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.
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
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.
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
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.
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
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.
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.
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.
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
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.
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
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.
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.
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
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
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.
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.
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.
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.
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.
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.
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.
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…
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.
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.
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
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
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.
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.
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) ...
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.
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 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.
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.
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.
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.
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).
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
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.
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
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
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.
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.
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.
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.
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
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.
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
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.
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.
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.
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.
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
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.
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.
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
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
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.
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.
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.
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
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
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
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.
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.
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.
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.
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.
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.
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
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.
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
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.
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.
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.
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.
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)
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.
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.
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…
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.
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.
3-D density models within an ellipsoidal-Earth from inversion of geoid anomalies
NASA Astrophysics Data System (ADS)
Chaves, C. M.; Ussami, N.
2013-12-01
Modeling density perturbations is very important to understand geodynamic processes which occur within the Earth's mantle. Commonly, the Earth's density is predicted by converting a velocity model into a density model using either a constant scaling factor or a relationship provided by mineral physics. Nonetheless, several factors such as temperature, composition and melting can affect the wave propagation speed so that a seismically converted density model may not retrieve the actual density distribution. This limitation may hamper the modeling the geodynamic processes. Due to advances in satellite-derived gravity data acquisition (e.g. GRACE, GOCE), the gravity field is now obtained with an unprecedented accuracy and resolution allowing us to estimate more uniformly the 3-D density distribution for the whole Earth. Here we present a computational algorithm to invert geoid anomalies in order to estimate density variations in the mantle. Using an ellipsoidal-Earth approximation, the model space is represented by a set of tesseroids. From a synthetic geoid anomaly caused by a plume tail ascending through the mantle with Gaussian noise added, the inversion code is capable to recover with good accuracy the density contrast and the body geometry when compared to the synthetic model. This algorithm was also tested in a natural case study, where geoid anomalies from the Yellowstone Province (YP) were inverted. The estimated density model (EDM) has a predominantly negative density contrast (~ -50 kg/m3) relative to the surrounding upper mantle and extends to the depth of 1000 km. The EDM exhibits an anti-correlation of up to -0.7 with one of the most recent S-velocity model for the western United States. The predicted dynamic topography from the EDM explains almost 80 % of the observed dynamic topography in the YP. From our results, we conclude that a joint-interpretation of density anomalies derived from geoid and velocity perturbations from seismic tomography models
Looking for symmetric Bell inequalities
NASA Astrophysics Data System (ADS)
Bancal, Jean-Daniel; Gisin, Nicolas; Pironio, Stefano
2010-09-01
Finding all Bell inequalities for a given number of parties, measurement settings and measurement outcomes is in general a computationally hard task. We show that all Bell inequalities which are symmetric under the exchange of parties can be found by examining a symmetrized polytope which is simpler than the full Bell polytope. As an illustration of our method, we generate 238 885 new Bell inequalities and 1085 new Svetlichny inequalities. We find, in particular, facet inequalities for Bell experiments involving two parties and two measurement settings that are not of the Collins-Gisin-Linden-Massar-Popescu type.
Bumblebee preference for symmetrical flowers.
Møller, A P
1995-03-14
Fluctuating asymmetry, which represents small random deviations from otherwise bilateral symmetry, is a measure of the phenotypic quality of individuals indicating the ability of controlled development under given environmental and genetic conditions. I tested whether floral symmetry reliably reflects phenotypic quality measured in terms of pollinator rewards and whether pollinators respond to floral symmetry in a series of observations and experiments on Epilobium angustifolium (Onagraceae). Lower petal asymmetry was negatively related to mean lower petal length, whereas asymmetry in leaf width was positively related to mean leaf width. Flowers visited by bumblebees were larger and more symmetrical than the nearest neighboring flower. This relationship between pollinator preference for large and symmetrical flowers was demonstrated to be causal in experiments in which the lower petals were manipulated symmetrically or asymmetrically. Nectar production was larger in symmetrical flowers, and this may explain the bumblebee preference for flower symmetry. Floral symmetry therefore reliably reflects nectar production and hence enhances pollen transport. Extensive embryo abortion has been documented in E. angustifolium and other outcrossing plant species. Floral fluctuating asymmetry, which reflects general developmental homeostasis, may explain such developmental selection in these plants. PMID:11607519
A scheme for symmetrization verification
NASA Astrophysics Data System (ADS)
Sancho, Pedro
2011-08-01
We propose a scheme for symmetrization verification in two-particle systems, based on one-particle detection and state determination. In contrast to previous proposals, it does not follow a Hong-Ou-Mandel-type approach. Moreover, the technique can be used to generate superposition states of single particles.
Cracked shells under skew-symmetric loading
NASA Technical Reports Server (NTRS)
Lelale, F.
1982-01-01
A shell containing a through crack in one of the principal planes of curvature and under general skew-symmetric loading is considered. By employing a Reissner type shell theory which takes into account the effect of transverse shear strains, all boundary conditions on the crack surfaces are satisfied separately. Consequently, unlike those obtained from the classical shell theory, the angular distributions of the stress components around the crack tips are shown to be identical to the distributions obtained from the plane and antiplane elasticity solutions. Extensive results are given for axially and circumferentially cracked cylindrical shells, spherical shells, and toroidal shells under uniform inplane shearing, out of plane shearing, and torsion. The effect of orthotropy on the results is also studied.
THE DISCOVERY OF ELLIPSOIDAL VARIATIONS IN THE KEPLER LIGHT CURVE OF HAT-P-7
Welsh, William F.; Orosz, Jerome A.; Seager, Sara; Fortney, Jonathan J.; Jenkins, Jon; Rowe, Jason F.; Koch, David; Borucki, William J.
2010-04-20
We present an analysis of the early Kepler observations of the previously discovered transiting planet HAT-P-7b. The light curve shows the transit of the star, the occultation of the planet, and the orbit phase-dependent light from the planet. In addition, phase-dependent light from the star is present, known as 'ellipsoidal variations'. The very nearby planet (only four stellar radii away) gravitationally distorts the star and results in a flux modulation twice per orbit. The ellipsoidal variations can confuse interpretation of the planetary phase curve if not self-consistently included in the modeling. We fit the light curve using the Roche potential approximation and derive improved planet and orbit parameters.
New fabrication method for an ellipsoidal neutron focusing mirror with a metal substrate.
Guo, Jiang; Takeda, Shin; Morita, Shin-ya; Hino, Masahiro; Oda, Tatsuro; Kato, Jun-ichi; Yamagata, Yutaka; Furusaka, Michihiro
2014-10-01
We propose an ellipsoidal neutron focusing mirror using a metal substrate made with electroless nickel-phosphorus (NiP) plated material for the first time. Electroless NiP has great advantages for realizing an ellipsoidal neutron mirror because of its amorphous structure, good machinability and relatively large critical angle of total reflection for neutrons. We manufactured the mirror by combining ultrahigh precision cutting and fine polishing to generate high form accuracy and low surface roughness. The form accuracy of the mirror was estimated to be 5.3 μm P-V and 0.8 μm P-V for the minor-axis and major-axis direction respectively, while the surface roughness was reduced to 0.2 nm rms. The effect of form error on focusing spot size was evaluated by using a laser beam and the focusing performance of the mirror was verified by neutron experiments. PMID:25322041
NASA Astrophysics Data System (ADS)
Hayrapetyan, D. B.; Kazaryan, E. M.; Sarkisyan, H. A.
2016-01-01
An electron gas in a strongly oblated ellipsoidal quantum dot with impenetrable walls in the presence of external magnetic field is considered. Influence of the walls of the quantum dot is assumed to be so strong in the direction of the minor axis (the OZ axis) that the Coulomb interaction between electrons in this direction can be neglected and considered as two-dimensional. On the basis of geometric adiabaticity we show that in the case of a few-particle gas a powerful repulsive potential of the quantum dot walls has a parabolic form and localizes the gas in the geometric center of the structure. Due to this fact, conditions occur to implement the generalized Kohn theorem for this system. The parabolic confinement potential depends on the geometry of the ellipsoid, which allows, together with the magnetic field to control resonance frequencies of transitions by changing the geometric dimensions of the QD.
ORTEP-III: Oak Ridge Thermal Ellipsoid Plot Program for crystal structure illustrations
Burnett, M.N.; Johnson, C.K.
1996-07-01
This report describes a computer program for drawing crystal structure illustrations. Ball-and-stick type illustrations of a quality suitable for publication are produced with either spheres or thermal-motion probability ellipsoids on the atomic sites. The program can also produce stereoscopic pairs of illustrations which aid in the visualization of complex packing arrangements of atoms and thermal motion patterns. Interatomic distances, bond angles, and principal axes of thermal motion are also calculated to aid the structural study.
NASA Astrophysics Data System (ADS)
Hu, Hai-Ping
2011-04-01
The theoretical study researched into heat transfer of turbulent film boiling on an isothermal ellipsoid under high and low velocity liquid. The flowing velocity of the saturated liquid at the boundary layer is determined by potential flow theory. The larger the eccentricity parameter is the smaller the mean Nusselt number will be. Besides, for the cases of turbulent film boiling under the flowing liquid, the increase in the Froude number will bring out an increase in the mean Nusselt number.
MISR Level 1B2 Ellipsoid Data (MI1B2E_V2)
NASA Technical Reports Server (NTRS)
Diner, David J. (Principal Investigator)
The MISR instrument consists of nine pushbroom cameras which measure radiance in four spectral bands. Global coverage is achieved in nine days. The cameras are arranged with one camera pointing toward the nadir, four cameras pointing forward and four cameras pointing aftward. It takes 7 minutes for all nine cameras to view the same surface location. The view angles relative to the surface reference ellipsoid, are 0, 26.1, 45.6, 60.0, and 70.5 degrees. The spectral band shapes are nominally gaussian, centered at 443, 555, 670, and 865 nm. The Ellipsoid product is referenced to the World Geodetic System 1984 (WGS84) ellipsoid, which approximates the Earth's shape at sea level. In this product, the radiances and associated altitudes are projected to the ellipsoid, so that higher elevation data appear displaced from their true location for non-nadir camera views, much as they are seen by the instrument. (A cloud at location F, or a mountain top at location T in the image below appears as if it is at location E.) The more oblique the camera view, or the higher in altitude the feature, the more displaced the elevated data will appear. This displacement is used to advantage in MISR stereo retrievals, and this product is the primary input to Level 2 top-of-atmosphere/cloud processing. [Location=GLOBAL] [Temporal_Coverage: Start_Date=2000-02-24; Stop_Date=] [Spatial_Coverage: Southernmost_Latitude=-90; Northernmost_Latitude=90; Westernmost_Longitude=-180; Easternmost_Longitude=180] [Data_Resolution: Latitude_Resolution=563.2 km (cross-track); Longitude_Resolution=140.8 km (along-track); Horizontal_Resolution_Range=500 meters - < 1 km; Temporal_Resolution=about 15 orbits/day; Temporal_Resolution_Range=about 15 orbits/day].
Experimental study of global-scale turbulence in a librating ellipsoid
NASA Astrophysics Data System (ADS)
Grannan, A. M.; Le Bars, M.; Cébron, D.; Aurnou, J. M.
2014-12-01
We present laboratory experimental results demonstrating that librational forcing of an ellipsoidal container of water can produce intense motions through the mechanism of a libration driven elliptical instability (LDEI). These libration studies are conducted using an ellipsoidal acrylic container filled with water. A particle image velocimetry method is used to measure the 2D velocity field in the equatorial plane over hundreds libration cycles for a fixed Ekman number, E = 2 × 10-5. In doing so, we recover the libration induced base flow and a time averaged zonal flow. Further, we show that LDEI in non-axisymmetric container geometries is capable of driving both intermittent and saturated turbulent motions in the bulk fluid. Additionally, we measure the growth rate and amplitude of the LDEI induced excited flow in a fully ellipsoidal container at more extreme parameters than previously studied [Noir et al., "Experimental study of libration-driven flows in nonaxisymmetric containers," Phys. Earth Planet. Inter. 204-205, 1 (2012); Cébron et al., Phys. Fluids 24, 061703, "Libration driven elliptical instability," (2012)]. Excitation of bulk filling turbulence by librational forcing provides a mechanism for transferring rotational energy into turbulent fluid motion and thus can play an important role in the thermal evolution, interior dynamics, and magneto-hydrodynamics of librating bodies, as appear to be common in solar system settings [e.g., Comstock and Bills, "A solar system survey of forced librations in longitude," J. Geophys. Res. Planets 108, 1 (2003)].
Orientational dynamics of colloidal ribbons self-assembled from microscopic magnetic ellipsoids.
Martinez-Pedrero, Fernando; Cebers, Andrejs; Tierno, Pietro
2016-04-20
We combine experiments and theory to investigate the orientational dynamics of dipolar ellipsoids, which self-assemble into elongated ribbon-like structures due to the presence of a permanent magnetic moment, perpendicular to the long axis in each particle. Monodisperse hematite ellipsoids are synthesized via the sol-gel technique and arrange into ribbons in the presence of static or time-dependent magnetic fields. We find that under an oscillating field, the ribbons reorient perpendicular to the field direction, in contrast with the behaviour observed under a static field. This observation is explained theoretically by treating a chain of interacting ellipsoids as a single particle with orientational and demagnetizing field energy. The model allows us to describe the orientational behaviour of the chain and captures well its dynamics at different strengths of the actuating field. The understanding of the complex dynamics and assembly of anisotropic magnetic colloids is a necessary step for controlling the structure formation, which has direct applications in different fluid-based microscale technologies. PMID:26936015
Maxwell’s Mixing Equation Revisited: Characteristic Impedance Equations for Ellipsoidal Cells
Stubbe, Marco; Gimsa, Jan
2015-01-01
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
Du, Zhengchun; Wu, Zhaoyong; Yang, Jianguo
2016-01-01
The use of three-dimensional (3D) data in the industrial measurement field is becoming increasingly popular because of the rapid development of laser scanning techniques based on the time-of-flight principle. However, the accuracy and uncertainty of these types of measurement methods are seldom investigated. In this study, a mathematical uncertainty evaluation model for the diameter measurement of standard cylindroid components has been proposed and applied to a 3D laser radar measurement system (LRMS). First, a single-point error ellipsoid analysis for the LRMS was established. An error ellipsoid model and algorithm for diameter measurement of cylindroid components was then proposed based on the single-point error ellipsoid. Finally, four experiments were conducted using the LRMS to measure the diameter of a standard cylinder in the laboratory. The experimental results of the uncertainty evaluation consistently matched well with the predictions. The proposed uncertainty evaluation model for cylindrical diameters can provide a reliable method for actual measurements and support further accuracy improvement of the LRMS. PMID:27213385
Du, Zhengchun; Wu, Zhaoyong; Yang, Jianguo
2016-01-01
The use of three-dimensional (3D) data in the industrial measurement field is becoming increasingly popular because of the rapid development of laser scanning techniques based on the time-of-flight principle. However, the accuracy and uncertainty of these types of measurement methods are seldom investigated. In this study, a mathematical uncertainty evaluation model for the diameter measurement of standard cylindroid components has been proposed and applied to a 3D laser radar measurement system (LRMS). First, a single-point error ellipsoid analysis for the LRMS was established. An error ellipsoid model and algorithm for diameter measurement of cylindroid components was then proposed based on the single-point error ellipsoid. Finally, four experiments were conducted using the LRMS to measure the diameter of a standard cylinder in the laboratory. The experimental results of the uncertainty evaluation consistently matched well with the predictions. The proposed uncertainty evaluation model for cylindrical diameters can provide a reliable method for actual measurements and support further accuracy improvement of the LRMS. PMID:27213385
The marginal band and its role in the ellipsoidal shape of Geochelone carbonaria erythrocytes.
Coiro, J R; Brunner, A; Mitsutani, C Y; Weisz, V M; Fiori, A M
1978-01-01
Erythrocytes from a chelonian (Geochelone carbonaria) were submitted to physical and chemical treatments. Observations of their change in shape from ellipsoidal to spherical were made by means of light microscopy. A 100% change to the spherical shape was attained with erythrocytes under high temperature treatment (42 degrees C) for 45 min., and at room temperature (29 degrees C) plus colchicine, for 60 min. Erythrocytes kept at room temperature present changes in shape while those kept at low temperature (10 degrees C) did not exhibit significant changes in their original ellipsoidal shape, but displayed an intact marginal band (MB). By direct examination the diameter of microtubules was found to be nearly 300 A in the dissociated form and 0.70 mu when bundled. In cross section the value found for microtubule diameter was up to 210 A. These measures are compatible with those found by several other authors. Counting of microtubules by ultrathin sectioning indicated approximately 70 tubules per cell, a value that is higher than that found in other species. By means of electron microscopy the marginal band can be observed intact or dissociated into several dense rings formed by parallel microtubules running nearly or accompanying the periphery of the stroma. Temperature and colchicine are responsible for the depolymerization of the microtubules. In the stroma of spherical erythrocytes a dense peripheric fold can be observed but microtubules were never found. It is suggested therefore that the role of the marginal band is essential to maintain the ellipsoidal shape of chelonian erythrocytes. PMID:751572
Viscosity in spherically symmetric accretion
NASA Astrophysics Data System (ADS)
Ray, Arnab K.
2003-10-01
The influence of viscosity on the flow behaviour in spherically symmetric accretion has been studied here. The governing equation chosen has been the Navier-Stokes equation. It has been found that at least for the transonic solution, viscosity acts as a mechanism that detracts from the effectiveness of gravity. This has been conjectured to set up a limiting scale of length for gravity to bring about accretion, and the physical interpretation of such a length scale has been compared with the conventional understanding of the so-called `accretion radius' for spherically symmetric accretion. For a perturbative presence of viscosity, it has also been pointed out that the critical points for inflows and outflows are not identical, which is a consequence of the fact that under the Navier-Stokes prescription, there is a breakdown of the invariance of the stationary inflow and outflow solutions - an invariance that holds good under inviscid conditions. For inflows, the critical point gets shifted deeper within the gravitational potential well. Finally, a linear stability analysis of the stationary inflow solutions, under the influence of a perturbation that is in the nature of a standing wave, has indicated that the presence of viscosity induces greater stability in the system than has been seen for the case of inviscid spherically symmetric inflows.
Symmetric Discrete Orthonormal Stockwell Transform
NASA Astrophysics Data System (ADS)
Wang, Yanwei; Orchard, Jeff
2008-09-01
The Stockwell Transform (ST) is a time-frequency signal decomposition that is gaining in popularity, likely because of its direct relation with the Fourier Transform (FT). A discrete and non-redundant version of the ST, denoted the Discrete Orthonormal Stockwell Transform (DOST), has made the use of the ST more feasible. However, the matrix multiplication required by the DOST can still be a formidable computation, especially for high-dimensional data. Moreover, the symmetric property of the ST and FT is not present in the DOST. In this paper, we investigate a new Symmetric Discrete Orthonormal Stockwell Transform (SDOST) that still keeps the non-redundant multiresolution features of the DOST, while maintaining a symmetry property similar to that of the FT. First, we give a brief introduction for the ST and the DOST. Then we analyze the DOST coefficients and modify the transform to get a symmetric version. A small experiment shows that the SDOST has kept the abilities of the DOST and demonstrates the advantage of symmetry when applying the SDOST.
NASA Astrophysics Data System (ADS)
Bender, Carl M.
2015-07-01
The average quantum physicist on the street would say that a quantum-mechanical Hamiltonian must be Dirac Hermitian (invariant under combined matrix transposition and complex conjugation) in order to guarantee that the energy eigenvalues are real and that time evolution is unitary. However, the Hamiltonian H = p2 + ix3, which is obviously not Dirac Hermitian, has a positive real discrete spectrum and generates unitary time evolution, and thus it defines a fully consistent and physical quantum theory. Evidently, the axiom of Dirac Hermiticity is too restrictive. While H = p2 + ix3 is not Dirac Hermitian, it is PT symmetric; that is, invariant under combined parity P (space reflection) and time reversal T. The quantum mechanics defined by a PT-symmetric Hamiltonian is a complex generalization of ordinary quantum mechanics. When quantum mechanics is extended into the complex domain, new kinds of theories having strange and remarkable properties emerge. In the past few years, some of these properties have been verified in laboratory experiments. A particularly interesting PT-symmetric Hamiltonian is H = p2 - x4, which contains an upside-down potential. This potential is discussed in detail, and it is explained in intuitive as well as in rigorous terms why the energy levels of this potential are real, positive, and discrete. Applications of PT-symmetry in quantum field theory are also discussed.
NASA Astrophysics Data System (ADS)
Rexer, Moritz; Claessens, Sten; Hirt, Christian
2016-04-01
The number of relevant terms of binominal series expansions used in spectral forward modelling of the gravitational potential is known to rise substantially as the resolution of the models increases. Here, we investigate and compare the binominal series expansions in forward modelling w.r.t. a sphere and w.r.t. an ellipsoid (Claessens and Hirt, 2013) in view of high degree forward modelling (d/o 10800). The series in each case depend on different parameters - such as elevation of the topographic function or ellipsoidal radius/co-latitude - and reveal different maximum orders of truncation for a 1% convergence level (=relative error). The results are verified in a real data scenario up to d/o 5400 by spot-checks using direct integral solutions that do not depend on binomial series expansions. As a conclusion, our study demonstrates that for d/o 10800 modelling up to 30 terms of the binominal series accounting for the radial integral are needed within the spherical and the ellipsoidal case, while up to 60 terms are needed for the binominal series accounting for the oblateness of Earth in the ellipsoidal case for a convergence at the 1% level. References: Claessens, S.J.; Hirt, C.: Ellipsoidal topographic potential - new solutions for spectral forward gravity modelling of topography with respect to a reference ellipsoid; Journal of Geophysical Research (JGR) - Solid Earth, Vol. 118, DOI: 10.1002/2013JB010457, 2013.
NASA Astrophysics Data System (ADS)
Chen, Xijiang; Hua, Xianghong; Zhang, Guang; Wu, Hao; Xuan, Wei; Li, Moxiao
2015-01-01
Evaluation of static three-dimensional (3-D) laser scanning point cloud accuracy has become a topical research issue. Point cloud accuracy is typically estimated by comparing terrestrial laser scanning data related to a finite number of check point coordinates against those obtained by an independent source of higher accuracy. These methods can only estimate the point accuracy but not the point cloud accuracy, which is influenced by the positional error and sampling interval. It is proposed that the point cloud error ellipsoid is favorable for inspecting the point cloud accuracy, which is determined by the individual point error ellipsoid volume. The kernel of this method is the computation of the point cloud error ellipsoid volume and the determination of the functional relationship between the error ellipsoid and accuracy. The proposed point cloud accuracy evaluation method is particularly suited for small sampling intervals when there exists an intersection of two error ellipsoids, and is suited not only for planar but also for nonplanar target surfaces. The performance of the proposed method (PM) is verified using both planar and nonplanar board point clouds. The results demonstrate that the proposed evaluation method significantly outperforms the existing methods when the target surface is nonplanar or there exists an intersection of two error ellipsoids. The PM therefore has the potential for improving the reliability of point cloud digital elevation models and static 3-D laser scanning-based deformation monitoring.
NASA Astrophysics Data System (ADS)
Blanco, Armando; Magnaudet, Jacques
1995-06-01
The structure of the flow around an oblate ellipsoidal bubble of fixed shape is studied by means of direct numerical simulation for Reynolds numbers Re up to 103. In agreement with a previous study by Dandy and Leal [Phys. Fluids 29, 1360 (1986)] the computations demonstrate that if the bubble aspect ratio χ is high enough a standing eddy can exist at the rear of the bubble in an intermediate range of Re. This eddy disappears beyond a certain Reynolds number and it is shown that its existence is governed by the competition between accumulation and evacuation of the vorticity in the flow. The range of Re where the eddy exists increases very rapidly with χ meaning that this structure is certainly present in many experimental situations. The evolution of the drag coefficient with Re reveals that the oblateness has a dramatic influence on the minimum value of Re beyond which Moore's theory [J. Fluid Mech. 23, 749 (1965)] can be used to predict the rise velocity of a bubble of fixed shape. In contrast, owing to the shape of the vorticity distribution at the surface of the bubble, no noticeable influence of the standing eddy on the drag is found. A quantitative comparison between the present results and those of previous authors shows that the computational description of the boundary layer around curved free surfaces is not a trivial matter since a strong influence of the numerical method is observed.
Manufacturing and applications of nonrotationally symmetric optics
NASA Astrophysics Data System (ADS)
Weck, Manfred; Klocke, Fritz; Oezmeral, H.; Hennig, Jan; Ruebenach, Olaf; Ehl, M.; Grosser, Norbert; Leiers, R.; Henning, Thomas F. E.; Unnebrink, Lars; Bernges, Joerg
1999-09-01
The use of lasers is more and more growing in industrial processing of different materials. Some examples of possible applications are the improvement of surface characteristics, drilling, welding, cutting and micro-structuring. An important aspect in this context is the necessity to adjust a specific intensity distribution for each application. This is usually realized by using special optics, which are able to form or shape the beam. These optics have complex geometries and in addition they have to fulfill high precision requirements regarding form and surface quality. The efficiency of laser system can be increased by using special designed optics with non-rotationally symmetric structures. Fabricating optics with these requirements is almost impossible using conventional manufacturing techniques. The only possibility for manufacturing is the use of fast tool servo system while the diamond turning process.
Symmetric spaces of exceptional groups
Boya, L. J.
2010-02-15
We address the problem of the reasons for the existence of 12 symmetric spaces with the exceptional Lie groups. The 1 + 2 cases for G{sub 2} and F{sub 4}, respectively, are easily explained from the octonionic nature of these groups. The 4 + 3 + 2 cases on the E{sub 6,7,8} series require the magic square of Freudenthal and, for the split case, an appeal to the supergravity chain in 5, 4, and 3 space-time dimensions.
Optically driven oscillations of ellipsoidal particles. Part II: ray-optics calculations.
Loudet, J-C; Mihiretie, B M; Pouligny, B
2014-12-01
We report numerical calculations on the mechanical effects of light on micrometer-sized dielectric ellipsoids immersed in water. We used a simple two-dimensional ray-optics model to compute the radiation pressure forces and torques exerted on the object as a function of position and orientation within the laser beam. Integration of the equations of motion, written in the Stokes limit, yields the particle dynamics that we investigated for different aspect ratios k. Whether the beam is collimated or focused, the results show that above a critical aspect ratio k(C), the ellipsoids cannot be stably trapped on the beam axis; the particle never comes to rest and rather oscillates permanently in a back-and-forth motion involving both translation and rotation in the vicinity of the beam. Such oscillations are a direct evidence of the non-conservative character of optical forces. Conversely, stable trapping can be achieved for k < k(C) with the particle standing idle in a vertical position. These predictions are in very good qualitative agreement with experimental observations. The physical origin of the instability may be understood from the force and torque fields whose structures greatly depend on the ellipsoid aspect ratio and beam diameter. The oscillations arise from a non-linear coupling of the forces and torques and the torque amplitude was identified as the bifurcation control parameter. Interestingly, simulations predict that sustained oscillations can be suppressed through the use of two coaxial counterpropagating beams, which may be of interest whenever a static equilibrium is required as in basic force and torque measurements or technological applications. PMID:25577403
Novel design for centrifugal counter-current chromatography: VI. Ellipsoid column.
Gu, Dongyu; Yang, Yi; Xin, Xuelei; Aisa, Haji Akber; Ito, Yoichiro
2015-01-01
A novel ellipsoid column was designed for centrifugal counter-current chromatography. Performance of the ellipsoid column with a capacity of 3.4 mL was examined with three different solvent systems composed of 1-butanol-acetic acid-water (4:1:5, v/v) (BAW), hexane-ethyl acetate-methanol-0.1 M HCl (1:1:1:1, v/v) (HEMH), and 12.5% (w/w) PEG1000 and 12.5% (w/w) dibasic potassium phosphate in water (PEG-DPP) each with suitable test samples. In dipeptide separation with BAW system, both stationary phase retention (Sf) and peak resolution (Rs) of the ellipsoid column were much higher at 0° column angle (column axis parallel to the centrifugal force) than at 90° column angle (column axis perpendicular to the centrifugal force), where elution with the lower phase at a low flow rate produced the best separation yielding Rs at 2.02 with 27.8% Sf at a flow rate of 0.07 ml/min. In the DNP-amino acid separation with HEMW system, the best results were obtained at a flow rate of 0.05 ml/min with 31.6% Sf yielding high Rs values at 2.16 between DNP-DL-glu and DNP-β-ala peaks and 1.81 between DNP-β-ala and DNP-L-ala peaks. In protein separation with PEG-DPP system, lysozyme and myolobin were resolved at Rs of 1.08 at a flow rate of 0.03 ml/min with 38.9% Sf. Most of those Rs values exceed those obtained from the figure-8 column under similar experimental conditions previously reported. PMID:25309116
Quantum mechanics of a constrained particle on an ellipsoid: Bein formalism and Geometric momentum
NASA Astrophysics Data System (ADS)
Panahi, H.; Jahangiri, L.
2016-09-01
In this work we apply the Dirac method in order to obtain the classical relations for a particle on an ellipsoid. We also determine the quantum mechanical form of these relations by using Dirac quantization. Then by considering the canonical commutation relations between the position and momentum operators in terms of curved coordinates, we try to propose the suitable representations for momentum operator that satisfy the obtained commutators between position and momentum in Euclidean space. We see that our representations for momentum operators are the same as geometric one.
Shape matters: Near-field fluid mechanics dominate the collective motions of ellipsoidal squirmers.
Kyoya, K; Matsunaga, D; Imai, Y; Omori, T; Ishikawa, T
2015-12-01
Microswimmers show a variety of collective motions. Despite extensive study, questions remain regarding the role of near-field fluid mechanics in collective motion. In this paper, we describe precisely the Stokes flow around hydrodynamically interacting ellipsoidal squirmers in a monolayer suspension. The results showed that various collective motions, such as ordering, aggregation, and whirls, are dominated by the swimming mode and the aspect ratio. The collective motions are mainly induced by near-field fluid mechanics, despite Stokes flow propagation over a long range. These results emphasize the importance of particle shape in collective motion. PMID:26764823
Xing, Xiaobo; Zheng, Jiapeng; Li, Fengjia; Sun, Chao; Cai, Xiang; Zhu, Debin; Lei, Liang; Wu, Ting; Zhou, Bin; Evans, Julian; Chen, Ziyi
2014-01-01
Thermal microbubbles generally grow directly from the heater and are spherical to minimize surface tension. We demonstrate a novel type of microbubble indirectly generated from a graphene oxide-microheater. Graphene oxide's photothermal properties allowed for efficient generation of a thermal gradient field on the microscale. A series of approximately ellipsoidal microbubbles were generated on the smooth microwire based on heterogeneous nucleation. Other dynamic behaviors induced by the microheater such as constant growth, directional transport and coalescence were also investigated experimentally and theoretically. The results are not only helpful for understanding the bubble dynamics but also useful for developing novel photothermal bubble-based devices. PMID:25124694
Velocity Ellipsoids for Crustal Seismic Anisotropy: Pumpkins and Melons Have Dimples and Bulges
NASA Astrophysics Data System (ADS)
Okaya, D.; Christensen, N.
2003-12-01
Geological causes of crustal anisotropy include regional fractures and cracks, isotropic heterogeneity or layering, and material composition and textural properties. In addition, shear or metamorphic foliations in fault zones or structural terranes serve as proxies for intracrustal deformation in a manner analogous to lattice preferred orientation of olivine produced by mantle shear. The primary factor in the production of crustal seismic anisotropy is the relative angle between a seismic wave and the (dipping) symmetry axes representing the crustal material even as either change along the propagation raypath. As a result, in order to analyze observations of crustal anisotropy we must understand the behavior of compressional and shear wave velocities in all propagation directions parallel to and in-between the principal symmetry axes which represent the crustal materials. In this poster we use Christoffel equations and physical properties obtained from petrophysical lab measurements in order to examine anisotropic velocities and travel-time effects for bulk rocks representative of different crustal levels. Ellipses and ellipsoids are commonly used to represent the P- and S-wave velocity directional behavior for materials described using hexagonal and orthorhombic symmetries, respectively. While olivine and pyroxene-based mantle rocks are characteristically fast symmetry axes (the "melons" of Levin and Park, 1997), crustal rocks are typically slow symmetry axes ("pumpkins") due to the predominance of fractures or textural foliations. Careful application of Christoffel solutions indicate that for most crustal (and mantle) rocks the surfaces of their pumpkins or melons are not exact analytical ellipsoids. Rather, the surfaces in the non-axial directions have second-order deflections (bulges or dimples) which potentially may produce observable azimuthal travel-time or shear splitting effects. In the case when the P-wave surface on average is slow (dimpled), due to SV
Volume integrals associated with the inhomogeneous Helmholtz equation. Part 1: Ellipsoidal region
NASA Technical Reports Server (NTRS)
Fu, L. S.; Mura, T.
1983-01-01
Problems of wave phenomena in 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 Helmholtz operator, nabla(2) to alpha(2), for the case of an ellipsoidal region. By using appropriate Taylor series expansions and multinomial theorem, these volume integrals are obtained in series form for regions r 4' and r r', where r and r' are distances from the origin to the point of observation and source, respectively. Derivatives of these integrals are easily evaluated. When the wave number approaches zero, the results reduce directly to the potentials of variable densities.
Stability of an ellipsoidal stellar cluster in the tidal force field of the Galaxy
NASA Astrophysics Data System (ADS)
Kozhanov, T. S.
1992-02-01
Attention is given to the dynamical characteristics of an ellipsoidal stellar cluster which rotates on an elliptical orbit relative to the center of the Galaxy in the field of its tidal forces. Regions of stability and instability of the cluster as a function of its form are defined on the basis of a numerical solution of the equations of the motion of stars inside the cluster. It is shown that, if the flattening of the cluster along the Y-axis, which coincides with the rotation direction, is larger than along the X-axis, which is directed toward the center of the Galaxy), the cluster is unstable.
Paramonov, Leonid; Yaliraki, Sophia N
2005-11-15
We obtain the distance of closest approach of the surfaces of two arbitrary ellipsoids valid at any orientation and separation measured along their intercenter vector. This directional distance is derived from the elliptic contact function. The geometric meaning behind this approach is clarified. An elliptic pair potential for modeling arbitrary mixtures of elliptic particles, whether hard or soft, is proposed based on this distance. Comparisons with Gay-Berne potentials are discussed. Analytic expressions for the forces and torques acting on the elliptic particles are given. PMID:16321080
NASA Astrophysics Data System (ADS)
Paramonov, Leonid; Yaliraki, Sophia N.
2005-11-01
We obtain the distance of closest approach of the surfaces of two arbitrary ellipsoids valid at any orientation and separation measured along their intercenter vector. This directional distance is derived from the elliptic contact function. The geometric meaning behind this approach is clarified. An elliptic pair potential for modeling arbitrary mixtures of elliptic particles, whether hard or soft, is proposed based on this distance. Comparisons with Gay-Berne potentials are discussed. Analytic expressions for the forces and torques acting on the elliptic particles are given.
Hydrodynamic coefficients of an oscillating ellipsoid moving in the free surface
NASA Astrophysics Data System (ADS)
Inglis, R. B.; Price, W. G.
1980-10-01
The frequency dependent heave, pitch, sway, and yaw hydrodynamic coefficients associated with an oscillating ellipsoid traveling with forward speed in the free surface are evaluated from a three-dimensional potential flow analysis. The free-surface boundary condition in the mathematical model either includes the influence of forward speed or is simplified to the equivalent zero speed case. This variation produces a velocity potential which is either frequency and speed dependent or just frequency dependent. The influence of forward speed on all the hydrodynamic coefficients is discussed.
Communication: equation of state of hard oblate ellipsoids by replica exchange Monte Carlo.
Odriozola, G; Guevara-Rodríguez, F de J
2011-05-28
We implemented the replica exchange Monte Carlo technique to produce the equation of state of hard 1:5 aspect-ratio oblate ellipsoids for a wide density range. For this purpose, we considered the analytical approximation of the overlap distance given by Bern and Pechukas and the exact numerical solution given by Perram and Wertheim. For both cases we capture the expected isotropic-nematic transition at low densities and a nematic-crystal transition at larger densities. For the exact case, these transitions occur at the volume fraction 0.341, and in the interval 0.584-0.605, respectively. PMID:21639414
Fixed-order H ∞ controller design for systems with ellipsoidal parametric uncertainty
NASA Astrophysics Data System (ADS)
Sadeghzadeh, Arash; Momeni, Hamidreza; Karimi, Alireza
2011-01-01
In this article, fixed-order robust H ∞ controller design for systems with ellipsoidal parametric uncertainty based on parameter-dependent Lyapunov functions is studied. Using the concept of Strictly Positive Realness (SPRness) of transfer functions, a fixed-order robust control design method in terms of solution to a set of Linear Matrix Inequalities (LMIs) is proposed. Since controller parameters are decision variables, any controller structure, such as PID, can be considered. The weighted infinity-norm of closed loop sensitivity functions are considered as performance specification in the synthesis problem. The simulation results show the effectiveness of the proposed method.
Exact reconstruction formula for the spherical mean Radon transform on ellipsoids
NASA Astrophysics Data System (ADS)
Haltmeier, Markus
2014-10-01
Many modern imaging and remote sensing applications require reconstructing a function from spherical averages (mean values). Examples include photoacoustic tomography, ultrasound imaging or SONAR. Several formulas of the back-projection type for recovering a function in n spatial dimensions from mean values over spheres centered on a sphere have been derived by D Finch, S K Patch and Rakesh (2004 SIAM J. Math. Anal. 35 1213-1240) for odd spatial dimension and by D Finch, M Haltmeier and Rakesh (2007 SIAM J. Appl. Math. 68 392-412) for even spatial dimension. In this paper we generalize some of these formulas to the case where the centers of integration lie on the boundary of an arbitrary ellipsoid. For the special cases n = 2 and n = 3 our results have recently been established by Y Salman (2014 J. Math. Anal. Appl. 420 612-20). For the higher dimensional case n\\gt 3 we establish proof techniques extending the ones in the above references. Back-projection type inversion formulas for recovering a function from spherical means with centers on an ellipsoid have first been derived by F Natterer (2012 Inverse Problems Imaging 6 315-20) for n = 3 and by V Palamodov (2012 Inverse Problems 28 065014) for arbitrary dimension. The results of Natterer have later been generalized to arbitrary dimension by M Haltmeier (2014 SIAM J. Math. Anal. 46 214-32). Note that these formulas are different from the ones derived in the present paper.
NASA Astrophysics Data System (ADS)
He, Xiang; Chen, Jianping; Zhang, Yachun; Chen, Yudong; Zeng, Xiaojun; Tang, Chunmei
2015-10-01
Some reports presented that the radar cross section (RCS) from the radar antenna of military airplanes can be reduced by using a low-temperature plasma screen. This paper gives a numerical and experimental analysis of this RCS-reduction method. The shape of the plasma screen was designed as a semi-ellipsoid in order to make full use of the space in the radar dome. In simulations, we discussed the scattering of the electromagnetic (EM) wave by a perfect electric conductor (PEC) covered with this plasma screen using the finite-difference-time-domain (FDTD) method. The variations of their return loss as a function of wave frequency, plasma density profile, and collision frequency were presented. In the experiments, a semi-ellipsoidal shaped plasma screen was produced. Electromagnetic attenuation of 1.5 GHz EM wave was measured for a radio frequency (RF) power of 5 kW at an argon pressure of 200-1150 Pa. A good agreement is found between simulated and experimental results. It can be confirmed that the plasma screen is useful in applications for stealth of radar antenna. supported by National Natural Science Foundation of China (No. 51107033) and the Fundamental Research Funds for the Central Universities, China (No. 2013B33614)
The pulsating/ellipsoidal variable hot B subdwarf KPD 1930+2752
NASA Astrophysics Data System (ADS)
Fontaine, G.
We propose to measure the projected rotational velocity of KPD 1930+2752, a unique binary system consisting of a sdB primary undergoing acoustic mode pulsations and ellipsoidally distorted by the presence of an unseen white dwarf companion. The orbital period of the system is 2.383 hrs. The measurement of v sin i is the one datum currently missing that prevents us from modeling the ellipsoidal light curve in terms of the basic parameters of the two stellar components. Once this measurement is secured, we should be able to derive the values of the masses and radii of these two stars. We should be able to verify if indeed KPD 1930+2752 is a genuine progenitor of a Type Ia supernova as was recently suggested by a British group. More importantly, by combining the values of the mass and the radius of the sdB pulsator with the period data, we should be able to model, for the first time, the interior structure of a sdB star through asteroseismological techniques. FUSE time tag observations are unique for this type of measurement. They allow us to remove the star's orbital velocity (348 km/s) that inevitably smears out the photospheric lines. We have already successfully implemented such a procedure in the CalFUSE pipeline. The projected equatorial velocity, v sin i, is then determined by comparing the star's line profiles to computed rotation profiles.
Aref's chaotic orbits tracked by a general ellipsoid using 3D numerical simulations
NASA Astrophysics Data System (ADS)
Shui, Pei; Popinet, Stéphane; Govindarajan, Rama; Valluri, Prashant
2015-11-01
The motion of an ellipsoidal solid in an ideal fluid has been shown to be chaotic (Aref, 1993) under the limit of non-integrability of Kirchhoff's equations (Kozlov & Oniscenko, 1982). On the other hand, the particle could stop moving when the damping viscous force is strong enough. We present numerical evidence using our in-house immersed solid solver for 3D chaotic motion of a general ellipsoidal solid and suggest criteria for triggering such motion. Our immersed solid solver functions under the framework of the Gerris flow package of Popinet et al. (2003). This solver, the Gerris Immersed Solid Solver (GISS), resolves 6 degree-of-freedom motion of immersed solids with arbitrary geometry and number. We validate our results against the solution of Kirchhoff's equations. The study also shows that the translational/ rotational energy ratio plays the key role on the motion pattern, while the particle geometry and density ratio between the solid and fluid also have some influence on the chaotic behaviour. Along with several other benchmark cases for viscous flows, we propose prediction of chaotic Aref's orbits as a key benchmark test case for immersed boundary/solid solvers.
PMMA/PMMA core-shell particles with ellipsoidal, fluorescent cores: accessing rotational dynamics.
Klein, Matthias K; Klinkenberg, Nele; Schuetter, Stefan; Saenger, Nicolai; Pfleiderer, Patrick; Zumbusch, Andreas
2015-03-10
For several decades, nonaqueous dispersions of PMMA particles have played an important role in colloid research. They have found application as colloidal model systems, which are used to probe glassy dynamics or to explore crystal nucleation. To date, most research has focused on spherical particles, in which only translational motion can be investigated. Recently, however, there has been a surge of interest in analyzing also rotational dynamics. In this contribution, we introduce a new class of core-shell particles, which can be used as rotational probes. The colloids described herein are composed of shape anisotropic, fluorescent cores covered with nonfluorescent PMMA shells. The core-shell particles are built up in four steps. In a first step, we produce fluorescent and photo-cross-linkable PMMA colloids. In the second step, these particles are thermomechanically elongated and fixed in defined ellipsoidal shapes by photo-cross-linking. Subsequently, we cover the cross-linked, fluorescent core with a nonfluorescent PMMA shell. The shape of the resulting core-shell colloids is tunable between the initial anisotropic and perfect spherical shape. For shaping, we apply a simple solvent swelling procedure. As one option, this method yields perfect PMMA spheres with ellipsoidal, fluorescent centers. We also report morphological particle characterization using various fluorescence microscopy techniques. Finally, we demonstrate that the rotational dynamics of individual colloids can be tracked and analyzed. PMID:25654438
NASA Astrophysics Data System (ADS)
Gheorghiu, Tamara; Ruchin, Vyacheslav; Vacaru, Olivia; Vacaru, Sergiu I.
2016-06-01
We study geometric relativistic flow and Ricci soliton equations which (for respective nonholonomic constraints and self-similarity conditions) are equivalent to the gravitational field equations of R2 gravity and/or to the Einstein equations with scalar field in general relativity, GR. Perelman's functionals are generalized for modified gravity theories, MGTs, which allows to formulate an analogous statistical thermodynamics for geometric flows and Ricci solitons. There are constructed and analyzed generic off-diagonal black ellipsoid, black hole and solitonic exact solutions in MGTs and GR encoding geometric flow evolution scenarios and nonlinear parametric interactions. Such new classes of solutions in MGTs can be with polarized and/or running constants, nonholonomically deformed horizons and/or embedded self-consistently into solitonic backgrounds. They exist also in GR as generic off-diagonal vacuum configurations with effective cosmological constant and/or mimicking effective scalar field interactions. Finally, we compute Perelman's energy and entropy for black ellipsoids and evolution solitons in R2 gravity.
Eshelby's solution for ellipsoidal inhomogeneous inclusions with applications to compaction bands
NASA Astrophysics Data System (ADS)
Meng, Chunfang; Pollard, David D.
2014-10-01
Eshelby's solution for an ellipsoidal inhomogeneous inclusion in an infinite elastic body is applied to compaction and shear-enhanced compaction bands in the Aztec sandstone at Valley of Fire State Park, NV. The inclusion and matrix are linear elastic and isotropic, but have different elastic moduli, and a remote stress represents tectonic loading. A prescribed uniform strain within the inclusion accounts for inelastic compaction for a porosity change from 25 to 10%. Differences in elastic moduli between the matrix and inclusion are based on laboratory data. We generalize earlier results, limited to 2D and axisymmetric geometries, by considering ellipsoids with different intermediate and greatest axial lengths, consistent with field observations. Stiffness contrasts and non-circular tip-line shapes produce modest concentrations of the remote stress, but compaction strains of 1-10% produce significant triaxial compressive stress concentrations, which presumably are responsible for band propagation. The plastic strain is triaxial, but dominated by the normal strain across the inclusion. The stress diminution on the band flank is easily overcome by minor increases in the tectonic loading, enabling bands to be closely spaced. For the shear-enhanced band, if the plastic shear and normal strains are approximately equal, the ratio of shear to normal stress is about 1.3 at the tip.
Instabilities of time-periodic, incompressible, inviscid flow in ellipsoidal domains.
NASA Astrophysics Data System (ADS)
Biello, Joseph A.; Saldanha, Kenneth I.; Lebovitz, Norman R.
1999-11-01
We consider the linear stability of exact, temporally periodic solutions of the Euler equations of incompressible, inviscid flow in an ellipsoidal domain. The problem of linear stability is reduced, without approximation, to a hierarchy of finite-dimensional Floquet problems governing fluid-dynamical perturbations of differing spatial scales and symmetries. We study two of these Floquet problems in detail, emphasizing parameter regimes of special physical significance. One of these regimes includes periodic flows differing only slightly from steady flows. Another includes long-period flows representing the nonlinear outcome of an instability of steady flows. In both cases much of the parameter space corresponds to instability, excepting a region adjacent to the spherical configuration. In the second case, even if the ellipsoid departs only moderately from a sphere, there are filamentary regions of instability in the parameter space. We relate this and other features of our results to properties of reversible and Hamiltonian systems, and compare our results with related studies of periodic flows.
Gietzelt, Matthias; Wolf, Klaus-Hendrik; Marschollek, Michael; Haux, Reinhold
2013-07-01
Calibration of accelerometers can be reduced to 3D-ellipsoid fitting problems. Changing extrinsic factors like temperature, pressure or humidity, as well as intrinsic factors like the battery status, demand to calibrate the measurements permanently. Thus, there is a need for fast calibration algorithms, e.g. for online analyses. The primary aim of this paper is to propose a non-iterative calibration algorithm for accelerometers with the focus on minimal execution time and low memory consumption. The secondary aim is to benchmark existing calibration algorithms based on 3D-ellipsoid fitting methods. We compared the algorithms regarding the calibration quality and the execution time as well as the number of quasi-static measurements needed for a stable calibration. As evaluation criterion for the calibration, both the norm of calibrated real-life measurements during inactivity and simulation data was used. The algorithms showed a high calibration quality, but the execution time differed significantly. The calibration method proposed in this paper showed the shortest execution time and a very good performance regarding the number of measurements needed to produce stable results. Furthermore, this algorithm was successfully implemented on a sensor node and calibrates the measured data on-the-fly while continuously storing the measured data to a microSD-card. PMID:23566707
Probabilistic cloning of three symmetric states
Jimenez, O.; Bergou, J.; Delgado, A.
2010-12-15
We study the probabilistic cloning of three symmetric states. These states are defined by a single complex quantity, the inner product among them. We show that three different probabilistic cloning machines are necessary to optimally clone all possible families of three symmetric states. We also show that the optimal cloning probability of generating M copies out of one original can be cast as the quotient between the success probability of unambiguously discriminating one and M copies of symmetric states.
Walking dynamics are symmetric (enough)
Ankaralı, M. Mert; Sefati, Shahin; Madhav, Manu S.; Long, Andrew; Bastian, Amy J.; Cowan, Noah J.
2015-01-01
Many biological phenomena such as locomotion, circadian cycles and breathing are rhythmic in nature and can be modelled as rhythmic dynamical systems. Dynamical systems modelling often involves neglecting certain characteristics of a physical system as a modelling convenience. For example, human locomotion is frequently treated as symmetric about the sagittal plane. In this work, we test this assumption by examining human walking dynamics around the steady state (limit-cycle). Here, we adapt statistical cross-validation in order to examine whether there are statistically significant asymmetries and, even if so, test the consequences of assuming bilateral symmetry anyway. Indeed, we identify significant asymmetries in the dynamics of human walking, but nevertheless show that ignoring these asymmetries results in a more consistent and predictive model. In general, neglecting evident characteristics of a system can be more than a modelling convenience—it can produce a better model.
Open String on Symmetric Product
NASA Astrophysics Data System (ADS)
Fuji, Hiroyuki; Matsuo, Yutaka
We discuss some basic properties of the open string on the symmetric product which is supposed to describe the open string field theory in discrete light-cone quantization (DLCQ). We first derive the consistent twisted boundary conditions for Annulus/Möbius/Klein Bottle diagrams and give the explicit form of the corresponding amplitude. They have the interpretation as the long open (or closed) string amplitude but the world sheet topology viewed from the short string and from the long string is in general different. Boundary (cross-cap) states of the short string are classified into three categories, the boundary (cross-cap) states of the long string and the "joint" state which connects two strings. The partition function has the typical structure of the string field theory in DLCQ. Tadpole condition is also analyzed and gives a reasonable gauge group SO(213).
Stamatakos, G S; Yova, D; Uzunoglu, N K
1997-09-01
A novel mathematical model of light scattering by an oriented monodisperse system of triaxial dielectric ellipsoids of complex index of refraction is presented. It is based on an integral equation solution to the scattering of a plane electromagnetic wave by a single triaxial dielectric ellipsoid. Both the position and the orientation of a single representative scatterer in a given coordinate system are considered arbitrary. A Monte Carlo simulation is developed to reproduce the diffraction pattern of a population of aligned ellipsoids. As an example of practical importance, light scattering by a population of erythrocytes subjected to intense shear stress is modeled. Agreement with experimental observations and the anomalous diffraction theory is illustrated. Thus a novel check of the electromagnetic basis of ektacytometry is provided. Furthermore, the versatility of the integral equation method, particularly in the advent of parallel processing systems, is demonstrated. PMID:18259511
NASA Astrophysics Data System (ADS)
Garmier, Romain; Barriot, Jean-Pierre; Konopliv, Alexander S.; Yeomans, Donald K.
2002-04-01
The gravity field for asteroid 433 Eros has been determined in terms of ellipsoidal harmonic functions by processing the Doppler tracking data of the NEAR spacecraft while it was in orbit about the asteroid. Using the same set of NEAR spacecraft Doppler tracking data, comparative descriptions of the Eros gravity field are provided for both the ellipsoidal and the traditional spherical harmonic models. It is shown that for elongated bodies, like the asteroid Eros, the ellipsoidal harmonics model permits a better representation of the gravity signature than does the spherical harmonics model. Eros has a nearly uniform density but there are negative gravity anomalies near the ends of Eros and positive gravity anomalies near the Psyche crater and the Himeros depression.
Yang, Xia; Chen, Qiu-Yun; Li, Xiang; Gao, Jing
2012-10-01
A functional ionic liquid (IL) (IL=4-acetyl-N-butyl pyridinium hexafluorophosphate) was synthesized and conjugated with low toxicity of nanospheres (RBITC@SiO(2)), forming a new kind of fluorescent core-shell ellipsoidal RBITC@SiO(2)-IL nanoparticle. In vitro assay results indicate that particle shape plays an important role in cellular interactions with NPs. Furthermore, the positively charged ellipsoidal RBITC@SiO(2)-IL nanoparticles can enter into HeLa cells and induce the cells to condense, split and decrease on the oxygen consumption. The enhanced cell image and decrease of mitochondria potential indicate that the ellipsoidal RBITC@SiO(2)-IL nanoparticles could be uptaken by HeLa cells through mitochondria involved path. Experimental results give us a new path to design nano-medicines through ionic liquid modified silica nanoparticles to target mitochondria. PMID:22659209
Continuity and Separation in Symmetric Topologies
ERIC Educational Resources Information Center
Harris, J.; Lynch, M.
2007-01-01
In this note, it is shown that in a symmetric topological space, the pairs of sets separated by the topology determine the topology itself. It is then shown that when the codomain is symmetric, functions which separate only those pairs of sets that are already separated are continuous, generalizing a result found by M. Lynch.
Baryon symmetric big bang cosmology
NASA Technical Reports Server (NTRS)
Stecker, F. W.
1978-01-01
Both the quantum theory and Einsteins theory of special relativity lead to the supposition that matter and antimatter were produced in equal quantities during the big bang. It is noted that local matter/antimatter asymmetries may be reconciled with universal symmetry by assuming (1) a slight imbalance of matter over antimatter in the early universe, annihilation, and a subsequent remainder of matter; (2) localized regions of excess for one or the other type of matter as an initial condition; and (3) an extremely dense, high temperature state with zero net baryon number; i.e., matter/antimatter symmetry. Attention is given to the third assumption, which is the simplest and the most in keeping with current knowledge of the cosmos, especially as pertains the universality of 3 K background radiation. Mechanisms of galaxy formation are discussed, whereby matter and antimatter might have collided and annihilated each other, or have coexisted (and continue to coexist) at vast distances. It is pointed out that baryon symmetric big bang cosmology could probably be proved if an antinucleus could be detected in cosmic radiation.
Heat conduction of symmetric lattices
NASA Astrophysics Data System (ADS)
Nie, Linru; Yu, Lilong; Zheng, Zhigang; Shu, Changzheng
2013-06-01
Heat conduction of symmetric Frenkel-Kontorova (FK) lattices with a coupling displacement was investigated. Through simplifying the model, we derived analytical expression of thermal current of the system in the overdamped case. By means of numerical calculations, the results indicate that: (i) As the coupling displacement d equals to zero, temperature oscillations of the heat baths linked with the lattices can control magnitude and direction of the thermal current; (ii) Whether there is a temperature bias or not, the thermal current oscillates periodically with d, whose amplitudes become greater and greater; (iii) As d is not equal to zero, the thermal current monotonically both increases and decreases with temperature oscillation amplitude of the heat baths, dependent on values of d; (iv) The coupling displacement also induces nonmonotonic behaviors of the thermal current vs spring constant of the lattice and coupling strength of the lattices; (v) These dynamical behaviors come from interaction of the coupling displacement with periodic potential of the FK lattices. Our results have the implication that the coupling displacement plays a crucial role in the control of heat current.
Parity-time-symmetric teleportation
NASA Astrophysics Data System (ADS)
Ra'di, Y.; Sounas, D. L.; Alù, A.; Tretyakov, S. A.
2016-06-01
We show that electromagnetic plane waves can be fully "teleported" through thin, nearly fully reflective sheets, assisted by a pair of parity-time-symmetric lossy and active sheets in front and behind the screen. The proposed structure is able to almost perfectly absorb incident waves over a wide range of frequency and incidence angles, while waves having a specific frequency and incidence angle are replicated behind the structure in synchronization with the input signal. It is shown that the proposed structure can be designed to teleport waves at any desired frequency and incidence angle. Furthermore, we generalize the proposed concept to the case of teleportation of electromagnetic waves over electrically long distances, enabling full absorption at one surface and the synthesis of the same signal at another point located electrically far away from the first surface. The physical principle behind this selective teleportation is discussed, and similarities and differences with tunneling and cloaking concepts based on PT symmetry are investigated. From the application point of view, the proposed structure works as an extremely selective filter, both in frequency and spatial domains.
Ellipsoidal plasma mirror focusing of high power laser pulses to ultra-high intensities
NASA Astrophysics Data System (ADS)
Wilson, R.; King, M.; Gray, R. J.; Carroll, D. C.; Dance, R. J.; Armstrong, C.; Hawkes, S. J.; Clarke, R. J.; Robertson, D. J.; Neely, D.; McKenna, P.
2016-03-01
The design and development of an ellipsoidal F/1 focusing plasma mirror capable of increasing the peak intensity achievable on petawatt level laser systems to >1022 W cm-2 is presented. A factor of 2.5 reduction in the focal spot size is achieved when compared to F/3 focusing with a conventional (solid state) optic. We find a factor of 3.6 enhancement in peak intensity, taking into account changes in plasma mirror reflectivity and focal spot quality. The sensitivity of the focusing plasma optic to misalignment is also investigated. It is demonstrated that an increase in the peak laser intensity from 3 ×1020 W cm-2 to 1021 W cm-2 results in a factor of 2 increase in the maximum energy of sheath-accelerated protons from a thin foil positioned at the focus of the intense laser light.
Wang, Ning; Er, Meng Joo; Han, Min
2015-12-01
In this paper, the motion dynamics of a large tanker is modeled by the generalized ellipsoidal function-based fuzzy neural network (GEBF-FNN). The reference model of tanker motion dynamics in the form of nonlinear difference equations is established to generate training data samples for the GEBF-FNN algorithm which begins with no hidden neuron. In the sequel, fuzzy rules associated with the GEBF-FNN-based model can be online self-constructed by generation criteria and parameter estimation, and can dynamically capture essential motion dynamics of the large tanker with high prediction accuracy. Simulation studies and comprehensive comparisons are conducted on typical zig-zag maneuvers with moderate and extreme steering, and demonstrate that the GEBF-FNN-based model of tanker motion dynamics achieves superior performance in terms of both approximation and prediction. PMID:25561605
The ellipsoidal nested sampling and the expression of the model uncertainty in measurements
NASA Astrophysics Data System (ADS)
Gervino, Gianpiero; Mana, Giovanni; Palmisano, Carlo
2016-07-01
In this paper, we consider the problems of identifying the most appropriate model for a given physical system and of assessing the model contribution to the measurement uncertainty. The above problems are studied in terms of Bayesian model selection and model averaging. As the evaluation of the “evidence” Z, i.e., the integral of Likelihood × Prior over the space of the measurand and the parameters, becomes impracticable when this space has 20 ÷ 30 dimensions, it is necessary to consider an appropriate numerical strategy. Among the many algorithms for calculating Z, we have investigated the ellipsoidal nested sampling, which is a technique based on three pillars: The study of the iso-likelihood contour lines of the integrand, a probabilistic estimate of the volume of the parameter space contained within the iso-likelihood contours and the random samplings from hyperellipsoids embedded in the integration variables. This paper lays out the essential ideas of this approach.
NASA Astrophysics Data System (ADS)
Hernández-Rodríguez, Cecilio; Fragoso-López, Ana Belén
2014-02-01
In 2007 Yin, Zhang and Tian [1] [Yin et al., 2007] derived the expressions of the refractive indices of biaxial crystals evaluated from the refractive indices ellipsoid equation. In the past we have researched about the simultaneous measurement of birefringence and optical activity in different crystals [2] [Hernández-Rodríguez et al., 2000], [3] [Hernández-Rodríguez and Gómez-Garrido, 2000], [4] [Herreros-Cedrés et al., 2003], [5] [Herreros-Cedrés et al., 2005] and [6] [Herreros-Cedrés et al., 2007], and recently, when we used their methods for the study of nonlinear crystals such as KTiOAsO4 (KTA) and KTiOPO4 (KTP), we found some errors in some expressions in their paper which were used by other authors [7] [Gao et al., 2003].
Itoh, Yuji; Vasanji, Amit; Ehlers, Justis P
2016-03-01
Objective assessment of retinal layer integrity with optical coherence tomography (OCT) is currently limited. The ellipsoid zone (EZ) has been identified as an important feature on OCT that has critical prognostic value in macular disorders. In this report, we describe a novel assessment tool for EZ integrity that provides visual and quantitative assessment across an OCT data set. Using this algorithm, we describe the findings in multiple clinical examples, including normal controls, age-related macular degeneration, drug effects (eg, ocriplasmin, hydroxychloroquine) and effects of surgical manipulation (eg, following membrane peeling using intraoperative OCT). EZ mapping provides both en face visualisation of EZ integrity and EZ-retinal pigment epithelium height. Additionally, volumetric, area and linear measurements are feasible using this assessment tool. PMID:26201354
Ptychographic phase retrieval method for characterizing ultra-precise ellipsoidal mirrors
NASA Astrophysics Data System (ADS)
Takeo, Yoko; Saito, Takahiro; Mimura, Hidekazu
2015-10-01
Focusing and imaging optics can be characterized by evaluating the wavefront error of the focused beam. We have bean developing a ptychographic phase retrieval method using a visible laser to measure the wavefront error. In this study, the measurement accuracy of the method is increased by improving both the phase retrieval algorithm and the experimental setup. The system is applied to the characterization of an ellipsoidal mirror used for the focusing of soft X-rays. The posture of the mirror can be measured with a resolution of 1.4 μrad. The wavefront error originating from the surface profile error can be detected with an accuracy of 0.01λ (root mean square).
Kinematics and Velocity Ellipsoid Parameters of Stellar Groups and Open Star Clusters: II Cool Stars
NASA Astrophysics Data System (ADS)
Elsanhoury, W. H.
2016-06-01
Based on the galactic space velocity components (U, V, W) and with aid of the vector and matrix analyses, we computed the velocity ellipsoid parameters for 790 late-type stars from CoRoT (Convection, Rotation and Transits) observations and 290 L dwarf stars. We ran the calculations for spectral types F, G, and K for late-type stars and L0, L1, L2, and L3 for L dwarf stars. We found that the ratio of the middle to the major axis in the galaxy ranged from 0.35 to 0.73. The vertex deviation from the galactic center was very small for the samples under investigation, which agrees well with earlier calculations.
Fiber optic refractometric sensors using a semi-ellipsoidal sensing element.
Castro Martinez, Amalia Nallely; Komanec, Matej; Nemecek, Tomas; Zvanovec, Stanislav; Khotiaintsev, Sergei
2016-04-01
We present theoretical and experimental results for a fiber optic refractometric sensor employing a semi-ellipsoidal sensing element made of polymethyl methacrylate. The double internal reflection of light inside the element provides sensitivity to the refractive index of the external analyte. We demonstrate that the developed sensor, operating at a wavelength of 632 nm, is capable of measurement within a wide range of refractive indices from n=1.00 to n=1.47 with sensitivity over 500 dB/RIU. A comparison of the developed sensor with two more complex refractometric sensors, one based on tapered optical fiber and the other based on suspended-core microstructure optical fiber, is presented. PMID:27139659
Anomalous diffusion of an ellipsoid in quasi-2D active fluids
NASA Astrophysics Data System (ADS)
Peng, Yi; Yang, Ou; Tang, Chao; Cheng, Xiang
Enhanced diffusion of a tracer particle is a unique feature in active fluids. Here, we studied the diffusion of an ellipsoid in a free-standing film of E. coli. Particle diffusion is linearly enhanced at low bacterial concentrations, whereas a non-linear enhancement is observed at high bacterial concentrations due to the giant fluctuation. More importantly, we uncover an anomalous coupling between the translational and rotational degrees of freedom that is strictly prohibited in the classical Brownian diffusion. Combining experiments with theoretical modeling, we show that such an anomaly arises from the stretching flow induced by the force dipole of swimming bacteria. Our work illustrates a novel universal feature of active matter and transforms the understanding of fundamental transport processes in microbiological systems. ACS Petroleum Research Fund #54168-DNI9, NSF Faculty Early Career Development Program, DMR-1452180.
Hydrodynamics of rotating stars and close binary interactions: Compressible ellipsoid models
NASA Technical Reports Server (NTRS)
Lai, Dong; Rasio, Frederic A.; Shapiro, Stuart L.
1994-01-01
We develop a new formalism to study the dynamics of fluid polytropes in three dimensions. The stars are modeled as compressible ellipsoids, and the hydrodynamic equations are reduced to a set of ordinary differential equations for the evolution of the principal axes and other global quantities. Both viscous dissipation and the gravitational radiation reaction are incorporated. We establish the validity of our approximations and demonstrate the simplicity and power of the method by rederiving a number of known results concerning the stability and dynamical oscillations of rapidly rotating polytropes. In particular, we present a generalization to compressible fluids of Chandrasekhar's classical results for the secular and dynamical instabilities of incompressible Maclaurin spheroids. We also present several applications of our method to astrophysical problems of great current interest, such as the tidal disruption of a star by a massive black hole, the coalescence of compact binaries driven by the emission of gravitational waves, and the development of instabilities in close binary systems.
Design of an ellipsoidal mirror for freewave characterization of materials at microwave frequencies
NASA Astrophysics Data System (ADS)
Rojo, M.; Muñoz, J.; Molina-Cuberos, G. J.; García-Collado, Á. J.; Margineda, J.
2016-03-01
Free-wave characterization of the electromagnetic properties of materials at microwave frequencies requires that scattering at the edges of the samples and/or holder be minimized. Here, an ellipsoidal mirror is designed and characterized in order to decrease the size of the beam, thereby avoiding the scattering problems, even when relatively small samples are used. In the experimental configuration, both the emitting antenna and sample are located at the mirror focuses. Since both the emitted and reflected (focused) beams are Gaussian in nature, we make use of Gaussian beam theory to carry out the design. The mirror parameters are optimized by numerical simulations (COMSOL Multiphysics®) and then experimentally tested. An experimental setup is presented for dielectric, magnetic and chiral measurement in the 4.5-18 GHz band.
The Bacterial Hydrophobin BslA is a Switchable Ellipsoidal Janus Nanocolloid.
Brandani, Giovanni B; Schor, Marieke; Morris, Ryan; Stanley-Wall, Nicola; MacPhee, Cait E; Marenduzzo, Davide; Zachariae, Ulrich
2015-10-27
BslA is an amphiphilic protein that forms a highly hydrophobic coat around Bacillus subtilis biofilms, shielding the bacterial community from external aqueous solution. It has a unique structure featuring a distinct partition between hydrophilic and hydrophobic surfaces. This surface property is reminiscent of synthesized Janus colloids. By investigating the behavior of BslA variants at water-cyclohexane interfaces through a set of multiscale simulations informed by experimental data, we show that BslA indeed represents a biological example of an ellipsoidal Janus nanoparticle, whose surface interactions are, moreover, readily switchable. BslA contains a local conformational toggle, which controls its global affinity for, and orientation at, water-oil interfaces. This adaptability, together with single-point mutations, enables the fine-tuning of its solvent and interfacial interactions, and suggests that BslA could be a basis for biotechnological applications. PMID:26378478
Energies and densities of electrons confined in elliptical and ellipsoidal quantum dots.
Halder, Avik; Kresin, Vitaly V
2016-10-01
We consider a droplet of electrons confined within an external harmonic potential well of elliptical or ellipsoidal shape, a geometry commonly encountered in work with semiconductor quantum dots and other nanoscale or mesoscale structures. For droplet sizes exceeding the effective Bohr radius, the dominant contribution to average system parameters in the Thomas-Fermi approximation comes from the potential energy terms, which allows us to derive expressions describing the electron droplet's shape and dimensions, its density, total and capacitive energy, and chemical potential. The analytical results are in very good agreement with experimental data and numerical calculations, and make it possible to follow the dependence of the properties of the system on its parameters (the total number of electrons, the axial ratios and curvatures of the confinement potential, and the dielectric constant of the material). An interesting feature is that the eccentricity of the electron droplet is not the same as that of its confining potential well. PMID:27502044
NASA Astrophysics Data System (ADS)
Takei, Yoshinori; Kume, Takehiro; Motoyama, Hiroto; Hiraguri, Kentaro; Hashizume, Hirokazu; Mimura, Hidekazu
2013-09-01
Ellipsoidal mirrors are one of the most promising types of X-ray mirror, because the mirror can focus X-rays to nanometer size with a large aperture and no chromatic aberration. However, so far ideal ellipsoidal mirrors cannot be realized by any manufacturing methods. One of the reasons is there is no fabrication method to process their inside surface with a diameter of several millimeters with nanometer-level accuracy. We propose and develop a manufacturing process of the ellipsoidal mirror. First, a master which has the reversed shape is prepared using grinding, polishing and Elastic Emission Machining (EEM). EEM can finish the surface shape to within 2nm (RMS). Then, the ellipsoidal mirror is produced by replicating the surface using an electroforming deposition method. By conducting the process without any stress at room temperature, replicating the surface roughness and shape with nanometer order accuracy is possible. In this paper, we report the current status of manufacturing of the ellipsoidal mirror.
A Unified Framework for the Orbital Structure of Bars and Triaxial Ellipsoids
NASA Astrophysics Data System (ADS)
Valluri, Monica; Shen, Juntai; Abbott, Caleb; Debattista, Victor P.
2016-02-01
We examine a large random sample of orbits in two self-consistent simulations of N-body bars. Orbits in these bars are classified both visually and with a new automated orbit classification method based on frequency analysis. The well-known prograde x1 orbit family originates from the same parent orbit as the box orbits in stationary and rotating triaxial ellipsoids. However, only a small fraction of bar orbits (∼4%) have predominately prograde motion like their periodic parent orbit. Most bar orbits arising from the x1 orbit have little net angular momentum in the bar frame, making them equivalent to box orbits in rotating triaxial potentials. In these simulations a small fraction of bar orbits (∼7%) are long-axis tubes that behave exactly like those in triaxial ellipsoids: they are tipped about the intermediate axis owing to the Coriolis force, with the sense of tipping determined by the sign of their angular momentum about the long axis. No orbits parented by prograde periodic x2 orbits are found in the pure bar model, but a tiny population (∼2%) of short-axis tube orbits parented by retrograde x4 orbits are found. When a central point mass representing a supermassive black hole (SMBH) is grown adiabatically at the center of the bar, those orbits that lie in the immediate vicinity of the SMBH are transformed into precessing Keplerian orbits that belong to the same major families (short-axis tubes, long-axis tubes and boxes) occupying the bar at larger radii. During the growth of an SMBH, the inflow of mass and outward transport of angular momentum transform some x1 and long-axis tube orbits into prograde short-axis tubes. This study has important implications for future attempts to constrain the masses of SMBHs in barred galaxies using orbit-based methods like the Schwarzschild orbit superposition scheme and for understanding the observed features in barred galaxies.
Detecting the Companions and Ellipsoidal Variations of RS CVn Primaries. I. σ Geminorum
NASA Astrophysics Data System (ADS)
Roettenbacher, Rachael M.; Monnier, John D.; Henry, Gregory W.; Fekel, Francis C.; Williamson, Michael H.; Pourbaix, Dimitri; Latham, David W.; Latham, Christian A.; Torres, Guillermo; Baron, Fabien; Che, Xiao; Kraus, Stefan; Schaefer, Gail H.; Aarnio, Alicia N.; Korhonen, Heidi; Harmon, Robert O.; ten Brummelaar, Theo A.; Sturmann, Judit; Sturmann, Laszlo; Turner, Nils H.
2015-07-01
To measure the properties of both components of the RS Canum Venaticorum binary σ Geminorum (σ Gem), we directly detect the faint companion, measure the orbit, obtain model-independent masses and evolutionary histories, detect ellipsoidal variations of the primary caused by the gravity of the companion, and measure gravity darkening. We detect the companion with interferometric observations obtained with the Michigan InfraRed Combiner at Georgia State University’s Center for High Angular Resolution Astronomy Array with a primary-to-secondary H-band flux ratio of 270 ± 70. A radial velocity curve of the companion was obtained with spectra from the Tillinghast Reflector Echelle Spectrograph on the 1.5 m Tillinghast Reflector at Fred Lawrence Whipple Observatory. We additionally use new observations from the Tennessee State University Automated Spectroscopic and Photometric Telescopes (AST and APT, respectively). From our orbit, we determine model-independent masses of the components ({M}1=1.28+/- 0.07 {M}⊙ , {M}2=0.73+/- 0.03 {M}⊙ ), and estimate a system age of 5∓ 1 Gyr. An average of the 27 year APT light curve of σ Gem folded over the orbital period (P=19.6027+/- 0.0005 days) reveals a quasi-sinusoidal signature, which has previously been attributed to active longitudes 180° apart on the surface of σ Gem. With the component masses, diameters, and orbit, we find that the predicted light curve for ellipsoidal variations due to the primary star partially filling its Roche lobe potential matches well with the observed average light curve, offering a compelling alternative explanation to the active longitudes hypothesis. Measuring gravity darkening from the light curve gives β <; 0.1, a value slightly lower than that expected from recent theory.
ELLIPSOIDAL VARIABLE V1197 ORIONIS: ABSOLUTE LIGHT-VELOCITY ANALYSIS FOR KNOWN DISTANCE
Wilson, R. E.; Chochol, D.; KomzIk, R.; Van Hamme, W.; Pribulla, T.; Volkov, I.
2009-09-01
V1197 Orionis light curves from a long-term observing program for red giant binaries show ellipsoidal variation of small amplitude in the V and R{sub C} bands, although not clearly in U and B. Eclipses are not detected. All four bands show large irregular intrinsic variations, including fleeting quasi-periodicities identified by power spectra, that degrade analysis and may be caused by dynamical tides generated by orbital eccentricity. To deal with the absence of eclipses and consequent lack of astrophysical and geometrical information, direct use is made of the Hipparcos parallax distance while the V and R{sub C} light curves and (older) radial velocity curves are analyzed simultaneously in terms of absolute flux. The red giant's temperature is estimated from new spectra. This type of analysis, called Inverse Distance Estimation for brevity, is new and can also be applied to other ellipsoidal variables. Advantages gained by utilization of definite distance and temperature are discussed in regard to how radius, fractional lobe filling, and mass ratio information are expressed in the observations. The advantages were tested in solutions of noisy synthetic data. Also discussed and tested by simulations are ideas on the optimal number of light curves to be solved simultaneously under various conditions. The dim companion has not been observed or discussed in the literature but most solutions find its mass to be well below that of the red giant. Solutions show red giant masses that are too low for evolution to the red giant stage within the age of the Galaxy, although that result is probably an artifact of the intrinsic brightness fluctuations.
PELDOR in rotationally symmetric homo-oligomers
NASA Astrophysics Data System (ADS)
Giannoulis, Angeliki; Ward, Richard; Branigan, Emma; Naismith, James H.; Bode, Bela E.
2013-10-01
Nanometre distance measurements by pulsed electron-electron double resonance (PELDOR) spectroscopy have become an increasingly important tool in structural biology. The theoretical underpinning of the experiment is well defined for systems containing two nitroxide spin-labels (spin pairs); however, recently experiments have been reported on homo-oligomeric membrane proteins consisting of up to eight spin-labelled monomers. We have explored the theory behind these systems by examining model systems based on multiple spins arranged in rotationally symmetric polygons. The results demonstrate that with a rising number of spins within the test molecule, increasingly strong distortions appear in distance distributions obtained from an analysis based on the simple spin pair approach. These distortions are significant over a range of system sizes and remain so even when random errors are introduced into the symmetry of the model. We present an alternative approach to the extraction of distances on such systems based on a minimisation that properly treats multi-spin correlations. We demonstrate the utility of this approach on a spin-labelled mutant of the heptameric Mechanosensitive Channel of Small Conductance of E. coli.
Orbital tomography for highly symmetric adsorbate systems
NASA Astrophysics Data System (ADS)
Stadtmüller, B.; Willenbockel, M.; Reinisch, E. M.; Ules, T.; Bocquet, F. C.; Soubatch, S.; Puschnig, P.; Koller, G.; Ramsey, M. G.; Tautz, F. S.; Kumpf, C.
2012-10-01
Orbital tomography is a new and very powerful tool to analyze the angular distribution of a photoemission spectroscopy experiment. It was successfully used for organic adsorbate systems to identify (and consequently deconvolute) the contributions of specific molecular orbitals to the photoemission data. The technique was so far limited to surfaces with low symmetry like fcc(110) oriented surfaces, owing to the small number of rotational domains that occur on such surfaces. In this letter we overcome this limitation and present an orbital tomography study of a 3,4,9,10-perylene-tetra-carboxylic-dianhydride (PTCDA) monolayer film adsorbed on Ag(111). Although this system exhibits twelve differently oriented molecules, the angular resolved photoemission data still allow a meaningful analysis of the different local density of states and reveal different electronic structures for symmetrically inequivalent molecules. We also discuss the precision of the orbital tomography technique in terms of counting statistics and linear regression fitting algorithm. Our results demonstrate that orbital tomography is not limited to low-symmetry surfaces, a finding which makes a broad field of complex adsorbate systems accessible to this powerful technique.
Symmetric weak ternary quantum homomorphic encryption schemes
NASA Astrophysics Data System (ADS)
Wang, Yuqi; She, Kun; Luo, Qingbin; Yang, Fan; Zhao, Chao
2016-03-01
Based on a ternary quantum logic circuit, four symmetric weak ternary quantum homomorphic encryption (QHE) schemes were proposed. First, for a one-qutrit rotation gate, a QHE scheme was constructed. Second, in view of the synthesis of a general 3 × 3 unitary transformation, another one-qutrit QHE scheme was proposed. Third, according to the one-qutrit scheme, the two-qutrit QHE scheme about generalized controlled X (GCX(m,n)) gate was constructed and further generalized to the n-qutrit unitary matrix case. Finally, the security of these schemes was analyzed in two respects. It can be concluded that the attacker can correctly guess the encryption key with a maximum probability pk = 1/33n, thus it can better protect the privacy of users’ data. Moreover, these schemes can be well integrated into the future quantum remote server architecture, and thus the computational security of the users’ private quantum information can be well protected in a distributed computing environment.
NASA Astrophysics Data System (ADS)
Buote, David A.; Humphrey, Philip J.
2012-02-01
This is the first of two papers investigating the deprojection and spherical averaging of ellipsoidal galaxy clusters. We specifically consider applications to hydrostatic X-ray and Sunyaev-Zel'dovich (SZ) studies, though many of the results also apply to isotropic dispersion-supported stellar dynamical systems. Here we present analytical formulae for galaxy clusters described by a gravitational potential that is a triaxial ellipsoid of constant shape and orientation. For this model type we show that the mass bias due to spherically averaging X-ray observations is independent of the temperature profile, and for the special case of a scale-free logarithmic potential, there is exactly zero mass bias for any shape, orientation and temperature profile. The ratio of spherically averaged intracluster medium (ICM) pressures obtained from SZ and X-ray measurements depends only on the ICM intrinsic shape, projection orientation and H0, which provides another illustration of how cluster geometry can be recovered through a combination of X-ray and SZ measurements. We also demonstrate that YSZ and YX have different biases owing to spherical averaging, which leads to an offset in the spherically averaged ? relation. A potentially useful application of the analytical formulae presented is to assess the error range of an observable (e.g. mass, YSZ) accounting for deviations from assumed spherical symmetry, without having to perform the ellipsoidal deprojection explicitly. Finally, for dedicated ellipsoidal studies, we also generalize the spherical onion peeling method to the triaxial case for a given shape and orientation.
Modelling non-symmetric collagen fibre dispersion in arterial walls
Holzapfel, Gerhard A.; Niestrawska, Justyna A.; Ogden, Ray W.; Reinisch, Andreas J.; Schriefl, Andreas J.
2015-01-01
New experimental results on collagen fibre dispersion in human arterial layers have shown that the dispersion in the tangential plane is more significant than that out of plane. A rotationally symmetric dispersion model is not able to capture this distinction. For this reason, we introduce a new non-symmetric dispersion model, based on the bivariate von Mises distribution, which is used to construct a new structure tensor. The latter is incorporated in a strain-energy function that accommodates both the mechanical and structural features of the material, extending our rotationally symmetric dispersion model (Gasser et al. 2006 J. R. Soc. Interface 3, 15–35. (doi:10.1098/rsif.2005.0073)). We provide specific ranges for the dispersion parameters and show how previous models can be deduced as special cases. We also provide explicit expressions for the stress and elasticity tensors in the Lagrangian description that are needed for a finite-element implementation. Material and structural parameters were obtained by fitting predictions of the model to experimental data obtained from human abdominal aortic adventitia. In a finite-element example, we analyse the influence of the fibre dispersion on the homogeneous biaxial mechanical response of aortic strips, and in a final example the non-homogeneous stress distribution is obtained for circumferential and axial strips under fixed extension. It has recently become apparent that this more general model is needed for describing the mechanical behaviour of a variety of fibrous tissues. PMID:25878125
Symmetric Achromatic Low-Beta Collider Interaction Region Design Concept
Morozov, Vasiliy S.; Derbenev, Yaroslav S.; Lin, Fanglei; Johnson, Rolland P.
2013-01-01
We present a new symmetry-based concept for an achromatic low-beta collider interaction region design. A specially-designed symmetric Chromaticity Compensation Block (CCB) induces an angle spread in the passing beam such that it cancels the chromatic kick of the final focusing quadrupoles. Two such CCB?s placed symmetrically around an interaction point allow simultaneous compensation of the 1st-order chromaticities and chromatic beam smear at the IP without inducing significant 2nd-order aberrations. We first develop an analytic description of this approach and explicitly formulate 2nd-order aberration compensation conditions at the interaction point. The concept is next applied to develop an interaction region design for the ion collider ring of an electron-ion collider. We numerically evaluate performance of the design in terms of momentum acceptance and dynamic aperture. The advantages of the new concept are illustrated by comparing it to the conventional distributed-sextupole chromaticity compensation scheme.
Study of striations in a spherically symmetric hydrogen discharge
NASA Astrophysics Data System (ADS)
Lowell Morgan, W.; Childs, Montgomery W.
2015-10-01
Experiments on a high power spherically symmetric positive corona discharge in molecular hydrogen are reported upon. These are collisional plasmas in the H2 pressure range of about 0.75 Torr to 3 Torr. Applied voltages ranged up to 600 V on the anode with currents ranging up to 3 A. As others have observed in prior published experiments going back to 1997, we have observed spherically symmetric striations or double layers. Others have observed such striations in O2, CO2, and in mixtures of N2 and acetone or methanol, or benzene. Like H2 all these gases, except N2 itself, readily dissociate and form negative ions by dissociative attachment with electrons. We propose that the striations are instabilities arising from copious formation of negative ions that modify the radial space charge and electric field distributions in such high aspect ratio spherical discharges.
Comparison of asymmetric with symmetric feed oil injection parameters in a riser reactor.
Bowman, B. J.; Chang, S. L.; Lottes, S. A.; Zhou, C. Q.
1999-04-20
A computational fluid dynamic (CFD) computer code was used to determine the effects of product yields of three feed injection parameters in a fluidized catalytic cracking (FCC) riser reactor. This study includes the effects of both symmetrical and non-symmetrical injection parameters. All these parameters have significant effects on the feed oil spray distribution, vaporization rates and the resulting product yields. This study also indicates that optimum parameter ranges exist for the investigated parameters.
Dugyala, Venkateshwar Rao; Anjali, Thiriveni G; Upendar, Siliveru; Mani, Ethayaraja; Basavaraj, Madivala G
2016-04-12
In this contribution, we discuss the role of surface charge on the adsorption of shape anisotropic particles to fluid-fluid interfaces in the context of their application in particle-stabilized emulsions. Starting with a pendent aqueous drop containing nano-ellipsoids of known surface charge density suspended in an oil medium, we study the kinetics of adsorption of the ellipsoids to the water-decane interface using pendant drop tensiometry. The interfacial tension of the drop is recorded as a function of time by analyzing the shape of the drop. We show that the particles that are weakly charged readily adsorb to the water-decane interface and the adsorption behavior is influenced by the particle surface charge density. Furthermore, as the area available for the particles deposited at the interface is reduced, the interface populated with self-assembled ellipsoids shows wrinkles indicating buckling of the particle-laden interface under compression. However, the buckling is not observed if nano-ellipsoids are highly charged confirming that the particles do not adsorb to the interface when they are highly charged. This suggests that in several examples where the particles at interfaces concept is exploited, the repulsive energy barrier due to the particle surface charge plays a key role in the adsorption of particles to the interfaces. However, once the particles are adsorbed, the interfacial properties of the monolayer depend on the particle-particle interactions. Thus a combination of these interactions determines the concentration of particles at the interface, their microstructure and interfacial properties. The effect of these interactions on the quantity and size of the emulsion drops stabilized by ellipsoidal particles is also explored. PMID:26780963
PT-Symmetric Quantum Field Theory
NASA Astrophysics Data System (ADS)
Bender, Carl M.
2011-09-01
In 1998 it was discovered that the requirement that a Hamiltonian be Dirac Hermitian (H = H†) can be weakened and generalized to the requirement that a Hamiltonian be PT symmetric ([H,PT] = 0); that is, invariant under combined space reflection and time reversal. Weakening the constraint of Hermiticity allows one to consider new kinds of physically acceptable Hamiltonians and, in effect, it amounts to extending quantum mechanics from the real (Hermitian) domain into the complex domain. Much work has been done on the analysis of various PT-symmetric quantum-mechanical models. However, only very little analysis has been done on PT-symmetric quantum-field-theoretic models. Here, we describe some of what has been done in the context of PT-symmetric quantum field theory and describe some possible fundamental applications.
Gaussian Multiplicative Chaos for Symmetric Isotropic Matrices
NASA Astrophysics Data System (ADS)
Chevillard, Laurent; Rhodes, Rémi; Vargas, Vincent
2013-02-01
Motivated by isotropic fully developed turbulence, we define a theory of symmetric matrix valued isotropic Gaussian multiplicative chaos. Our construction extends the scalar theory developed by J.P. Kahane in 1985.
Origin of symmetric PMNS and CKM matrices
NASA Astrophysics Data System (ADS)
Rodejohann, Werner; Xu, Xun-Jie
2015-03-01
The Pontecorvo-Maki-Nakagawa-Sakata and Cabibbo-Kobayashi-Maskawa matrices are phenomenologically close to symmetric, and a symmetric form could be used as zeroth-order approximation for both matrices. We study the possible theoretical origin of this feature in flavor symmetry models. We identify necessary geometric properties of discrete flavor symmetry groups that can lead to symmetric mixing matrices. Those properties are actually very common in discrete groups such as A4 , S4 , or Δ (96 ) . As an application of our theorem, we generate a symmetric lepton mixing scheme with θ12=θ23=36.21 ° ; θ13=12.20 ° , and δ =0 , realized with the group Δ (96 ) .
Scattering properties of PT-symmetric objects
NASA Astrophysics Data System (ADS)
Miri, Mohammad-Ali; Eftekhar, Mohammad Amin; Facao, Margarida; Abouraddy, Ayman F.; Bakry, Ahmed; Razvi, Mir A. N.; Alshahrie, Ahmed; Alù, Andrea; Christodoulides, Demetrios N.
2016-07-01
We investigate the scattering response of parity-time (PT) symmetric structures. We show that, due to the local flow of energy between gain and loss regions, such systems can deflect light in unusual ways, as a function of the gain/loss contrast. Such structures are highly anisotropic and their scattering patterns can drastically change as a function of the angle of incidence. In addition, we derive a modified optical theorem for PT-symmetric scattering systems, and discuss its ramifications.
Lax Operator for Macdonald Symmetric Functions
NASA Astrophysics Data System (ADS)
Nazarov, Maxim; Sklyanin, Evgeny
2015-07-01
Using the Lax operator formalism, we construct a family of pairwise commuting operators such that the Macdonald symmetric functions of infinitely many variables and of two parameters q, t are their eigenfunctions. We express our operators in terms of the Hall-Littlewood symmetric functions of the variables and of the parameter t corresponding to the partitions with one part only. Our expression is based on the notion of Baker-Akhiezer function.
Image registration under symmetric conditions: novel approach
NASA Astrophysics Data System (ADS)
Duraisamy, Prakash; Yousef, Amr; Buckles, Bill; Jackson, Steve
2015-03-01
Registering the 2D images is one of the important pre-processing steps in many computer vision applications like 3D reconstruction, building panoramic images. Contemporary registration algorithm like SIFT (Scale Invariant Feature transform) was not quite success in registering the images under symmetric conditions and under poor illuminations using DoF (Difference of Gaussian) features. In this paper, we introduced a novel approach for registering the images under symmetric conditions.
Symmetric states: Their nonlocality and entanglement
Wang, Zizhu; Markham, Damian
2014-12-04
The nonlocality of permutation symmetric states of qubits is shown via an extension of the Hardy paradox and the extension of the associated inequality. This is achieved by using the Majorana representation, which is also a powerful tool in the study of entanglement properties of symmetric states. Through the Majorana representation, different nonlocal properties can be linked to different entanglement properties of a state, which is useful in determining the usefulness of different states in different quantum information processing tasks.
NASA Astrophysics Data System (ADS)
Reimond, Stefan; Baur, Oliver
2016-03-01
Gravitational features are a fundamental source of information to learn more about the interior structure and composition of planets, moons, asteroids, and comets. Gravitational field modeling typically approximates the target body with a sphere, leading to a representation in spherical harmonics. However, small celestial bodies are often irregular in shape and hence poorly approximated by a sphere. A much better suited geometrical fit is achieved by a triaxial ellipsoid. This is also mirrored in the fact that the associated harmonic expansion (ellipsoidal harmonics) shows a significantly better convergence behavior as opposed to spherical harmonics. Unfortunately, complex mathematics and numerical problems (arithmetic overflow) so far severely limited the applicability of ellipsoidal harmonics. In this paper, we present a method that allows expanding ellipsoidal harmonics to a considerably higher degree compared to existing techniques. We apply this novel approach to model the gravitational field of comet 67P, the final target of the Rosetta mission. The comparison of results based on the ellipsoidal parameterization with those based on the spheroidal and spherical approximations reveals that the latter is clearly inferior; the spheroidal solution, on the other hand, is virtually just as accurate as the ellipsoidal one. Finally, in order to generalize our findings, we assess the gravitational field modeling performance for some 400 small bodies in the Solar System. From this investigation we generally conclude that the spheroidal representation is an attractive alternative to the complex ellipsoidal parameterization, on the one hand, and the inadequate spherical representation, on the other hand.
The lack of large compact symmetric objects
NASA Astrophysics Data System (ADS)
Augusto, P.
2009-02-01
In recent years, `baby' (< 103 yr) and `young' (103-105 yr) radio galaxies have been found and classified, although their numbers are still small (tens). Also, they have many different names, depending on the type of survey and scientific context in which they were found: compact steep spectrum sources (CSS), giga-Hertz peaked spectrum sources (GPS) and compact-medium symmetric objects (C-MSO). The latter have the radio galaxy structure more obvious and correspond to the `babies' (CSOs; < 1 kpc) and `young' (MSOs; 1-15 kpc) radio galaxies. The log-size distribution of CSOs shows a sharp drop at 0.3 kpc. This trend continues through flat-spectrum MSOs (over the full 1-15 kpc size range). In order to find out if this lack of large CSOs and flat-spectrum MSOs is due to poor sampling (lack of surveys that probe efficiently the 0.3-15 kpc size range) and/or has physical meaning (e.g. if the lobes of CSOs expand as they grow and age, they might become CSSs, `disappearing' from the flat-spectrum MSO statistics), we have built a sample of 157 flat-spectrum radio sources with structure on ˜0.3-15 kpc scales. We are using new, archived and published data to produce and inspect hundreds of multi-frequency multi-instrument maps and models. We have already found 13 new secure CSO/MSOs. We expect to uncover ˜30-40 new CSOs and MSOs, most on the 0.3-15 kpc size range, when our project is complete.
Novel optical characteristics of a Fabry-Perot resonator with embedded PT-symmetrical grating.
Kulishov, Mykola; Kress, Bernard; Jones, H F
2014-09-22
We explore the optical properties of a Fabry-Perot resonator with an embedded Parity-Time (PT) symmetrical grating. This PT-symmetrical grating is non diffractive (transparent) when illuminated from one side and diffracting (Bragg reflection) when illuminated from the other side, thus providing a unidirectional reflective functionality. The incorporated PT-symmetrical grating forms a resonator with two embedded cavities. We analyze the transmission and reflection properties of these new structures through a transfer matrix approach. Depending on the resonator geometry these cavities can interact with different degrees of coherency: fully constructive interaction, partially constructive interaction, partially destructive interaction, and finally their interaction can be completely destructive. A number of very unusual (exotic) nonsymmetrical absorption and amplification behaviors are observed. The proposed structure also exhibits unusual lasing performance. Due to the PT-symmetrical grating, there is no chance of mode hopping; it can lase with only a single longitudinal mode for any distance between the distributed reflectors. PMID:25321786
Symmetric Galerkin boundary formulations employing curved elements
NASA Technical Reports Server (NTRS)
Kane, J. H.; Balakrishna, C.
1993-01-01
Accounts of the symmetric Galerkin approach to boundary element analysis (BEA) have recently been published. This paper attempts to add to the understanding of this method by addressing a series of fundamental issues associated with its potential computational efficiency. A new symmetric Galerkin theoretical formulation for both the (harmonic) heat conduction and the (biharmonic) elasticity problem that employs regularized singular and hypersingular boundary integral equations (BIEs) is presented. The novel use of regularized BIEs in the Galerkin context is shown to allow straightforward incorporation of curved, isoparametric elements. A symmetric reusable intrinsic sample point (RISP) numerical integration algorithm is shown to produce a Galerkin (i.e., double) integration strategy that is competitive with its counterpart (i.e., singular) integration procedure in the collocation BEA approach when the time saved in the symmetric equation solution phase is also taken into account. This new formulation is shown to be capable of employing hypersingular BIEs while obviating the requirement of C 1 continuity, a fact that allows the employment of the popular continuous element technology. The behavior of the symmetric Galerkin BEA method with regard to both direct and iterative equation solution operations is also addressed. A series of example problems are presented to quantify the performance of this symmetric approach, relative to the more conventional unsymmetric BEA, in terms of both accuracy and efficiency. It is concluded that appropriate implementations of the symmetric Galerkin approach to BEA indeed have the potential to be competitive with, if not superior to, collocation-based BEA, for large-scale problems.
2 × 2 random matrix ensembles with reduced symmetry: from Hermitian to {PT} -symmetric matrices
NASA Astrophysics Data System (ADS)
Gong, Jiangbin; Wang, Qing-hai
2012-11-01
A possibly fruitful extension of conventional random matrix ensembles is proposed by imposing symmetry constraints on conventional Hermitian matrices or parity-time ( {PT})-symmetric matrices. To illustrate the main idea, we first study 2 × 2 complex Hermitian matrix ensembles with O(2)-invariant constraints, yielding novel level-spacing statistics such as singular distributions, the half-Gaussian distribution, distributions interpolating between the GOE (Gaussian orthogonal ensemble) distribution and half-Gaussian distributions, as well as the gapped-GOE distribution. Such a symmetry-reduction strategy is then used to explore 2 × 2 {PT}-symmetric matrix ensembles with real eigenvalues. In particular, {PT}-symmetric random matrix ensembles with U(2) invariance can be constructed, with the conventional complex Hermitian random matrix ensemble being a special case. In two examples of {PT}-symmetric random matrix ensembles, the level-spacing distributions are found to be the standard GUE (Gaussian unitary ensemble) statistics or the ‘truncated-GUE’ statistics. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Quantum physics with non-Hermitian operators’.
Zhu, Weifang; Chen, Haoyu; Zhao, Heming; Tian, Bei; Wang, Lirong; Shi, Fei; Xiang, Dehui; Luo, Xiaohong; Gao, Enting; Zhang, Li; Yin, Yilong; Chen, Xinjian
2016-01-01
Detection and assessment of the integrity of the photoreceptor ellipsoid zone (EZ) are important because it is critical for visual acuity in retina trauma and other diseases. We have proposed and validated a framework that can automatically analyse the 3D integrity of the EZ in optical coherence tomography (OCT) images. The images are first filtered and automatically segmented into 10 layers, of which EZ is located in the 7th layer. For each voxel of the EZ, 57 features are extracted and a principle component analysis is performed to optimize the features. An Adaboost classifier is trained to classify each voxel of the EZ as disrupted or non-disrupted. Finally, blood vessel silhouettes and isolated points are excluded. To demonstrate its effectiveness, the proposed framework was tested on 15 eyes with retinal trauma and 15 normal eyes. For the eyes with retinal trauma, the sensitivity (SEN) was 85.69% ± 9.59%, the specificity (SPE) was 85.91% ± 5.48%, and the balanced accuracy rate (BAR) was 85.80% ± 6.16%. For the normal eyes, the SPE was 99.03% ± 0.73%, and the SEN and BAR levels were not relevant. Our framework has the potential to become a useful tool for studying retina trauma and other conditions involving EZ integrity. PMID:27157473
Velocity relaxation of an ellipsoid immersed in a viscous incompressible fluid
NASA Astrophysics Data System (ADS)
Felderhof, B. U.
2013-01-01
The motion of an ellipsoid in a viscous incompressible fluid, caused by a small time-dependent applied force, is studied on the basis of the linearized Navier-Stokes equations in terms of the frequency-dependence of the friction tensor. The asymptotic behavior of the hydrodynamic force at high frequency contains a term linear in frequency, with an added mass coefficient, and a term proportional to the square root of frequency, with a Basset coefficient. The latter is calculated from an expression derived by Batchelor [An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1967)]. A simple approximate three-pole expression is proposed for the frequency-dependent admittance for each principal direction, embodying added mass, particle mass, the steady state friction coefficient, and the Basset coefficient. It is suggested that a remaining unknown coefficient in the expression be determined by experiment, computer simulation, or numerical solution of an integral equation derived by Pozrikidis ["A study of linearized oscillatory flow past particles by the boundary-integral method," J. Fluid Mech. 202, 17 (1989), 10.1017/S0022112089001084].
Zhu, Weifang; Chen, Haoyu; Zhao, Heming; Tian, Bei; Wang, Lirong; Shi, Fei; Xiang, Dehui; Luo, Xiaohong; Gao, Enting; Zhang, Li; Yin, Yilong; Chen, Xinjian
2016-01-01
Detection and assessment of the integrity of the photoreceptor ellipsoid zone (EZ) are important because it is critical for visual acuity in retina trauma and other diseases. We have proposed and validated a framework that can automatically analyse the 3D integrity of the EZ in optical coherence tomography (OCT) images. The images are first filtered and automatically segmented into 10 layers, of which EZ is located in the 7(th) layer. For each voxel of the EZ, 57 features are extracted and a principle component analysis is performed to optimize the features. An Adaboost classifier is trained to classify each voxel of the EZ as disrupted or non-disrupted. Finally, blood vessel silhouettes and isolated points are excluded. To demonstrate its effectiveness, the proposed framework was tested on 15 eyes with retinal trauma and 15 normal eyes. For the eyes with retinal trauma, the sensitivity (SEN) was 85.69% ± 9.59%, the specificity (SPE) was 85.91% ± 5.48%, and the balanced accuracy rate (BAR) was 85.80% ± 6.16%. For the normal eyes, the SPE was 99.03% ± 0.73%, and the SEN and BAR levels were not relevant. Our framework has the potential to become a useful tool for studying retina trauma and other conditions involving EZ integrity. PMID:27157473
Study of the Effect of Ellipsoidal Shape on the Kern and Frenkel Patch Model
NASA Astrophysics Data System (ADS)
Nguyen, Thienbao; Gunton, James; Rickman, Jeffrey
In their work on the self-assembly of complex structures, Glotzer and Solomon (Nature Materials 6, 557 - 562 (2007)) identified both interaction and shape anisotropy as two of several means to build complex structures. Advances in fabricating materials and new insights into protein biology have revealed the importance of these types of interactions. The Kern and Frenkel (J. Chem. Phys. 118, 9882 (2003) model of hard spheres carrying interaction patches of various sizes has been used extensively to describe interaction anisotropies important in protein phase transitions. However their model did not also account for shape anisotropy. We studied the role of both shape and interaction anisotropy by applying N=2 and N=4 attractive Kern and Frenkel patches with an interaction range to hard ellipsoids with various aspect ratios and patch coverages. Following Kern and Frenkel, we studied the liquid-liquid phase separation of our particles using a Monte Carlo simulation. We found the critical temperatures for our model using the approximate law of rectilinear diameter and compared them with the original results of Kern and Frenkel. We found that the critical temperatures increased both with aspect ratio and percent coverage. G Harold and Leila Y Mathers Foundation.
NASA Astrophysics Data System (ADS)
Gao, Ge; Li, Juntao; Wang, Xuehua
2015-10-01
Ultrathin crystalline silicon (c-Si) solar cells, which are of several micrometers thick, have attracted much attention in recent years, since it can greatly save raw materials than the traditional ones. To enhance the absorption, as well as to improve the cell efficiency, of the ultrathin c-Si, light trapping nanostructures are used to increase the effective absorption length to close to the 4n2 of the materials thickness, which is determined by the Lambertian limit. Here, we propose a novel interlaced semi-ellipsoid nanostructures (ISENs) to improve the performance of ultrathin c-Si solar cells. In this structure, the large and small periods in x and y direction can improve the light trapping capability at long and short wavelengths respectively. Meanwhile, the graded refractive index of the surface can act as the antireflection coating. By optimizing the ISENs, the short circuit current density of 30.15mA/cm2 was achieved by simulations for a 2 μm thick c-Si solar cell with rx = 500 nm, ry = 200 nm, rz= 550 nm and without antireflection coating and metal back reflector. The absorption is close to 87% of the Lambertian limit with equivalent thickness. We expect this structure can be fabricated by low cost nanosphere lithography technology and used to improve the efficiency of the ultrathin c-Si solar cells.
Turbulent Flows Driven by the Mechanical Forcing of an Ellipsoidal Container
NASA Astrophysics Data System (ADS)
Favier, Benjamin; Le Bars, Michael; Grannan, Alexander; Ribeiro, Adolfo; Aurnou, Jonathan; Irphe Team; Spinlab Team
2015-11-01
We present a combination of laboratory experiments and numerical simulations modelling geophysically relevant mechanical forcings. Libration and tides correspond to the periodic perturbation of a body's rotation rate and shape, and are both due to gravitational interactions with orbiting companions. Such mechanical forcings can convey a fraction of the rotational energy available and generate intense turbulence in the fluid interior of satellites and planets. We investigate the fluid motions inside a librating or tidally deformed triaxial ellipsoidal container filled with an incompressible fluid. In both cases, the turbulent flow is driven by the elliptic instability which is a triadic resonance between two inertial modes and the base flow. We characterize the transition to turbulence as triadic resonances develop while also investigating both intermittent and sustained regimes. It is shown that the flow is largely independent of the properties of the mechanical forcing, hinting at a possible universal behaviour of the saturated elliptical instability. The existence of such intense flows may play an important role in understanding the thermal and magnetic evolution of celestial bodies. This work was funded by the French Agence Nationale pour la Recherche and the National Science Foundation Geophysics Program.
Preliminary Results of Heat Transfer from a Stationary and Rotating Ellipsoidal Spinner
NASA Technical Reports Server (NTRS)
vonGlahn, U.
1953-01-01
Convective heat-transfer coefficients in dry air were obtained for an ellipsoidal spinner of 30-inch maximum diameter for both stationary and rotating operation over a range of conditions including airspeeds up to 275 miles per hour, rotational speeds up to 1200 rpm, and angles of attack of zero and 40 The results are presented in terms of Nusselt numbers, Reynolds numbers, and convective heat-transfer coefficients. The studies included both uniform heating densities over the spinner and uniform surface temperatures.. In general, the results showed that rotation will increase the convective heat transfer from a spinner, especially in the turbulent-flow regions. Rotation of the spinner at 1200 rpm and at a free-stream velocity of 275 miles per hour increased the Nusselt number parameter in the turbulent-flow region by 32 percent over that obtained with a stationary spinner; whereas in the nose region, where the flow was laminar, an increase of only 18 percent was observed. Transition from laminar to turbulent flow occurred over a large range of Reynolds numbers primarily because of surface roughness of the spinner. Operation at an angle of attack of 40 had only small effects on the local convective heat transfer for the model studied.
Single-shot femtosecond x-ray diffraction from randomly oriented ellipsoidal nanoparticles
NASA Astrophysics Data System (ADS)
Bogan, M. J.; Boutet, S.; Barty, A.; Benner, W. H.; Frank, M.; Lomb, L.; Shoeman, R.; Starodub, D.; Seibert, M. M.; Hau-Riege, S. P.; Woods, B.; Decorwin-Martin, P.; Bajt, S.; Schulz, J.; Rohner, U.; Iwan, B.; Timneanu, N.; Marchesini, S.; Schlichting, I.; Hajdu, J.; Chapman, H. N.
2010-09-01
Coherent diffractive imaging of single particles using the single-shot “diffract and destroy” approach with an x-ray free electron laser (FEL) was recently demonstrated. A high-resolution low-noise coherent diffraction pattern, representative of the object before it turns into a plasma and explodes, results from the interaction of the FEL with the particle. Iterative phase retrieval algorithms are used to reconstruct two-dimensional projection images of the object from the recorded intensities alone. Here we describe the first single-shot diffraction data set that mimics the data proposed for obtaining 3D structure from identical particles. Ellipsoidal iron oxide nanoparticles (250nm×50nm) were aerosolized and injected through an aerodynamic lens stack into a soft x-ray FEL. Particle orientation was not controlled with this injection method. We observed that, at the instant the x-ray pulse interacts with the particle, a snapshot of the particle’s orientation is encoded in the diffraction pattern. The results give credence to one of the technical concepts of imaging individual nanometer and subnanometer-sized objects such as single molecules or larger clusters of molecules using hard x-ray FELs and will be used to help develop robust algorithms for determining particle orientations and 3D structure.
A semi-ellipsoid-model based fuzzy classifier to map grassland in Inner Mongolia, China
NASA Astrophysics Data System (ADS)
Lan, Hai; Xie, Yichun
2013-11-01
Remote sensing techniques offer effective means for mapping plant communities. However, mapping grassland with fine vegetative classes over large areas has been challenging for either the coarse resolutions of remotely sensed images or the high costs of acquiring images with high-resolutions. An improved hybrid-fuzzy-classifier (HFC) derived from a semi-ellipsoid-model (SEM) is developed in this paper to achieve higher accuracy for classifying grasslands with Landsat images. The Xilin River Basin, Inner Mongolia, China, is chosen as the study area, because an acceptable volume of ground truthing data was previously collected by multiple research communities. The accuracy assessment is based on the comparison of the classification outcomes from four types of image sets: (1) Landsat ETM+ August 14, 2004, (2) Landsat TM August 12, 2009, (3) the fused images of ETM+ with CBERS, and (4) TM with CBERS, respectively, and by three classifiers, the proposed HFC-SEM, the tetragonal pyramid model (TPM) based HFC, and the support vector machine method. In all twelve classification experiments, the HFC-SEM classifier had the best overall accuracy statistics. This finding indicates that the medium resolution Landsat images can be used to map grassland vegetation with good vegetative detail when the proper classifier is applied.
Robust Linear MIMO in the Downlink: A Worst-Case Optimization with Ellipsoidal Uncertainty Regions
NASA Astrophysics Data System (ADS)
Zheng, Gan; Wong, Kai-Kit; Ng, Tung-Sang
2008-12-01
This paper addresses the joint robust power control and beamforming design of a linear multiuser multiple-input multiple-output (MIMO) antenna system in the downlink where users are subjected to individual signal-to-interference-plus-noise ratio (SINR) requirements, and the channel state information at the transmitter (CSIT) with its uncertainty characterized by an ellipsoidal region. The objective is to minimize the overall transmit power while guaranteeing the users' SINR constraints for every channel instantiation by designing the joint transmitreceive beamforming vectors robust to the channel uncertainty. This paper first investigates a multiuser MISO system (i.e., MIMO with single-antenna receivers) and by imposing the constraints on an SINR lower bound, a robust solution is obtained in a way similar to that with perfect CSI. We then present a reformulation of the robust optimization problem using S-Procedure which enables us to obtain the globally optimal robust power control with fixed transmit beamforming. Further, we propose to find the optimal robust MISO beamforming via convex optimization and rank relaxation. A convergent iterative algorithm is presented to extend the robust solution for multiuser MIMO systems with both perfect and imperfect channel state information at the receiver (CSIR) to guarantee the worst-case SINR. Simulation results illustrate that the proposed joint robust power and beamforming optimization significantly outperforms the optimal robust power allocation with zeroforcing (ZF) beamformers, and more importantly enlarges the feasibility regions of a multiuser MIMO system.
Computational methods for hypersonic viscous flow over finite ellipsoid-cones at incidence
NASA Technical Reports Server (NTRS)
Li, C. P.
1985-01-01
A numerical method, which is simpler than others currently in use, is proposed for determining the full viscous flow over a finite body in hypersonic stream at high altitude. It treats the shock layer surrounding the blunt foebody and the near wake behind the base simultaneously by formulating the Navier-Stokes equations in conformal and azimuthal-angle coordinates. The computational domain is confined to the body wall, outflow surface and the bow shock, which is adjusted along the coordinate normal to the wall in the course of iterations. Because of the optimal grid and a well developed alternating direction implicit factorization technique for the governing equations, reasonably accurate results can be obtained on a 30 by 36 by 6 grid with 400 time-marching iterations. Results for body shapes belonging to the ellipsoid-cone family are compared with the experimental data for the Apollo command module and the Viking aeroshell. Validation of the method based on self-consistency is also discussed.
Cryogenic Pressure Control Modeling for Ellipsoidal Space Tanks in Reduced Gravity
NASA Technical Reports Server (NTRS)
Hedayat, Ali; Lopez, Alfredo; Grayson, Gary D.; Chandler, Frank O.; Hastings, Leon J.
2008-01-01
A computational fluid dynamics (CFD) model is developed to simulate pressure control of an ellipsoidal-shaped liquid hydrogen tank under external heating in low 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-3D software and simulates low gravity extrapolations of engineering checkout tests performed at Marshall Space Flight Center in 1999 in support of the Solar Thermal Upper Stage Technology Demonstrator (STUSTD) program. Model results illustrate that stable low gravity liquid-gas interfaces are maintained during all phases of the pressure control cycle. Steady and relatively smooth ullage pressurization rates are predicted. This work advances current low gravity CFD modeling capabilities for cryogenic pressure control and aids the development of a low cost CFD-based design process for space hardware.
Ma, Ruiqing; Kawamoto, Ken-Ichiro; Shinomori, Keizo
2016-03-01
We explored the color constancy mechanisms of color-deficient observers under red, green, blue, and yellow illuminations. The red and green illuminations were defined individually by the longer axis of the color discrimination ellipsoid measured by the Cambridge Colour Test. Four dichromats (3 protanopes and 1 deuteranope), two anomalous trichromats (2 deuteranomalous observers), and five color-normal observers were asked to complete the color constancy task by making a simultaneous paper match under asymmetrical illuminations in haploscopic view on a monitor. The von Kries adaptation model was applied to estimate the cone responses. The model fits showed that for all color-deficient observers under all illuminations, the adjustment of the S-cone response or blue-yellow chromatically opponent responses modeled with the simple assumption of cone deletion in a certain type (S-M, S-L or S-(L+M)) was consistent with the principle of the von Kries model. The degree of adaptation was similar to that of color-normal observers. The results indicate that the color constancy of color-deficient observers is mediated by the simplified blue-yellow color system with a von Kries-type adaptation effect, even in the case of brightness match, as well as by a possible cone-level adaptation to the S-cone when the illumination produces a strong S-cone stimulation, such as blue illumination. PMID:26974935
Restoration of the Ellipsoid Zone and Visual Prognosis at 1 Year after Surgical Macular Hole Closure
Hasebe, Hiruma; Matsuoka, Naoki; Terashima, Hiroko; Sasaki, Ryo; Ueda, Eriko; Fukuchi, Takeo
2016-01-01
Purpose. To evaluate the restoration of the ellipsoid zone (EZ) and its influence on visual prognosis 1 year after surgical macular hole (MH) closure. Method. Subjects were patients with stage 2, 3, or 4 idiopathic MH who underwent primary vitrectomy that resulted in successful hole closure. Nineteen eyes with both EZ disruption with foveal detachment and a continuous external limiting membrane on optical coherence tomography during the early postoperative period were included in this study. Result. EZ disruption was restored in 10 eyes (53%, Group A) and remained in 9 eyes (47%, Group B) at 1 year after surgery. In Group B, the diameter of the residual EZ disruption was 54.7 ± 33.1 μm. LogMAR visual acuity (VA) 1 year after surgery was significantly better than preoperative VA in each group (Group A: −0.007 ± 0.102; P < 0.001; Group B: 0.051 ± 0.148; P < 0.001), but there was no significant difference between the 2 groups (P = 0.332). There was no significant correlation between logMAR VA and EZ disruption diameter at 1 year after surgery. Conclusion. EZ was restored in 53% of eyes at 1 year after surgical closure of idiopathic MH. Mean residual EZ disruption diameter was 54.7 ± 33.1 μm. Neither resolved nor residual EZ disruption influenced postoperative VA. PMID:26941999
3D positional tracking of ellipsoidal particles in a microtube flow using holographic microscopy
NASA Astrophysics Data System (ADS)
Byeon, Hyeok Jun; Seo, Kyung Won; Lee, Sang Joon
2014-11-01
Understanding of micro-scale flow phenomena is getting large attention under advances in micro-scale measurement technologies. Especially, the dynamics of particles suspended in a fluid is essential in both scientific and industrial fields. Moreover, most particles handled in research and industrial fields have non-spherical shapes rather than a simple spherical shape. Under various flow conditions, these non-spherical particles exhibit unique dynamic behaviors. To analyze these dynamic behaviors in a fluid flow, 3D positional information of the particles should be measured accurately. In this study, digital holographic microscopy (DHM) is employed to measure the 3D positional information of non-spherical particles, which are fabricated by stretching spherical polystyrene particles. 3D motions of those particles are obtained by interpreting the holograms captured from particles. Ellipsoidal particles with known size and shape are observed to verify the performance of the DHM technique. In addition, 3D positions of particles in a microtube flow are traced. This DHM technique exhibits promising potential in the analysis of dynamic behaviors of non-spherical particles suspended in micro-scale fluid flows.
Symmetric reconfigurable capacity assignment in a bidirectional DWDM access network.
Ortega, Beatriz; Mora, José; Puerto, Gustavo; Capmany, José
2007-12-10
This paper presents a novel architecture for DWDM bidirectional access networks providing symmetric dynamic capacity allocation for both downlink and uplink signals. A foldback arrayed waveguide grating incorporating an optical switch enables the experimental demonstration of flexible assignment of multiservice capacity. Different analog and digital services, such as CATV, 10 GHz-tone, 155Mb/s PRBS and UMTS signals have been transmitted in order to successfully test the system performance under different scenarios of total capacity distribution from the Central Station to different Base Stations with two reconfigurable extra channels for each down and upstream direction. PMID:19550967
Static spherically symmetric solutions in f(G) gravity
NASA Astrophysics Data System (ADS)
Sharif, M.; Fatima, H. Ismat
2016-05-01
We investigate interior solutions for static spherically symmetric metric in the background of f(G) gravity. We use the technique of conformal Killing motions to solve the field equations with both isotropic and anisotropic matter distributions. These solutions are then used to obtain density, radial and tangential pressures for power-law f(G) model. For anisotropic case, we assume a linear equation-of-state and investigate solutions for the equation-of-state parameter ω = ‑1.5. We check physical validity of the solutions through energy conditions and also examine its stability. Finally, we study equilibrium configuration using Tolman-Oppenheimer-Volkoff equation.
Static spherically symmetric space-times with six Killing vectors
Qadir, A.; Ziad, M.
1988-11-01
It had been proved earlier that spherically symmetric, static space-times have ten, seven, six, or four independent Killing vectors (KV's), but there are no cases in between. The case of six KV's is investigated here. It is shown that the space-time corresponds to a hyperboloid cross a sphere, reminiscent of Kaluza--Klein theory, with a compactification from four down to two dimensions. In effect, there is a unique metric for this space-time corresponding to a uniform mass distribution over all space.
Control of power in parity-time symmetric lattices
NASA Astrophysics Data System (ADS)
Kozlov, Maksim; Tsironis, G. P.
2015-10-01
We investigate wave transport properties of parity-time (PT) symmetric lattices that are periodically modulated along the direction of propagation. We demonstrate that in the regime of unbroken PT-symmetry, the system Floquet-Bloch modes may interfere constructively leading to either controlled oscillations or power absorption and unlimited amplification occurring exactly at the phase-transition point. The differential power response is affected by the overlap of the gain and loss system distribution with wave intensity pattern that is formed through Rabi oscillations engaging the coupled Floquet-Bloch modes.
Incorrectness of the usual gyrokinetic treatment in cylindrically symmetric systems
Linsker, R.
1980-07-01
It is shown that the usual gyrokinetic theory does not consistently retain all terms of leading order in the expansion parameter epsilon = gyroradius/equilibrium scale length. This is illustrated for cylindrically symmetric systems by comparing the perturbed distribution function calculated by the gyrokinetic method with that obtained by explicitly integrating the Vlasov equation over the unperturbed orbit. The integral equation used in some recent treatments of drift waves in sheared-slab geometry is shown to be incorrect. The correct calculation of the ion density perturbation for a collisionless ..beta.. = 0 plasma with cylindrical symmetry is presented.
Thermoelastic analysis of laminated plates. I - Symmetric specially orthotropic laminates
Wu, C.H.; Tauchert, T.R.
1980-04-01
Thermally induced deformations and stress resultants in symmetric laminated plates are analyzed. The method of M. Levy is used to study the transverse bending of a specially orthotropic laminate having two simply supported edges and subject to a temperature distribution that does not vary in a direction parallel to the simple supports. A solution is also obtained for the problem of in-plane stretching of the plate middle surface caused by a general three-dimensional temperature field. As an illustrative example, the thermoelastic response of a unidirectionally fiber-reinforced plate to a temperature variation that is linear in the thickness direction is computed.
Lopes, Daniel Simões; Neptune, Richard R; Gonçalves, Artur A; Ambrósio, Jorge A; Silva, Miguel T
2015-11-01
In this work, MacConaill's classification that the articular surface of the femoral head is better represented by ovoidal shapes rather than purely spherical shapes is computationally tested. To test MacConaill's classification, a surface fitting framework was developed to fit spheres, ellipsoids, superellipsoids, ovoids, and superovoids to computed tomography (CT) data of the femoral proximal epiphysis. The framework includes several image processing and computational geometry techniques, such as active contour segmentation and mesh smoothing, where implicit surface fitting is performed with genetic algorithms. By comparing the surface fitting error statistics, the results indicate that (super)ovoids fit femoral articular surfaces better than spherical or (super)ellipsoidal shapes. PMID:26399629
NASA Technical Reports Server (NTRS)
Hemsch, Michael J.
1990-01-01
The accuracy of high-alpha slender-body theory (HASBT) for bodies with elliptical cross-sections is presently demonstrated by means of a comparison with exact solutions for incompressible potential flow over a wide range of ellipsoid geometries and angles of attack and sideslip. The addition of the appropriate trigonometric coefficients to the classical slender-body theory decomposition yields the formally correct HASBT, and results in accuracies previously considered unattainable.
Pan, Yufeng; Zhou, Yanqiong; Guo, Chao; Gong, Haiyun; Gong, Zhefeng; Liu, Li
2009-05-01
The central complex is a prominent structure in the Drosophila brain. Visual learning experiments in the flight simulator, with flies with genetically altered brains, revealed that two groups of horizontal neurons in one of its substructures, the fan-shaped body, were required for Drosophila visual pattern memory. However, little is known about the role of other components of the central complex for visual pattern memory. Here we show that a small set of neurons in the ellipsoid body, which is another substructure of the central complex and connected to the fan-shaped body, is also required for visual pattern memory. Localized expression of rutabaga adenylyl cyclase in either the fan-shaped body or the ellipsoid body is sufficient to rescue the memory defect of the rut(2080) mutant. We then performed RNA interference of rutabaga in either structure and found that they both were required for visual pattern memory. Additionally, we tested the above rescued flies under several visual pattern parameters, such as size, contour orientation, and vertical compactness, and revealed differential roles of the fan-shaped body and the ellipsoid body for visual pattern memory. Our study defines a complex neural circuit in the central complex for Drosophila visual pattern memory. PMID:19389914
NASA Astrophysics Data System (ADS)
Drummond, Jack D.; Merline, W. J.; Conrad, A.; Dumas, C.; Tamblyn, P.; Christou, J.; Carry, B.; Chapman, C.
2012-10-01
From Adaptive Optics (AO) images of (9) Metis at 14 epochs over 2008 December 8 and 9 at Gemini North, triaxial ellipsoid diameters of 218x175x112 km are derived with fitting uncertainties of 3x3x47 km. However, by including just two more AO images from Keck-II in June and August of 2003 in a global fit, the fitting uncertainty of the small axis drops by more than a third because of the lower sub-Earth latitude afforded in 2003 (-28°) compared to 2008 (+47°), and the triaxial ellipsoid diameters become 218x175x129 km with fitting uncertainties of 3x3x14 km. We have estimated the systematic uncertainty of our method to be 4.1, 2.7, and 3.8%, respectively, for the three diameters. These values were recently derived (Drummond et al., in prep) from a comparison of KOALA (Carry et al, Planetary and Space Science 66, 200-212) and our triaxial ellipsoid analysis of four asteroids. Quadratically adding this systematic error with the fitting error, the total uncertainty for Metis becomes 9x5x15 km. Concurrently, we find an EQJ2000 rotational pole at [RA; Dec]=[185° +19°] or in ecliptic coordinates, [λ ; β ]=[176° +20°] (ECJ2000).
Communication-avoiding symmetric-indefinite factorization
Ballard, Grey Malone; Becker, Dulcenia; Demmel, James; Dongarra, Jack; Druinsky, Alex; Peled, Inon; Schwartz, Oded; Toledo, Sivan; Yamazaki, Ichitaro
2014-11-13
We describe and analyze a novel symmetric triangular factorization algorithm. The algorithm is essentially a block version of Aasen's triangular tridiagonalization. It factors a dense symmetric matrix A as the product A=PLTL^{T}P^{T} where P is a permutation matrix, L is lower triangular, and T is block tridiagonal and banded. The algorithm is the first symmetric-indefinite communication-avoiding factorization: it performs an asymptotically optimal amount of communication in a two-level memory hierarchy for almost any cache-line size. Adaptations of the algorithm to parallel computers are likely to be communication efficient as well; one such adaptation has been recently published. As a result, the current paper describes the algorithm, proves that it is numerically stable, and proves that it is communication optimal.
Communication-avoiding symmetric-indefinite factorization
Ballard, Grey Malone; Becker, Dulcenia; Demmel, James; Dongarra, Jack; Druinsky, Alex; Peled, Inon; Schwartz, Oded; Toledo, Sivan; Yamazaki, Ichitaro
2014-11-13
We describe and analyze a novel symmetric triangular factorization algorithm. The algorithm is essentially a block version of Aasen's triangular tridiagonalization. It factors a dense symmetric matrix A as the product A=PLTLTPT where P is a permutation matrix, L is lower triangular, and T is block tridiagonal and banded. The algorithm is the first symmetric-indefinite communication-avoiding factorization: it performs an asymptotically optimal amount of communication in a two-level memory hierarchy for almost any cache-line size. Adaptations of the algorithm to parallel computers are likely to be communication efficient as well; one such adaptation has been recently published. As a result,more » the current paper describes the algorithm, proves that it is numerically stable, and proves that it is communication optimal.« less
The Robust Assembly of Small Symmetric Nanoshells
Wagner, Jef; Zandi, Roya
2015-01-01
Highly symmetric nanoshells are found in many biological systems, such as clathrin cages and viral shells. Many studies have shown that symmetric shells appear in nature as a result of the free-energy minimization of a generic interaction between their constituent subunits. We examine the physical basis for the formation of symmetric shells, and by using a minimal model, demonstrate that these structures can readily grow from the irreversible addition of identical subunits. Our model of nanoshell assembly shows that the spontaneous curvature regulates the size of the shell while the mechanical properties of the subunit determine the symmetry of the assembled structure. Understanding the minimum requirements for the formation of closed nanoshells is a necessary step toward engineering of nanocontainers, which will have far-reaching impact in both material science and medicine. PMID:26331253
The Robust Assembly of Small Symmetric Nanoshells.
Wagner, Jef; Zandi, Roya
2015-09-01
Highly symmetric nanoshells are found in many biological systems, such as clathrin cages and viral shells. Many studies have shown that symmetric shells appear in nature as a result of the free-energy minimization of a generic interaction between their constituent subunits. We examine the physical basis for the formation of symmetric shells, and by using a minimal model, demonstrate that these structures can readily grow from the irreversible addition of identical subunits. Our model of nanoshell assembly shows that the spontaneous curvature regulates the size of the shell while the mechanical properties of the subunit determine the symmetry of the assembled structure. Understanding the minimum requirements for the formation of closed nanoshells is a necessary step toward engineering of nanocontainers, which will have far-reaching impact in both material science and medicine. PMID:26331253
Symmetric extension of two-qubit states
NASA Astrophysics Data System (ADS)
Chen, Jianxin; Ji, Zhengfeng; Kribs, David; Lütkenhaus, Norbert; Zeng, Bei
2014-09-01
A bipartite state ρAB is symmetric extendible if there exists a tripartite state ρABB' whose AB and AB' marginal states are both identical to ρAB. Symmetric extendibility of bipartite states is of vital importance in quantum information because of its central role in separability tests, one-way distillation of Einstein-Podolsky-Rosen pairs, one-way distillation of secure keys, quantum marginal problems, and antidegradable quantum channels. We establish a simple analytic characterization for symmetric extendibility of any two-qubit quantum state ρAB; specifically, tr(ρB2)≥tr(ρAB2)-4√ detρAB . As a special case we solve the bosonic three-representability problem for the two-body reduced density matrix.
On symmetric and upwind TVD schemes
NASA Technical Reports Server (NTRS)
Yee, H. C.
1985-01-01
A class of explicit and implicit total variation diminishing (TVD) schemes for the compressible Euler and Navier-Stokes equations was developed. They do not generate spurious oscillations across shocks and contact discontinuities. In general, shocks can be captured within 1 to 2 grid points. For the inviscid case, these schemes are divided into upwind TVD schemes and symmetric (nonupwind) TVD schemes. The upwind TVD scheme is based on the second-order TVD scheme. The symmetric TVD scheme is a generalization of Roe's and Davis' TVD Lax-Wendroff scheme. The performance of these schemes on some viscous and inviscid airfoil steady-state calculations is investigated. The symmetric and upwind TVD schemes are compared.
Self-bending symmetric cusp beams
Gong, Lei; Liu, Wei-Wei; Lu, Yao; Li, Yin-Mei; Ren, Yu-Xuan
2015-12-07
A type of self-bending symmetric cusp beams with four accelerating intensity maxima is theoretically and experimentally presented. Distinguished from the reported regular polygon beams, the symmetric cusp beams simultaneously exhibit peculiar features of natural autofocusing and self-acceleration during propagation. Further, such beams take the shape of a fine longitudinal needle-like structure at the focal region and possess the strong ability of self-healing over obstacles. All these intriguing properties were verified experimentally. Particularly, the spatial profile of the reconstructed beam exhibits spatially sculpted optical structure with four siamesed curved arms. Thus, we anticipate that the structured beam will benefit optical guiding and optofluidics in surprising ways.
All-optical symmetric ternary logic gate
NASA Astrophysics Data System (ADS)
Chattopadhyay, Tanay
2010-09-01
Symmetric ternary number (radix=3) has three logical states (1¯, 0, 1). It is very much useful in carry free arithmetical operation. Beside this, the logical operation using this type of number system is also effective in high speed computation and communication in multi-valued logic. In this literature all-optical circuits for three basic symmetrical ternary logical operations (inversion, MIN and MAX) are proposed and described. Numerical simulation verifies the theoretical model. In this present scheme the different ternary logical states are represented by different polarized state of light. Terahertz optical asymmetric demultiplexer (TOAD) based interferometric switch has been used categorically in this manuscript.
Symmetric and irregular aromatic silicon nanoclusters
NASA Astrophysics Data System (ADS)
Vach, Holger
2014-10-01
Based on first-principles calculations, we predict the existence of two classes of aromatic hydrogenated silicon nanoclusters. Despite their completely different structure, they both exhibit quite comparable physical and chemical properties due to the common presence of overcoordinated silicon atoms inducing extensive electron delocalization. Due to a complex interplay between strain relaxation and aromatic stabilization, apparently ill-defined nanoclusters might sometimes turn out to be more stable than their symmetric counterparts. Both symmetric and irregular aromatic silicon nanoclusters are extremely stable at ambient conditions and might readily find applications in future nano-technological devices.
Observational tests of Baryon symmetric cosmology
NASA Technical Reports Server (NTRS)
Stecker, F. W.
1982-01-01
Observational evidence for Baryon symmetric (matter/antimatter) cosmology and future observational tests are reviewed. The most significant consequences of Baryon symmetric cosmology lie in the prediction of an observable cosmic background of gamma radiation from the decay of pi(0)-mesons produced in nucleon-antinucleon annihilations. Equations for the prediction of the amma ray background spectrum for the case of high redshifts are presented. The theoretical and observational plots of the background spectrum are shown to be in good agreement. Measurement of cosmic ray antiprotons and the use of high energy neutrino astronomy to look for antimatter elsewhere in the universe are also addressed.
Self-bending symmetric cusp beams
NASA Astrophysics Data System (ADS)
Gong, Lei; Liu, Wei-Wei; Ren, Yu-Xuan; Lu, Yao; Li, Yin-Mei
2015-12-01
A type of self-bending symmetric cusp beams with four accelerating intensity maxima is theoretically and experimentally presented. Distinguished from the reported regular polygon beams, the symmetric cusp beams simultaneously exhibit peculiar features of natural autofocusing and self-acceleration during propagation. Further, such beams take the shape of a fine longitudinal needle-like structure at the focal region and possess the strong ability of self-healing over obstacles. All these intriguing properties were verified experimentally. Particularly, the spatial profile of the reconstructed beam exhibits spatially sculpted optical structure with four siamesed curved arms. Thus, we anticipate that the structured beam will benefit optical guiding and optofluidics in surprising ways.
Familial multiple symmetric lipomatosis with peripheral neuropathy.
Chalk, C H; Mills, K R; Jacobs, J M; Donaghy, M
1990-08-01
We describe coexisting peripheral neuropathy and multiple symmetric lipomatosis in 4 of 7 siblings. The absence of either condition in 3 other generations of this family suggests autosomal recessive inheritance. None of the affected siblings were alcoholic, a factor some have proposed to explain the frequent occurrence of peripheral neuropathy in sporadic multiple symmetric lipomatosis. Serum lipid studies, including apoprotein A levels, were normal. Sural nerve biopsy from 1 patient showed nerve fiber loss, predominantly affecting large myelinated fibers. The relationship between myelin sheath thickness and axon diameter was normal, arguing that this neuropathy is not due to primary axonal atrophy. PMID:2166247
Numerical Analysis of the Symmetric Methods
NASA Astrophysics Data System (ADS)
Xu, Ji-Hong; Zhang, A.-Li
1995-03-01
Aimed at the initial value problem of the particular second-order ordinary differential equations,y ″=f(x, y), the symmetric methods (Quinlan and Tremaine, 1990) and our methods (Xu and Zhang, 1994) have been compared in detail by integrating the artificial earth satellite orbits in this paper. In the end, we point out clearly that the integral accuracy of numerical integration of the satellite orbits by applying our methods is obviously higher than that by applying the same order formula of the symmetric methods when the integration time-interval is not greater than 12000 periods.
NASA Astrophysics Data System (ADS)
Drummond, J. D.; Conrad, A.; Merline, W. J.; Carry, B.; Chapman, C. R.; Weaver, H. A.; Tamblyn, P. M.; Christou, J. C.; Dumas, C.
2010-11-01
Context. Asteroid (21) Lutetia was the target of the ESA Rosetta mission flyby in 2010 July. Aims: We seek the best size estimates of the asteroid, the direction of its spin axis, and its bulk density, assuming its shape is well described by a smooth featureless triaxial ellipsoid. We also aim to evaluate the deviations from this assumption. Methods: We derive these quantities from the outlines of the asteroid in 307 images of its resolved apparent disk obtained with adaptive optics (AO) at Keck II and VLT, and combine these with recent mass determinations to estimate a bulk density. Results: Our best triaxial ellipsoid diameters for Lutetia, based on our AO images alone, are a × b × c = 132 × 101 × 93 km, with uncertainties of 4 × 3 × 13 km including estimated systematics, with a rotational pole within 5° of ECJ2000 [λβ] = [45° - 7°] , or EQJ2000 [RA Dec] = [44° + 9°] . The AO model fit itself has internal precisions of 1 × 1 × 8 km, but it is evident both from this model derived from limited viewing aspects and the radius vector model given in a companion paper, that Lutetia significantly departs from an idealized ellipsoid. In particular, the long axis may be overestimated from the AO images alone by about 10 km. Therefore, we combine the best aspects of the radius vector and ellipsoid model into a hybrid ellipsoid model, as our final result, of diameters 124 ± 5 × 101 ± 4 × 93 ± 13 km that can be used to estimate volumes, sizes, and projected areas. The adopted pole position is within 5° of [λβ] = [52° - 6°] or [RA Dec] = [52° + 12°]. Conclusions: Using two separately determined masses and the volume of our hybrid model, we estimate a density of 3.5±1.1 or 4.3±0.8 g cm-3. From the density evidence alone, we argue that this favors an enstatite-chondrite composition, although other compositions are formally allowed at the extremes (low-porosity CV/CO carbonaceous chondrite or high-porosity metallic). We discuss this in the context of
Ellipsoidal Variation Analysis of Kepler Observations Using the EVIL-MC Model
NASA Astrophysics Data System (ADS)
Jackson, Brian; Carlberg, J. K.
2012-10-01
Follow-up and confirmation of the thousands of planetary candidates from the Kepler mission requires a sizable investment of astronomical resources. Thus, it is essential to identify signals already present in the data that can elucidate the nature of the transiting objects. Tidal distortion of a star by a close companion produces such a signal: as a short-period companion orbits, the tidal bulge raised on the primary rotates in and out of view, and the amplitude of these ``ellipsoidal variations'' (EVs) depends, among other things, on the mass ratio between the primary and companion. For example, a few Jupiter-mass planet orbiting 4 stellar radii from a solar mass star can induce brightness variations 30 parts per million, small but measurable for some Kepler targets. EVs induced by such low-mass companions have been observed for only a handful of Kepler (and CoRoT) targets. Here we report the discovery of EVs in another Kepler system with a candidate transiting companion. The Kepler Input Catalog suggests the host star is an evolved red giant, and the star shows signs of solar-like oscillations, similar to p-mode acoustic oscillations observed in the Sun. Such oscillations have been observed for thousand other red giants observed by Kepler, providing tight constraints on the stars' masses and radii, if the effective temperatures are known. In this presentation, we will discuss constraints on the transiting companion's mass and brightness temperature derived from analysis of the transits and EVs present in the publicly available Kepler data using the recently developed EVIL-MC model. Preliminary results suggest the candidate transiting object has a mass comparable to Jupiter's but a radius many times larger, while the apparent lack of a secondary eclipse suggests its brightness temperature is less than 2700 K. BKJ acknowledges support from Carnegie DTM.
NASA Astrophysics Data System (ADS)
Schubert, Gerald; Anderson, John; Zhang, Keke; Kong, D.; Helled, Ravit
2011-08-01
The exact solution for the shape and gravitational field of a rotating two-layer Maclaurin ellipsoid of revolution is compared with predictions of the theory of figures up to third order in the small rotational parameter of the theory of figures. An explicit formula is derived for the external gravitational coefficient J2 of the exact solution. A new approach to the evaluation of the theory of figures based on numerical integration of ordinary differential equations is presented. The classical Radau-Darwin formula is found not to be valid for the rotational parameter ɛ2 = Ω2/(2 πG ρ2) ⩾ 0.17 since the formula then predicts a surface eccentricity that is smaller than the eccentricity of the core-envelope boundary. Interface eccentricity must be smaller than surface eccentricity. In the formula for ɛ2, Ω is the angular velocity of the two-layer body, ρ2 is the density of the outer layer, and G is the gravitational constant. For an envelope density of 3000 kg m -3 the failure of the Radau-Darwin formula corresponds to a rotation period of about 3 h. Application of the exact solution and the theory of figures is made to models of Earth, Mars, Uranus, and Neptune. The two-layer model with constant densities in the layers can provide realistic approximations to terrestrial planets and icy outer planet satellites. The two-layer model needs to be generalized to allow for a continuous envelope (outer layer) radial density profile in order to realistically model a gas or ice giant planet.
Periyasamy, Vijitha; Pramanik, Manojit
2014-04-01
Monte Carlo modeling of light transport in multilayered tissue (MCML) is modified to incorporate objects of various shapes (sphere, ellipsoid, cylinder, or cuboid) with a refractive-index mismatched boundary. These geometries would be useful for modeling lymph nodes, tumors, blood vessels, capillaries, bones, the head, and other body parts. Mesh-based Monte Carlo (MMC) has also been used to compare the results from the MCML with embedded objects (MCML-EO). Our simulation assumes a realistic tissue model and can also handle the transmission/reflection at the object-tissue boundary due to the mismatch of the refractive index. Simulation of MCML-EO takes a few seconds, whereas MMC takes nearly an hour for the same geometry and optical properties. Contour plots of fluence distribution from MCML-EO and MMC correlate well. This study assists one to decide on the tool to use for modeling light propagation in biological tissue with objects of regular shapes embedded in it. For irregular inhomogeneity in the model (tissue), MMC has to be used. If the embedded objects (inhomogeneity) are of regular geometry (shapes), then MCML-EO is a better option, as simulations like Raman scattering, fluorescent imaging, and optical coherence tomography are currently possible only with MCML. PMID:24727908
NASA Astrophysics Data System (ADS)
Saadat, Fatemeh; Birman, Victor; Thomopoulos, Stavros; Genin, Guy M.
2015-09-01
Estimates of the effective stiffness of a composite containing multiple types of inclusions are needed for the design and study of a range of material systems in engineering and physiology. While excellent estimates and tight bounds exist for composite systems containing specific classes and distributions of identical inclusions, these are not easily generalized to systems with multiple types of inclusions. The best estimate available for a composite containing multiple classes of inclusions arises from the Kanaun-Jeulin approach. However, this method is analogous to a generalized Benveniste approach, and therefore suffers from the same limitations: while excellent for low volume fractions of inclusions, the Kanaun-Jeullin and Benveniste estimates liebelow three-point bounds at higher volume fractions. Here, we present an estimate for composites containing multiple classes of aligned ellipsoidal inclusions that lies within known three-point bounds at relatively higher volume fractions of inclusions and that is applicable to many engineering and biological composites. The approach involves replacing the averaged strains used in the Kanaun-Jeulin method with an effective strain measure. We demonstrate application of the constitutive model to the graded tissue system at the attachment of tendon to bone.
NASA Astrophysics Data System (ADS)
Zhang, Yu; Wang, Fang-rong; Zhao, Yan-hui; Wang, Yi-ding; Cui, Tian; Kan, Ru-wen; Wu, Li-chun; Zhang, Tie-qiang; Zhang, Yuan-kun
2012-07-01
The intensity distribution of absorption spectroscopy of methane mid-infrared fundamental absorption bands, near-infrared combination band of v2 + 2v3 and overtone band of 2v3 were discussed in details in this paper. Quantitative data showed that the absorption intensities of fundamental bands are twice larger than overtone bands, and three times larger than combination bands. Based on the methane 3.31 μm (v3) fundamental absorption bands and differential signal disposal method, a rotational ellipsoidal light structure was designed using ordinary light source and detector to improve gas detection sensitivity. The experimental results of concentration detection showed that the precision of concentration measurement can reach 3% and detection sensitivity is 50 ppm. Meanwhile, experiment was performed to investigate the influence of temperature on mid-infrared absorption performance of methane and the experience curve of 3.31 μm (v3) fundamental absorption signal depending on temperature and its rate of change was drawn.
Dissociative recombination of highly symmetric polyatomic ions.
Douguet, Nicolas; Orel, Ann E; Greene, Chris H; Kokoouline, Viatcheslav
2012-01-13
A general first-principles theory of dissociative recombination is developed for highly symmetric molecular ions and applied to H(3)O(+) and CH(3)(+), which play an important role in astrophysical, combustion, and laboratory plasma environments. The theoretical cross sections obtained for the dissociative recombination of the two ions are in good agreement with existing experimental data from storage ring experiments. PMID:22324682
Onthe static and spherically symmetric gravitational field
NASA Astrophysics Data System (ADS)
Gottlieb, Ioan; Maftei, Gheorghe; Mociutchi, Cleopatra
Starting from a generalization of Einstein 's theory of gravitation, proposed by one of the authors (Cleopatra Mociutchi), the authors study a particular spherical symmetric case. Among other one obtain the compatibility conditions for the existence of the static and spherically symmetruic gravitational filed in the case of extended Einstein equation.
Small diameter symmetric networks from linear groups
NASA Technical Reports Server (NTRS)
Campbell, Lowell; Carlsson, Gunnar E.; Dinneen, Michael J.; Faber, Vance; Fellows, Michael R.; Langston, Michael A.; Moore, James W.; Multihaupt, Andrew P.; Sexton, Harlan B.
1992-01-01
In this note is reported a collection of constructions of symmetric networks that provide the largest known values for the number of nodes that can be placed in a network of a given degree and diameter. Some of the constructions are in the range of current potential engineering significance. The constructions are Cayley graphs of linear groups obtained by experimental computation.
Amplituhedron Cells and Stanley Symmetric Functions
NASA Astrophysics Data System (ADS)
Lam, Thomas
2016-05-01
The amplituhedron was recently introduced in the study of scattering amplitudes in {N = 4} super Yang-Mills. We compute the cohomology class of a tree amplituhedron subvariety of the Grassmannian to be the truncation of an affine Stanley symmetric function.
Symmetric stiffness matrix for incompressible hyperelastic materials
NASA Technical Reports Server (NTRS)
Takamatsu, T.; Stricklin, J. A.; Key, J. E.
1976-01-01
Symmetric structure matrices are derived for solving plane strain and axisymmetric problems involving incompressible hyperelastic materials. An infinite hollow cylinder subjected to internal pressure is considered as an example. Displacement and hydrostatic pressure profiles are calculated using the Newton-Raphson iteration technique. The results are in good agreement with the exact curves.
Super-symmetric informationally complete measurements
NASA Astrophysics Data System (ADS)
Zhu, Huangjun
2015-11-01
Symmetric informationally complete measurements (SICs in short) are highly symmetric structures in the Hilbert space. They possess many nice properties which render them an ideal candidate for fiducial measurements. The symmetry of SICs is intimately connected with the geometry of the quantum state space and also has profound implications for foundational studies. Here we explore those SICs that are most symmetric according to a natural criterion and show that all of them are covariant with respect to the Heisenberg-Weyl groups, which are characterized by the discrete analog of the canonical commutation relation. Moreover, their symmetry groups are subgroups of the Clifford groups. In particular, we prove that the SIC in dimension 2, the Hesse SIC in dimension 3, and the set of Hoggar lines in dimension 8 are the only three SICs up to unitary equivalence whose symmetry groups act transitively on pairs of SIC projectors. Our work not only provides valuable insight about SICs, Heisenberg-Weyl groups, and Clifford groups, but also offers a new approach and perspective for studying many other discrete symmetric structures behind finite state quantum mechanics, such as mutually unbiased bases and discrete Wigner functions.
Conformal cylindrically symmetric spacetimes in modified gravity
NASA Astrophysics Data System (ADS)
Türkog˜lu, Murat Metehan; Dog˜ru, Melis Ulu
2015-11-01
We investigate cylindrically symmetric spacetimes in the context of f(R) gravity. We firstly attain conformal symmetry of the cylindrically symmetric spacetime. We obtain solutions to use features of the conformal symmetry, field equations and their solutions for cylindrically symmetric spacetime filled with various cosmic matters such as vacuum state, perfect fluid, anisotropic fluid, massive scalar field and their combinations. With the vacuum state solutions, we show that source of the spacetime curvature is considered as Casimir effect. Casimir force for given spacetime is found using Wald’s axiomatic analysis. We expose that the Casimir force for Boulware, Hartle-Hawking and Unruh vacuum states could have attractive, repulsive and ineffective features. In the perfect fluid state, we show that matter form of the perfect fluid in given spacetime must only be dark energy. Also, we offer that potential of massive and massless scalar field are developed as an exact solution from the modified field equations. All solutions of field equations for vacuum case, perfect fluid and scalar field give a special f(R) function convenient to Λ-CDM model. In addition to these solutions, we introduce conformal cylindrical symmetric solutions in the cases of different f(R) models. Finally, geometrical and physical results of the solutions are discussed.
Miniaturized symmetrization optics for junction laser
NASA Technical Reports Server (NTRS)
Hammer, Jacob M. (Inventor); Kaiser, Charlie J. (Inventor); Neil, Clyde C. (Inventor)
1982-01-01
Miniaturized optics comprising transverse and lateral cylindrical lenses composed of millimeter-sized rods with diameters, indices-of-refraction and spacing such that substantially all the light emitted as an asymmetrical beam from the emitting junction of the laser is collected and translated to a symmetrical beam.
The deuterium puzzle in the symmetric universe
NASA Technical Reports Server (NTRS)
Leroy, B.; Nicolle, J. P.; Schatzman, E.
1973-01-01
An attempt was made to use deuterium abundance in the symmetric universe to prove that no nucleosynthesis takes place during annihilation and therefore neutrons were loss before nucleosynthesis. Data cover nucleosynthesis during the radiative era, cross section estimates, maximum abundance of He-4 at the end of nucleosynthesis area, and loss rate.
Resonances for Symmetric Two-Barrier Potentials
ERIC Educational Resources Information Center
Fernandez, Francisco M.
2011-01-01
We describe a method for the accurate calculation of bound-state and resonance energies for one-dimensional potentials. We calculate the shape resonances for symmetric two-barrier potentials and compare them with those coming from the Siegert approximation, the complex scaling method and the box-stabilization method. A comparison of the…
Entanglement classes of symmetric Werner states
Lyons, David W.; Walck, Scott N.
2011-10-15
The symmetric Werner states for n qubits, important in the study of quantum nonlocality and useful for applications in quantum information, have a surprisingly simple and elegant structure in terms of tensor products of Pauli matrices. Further, each of these states forms a unique local unitary equivalence class, that is, no two of these states are interconvertible by local unitary operations.
Symmetrical peripheral gangrene caused by septic shock
Shimbo, Keisuke; Yokota, Kazunori; Miyamoto, Junpei; Okuhara, Yukako; Ochi, Mitsuo
2015-01-01
We report three cases of symmetrical peripheral gangrene (SPG) caused by septic shock. Most of sepsis survivors with SPG require amputation of the affected extremities. To preserve the length of the thumb and fingers, we performed surgical amputation and used flaps to cover the amputated peripheral extremities.
Chakrabarty, Ayan; Wang, Feng; Sun, Kai; Wei, Qi-Huo
2016-05-11
Prior studies have shown that low symmetry particles such as micro-boomerangs exhibit behaviour of Brownian motion rather different from that of high symmetry particles because convenient tracking points (TPs) are usually inconsistent with their center of hydrodynamic stress (CoH) where the translational and rotational motions are decoupled. In this paper we study the effects of the translation-rotation coupling on the displacement probability distribution functions (PDFs) of the boomerang colloid particles with symmetric arm length. By tracking the motions of different points on the particle symmetry axis, we show that as the distance between the TP and the CoH is increased, the effects of translation-rotation coupling becomes pronounced, making the short-time 2D PDF for fixed initial orientation to change from elliptical, to bean and then to crescent shape, and the angle averaged PDFs change from ellipsoidal-particle-like PDF to a shape with a Gaussian top and long displacement tails. We also observed that at long times the PDFs revert to Gaussian. These 2D PDF shapes provide a clear physical picture of the non-zero mean displacements observed in boomerangs particles. PMID:27079870
Cracked shells under skew-symmetric loading. [Reissner theory
NASA Technical Reports Server (NTRS)
Delale, F.
1981-01-01
The general problem of a shell containing a through crack in one of the principal planes of curvature and under general skew-symmetric loading is considered. By employing a Reissner type shell theory which takes into account the effect of transverse shear strains, all boundary conditions on the crack surfaces are satisfied separately. Consequently, unlike those obtained from the classical shell theory, the angular distributions of the stress components around the crack tips are shown to be identical to the distributions obtained from the plane and anti-plane elasticity solutions. Results are given for axially and circumferentially cracked cylindrical shells, spherical shells, and toroidal shells under uniform in-plane shearing, out of plane shearing, and torsion. The problem is formulated for specially orthostropic materials, therefore, the effect of orthotropy on the results is also studied.
Adaptive Load-Balancing Algorithms using Symmetric Broadcast Networks
NASA Technical Reports Server (NTRS)
Das, Sajal K.; Harvey, Daniel J.; Biswas, Rupak; Biegel, Bryan A. (Technical Monitor)
2002-01-01
In a distributed computing environment, it is important to ensure that the processor workloads are adequately balanced, Among numerous load-balancing algorithms, a unique approach due to Das and Prasad defines a symmetric broadcast network (SBN) that provides a robust communication pattern among the processors in a topology-independent manner. In this paper, we propose and analyze three efficient SBN-based dynamic load-balancing algorithms, and implement them on an SGI Origin2000. A thorough experimental study with Poisson distributed synthetic loads demonstrates that our algorithms are effective in balancing system load. By optimizing completion time and idle time, the proposed algorithms are shown to compare favorably with several existing approaches.
Adaptive Load-Balancing Algorithms Using Symmetric Broadcast Networks
NASA Technical Reports Server (NTRS)
Das, Sajal K.; Biswas, Rupak; Chancellor, Marisa K. (Technical Monitor)
1997-01-01
In a distributed-computing environment, it is important to ensure that the processor workloads are adequately balanced. Among numerous load-balancing algorithms, a unique approach due to Dam and Prasad defines a symmetric broadcast network (SBN) that provides a robust communication pattern among the processors in a topology-independent manner. In this paper, we propose and analyze three novel SBN-based load-balancing algorithms, and implement them on an SP2. A thorough experimental study with Poisson-distributed synthetic loads demonstrates that these algorithms are very effective in balancing system load while minimizing processor idle time. They also compare favorably with several other existing load-balancing techniques. Additional experiments performed with real data demonstrate that the SBN approach is effective in adaptive computational science and engineering applications where dynamic load balancing is extremely crucial.
Weakly Interacting Symmetric and Anti-Symmetric States in the Bilayer Systems
NASA Astrophysics Data System (ADS)
Marchewka, M.; Sheregii, E. M.; Tralle, I.; Tomaka, G.; Ploch, D.
We have studied the parallel magneto-transport in DQW-structures of two different potential shapes: quasi-rectangular and quasi-triangular. The quantum beats effect was observed in Shubnikov-de Haas (SdH) oscillations for both types of the DQW structures in perpendicular magnetic filed arrangement. We developed a special scheme for the Landau levels energies calculation by means of which we carried out the necessary simulations of beating effect. In order to obtain the agreement between our experimental data and the results of simulations, we introduced two different quasi-Fermi levels which characterize symmetric and anti-symmetric states in DQWs. The existence of two different quasi Fermi-Levels simply means, that one can treat two sub-systems (charge carriers characterized by symmetric and anti-symmetric wave functions) as weakly interacting and having their own rate of establishing the equilibrium state.
Renard, D; Garnier, C; Lapp, A; Schmitt, C; Sanchez, C
2012-09-01
The structure of the arabinogalactan-protein (AGP) fraction of the gum exudate of Acacia senegal (gum Arabic) isolated from hydrophobic interaction chromatography was investigated using HPSEC-MALLS, small angle neutron scattering and TEM observations. Literature reported that the AGP structure of gum Arabic adopts a very compact conformation in solution due to the attachment of short arabinoside side chains and much larger blocks of carbohydrate to the polypeptidic backbone. The present study revealed that AGP in solution had a weight average molecular weight Mw of 1.86×10(6) g mol(-1) and a radius of gyration Rg of 30 nm. In addition, two exponent values were identified in the Rg, [η], Rh and ρ vs. Mw relationships highlighting two types of conformations depending on the molecular weight range considered: a low molar mass population with long-chain branching and a compact conformation and a high molar mass population with short-chain branching and an elongated conformation. AGP would behave in solution as a branched or hyper-branched polymer with conformations ranging from globular to elongated shape depending on the size of the carbohydrate branches. Small angle scattering form factor revealed an elongated average conformation corresponding to a triaxial ellipsoid while inverse Fourier transform of the scattering form factor gave a maximum dimension for AGP of 64 nm. Transmission electron microscopy highlighted the existence of two types of flat objects with thicknesses below 3-5 nm, single particles with a more or less anisotropic spheroidal shape and aggregated structures with a more elongated shape. A remarkable feature of all particle morphologies was the presence of an outer structure combined to an inner more or less porous network of interspersed chains or interacting structural blocks, as previously found for the arabinogalactan (AG) main molecular fraction of Acacia gum. However, clear differences were observed in the density and morphology of the
NASA Astrophysics Data System (ADS)
Mishra, Chandan K.; Rangarajan, Amritha; Ganapathy, Rajesh
2013-05-01
We study experimentally the glass transition dynamics in quasi-two-dimensional suspensions of colloidal ellipsoids, aspect ratio α=2.1, with repulsive as well as attractive interactions. For the purely repulsive case, we find that the orientational and translational glass transitions occur at the same area fraction. Strikingly, for intermediate depletion attraction strengths, we find that the orientational glass transition precedes the translational one. By quantifying structure and dynamics, we show that quasi-long-range ordering is promoted at these attraction strengths, which subsequently results in a two-step glass transition. Most interestingly, within experimental certainty, we observe reentrant glass dynamics only in the translational degrees of freedom.
NASA Astrophysics Data System (ADS)
Shi, L.; Yan, Z. W.
2016-06-01
In the present work, the optical properties of GaAs/AlxGa1-xAs/GaAs multi-shell ellipsoidal quantum dot heterostructures with a shallow hydrogenic impurity in the presence of an external electric field have been studied. The results show how the linear and nonlinear optical absorption coefficients and refraction index changes are changed by the variations of the size and shape of the multi-shell structure. Moreover, how the optical properties of this structure are affected by the electric field has also been shown. The physical reasons for the results have been discussed in detail.
NASA Technical Reports Server (NTRS)
Maggiori, D.
1981-01-01
All of the phenomena which influence the propagation of radiowaves at frequencies above 10 GHz (attenuation, depolarization, scintillation) can by intensified by parameters directly derived from a solution of individual scatter, naturally in addition to be meteorological elements which characterize the physical medium. The diffusion caused by rainy precipitation was studied using Mie's algorithm for rain composed of spherical drops, and Oguchi's algorithm for rain composed of drops in an ellipsoidal form with axes of rotational symmetry arrange along the vertical line of a generic reference point. Specific phase displacement and attenuation along the principal planes, propagation of radiowaves in generic polarization, and propagation with inclined axes are also considered.
Stochastic modeling of cell growth with symmetric or asymmetric division
NASA Astrophysics Data System (ADS)
Marantan, Andrew; Amir, Ariel
2016-07-01
We consider a class of biologically motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final amount of the resource is controlled by a growth policy and subject to additive and multiplicative noise, we derive the recursive integral equation describing the evolution of the resource distribution over subsequent generations and use it to study the properties of stable resource distributions. We find conditions under which a unique stable resource distribution exists and calculate its moments for the class of affine linear growth policies. Moreover, we apply an asymptotic analysis to elucidate the conditions under which the stable distribution (when it exists) has a power-law tail. Finally, we use the results of this asymptotic analysis along with the moment equations to draw a stability phase diagram for the system that reveals the counterintuitive result that asymmetry serves to increase stability while at the same time widening the stable distribution. We also briefly discuss how cells can divide damaged proteins asymmetrically between their progeny as a form of damage control. In the appendixes, motivated by the asymmetric division of cell volume in Saccharomyces cerevisiae, we extend our results to the case wherein mother and daughter cells follow different growth policies.
Stochastic modeling of cell growth with symmetric or asymmetric division.
Marantan, Andrew; Amir, Ariel
2016-07-01
We consider a class of biologically motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final amount of the resource is controlled by a growth policy and subject to additive and multiplicative noise, we derive the recursive integral equation describing the evolution of the resource distribution over subsequent generations and use it to study the properties of stable resource distributions. We find conditions under which a unique stable resource distribution exists and calculate its moments for the class of affine linear growth policies. Moreover, we apply an asymptotic analysis to elucidate the conditions under which the stable distribution (when it exists) has a power-law tail. Finally, we use the results of this asymptotic analysis along with the moment equations to draw a stability phase diagram for the system that reveals the counterintuitive result that asymmetry serves to increase stability while at the same time widening the stable distribution. We also briefly discuss how cells can divide damaged proteins asymmetrically between their progeny as a form of damage control. In the appendixes, motivated by the asymmetric division of cell volume in Saccharomyces cerevisiae, we extend our results to the case wherein mother and daughter cells follow different growth policies. PMID:27575162
Observational tests of baryon symmetric cosmology
NASA Technical Reports Server (NTRS)
Stecker, F. W.
1983-01-01
Observational evidence for Baryon symmetric (matter/antimatter) cosmology and future observational tests are reviewed. The most significant consequences of Baryon symmetric cosmology lie in the prediction of an observable cosmic background of gamma radiation from the decay of Pi(O)-mesons produced in nucleon-antinucleon annihilations. Equations for the prediction of the gamma ray background spectrum for the case of high redshifts are presented. The theoretical and observational plots of the background spectrum are shown to be in good agreement. Measurements of cosmic ray antiprotons and the use of high energy neutrino astronomy to look for antimatter elsewhere in the universe are also addressed. Previously announced in STAR as N83-10996
Integrability of PT-symmetric dimers
NASA Astrophysics Data System (ADS)
Pickton, J.; Susanto, H.
2013-12-01
The coupled discrete linear and Kerr nonlinear Schrödinger equations with gain and loss describing transport on dimers with parity-time (PT)-symmetric potentials are considered. The model is relevant among others to experiments in optical couplers and proposals on Bose-Einstein condensates in PT-symmetric double-well potentials. It is known that the models are integrable. Here, the integrability is exploited further to construct the phase portraits of the system. A pendulum equation with a linear potential and a constant force for the phase difference between the fields is obtained, which explains the presence of unbounded solutions above a critical threshold parameter. The behavior of all solutions of the system, including changes in the topological structure of the phase plane, is then discussed.
Static spherically symmetric wormholes with isotropic pressure
NASA Astrophysics Data System (ADS)
Cataldo, Mauricio; Liempi, Luis; Rodríguez, Pablo
2016-06-01
In this paper we study static spherically symmetric wormhole solutions sustained by matter sources with isotropic pressure. We show that such spherical wormholes do not exist in the framework of zero-tidal-force wormholes. On the other hand, it is shown that for the often used power-law shape function there are no spherically symmetric traversable wormholes sustained by sources with a linear equation of state p = ωρ for the isotropic pressure, independently of the form of the redshift function ϕ (r). We consider a solution obtained by Tolman at 1939 for describing static spheres of isotropic fluids, and show that it also may describe wormhole spacetimes with a power-law redshift function, which leads to a polynomial shape function, generalizing a power-law shape function, and inducing a solid angle deficit.
Cusped Wilson lines in symmetric representations
NASA Astrophysics Data System (ADS)
Correa, Diego H.; Massolo, Fidel I. Schaposnik; Trancanelli, Diego
2015-08-01
We study the cusped Wilson line operators and Bremsstrahlung functions associated to particles transforming in the rank- k symmetric representation of the gauge group U( N) for super Yang-Mills. We find the holographic D3-brane description for Wilson loops with internal cusps in two different limits: small cusp angle and . This allows for a non-trivial check of a conjectured relation between the Bremsstrahlung function and the expectation value of the 1/2 BPS circular loop in the case of a representation other than the fundamental. Moreover, we observe that in the limit of k ≫ N, the cusped Wilson line expectation value is simply given by the exponential of the 1-loop diagram. Using group theory arguments, this eikonal exponentiation is conjectured to take place for all Wilson loop operators in symmetric representations with large k, independently of the contour on which they are supported.
Spherically symmetric solutions in higher-derivative gravity
NASA Astrophysics Data System (ADS)
Lü, H.; Perkins, A.; Pope, C. N.; Stelle, K. S.
2015-12-01
Extensions of Einstein gravity with quadratic curvature terms in the action arise in most effective theories of quantized gravity, including string theory. This article explores the set of static, spherically symmetric and asymptotically flat solutions of this class of theories. An important element in the analysis is the careful treatment of a Lichnerowicz-type "no-hair" theorem. From a Frobenius analysis of the asymptotic small-radius behavior, the solution space is found to split into three asymptotic families, one of which contains the classic Schwarzschild solution. These three families are carefully analyzed to determine the corresponding numbers of free parameters in each. One solution family is capable of arising from coupling to a distributional shell of matter near the origin; this family can then match onto an asymptotically flat solution at spatial infinity without encountering a horizon. Another family, with horizons, contains the Schwarzschild solution but includes also non-Schwarzschild black holes. The third family of solutions obtained from the Frobenius analysis is nonsingular and corresponds to "vacuum" solutions. In addition to the three families identified from near-origin behavior, there are solutions that may be identified as "wormholes," which can match symmetrically onto another sheet of spacetime at finite radius.
Symmetric space description of carbon nanotubes
NASA Astrophysics Data System (ADS)
Caselle, Michele; Magnea, Ulrika
2006-01-01
Using an innovative technique arising from the theory of symmetric spaces, we obtain an approximate analytic solution of the Dorokhov-Mello-Pereyra-Kumar (DMPK) equation in the insulating regime of a metallic carbon nanotube with symplectic symmetry and an odd number of conducting channels. This symmetry class is characterized by the presence of a perfectly conducting channel in the limit of infinite length of the nanotube. The derivation of the DMPK equation for this system has recently been performed by Takane, who also obtained the average conductance both analytically and numerically. Using the Jacobian corresponding to the transformation to radial coordinates and the parametrization of the transfer matrix given by Takane, we identify the ensemble of transfer matrices as the symmetric space of negative curvature SO*(4m + 2)/[SU(2m + 1) × U(1)] belonging to the DIII-odd Cartan class. We rederive the leading-order correction to the conductance of the perfectly conducting channel \\langle \\ln \\delta g \\rangle and its variance Var(ln δg). Our results are in complete agreement with Takane's. In addition, our approach based on the mapping to a symmetric space enables us to obtain new universal quantities: a universal group theoretical expression for the ratio \\mathrm {Var}(\\ln \\delta g)/\\langle \\ln \\delta g\\rangle , and as a by-product a novel expression for the localization length for the most general case of a symmetric space with BCm root system, in which all three types of roots are present.
Wave equation on spherically symmetric Lorentzian metrics
Bokhari, Ashfaque H.; Al-Dweik, Ahmad Y.; Zaman, F. D.; Kara, A. H.; Karim, M.
2011-06-15
Wave equation on a general spherically symmetric spacetime metric is constructed. Noether symmetries of the equation in terms of explicit functions of {theta} and {phi} are derived subject to certain differential constraints. By restricting the metric to flat Friedman case the Noether symmetries of the wave equation are presented. Invertible transformations are constructed from a specific subalgebra of these Noether symmetries to convert the wave equation with variable coefficients to the one with constant coefficients.
Spherically symmetric solutions in a FRW background
NASA Astrophysics Data System (ADS)
Moradpour, H.; Riazi, N.
2015-02-01
We impose perfect fluid concept along with slow expansion approximation to derive new solutions which, considering non-static spherically symmetric metrics, can be treated as Black Holes (BHs). We will refer to these solutions as Quasi BHs. Mathematical and physical features such as Killing vectors, singularities, and mass have been studied. Their horizons and thermodynamic properties have also been investigated. In addition, relationship with other related works (including McVittie's) are described.
Parity time-symmetric vertical cavities: intrinsically single-mode regime in longitudinal direction.
Jones, Hugh F; Kulishov, Mykola; Kress, Bernard
2016-07-25
We explore a new class of distributed feedback (DFB) structures that employ the recently-developed concept of parity-time (PT) symmetry in optics. We show that, based on PT-symmetric pure reflective volume gratings, a vertical surface-emitting cavity can be constructed. We provide a detailed analysis of the threshold conditions as well as the wavelength and angular spectral characteristics using the Kogelnik coupled-wave approximation, backed up by an exact solution of the Helmholtz equation. We show that such a PT-symmetric cavity can be configured to support one and only one longitudinal mode, leading to inherently single-mode lasing. PMID:27464163
Symmetric scrolled packings of multilayered carbon nanoribbons
NASA Astrophysics Data System (ADS)
Savin, A. V.; Korznikova, E. A.; Lobzenko, I. P.; Baimova, Yu. A.; Dmitriev, S. V.
2016-06-01
Scrolled packings of single-layer and multilayer graphene can be used for the creation of supercapacitors, nanopumps, nanofilters, and other nanodevices. The full atomistic simulation of graphene scrolls is restricted to consideration of relatively small systems in small time intervals. To overcome this difficulty, a two-dimensional chain model making possible an efficient calculation of static and dynamic characteristics of nanoribbon scrolls with allowance for the longitudinal and bending stiffness of nanoribbons is proposed. The model is extended to the case of scrolls of multilayer graphene. Possible equilibrium states of symmetric scrolls of multilayer carbon nanotribbons rolled up so that all nanoribbons in the scroll are equivalent are found. Dependences of the number of coils, the inner and outer radii, lowest vibrational eigenfrequencies of rolled packages on the length L of nanoribbons are obtained. It is shown that the lowest vibrational eigenfrequency of a symmetric scroll decreases with a nanoribbon length proportionally to L -1. It is energetically unfavorable for too short nanoribbons to roll up, and their ground state is a stack of plane nanoribbons. With an increasing number k of layers, the nanoribbon length L necessary for creation of symmetric scrolls increases. For a sufficiently small number of layers k and a sufficiently large nanoribbon length L, the scrolled packing has the lowest energy as compared to that of stack of plane nanoribbons and folded structures. The results can be used for development of nanomaterials and nanodevices on the basis of graphene scrolled packings.
Chirally symmetric but confining dense, cold matter
Glozman, L. Ya.; Wagenbrunn, R. F.
2008-03-01
The folklore tradition about the QCD phase diagram is that at the chiral restoration phase transition at finite density hadrons are deconfined and there appears the quark matter. We address this question within the only known exactly solvable confining and chirally symmetric model. It is postulated within this model that there exists linear Coulomb-like confining interaction. The chiral symmetry breaking and the quark Green function are obtained from the Schwinger-Dyson (gap) equation while the color-singlet meson spectrum results from the Bethe-Salpeter equation. We solve this model at T=0 and finite chemical potential {mu} and obtain a clear chiral restoration phase transition at the critical value {mu}{sub cr}. Below this value the spectrum is similar to the previously obtained one at {mu}=0. At {mu}>{mu}{sub cr} the quarks are still confined and the physical spectrum consists of bound states which are arranged into a complete set of exact chiral multiplets. This explicitly demonstrates that a chirally symmetric matter consisting of confined but chirally symmetric hadrons at finite chemical potential is also possible in QCD. If so, there must be nontrivial implications for astrophysics.
Chirally symmetric but confining dense, cold matter
NASA Astrophysics Data System (ADS)
Glozman, L. Ya.; Wagenbrunn, R. F.
2008-03-01
The folklore tradition about the QCD phase diagram is that at the chiral restoration phase transition at finite density hadrons are deconfined and there appears the quark matter. We address this question within the only known exactly solvable confining and chirally symmetric model. It is postulated within this model that there exists linear Coulomb-like confining interaction. The chiral symmetry breaking and the quark Green function are obtained from the Schwinger-Dyson (gap) equation while the color-singlet meson spectrum results from the Bethe-Salpeter equation. We solve this model at T=0 and finite chemical potential μ and obtain a clear chiral restoration phase transition at the critical value μcr. Below this value the spectrum is similar to the previously obtained one at μ=0. At μ>μcr the quarks are still confined and the physical spectrum consists of bound states which are arranged into a complete set of exact chiral multiplets. This explicitly demonstrates that a chirally symmetric matter consisting of confined but chirally symmetric hadrons at finite chemical potential is also possible in QCD. If so, there must be nontrivial implications for astrophysics.
Asymmetric versus symmetric pulses for cortical microstimulation.
Koivuniemi, Andrew S; Otto, Kevin J
2011-10-01
Intracortical microstimulation (ICMS), which has shown promise in the visual, auditory and somatosensory systems as a platform for sensory prostheses, typically relies on charged balanced, symmetric, biphasic stimulation. However, neural stimulation models as well as experiments conducted in cochlear implant users have suggested that charge balanced asymmetric pulses could generate lower detection thresholds for stimulation in terms of charge per phase. For this study, rats were chronically implanted with microelectrode arrays unilaterally in their right auditory cortex and then trained to detect ICMS delivered through a single electrode site in order to determine their behavioral threshold. This model was used in two experiments. The first experiment addressed the effect of lead phase direction, asymmetry, and phase duration on detection threshold. The second experiment fixed the cathode phase duration at 123 μs and varied only the phase asymmetry and lead phase direction. Taken together, the results of these experiments suggest that, for ICMS, the primary determinant of threshold level is cathode phase duration, and that asymmetry provides no significant advantage when compared to symmetric, cathode leading pulses. However, symmetric anode leading pulses of less than or equal to 205 μs per phase consistently showed higher thresholds when compared to all other pulses of equal cathode phase duration. PMID:21968793
Nonlinear waves in PT -symmetric systems
NASA Astrophysics Data System (ADS)
Konotop, Vladimir V.; Yang, Jianke; Zezyulin, Dmitry A.
2016-07-01
Recent progress on nonlinear properties of parity-time (PT )-symmetric systems is comprehensively reviewed in this article. PT symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying PT symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a PT -symmetric system. The natural inclusion of nonlinearity into these PT systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above PT -symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear PT -symmetric systems arising from various physical disciplines are presented, nonlinear properties of these systems are thoroughly elucidated, and relevant experimental results are described. In addition, emerging applications of PT symmetry are pointed out.
Symmetric multilayer megampere X-pinch
Shelkovenko, T. A.; Pikuz, S. A.; McBride, R. D.; Knapp, P. F.; Wilhelm, G.; Sinars, D. B.; Hammer, D. A.; Orlov, N. Yu.
2010-01-15
Raising the power of X-ray emission from an X-pinch by increasing the pinch current to the megampere level requires the corresponding increase in the initial linear mass of the load. This can be achieved by increasing either the number of wires or their diameter. In both cases, special measures should be undertaken to prevent the formation of a complicated configuration with an uncontrolled spatial structure in the region of wire crossing, because such a structure breaks the symmetry of the neck formed in the crossing region, destabilizes plasma formation, and degrades X-ray generation. To improve the symmetry of the wire crossing region, X-pinch configurations with a regular multilayer arrangement of wires in this region were proposed and implemented. The results of experiments with various symmetric X-pinch configurations on the COBRA facility at currents of {approx}1MA are presented. It is shown that an X-pinch with a symmetric crossing region consisting of several layers of wires made of different materials can be successfully used in megampere facilities. The most efficient combinations of wires in symmetric multilayer X-pinches are found in which only one hot spot forms and that are characterized by a high and stable soft X-ray yield.
Spherically symmetric thick branes cosmological evolution
NASA Astrophysics Data System (ADS)
Bernardini, A. E.; Cavalcanti, R. T.; da Rocha, Roldão
2015-01-01
Spherically symmetric time-dependent solutions for the 5D system of a scalar field canonically coupled to gravity are obtained and identified as an extension of recent results obtained by Ahmed et al. (JHEP 1404:061. arXiv:1312.3576 [hep-th], 2014). The corresponding cosmology of models with regularized branes generated by such a 5D scalar field scenario is also investigated. It has been shown that the anisotropic evolution of the warp factor and consequently the Hubble like parameter are both driven by the radial coordinate on the brane, which leads to an emergent thick brane-world scenario with spherically symmetric time dependent warp factor. Meanwhile, the separability of variables depending on fifth dimension, , which is exhibited by the equations of motion, allows one to recover the extra dimensional profiles obtained in Ahmed et al. (2014), namely the extra dimensional part of the scale (warp) factor and the scalar field dependence on . Therefore, our results are mainly concerned with the time dependence of a spherically symmetric warp factor. Besides evincing possibilities for obtaining asymmetric stable brane-world scenarios, the extra dimensional profiles here obtained can also be reduced to those ones investigated in Ahmed et al. (2014).
NASA Astrophysics Data System (ADS)
Koumi, Koffi Espoir; Chaise, Thibaut; Nelias, Daniel
2015-07-01
In this paper, the frictionless rolling contact problem between a rigid sphere and a viscoelastic half-space containing one elastic inhomogeneity is solved. The problem is equivalent to the frictionless sliding of a spherical tip over a viscoelastic body. The inhomogeneity may be of spherical or ellipsoidal shape, the later being of any orientation relatively to the contact surface. The model presented here is three dimensional and based on semi-analytical methods. In order to take into account the viscoelastic aspect of the problem, contact equations are discretized in the spatial and temporal dimensions. The frictionless rolling of the sphere, assumed rigid here for the sake of simplicity, is taken into account by translating the subsurface viscoelastic fields related to the contact problem. Eshelby's formalism is applied at each step of the temporal discretization to account for the effect of the inhomogeneity on the contact pressure distribution, subsurface stresses, rolling friction and the resulting torque. A Conjugate Gradient Method and the Fast Fourier Transforms are used to reduce the computation cost. The model is validated by a finite element model of a rigid sphere rolling upon a homogeneous vciscoelastic half-space, as well as through comparison with reference solutions from the literature. A parametric analysis of the effect of elastic properties and geometrical features of the inhomogeneity is performed. Transient and steady-state solutions are obtained. Numerical results about the contact pressure distribution, the deformed surface geometry, the apparent friction coefficient as well as subsurface stresses are presented, with or without heterogeneous inclusion.
Nonlinear light behaviors near phase transition in non-parity-time-symmetric complex waveguides.
Nixon, Sean; Yang, Jianke
2016-06-15
Many classes of non-parity-time (PT)-symmetric waveguides with arbitrary gain and loss distributions still possess all-real linear spectrum or exhibit phase transition. In this Letter, nonlinear light behaviors in these complex waveguides are probed analytically near a phase transition. Using multi-scale perturbation methods, a nonlinear ordinary differential equation (ODE) is derived for the light's amplitude evolution. This ODE predicts that a single class of these non-PT-symmetric waveguides supports soliton families and amplitude-oscillating solutions both above and below linear phase transition, in close analogy with PT-symmetric systems. For the other classes of waveguides, the light's intensity always amplifies under the effect of nonlinearity, even if the waveguide is below the linear phase transition. These analytical predictions are confirmed by direct computations of the full system. PMID:27304279
Nonlinear light behaviors near phase transition in non-parity-time-symmetric complex waveguides
NASA Astrophysics Data System (ADS)
Nixon, Sean; Yang, Jianke
2016-06-01
Many classes of non-parity-time (PT) symmetric waveguides with arbitrary gain and loss distributions still possess all-real linear spectrum or exhibit phase transition. In this article, nonlinear light behaviors in these complex waveguides are probed analytically near a phase transition. Using multi-scale perturbation methods, a nonlinear ordinary differential equation (ODE) is derived for the light's amplitude evolution. This ODE predicts that the first class of these non-PT-symmetric waveguides support continuous families of solitons and robust amplitude-oscillating solutions both above and below phase transition, in close analogy with PT-symmetric systems. For the other classes of waveguides, the light's intensity always amplifies under the effect of nonlinearity even if the waveguide is below phase transition. These analytical predictions are confirmed by direct computations of the full system.
An inverse problem design method for branched and unbranched axially symmetrical ducts
NASA Technical Reports Server (NTRS)
Nelson, C. D.; Yang, T.
1976-01-01
This paper concerns the potential flow design of axially symmetrical ducts of both circular and annular cross section with or without wall suction or blowing slots. The objective of the work was to develop a method by which such ducts could be designed with directly prescribed wall pressure variation. Previous axially symmetrical design methods applied only to circular cross sectional ducts and required that the pressure distribution be prescribed along the duct centerline and not along the duct wall. The present method uses an inverse problem approach which extends the method of Stanitz to the axially symmetrical case, and an approximation is used to account for the stagnation point in branched duct designs. Two examples of successful designs of diffusers with suction slots are presented.
Excitation of anti-symmetric coupled spoof SPPs in 3D SIS waveguides based on coupling
NASA Astrophysics Data System (ADS)
Li-li, Tian; Yang, Chen; Jian-long, Liu; Kai, Guo; Ke-ya, Zhou; Yang, Gao; Shu-tian, Liu
2016-07-01
According to the electromagnetic field distributions, there exist two kinds of coupled spoof surface plasmon polaritons (SSPPs), the symmetric and anti-symmetric modes, in the three-dimensional (3D) subwavelength spoof–insulator–spoof (SIS) waveguide. We study the dispersion and excitation of the two kinds of coupled SSPPs supported by the 3D SIS waveguide. The evolution of the dispersion with the thickness and gap width of the waveguide is numerically investigated, and we give a theoretical analysis according to the coupling mechanism. Specially, based on the coupling mechanism, we design a zipper structure, through which the excitation and propagation of the anti-symmetric coupled modes can be realized effectively. Project supported by the National Basic Research Program of China (Grant No. 2013CBA01702) and the National Natural Science Foundation of China (Grant Nos. 61377016, 61575055, 10974039, 61307072, 61308017, and 61405056).
NASA Astrophysics Data System (ADS)
Cho, In-Sun; Kim, Dong Wook; Cho, Chin Moo; An, Jae-Sul; Roh, Hee-Suk; Hong, Kug Sun
2010-06-01
Ellipsoid-like two-dimensional (2D) plates of calcium niobate (CaNb 2O 6) were synthesized via the hydrothermal route without any surfactants or templates by controlling the reaction conditions, viz. the pH value, reaction time and temperature. The prepared powders were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), transmission electron microscopy (TEM), fluorescence spectroscopy, and diffuse reflectance UV-vis spectroscopy. It was found that the plates were consisted of uniaxially aligned nanorods and can absorb UV light with wavelengths of less than 340 nm. Compared with the powder of the same material prepared by the solid-state reaction method, the ellipsoid-like 2D plates exhibited a much lower room temperature luminescence intensity and higher photocatalytic activity for the degradation of Rhodamine B dye solution under UV light irradiation. The enhanced photocatalytic activity of the plates was assigned to their higher optical absorption capability, higher diffusion rate of charge carriers and higher surface area resulting from their reduced dimensionality.
Sarman, Sten; Laaksonen, Aatto
2011-04-01
We have applied a nonequilibrium molecular dynamics heat flow algorithm to calculate the heat conductivity of a molecular model system, which forms uniaxial and biaxial nematic liquid crystals. The model system consists of a soft ellipsoid string-fluid where the ellipsoids interact according to a repulsive version of the Gay-Berne potential. On compression, this system forms discotic or calamitic uniaxial nematic phases depending on the dimensions of the molecules, and on further compression a biaxial nematic phase is formed. In the discotic nematic phase, the heat conductivity has two components, one parallel and one perpendicular to the director, where the last mentioned component is the largest one. This order of magnitudes is reversed in the calamitic nematic phase. In the biaxial nematic phase there are three components of the heat conductivity, one in the direction around which the long axes of the molecules are oriented, this is the largest component, another one in the direction around which the normals of the broadsides of the molecules are oriented, this is the smallest component, and one in the direction perpendicular to these two directions with a magnitude in between those of the first mentioned components. The relative magnitudes of the components of the heat conductivity span a fairly wide interval so it should be possible to use the model to parameterise experimental data. PMID:21336361
An exact solution for orbit view-periods from a station on a tri-axial ellipsoidal planet
NASA Technical Reports Server (NTRS)
Tang, C. C. H.
1986-01-01
This paper presents the concise exact solution for predicting view-periods to be observed from a masked or unmasked tracking station on a tri-axial ellipsoidal surface. The new exact approach expresses the azimuth and elevation angles of a spacecraft in terms of the station-centered geodetic topocentric coordinates in an elegantly concise manner. A simple and efficient algorithm is developed to avoid costly repetitive computations in searching for neighborhoods near the rise and set times of each satellite orbit for each station. Only one search for each orbit is necessary for each station. Sample results indicate that the use of an assumed spherical earth instead of an 'actual' tri-axial ellipsoidal earth could introduce an error up to a few minutes in a view-period prediction for circular orbits of low or medium altitude. For an elliptical orbit of high eccentricity and long period, the maximum error could be even larger. The analytic treatment and the efficient algorithm are designed for geocentric orbits, but they should be applicable to interplanetary trajectories by an appropriate coordinates transformation at each view-period calculation. This analysis can be accomplished only by not using the classical orbital elements.
Lee, Myoung-Jae; Jung, Young-Dae
2015-02-15
The nonthermal and geometric effects on the propagation of the surface dust acoustic waves are investigated in a Lorentzian dusty plasma slab. The symmetric and anti-symmetric dispersion modes of the dust acoustic waves are obtained by the plasma dielectric function with the spectral reflection conditions the slab geometry. The variation of the nonthermal and geometric effects on the symmetric and the anti-symmetric modes of the surface plasma waves is also discussed.
NASA Astrophysics Data System (ADS)
Mille, Matthew M.
Positron emission tomography (PET) with 2-[18F]fluoro-2-deoxy-D-glucose (FDG) is being increasingly recognized as an important tool for quantitative assessment of tumor response because of its ability to capture functional information about the tumor's metabolism. However, despite many advances in PET technology, measurements of tumor radiopharmaceutical uptake in PET are still challenged by issues of accuracy and consistency, thereby compromising the use of PET as a surrogate endpoint in clinical trials. One limiting component of the overall uncertainty in PET is the relatively poor spatial resolution of the images which directly affects the accuracy of the tumor radioactivity measurements. These spatial resolution effects, colloquially known as the partial volume effect (PVE), are a function of the characteristics of the scanner as well as the tumor being imaged. Previous efforts have shown that the PVE depends strongly on the tumor volume and the background-to-tumor activity concentration ratio. The PVE is also suspected to be a function of tumor shape, although to date no systematic study of this effect has been performed. This dissertation seeks to help fill the gap in the current knowledge about the shape-dependence of the PVE by attempting to quantify, through both theoretical calculation and experimental measurement, the magnitude of the shape effect for ellipsoidal tumors. An experimental investigation of the tumor shape effect necessarily requires tumor phantoms of multiple shapes. Hence, a prerequisite for this research was the design and fabrication of hollow tumor phantoms which could be filled uniformly with radioactivity and imaged on a PET scanner. The phantom fabrication was achieved with the aid of stereolithography and included prolate ellipsoids of various axis ratios. The primary experimental method involved filling the tumor phantoms with solutions of 18F whose activity concentrations were known and traceable to primary radioactivity standards
NASA Astrophysics Data System (ADS)
Cubarsi, Rafael
2014-07-01
Under a common potential, a finite mixture of ellipsoidal velocity distributions satisfying the Boltzmann collisionless equation provides a set of integrability conditions that may constrain the population kinematics. They are referred to as conditions of consistency and were discussed in a previous paper on mixtures of axisymmetric populations. As a corollary, these conditions are now extended to point-axial symmetry, that is, point symmetry around the rotation axis or bisymmetry, by determining which potentials are connected with a more flexible superposition of stellar populations. Under point-axial symmetry, the potential is still axisymmetric, but the velocity and mass distributions are not necessarily. A point-axial stellar system is, in a natural way, consistent with a flat velocity distribution of a disc population. Therefore, no additional integrability conditions are required to solve the Boltzmann collisionless equation for such a population. For other populations, if the potential is additively separable in cylindrical coordinates, the populations are not kinematically constrained, although under point-axial symmetry, the potential is reduced to the harmonic function, which, for the Galaxy, is proven to be non-realistic. In contrast, a non-separable potential provides additional conditions of consistency. When mean velocities for the populations are unconstrained, the potential becomes quasi-stationary, being a particular case of the axisymmetric model. Then, the radial and vertical mean velocities of the populations can differ and produce an apparent vertex deviation of the whole velocity distribution. However, single population velocity ellipsoids still have no vertex deviation in the Galactic plane and no tilt in their intersection with a meridional Galactic plane. If the thick disc and halo ellipsoids actually have non-vanishing tilt, as the surveys of the solar neighbourhood that include RAdial Velocity Experiment (RAVE) data seem to show, the
Symmetric and Asymmetric Tendencies in Stable Complex Systems
Tan, James P. L.
2016-01-01
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by obtaining eigenvalue bounds of the Jacobian, we show that stable complex systems will favor mutualistic and competitive relationships that are asymmetrical (non-reciprocative) and trophic relationships that are symmetrical (reciprocative). Additionally, we define a measure called the interdependence diversity that quantifies how distributed the dependencies are between the dynamical variables in the system. We find that increasing interdependence diversity has a destabilizing effect on the equilibrium point, and the effect is greater for trophic relationships than for mutualistic and competitive relationships. These predictions are consistent with empirical observations in ecology. More importantly, our findings suggest stabilization algorithms that can apply very generally to a variety of complex systems. PMID:27545722
Axially symmetric dissipative fluids in the quasi-static approximation
NASA Astrophysics Data System (ADS)
Herrera, L.; di Prisco, A.; Ospino, J.; Carot, J.
2016-01-01
Using a framework based on the 1 + 3 formalism, we carry out a study on axially and reflection symmetric dissipative fluids, in the quasi-static regime. We first derive a set of invariantly defined “velocities”, which allow for an inambiguous definition of the quasi-static approximation. Next, we rewrite all the relevant equations in this approximation and extract all the possible, physically relevant, consequences ensuing the adoption of such an approximation. In particular, we show how the vorticity, the shear and the dissipative flux, may lead to situations where different kind of “velocities” change their sign within the fluid distribution with respect to their sign on the boundary surface. It is shown that states of gravitational radiation are not a priori incompatible with the quasi-static regime. However, any such state must last for an infinite period of time, thereby diminishing its physical relevance.
NASA Astrophysics Data System (ADS)
Mishra, Chandan K.; Ganapathy, Rajesh
2015-05-01
We examine the influence of the shape of dynamical heterogeneities on the Stokes-Einstein (SE) and Stokes-Einstein-Debye (SED) relations in quasi-two-dimensional suspensions of colloidal ellipsoids. For ellipsoids with repulsive interactions, both SE and SED relations are violated at all area fractions. On approaching the glass transition, however, the extent to which this violation occurs changes beyond a crossover area fraction. Quite remarkably, we find that it is not just the presence of dynamical heterogeneities but their change in the shape from stringlike to compact that coincides with this crossover. On introducing a suitable short-range depletion attraction between the ellipsoids, associated with the lack of morphological evolution of dynamical heterogeneities, the extent to which the SE and SED relations are violated remains unchanged even for deep supercooling.
NASA Astrophysics Data System (ADS)
Kaur, Bhavneet; Aggarwal, Rajiv
2014-01-01
In this problem, one of the primaries of mass m 1 is a Roche ellipsoid filled with a homogeneous incompressible fluid of density ρ 1. The smaller primary of mass m 2 is an oblate body outside the Ellipsoid. The third and the fourth bodies (of mass m 3 and m 4 respectively) are small solid spheres of density ρ 3 and ρ 4 respectively inside the Ellipsoid, with the assumption that the mass and the radius of the third and the fourth body are infinitesimal. We assume that m 2 is describing a circle around m 1. The masses m 3 and m 4 mutually attract each other, do not influence the motions of m 1 and m 2 but are influenced by them. We have extended the Robe's restricted three-body problem to 2+2 body problem under the assumption that the fluid body assumes the shape of the Roche ellipsoid (Chandrashekhar in Ellipsoidal figures of equilibrium, Chap. 8, Dover, New York, 1987). We have taken into consideration all the three components of the pressure field in deriving the expression for the buoyancy force viz (i) due to the own gravitational field of the fluid (ii) that originating in the attraction of m 2 (iii) that arising from the centrifugal force. In this paper, equilibrium solutions of m 3 and m 4 and their linear stability are analyzed. We have proved that there exist only six equilibrium solutions of the system, provided they lie within the Roche ellipsoid. In a system where the primaries are considered as Earth-Moon and m 3, m 4 as submarines, the equilibrium solutions of m 3 and m 4 respectively when the displacement is given in the direction of x 1-axis or x 2-axis are unstable.
NASA Technical Reports Server (NTRS)
Hess, Robert V; Gardner, Clifford S
1947-01-01
By using the Prandtl-Glauert method that is valid for three-dimensional flow problems, the value of the maximum incremental velocity for compressible flow about thin ellipsoids at zero angle of attack is calculated as a function of the Mach number for various aspect ratios and thickness ratios. The critical Mach numbers of the various ellipsoids are also determined. The results indicate an increase in critical Mach number with decrease in aspect ratio which is large enough to explain experimental results on low-aspect-ratio wings at zero lift.
Symmetrical band-pass loudspeaker systems
NASA Astrophysics Data System (ADS)
Matusiak, Grzegorz Piotr
2001-12-01
Loudspeaker systems are analyzed in a doctoral dissertation. The dissertation concerns loudspeaker systems, which are known as subwoofers or band-pass loudspeaker systems. Their advantages include: high- quality sound reproduction in the low-frequency range, small dimensions, small nonlinear distortions and the fact that they can be placed anywhere in a room or car. Band-pass loudspeaker systems are used widely in the so- called Home Theatre as well as to provide sound in cinema, theatre, concert, discotheque, opera, operetta, philharmonic and amphitheater halls, at open-air concerts, and so on. Various designs are mass-produced by a large number of manufacturers. The study covers an analysis of band-pass loudspeaker systems to which the frequency transformation, i.e. the reactance transformation, has been applied. Since this is a symmetrical transformation, amplitude frequency responses of the studied band-pass systems are also symmetrical (logarithmic scale of a frequency). As a result, the high-pass loudspeaker system design method, known as the Thiele-Small, Benson analysis, can be employed. The investigations include the formulation of band-pass system equations (fourth, sixth and eighth-order polynomials) and the subsequent derivation of relations for the calculation of system parameters. The obtained results enable the calculation of optimum designs for prescribed alignments, e.g. (Chebyshev) equal-ripple, (Butterworth) maximally flat, or quasi-maximally flat (QB). The analysis covers fourth, sixth and eighth-order symmetrical systems. Eighth-order systems have been divided into three kinds according to three ways of physical realization. The doctoral dissertation includes band-pass loudspeaker systems, which can be designed with active or passive filters or without the filter. Designed systems consist of a loudspeaker whose front of a diaphragm is loaded with a Helmholtz resonator, i.e. an enclosure with a vent, which radiates sound outwards. The back is
2d PDE Linear Symmetric Matrix Solver
1983-10-01
ICCG2 (Incomplete Cholesky factorized Conjugate Gradient algorithm for 2d symmetric problems) was developed to solve a linear symmetric matrix system arising from a 9-point discretization of two-dimensional elliptic and parabolic partial differential equations found in plasma physics applications, such as resistive MHD, spatial diffusive transport, and phase space transport (Fokker-Planck equation) problems. These problems share the common feature of being stiff and requiring implicit solution techniques. When these parabolic or elliptic PDE''s are discretized withmore » finite-difference or finite-element methods,the resulting matrix system is frequently of block-tridiagonal form. To use ICCG2, the discretization of the two-dimensional partial differential equation and its boundary conditions must result in a block-tridiagonal supermatrix composed of elementary tridiagonal matrices. The incomplete Cholesky conjugate gradient algorithm is used to solve the linear symmetric matrix equation. Loops are arranged to vectorize on the Cray1 with the CFT compiler, wherever possible. Recursive loops, which cannot be vectorized, are written for optimum scalar speed. For matrices lacking symmetry, ILUCG2 should be used. Similar methods in three dimensions are available in ICCG3 and ILUCG3. A general source containing extensions and macros, which must be processed by a pre-compiler to obtain the standard FORTRAN source, is provided along with the standard FORTRAN source because it is believed to be more readable. The pre-compiler is not included, but pre-compilation may be performed by a text editor as described in the UCRL-88746 Preprint.« less
Symmetrical and anti-symmetrical coherent perfect absorption for acoustic waves
Wei, Pengjiang; Croënne, Charles; Tak Chu, Sai; Li, Jensen
2014-03-24
We investigate tunable acoustic absorption enabled by the coherent control of input waves. It relies on coherent perfect absorption originally proposed in optics. By designing appropriate acoustic metamaterial structures with resonating effective bulk modulus or density, we show that complete absorption of incident waves impinging on the metamaterial can be achieved for either symmetrical or anti-symmetrical inputs in the forward and backward directions. By adjusting the relative phase between the two incident beams, absorption can be tuned effectively from unity to zero, making coherent control useful in applications like acoustic modulators, noise controllers, transducers, and switches.
Kinetic models of two-dimensional plane and axially symmetric current sheets: Group theory approach
Vasko, I. Y.; Artemyev, A. V.; Popov, V. Y.; Malova, H. V.
2013-02-15
In this paper, we present new class of solutions of Grad-Shafranov-like (GS-like) equations, describing kinetic plane and axially symmetric 2D current sheets. We show that these equations admit symmetry groups only for Maxwellian and {kappa}-distributions of charged particles. The admissible symmetry groups are used to reduce GS-like equations to ordinary differential equations for invariant solutions. We derive asymptotes of invariant solutions, while invariant solutions are found analytically for the {kappa}-distribution with {kappa}=7/2. We discuss the difference of obtained solutions from equilibria widely used in other studies. We show that {kappa} regulates the decrease rate of plasma characteristics along the current sheet and determines the spatial distribution of magnetic field components. The presented class of plane and axially symmetric (disk-like) current sheets includes solutions with the inclined neutral plane.
Communities and classes in symmetric fractals
NASA Astrophysics Data System (ADS)
Krawczyk, Małgorzata J.
2015-07-01
Two aspects of fractal networks are considered: the community structure and the class structure, where classes of nodes appear as a consequence of a local symmetry of nodes. The analyzed systems are the networks constructed for two selected symmetric fractals: the Sierpinski triangle and the Koch curve. Communities are searched for by means of a set of differential equations. Overlapping nodes which belong to two different communities are identified by adding some noise to the initial connectivity matrix. Then, a node can be characterized by a spectrum of probabilities of belonging to different communities. Our main goal is that the overlapping nodes with the same spectra belong to the same class.
Synthesis of controllers for symmetric systems
NASA Astrophysics Data System (ADS)
Ameur Abid, Chiheb; Zouari, Belhassen
2010-11-01
This article deals with supervisory control problem for coloured Petri (CP) nets. Considering a CP-net, we build a condensed version of the ordinary state-space, namely the symbolic reachability graph (SRG). This latter graph allows to cope with state-space explosion problem for symmetric systems. The control specification can be expressed in terms of either forbidden states or forbidden sequences of transitions. According to these specifications, we derive the controller by applying the theory of regions on the basis of the SRG. Thanks to expressiveness power of CP-nets, the obtained controller to be connected to the plant model is reduced to one single place.
Fast Multipole Method for Coulomb Interaction Based on Traceless Totally Symmetric Tensor
NASA Astrophysics Data System (ADS)
Huang, He; Li, Rui; Chen, Jie; Luo, Li-Shi; Zhang, He
2015-04-01
The fast multipole method (FMM) is widely used to calculate the Coulomb interaction between a huge amount of charged particles. The efficiency of FMM scales with O(N) for N particles with any arbitrary distribution. Hence it is apposite for problems with complicated charge distribution or geometry. Under the same FMM framework, there are different approaches, such as using spherical harmonic functions or Maxwell Cartesian tensors. Here we will present a version using traceless totally symmetric Maxwell Cartesian tensor. The previous Maxwell Cartesian tensor based FMM uses totally symmetric tensor. There are (n + 1)(n + 2) / 2 independent elements in a rank n totally symmetric tensor. However, there are only 2 n + 1 independent elements in a rank n traceless totally symmetric tensor, due to which the efficiency of the traceless version is highly improved compared with the old version, especially when high accuracy is needed and high rank tensors are used. Work supported by the Department of Energy, Laboratory Directed Research and Development Funding, under Contract No. DE-AC05-06OR23177.
The modelling of symmetric airfoil vortex generators
NASA Technical Reports Server (NTRS)
Reichert, B. A.; Wendt, B. J.
1996-01-01
An experimental study is conducted to determine the dependence of vortex generator geometry and impinging flow conditions on shed vortex circulation and crossplane peak vorticity for one type of vortex generator. The vortex generator is a symmetric airfoil having a NACA 0012 cross-sectional profile. The geometry and flow parameters varied include angle-of-attack alfa, chordlength c, span h, and Mach number M. The vortex generators are mounted either in isolation or in a symmetric counter-rotating array configuration on the inside surface of a straight pipe. The turbulent boundary layer thickness to pipe radius ratio is delta/R = 0. 17. Circulation and peak vorticity data are derived from crossplane velocity measurements conducted at or about 1 chord downstream of the vortex generator trailing edge. Shed vortex circulation is observed to be proportional to M, alfa, and h/delta. With these parameters held constant, circulation is observed to fall off in monotonic fashion with increasing airfoil aspect ratio AR. Shed vortex peak vorticity is also observed to be proportional to M, alfa, and h/delta. Unlike circulation, however, peak vorticity is observed to increase with increasing aspect ratio, reaching a peak value at AR approx. 2.0 before falling off.
Cyclicity of some symmetric nilpotent centers
NASA Astrophysics Data System (ADS)
García, Isaac A.
2016-03-01
In this work we present techniques for bounding the cyclicity of a wide class of monodromic nilpotent singularities of symmetric polynomial planar vector fields. The starting point is identifying a broad family of nilpotent symmetric fields for which existence of a center is equivalent to existence of a local analytic first integral, which, unlike the degenerate case, is not true in general for nilpotent singularities. We are able to relate so-called "focus quantities" to the "Poincaré-Lyapunov quantities" arising from the Poincaré first return map. When we apply the method to concrete examples, we show in some cases that the upper bound is sharp. Our approach is based on computational algebra methods for determining a minimal basis (constructed by focus quantities instead of by Poincaré-Lyapunov quantities because of the easier computability of the former) of the associated polynomial Bautin ideal in the parameter space of the family. The case in which the Bautin ideal is not radical is also treated.
Electroweak Baryogenesis in R-symmetric Supersymmetry
Fok, R.; Kribs, Graham D.; Martin, Adam; Tsai, Yuhsin
2013-03-01
We demonstrate that electroweak baryogenesis can occur in a supersymmetric model with an exact R-symmetry. The minimal R-symmetric supersymmetric model contains chiral superfields in the adjoint representation, giving Dirac gaugino masses, and an additional set of "R-partner" Higgs superfields, giving R-symmetric \\mu-terms. New superpotential couplings between the adjoints and the Higgs fields can simultaneously increase the strength of the electroweak phase transition and provide additional tree-level contributions to the lightest Higgs mass. Notably, no light stop is present in this framework, and in fact, we require both stops to be above a few TeV to provide sufficient radiative corrections to the lightest Higgs mass to bring it up to 125 GeV. Large CP-violating phases in the gaugino/higgsino sector allow us to match the baryon asymmetry of the Universe with no constraints from electric dipole moments due to R-symmetry. We briefly discuss some of the more interesting phenomenology, particularly of the of the lightest CP-odd scalar.
Conditional symmetric instability and mesoscale rainbands
NASA Technical Reports Server (NTRS)
Xu, Q.
1986-01-01
The linear theory of conditional symmetric instability (CSI) is re-examined in a rigorous framework. In comparison with symmetric instability a new feature of CSI is that the moist updraught tends to be narrow, as with conditional buoyancy instability (CBI). As the width of the moist updraught varies from its tolerance maximum to infinitesimal, the inviscid growth rate increases from zero to its maximum and the slope of the moist updraught increases from the absolute momentum surface to the moist most unstable surface. The fact that CSI circulations absorb energy from the basic shear and moist thermal field but lose energy to the dry basic thermal field is responsible for the narrow and slant feature of the moist updraught. When a bulk viscosity is accounted for, the most rapidly growing CSI modes bear a qualitative resemblance to some observed rainbands. The stability criterion of viscous CSI also shows a better comparison with observational data than inviscid CSI. The linear CSI theory here predicts that the isolated mode is preferred to other non-isolated (periodic or irregular spacing) modes. The preference of non-isolated modes is speculated to occur in the nonlinear stage.
Spherically Symmetric Solutions of Light Galileon
NASA Astrophysics Data System (ADS)
Momeni, D.; Houndjo, M. J. S.; Güdekli, E.; Rodrigues, M. E.; Alvarenga, F. G.; Myrzakulov, R.
2016-02-01
We have been studied the model of light Galileon with translational shift symmetry ϕ → ϕ + c. The matter Lagrangian is presented in the form {L}_{φ }= -η (partial φ )2+β G^{μ ν }partial _{μ }φ partial _{ν }φ . We have been addressed two issues: the first is that, we have been proven that, this type of Galileons belong to the modified matter-curvature models of gravity in type of f(R,R^{μ ν }T_{μ ν }m). Secondly, we have been investigated exact solution for spherically symmetric geometries in this model. We have been found an exact solution with singularity at r = 0 in null coordinates. We have been proven that the solution has also a non-divergence current vector norm. This solution can be considered as an special solution which has been investigated in literature before, in which the Galileon's field is non-static (time dependence). Our scalar-shift symmetrized Galileon has the simple form of ϕ = t, which it is remembered by us dilaton field.
Fast numerical determination of symmetric sparsity patterns
Carter, R.G.
1994-08-01
The author considers a function g: {Re}{sup n} {yields} {Re}{sup n} for which the Jacobian is symmetric and sparse. Such functions often arise, for instance, in numerical optimization, where g is the gradient of some objective function f so that the Jacobian of g is the Hessian of f. In many such applications one can generate extremely efficient algorithms by taking advantage of the sparsity structure of the problem if this pattern is known a priori. Unfortunately, determining such sparsity structures by hand is often difficult and prone to error. If one suspects a mistake has been made, or if g is a {open_quotes}black box{close_quotes} so that the true structure is completely unknown, one often has no alternative but to compute the entire matrix by finite differences - a prohibitively expensive task for large problems. The author shows that it is possible to numerically determine symmetric sparsity patterns using a relatively small number of g evaluations. Numerical results are shown for n up to 100,000 in which all nonzeros in the Jacobian are correctly identified in about one-hundredth of the time required to estimate the sparsity structure by a full finite difference calculation. When a good initial guess for the sparsity structure is available, numerical results are presented for n up to 500,000, in which all missing nonzeros are correctly located almost five-thousand times faster than would be possible with a full finite difference calculation.
Decay Structure for Symmetric Hyperbolic Systems with Non-Symmetric Relaxation and its Application
NASA Astrophysics Data System (ADS)
Ueda, Yoshihiro; Duan, Renjun; Kawashima, Shuichi
2012-07-01
This paper is concerned with the decay structure for linear symmetric hyperbolic systems with relaxation. When the relaxation matrix is symmetric, the dissipative structure of the systems is completely characterized by the Kawashima-Shizuta stability condition formulated in Umeda et al. (Jpn J Appl Math 1:435-457, 1984) and Shizuta and Kawashima (Hokkaido Math J 14:249-275, 1985) and we obtain the asymptotic stability result together with the explicit time-decay rate under that stability condition. However, some physical models which satisfy the stability condition have non-symmetric relaxation term (for example, the Timoshenko system and the Euler-Maxwell system). Moreover, it had been already known that the dissipative structure of such systems is weaker than the standard type and is of the regularity-loss type (see Duan in J Hyperbolic Differ Equ 8:375-413, 2011; Ide et al. in Math Models Meth Appl Sci 18:647-667, 2008; Ide and Kawashima in Math Models Meth Appl Sci 18:1001-1025, 2008; Ueda et al. in SIAM J Math Anal 2012; Ueda and Kawashima in Methods Appl Anal 2012). Therefore our purpose in this paper is to formulate a new structural condition which includes the Kawashima-Shizuta condition, and to analyze the weak dissipative structure for general systems with non-symmetric relaxation.
Du, Hai-Jian; Chen, Yi-Ran; Zhang, Rui; Pan, Hong-Miao; Zhang, Wen-Yan; Zhou, Ke; Wu, Long-Fei; Xiao, Tian
2015-06-01
Two morphotypes (spherical and ellipsoidal) of multicellular magnetotactic prokaryotes (MMPs) have been reported from the sediments of Lake Yuehu, China. Here, their temporal distributions and their relationships with biogeochemical parameters are studied. Samples were collected at approximately 2-week intervals from two sites (A and B) during the period September 2012 to December 2013. The abundance of MMPs was high in summer and autumn, but low in winter and spring. Furthermore, the peaks in the numbers of the two types of MMPs were sequential, with the highest concentration of the spherical MMPs occurring prior to that of the ellipsoidal MMPs. This may be related to different optimal growth temperatures for the two types. Although the two types of MMP coexisted at both sites, their numbers were different; at most times, spherical MMPs dominated at site A, whereas ellipsoidal MMPs dominated at site B. Geochemical analysis revealed that the environmental conditions at site A varied more than at site B. Compared with the widely distributed spherical MMPs, ellipsoidal MMPs seemed to prefer more stable habitats. This is the first report of the temporal distribution of ellipsoidal MMPs in sediments, suggesting that their environmental adaptations differ from those of spherical MMPs. PMID:25727488
The study on the methods of ellipsoid expansion in high-speed railway in high elevation area
NASA Astrophysics Data System (ADS)
Yang, Zhi; Wen, HongYan; Nie, GuangYu; Gao, Hong
2015-12-01
With the development of high-speed railway in recent years, the previous precision of control surveying and the methods of data processing will not meet the requirement of high-speed railway any longer. In view of the characteristics of precision is much higher in large-scale precise construction and the superiority of precision in reform of large-scale engineering control networks, in this paper, using the algorithm of ellipsoid expansion to deal with overrun coordinate projection distortion in high-speed railway, then compares with common calculation method of surveying, we get a conclusion that this method can get minimum projection and it accord with the requirement of high-precision control surveying.
Acoustic field distribution of sawtooth wave with nonlinear SBE model
Liu, Xiaozhou Zhang, Lue; Wang, Xiangda; Gong, Xiufen
2015-10-28
For precise prediction of the acoustic field distribution of extracorporeal shock wave lithotripsy with an ellipsoid transducer, the nonlinear spheroidal beam equations (SBE) are employed to model acoustic wave propagation in medium. To solve the SBE model with frequency domain algorithm, boundary conditions are obtained for monochromatic and sawtooth waves based on the phase compensation. In numerical analysis, the influence of sinusoidal wave and sawtooth wave on axial pressure distributions are investigated.
Pakrashi, Sunandan; Dalai, Swayamprava; Chandrasekaran, Natarajan; Mukherjee, Amitava
2014-07-01
The transfer of nanoparticles through the food chain can lead to bioaccumulation and biomagnification resulting in a long term negative impact on the ecosystem functions. The primary objective of this study was evaluation of aluminium oxide nanoparticles transfer from primary producers to primary consumers. A simple set up consisting of a primary producer (Chlorella ellipsoides) and a primary consumer (Ceriodaphnia dubia) was used. Here, C. ellipsoides were exposed to the varying concentrations of the nanoparticles ranging from 20 to 120μg/mL (196 to 1176μM) for 48h and the infested algal cells were used as the feed to C. dubia. The bioaccumulation of the nanoparticles into the daphnids was noted and the biomagnification factors were computed. The exposure was noted to cause subtle alterations in the feeding behaviour of the daphnids. This might have long term consequences in the energy flow through the food chain. The reproductive behaviour of the daphnids remained unaffected upon exposure to nanoparticle infested algal feed. Distinct observations at ultra-structural scale using transmission electron microscopy provided visual evidences for the disrupted feeding behaviour upon exposure to nanoparticle treated algae. Internalization of nanoparticle like inclusion bodies in the intracellular space of algae was also detected. The findings were further substantiated by a detailed analysis of hydrodynamic stability, bioavailability and dissolution of ions from the nanoparticles over the exposure period. Altogether, the study brings out the first of its kind of observation of trophic transfer potential/behaviour of aluminium oxide nanoparticles and its probable impacts on the energy flow in the fresh water aquatic ecosystem. PMID:24736130
Fission product studies in the symmetric mass region
De Laeter, J.R.; Rosman, K.J.R.; Loss, R.D.
1993-05-01
Fission yields can be determined by radiochemical or mass spectrometric techniques. Mass spectrometry can provide more accurate data, particularly in the symmetric mass region where the probability of fission is low and uncertainties in isometric ratios occur. Fine structure in the mass distribution can usually only be determined by mass spectrometry. Many of the elements in the valley of symmetry have high ionization potentials and are therefore difficult to measure by solid source mass spectrometry. Analytical techniques have been developed to provide the sensitivity required to measure the small sample sizes available in fission product studies. Cumulative fission yields for ruthenium, palladium, cadmium, tin, and tellurium have been measured by mass spectrometry for the thermal and epicadmium fission of {sup 233}U and for thermal and epicadmium fission of {sup 239}Pu. These fission yields, which span the mass range 101 {le} A {le} 130, can be combined to give a mass yield curve for {sup 235}U in the valley region, which is symmetrical about A = 116.8 and exhibits fine structure in the mass 113 to 114 region. Fine structure in {sup 233}U is also present at mass 111. Mass spectrometric determinations of the fission yields of uranium ore at the Oklo mine site in Gabon enable the nuclear parameters of this natural reactor to be evaluated. This in turn enables the amounts of fission products produced in the reactor zone and the surrounding rocks enables an assessment to be made of the efficiency of this geological repository for containing radioactive waste. The elemental abundances can be determined by isotope dilution mass spectrometry. Unfortunately, the paucity of good fission yield data available for {sup 238}U by fast neutrons is a severe constraint in this evaluation.
Symmetric instability in the Gulf Stream
NASA Astrophysics Data System (ADS)
Thomas, Leif N.; Taylor, John R.; Ferrari, Raffaele; Joyce, Terrence M.
2013-07-01
Analyses of wintertime surveys of the Gulf Stream (GS) conducted as part of the CLIvar MOde water Dynamic Experiment (CLIMODE) reveal that water with negative potential vorticity (PV) is commonly found within the surface boundary layer (SBL) of the current. The lowest values of PV are found within the North Wall of the GS on the isopycnal layer occupied by Eighteen Degree Water, suggesting that processes within the GS may contribute to the formation of this low-PV water mass. In spite of large heat loss, the generation of negative PV was primarily attributable to cross-front advection of dense water over light by Ekman flow driven by winds with a down-front component. Beneath a critical depth, the SBL was stably stratified yet the PV remained negative due to the strong baroclinicity of the current, suggesting that the flow was symmetrically unstable. A large eddy simulation configured with forcing and flow parameters based on the observations confirms that the observed structure of the SBL is consistent with the dynamics of symmetric instability (SI) forced by wind and surface cooling. The simulation shows that both strong turbulence and vertical gradients in density, momentum, and tracers coexist in the SBL of symmetrically unstable fronts. SI is a shear instability that draws its energy from geostrophic flows. A parameterization for the rate of kinetic energy (KE) extraction by SI applied to the observations suggests that SI could result in a net dissipation of 33 mW m-2 and 1 mW m-2 for surveys with strong and weak fronts, respectively. The surveys also showed signs of baroclinic instability (BCI) in the SBL, namely thermally direct vertical circulations that advect biomass and PV. The vertical circulation was inferred using the omega equation and used to estimate the rate of release of available potential energy (APE) by BCI. The rate of APE release was found to be comparable in magnitude to the net dissipation associated with SI. This result points to an
Operational multipartite entanglement classes for symmetric photonic qubit states
Kiesel, N.; Wieczorek, W.; Weinfurter, H.; Krins, S.; Bastin, T.; Solano, E.
2010-03-15
We present experimental schemes that allow us to study the entanglement classes of all symmetric states in multiqubit photonic systems. We compare the efficiency of the proposed schemes and highlight the relation between the entanglement properties of symmetric Dicke states and a recently proposed entanglement scheme for atoms. In analogy to the latter, we obtain a one-to-one correspondence between well-defined sets of experimental parameters and multiqubit entanglement classes inside the symmetric subspace of the photonic system.
Radially symmetric transmon with long lifetime
NASA Astrophysics Data System (ADS)
Sandberg, Martin; Vissers, Michael; Gao, Jiansong; Pappas, David
2014-03-01
We present a radially symmetric design for a large pad transmon qubit. The symmetry reduces the dipole radiation by orders of magnitude relative to axial large pad qubits that are widely used for 3D-circuit QED experiments. The reduction in radiation allows for the use of large area structures that are needed to reduce the effects of interface losses. This enables long qubit lifetimes without the use of a high-Q cavity resonator. Energy relaxation and coherence times of up to 35 microseconds have been measured. The qubit can be implemented in a microstrip geometry. This gives the advantage of removing discontinuous ground planes that can cause stray resonances. In addition, this geometry is well suited for implementing and exploring circuits with direct qubit-qubit coupling.
Symmetrical Taylor impact of glass bars
NASA Astrophysics Data System (ADS)
Murray, N. H.; Bourne, N. K.; Field, J. E.; Rosenberg, Z.
1998-07-01
Brar and Bless pioneered the use of plate impact upon bars as a technique for investigating the 1D stress loading of glass but limited their studies to relatively modest stresses (1). We wish to extend this technique by applying VISAR and embedded stress gauge measurements to a symmetrical version of the test in which two rods impact one upon the other. Previous work in the laboratory has characterised the glass types (soda-lime and borosilicate)(2). These experiments identify the failure mechanisms from high-speed photography and the stress and particle velocity histories are interpreted in the light of these results. The differences in response of the glasses and the relation of the fracture to the failure wave in uniaxial strain are discussed.
Scaling model for symmetric star polymers
NASA Astrophysics Data System (ADS)
Ramachandran, Ram; Rai, Durgesh K.; Beaucage, Gregory
2010-03-01
Neutron scattering data from symmetric star polymers with six poly (urethane-ether) arms, chemically bonded to a C-60 molecule are fitted using a new scaling model and scattering function. The new scaling function can describe both good solvent and theta solvent conditions as well as resolve deviations in chain conformation due to steric interactions between star arms. The scaling model quantifies the distinction between invariant topological features for this star polymer and chain tortuosity which changes with goodness of solvent and steric interaction. Beaucage G, Phys. Rev. E 70 031401 (2004).; Ramachandran R, et al. Macromolecules 41 9802-9806 (2008).; Ramachandran R, et al. Macromolecules, 42 4746-4750 (2009); Rai DK et al. Europhys. Lett., (Submitted 10/2009).
Circularly symmetric light scattering from nanoplasmonic spirals.
Trevino, Jacob; Cao, Hui; Dal Negro, Luca
2011-05-11
In this paper, we combine experimental dark-field imaging, scattering, and fluorescence spectroscopy with rigorous electrodynamics calculations in order to investigate light scattering from planar arrays of Au nanoparticles arranged in aperiodic spirals with diffuse, circularly symmetric Fourier space. In particular, by studying the three main types of Vogel's spirals fabricated by electron-beam lithography on quartz substrates, we demonstrate polarization-insensitive planar light diffraction in the visible spectral range. Moreover, by combining dark-field imaging with analytical multiparticle calculations in the framework of the generalized Mie theory, we show that plasmonic spirals support distinctive structural resonances with circular symmetry carrying orbital angular momentum. The engineering of light scattering phenomena in deterministic structures with circular Fourier space provides a novel strategy for the realization of optical devices that fully leverage on enhanced, polarization-insensitive light-matter coupling over planar surfaces, such as thin-film plasmonic solar cells, plasmonic polarization devices, and optical biosensors. PMID:21466155
A symmetric bipolar nebula around MWC 922.
Tuthill, P G; Lloyd, J P
2007-04-13
We report regular and symmetric structure around dust-enshrouded Be star MWC 922 obtained with infrared imaging. Biconical lobes that appear nearly square in aspect, forming this "Red Square" nebula, are crossed by a series of rungs that terminate in bright knots or "vortices," and an equatorial dark band crossing the core delimits twin hyperbolic arcs. The intricate yet cleanly constructed forms that comprise the skeleton of the object argue for minimal perturbation from global turbulent or chaotic effects. We also report the presence of a linear comb structure, which may arise from optically projected shadows of a periodic feature in the inner regions, such as corrugations in the rim of a circumstellar disk. The sequence of nested polar rings draws comparison with the triple-ring system seen around the only naked-eye supernova in recent history: SN1987A. PMID:17431173
Jamming anomaly in PT-symmetric systems
NASA Astrophysics Data System (ADS)
Barashenkov, I. V.; Zezyulin, D. A.; Konotop, V. V.
2016-07-01
The Schrödinger equation with a { P }{ T }-symmetric potential is used to model an optical structure consisting of an element with gain coupled to an element with loss. At low gain–loss amplitudes γ, raising the amplitude results in the energy flux from the active to the leaky element being boosted. We study the anomalous behaviour occurring for larger γ, where the increase of the amplitude produces a drop of the flux across the gain–loss interface. We show that this jamming anomaly is either a precursor of the exceptional point, where two real eigenvalues coalesce and acquire imaginary parts, or precedes the eigenvalue's immersion in the continuous spectrum.
Highly symmetric POVMs and their informational power
NASA Astrophysics Data System (ADS)
Słomczyński, Wojciech; Szymusiak, Anna
2016-01-01
We discuss the dependence of the Shannon entropy of normalized finite rank-1 POVMs on the choice of the input state, looking for the states that minimize this quantity. To distinguish the class of measurements where the problem can be solved analytically, we introduce the notion of highly symmetric POVMs and classify them in dimension 2 (for qubits). In this case, we prove that the entropy is minimal, and hence, the relative entropy (informational power) is maximal, if and only if the input state is orthogonal to one of the states constituting a POVM. The method used in the proof, employing the Michel theory of critical points for group action, the Hermite interpolation, and the structure of invariant polynomials for unitary-antiunitary groups, can also be applied in higher dimensions and for other entropy-like functions. The links between entropy minimization and entropic uncertainty relations, the Wehrl entropy, and the quantum dynamical entropy are described.
Torus quantization of symmetrically excited helium
Mueller, J. ); Burgdoerfer, J. Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6377 ); Noid, D. )
1992-02-01
The recent discovery by Richter and Wintgen (J. Phys. B 23, L197 (1990)) that the classical helium atom is not globally ergodic has stimulated renewed interest in its semiclassical quantization. The Einstein-Brillouin-Keller quantization of Kolmogorov-Arnold-Moser tori around stable periodic orbits becomes locally possible in a selected region of phase space. Using a hyperspherical representation we have found a dynamically confining potential allowing for a stable motion near the Wannier ridge. The resulting semiclassical eigenenergies provide a test for full quantum calculations in the limit of very high quantum numbers. The relations to frequently used group-theoretical classifications for doubly excited states and to the periodic-orbit quantization of the chaotic portion of the phase space are discussed. The extrapolation of the semiclassical quantization to low-lying states give remarkably accurate estimates for the energies of all symmetric {ital L}=0 states of helium.
Symmetric Satellite Swarms and Choreographic Crystals
NASA Astrophysics Data System (ADS)
Boyle, Latham; Khoo, Jun Yong; Smith, Kendrick
2016-01-01
In this Letter, we introduce a natural dynamical analogue of crystalline order, which we call choreographic order. In an ordinary (static) crystal, a high degree of symmetry may be achieved through a careful arrangement of the fundamental repeated elements. In the dynamical analogue, a high degree of symmetry may be achieved by having the fundamental elements perform a carefully choreographed dance. For starters, we show how to construct and classify all symmetric satellite constellations. Then we explain how to generalize these ideas to construct and classify choreographic crystals more broadly. We introduce a quantity, called the "choreography" of a given configuration. We discuss the possibility that some (naturally occurring or artificial) many-body or condensed-matter systems may exhibit choreographic order, and suggest natural experimental signatures that could be used to identify and characterize such systems.
Symmetric Satellite Swarms and Choreographic Crystals.
Boyle, Latham; Khoo, Jun Yong; Smith, Kendrick
2016-01-01
In this Letter, we introduce a natural dynamical analogue of crystalline order, which we call choreographic order. In an ordinary (static) crystal, a high degree of symmetry may be achieved through a careful arrangement of the fundamental repeated elements. In the dynamical analogue, a high degree of symmetry may be achieved by having the fundamental elements perform a carefully choreographed dance. For starters, we show how to construct and classify all symmetric satellite constellations. Then we explain how to generalize these ideas to construct and classify choreographic crystals more broadly. We introduce a quantity, called the "choreography" of a given configuration. We discuss the possibility that some (naturally occurring or artificial) many-body or condensed-matter systems may exhibit choreographic order, and suggest natural experimental signatures that could be used to identify and characterize such systems. PMID:26799028
Consistency of PT-symmetric quantum mechanics
NASA Astrophysics Data System (ADS)
Brody, Dorje C.
2016-03-01
In recent reports, suggestions have been put forward to the effect that parity and time-reversal (PT) symmetry in quantum mechanics is incompatible with causality. It is shown here, in contrast, that PT-symmetric quantum mechanics is fully consistent with standard quantum mechanics. This follows from the surprising fact that the much-discussed metric operator on Hilbert space is not physically observable. In particular, for closed quantum systems in finite dimensions there is no statistical test that one can perform on the outcomes of measurements to determine whether the Hamiltonian is Hermitian in the conventional sense, or PT-symmetric—the two theories are indistinguishable. Nontrivial physical effects arising as a consequence of PT symmetry are expected to be observed, nevertheless, for open quantum systems with balanced gain and loss.
Pseudo-Z symmetric space-times
Mantica, Carlo Alberto; Suh, Young Jin
2014-04-15
In this paper, we investigate Pseudo-Z symmetric space-time manifolds. First, we deal with elementary properties showing that the associated form A{sub k} is closed: in the case the Ricci tensor results to be Weyl compatible. This notion was recently introduced by one of the present authors. The consequences of the Weyl compatibility on the magnetic part of the Weyl tensor are pointed out. This determines the Petrov types of such space times. Finally, we investigate some interesting properties of (PZS){sub 4} space-time; in particular, we take into consideration perfect fluid and scalar field space-time, and interesting properties are pointed out, including the Petrov classification. In the case of scalar field space-time, it is shown that the scalar field satisfies a generalized eikonal equation. Further, it is shown that the integral curves of the gradient field are geodesics. A classical method to find a general integral is presented.
Parametric separation of symmetric pure quantum states
NASA Astrophysics Data System (ADS)
Solís-Prosser, M. A.; Delgado, A.; Jiménez, O.; Neves, L.
2016-01-01
Quantum state separation is a probabilistic map that transforms a given set of pure states into another set of more distinguishable ones. Here we investigate such a map acting onto uniparametric families of symmetric linearly dependent or independent quantum states. We obtained analytical solutions for the success probability of the maps—which is shown to be optimal—as well as explicit constructions in terms of positive operator valued measures. Our results can be used for state discrimination strategies interpolating continuously between minimum-error and unambiguous (or maximum-confidence) discrimination, which, in turn, have many applications in quantum information protocols. As an example, we show that quantum teleportation through a nonmaximally entangled quantum channel can be accomplished with higher probability than the one provided by unambiguous (or maximum-confidence) discrimination and with higher fidelity than the one achievable by minimum-error discrimination. Finally, an optical network is proposed for implementing parametric state separation.
Topological Analyses of Symmetric Eruptive Prominences
NASA Astrophysics Data System (ADS)
Panasenco, O.; Martin, S. F.
Erupting prominences (filaments) that we have analyzed from Hα Doppler data at Helio Research and from SOHO/EIT 304 Å, show strong coherency between their chirality, the direction of the vertical and lateral motions of the top of the prominences, and the directions of twisting of their legs. These coherent properties in erupting prominences occur in two patterns of opposite helicity; they constitute a form of dynamic chirality called the ``roll effect." Viewed from the positive network side as they erupt, many symmetrically-erupting dextral prominences develop rolling motion toward the observer along with right-hand helicity in the left leg and left-hand helicity in the right leg. Many symmetricaly-erupting sinistral prominences, also viewed from the positive network field side, have the opposite pattern: rolling motion at the top away from the observer, left-hand helical twist in the left leg, and right-hand twist in the right leg. We have analysed the motions seen in the famous movie of the ``Grand Daddy" erupting prominence and found that it has all the motions that define the roll effect. From our analyses of this and other symmetric erupting prominences, we show that the roll effect is an alternative to the popular hypothetical configuration of an eruptive prominence as a twisted flux rope or flux tube. Instead we find that a simple flat ribbon can be bent such that it reproduces nearly all of the observed forms. The flat ribbon is the most logical beginning topology because observed prominence spines already have this topology prior to eruption and an initial long magnetic ribbon with parallel, non-twisted threads, as a basic form, can be bent into many more and different geometrical forms than a flux rope.
Focal symmetrical encephalomalacia in a goat.
Oliveira, Diego M; Pimentel, Luciano A; Pessoa, André F; Dantas, Antônio F M; Uzal, Francisco; Riet-Correa, Franklin
2010-09-01
Focal symmetrical encephalomalacia (FSE) is the most prominent lesion seen in the chronic form of enterotoxemia caused by Clostridium perfringens type D in sheep. However, this lesion has not been reported in goats. The current paper reports a case of FSE in a goat from the state of Paraíba in the Brazilian semiarid region. As reported by the farmer, 30, 4-48-month-old animals from a flock of 150 goats died after showing nervous signs, including blindness and recumbence, for periods varying between 1 and 14 days. The flock was grazing native pasture supplemented with wheat and corn bran. Additionally, lactating goats were supplemented with soybeans. A 4-month-old goat with nervous signs was examined clinically and then necropsied 3 days after the onset of clinical signs. Bilateral, focal, and symmetrical areas of brown discoloration were observed in the internal capsule and thalamus. Histologic lesions in these areas consisted of multifocal, bilateral malacia with a few neutrophils; endothelial cell swelling; perivascular edema; and hemorrhages. The etiology of these lesions was not determined. However, FSE is considered pathognomonic for C. perfringens type D enterotoxemia in sheep, and it is speculated that this microorganism was the etiologic agent in the present case. The flock had been vaccinated against type D enterotoxemia only once, approximately 3 months before the beginning of the outbreak. Insufficient immunity due to the incorrect vaccination protocol, low efficacy of the vaccine used, and a diet including large amounts of highly fermentable carbohydrates were suspected to be predisposing factors for this outbreak. PMID:20807946
Analysis of interlaminar stresses in symmetric and unsymmetric laminates under various loadings
NASA Astrophysics Data System (ADS)
Leger, C. A.; Chan, W. S.
1993-04-01
A quasi-three-dimensional finite-element model is developed to investigate the interlaminar stresses in a composite laminate under combined loadings. An isoparametric quadrilateral element with eight nodes and three degrees of freedom per node is the finite element used in this study. The element is used to model a composite laminate cross section loaded by tension, torsion, transverse shear, and both beam and chord bending which are representative of loading in a helicopter rotor system. Symmetric and unsymmetric laminates are examined with comparisons made between the interlaminar stress distributions and magnitudes for each laminate. Unsymmetric results are compared favorably to limited results found in literature. The unsymmetric interlaminar normal stress distribution in a symmetric laminate containing a free edge delamination is also examined.
The equatorial position of the metaphase plate ensures symmetric cell divisions.
Tan, Chia Huei; Gasic, Ivana; Huber-Reggi, Sabina P; Dudka, Damian; Barisic, Marin; Maiato, Helder; Meraldi, Patrick
2015-01-01
Chromosome alignment in the middle of the bipolar spindle is a hallmark of metazoan cell divisions. When we offset the metaphase plate position by creating an asymmetric centriole distribution on each pole, we find that metaphase plates relocate to the middle of the spindle before anaphase. The spindle assembly checkpoint enables this centering mechanism by providing cells enough time to correct metaphase plate position. The checkpoint responds to unstable kinetochore-microtubule attachments resulting from an imbalance in microtubule stability between the two half-spindles in cells with an asymmetric centriole distribution. Inactivation of the checkpoint prior to metaphase plate centering leads to asymmetric cell divisions and daughter cells of unequal size; in contrast, if the checkpoint is inactivated after the metaphase plate has centered its position, symmetric cell divisions ensue. This indicates that the equatorial position of the metaphase plate is essential for symmetric cell divisions. PMID:26188083
Passive PT -symmetric couplers without complex optical potentials
NASA Astrophysics Data System (ADS)
Lee, Yi-Chan; Liu, Jibing; Chuang, You-Lin; Hsieh, Min-Hsiu; Lee, Ray-Kuang
2015-11-01
In addition to the implementation of parity-time-(PT -) symmetric optical systems by carefully and actively controlling the gain and loss, we show that a 2 ×2 PT -symmetric Hamiltonian has a unitarily equivalent representation without complex optical potentials in the resulting optical coupler. Through the Naimark dilation in operator algebra, passive PT -symmetric couplers can thus be implemented with a refractive index of real values and asymmetric coupling coefficients. This opens up the possibility to implement general PT -symmetric systems with state-of-the-art asymmetric slab waveguides, dissimilar optical fibers, or cavities with chiral mirrors.
Integrable nonlinear parity-time-symmetric optical oscillator
NASA Astrophysics Data System (ADS)
Hassan, Absar U.; Hodaei, Hossein; Miri, Mohammad-Ali; Khajavikhan, Mercedeh; Christodoulides, Demetrios N.
2016-04-01
The nonlinear dynamics of a balanced parity-time-symmetric optical microring arrangement are analytically investigated. By considering gain and loss saturation effects, the pertinent conservation laws are explicitly obtained in the Stokes domain, thus establishing integrability. Our analysis indicates the existence of two regimes of oscillatory dynamics and frequency locking, both of which are analogous to those expected in linear parity-time-symmetric systems. Unlike other saturable parity-time-symmetric systems considered before, the model studied in this work first operates in the symmetric regime and then enters the broken parity-time phase.
Static, cylindrically symmetric strings in general relativity with cosmological constant
Linet, B.
1986-07-01
The static, cylindrically symmetric solutions to Einstein's equations with a cosmological term describing cosmic strings are determined. The discussion depends on the sign of the cosmological constant.
Polarization converters based on axially symmetric twisted nematic liquid crystal.
Ko, Shih-Wei; Ting, Chi-Lun; Fuh, Andy Y-G; Lin, Tsung-Hsien
2010-02-15
An axially symmetric twisted nematic liquid crystal (ASTNLC) device, based on axially symmetric photoalignment, was demonstrated. Such an ASTNLC device can convert axial (azimuthal) to azimuthal (axial) polarization. The optical properties of the ASTNLC device are analyzed and found to agree with simulation results. The ASTNLC device with a specific device can be adopted as an arbitrary axial symmetric polarization converter or waveplate for axially, azimuthally or vertically polarized light. A design for converting linear polarized light to axially symmetric circular polarized light is also demonstrated. PMID:20389369
Concrete Representation and Separability Criteria for Symmetric Quantum State
NASA Astrophysics Data System (ADS)
Li, Chang'e.; Tao, Yuanhong; Zhang, Jun; Li, Linsong; Nan, Hua
2014-09-01
Using the typical generators of the special unitary groups S U(2), the concrete representation of symmetric quantum state is established, then the relations satisfied by those coefficients in the representation are presented. Based on the representation of density matrix, the PPT criterion and CCNR criterion are proved to be equivalent on judging the separability of symmetric quantum states. Moreover, it is showed that the matrix Γ ρ of symmetric quantum state only has five efficient entries, thus the calculation of ∥Γ ρ ∥ is simplified. Finally, the quantitative expressions of real symmetric quantum state under the ∥Γ ρ ∥ separability criterion are obtained.
Entanglement equivalence of N-qubit symmetric states
Mathonet, P.; Krins, S.; Bastin, T.; Godefroid, M.; Solano, E.
2010-05-15
We study the interconversion of multipartite symmetric N-qubit states under stochastic local operations and classical communication (SLOCC). We demonstrate that if two symmetric states can be connected with a nonsymmetric invertible local operation (ILO), then they belong necessarily to the separable, W, or Greenberger-Horne-Zeilinger (GHZ) entanglement class, establishing a practical method of discriminating subsets of entanglement classes. Furthermore, we prove that there always exists a symmetric ILO connecting any pair of symmetric N-qubit states equivalent under SLOCC, simplifying the requirements for experimental implementations of local interconversion of those states.
Nonlinear dynamic analysis of quasi-symmetric anisotropic structures
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Peters, Jeanne M.
1987-01-01
An efficient computational method for the nonlinear dynamic analysis of quasi-symmetric anisotropic structures is proposed. The application of mixed models simplifies the analytical development and improves the accuracy of the response predictions, and operator splitting allows the reduction of the analysis model of the quasi-symmetric structure to that of the corresponding symmetric structure. The preconditoned conjugate gradient provides a stable and effective technique for generating the unsymmetric response of the structure as the sum of a symmetrized response plus correction modes. The effectiveness of the strategy is demonstrated with the example of a laminated anisotropic shallow shell of quadrilateral planform subjected to uniform normal loading.
{ital K}{sup +} Emission in Symmetric Heavy Ion Reactions at Subthreshold Energies
Elmer, R.; Berg, M.; Carlen, L.; Jakobsson, B.; Noren, B.; Oskarsson, A.; Ericsson, G.; Julien, J.; Thorsteinsen, T.; Guttormsen, M.; Lo Bellini, V.; Grosse, E.; Muentz, C.; Senger, P.; Westerberg, L.
1996-12-01
Subthreshold {ital K}{sup +} production cross sections have been measured in symmetric Ne+NaF, Ni+Ni, and Au+Au collisions at 1.0{ital A} GeV. The mass dependence is strong, close to {ital A}{sup 2}. The angular distributions are nonisotropic in the center-of-mass system. Introducing rescattering seems to explain this effect to a large extent. {copyright} {ital 1996 The American Physical Society.}
Symmetric and asymmetric modes of {sup 232}Th photofission at intermediate energies
Demekhina, N. A.; Karapetyan, G. S.
2010-01-15
Yields of fragments originating from {sup 232}Th photofission were measured at bremsstrahlungphoton endpoint energies of 50 and 3500 MeV. Charge and mass distributions of fission fragments were analyzed. On the basis of the model of multimode fission, symmetric and asymmetric channels are singled out in {sup 232}Th photofission at intermediate energies. This decomposition made it possible to estimate the contributions of various fission components and the fissility of {sup 232}Th.
Familial multiple symmetric lipomatosis associated with the A8344G mutation of mitochondrial DNA.
Gámez, J; Playán, A; Andreu, A L; Bruno, C; Navarro, C; Cervera, C; Arbós, M A; Schwartz, S; Enriquez, J A; Montoya, J
1998-07-01
We describe familial multiple symmetric lipomatosis in a pedigree harboring the 8344 mutation in the tRNA(Lys) gene of mitochondrial DNA (mtDNA). The proband showed neuromuscular involvement but lacked the typical manifestations of myoclonic epilepsy and ragged-red fibers disease. The distribution of the mutation was unusual because the proportion of mutated genomes was higher in blood and lipomas than in muscle tissue. PMID:9674814
NASA Astrophysics Data System (ADS)
Romano, Marcello
2008-08-01
New exact analytic solutions are introduced for the rotational motion of a rigid body having two equal principal moments of inertia and subjected to an external torque which is constant in magnitude. In particular, the solutions are obtained for the following cases: (1) Torque parallel to the symmetry axis and arbitrary initial angular velocity; (2) Torque perpendicular to the symmetry axis and such that the torque is rotating at a constant rate about the symmetry axis, and arbitrary initial angular velocity; (3) Torque and initial angular velocity perpendicular to the symmetry axis, with the torque being fixed with the body. In addition to the solutions for these three forced cases, an original solution is introduced for the case of torque-free motion, which is simpler than the classical solution as regards its derivation and uses the rotation matrix in order to describe the body orientation. This paper builds upon the recently discovered exact solution for the motion of a rigid body with a spherical ellipsoid of inertia. In particular, by following Hestenes’ theory, the rotational motion of an axially symmetric rigid body is seen at any instant in time as the combination of the motion of a “virtual” spherical body with respect to the inertial frame and the motion of the axially symmetric body with respect to this “virtual” body. The kinematic solutions are presented in terms of the rotation matrix. The newly found exact analytic solutions are valid for any motion time length and rotation amplitude. The present paper adds further elements to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.
Magnetospectroscopy of symmetric and anti-symmetric states in double quantum wells
NASA Astrophysics Data System (ADS)
Marchewka, M.; Sheregii, E. M.; Tralle, I.; Ploch, D.; Tomaka, G.; Furdak, M.; Kolek, A.; Stadler, A.; Mleczko, K.; Zak, D.; Strupinski, W.; Jasik, A.; Jakiela, R.
2008-02-01
The experimental results obtained for magnetotransport in the InGaAs/InAlAs double quantum well (DQW) structures of two different shapes of wells are reported. A beating effect occurring in the Shubnikov-de Haas (SdH) oscillations was observed for both types of structures at low temperatures in the parallel transport when the magnetic field was perpendicular to the layers. An approach for the calculation of the Landau level energies for DQW structures was developed and then applied to the analysis and interpretation of the experimental data related to the beating effect. We also argue that in order to account for the observed magnetotransport phenomena (SdH and integer quantum Hall effect), one should introduce two different quasi-Fermi levels characterizing two electron subsystems regarding the symmetry properties of their states, symmetric and anti-symmetric ones, which are not mixed by electron-electron interaction.
NASA Astrophysics Data System (ADS)
Jimenez, Carmen; Kurdyumov, Vadim
2015-11-01
Direct numerical simulations, including detailed chemistry and transport, are used to investigate the structure and stability of freely propagating lean hydrogen flames in planar narrow channels. Depending on the flame burning rate and the wall properties, the flame-wall heat exchange can result in flame extinction. For large heat losses only the fastest burning flames, corresponding to fast reactant flowing rates can propagate. We show that double flame solutions, symmetric and non-symmetric, can coexist for the same set of parameters. The symmetric solutions are calculated imposing symmetric boundary conditions in the channel mid-plane and when this restriction is relaxed non-symmetric solutions develop. This indicates that the symmetric flames are unstable to non-symmetric perturbations, as predicted before within the context of a constant density model. Moreover, the burning rates of the non-symmetric flames are found to be significantly larger than those of the corresponding symmetric solution and therefore the range of conditions for flame extinction and flashback also differ. This shows that assuming in CFD that the flame should reproduce the symmetry of the cold flow can have important safety implications in micro scale combustion devices burning lean hydrogen mixture.
Geography of the rotational resonances and their stability in the ellipsoidal full two body problem
NASA Astrophysics Data System (ADS)
Jafari Nadoushan, Mahdi; Assadian, Nima
2016-02-01
A fourth-order Hamiltonian describing the planar full two body problem is obtained, allowing for a mapping out of the geography of spin-spin-orbit resonances. The expansion of the mutual potential function up to the fourth-order results in the angles to come through one single harmonic and consequently the rotation of both bodies and mutual orbit are coupled. Having derived relative equilibria, stability analysis showed that the stability conditions are independent of physical and orbital characteristics. Simultaneously chaotic motion of bodies is investigated through the Chirikov diffusion utilizing geographic information of the complete resonances. The results show that simultaneous chaos among the binary asteroids is not expected to be prevalent due to the mass distribution of primary in compare with secondary. If mass distribution of bodies is of the same order, simultaneous chaos and global instability are achievable.
47 CFR 51.711 - Symmetrical reciprocal compensation.
Code of Federal Regulations, 2012 CFR
2012-10-01
... 47 Telecommunication 3 2012-10-01 2012-10-01 false Symmetrical reciprocal compensation. 51.711 Section 51.711 Telecommunication FEDERAL COMMUNICATIONS COMMISSION (CONTINUED) COMMON CARRIER SERVICES... Traffic § 51.711 Symmetrical reciprocal compensation. (a) Rates for transport and termination of...
The unsuitability of ellipsoids as test cases for line-source methods
NASA Astrophysics Data System (ADS)
Hess, J. L.
1985-04-01
The fact that the axisymmetric flow about a prolate spheroid can be obtained through the superposition of a uniform stream and the flow due to a linearly varying line source between the foci, can be derived from first principles by equating to zero the combined stream function of the uniform stream and the line source. The prolate spheroid furnishes a counter example to the claim that axial source distributions can only represent thin boides, since prolate spheroids can also be represented exactly up to a thickness ratio of unity.
Bicriterion seriation methods for skew-symmetric matrices.
Brusco, Michael J; Stahl, Stephanie
2005-11-01
The decomposition of an asymmetric proximity matrix into its symmetric and skew-symmetric components is a well-known principle in combinatorial data analysis. The seriation of the skew-symmetric component can emphasize information corresponding to the sign or absolute magnitude of the matrix elements, and the choice of objective criterion can have a profound impact on the ordering. In this research note, we propose a bicriterion approach for seriation of a skew-symmetric matrix incorporating both sign and magnitude information. Two numerical demonstrations reveal that the bicriterion procedure is an effective alternative to direct seriation of the skew-symmetric matrix, facilitating favourable trade-offs among sign and magnitude information. PMID:16293204
5D non-symmetric gravity and geodesic confinement
NASA Astrophysics Data System (ADS)
Ghosh, Suman; Shankaranarayanan, S.
2013-09-01
This work focuses on an unexplored aspect of non-symmetric geometry where only the off-diagonal metric components along the extra dimension, in a 5-dimensional spacetime, are non-symmetric. We show that the energy densities of the stationary non-symmetric models are similar to that of brane models thereby mimicking the thick-brane scenario. We find that the massive test particles are confined near the location of the brane for both growing and decaying warp factors. This feature is unique to the non-symmetric nature of our model. We have also studied the dynamical models where standard 4D FLRW brane is embedded. Our analysis shows that the non-symmetric terms deconfine energy density at the early universe while automatically confine at late times.