsoid show shock-shock and shock-boundary layer interactions in connection with separated flow. Wall flow lines and heat transfer agree qualitatively very well with film-of-oil and thermographic pictures.
The Characteristic Ellipsoid Methodology and Its Application in Power Systems
Ma, Jian; Makarov, Yuri V.; Diao, Ruisheng; Etingov, Pavel V.; Dagle, Jeffery E.; De Tuglie, Enrico E.
2012-11-01
The characteristic ellipsoid (CELL) method to monitor dynamic behaviors of a power system is proposed. Multidimensional minimum-volume-enclosing characteristic ellipsoids are built using synchronized phasor measurements. System dynamic behaviors are identified by tracking the change rate of the CELL’s characteristic indices. Decision tree techniques are used to link the CELL’s characteristic indices and the system’s dynamic behaviors and to determine types, locations and related information about the dynamic behaviors. The knowledge base of representative transient events is created by offline simulations based on the full Western Electric Coordinating Council (WECC) model. Two case studies demonstrate that the CELL method combined with the decision trees can detect transient events and their features with good accuracy.
Complete gravity field of an ellipsoidal prism by Gauss-Legendre quadrature
NASA Astrophysics Data System (ADS)
Roussel, C.; Verdun, J.; Cali, J.; Masson, F.
2015-12-01
The increasing availability of geophysical models of the Earth's lithosphere and mantle has generated renewed interest in computation of theoretical gravity effects at global and regional scales. At the same time, the increasing availability of gravity gradient anomalies derived from satellite measurements, such as those provided by GOCE satellite, requires mathematical methods that directly model the gravity gradient anomalies in the same reference frame as GOCE gravity gradients. Our main purpose is to interpret these anomalies in terms of source and density distribution. Numerical integration methods for calculating gravity gradient values are generally based on a mass discretization obtained by decomposing the Earth's layers into a finite number of elementary solid bodies. In order to take into account the curvature of the Earth, spherical prisms or `tesseroids' have been established unequivocally as accurate computation tools for determining the gravitational effects of large-scale structures. The question which then arises from, is whether gravity calculation methods using spherical prisms remain valid when factoring in the ellipticity of the Earth. In the paper, we outline a comprehensive method to numerically compute the complete gravity field with the help of the Gauss-Legendre quadrature involving ellipsoidal shaped prisms. The assessment of this new method is conducted by comparison between the gravity gradient values of simple sources obtained by means of numerical and analytical calculations, respectively. A comparison of the gravity gradients obtained from PREM and LITHO1.0 models using spherical- and ellipsoidal-prism-based methods is also presented. Numerical results indicate that the error on gravity gradients, caused by the use of the spherical prism instead of its ellipsoidal counterpart to describe an ellipsoidally shaped Earth, is useful for a joint analysis with those deduced from GOCE satellite measurements. Provided that a suitable scaling
Sedimentation of an oblate ellipsoid in narrow tubes
NASA Astrophysics Data System (ADS)
Yang, Xin; Huang, Haibo; Lu, Xiyun
2015-12-01
Sedimentation behaviors of an oblate ellipsoidal particle inside narrow [R /a ∈(1.2 ,2.0 )] infinitely long circular tubes are studied by the lattice Boltzmann method, where R and a are the radius of the tube and the length of the semimajor axis of the ellipsoid, respectively. The Archimedes numbers (Ar) up to 70 are considered. Four periodic and two steady sedimentation modes are identified. It is the first time that the anomalous mode has been found in a circular tube for an ellipsoidal particle. The phase diagram of the modes as a function of Ar and R /a is obtained. The anomalous mode is observed in the larger R /a and lower-Ar regime. Through comparisons between the anomalous and oscillatory modes, it is found that R/a plays a critical role for the anomalous mode. Some constrained cases with two steady modes are simulated. It is found that the particle settles faster in the unconstrained modes than in the corresponding constrained modes. This might inspire further study on why the particle adopts a specific mode under a certain circumstance.
Sedimentation of an oblate ellipsoid in narrow tubes.
Yang, Xin; Huang, Haibo; Lu, Xiyun
2015-12-01
Sedimentation behaviors of an oblate ellipsoidal particle inside narrow [R/a∈(1.2,2.0)] infinitely long circular tubes are studied by the lattice Boltzmann method, where R and a are the radius of the tube and the length of the semimajor axis of the ellipsoid, respectively. The Archimedes numbers (Ar) up to 70 are considered. Four periodic and two steady sedimentation modes are identified. It is the first time that the anomalous mode has been found in a circular tube for an ellipsoidal particle. The phase diagram of the modes as a function of Ar and R/a is obtained. The anomalous mode is observed in the larger R/a and lower-Ar regime. Through comparisons between the anomalous and oscillatory modes, it is found that R/a plays a critical role for the anomalous mode. Some constrained cases with two steady modes are simulated. It is found that the particle settles faster in the unconstrained modes than in the corresponding constrained modes. This might inspire further study on why the particle adopts a specific mode under a certain circumstance. PMID:26764806
Maxwell's mixing equation revisited: characteristic impedance equations for ellipsoidal cells.
Stubbe, Marco; Gimsa, Jan
2015-07-21
We derived a series of, to our knowledge, new analytic expressions for the characteristic features of the impedance spectra of suspensions of homogeneous and single-shell spherical, spheroidal, and ellipsoidal objects, e.g., biological cells of the general ellipsoidal shape. In the derivation, we combined the Maxwell-Wagner mixing equation with our expression for the Clausius-Mossotti factor that had been originally derived to describe AC-electrokinetic effects such as dielectrophoresis, electrorotation, and electroorientation. The influential radius model was employed because it allows for a separation of the geometric and electric problems. For shelled objects, a special axial longitudinal element approach leads to a resistor-capacitor model, which can be used to simplify the mixing equation. Characteristic equations were derived for the plateau levels, peak heights, and characteristic frequencies of the impedance as well as the complex specific conductivities and permittivities of suspensions of axially and randomly oriented homogeneous and single-shell ellipsoidal objects. For membrane-covered spherical objects, most of the limiting cases are identical to-or improved with respect to-the known solutions given by researchers in the field. The characteristic equations were found to be quite precise (largest deviations typically <5% with respect to the full model) when tested with parameters relevant to biological cells. They can be used for the differentiation of orientation and the electric properties of cell suspensions or in the analysis of single cells in microfluidic systems. PMID:26200856
Evolute-based Hough transform method for characterization of ellipsoids.
Kaytanli, B; Valentine, M T
2013-03-01
We propose a novel and algorithmically simple Hough transform method that exploits the geometric properties of ellipses to enable the robust determination of the ellipse position and properties. We make use of the unique features of the evolute created by Hough voting along the gradient vectors of a two-dimensional image to determine the ellipse centre, orientation and aspect ratio. A second one-dimensional voting is performed on the minor axis to uniquely determine the ellipse size. This reduction of search space substantially simplifies the algorithmic complexity. To demonstrate the accuracy of our method, we present analysis of single and multiple ellipsoidal particles, including polydisperse and imperfect ellipsoids, in both simulated images and electron micrographs. Given its mathematical simplicity, ease of implementation and reasonable algorithmic completion time, we anticipate that the proposed method will be broadly useful for image processing of ellipsoidal particles, including their detection and tracking for studies of colloidal suspensions, and for applications to drug delivery and microrheology. PMID:23301634
Brownian dynamics simulations of ellipsoidal magnetizable particle suspensions
NASA Astrophysics Data System (ADS)
Torres-Díaz, I.; Rinaldi, C.
2014-06-01
The rotational motion of soft magnetic tri-axial ellipsoidal particles suspended in a Newtonian fluid has been studied using rotational Brownian dynamics simulations by solving numerically the stochastic angular momentum equation in an orientational space described by the quaternion parameters. The model is applicable to particles where the effect of shape anisotropy is dominant. The algorithm quantifies the magnetization of a monodisperse suspension of tri-axial ellipsoids in dilute limit conditions under applied constant and time-varying magnetic fields. The variation of the relative permeability with the applied magnetic field of the particle's bulk material was included in the simulations. The results show that the equilibrium magnetization of a suspension of magnetizable tri-axial ellipsoids saturates at high magnetic field amplitudes. Additionally, the dynamic susceptibility at low magnetic field intensity presents a peak in the out-of-phase component, which is significantly smaller than the in-phase component and depends on the Langevin parameter. The dynamic magnetization of the particle suspension is in phase with the magnetic field at low and high frequencies far from the peak of the out-of-phase component.
Optically driven oscillations of ellipsoidal particles. Part I: experimental observations.
Mihiretie, B M; Snabre, P; Loudet, J-C; Pouligny, B
2014-12-01
We report experimental observations of the mechanical effects of light on ellipsoidal micrometre-sized dielectric particles, in water as the continuous medium. The particles, made of polystyrene, have shapes varying between near disk-like (aspect ratio k = 0.2) to very elongated needle-like (k = 8). Rather than the very tightly focused beam geometry of optical tweezers, we use a moderately focused laser beam to manipulate particles individually by optical levitation. The geometry allows us varying the longitudinal position of the particle, and to capture images perpendicular to the beam axis. Experiments show that moderate-k particles are radially trapped with their long axis lying parallel to the beam. Conversely, elongated (k > 3) or flattened (k < 0.3) ellipsoids never come to rest, and permanently "dance" around the beam, through coupled translation-rotation motions. The oscillations are shown to occur in general, be the particle in bulk water or close to a solid boundary, and may be periodic or irregular. We provide evidence for two bifurcations between static and oscillating states, at k ≈ 0.33 and k ≈ 3 for oblate and prolate ellipsoids, respectively. Based on a recently developed 2-dimensional ray-optics simulation (Mihiretie et al., EPL 100, 48005 (2012)), we propose a simple model that allows understanding the physical origin of the oscillations. PMID:25577402
The motion of ellipsoids in a second order fluid
NASA Astrophysics Data System (ADS)
Kim, S.
1985-09-01
The rigid body motion of an ellipsoid in a second order fluid (SOF) under the action of specified (time independent) external forces and torques have been obtained to first order in the Weissenberg number by inverting the resistance relations for the force an torque under specified rigid body motions. The reciprocal theorem of Lorentz was used to bypass the calculation of the O(W) velocity field. The results agree with known analytic solutions for SOF with the secondary to primary normal stress ratio of -1/2. The solution procedure was also tested by computing the torque on a translating prolate spheroid with aspect ratios ranging from slender bodies to near-spheres. One result is that for a SOF with zero secondary normal stress (Weissenberg fluid), previous asymptotic results for near-spheres were found to be accurate even at fairly large aspect ratios. New results of nondegenerate ellipsoids suggest that the orientation (as monitored by Euler angles) and trajectory of sedimenting, nonaxisymmetric particles such as ellipsoids provide useful information on the rheology of the suspending fluid.
Three-dimensional wake of a surface-mounted ellipsoid
NASA Astrophysics Data System (ADS)
Walter, Joel Allan
1997-11-01
A tri-axial ellipsoid mounted on a plane wall serves as a prototypical body for the study of three-dimensional flow phenomena. Extensive measurements of mean velocity and Reynolds stresses were made in the wake of the ellipsoid for three cases: at zero incidence, when the separating boundary layer of the ellipsoid was either laminar or turbulent, and at 6 degrees incidence when the separating boundary layer was turbulent. This thesis describes the main features of these flows and compares the three cases. Near the wall, the wake structure was dominated by fluid swept into the wall region by inboard flow from the tip, which is a consequence of the finite span of the body. In the central wake, the structure in the zero incidence cases differed dramatically depending on whether the originating ellipsoid boundary layer was laminar or turbulent. In the laminar case, organized counter- rotating longitudinal vortex cells were observed aligned along the wake centerline. Although the strongest pair could still be detected 5 chord lengths downstream of the tip, their strength and spatial coherence decayed more rapidly than the tip vortex observed in the at-incidence case. The organized secondary flow disappeared when the originating boundary layer was turbulent. The origins of the two different wakes that developed from the same (symmetry) condition were investigated using surface flow visualization. In the at-incidence case, the influence of the tip vortex was felt all the way into the junction region. The main difference in turbulence structure from the zero- incidence case appeared to be caused by two opposing inviscid mechanisms: the tip vortex-induced flow and the ellipsoid's potential flow. In the central part of the wake, mean velocity data exhibited self-similarity in all three cases and showed surprising quantitative agreement with asymptotic plane wake theory. In some cases, the primary turbulent shear stress and turbulence kinetic energy exhibited self- similarity
NASA Technical Reports Server (NTRS)
Krenkel, A. R.
1978-01-01
The finite-step method was programmed for computing the span loading and stability derivatives of trapezoidal shaped wings in symmetric, yawed, and rotary flight. Calculations were made for a series of different wing planforms and the results compared with several available methods for estimating these derivatives in the linear angle of attack range. The agreement shown was generally good except in a few cases. An attempt was made to estimate the nonlinear variation of lift with angle of attack in the high alpha range by introducing the measured airfoil section data into the finite-step method. The numerical procedure was found to be stable only at low angles of attack.
NASA Astrophysics Data System (ADS)
Kwon, H.
2011-12-01
The impact of climate variation on monsoon seasonal rainfall has been generally well documented in the climate literature. However, rather limited efforts have been done to understand moisture transport and their impact on extreme rainfall in the hydrology field. This study developed a new model for extracting moisture tracks associated with extreme events as a way to characterize large scale climate system. Main interests are to derive location, size and direction of the rainfall field and this study developed an algorithm to extract the above characteristics from global climate data set. In order to facilitate characterization of synoptic patterns, geometric moment based ellipsoid models are introduced. Local weather station data in Korea and NCEP reanalysis data are mainly utilized to identify synoptic patterns. The proposed geometric moments based ellipsoid model works equally well with regularly and irregularly distributed synthetic grid data. Finally, the proposed model was applied to space-time real moisture transport. We extracted daily wind patterns and specific humidity on top 20 extreme rainfall events and apply a 90% threshold to isolate high magnitude of moisture transport associated with extreme rainfall in South Korea. It was found that location, size and direction of the rainfall field was successfully extracted. Our analyses of daily synoptic moisture transport patterns defined by geometric moments suggest can be possibly clustered given their intensity, direction and position properties. Acknowledgement : This work was supported by National Research Foundation of Korea Grant funded by the Korean Government (NRF-2010-220-D00083)
Production of quasi ellipsoidal laser pulses for next generation high brightness photoinjectors
NASA Astrophysics Data System (ADS)
Rublack, T.; Good, J.; Khojoyan, M.; Krasilnikov, M.; Stephan, F.; Hartl, I.; Schreiber, S.; Andrianov, A.; Gacheva, E.; Khazanov, E.; Mironov, S.; Potemkin, A.; Zelenogorskii, V. V.; Syresin, E.
2016-09-01
The use of high brightness electron beams in Free Electron Laser (FEL) applications is of increasing importance. One of the most promising methods to generate such beams is the usage of shaped photocathode laser pulses. It has already demonstrated that temporal and transverse flat-top laser pulses can produce very low emittance beams [1]. Nevertheless, based on beam simulations further improvements can be achieved using quasi-ellipsoidal laser pulses, e.g. 30% reduction in transverse projected emittance at 1 nC bunch charge. In a collaboration between DESY, the Institute of Applied Physics of the Russian Academy of Science (IAP RAS) in Nizhny Novgorod and the Joint Institute of Nuclear Research (JINR) in Dubna such a laser system capable of producing trains of laser pulses with a quasi-ellipsoidal distribution, has been developed. The prototype of the system was installed at the Photo Injector Test facility at DESY in Zeuthen (PITZ) and is currently in the commissioning phase. In the following, the laser system will be introduced, the procedure of pulse shaping will be described and the last experimental results will be shown.
Conformally symmetric traversable wormholes
Boehmer, Christian G.; Harko, Tiberiu; Lobo, Francisco S. N.
2007-10-15
Exact solutions of traversable wormholes are found under the assumption of spherical symmetry and the existence of a nonstatic conformal symmetry, which presents a more systematic approach in searching for exact wormhole solutions. In this work, a wide variety of solutions are deduced by considering choices for the form function, a specific linear equation of state relating the energy density and the pressure anisotropy, and various phantom wormhole geometries are explored. A large class of solutions impose that the spatial distribution of the exotic matter is restricted to the throat neighborhood, with a cutoff of the stress-energy tensor at a finite junction interface, although asymptotically flat exact solutions are also found. Using the 'volume integral quantifier', it is found that the conformally symmetric phantom wormhole geometries may, in principle, be constructed by infinitesimally small amounts of averaged null energy condition violating matter. Considering the tidal acceleration traversability conditions for the phantom wormhole geometry, specific wormhole dimensions and the traversal velocity are also deduced.
Space-charge calculation for bunched beams with 3-D ellipsoidal symmetry
Garnett, R.W.; Wangler, T.P.
1991-01-01
A method for calculating 3-D space-charge forces has been developed that is suitable for bunched beams of either ions or relativistic electrons. The method is based on the analytic relations between charge-density and electric fields for a distribution with 3-D ellipsoidal symmetry in real space. At each step we use a Fourier-series representation for the smooth particle-density function obtained from the distribution of the macroparticles being tracked through the elements of the system. The resulting smooth electric fields reduce the problem of noise from artificial collisions, associated with small numbers of interacting macroparticles. Example calculations will be shown for comparison with other methods. 4 refs., 2 figs., 1 tab.
NASA Astrophysics Data System (ADS)
Bose, Tushar Kanti; Saha, Jayashree
2014-04-01
In a recent article [T. K. Bose and J. Saha, Phys. Rev. E 86, 050701 (2012), 10.1103/PhysRevE.86.050701], we have presented the results of a Monte Carlo simulation study of the systems of dipolar Gay-Berne ellipsoids where two terminal antiparallel dipoles are placed symmetrically on the long axis of each ellipsoid, and the results revealed the combined contribution of dipolar separation and transverse orientations in controlling the tilt angle in the tilted hexatic smectic phase. The tilt angle changed from zero to a significant value, in the case of transverse dipoles, with a change in the dipolar separation. In the related comment, Madhusudana [preceding Comment, Phys. Rev. E 89, 046501 (2014), 10.1103/PhysRevE.89.046501] has claimed that the physical origin of the molecular tilt in the significantly tilted phases found in the simulations is similar to that proposed by McMillan [Phys. Rev. A 8, 1921 (1973), 10.1103/PhysRevA.8.1921]. Here, we explain that the claim is not correct and make it clear that the two compared pictures are quite different. In the preceding Comment, Madhusudana has also suggested an alternative explanation for tilt generation in the simulations by criticizing the original one proposed by us. We argue here in support of the original explanation and clarify that his explanation does not follow the simulation results.
Bose, Tushar Kanti; Saha, Jayashree
2014-04-01
In a recent article [T. K. Bose and J. Saha, Phys. Rev. E 86, 050701 (2012)], we have presented the results of a Monte Carlo simulation study of the systems of dipolar Gay-Berne ellipsoids where two terminal antiparallel dipoles are placed symmetrically on the long axis of each ellipsoid, and the results revealed the combined contribution of dipolar separation and transverse orientations in controlling the tilt angle in the tilted hexatic smectic phase. The tilt angle changed from zero to a significant value, in the case of transverse dipoles, with a change in the dipolar separation. In the related comment, Madhusudana [preceding Comment, Phys. Rev. E 89, 046501 (2014)] has claimed that the physical origin of the molecular tilt in the significantly tilted phases found in the simulations is similar to that proposed by McMillan [Phys. Rev. A 8, 1921 (1973)]. Here, we explain that the claim is not correct and make it clear that the two compared pictures are quite different. In the preceding Comment, Madhusudana has also suggested an alternative explanation for tilt generation in the simulations by criticizing the original one proposed by us. We argue here in support of the original explanation and clarify that his explanation does not follow the simulation results. PMID:24827369
Ryabov, Yaroslav E; Geraghty, Charles; Varshney, Amitabh; Fushman, David
2006-12-01
We propose a new computational method for predicting rotational diffusion properties of proteins in solution. The method is based on the idea of representing protein surface as an ellipsoid shell. In contrast to other existing approaches this method uses principal component analysis of protein surface coordinates, which results in a substantial increase in the computational efficiency of the method. Direct comparison with the experimental data as well as with the recent computational approach (Garcia de la Torre; et al. J. Magn. Reson. 2000, B147, 138-146), based on representation of protein surface as a set of small spherical friction elements, shows that the method proposed here reproduces experimental data with at least the same level of accuracy and precision as the other approach, while being approximately 500 times faster. Using the new method we investigated the effect of hydration layer and protein surface topography on the rotational diffusion properties of a protein. We found that a hydration layer constructed of approximately one monolayer of water molecules smoothens the protein surface and effectively doubles the overall tumbling time. We also calculated the rotational diffusion tensors for a set of 841 protein structures representing the known protein folds. Our analysis suggests that an anisotropic rotational diffusion model is generally required for NMR relaxation data analysis in single-domain proteins, and that the axially symmetric model could be sufficient for these purposes in approximately half of the proteins. PMID:17132010
Panprasitwech, Oranit; Laohakosol, Vichian; Chaichana, Tuangrat
2010-11-11
Explicit formulae for continued fractions with symmetric patterns in their partial quotients are constructed in the field of formal power series. Similar to the work of Cohn in 1996, which generalized the so-called folding lemma to {kappa}-fold symmetry, the notion of {kappa}-duplicating symmetric continued fractions is investigated using a modification of the 1995 technique due to Clemens, Merrill and Roeder.
Caffrey, Emily A; Johansen, Mathew P; Higley, Kathryn A
2015-10-01
Radiological dosimetry for nonhuman biota typically relies on calculations that utilize the Monte Carlo simulations of simple, ellipsoidal geometries with internal radioactivity distributed homogeneously throughout. In this manner it is quick and easy to estimate whole-body dose rates to biota. Voxel models are detailed anatomical phantoms that were first used for calculating radiation dose to humans, which are now being extended to nonhuman biota dose calculations. However, if simple ellipsoidal models provide conservative dose-rate estimates, then the additional labor involved in creating voxel models may be unnecessary for most scenarios. Here we show that the ellipsoidal method provides conservative estimates of organ dose rates to small mammals. Organ dose rates were calculated for environmental source terms from Maralinga, the Nevada Test Site, Hanford and Fukushima using both the ellipsoidal and voxel techniques, and in all cases the ellipsoidal method yielded more conservative dose rates by factors of 1.2-1.4 for photons and 5.3 for beta particles. Dose rates for alpha-emitting radionuclides are identical for each method as full energy absorption in source tissue is assumed. The voxel procedure includes contributions to dose from organ-to-organ irradiation (shown here to comprise 2-50% of total dose from photons and 0-93% of total dose from beta particles) that is not specifically quantified in the ellipsoidal approach. Overall, the voxel models provide robust dosimetry for the nonhuman mammals considered in this study, and though the level of detail is likely extraneous to demonstrating regulatory compliance today, voxel models may nevertheless be advantageous in resolving ongoing questions regarding the effects of ionizing radiation on wildlife. PMID:26414505
Forces on ellipsoidal bubbles in a turbulent shear layer
NASA Astrophysics Data System (ADS)
Ford, Barry; Loth, Eric
1998-01-01
The objective of this research was to gain fundamental knowledge of the drag and lift forces on ellipsoidal air bubbles in water in a turbulent flow. This was accomplished by employing a cinematic two-phase particle image velocimetry (PIV) system to evaluate bubbly flow in a two-stream, turbulent, planar free shear layer of filtered tap water. Ellipsoidal air bubbles with nominal diameters from 1.5 to 4.5 mm were injected directly into the shear layer through a single slender tube. The cinematic PIV allowed for high resolution of the unsteady liquid velocity vector field. Triple-pulsed bubble images were obtained in a temporal sequence, such that the bubble size and bubble trajectory could be accurately determined. The bubble's oscillation characteristics, velocity, acceleration, and buoyancy force were obtained from the trajectory data. A bubble dynamic equation was then applied to allow determination of the time-evolving lift and drag forces acting upon bubbles within the shear layer. The results indicate that for a fixed bubble diameter (and fixed Bond and Morton numbers), the drag coefficient decreases for an increasing Reynolds number. This is fundamentally different than the increasing drag coefficient trend seen for ellipsoidal bubbles rising in quiescent baths for increasing diameter (and increasing Bond number), but is qualitatively consistent with the trend for spherical bubbles. A new empirical expression for the dependence of the drag coefficient on Reynolds number for air bubbles in tap water for both quiescent and turbulent flows is constructed herein. Finally, the instantaneous side forces measured in this study were dominated by the inherent deformation-induced vortex shedding of the bubble wake rather than the inviscid lift force based on the background fluid vorticity.
An Ellipsoidal Model for Secondary Breakup of Spray Droplets
NASA Astrophysics Data System (ADS)
Lundgren, T. S.
1998-11-01
In sprays of liquid drops dynamic interaction with the gas can cause drops to breakup into daughter drops. To analyse this situation it is assumed that the drop has the shape of a deformable ellipsoid of revolution. When placed in a stream the high stagnation pressure at the symmetry axis, coupled with Bernoulli suction around the equator tends to squeeze the drop into a lenticular shape. This is resisted by the inertia of the liquid and surface tension forces. This problem has been solved by matching together two exact potential flow solutions, allowing slip along the interface. The external flow is the solution for flow around an ellipsoidal body when it is moving with relative velocity into the gas. The internal flow of the liquid is an exact solution for flow inside a deforming ellipsoid, a uniform flow plus a uniaxial strain flow (a stagnation point flow). The boundary condition which matches the solutions at the interface, the balance of normal stresses with surface tension, is imposed only at the upstream axis and along the equator. The resulting equations give a second order differential equation for the aspect ratio of the drop. This is similar to the TAB model but nonlinear. A nonlinear oscillator. For small enough (constant) Weber number there is a stable solution at a certain aspect ratio; the drop can oscillate about this shape. When the Weber number is larger than a critical value the stable critical point disapears and the drop becomes unstable, with the equatorial radius growing until unbounded; the drop breaks.
Hemi-ellipsoidal mirror infrared reflectometer: development and operation.
Wood, B E; Pipes, J G; Smith, A M; Roux, J A
1976-04-01
The development and testing of an ir hemi-ellipsoidal mirror reflectometer (HEMR), operational over a wavelength interval of 2-34 microm, are described. This optical system measures the hemispherical-directional reflectance of room temperature samples relative to a specular gold-coated surface. For a source and sample area commensurate with detectable energy requirements, it is shown experimentally that the HEMR is functional with very tolerable errors. Finally, the hemispherical-directional reflectance of test samples, e.g., black paints, gold diffuser, sulfur, cesium iodide, and others, is presented for wavelengths from 2 microm to 34 microm. PMID:20165100
NASA Astrophysics Data System (ADS)
Schneider, John B.; Peden, Irene C.
1988-09-01
The extended boundary condition method is applied to ellipsoidal dielectric scatterers, which in general have no rotational symmetry. This represents a more general study of single-object scattering in the resonant range with the goal of extending the practical applications to a wider class of targets, including irregular shapes that can be described in terms of a best-fit ellipsoid. Expressions are presented, and calculated results provided, for an ellipsoid in the resonant range, and comparison is made with an oblate spheroid of approximately the same volume as the ellipsoid. The importance of differences in the surface and internal propagation paths provided by the two scatterers is noted.
NASA Astrophysics Data System (ADS)
Tan, Teng; Wolak, Matthaeus; Tajima, Tsuyoshi; Xi, Xiaoxing; Civale, Leonardo
2015-03-01
Superconducting rf (SRF) cavities fabricated from bulk niobium (Nb) are a key component for modern particle accelerators. The magnetic field distribution on the inner wall of an SRF cavity is inversely similar to the field distribution on top of a superconducting ellipsoid when we put it in a magnetic field parallel to its axis. By measuring the vortex penetration into the magnetized superconducting ellipsoids, we can deduct the behavior of SRF cavities. Magnesium diboride (MgB2) has potential to replace Nb as it has a higher Tc of 39 K, a lower residual resistivity of ~ 0.1 μΩ cm (at 42 K), and a higher thermodynamic critical field Hc value compared to Nb. In this work, we successfully coated uniform MgB2 layers on top of molybdenum and niobium ellipsoids. SQUID magnetometer measurements showed that the coated MgB2 layer has a Tc above 38.5 K, and can provide a perfect magnetic shielding up to ~ 500 Oe at 1.8K. By coating MgB2 on Nb ellipsoids, we increased the vortex penetration field (the maximum field at which a cavity can be operated) by ~ 500 Oe at 2 K.
Fogolari, F; Esposito, G; Viglino, P; Cattarinussi, S
1996-03-01
In an effort to reduce the number of degrees of freedom necessary to describe a polypeptide chain we analyze the statistical behavior of polypeptide chains when represented as C alpha chains, C alpha chains with C beta atoms attached, and C alpha chains with rotational ellipsoids as models of side chains. A statistical analysis on a restricted data set of 75 unrelated protein structures is performed. The comparison of the database distributions with those obtained by model calculation on very short polypeptide stretches allows the dissection of local versus nonlocal features of the distributions. The database distribution of the bend angles of polypeptide chains of pseudo bonded C alpha atoms spans a restricted range of values and shows a bimodal structure. On the other hand, the torsion angles of the C alpha chain may assume almost all possible values. The distribution is bimodal, but with a much broader probability distribution than for bend angles. The C alpha - C beta vectors may be taken as representative of the orientation of the lateral chain, as the direction of the bond is close to the direction of the vector joining C alpha to the ad hoc defined center of the "steric mass" of the side chain. Interestingly, both the bend angle defined by C alpha i-C alpha i+1-C beta i+1 and the torsional angle offset of the pseudo-dihedral C alpha i-C alpha i+1-C alpha i+2-C beta i+2 with respect to C alpha i-C alpha i+1-C alpha i+2-C alpha i+3 span a limited range of values. The latter results show that it is possible to give a more realistic representation of polypeptide chains without introducing additional degrees of freedom, i.e., by just adding to the C alpha chain a C beta with given side-chain properties. However, a more realistic description of side chains may be attained by modeling side chains as rotational ellipsoids that have roughly the same orientation and steric hindrance. To this end, we define the steric mass of an atom as proportional to its van der
CAST: Contraction Algorithm for Symmetric Tensors
Rajbhandari, Samyam; NIkam, Akshay; Lai, Pai-Wei; Stock, Kevin; Krishnamoorthy, Sriram; Sadayappan, Ponnuswamy
2014-09-22
Tensor contractions represent the most compute-intensive core kernels in ab initio computational quantum chemistry and nuclear physics. Symmetries in these tensor contractions makes them difficult to load balance and scale to large distributed systems. In this paper, we develop an efficient and scalable algorithm to contract symmetric tensors. We introduce a novel approach that avoids data redistribution in contracting symmetric tensors while also avoiding redundant storage and maintaining load balance. We present experimental results on two parallel supercomputers for several symmetric contractions that appear in the CCSD quantum chemistry method. We also present a novel approach to tensor redistribution that can take advantage of parallel hyperplanes when the initial distribution has replicated dimensions, and use collective broadcast when the final distribution has replicated dimensions, making the algorithm very efficient.
Hydrodynamics of coalescing binary neutron stars: Ellipsoidal treatment
NASA Technical Reports Server (NTRS)
Lai, Dong; Shapiro, Stuart L.
1995-01-01
We employ an approximate treatment of dissipative hydrodynamics in three dimensions to study the coalescence of binary neutron stars driven by the emission of gravitational waves. The stars are modeled as compressible ellipsoids obeying a polytropic equation of state; all internal fluid velocities are assumed to be linear functions of the coordinates. The hydrodynamics equations then reduce to a set of coupled ordinary differential equations for the evolution of the principal axes of the ellipsoids, the internal velocity parameters, and the binary orbital parameters. Gravitational radiation reaction and viscous dissipation are both incorporated. We set up exact initial binary equilibrium configurations and follow the transition from the quasi-static, secular decay of the orbit at large separation to the rapid dynamical evolution of the configurations just prior to contact. A hydrodynamical instability resulting from tidal interactions significantly accelerates the coalescence at small separation, leading to appreciable radial infall velocity and tidal lag angles near contact. This behavior is reflected in the gravitational waveforms and may be observable by gravitational wave detectors under construction. In cases where the neutron stars have spins which are not aligned with the orbital angular momentum, the spin-induced quadrupole moment can lead to precession of the orbital plane and therefore modulation of the gravitational wave amplitude even at large orbital radius. However, the amplitude of the modulation is small for typical neutron star binaries with spins much smaller than the orbital angular momentum.
Observations of Ellipsoidal Variations in the LMXB V1727 Cygni
NASA Astrophysics Data System (ADS)
Price, Alex; Mason, P. A.; Robinson, E. L.
2012-01-01
We report the first detection of ellipsoidal variations in the quiescent low mass X-ray binary, V1727 Cygni. We obtained 10s integrations over 19 nights during 2010-2011, with 1 orbital period observed each night using the 82in, Otto Struve Telescope, of McDonald Observatory. A power spectrum analysis detected a signal at 1/2 of the orbital period. The detected period is at 0.10913 +/- 0.00001 days, giving an orbital period of 0.21826 +/- 0.00002 days. The amplitude of the variations is small due to the strong dilution of optical light from an F-type star, apparently in a hierarchal triple with the LMXB. Thorstensen (1979) observed the system in outburst with an amplitude of 1 mag at the orbital period, and nothing at half the orbital period. We see no power at the orbital period, because the ellipsoidal variations display nearly identical minima. Comparison with light curve model calculations suggest that a small amount of X-ray heating is taking place, consistent with the compact object being a neutron star. This work is part of the NSF/PAARE program for Education and Research.
Effect of orientational restriction on monolayers of hard ellipsoids.
Varga, Szabolcs; Martínez-Ratón, Yuri; Velasco, Enrique; Bautista-Carbajal, Gustavo; Odriozola, Gerardo
2016-02-14
The effect of out-of-plane orientational freedom on the orientational ordering properties of a monolayer of hard ellipsoids is studied using the Parsons-Lee scaling approach and replica exchange Monte Carlo computer simulation. Prolate and oblate ellipsoids exhibit very different ordering properties, namely, the axes of revolution of prolate particles tend to lean out, while those of oblate ones prefer to lean into the confining plane. The driving mechanism of this is that the particles try to maximize the available free area on the confining surface, which can be achieved by minimizing the cross section areas of the particles with the plane. In the lack of out-of-plane orientational freedom the monolayer of prolate particles is identical to a two-dimensional hard ellipse system, which undergoes an isotropic-nematic ordering transition with increasing density. With gradually switching on the out-of-plane orientational freedom the prolate particles lean out from the confining plane and destabilisation of the in-plane isotropic-nematic phase transition is observed. The system of oblate particles behaves oppositely to that of prolates. It corresponds to a two-dimensional system of hard disks in the lack of out-of-plane freedom, while it behaves similar to that of hard ellipses in the freely rotating case. Solid phases can be realised by lower surface coverage due to the out-of-plane orientation freedom for both oblate and prolate shapes. PMID:26796794
A fast ellipsoid model for asteroids inverted from lightcurves
NASA Astrophysics Data System (ADS)
Lu, Xiao-Ping; Zhao, Hai-Bin; You, Zhong
2013-04-01
Research about asteroids has recently attracted more and more attention, especially focusing on their physical structures, such as their spin axis, rotation period and shape. The long distance between observers on Earth and asteroids makes it impossible to directly calculate the shape and other parameters of asteroids, with the exception of Near Earth Asteroids and others that have passed by some spacecrafts. Photometric measurements are still generally the main way to obtain research data on asteroids, i.e. the lightcurves recording the brightness and positions of asteroids. Supposing that the shape of the asteroid is a triaxial ellipsoid with a stable spin, a new method is presented in this article to reconstruct the shape models of asteroids from the lightcurves, together with other physical parameters. By applying a special curvature function, the method calculates the brightness integration on a unit sphere and Lebedev quadrature is employed for the discretization. Finally, the method searches for the optimal solution by the Levenberg-Marquardt algorithm to minimize the residual of the brightness. By adopting this method, not only can related physical parameters of asteroids be obtained at a reasonable accuracy, but also a simple shape model of an ellipsoid can be generated for reconstructing a more sophisticated shape model.
Tunable scattering cancellation cloak with plasmonic ellipsoids in the visible
NASA Astrophysics Data System (ADS)
Fruhnert, Martin; Monti, Alessio; Fernandez-Corbaton, Ivan; Alù, Andrea; Toscano, Alessandro; Bilotti, Filiberto; Rockstuhl, Carsten
2016-06-01
The scattering cancellation technique is a powerful tool to reduce the scattered field from electrically small objects in a specific frequency window. The technique relies on covering the object of interest with a shell that scatters light into a far field of equal strength as the object but with a phase shift of π . The resulting destructive interference prohibits its detection in measurements that probe the scattered light. Whereas at radio or microwave frequencies feasible designs have been proposed that allow us to tune the operational frequency upon request, similar capabilities have not yet been explored in the visible. However, such an ability is necessary to capitalize on the technique in many envisioned applications. Here, we solve the problem and study the use of small metallic nanoparticles with an ellipsoidal shape as the material from which the shell is made to build an isotropic geometry. Changing the aspect ratio of the ellipsoids allows us to change the operational frequency. The basic functionality is explored with two complementary analytical approaches. Additionally, we present a powerful multiscattering algorithm that can be used to perform full-wave simulations of clusters of arbitrary particles. We utilize this method to analyze the scattering of the presented designs numerically. Herein we provide useful guidelines for the fabrication of this cloak with self-assembly methods by investigating the effects of disorder.
Phase structure of mathcal{N} = 2* SYM on ellipsoids
NASA Astrophysics Data System (ADS)
Marmiroli, Daniele
2016-06-01
We analyse the phase structure of an mathcal{N} = 2 massive deformation of mathcal{N} = 4 SYM theory on a four-dimensional ellipsoid using recent results on supersymmetric localisation. Besides the 't Hooft coupling λ, the relevant parameters appearing in the theory and discriminating between the different phases are the hypermultiplet mass M and the deformation (or squashing) parameter Q. Geometric deformation manifests itself as an effective mass term, thus braking the conformal invariance of the theory with massless hypermultiplets. The structure of perturbative corrections around the spherical geometry is analysed in the details and a systematic computational procedure is given, together with the first few corrections. The master field approximation of the matrix model associated to the analytically continued theory in the regime Q 2 M and on the compact space is exactly solvable and does not display any phase transition, similarly to mathcal{N} = 2 SU ( N) SYM with 2 N massive hypermultiplets. In the strong coupling limit, equivalent in our settings to the decompactification of the four-dimensional ellipsoid, we find evidence that the theory undergoes an infinite number of phase transitions starting at finite coupling and accumulating at λ = 8. Quite interestingly, the threshold points at which transitions occur can be pushed towards the weak coupling region by drifting Q to the value 2 M.
Hard ellipsoids: analytically approaching the exact overlap distance.
Guevara-Rodríguez, F de J; Odriozola, G
2011-08-28
Following previous work [G. Odriozola and F. de J. Guevara-Rodríguez, J. Chem. Phys. 134, 201103 (2011)], the replica exchange Monte Carlo technique is used to produce the equation of state of hard 1:5 aspect-ratio oblate ellipsoids for a wide density range. Here, in addition to the analytical approximation of the overlap distance given by Berne and Pechukas (BP) and the exact numerical solution of Perram and Wertheim, we tested a simple modification of the original BP approximation (MBP) which corrects the known T-shape mismatch of BP for all aspect ratios. We found that the MBP equation of state shows a very good quantitative agreement with the exact solution. The MBP analytical expression allowed us to study size effects on the previously reported results. For the thermodynamic limit, we estimated the exact 1:5 hard ellipsoid isotropic-nematic transition at the volume fraction 0.343 ± 0.003, and the nematic-solid transition in the volume fraction interval (0.592 ± 0.006)-(0.634 ± 0.008). PMID:21895200
The microdosimetry of boron neutron capture therapy in a randomised ellipsoidal cell geometry.
Nichols, T L; Miller, L F; Kabalka, G W
2005-01-01
Two reactions deliver the majority of local dose in boron neutron capture therapy. The ionised particles (protons, alpha particles and lithium nuclei) produced in the two reactions, 10B(n,alpha,gamma)7Li and 14N(n,p)14O, have short ranges that are less than -14 microm (which is on the order of the diameter of a typical human cell). The ionised particles are heavy and are in the 2+ charge state in the case of the boron reactions. These heavy 2+ ions will do significant damage to molecules near their tracks. Thus, the distribution of nitrogen and, in particular, of boron determines the spatial characteristics of the radiation field. Since the distribution of nitrogen is nearly homogeneous in the brain and is not easily altered for the purpose of radiotherapy, the spatial variation in the radiation dose is due mainly to the spatial distribution of boron. This implies that the spatial distribution of boron determines the microscopic energy deposition and therefore the spatial characteristics of the microscopic dose. The microscopic dose from the (n,alpha) and (n,p) reactions has been examined in detail and, as averred, the proton dose is relatively homogeneous except for statistical variability. The statistical variability in essence adds a false spatial variability that would not be seen if a large number of histories were performed. Since the majority of spatial variability occurs in the boron distribution, the (n,p) reaction can be suppressed to better understand the spatial distribution effects on the microscopic dose. Programs have been written in FORTRAN using Monte Carlo techniques to model ellipsoidal cells that are either randomly sized and located in the region of interest or are arranged in a face centred cubic array and are identical except for the location of the nuclei, which may be random. It is shown that closely packed prolate ellipsoidal cells with a large eccentricity in one dimension will receive a larger nuclear dose than cells that are more
Integrability and symmetric spaces
Ferreira, L.A.
1989-01-01
It is shown that a sufficient condition for a model describing the motion of a particle on a coset space to possess a Fundamental Poisson bracket Relation, and consequently charges in involution, is that it must be a symmetric space. The conditions, a Hamiltonian, or any functions of the canonical variables, has to satisfy in order to commute with these charges, are studied. It is show that, for the case of the noncompact symmetric spaces, these conditions lead to an algebraic structure which lays an important role in the construction of conserved quantities.
Braids, shuffles and symmetrizers
NASA Astrophysics Data System (ADS)
Isaev, A. P.; Ogievetsky, O. V.
2009-07-01
Multiplicative analogues of the shuffle elements of the braid group rings are introduced; in local representations they give rise to certain graded associative algebras (b-shuffle algebras). For the Hecke and BMW algebras, the (anti)-symmetrizers have simple expressions in terms of the multiplicative shuffles. The (anti)-symmetrizers can be expressed in terms of the highest multiplicative 1-shuffles (for the Hecke and BMW algebras) and in terms of the highest additive 1-shuffles (for the Hecke algebras). The spectra and multiplicities of eigenvalues of the operators of the multiplication by the multiplicative and additive 1-shuffles are examined. Dedicated to the memory of Aleosha Zamolodchikov.
NASA Astrophysics Data System (ADS)
Soszynski, I.; Udalski, A.; Kubiak, M.; Szymanski, M. K.; Pietrzynski, G.; Zebrun, K.; Szewczyk, O.; Wyrzykowski, L.; Dziembowski, W. A.
2004-12-01
We used the OGLE-II and OGLE-III photometry of red giants in the Large Magellanic Cloud to select and study objects revealing ellipsoidal variability. We detected 1546 candidates for long period ellipsoidal variables and 121 eclipsing binary systems with clear ellipsoidal modulation. The ellipsoidal red giants follow a period--luminosity (PL) relationship (sequence E), and the scatter of the relation is correlated with the amplitude of variability: the larger the amplitude, the smaller the scatter. We note that some of the ellipsoidal candidates exhibit simultaneously OGLE Small Amplitude Red Giants pulsations. Thus, in some cases the Long Secondary Period (LSP) phenomenon can be explained by the ellipsoidal modulation. We also select about 1600 red giants with distinct LSP, which are not ellipsoidal variables. We discover that besides the sequence D in the PL diagram known before, the LSP giants form additional less numerous sequence for longer periods. We notice that the PL sequence of the ellipsoidal candidates is a direct continuation of the LSP sequence toward fainter stars, what might suggest that the LSP phenomenon is related to binarity but there are strong arguments against such a possibility. About 10% of the presented light curves reveal clear deformation by the eccentricity of the system orbits. The largest estimated eccentricity in our sample is about 0.4. All presented data, including individual BVI observations and finding charts are available from the OGLE Internet archive.
Liu, Chang; Wang, Guofeng; Xie, Qinglu; Zhang, Yanchao
2014-01-01
Effective fault classification of rolling element bearings provides an important basis for ensuring safe operation of rotating machinery. In this paper, a novel vibration sensor-based fault diagnosis method using an Ellipsoid-ARTMAP network (EAM) and a differential evolution (DE) algorithm is proposed. The original features are firstly extracted from vibration signals based on wavelet packet decomposition. Then, a minimum-redundancy maximum-relevancy algorithm is introduced to select the most prominent features so as to decrease feature dimensions. Finally, a DE-based EAM (DE-EAM) classifier is constructed to realize the fault diagnosis. The major characteristic of EAM is that the sample distribution of each category is realized by using a hyper-ellipsoid node and smoothing operation algorithm. Therefore, it can depict the decision boundary of disperse samples accurately and effectively avoid over-fitting phenomena. To optimize EAM network parameters, the DE algorithm is presented and two objectives, including both classification accuracy and nodes number, are simultaneously introduced as the fitness functions. Meanwhile, an exponential criterion is proposed to realize final selection of the optimal parameters. To prove the effectiveness of the proposed method, the vibration signals of four types of rolling element bearings under different loads were collected. Moreover, to improve the robustness of the classifier evaluation, a two-fold cross validation scheme is adopted and the order of feature samples is randomly arranged ten times within each fold. The results show that DE-EAM classifier can recognize the fault categories of the rolling element bearings reliably and accurately. PMID:24936949
Amore, Paolo; Fernández, Francisco M.; Garcia, Javier; Gutierrez, German
2014-04-15
We study both analytically and numerically the spectrum of inhomogeneous strings with PT-symmetric density. We discuss an exactly solvable model of PT-symmetric string which is isospectral to the uniform string; for more general strings, we calculate exactly the sum rules Z(p)≡∑{sub n=1}{sup ∞}1/E{sub n}{sup p}, with p=1,2,… and find explicit expressions which can be used to obtain bounds on the lowest eigenvalue. A detailed numerical calculation is carried out for two non-solvable models depending on a parameter, obtaining precise estimates of the critical values where pair of real eigenvalues become complex. -- Highlights: •PT-symmetric Hamiltonians exhibit real eigenvalues when PT symmetry is unbroken. •We study PT-symmetric strings with complex density. •They exhibit regions of unbroken PT symmetry. •We calculate the critical parameters at the boundaries of those regions. •There are exact real sum rules for some particular complex densities.
Souza Dutra, A. de; Santos, V. G. C. S. dos; Amaro de Faria, A. C. Jr.
2007-06-15
Some kinks for non-Hermitian quantum field theories in 1+1 dimensions are constructed. A class of models where the soliton energies are stable and real are found. Although these kinks are not Hermitian, they are symmetric under PT transformations.
Anisotropic hypersonic phonon propagation in films of aligned ellipsoids.
Beltramo, Peter J; Schneider, Dirk; Fytas, George; Furst, Eric M
2014-11-14
A material with anisotropic elastic mechanical properties and a direction-dependent hypersonic band gap is fabricated using ac electric field-directed convective self-assembly of colloidal ellipsoids. The frequency of the gap, which is detected in the direction perpendicular to particle alignment and entirely absent parallel to alignment, and the effective sound velocities can be tuned by the particle aspect ratio. We hypothesize that the band gap originates from the primary eigenmode peak, the m-splitted (s,1,2) mode, of the particle resonating with the effective medium. These results reveal the potential for powerful control of the hypersonic phononic band diagram by combining anisotropic particles and self-assembly. PMID:25432048
Development of ellipsoidal focusing mirror for soft x-ray and extreme ultraviolet light
NASA Astrophysics Data System (ADS)
Mimura, Hidekazu; Takei, Yoshinori; Saito, Takahiro; Kume, Takehiro; Motoyama, Hiroto; Egawa, Satoru; Takeo, Yoko; Higashi, Takahiro
2015-08-01
Mirrors are key devices for creating various systems in optics. Focusing X-ray and extreme ultraviolet (EUV) light requires mirror surfaces with an extremely high accuracy. The figure of an ellipsoidal mirror is obtained by rotating an elliptical profile, and using such a mirror, soft X-ray and EUV light can be focused to dimensions on the order of nanometers without chromatic aberration. Although the theoretical performance of ellipsoidal mirrors is extremely high, the fabrication of an ideal ellipsoidal mirror remains problematic. Based on this background, we have been working to develop a fabrication system for ellipsoidal mirrors. In this proceeding, we briefly introduce the fabrication process and the soft X-ray focusing performance of the ellipsoidal mirror fabricated using the proposed process.
Equilibrium of a galactic bar. II. Stellar-dynamical counterparts of the S-type Riemann ellipsoids
Vandervoort, P.O.; Welty, D.E.
1982-12-15
The family of triaxial stellar systems described in Paper I of this series is generalized to include, in addition to the previous dependence on Jacobi's integral, a dependence of the distribution function on a second isolating integral of the motion of a star in the prevailing gravitational field. The second integral is approximated with the aid of a model of the stellar orbits which is valid in the absence of important resonances and which should be accurate in the systems of relatively small central concentration on which this investigation concentrates. The new stellar systems are stellar-dynamical counterparts of the classical S-type Riemann ellipsoids well known in the study of self-gravitating fluid systems, and, within the framework of stellar dynamics, they are also three-dimensional counterparts of the elliptical disks studied by Freeman and by Hunter. The Riemann-like stellar systems form an extensive family, and they exhibit a rich interplay of effects of the rotations of their triaxial figures and effects of the dependence of their distribution functions on the second integral of the motion. The family includes stellar-dynamical counterparts of the classical Maclaurin spheroids, Jacobi ellipsoids, and Dedekind ellipsoids. The study of triaxial, Riemann-like systems is related to the study of bar modes of oscillation in corresponding axisymmetric, Maclaurin-like systems. On the basis of this relationship, it is shown that an axisymmetric stellar system having the structure of a uniformly rotating polytrope of index n = 0.5 is dynamically unstable with respect to a bar mode if the ratio of the rotational kinetic energy to the magnitude of the gravitational potential energy exceeds 0.166.
Rome, J.A.; Harris, J.H.
1984-01-01
A fusion reactor device is provided in which the magnetic fields for plasma confinement in a toroidal configuration is produced by a plurality of symmetrical modular coils arranged to form a symmetric modular torsatron referred to as a symmotron. Each of the identical modular coils is helically deformed and comprise one field period of the torsatron. Helical segments of each coil are connected by means of toroidally directed windbacks which may also provide part of the vertical field required for positioning the plasma. The stray fields of the windback segments may be compensated by toroidal coils. A variety of magnetic confinement flux surface configurations may be produced by proper modulation of the winding pitch of the helical segments of the coils, as in a conventional torsatron, winding the helix on a noncircular cross section and varying the poloidal and radial location of the windbacks and the compensating toroidal ring coils.
Symmetric splitting of very light systems
Grotowski, K.; Majka, Z.; Planeta, R.; Szczodrak, M.; Chan, Y.; Guarino, G.; Moretto, L.G.; Morrissey, D.J.; Sobotka, L.G.; Stokstad, R.G.; Tserruya, I.; Wald, S.; Wozniak, G.J.
1984-10-01
Inclusive and coincidence measurements have been performed to study symmetric products from the reactions 74--186 MeV /sup 12/C+ /sup 40/Ca, 141 MeV /sup 9/Be+ /sup 40/Ca, and 153 MeV /sup 6/Li+ /sup 40/Ca. The binary decay of the composite system has been verified. Energy spectra, angular distributions, and fragment correlations are presented. The total kinetic energies for the symmetric products from these very light composite systems are compared to liquid drop model calculations and fission systematics.
Static cylindrically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Fjällborg, Mikael
2007-05-01
We prove the existence of static solutions to the cylindrically symmetric Einstein Vlasov system, and we show that the matter cylinder has finite extension in two of the three spatial dimensions. The same results are also proved for a quite general class of equations of state for perfect fluids coupled to the Einstein equations, extending the class of equations of state considered by Bicak et al (2004 Class. Quantum Grav.21 1583). We also obtain this result for the Vlasov Poisson system.
Multiple symmetric lipomatosis.
Lee, M S; Lee, M H; Hur, K B
1988-12-01
Multiple symmetric lipomatosis (MSL) is an extremely uncommon disorder. In the medical literatures about 200 cases have been reported. MSL is not associated with other generalized lipomatous disorders, nor are these patient to be necessarily obese. The cause of MSL is unknown. The disorder usually occurs in middle-aged males and there is frequently a history of alcoholism. Some instances of familial occurrence have been reported, but the majority of cases are sporadic. Two cases of MSL are presented. PMID:3267365
Ellipsoidally-shaped local absorbing boundaries for three-dimensional scalar wave propagation
NASA Astrophysics Data System (ADS)
Kallivokas, L. F.; Lee, S.
2004-12-01
In this paper we discuss the performance of second-order absorbing conditions prescribed on ellipsoidally-shaped truncation boundaries for the resolution of scalar wave phenomena in three dimensions. The second-order conditions employed herein belong to a larger class of arbitrarily-shaped convex absorbing boundaries developed earlier [21] for acoustic scattering and radiation problems in unbounded domains. In [21] we discussed their performance when used on spherical truncation boundaries for applications in both the time- and frequency-domains. Here, we extend their applicability to ellipsoidal geometries and demonstrate that significant computational savings are attainable due to the reduced computational domain afforded by the ellipsoid.
Figure correction of a metallic ellipsoidal neutron focusing mirror
Guo, Jiang Yamagata, Yutaka; Morita, Shin-ya; Kato, Jun-ichi; Takeda, Shin; Hino, Masahiro; Furusaka, Michihiro
2015-06-15
An increasing number of neutron focusing mirrors is being adopted in neutron scattering experiments in order to provide high fluxes at sample positions, reduce measurement time, and/or increase statistical reliability. To realize a small focusing spot and high beam intensity, mirrors with both high form accuracy and low surface roughness are required. To achieve this, we propose a new figure correction technique to fabricate a two-dimensional neutron focusing mirror made with electroless nickel-phosphorus (NiP) by effectively combining ultraprecision shaper cutting and fine polishing. An arc envelope shaper cutting method is introduced to generate high form accuracy, while a fine polishing method, in which the material is removed effectively without losing profile accuracy, is developed to reduce the surface roughness of the mirror. High form accuracy in the minor-axis and the major-axis is obtained through tool profile error compensation and corrective polishing, respectively, and low surface roughness is acquired under a low polishing load. As a result, an ellipsoidal neutron focusing mirror is successfully fabricated with high form accuracy of 0.5 μm peak-to-valley and low surface roughness of 0.2 nm root-mean-square.
Local Origin of Global Contact Numbers in Frictional Ellipsoid Packings
NASA Astrophysics Data System (ADS)
Schaller, Fabian M.; Neudecker, Max; Saadatfar, Mohammad; Delaney, Gary W.; Schröder-Turk, Gerd E.; Schröter, Matthias
2015-04-01
In particulate soft matter systems the average number of contacts Z of a particle is an important predictor of the mechanical properties of the system. Using x-ray tomography, we analyze packings of frictional, oblate ellipsoids of various aspect ratios α , prepared at different global volume fractions ϕg. We find that Z is a monotonically increasing function of ϕg for all α . We demonstrate that this functional dependence can be explained by a local analysis where each particle is described by its local volume fraction ϕl computed from a Voronoi tessellation. Z can be expressed as an integral over all values of ϕl: Z (ϕg,α ,X )=∫Zl(ϕl,α ,X )P (ϕl|ϕg)d ϕl . The local contact number function Zl(ϕl,α ,X ) describes the relevant physics in term of locally defined variables only, including possible higher order terms X . The conditional probability P (ϕl|ϕg) to find a specific value of ϕl given a global packing fraction ϕg is found to be independent of α and X . Our results demonstrate that for frictional particles a local approach is not only a theoretical requirement but also feasible.
Entropy production of a Brownian ellipsoid in the overdamped limit.
Marino, Raffaele; Eichhorn, Ralf; Aurell, Erik
2016-01-01
We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called "anomalous" contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the "anomalous" entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the "anomalous entropy" for prolate and oblate spheroids and for near-spherical Brownian particles. PMID:26871049
Local origin of global contact numbers in frictional ellipsoid packings.
Schaller, Fabian M; Neudecker, Max; Saadatfar, Mohammad; Delaney, Gary W; Schröder-Turk, Gerd E; Schröter, Matthias
2015-04-17
In particulate soft matter systems the average number of contacts Z of a particle is an important predictor of the mechanical properties of the system. Using x-ray tomography, we analyze packings of frictional, oblate ellipsoids of various aspect ratios α, prepared at different global volume fractions ϕg. We find that Z is a monotonically increasing function of ϕg for all α. We demonstrate that this functional dependence can be explained by a local analysis where each particle is described by its local volume fraction ϕl computed from a Voronoi tessellation. Z can be expressed as an integral over all values of ϕl: Z(ϕg,α,X)=∫Zl(ϕl,α,X)P(ϕl|ϕg)dϕl. The local contact number function Zl(ϕl,α,X) describes the relevant physics in term of locally defined variables only, including possible higher order terms X. The conditional probability P(ϕl|ϕg) to find a specific value of ϕl given a global packing fraction ϕg is found to be independent of α and X. Our results demonstrate that for frictional particles a local approach is not only a theoretical requirement but also feasible. PMID:25933340
Cryogenic Pressure Control Modeling for Ellipsoidal Space Tanks
NASA Technical Reports Server (NTRS)
Lopez, Alfredo; Grayson, Gary D.; Chandler, Frank O.; Hastings, Leon J.; Heyadat, Ali
2007-01-01
A computational fluid dynamics (CFD) model is developed to simulate pressure control of an ellipsoidal-shaped liquid hydrogen tank under external heating in normal gravity. Pressure control is provided by an axial jet thermodynamic vent system (TVS) centered within the vessel that injects cooler liquid into the tank, mixing the contents and reducing tank pressure. The two-phase cryogenic tank model considers liquid hydrogen in its own vapor with liquid density varying with temperature only and a fully compressible ullage. The axisymmetric model is developed using a custom version of the commercially available FLOW-31) software. Quantitative model validation is ,provided by engineering checkout tests performed at Marshall Space Flight Center in 1999 in support of the Solar Thermal Upper Stage_ Technology Demonstrator (STUSTD) program. The engineering checkout tests provide cryogenic tank self-pressurization test data at various heat leaks and tank fill levels. The predicted self-pressurization rates, ullage and liquid temperatures at discrete locations within the STUSTD tank are in good agreement with test data. The work presented here advances current CFD modeling capabilities for cryogenic pressure control and helps develop a low cost CFD-based design process for space hardware.
Dynamical facilitation governs glassy dynamics in suspensions of colloidal ellipsoids
Mishra, Chandan K.; Hima Nagamanasa, K.; Ganapathy, Rajesh; Sood, A. K.; Gokhale, Shreyas
2014-01-01
One of the greatest challenges in contemporary condensed matter physics is to ascertain whether the formation of glasses from liquids is fundamentally thermodynamic or dynamic in origin. Although the thermodynamic paradigm has dominated theoretical research for decades, the purely kinetic perspective of the dynamical facilitation (DF) theory has attained prominence in recent times. In particular, recent experiments and simulations have highlighted the importance of facilitation using simple model systems composed of spherical particles. However, an overwhelming majority of liquids possess anisotropy in particle shape and interactions, and it is therefore imperative to examine facilitation in complex glass formers. Here, we apply the DF theory to systems with orientational degrees of freedom as well as anisotropic attractive interactions. By analyzing data from experiments on colloidal ellipsoids, we show that facilitation plays a pivotal role in translational as well as orientational relaxation. Furthermore, we demonstrate that the introduction of attractive interactions leads to spatial decoupling of translational and rotational facilitation, which subsequently results in the decoupling of dynamical heterogeneities. Most strikingly, the DF theory can predict the existence of reentrant glass transitions based on the statistics of localized dynamical events, called excitations, whose duration is substantially smaller than the structural relaxation time. Our findings pave the way for systematically testing the DF approach in complex glass formers and also establish the significance of facilitation in governing structural relaxation in supercooled liquids. PMID:25313030
Entropy production of a Brownian ellipsoid in the overdamped limit
NASA Astrophysics Data System (ADS)
Marino, Raffaele; Eichhorn, Ralf; Aurell, Erik
2016-01-01
We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called "anomalous" contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the "anomalous" entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the "anomalous entropy" for prolate and oblate spheroids and for near-spherical Brownian particles.
Electro-orientation of ellipsoidal erythrocytes. Theory and experiment.
Miller, R D; Jones, T B
1993-01-01
The frequency-dependent orientation of human and llama erythrocytes suspended in isotonic solutions and subjected to linearly polarized electric fields is examined. Human erythrocytes may be represented as oblate spheroids (3.9:3.9:1.1 microns) with two distinguishable orientations, while the llama cells are approximated as ellipsoids with three distinct axes (4.0:2.0:1.1 microns). Under appropriate experimental conditions, both orientations of the human cells and all three orientations of the llama cells are observed. A theoretical cell model which accounts for the membrane as a thin confocal layer of ideal capacitance is used to predict the orientational spectra. The predicted spectra compare favorably in frequency range and orientational sequence with experimental data. Estimates for cell internal conductivity and permittivity are obtained by adjusting the values of these important parameters to achieve the closet fit of the theoretical curves to the data. By the use of this method, the internal conductivity of llama erythrocytes is estimated to be 0.26 S/m (+/- 20%), while the effective internal dielectric constant and conductivity of Euglena gracilis are estimated to be 120 (+/- 10%) and 0.43 S/m (+/- 20%), respectively. PMID:8324193
Photometry of 20 eclipsing and ellipsoidal binary systems
NASA Astrophysics Data System (ADS)
Shobbrook, R. R.
2004-12-01
A total of almost 2000 V observations of 20 eclipsing and ellipsoidal bright binary stars was collected between 1991 and 2001 for the purpose of determining more recent epoch ephemerides for the light curves than are available in the literature. The original purpose was to provide the Sydney University Stellar Interferometer (SUSI) with orbital periods and particularly the accurate times of minimum separation (light curve minima), so that the SUSI observations need not be used to determine them. This paper provides the periods, the times of primary minima and the phases of secondary minima for the 20 stars at an epoch as near as possible to the year 2000. No attempt has been made in this report to determine other parameters such as {apsidal motion} or stellar radii. Since the program was started in 1991, data for these stars taken in the period from late 1989 to early 1993 has also been available from the Hipparcos satellite; the light curves shown here include both sets of observations.
Photometry of 20 eclipsing and ellipsoidal binary systems
NASA Astrophysics Data System (ADS)
Shobbrook, R. R.
2005-12-01
ERRATUM: In the published paper the phase diagrams of pi Sco and AL Scl were ommitted. The version reproduced in JAD11, 7 is the complete version. A total of almost 2000 V observations of 20 eclipsing and ellipsoidal bright binary stars was collected between 1991 and 2001 for the purpose of determining more recent epoch ephemerides for the light curves than are available in the literature. The original purpose was to provide the Sydney University Stellar Interferometer (SUSI) with orbital periods and particularly the accurate times of minimum separation (light curve minima), so that the SUSI observations need not be used to determine them. This paper provides the periods, the times of primary minima and the phases of secondary minima for the 20 stars at an epoch as near as possible to the year 2000. No attempt has been made in this report to determine other parameters such as {apsidal motion} or stellar radii. Since the program was started in 1991, data for these stars taken in the period from late 1989 to early 1993 has also been available from the Hipparcos satellite; the light curves shown here include both sets of observations.
Figure correction of a metallic ellipsoidal neutron focusing mirror
NASA Astrophysics Data System (ADS)
Guo, Jiang; Yamagata, Yutaka; Morita, Shin-ya; Takeda, Shin; Kato, Jun-ichi; Hino, Masahiro; Furusaka, Michihiro
2015-06-01
An increasing number of neutron focusing mirrors is being adopted in neutron scattering experiments in order to provide high fluxes at sample positions, reduce measurement time, and/or increase statistical reliability. To realize a small focusing spot and high beam intensity, mirrors with both high form accuracy and low surface roughness are required. To achieve this, we propose a new figure correction technique to fabricate a two-dimensional neutron focusing mirror made with electroless nickel-phosphorus (NiP) by effectively combining ultraprecision shaper cutting and fine polishing. An arc envelope shaper cutting method is introduced to generate high form accuracy, while a fine polishing method, in which the material is removed effectively without losing profile accuracy, is developed to reduce the surface roughness of the mirror. High form accuracy in the minor-axis and the major-axis is obtained through tool profile error compensation and corrective polishing, respectively, and low surface roughness is acquired under a low polishing load. As a result, an ellipsoidal neutron focusing mirror is successfully fabricated with high form accuracy of 0.5 μm peak-to-valley and low surface roughness of 0.2 nm root-mean-square.
Inertia Factors of Ellipsoids for Use in Airship Design
NASA Technical Reports Server (NTRS)
Tuckerman, L. B.
1926-01-01
This report is based on a study made by the writer as a member of the Special Committee on Design of Army Semirigid Airship RS-1 appointed by the National Advisory Committee for Aeronautics. The increasing interest in airships has made the problem of the potential flow of a fluid about an ellipsoid of considerable practical importance. In 1833 George Green, in discussing the effect of the surrounding medium upon the period of a pendulum, derived three elliptic integrals, in terms of which practically all the characteristics of this type of motion can be expressed. The theory of this type of motion is very fully given by Horace Lamb in his "Hydrodynamics," and applications to the theory of airships by many other writers. Tables of the inertia coefficients derived from these integrals are available for the most important special cases. These tables are adequate for most purposes, but occasionally it is desirable to know the values of these integrals in other cases where tabulated values are not available. For this reason it seems worth while to assemble a collection of formulae which would enable them to be computed directly from standard tables of elliptic integrals, circular and hyperbolic functions and logarithms without the need of intermediate transformations. Some of the formulae for special cases (elliptic cylinder, prolate spheroid, oblate spheroid, etc.) have been published before, but the general forms and some special cases have not been found in previous publications. (author)
Concentration, ellipsoidal collapse, and the densest dark matter haloes
NASA Astrophysics Data System (ADS)
Okoli, Chiamaka; Afshordi, Niayesh
2016-03-01
The smallest dark matter haloes are the first objects to form in the hierarchical structure formation of cold dark matter (CDM) cosmology and are expected to be the densest and most fundamental building blocks of CDM structures in our Universe. Nevertheless, the physical characteristics of these haloes have stayed illusive, as they remain well beyond the current resolution of N-body simulations (at redshift zero). However, they dominate the predictions (and uncertainty) in expected dark matter annihilation signal, amongst other astrophysical observables. Using the conservation of total energy and the ellipsoidal collapse framework, we can analytically find the mean and scatter of concentration c and 1D velocity dispersion σ1d for haloes of different virial mass M200. Both c and σ _1d/M_{200}^{1/3} are in good agreement with numerical results within the regime probed by simulations - slowly decreasing functions of mass that approach constant values at large masses. In particular, the predictions for the 1D velocity dispersion of cluster mass haloes are surprisingly robust as the inverse heat capacity of cosmological haloes crosses zero at M200 ˜ 1014 M⊙. However, we find that current extrapolations from simulations to smallest CDM haloes dramatically depend on the assumed profile (e.g. NFW versus Einasto) and fitting function, which is why theoretical considerations, such as the one presented here, can significantly constrain the range of feasible predictions.
Collective Swimming in a Suspension of Ellipsoidal Squirmers
NASA Astrophysics Data System (ADS)
Kyoya, Kohei; Matsunaga, Daiki; Imai, Yohsuke; Yamaguchi, Takami; Ishikawa, Takuji
2013-11-01
Some recent research efforts have demonstrated the importance of biomechanics in understanding certain aspects of microorganism behaviors such as locomotion and collective motions of cells. However, former studies had problems in accurately computing many-body interaction of model microorganisms. In this study, we propose a boundary element method, based on the double-layer representation, for calculating interactions of many-body swimmers in Stokes flow regime. The proposed method allows us to analyze a large system size that could not be handled before. The model microorganism is assumed to be ellipsoid and propels itself by generating tangential velocities on its surface. Two types of microorganisms were modeled by varying the surface velocity; one is a ``puller'' which has the thrust-generating apparatus in front of the body such as Chlamydomonas, and the other is a ``pusher'' which has the thrust behind the body such as bacteria or spermatozoa. We then analyze interactions of 100 pullers or pushers. In both cases, some sorts of collective swimming were observed. In particular, pullers and neutral swimmers created large clusters and generated coherent structures.
The impact of ellipsoidal particle shape on pebble breakage in gravel
Tuitz, Christoph; Exner, Ulrike; Frehner, Marcel; Grasemann, Bernhard
2012-01-01
We have studied the influence of particle shape and consequently loading configuration on the breakage load of fluvial pebbles. Unfortunately, physical strength tests on pebbles, i.e., point-load tests, can only be conducted under one specific stable loading configuration. Therefore, the physical uniaxial strength tests performed in this study were extended by a two-dimensional finite-element stress analysis, which is capable of investigating those scenarios that are not possible in physical tests. Breakage load, equivalent to that measured in unidirectional physical tests, was determined from the results of the stress analysis by a maximum tensile stress-based failure criterion. Using this assumption, allows the determination of breakage load for a range of different kind of synthetic loading configurations and its comparison with the natural breakage load distribution of the physical strength tests. The results of numerical modelling indicated that the configuration that required the least breakage load corresponded with the minor principal axis of the ellipsoidal pebbles. In addition, most of the simulated gravel-hosted loading configurations exceeded the natural breakage load distribution of fluvial pebbles obtained from the physical strength tests. PMID:26321870
Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation
Yang, Jaw-Yen; Yan, Chin-Yuan; Huang, Juan-Chen; Li, Zhihui
2014-01-01
Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidal-statistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied. PMID:25104904
Ellipsoidal universe can solve the cosmic microwave background quadrupole problem.
Campanelli, L; Cea, P; Tedesco, L
2006-09-29
The recent 3 yr Wilkinson Microwave Anisotropy Probe data have confirmed the anomaly concerning the low quadrupole amplitude compared to the best-fit Lambda-cold dark matter prediction. We show that by allowing the large-scale spatial geometry of our universe to be plane symmetric with eccentricity at decoupling or order 10(-2), the quadrupole amplitude can be drastically reduced without affecting higher multipoles of the angular power spectrum of the temperature anisotropy. PMID:17026023
Study of electron trapping by a transversely ellipsoidal bubble in the laser wake-field acceleration
Cho, Myung-Hoon; Kim, Young-Kuk; Hur, Min Sup
2013-09-15
We present electron trapping in an ellipsoidal bubble which is not well explained by the spherical bubble model by [Kostyukov et al., Phys. Rev. Lett. 103, 175003 (2009)]. The formation of an ellipsoidal bubble, which is elongated transversely, frequently occurs when the spot size of the laser pulse is large compared to the plasma wavelength. First, we introduce the relation between the bubble size and the field slope inside the bubble in longitudinal and transverse directions. Then, we provide an ellipsoidal model of the bubble potential and investigate the electron trapping condition by numerical integration of the equations of motion. We found that the ellipsoidal model gives a significantly less restrictive trapping condition than that of the spherical bubble model. The trapping condition is compared with three-dimensional particle-in-cell simulations and the electron trajectory in test potential simulations.
MERIDIONAL TILT OF THE STELLAR VELOCITY ELLIPSOID DURING BAR BUCKLING INSTABILITY
Saha, Kanak; Pfenniger, Daniel; Taam, Ronald E.
2013-02-20
The structure and evolution of the stellar velocity ellipsoid play an important role in shaping galaxies undergoing bar-driven secular evolution and the eventual formation of a boxy/peanut bulge such as is present in the Milky Way. Using collisionless N-body simulations, we show that during the formation of such a boxy/peanut bulge, the meridional shear stress of stars, which can be measured by the meridional tilt of the velocity ellipsoid, reaches a characteristic peak in its time evolution. It is shown that the onset of a bar buckling instability is closely connected to the maximum meridional tilt of the stellar velocity ellipsoid. Our findings bring a new insight to this complex gravitational instability of the bar which complements the buckling instability studies based on orbital models. We briefly discuss the observed diagnostics of the stellar velocity ellipsoid during such a phenomenon.
Generation of 3D ellipsoidal laser beams by means of a profiled volume chirped Bragg grating
NASA Astrophysics Data System (ADS)
Mironov, S. Yu; Poteomkin, A. K.; Gacheva, E. I.; Andrianov, A. V.; Zelenogorskii, V. V.; Vasiliev, R.; Smirnov, V.; Krasilnikov, M.; Stephan, F.; Khazanov, E. A.
2016-05-01
A method for shaping photocathode laser driver pulses into 3D ellipsoidal form has been proposed and implemented. The key idea of the method is to use a chirped Bragg grating recorded within the ellipsoid volume and absent outside it. If a beam with a constant (within the grating reflection band) spectral density and uniform (within the grating aperture) cross-section is incident on such a grating, the reflected beam will be a 3D ellipsoid in space and time. 3D ellipsoidal beams were obtained in experiment for the first time. It is expected that such laser beams will allow the electron bunch emittance to be reduced when applied at R± photo injectors.
Evaluation of surface figure error profile of ellipsoidal mirror for soft x-ray focusing
NASA Astrophysics Data System (ADS)
Takeo, Yoko; Saito, Takahiro; Mimura, Hidekazu
2015-08-01
It is possible to achieve soft X-ray nanofocusing with a high efficiency and no chromatic aberration by using an ultraprecise ellipsoidal mirror. Surface figure metrology is key in the improvement of surface figure accuracy. In this study, we propose a ptychographic phase retrieval method using a visible light laser to measure the surface figure error profile of an ellipsoidal mirror. We introduce a simple experimental system for ptychographic phase retrieval and demonstrate the basic performance of the proposed system. Obtainable wavefront information provides both the figure error and the alignment of the ellipsoidal mirror that yield the best focusing. This developed method is required for offline adjustments when an ellipsoidal mirror is installed in the beamline of synchrotron radiation or X-ray free-electron laser light sources.
Impingement of Water Droplets on an Ellipsoid with Fineness Ration 10 in Axisymmetric Flow
NASA Technical Reports Server (NTRS)
Brun, Rinaldo J; Dorsch, Robert G
1954-01-01
The presence of radomes and instruments that are sensitive to water films or ice formations in the nose section of all-weather aircraft and missiles necessitates a knowledge of the droplet impingement characteristics of bodies of revolution. Because it is possible to approximate many of these bodies with an ellipsoid of revolution, droplet trajectories about an ellipsoid of revolution with a fineness ratio of 10 were computed for incompressible axisymmetric air flow. From the computed droplet trajectories, the following impingement characteristics of the ellipsoid surface were obtained and are presented in terms of dimensionless parameters: (1) total rate of water impingement, (2) extent of droplet impingement zone, and (3) local rate of water impingement. These impingement characteristics are compared briefly with those previously reported for an ellipsoid of revolution with a fineness ratio of 5.
Symmetrization for redundant channels
NASA Technical Reports Server (NTRS)
Tulplue, Bhalchandra R. (Inventor); Collins, Robert E. (Inventor)
1988-01-01
A plurality of redundant channels in a system each contain a global image of all the configuration data bases in each of the channels in the system. Each global image is updated periodically from each of the other channels via cross channel data links. The global images of the local configuration data bases in each channel are separately symmetrized using a voting process to generate a system signal configuration data base which is not written into by any other routine and is available for indicating the status of the system within each channel. Equalization may be imposed on a suspect signal and a number of chances for that signal to heal itself are provided before excluding it from future votes. Reconfiguration is accomplished upon detecting a channel which is deemed invalid. A reset function is provided which permits an externally generated reset signal to permit a previously excluded channel to be reincluded within the system. The updating of global images and/or the symmetrization process may be accomplished at substantially the same time within a synchronized time frame common to all channels.
Pietanza, L D; Colonna, G; Laporta, V; Celiberto, R; D'Ammando, G; Laricchiuta, A; Capitelli, M
2016-05-01
A new set of electron-vibrational (e-V) processes linking the first 10 vibrational levels of the symmetric mode of CO2 is derived by using a decoupled vibrational model and inserted in the Boltzmann equation for the electron energy distribution function (eedf). The new eedf and dissociation rates are in satisfactory agreement with the corresponding ones obtained by using the e-V cross sections reported in the database of Hake and Phelps (H-P). Large differences are, on the contrary, found when the experimental dissociation cross sections of Cosby and Helm are inserted in the Boltzman equation. Comparison of the corresponding rates with those obtained by using the low-energy threshold energy, reported in the H-P database, shows differences up to orders of magnitude, which decrease with the increasing of the reduced electric field. In all cases, we show the importance of superelastic vibrational collisions in affecting eedf and dissociation rates either in the direct electron impact mechanism or in the pure vibrational mechanism. PMID:27064438
Energy spectra of a particle confined in a finite ellipsoidal shaped potential well
NASA Astrophysics Data System (ADS)
Kereselidze, Tamaz; Tchelidze, Tamar; Nadareishvili, Teimuraz; Kezerashvili, Roman Ya.
2016-07-01
A charged particle confined in a strongly prolate ellipsoidal shaped finite potential well is studied. In the case when a distance R between foci is large and accordingly R-1 is small, the asymptotic solutions of quasiradial and quasiangular equations in prolate spheroidal coordinates are found. We demonstrate that quasiangular wave functions inside and outside of the potential well coincide on the entire surface of strongly prolate ellipsoid if separation parameters are chosen appropriately. This allows us to obtain the transcendental equation for the energy levels by equating the quasiradial wave function and its derivative on the surface of ellipsoid. The obtained equation is solved numerically and algebraically. The calculated energies are in good qualitative and quantitative agreement with the results obtained earlier for the infinitely high ellipsoidal potential well via a numerical solution of the quasiradial and quasiangular equations. An importance of the actual shape of ellipsoidal potential well for calculation of the energy spectrum for the trapped particle is shown. A dependence of the energy spectrum on the effective mass when it is a different constant inside and outside of the ellipsoid is addressed.
Further Evidence for an Elliptical Instability in Rotating Fluid Bars and Ellipsoidal Stars
NASA Astrophysics Data System (ADS)
Ou, Shangli; Tohline, Joel E.; Motl, Patrick M.
2007-08-01
Using a three-dimensional nonlinear hydrodynamic code, we examine the dynamical stability of more than 20 self-gravitating, compressible, ellipsoidal fluid configurations that initially have the same velocity structure as Riemann S-type ellipsoids. Our focus is on ``adjoint'' configurations, in which internal fluid motions dominate over the collective spin of the ellipsoidal figure; Dedekind-like configurations are among this group. We find that, although some models are stable and some are moderately unstable, the majority are violently unstable toward the development of m=1, m=3, and higher-order azimuthal distortions that destroy the coherent, m=2 barlike structure of the initial ellipsoidal configuration on a dynamical timescale. The parameter regime over which our models are found to be unstable generally corresponds with the regime over which incompressible Riemann S-type ellipsoids have been found to be susceptible to an elliptical strain instability. We therefore suspect that an elliptical instability is responsible for the destruction of our compressible analogs of Riemann ellipsoids. The existence of the elliptical instability raises concerns regarding the final fate of neutron stars that encounter the secular bar-mode instability and regarding the spectrum of gravitational waves that will be radiated from such systems.
Empty liquid phase of colloidal ellipsoids: the role of shape and interaction anisotropy.
Varga, Szabolcs; Meneses-Júarez, Efrain; Odriozola, Gerardo
2014-04-01
We study the effect of anisotropic excluded volume and attractive interactions on the vapor-liquid phase transition of colloidal ellipsoids. In our model, the hard ellipsoid is embedded into an ellipsoidal well, where both the shape of the hard ellipsoid and that of the added enclosing ellipsoidal well can be varied independently. The bulk properties of these particles are examined by means of a van der Waals type perturbation theory and validated with replica exchange Monte Carlo simulations. It is shown that both the critical volume fraction (ηc) and the critical temperature (Tc) of the vapor-liquid phase transition vanish with increasing shape anisotropy for oblate shapes, while ηc → 0 and Tc ≠ 0 are obtained for very elongated prolate shapes. These results suggest that the chance to stabilize empty liquids (a liquid phase with vanishing density) is higher in suspensions of rod-like colloidal ellipsoids than in those of plate-like ones. PMID:24712814
Ma, Jian; Diao, Ruisheng; Makarov, Yuri V.; Etingov, Pavel V.; Zhou, Ning; Dagle, Jeffery E.
2010-12-01
The characteristic ellipsoid is a new method to monitor the dynamics of power systems. Decision trees (DTs) play an important role in applying the characteristic ellipsoid method to system operation and analysis. This paper presents the idea and initial results of building DTs for detecting transient dynamic events using the characteristic ellipsoid method. The objective is to determine fault types, fault locations and clearance time in the system using decision trees based on ellipsoids of system transient responses. The New England 10-machine 39-bus system is used for running dynamic simulations to generate a sufficiently large number of transient events in different system configurations. Comprehensive transient simulations considering three fault types, two fault clearance times and different fault locations were conducted in the study. Bus voltage magnitudes and monitored reactive and active power flows are recorded as the phasor measurements to calculate characteristic ellipsoids whose volume, eccentricity, center and projection of the longest axis are used as indices to build decision trees. The DT performances are tested and compared by considering different sets of PMU locations. The proposed method demonstrates that the characteristic ellipsoid method is a very efficient and promising tool to monitor power system dynamic behaviors.
Calculating the torque of the optical vortex tweezer to the ellipsoidal micro-particles
NASA Astrophysics Data System (ADS)
Zhu, Lie; Guo, Zhongyi; Xu, Qiang; Zhang, Jingran; Zhang, Anjun; Wang, Wei; Liu, Yi; li, Yan; Wang, Xinshun; Qu, Shiliang
2015-11-01
In this paper, we have accurately computed the torque of the optical vortex tweezers to the ellipsoidal micro-particles with the method of finite-difference time-domain (FDTD). The transferred orbital angular momentum (OAM) from the vortex beam to the micro-particles can be obtained based on the scattering phase function (SPF) of the micro-particles. We have verified that the calculated SPF of a spherical particle by FDTD agrees well with that by Mie theory, which indicates that the SPF of micro-particles with any shapes can be calculated by FDTD accurately. In addition, with the method of FDTD, we have obtained the SPFs of the different-shape ellipsoidal micro-particles with same volume, including prolate ellipsoids and oblate ellipsoids. Meanwhile, the transferred OAM between the light and the ellipsoidal micro-particles have been deduced analytically by the relative formulas. And the rotating angular velocities of the trapped ellipsoidal micro-particles have been investigated and discussed in detail based on the obtained corresponding SPFs.
NASA Technical Reports Server (NTRS)
Dorsch, Robert G.; Brun, Rinaldo J.
1954-01-01
Trajectories of water droplets about an ellipsoid of revolution with a fineness ratio of 5 (which often approximates the shape of an aircraft fuselage or missile) were computed with the aid of a differential analyzer. Analyses of these trajectories indicate that the local concentration of liquid water at various points about an ellipsoid in flight through a droplet field varies considerably and under some conditions may be several times the free-stream concentration. Curves of the local concentration factor as a function of spatial position were obtained and are presented in terms of dimensionless parameters Re(sub 0) (free-stream Reynolds number) and K (inertia), which contain flight and atmospheric conditions. These curves show that the local concentration factor at any point is very sensitive to change in the dimensionless parameters Re(sub 0) and K. These data indicate that the expected local concentration factors should be considered when choosing the location of, or when determining antiicing heat requirements for, water- or ice-sensitive devices that protrude into the stream from an aircraft fuselage or missile. Similarly, the concentration factor should be considered when choosing the location on an aircraft of instruments that measure liquid-water content or droplet-size distribution in the atmosphere.
Symmetric Waveguide Orthomode Junctions
NASA Technical Reports Server (NTRS)
Wollack, E. J.; Grammer, W.
2003-01-01
Imaging applications at millimeter and submillimeter wavelengths demand precise characterization of the amplitude, spectrum, and polarization of the electromagnetic radiation. The use of a waveguide orthomode transducer (OMT) can help achieve these goals by increasing spectral coverage and sensitivity while reducing exit aperture size, optical spill, instrumental polarization offsets, and lending itself to integration in focal plane arrays. For these reasons, four-old symmetric OMTs are favored over a traditional quasi-optical wire grid for focal plane imaging arrays from a systems perspective. The design, fabrication, and test of OMTs realized with conventional split-block techniques for millimeter wave-bands are described. The design provides a return loss is -20 dB over a full waveguide band (40% bandwidth), and the cross-polarization and isolation are greater than -40 dB for tolerances readily achievable in practice. Prototype examples realized in WR10.0 and WR3.7 wavebands will be considered in detail.
Symmetric Waveguide Orthomode Junctions
NASA Technical Reports Server (NTRS)
Wollack, E. J.; Grammer, W.
2003-01-01
Imaging applications at millimeter and submillimeter wavelengths demand precise characterization of the amplitude, spectrum, and polarization of the electromagnetic radiation. The use of a waveguide orthomode transducer (OMT) can help achieve these goals by increasing spectral coverage and sensitivity while reducing exit aperture size, optical spill, instrumental polarization offsets, and lending itself to integration in focal plane arrays. For these reasons, four-fold symmetric OMTs are favored over a traditional quasi-optical wire grid for focal plane imaging arrays from a systems perspective. The design, fabrication, and test of OMTs realized with conventional split-block techniques for millimeter wave-bands are described. The design provides a return loss is -20 dB over a full waveguide band (40% bandwidth), and the cross-polarization and isolation are greater than -40 dB for tolerances readily achievable in practice. Prototype examples realized in WR10.0 and WR3.7 wavebands will be considered in detail.
Optimal symmetric flight studies
NASA Technical Reports Server (NTRS)
Weston, A. R.; Menon, P. K. A.; Bilimoria, K. D.; Cliff, E. M.; Kelley, H. J.
1985-01-01
Several topics in optimal symmetric flight of airbreathing vehicles are examined. In one study, an approximation scheme designed for onboard real-time energy management of climb-dash is developed and calculations for a high-performance aircraft presented. In another, a vehicle model intermediate in complexity between energy and point-mass models is explored and some quirks in optimal flight characteristics peculiar to the model uncovered. In yet another study, energy-modelling procedures are re-examined with a view to stretching the range of validity of zeroth-order approximation by special choice of state variables. In a final study, time-fuel tradeoffs in cruise-dash are examined for the consequences of nonconvexities appearing in the classical steady cruise-dash model. Two appendices provide retrospective looks at two early publications on energy modelling and related optimal control theory.
Cohen, A P; Janai, E; Rapaport, D C; Schofield, A B; Sloutskin, E
2012-11-14
The microscopic structure of fluids of simple spheres is well known. However, the constituents of most real-life fluids are non-spherical, leading to a coupling between the rotational and translational degrees of freedom. The structure of simple dense fluids of spheroids - ellipsoids of revolution - was only recently determined by direct experimental techniques [A. P. Cohen, E. Janai, E. Mogilko, A. B. Schofield, and E. Sloutskin, Phys. Rev. Lett. 107, 238301 (2011)]. Using confocal microscopy, it was demonstrated that the structure of these simple fluids cannot be described by hard particle models based on the widely used Percus-Yevick approximation. In this paper, we describe a new protocol for determining the shape of the experimental spheroids, which allows us to expand our previous microscopy measurements of these fluids. To avoid the approximations in the theoretical approach, we have also used molecular dynamics simulations to reproduce the experimental radial distribution functions g(r) and estimate the contribution of charge effects to the interactions. Accounting for these charge effects within the Percus-Yevick framework leads to similar agreement with the experiment. PMID:23163381
Cerveri, Pietro; Manzotti, Alfonso; Baroni, Guido
2014-04-01
The shape of the human acetabular cup was commonly represented as a hemisphere, but different geometries and patient-specific shapes have been recently proposed in the literature. Our aim was to test the limits of the sphericity assumption by comparing three different parameterisations, namely the sphere, the ellipsoid and the rotational conchoid. Models of hip surfaces, reconstructed from CT scans taken from Caucasian race cadavers and patients, were automatically processed to extract the acetabular surface. Two separate analyses were carried out on the overall acetabular shape, including both the acetabular fossa and the lunate surface (case A) and acetabular cup represented by the lunate surface only (case B). Nonlinear gradient-based and evolutionary computation approaches were implemented for the fitting process. Minor differences from the three idealised geometries were detected (median values of the fitting errors < 1 mm). Nonetheless, the sphere fitting was found to be statistically different from both the ellipsoid (p < 2.50e - 10) and the conchoid (p < 1.07e - 09), whereas no statistical difference was detected between the ellipsoid and the conchoid for case A. Significance of the difference between ellipsoid and sphere (p < 4.55e - 12) and between conchoid and sphere (p < 1.93e - 11) was found for case B as well. Interestingly, for case B statistical difference was detected between the ellipsoid and the conchoid. In conclusion, we synthesise that the morphology of the overall acetabular cup can be parameterised both with an ellipsoid shape and with a conchoid shape as well with superior quality than the simple sphere. Differently, if one considers just the lunate surface, better fitting results are expected when using the ellipsoid. PMID:22789071
Orientational order of solutes in liquid crystals: The effect of distributed electric quadrupoles
NASA Astrophysics Data System (ADS)
Lee, J. S. J.; Sokolovskii, R. O.; Berardi, R.; Zannoni, C.; Burnell, E. E.
2008-03-01
We perform Monte Carlo simulations of a mixture of soft ellipsoids with embedded quadrupoles as a model of various small molecules dissolved in nematic liquid crystals. We find that Gay-Berne ellipsoids with distributed embedded quadrupoles qualitatively reproduce the trend in the order parameters observed experimentally in NMR spectra. In contrast, ellipsoids with a single embedded quadrupole cannot reproduce the negative order parameter of acetylene in EBBA.
Relationship between the velocity ellipsoids of galactic-disk stars and their ages and metallicities
NASA Astrophysics Data System (ADS)
Koval', V. V.; Marsakov, V. A.; Borkova, T. V.
2009-09-01
The dependences of the velocity ellipsoids of F-G stars of the thin disk of the Galaxy on their ages and metallicities are analyzed based on the new version of the Geneva-Copenhagen Catalog. The age dependences of the major, middle, and minor axes of the ellipsoids, and also of the dispersion of the total residual velocity, obey power laws with indices 0.25, 0.29, 0.32, and 0.27 (with uncertainties ±0.02). Due to the presence of thick-disk objects, the analogous indices for all nearby stars are about a factor of 1.5 larger. Attempts to explain such values are usually based on modeling relaxation processes in the Galactic disk. Elimination of stars in the most numerous moving groups from the sample slightly reduces the corresponding indices (0.22, 0.26, 0.27, and 0.24). Limiting the sample to stars within 60 pc of the Sun, so that the sample can be considered to be complete, leaves both the velocity ellipsoids and their age dependences virtually unchanged. With increasing age, the velocity ellipsoid increases in size and becomes appreciablymore spherical, turns toward the direction of the Galactic center, and loses angular momentum. The shape of the velocity ellipsoid remains far from equilibrium. With increasing metallicity, the velocity ellipsoid for stars of mixed age increases in size, displays a weak tendency to become more spherical, and turns toward the direction of the Galactic center (with these changes occurring substantially more rapidly in the transition through the metallicity [Fe/H]≈-0.25). Thus, the ellipsoid changes similarly to the way it does with age; however, with decreasing metallicity, the rotational velocity about the Galactic center monotonically increases, rather than decreases (!). Moreover, the power-law indices for the age dependences of the axes depend on the metallicity, and display a maximum near [Fe/H] ≈-0.1. The age dependences of all the velocity-ellipsoid parameters for stars with equal metallicity are roughly the same. It is
Necessity of using heterogeneous ellipsoidal Earth model with terrain to calculate co-seismic effect
NASA Astrophysics Data System (ADS)
Cheng, Huihong; Zhang, Bei; Zhang, Huai; Huang, Luyuan; Qu, Wulin; Shi, Yaolin
2016-04-01
-seismic displacement and strain are no longer symmetric with different latitudes in plane model while always theoretically symmetrical in spherical model. 2) The errors of co-seismic strain will be increased when using corresponding formulas in plane coordinate. When we set the strike-slip fault along the equator, the maximum relative error can reach to several tens of thousand times in high latitude while 30 times near the fault. 3) The style of strain changes are eight petals while the errors are four petals, and apparent distortion at high latitudes. Furthermore, the influence of the earth's ellipticity and heterogeneity and terrain were calculated respectively. Especially the effect of terrain, which induced huge differences, should not be overlooked during the co-seismic calculations. Finally, taking all those affecting factors into account, we calculated the co-seismic effect of the 2008 Wenchuan earthquake and its adjacent area and faults using the heterogeneous ellipsoidal Earth model with terrain.
Effect of topographic bias on geoid and reference ellipsoid of Venus, Mars, and the Moon
NASA Astrophysics Data System (ADS)
Ardalan, A. A.; Karimi, R.
2014-01-01
Since the continuation of an external gravity field inside topographic masses by a harmonic function results in topographic bias, geoid computation by means of global gravity models (GGMs) in terms of external-type series of spherical harmonics, at locations where the GGMs are evaluated inside the topographic masses, will be biased. Consequently, if the reference ellipsoid is defined based on the geoid, it will also be biased. In this paper, the effects of topographic bias on the geoid and reference ellipsoid of Venus, Mars, and the Moon are studied. Moreover, a thorough error analysis in the geoid and reference ellipsoid computation is presented, and it is shown that the estimated standard deviation (STD) of the geoid potential value, the geoidal heights, and the semimajor and semiminor axes of the reference ellipsoid are independent of the topographic bias. According to the results, the effects of topographic bias on the geoid potential value and the semimajor and semiminor axes of the reference ellipsoid in comparison with their estimated STDs are insignificant for Venus, Mars, and the Moon. Moreover, the effect of topographic bias on the geoidal heights of Venus as compared with the estimated STD of its geoidal heights is insignificant. However, the effects of topographic bias on the geoidal heights of Mars and the Moon can be significant, especially in high mountains such as the Tharsis volcanic region on Mars.
Radial velocity curves of ellipsoidal red giant binaries in the Large Magellanic Cloud
Nie, J. D.; Wood, P. R. E-mail: peter.wood@anu.edu.au
2014-12-01
Ellipsoidal red giant binaries are close binary systems where an unseen, relatively close companion distorts the red giant, leading to light variations as the red giant moves around its orbit. These binaries are likely to be the immediate evolutionary precursors of close binary planetary nebula and post-asymptotic giant branch and post-red giant branch stars. Due to the MACHO and OGLE photometric monitoring projects, the light variability nature of these ellipsoidal variables has been well studied. However, due to the lack of radial velocity curves, the nature of their masses, separations, and other orbital details has so far remained largely unknown. In order to improve this situation, we have carried out spectral monitoring observations of a large sample of 80 ellipsoidal variables in the Large Magellanic Cloud and we have derived radial velocity curves. At least 12 radial velocity points with good quality were obtained for most of the ellipsoidal variables. The radial velocity data are provided with this paper. Combining the photometric and radial velocity data, we present some statistical results related to the binary properties of these ellipsoidal variables.
Reference-ellipsoid and the normal gravity field in post-Newtonian geodesy
NASA Astrophysics Data System (ADS)
Kopeikin, Sergei; Mazurova, Elena
2016-07-01
We apply general relativity to construct the post-Newtonian background manifold that serves as a reference spacetime in relativistic geodesy for conducting relativistic calculation of the geoid undulation and the deflection of the plumb line from the vertical. We chose an axisymmetric ellipsoidal body made up of a perfect homogeneous fluid uniformly rotating around a fixed axis, as a source generating the reference geometry. We reformulate and extend hydrodynamic calculations of rotating fluids done by previous researchers to the realm of relativistic geodesy to set up the algebraic equations defining the shape of the post-Newtonian reference ellipsoid. We explicitly perform all integrals characterizing gravitational field inside and outside the fluid body and represent them in terms of the elementary functions depending on its eccentricity. We fully explore the coordinate freedom of the equations describing the post-Newtonian ellipsoid and evaluate the deviation of the post-Newtonian level surface from the Newtonian (Maclaurin) ellipsoid. We also derive the post-Newtonian normal gravity field of the rotating fluid in terms of the parameters characterizing the post-Newtonian ellipsoid including relativistic mass, angular velocity and eccentricity. We formulate the post-Newtonian theorems of Pizzetti and Clairaut that are used in geodesy to connect the geometric parameters of the Earth figure to physically measurable force of gravity at its pole and equator.
Sánchez, J H; Rinaldi, C
2009-03-15
The magnetic field dependent viscosity (magnetoviscosity) of dilute suspensions of magnetic tri-axial ellipsoidal particles suspended in a Newtonian fluid and under applied shear and magnetic fields was studied numerically. Brownian dynamics simulations were performed to compute the intrinsic magnetoviscosity of the suspension. Results are presented for the response of dilute suspensions of ellipsoidal particles to constant magnetic and shear flow fields. Suspensions of ellipsoidal particles show a significant effect of aspect ratio on the intrinsic magnetoviscosity of the suspension, and this effect is more pronounced as the aspect ratio becomes more extreme. The use of an effective rotational diffusion coefficient D(r,eff) collapses the normalized intrinsic magnetoviscosity of all suspensions to a master curve as a function of Péclet number with the Langevin parameter alpha=(mu(0)muH)/(k(B)T) as parameter, up to a critical value of alpha for which the results for suspensions of spherical particles deviate from those of suspensions of ellipsoids. This discrepancy is attributed to the action of the shear-torque on the ellipsoidal particles, which tends to orient these particles in the direction of maximum deformation of the simple shear flow, and which does not act on spherical particles. PMID:19100560
Non-ellipsoidal inclusions as geological strain markers and competence indicators
NASA Astrophysics Data System (ADS)
Treagus, S. H.; Hudleston, P. J.; Lan, L.
1996-09-01
Geological objects that do not deform homogeneously with their matrix can be considered as inclusions with viscosity contrast. Such inclusions are generally treated as initially spherical or ellipsoidal. Theory shows that ellipsoidal inclusions deform homogeneously, so they maintain an ellipsoidal shape, regardless of the viscosity difference. However, non-ellipsoidal inclusions deform inhomogeneously, so will become irregular in shape. Geological objects such as porphyroblasts, porphyroclasts and sedimentary clasts are likely to be of this kind, with initially rectilinear, prismatic or superelliptical section shapes. We present two-dimensional finite-element models of deformed square inclusions, in pure shear (parallel or diagonal to the square), as a preliminary investigation of the deformation of non-ellipsoidal inclusions with viscosity contrast. Competent inclusions develop marked barrel shapes with horn-like corners, as described for natural ductile boudins, or slightly wavy rhombs. Incompetent inclusions develop 'dumb-bell' or bone shapes, with a surprising degree of bulging of the shortened edges, or rhomb to sheath shapes. The results lead to speculation for inclusions in the circle to square shape range, and for asymmetric orientations. Anticipated shapes range from asymmetric barrels, lemons or flags for competent inclusions, to ribbon or fish shapes for incompetent inclusions. We conclude that shapes of inclusions and clasts provide an important new type of strain marker and competence criterion.
A novel species of ellipsoidal multicellular magnetotactic prokaryotes from Lake Yuehu in China.
Chen, Yi-Ran; Zhang, Rui; Du, Hai-Jian; Pan, Hong-Miao; Zhang, Wen-Yan; Zhou, Ke; Li, Jin-Hua; Xiao, Tian; Wu, Long-Fei
2015-03-01
Two morphotypes of multicellular magnetotactic prokaryotes (MMPs) have been identified: spherical (several species) and ellipsoidal (previously one species). Here, we report novel ellipsoidal MMPs that are ∼ 10 × 8 μm in size, and composed of about 86 cells arranged in six to eight interlaced circles. Each MMP was composed of cells that synthesized either bullet-shaped magnetite magnetosomes alone, or both bullet-shaped magnetite and rectangular greigite magnetosomes. They showed north-seeking magnetotaxis, ping-pong motility and negative phototaxis at a velocity up to 300 μm s(-1) . During reproduction, they divided along either their long- or short-body axes. For genetic analysis, we sorted the ellipsoidal MMPs with micromanipulation and amplified their genomes using multiple displacement amplification. We sequenced the 16S rRNA gene and found 6.9% sequence divergence from that of ellipsoidal MMPs, Candidatus Magnetananas tsingtaoensis and > 8.3% divergence from those of spherical MMPs. Therefore, the novel MMPs belong to different species and genus compared with the currently known ellipsoidal and spherical MMPs respectively. The novel MMPs display a morphological cell differentiation, implying a potential division of labour. These findings provide new insights into the diversity of MMPs in general, and contribute to our understanding of the evolution of multicellularity among prokaryotes. PMID:24725306
Research on process technology of off-axis ellipsoid aspheric mirror
NASA Astrophysics Data System (ADS)
Liu, Dongmei; Ma, Ke; Jia, Zonghe
2015-02-01
In recent years, the off-axis aspheric surface is widely used in wide coverage and high-resolution space optical systems. In this paper, research on processing technology of high precision and high efficiency off-axis ellipsoid aspheric mirror was studied deeply. With the help of CNC milling and polishing machine, off-axis ellipsoid aspheric mirror with diameter of 58mm was developed, by optimizing the concentration of polish liquid, grinding size, machining direction and other process parameters, based on the disadvantage of traditional processing that off-axis aspheric is easy to generate edge splitting and secondary surface damage, a new processing method "vertical off-axis ellipsoid aspheric surface processing method" was put forward. This method not only ensures the accuracy of work piece of optical axis, surface accuracy and accuracy of the edge, but also reduces secondary surface damage, improves processing efficiency and achieves high precision and high efficiency processing of off-axis ellipsoid aspheric surface, which is conducive to mass production. Through the detection of off-axis ellipsoid aspheric mirror by Taylor Profiler , surface accuracy (PV value) is 0.1981μm, the aspheric surface finish is level II and the optical axis accuracy is 0.01mm that it meets the requirements.
Event Classification and Identification Based on the Characteristic Ellipsoid of Phasor Measurement
Ma, Jian; Diao, Ruisheng; Makarov, Yuri V.; Etingov, Pavel V.; Dagle, Jeffery E.
2011-09-23
In this paper, a method to classify and identify power system events based on the characteristic ellipsoid of phasor measurement is presented. The decision tree technique is used to perform the event classification and identification. Event types, event locations and clearance times are identified by decision trees based on the indices of the characteristic ellipsoid. A sufficiently large number of transient events were simulated on the New England 10-machine 39-bus system based on different system configurations. Transient simulations taking into account different event types, clearance times and various locations are conducted to simulate phasor measurement. Bus voltage magnitudes and recorded reactive and active power flows are used to build the characteristic ellipsoid. The volume, eccentricity, center and projection of the longest axis in the parameter space coordinates of the characteristic ellipsoids are used to classify and identify events. Results demonstrate that the characteristic ellipsoid and the decision tree are capable to detect the event type, location, and clearance time with very high accuracy.
En-face imaging of the ellipsoid zone in the retina from optical coherence tomography B-scans
NASA Astrophysics Data System (ADS)
Holmes, T.; Larkin, S.; Downing, M.; Csaky, K.
2015-03-01
It is generally believed that photoreceptor integrity is related to the ellipsoid zone appearance in optical coherence tomography (OCT) B-scans. Algorithms and software were developed for viewing and analyzing the ellipsoid zone. The software performs the following: (a), automated ellipsoid zone isolation in the B-scans, (b), en-face view of the ellipsoid-zone reflectance, (c), alignment and overlay of (b) onto reflectance images of the retina, and (d), alignment and overlay of (c) with microperimetry sensitivity points. Dataset groups were compared from normal and dry age related macular degeneration (DAMD) subjects. Scalar measurements for correlation against condition included the mean and standard deviation of the ellipsoid zone's reflectance. The imageprocessing techniques for automatically finding the ellipsoid zone are based upon a calculation of optical flow which tracks the edges of laminated structures across an image. Statistical significance was shown in T-tests of these measurements with the population pools separated as normal and DAMD subjects. A display of en-face ellipsoid-zone reflectance shows a clear and recognizable difference between any of the normal and DAMD subjects in that they show generally uniform and nonuniform reflectance, respectively, over the region near the macula. Regions surrounding points of low microperimetry (μP) sensitivity have nonregular and lower levels of ellipsoid-zone reflectance nearby. These findings support the idea that the photoreceptor integrity could be affecting both the ellipsoid-zone reflectance and the sensitivity measurements.
Topological States in Partially-PT-Symmetric Azimuthal Potentials.
Kartashov, Yaroslav V; Konotop, Vladimir V; Torner, Lluis
2015-11-01
We introduce partially-parity-time (pPT)-symmetric azimuthal potentials composed from individual PT-symmetric cells located on a ring, where two azimuthal directions are nonequivalent in a sense that in such potential excitations carrying topological dislocations exhibit different dynamics for different directions of energy circulation in the initial field distribution. Such nonconservative ratchetlike structures support rich families of stable vortex solitons in cubic nonlinear media, whose properties depend on the sign of the topological charge due to the nonequivalence of azimuthal directions. In contrast, oppositely charged vortex solitons remain equivalent in similar fully-PT-symmetric potentials. The vortex solitons in the pPT- and PT-symmetric potentials are shown to feature qualitatively different internal current distributions, which are described by different discrete rotation symmetries of the intensity profiles. PMID:26588383
Han, Chengliang; Han, Jie; Li, Qiankun; Xie, Jingsong
2013-01-01
A facile and economic route has been presented for mass production of micro/nanostructured hematite microcrystals based on the wet chemical controllable method. The as-prepared samples were characterized using X-ray diffraction, scanning electron microscopy, transmission electron microscopy, and UV-Vis absorption spectroscopy. The results showed that the product was mesoporous α-Fe2O3 and nearly elliptical in shape. Each hematite ellipsoid was packed by many α-Fe2O3 nanoparticles. The values of vapor pressure in reaction systems played vital roles in the formation of porous hematite ellipsoids. Optical tests demonstrated that the micro/nanostructured elliptical hematite exhibited enhanced visible light property at room temperature. The formation of these porous hematite ellipsoids could be attributed to the vapor pressure induced oriented assembling of lots of α-Fe2O3 nanoparticles. PMID:24222735
An Ellipsoidal Particle-Finite Element Method for Hypervelocity Impact Simulation. Chapter 1
NASA Technical Reports Server (NTRS)
Shivarama, Ravishankar; Fahrenthold, Eric P.
2004-01-01
A number of coupled particle-element and hybrid particle-element methods have been developed for the simulation of hypervelocity impact problems, to avoid certain disadvantages associated with the use of pure continuum based or pure particle based methods. To date these methods have employed spherical particles. In recent work a hybrid formulation has been extended to the ellipsoidal particle case. A model formulation approach based on Lagrange's equations, with particles entropies serving as generalized coordinates, avoids the angular momentum conservation problems which have been reported with ellipsoidal smooth particle hydrodynamics models.
Cylindrically symmetric electrohydrodynamic patterning.
Deshpande, Paru; Pease, Leonard F; Chen, Lei; Chou, Stephen Y; Russel, William B
2004-10-01
Cylindrically symmetric structures such as concentric rings and rosettes arise out of thin polymeric films subjected to strong electric fields. Experiments that formed concentric rings and theory capable of explaining these and other cylindrical structures are presented. These rings represent an additional member of a class of structures, including pillars and holes, formed by electrohydrodynamic patterning of thin films, occasionally referred to as lithographically induced self-assembly. Fabrication of a set of concentric rings begins by spin coating a thin poly(methyl methacrylate) film onto a silicon wafer. A mask is superimposed parallel to the film leaving a similarly thin air gap. Electric fields, acting in opposition to surface tension, destabilize the free interface when raised above the glass transition temperature. Central pillars nucleate under small cylindrical protrusions patterned on the mask. Rings then emerge sequentially, with larger systems having as many as 10 fully formed rings. Ring-to-ring spacings and annular widths, typically on the order of a micron, are approximately constant within a concentric cluster. The formation rate is proportional to the viscosity and, consequently, has the expected Williams-Landel-Ferry dependence on temperature. In light of these developments we have undertaken a linear stability analysis in cylindrical coordinates to describe these rings and ringlike structures. The salient feature of this analysis is the use of perturbations that incorporate their radial dependence in terms of Bessel functions as opposed to the traditional sinusoids of Cartesian coordinates. The theory predicts approximately constant ring-to-ring spacings, constant annular widths, and growth rates that agree with experiment. A secondary instability is observed at higher temperatures, which causes the rings to segment into arcs or pillar arrays. The cylindrical theory may be generalized to describe hexagonal pillar/hole packing, gratings, and
Symmetric Composite Laminate Stress Analysis
NASA Technical Reports Server (NTRS)
Wang, T.; Smolinski, K. F.; Gellin, S.
1985-01-01
It is demonstrated that COSMIC/NASTRAN may be used to analyze plate and shell structures made of symmetric composite laminates. Although general composite laminates cannot be analyzed using NASTRAN, the theoretical development presented herein indicates that the integrated constitutive laws of a symmetric composite laminate resemble those of a homogeneous anisotropic plate, which can be analyzed using NASTRAN. A detailed analysis procedure is presented, as well as an illustrative example.
Optimum Electron Distributions for Space Charge Dominated Beams in Photoinjectors
Limborg-Deprey, C.; Bolton, P.R.; /SLAC
2006-06-15
The optimum photo-electron distribution from the cathode of an RF photoinjector producing a space charge dominated beam is a uniform distribution contained in an ellipsoid. For such a bunch distribution, the space charge forces are linear and the emittance growth induced by those forces is totally reversible and consequently can be compensated. With the appropriate tuning of the emittance compensation optics, the emittance, at the end of photoinjector beamline, for an ellipsoidal laser pulse, would only have two contributions, the cathode emittance and the RF emittance. For the peak currents of 50A and 100 A required from the SBand and L-Band RF gun photoinjectors discussed here, the RF emittance contribution is negligible. If such an ellipsoidal photo-electron distribution were available, the emittance at the end of the beamline could be reduced to the cathode emittance. Its value would be reduced by more than 40% from that obtained using cylindrical shape laser pulses. This potentially dramatic improvement warrants review of the challenges associated with the production of ellipsoidal photo-electrons. We assume the photo-electrons emission time to be short enough that the ellipsoidal electron pulse shape will come directly from the laser pulse. We shift the challenge to ellipsoidal laser pulse shaping. To expose limiting technical issues, we consider the generation of ellipsoidal laser pulse shape in terms of three different concepts.
NASA Astrophysics Data System (ADS)
Chia, T. T.; Pung, S. Y.
1995-07-01
Earlier work on the oscillations of an ellipsoid is extended to investigate the behaviour of a nonequilibrium compressible homogeneous rotating gaseous ellipsoid, with the components of the velocity field as linear functions of the coordinates, and with parallel angular velocity and uniform vorticity. The dynamical behaviour of the ellipsoid is obtained by numerically integrating the relevant differential equations for different values of the initial angular velocity and vorticity. This behaviour is displayed by the (a 1,a 2) and (a 1,a 3) phase plots, where thea i's (i = 1, 2, 3) are the semi-diameters, and by the graphs ofa 1,a 2,a 3, the volume, and the angular velocity as functions of time. The dynamical behaviour of the nonequilibrium ellipsoid depends on the deviation of the angular momentum from its equilibrium value; for larger deviations, the oscillations are more nonperiodic with larger amplitudes. An initially ellipsoidal configuration always remains ellipsoidal, but it cannot become spheroidal about its rotation axis, though it may become spheroidal instantaneously about either one of the other two principal axes. For an ellipsoid approaching axisymmetry about its axis of rotation, the angular velocity can suddenly increase by a large amount. Thus if an astrophysical object can be modelled by a nonequilibrium ellipsoid, it may occasionally undergo sudden large increases of angular velocity.
Ren, Xianwen; Wang, Yong; Chen, Luonan; Zhang, Xiang-Sun; Jin, Qi
2013-02-01
Computationally identifying effective biomarkers for cancers from gene expression profiles is an important and challenging task. The challenge lies in the complicated pathogenesis of cancers that often involve the dysfunction of many genes and regulatory interactions. Thus, sophisticated classification model is in pressing need. In this study, we proposed an efficient approach, called ellipsoidFN (ellipsoid Feature Net), to model the disease complexity by ellipsoids and seek a set of heterogeneous biomarkers. Our approach achieves a non-linear classification scheme for the mixed samples by the ellipsoid concept, and at the same time uses a linear programming framework to efficiently select biomarkers from high-dimensional space. ellipsoidFN reduces the redundancy and improves the complementariness between the identified biomarkers, thus significantly enhancing the distinctiveness between cancers and normal samples, and even between cancer types. Numerical evaluation on real prostate cancer, breast cancer and leukemia gene expression datasets suggested that ellipsoidFN outperforms the state-of-the-art biomarker identification methods, and it can serve as a useful tool for cancer biomarker identification in the future. The Matlab code of ellipsoidFN is freely available from http://doc.aporc.org/wiki/EllipsoidFN. PMID:23262226
NASA Astrophysics Data System (ADS)
Huang, B.; Piper, J. D.; Zhu, R.
2006-12-01
Magnetostratigraphic study on 1006 horizons in Paleogene and Neogene sediments between the upper Kumugeliemu Formation and the base of the Kuche Formation within the Kuche Depression of the Tarim Basin, NW China, identifies 41 pairs of normal and reversed polarity zones and two substantial increases in accumulation rate at ca. 16-17 and 7 Ma. The observed nature of the AMS fabric is comparable to embryonic magnetic fabrics in weakly deformed mudrocks and the height-dependent changes of AMS ellipsoids, Pj-T data and the distribution of k3 (and k2) directions can be related to a general Pj-T path for the development of AMS ellipsoids in weakly deformed rocks with increasing deformation intensity. The dominant prolate shapes and nearly N-S girdle of the k3 directions in rocks accumulated before ca. 15 Ma are in the older and more deeply buried part of the succession presumably exposed to more intense strains than the succession accumulated after ca. 15 Ma. This implies that the rocks in this succession have been subjected to incipient deformation with the succession accumulated before ca. 15 Ma recording the effects of compressive deformation. The changes in rock magnetic susceptibility parameters could therefore be used as proxies for changes in sediment provenance accompanying changes in the regional tectonic regime. The magnetostratigraphic correlation proposed in this study implies that the southern Tian Shan Range was reactivated at ca. 20 Ma with initiation of uplift presumably induced by tectonic stress imparted during the interval ca. 20-15 Ma.
NASA Astrophysics Data System (ADS)
Grafarend, E. W.; Ardalan, A.; Finn, G.
In terms of elliptic coordinates of Jacobi type (longitude, latitude, semi-minor axis) the horizontal derivative is computed as a linear operator acting on an ellipsoidal har- monic disturbing/incremental gravitational potential. Such disturbing potential is de- fined with respect to the Somigliana-Pizzetti Reference Potential, the potential field of a level ellipsoid, and the International Reference Ellipsoid/WGS84 or World Geode- tic Datum 2000/WGD2000. Case studies of those vertical deflections on a global as well as regional scale are presented which take advantage of SEGEN (Special Ellipsoidal Gravity Earth Normal: ellipsoidal harmonics expansion 130321 coeffi- cients: http://www.uni-stuttgart.de/gi/research/paper/coefficients/coefficients.zip) and of CENT (precise centrifugal potential)
Compensator configurations for load currents' symmetrization
NASA Astrophysics Data System (ADS)
Rusinaru, D.; Manescu, L. G.; Dinu, R. C.
2016-02-01
This paper approaches aspects regarding the mitigation effects of asymmetries in 3-phase 3-wire networks. The measure consisting in connecting of load current symmetrization devices at the load coupling point is presented. A time-variation of compensators parameters is determined as a function of the time-recorded electrical values. The general sizing principle of the load current symmetrization reactive components is based on a simple equivalent model of the unbalanced 3-phase loads. By using these compensators a certain control of the power components transits is ensured in the network. The control is based on the variations laws of the compensators parameters as functions of the recorded electrical values: [B] = [T]·[M]. The link between compensator parameters and measured values is ensured by a transformation matrix [T] for each operation conditions of the supply network. Additional conditions for improving of energy and efficiency performance of the compensator are considered: i.e. reactive power compensation. The compensator sizing algorithm was implemented into a MATLAB environment software, which generate the time-evolution of the parameters of load current symmetrization device. The input data of application takes into account time-recording of the electrical values. By using the compensator sizing software, some results were achieved for the case of a consumer connected at 20 kV busbar of a distribution substation, during 24 hours measurement session. Even the sizing of the compensators aimed some additional network operation aspects (power factor correction) correlated with the total or major load symmetrizations, the harmonics aspects of the network values were neglected.
Experimental Study of the Moment of Inertia of a Cone--Angular Variation and Inertia Ellipsoid
ERIC Educational Resources Information Center
Pintao, Carlos A. F.; de Souza Filho, Moacir P.; Usida, Wesley F.; Xavier, Jose A.
2007-01-01
In this paper, an experimental set-up which differs from the traditional ones is established in order to determine the moment of inertia of a right circular cone. Its angular variation and inertia ellipsoid are determined by means of an experimental study. In addition, a system that allows for the evaluation of the angular acceleration and torque…
Tsebers, A.O.
1985-04-01
This paper is an attempt to simulate the magnetorheological behavior of a suspension of ellipsoidal ferromagnetic particles in a numerical experiment. Accuracy of the calculations used are achieved and illustrated in the paper. It is shown that the relative error in the calculation of the characteristic viscosity does not exceed 5%.
Disk-integrated brightness of a Lommel-Seeliger scattering ellipsoidal asteroid
NASA Astrophysics Data System (ADS)
Muinonen, K.; Lumme, K.
2015-12-01
Context. The scattering of light by an asteroid's surface depends on the properties of its particles, volume density, and roughness. It is described by the reflection coefficient which, upon integration over the illuminated and observed part of the surface, yields the disk-integrated photometric brightness of the asteroid. The Lommel-Seeliger reflection coefficient is applicable to dark, low-albedo C-class asteroids, with prospects for moderate-albedo S-class and M-class asteroids. Aims: We calculate the disk-integrated brightness for an ellipsoidal asteroid with a Lommel-Seeliger reflection coefficient (LS ellipsoid). Furthermore, we calculate the photocenter for the LS ellipsoid, that is, the distance of the center of light from the barycenter. Methods: Because of their analytical nature, the closed-form expressions can be readily utilized in numerical simulations. Results: We show lightcurves and photocenter variations for realistic examples of ellipsoidal shapes for a number of pole orientations. The results highlight the reciprocity principle of the radiative-transfer theory and suggest a nontrivial dependence of the photocenter on the pole orientation and viewing geometry. Conclusions: Finally, we outline a number of applications and future prospects.
Robust Means and Covariance Matrices by the Minimum Volume Ellipsoid (MVE).
ERIC Educational Resources Information Center
Blankmeyer, Eric
P. Rousseeuw and A. Leroy (1987) proposed a very robust alternative to classical estimates of mean vectors and covariance matrices, the Minimum Volume Ellipsoid (MVE). This paper describes the MVE technique and presents a BASIC program to implement it. The MVE is a "high breakdown" estimator, one that can cope with samples in which as many as half…
Fast Multidimensional Ellipsoid-Specific Fitting by Alternating Direction Method of Multipliers.
Lin, Zhouchen; Huang, Yameng
2016-05-01
Many problems in computer vision can be formulated as multidimensional ellipsoid-specific fitting, which is to minimize the residual error such that the underlying quadratic surface is a multidimensional ellipsoid. In this paper, we present a fast and robust algorithm for solving ellipsoid-specific fitting directly. Our method is based on the alternating direction method of multipliers, which does not introduce extra positive semi-definiteness constraints. The computation complexity is thus significantly lower than those of semi-definite programming (SDP) based methods. More specifically, to fit n data points into a p dimensional ellipsoid, our complexity is O(p(6) + np(4))+O(p(3)), where the former O results from preprocessing data once, while that of the state-of-the-art SDP method is O(p(6) + np(4) + n(3/2)p(2)) for each iteration. The storage complexity of our algorithm is about 1/2np(2), which is at most 1/4 of those of SDP methods. Extensive experiments testify to the great speed and accuracy advantages of our method over the state-of-the-art approaches. The implementation of our method is also much simpler than SDP based methods. PMID:27046842
Recognition of 3-D symmetric objects from range images in automated assembly tasks
NASA Technical Reports Server (NTRS)
Alvertos, Nicolas; Dcunha, Ivan
1990-01-01
A new technique is presented for the three dimensional recognition of symmetric objects from range images. Beginning from the implicit representation of quadrics, a set of ten coefficients is determined for symmetric objects like spheres, cones, cylinders, ellipsoids, and parallelepipeds. Instead of using these ten coefficients trying to fit them to smooth surfaces (patches) based on the traditional way of determining curvatures, a new approach based on two dimensional geometry is used. For each symmetric object, a unique set of two dimensional curves is obtained from the various angles at which the object is intersected with a plane. Using the same ten coefficients obtained earlier and based on the discriminant method, each of these curves is classified as a parabola, circle, ellipse, or hyperbola. Each symmetric object is found to possess a unique set of these two dimensional curves whereby it can be differentiated from the others. It is shown that instead of using the three dimensional discriminant which involves evaluation of the rank of its matrix, it is sufficient to use the two dimensional discriminant which only requires three arithmetic operations.
Possible origin of transition from symmetric to asymmetric fission
NASA Astrophysics Data System (ADS)
Paşca, H.; Andreev, A. V.; Adamian, G. G.; Antonenko, N. V.
2016-09-01
The charged distributions of fragments produced in the electromagnetic-induced fission of the even-even isotopes of Rn, Ra, Th, and U are described within an improved scission-point model and compared with the available experimental data. The three-equal-peaked charge distributions are predicted for several fissioning nuclei with neutron number N = 136. The possible explanation of the transition from a symmetric fission mode to an asymmetric one around N ∼ 136 is presented. The excitation energy dependencies of the asymmetric and symmetric fission modes are anticipated.