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
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.
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.
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
Ground effect on the pressure distribution on an ellipsoid of rotation immersed in flow
NASA Astrophysics Data System (ADS)
Schmitt, Heiko; Schneider, Gert R.
The steady three-dimensional laminar flow of an incompressible viscous fluid around an ellipsoid of rotation is investigated analytically, with a focus on the case where (1) the ellipsoid axis of rotation forms an angle (alpha) with an infinite ground plane and (2) the flow direction is parallel to the ground plane and to the vertical projection of the rotation axis on the plane. The problem formulation and the numerical solution method are outlined, and results for alpha = 10 deg are presented in graphs. It is found that, near the ground, the ellipsoid is acted on by an additional force directed toward the ground.
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.
Heating distribution comparison between asymmetric and symmetric blunt cones
NASA Technical Reports Server (NTRS)
Stewart, D. A.; Kolodziej, P.
1986-01-01
An experiment was performed to compare the heating distribution between symmetric and asymmetric large-angle blunt cones, with cone angles of 100, 120, and 140 deg. These hot-wall data were obtained from models made from typical thermal protection insulation for proposed aeroassisted orbital transfer vehicles. Experimental data are compared with predictions using a boundary-layer integral matrix procedure with kinetics to determine how well the heating distribution over an asymmetric cone could be approximated using axisymmetric solutions for a cone and spherical segment. In addition, a relationship between the stagnation-point heat-transfer rate and the bow-shock standoff distance for these cones is discussed. The heat-distribution data from the symmetric and asymmetric cones were very similar. Numerical results compared well with the measured wall temperatures at the stagnation point but slightly underpredicted them over the conical portion of the models.
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.
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.
NASA Astrophysics Data System (ADS)
Xu, W. X.; Lv, Z.; Chen, H. S.
2013-02-01
Concrete can be viewed as granular materials at the mesoscopic level. A specific distribution of aggregate particles in boundary layers, known as the wall effect, plays an important role in the mechanical properties and durability of concrete. However, the detailed and systematic experimental and simulated data about the wall effect of concrete is hardly adequate yet. Specially, the modeling study of spherical and two-dimensional (2D) elliptical aggregates distribution for the wall effect has been focused on in previous work, little is known about three-dimensional (3D) ellipsoidal aggregates. In the present work, based on a mesostructure model of concrete, the wall effect of concrete is quantified by configuration parameters such as the volume fraction, the specific surface area and the meaning free spacing of the solid phase. In addition, the influences of ellipsoidal particle size distribution (EPSD), shape and volume fraction (Vf) of ellipsoidal aggregates on the configuration parameters are evaluated by stereological methods and serial section analysis technique. Furthermore, the effect mechanisms of EPSD, shape and Vf are analyzed and discussed in this paper. The reliability of the statistical results is verified by experimental data and theoretical analytical results.
Low energy ion distribution measurements in Madison Symmetric Torus plasmas
NASA Astrophysics Data System (ADS)
Titus, J. B.; Mezonlin, E. D.; Johnson, J. A.
2014-06-01
Charge-exchange neutrals contain information about the contents of a plasma and can be detected as they escape confinement. The Florida A&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).
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)
Cylindrically symmetric distributions of matter taking into account pressure
Dandash, N.F.
1986-06-01
This paper considers a non-steady-state cosmological field for describing the distribution of matter with nonzero pressure; the assumption of cylindrical symmetry is taken into consideration. A new class of non-steady-state solutions to the Einstein equations is found. A homogeneous, anisotropic universe and an analog of the Schwarzschild solution are considered as particular cases. The obtained results can be used for describing cylindrical regions in the universe, especially in the vicinity of linear mass ejection from galaxies and quasars and linear super-large-scale structures.
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.
NASA Astrophysics Data System (ADS)
Tóth, László; Goto, Kentaro; Matsuda, Hiroyuki; Matsui, Fumihiko; Daimon, Hiroshi
2011-08-01
We propose a Display-type Ellipsoidal Mesh Analyzer (DELMA) using a newly developed 1π sr wide acceptance angle electrostatic lens (WAAEL), energy aperture and some other electrostatic lenses [1-5]. It can display two-dimensional angular distributions of charged particles within the acceptance angle of ±60°, which is much larger than the largest acceptance angle range so far and comparable to the display-type spherical mirror analyzer (DIANA) developed by Daimon et al. [6,8-11]. It also has a focusing capability with 5 times magnification and ˜30 μm lateral resolution. The relative energy resolution is typically from 2 to 5×10-3 depending on the emission area of the sample, as well as on the diameter of energy aperture.Because this new analyzer has a function of low-magnification photoemission electron microscope, this instrument will be extended and applied as a new type Stereo-PEEM [7] in near future.
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.
THE AXISYMMETRIC CASE FOR THE POST-NEWTONIAN DEDEKIND ELLIPSOIDS
Guerlebeck, Norman; Petroff, David E-mail: D.Petroff@tpi.uni-jena.d
2010-10-20
We consider the post-Newtonian approximation for the Dedekind ellipsoids in the case of axisymmetry. The approach taken by Chandrasekhar and Elbert excludes the possibility of finding a uniformly rotating (deformed) spheroid in the axially symmetric limit, though the solution exists at the point of axisymmetry. We consider an extension to their work that permits the possibility of such a limit.
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.
The Stokes problem for the ellipsoid using ellipsoidal kernels
NASA Technical Reports Server (NTRS)
Zhu, Z.
1981-01-01
A brief review of Stokes' problem for the ellipsoid as a reference surface is given. Another solution of the problem using an ellipsoidal kernel, which represents an iterative form of Stokes' integral, is suggested with a relative error of the order of the flattening. On studying of Rapp's method in detail the procedures of improving its convergence are discussed.
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.
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.
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.
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.
Absorbed fractions for electrons in ellipsoidal volumes.
Amato, E; Lizio, D; Baldari, S
2011-01-21
We applied a Monte Carlo simulation in Geant4 in order to calculate the absorbed fractions for monoenergetic electrons in the energy interval between 10 keV and 2 MeV, uniformly distributed in ellipsoids made from soft tissue. For each volume, we simulated a spherical shape, four oblate and four prolate ellipsoids, and one scalene shape. For each energy and for every geometrical configuration, an analytical relationship between the absorbed fraction and a 'generalized radius' was found, and the dependence of the fit parameters from electron energy is discussed and fitted by proper parametric functions. With the proposed formulation, the absorbed fraction for electrons in the 10-2000 keV energy range can be calculated for all volumes and for every ellipsoidal shape of practical interest. This method can be directly applied to evaluation of the absorbed fraction from the radionuclide emission of monoenergetic electrons, such as Auger or conversion electrons. The average deposited energy per disintegration in the case of extended beta spectra can be evaluated through integration. Two examples of application to a pure beta emitter such as (90)Y and to (131)I, whose emission include monoenergetic and beta electrons plus gamma photons, are presented. This approach represent a generalization of our previous studies, allowing a comprehensive treatment of absorbed fractions from electron and photon sources uniformly distributed in ellipsoidal volumes of any ellipticity and volume, in the whole range of practical interest for internal dosimetry in nuclear medicine applications, as well as in radiological protection estimations of doses from an internal contamination.
Absorbed fractions for electrons in ellipsoidal volumes
NASA Astrophysics Data System (ADS)
Amato, E.; Lizio, D.; Baldari, S.
2011-01-01
We applied a Monte Carlo simulation in Geant4 in order to calculate the absorbed fractions for monoenergetic electrons in the energy interval between 10 keV and 2 MeV, uniformly distributed in ellipsoids made from soft tissue. For each volume, we simulated a spherical shape, four oblate and four prolate ellipsoids, and one scalene shape. For each energy and for every geometrical configuration, an analytical relationship between the absorbed fraction and a 'generalized radius' was found, and the dependence of the fit parameters from electron energy is discussed and fitted by proper parametric functions. With the proposed formulation, the absorbed fraction for electrons in the 10-2000 keV energy range can be calculated for all volumes and for every ellipsoidal shape of practical interest. This method can be directly applied to evaluation of the absorbed fraction from the radionuclide emission of monoenergetic electrons, such as Auger or conversion electrons. The average deposited energy per disintegration in the case of extended beta spectra can be evaluated through integration. Two examples of application to a pure beta emitter such as 90Y and to 131I, whose emission include monoenergetic and beta electrons plus gamma photons, are presented. This approach represent a generalization of our previous studies, allowing a comprehensive treatment of absorbed fractions from electron and photon sources uniformly distributed in ellipsoidal volumes of any ellipticity and volume, in the whole range of practical interest for internal dosimetry in nuclear medicine applications, as well as in radiological protection estimations of doses from an internal contamination.
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.
Violent relaxation of ellipsoidal clouds
NASA Astrophysics Data System (ADS)
Benhaiem, David; Sylos Labini, Francesco
2015-04-01
An isolated, initially cold and ellipsoidal cloud of self-gravitating particles represents a relatively simple system in which to study the effects of deviations from spherical symmetry in the mechanism of violent relaxation. Initial deviations from spherical symmetry are shown to play a dynamical role that is equivalent to that of density fluctuations in the case of an initially spherical cloud. Indeed, these deviations control the amount of particle-energy change and thus determine the properties of the final energy distribution, particularly the appearance of two species of particles: bound and free. Ejection of mass and energy from the system, together with the formation of a density profile decaying as ρ(r) ˜ r-4 and a Keplerian radial velocity dispersion profile, are prominent features similar to those observed after the violent relaxation of spherical clouds. In addition, we find that ejected particles are characterized by highly non-spherical shapes, the features of which can be traced in the initial deviations from spherical symmetry that are amplified during the dynamical evolution: particles can indeed form anisotropic configurations, like bars and/or discs, even though the initial cloud was very close to spherical.
NASA Astrophysics Data System (ADS)
Kuang, Z.
2010-12-01
Spectral analyses of sub-seasonal variations of tropical convection revealed features such as convectively coupled equatorial waves (CCEW) and the Madden-Julian Oscillations (MJO) over a red noise background. In this work, the super-parameterized Community Atmosphere Model (SPCAM) is used in aquaplanet experiments forced with zonally symmetric sea surface temperature distributions to investigate the roles of various processes in shaping the tropical spectra. Control experiments with the SPCAM model were able to produce the red noise background spectrum, CCEWs, and in some Intertropical Convergence Zone (ITCZ) configurations, “MJO-like” disturbances. To unravel the roles of various processes, experiments with simplified dynamics/settings are performed. In experiments where the large-scale dynamics in the model is largely linearized and with no feedbacks from radiative heating or surface sensible/latent heat and momentum fluxes, the spectra of large-scale tropical convectively coupled transients are dominated by the CCEWs, in ways generally consistent with results from the simple model of Andersen and Kuang (2008), and there are no red noise background spectra. Additional experiments show that the red noise aspect of the spectrum is mostly due to eddy stirring of the moisture field across its meridional gradient at the edge of the ITCZ, in particular the deep dry intrusions from the subtropics to the tropics. We will also discuss the effects of surface friction and idealized moist static energy sources, and use a simple model to understand these behaviors. It is hoped that through these and additional idealized studies, the various mechanisms that shape the tropical spectra can be elucidated. Ref:Andersen, J. A., Z. Kuang, A toy model of the instability in the equatorially trapped convectively coupled waves on the equatorial beta plane, Journal of Atmospheric Sciences, 65, 3736-3757, (2008)
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)
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.
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.
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.
NASA Technical Reports Server (NTRS)
Mishchenko, Michael I.
1993-01-01
Rigorously light scattering by size-shape distributions of randomly oriented axially symmetric particles are calculated by the T-matrix method, as extended to randomly oriented scatterers. The computational scheme is described along with a newly developed convergence procedure that makes it possible to substantially reduce computer time and storage requirements. The elements of the Stokes scattering matrix for a power-law size distribution of randomly oriented moderately aspherical spheroids are shown to be much smoother than and differ substantially from those of equivalent monodisperse spheroids; averaging over orientations does not eliminate the necessity of averaging over particle sizes. The angular-scattering behavior of the ensembles of nonspherical particles is found to be significantly different from that of the equivalent polydisperse spheres.
NASA Astrophysics Data System (ADS)
Cerkaski, M.
2009-10-01
The Cartan model of SO(3)/SO(2) matrices is applied to reduce the rotational degrees of freedom on coadjoint orbits of u∗(3) Poisson algebra. The seven-dimensional Poisson algebra uSO(3) obtained by SO(3) reduction in u∗(3) algebra is found and canonical parametrization of u∗(3) orbits [p1,p2,p3]∗ is studied. The structure of bands formed by so-called families of S and P ellipsoids obtained by searching extremes of many-body SO(3) invariant Hamiltonians is investigated. The reduced four-dimensional system of equations of motion describing the simple schematic Hamiltonian based on the volume conservation is presented. A new set of canonical coordinates regarding the separation of motion for independent modes is found with the help of the Jacobi approach. Bohr-Somerfield quantization of new momentum space is studied.
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.
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. PMID:27413598
Cerkaski, M.
2009-10-15
The Cartan model of SO(3)/SO(2) matrices is applied to reduce the rotational degrees of freedom on coadjoint orbits of u*(3) Poisson algebra. The seven-dimensional Poisson algebra u{sub SO}(3) obtained by SO(3) reduction in u*(3) algebra is found and canonical parametrization of u*(3) orbits [p{sub 1},p{sub 2},p{sub 3}]{sub *} is studied. The structure of bands formed by so-called families of S and P ellipsoids obtained by searching extremes of many-body SO(3) invariant Hamiltonians is investigated. The reduced four-dimensional system of equations of motion describing the simple schematic Hamiltonian based on the volume conservation is presented. A new set of canonical coordinates regarding the separation of motion for independent modes is found with the help of the Jacobi approach. Bohr-Somerfield quantization of new momentum space is studied.
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.
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
Kuznetsov, Alexey A.; Nita, Gelu M.; Fleishman, Gregory D.
2011-12-01
Microwave emission of solar flares is formed primarily by incoherent gyrosynchrotron radiation generated by accelerated electrons in coronal magnetic loops. The resulting emission depends on many factors, including pitch-angle distribution of the emitting electrons and the source geometry. In this work, we perform systematic simulations of solar microwave emission using recently developed tools (GS Simulator and fast gyrosynchrotron codes) capable of simulating maps of radio brightness and polarization as well as spatially resolved emission spectra. A three-dimensional model of a symmetric dipole magnetic loop is used. We compare the emission from isotropic and anisotropic (of loss-cone type) electron distributions. We also investigate effects caused by inhomogeneous distribution of the emitting particles along the loop. It is found that the effect of the adopted moderate electron anisotropy is the most pronounced near the footpoints and it also depends strongly on the loop orientation. Concentration of the emitting particles at the looptop results in a corresponding spatial shift of the radio brightness peak, thus reducing effects of the anisotropy. The high-frequency ({approx}> 50 GHz) emission spectral index is specified mainly by the energy spectrum of the emitting electrons; however, at intermediate frequencies (around 10-20 GHz), the spectrum shape is strongly dependent on the electron anisotropy, spatial distribution, and magnetic field nonuniformity. The implications of the obtained results for the diagnostics of the energetic electrons in solar flares are discussed.
Focusing of electromagnetic radiation by hyperboloidal and ellipsoidal lenses
NASA Astrophysics Data System (ADS)
Varga, Peter
2002-08-01
A solution to the problem of plane electromagnetic waves focused by an ellipsoidal or a hyperboloidal lens is derived from the Stratton-Chu integral by solving a boundary-value problem. The current method is more rigorous than those hitherto published in the literature. Results show that for linearly polarized incident illumination and in the vicinity of the focus, the distribution of the time-averaged electric energy density is almost fully transverse electric.
Focusing of electromagnetic radiation by hyperboloidal and ellipsoidal lenses.
Varga, Peter
2002-08-01
A solution to the problem of plane electromagnetic waves focused by an ellipsoidal or a hyperboloidal lens is derived from the Stratton-Chu integral by solving a boundary-value problem. The current method is more rigorous than those hitherto published in the literature. Results show that for linearly polarized incident illumination and in the vicinity of the focus, the distribution of the time-averaged electric energy density is almost fully transverse electric.
Sherley, James L
2013-11-01
A total of eight cellular alterations associated with human carcinogenesis have been framed as the 'hallmarks of cancer'. This representation overlooks a ninth hallmark of cancer: the requirement for tumor-originating distributed stem cells to shift sufficiently from asymmetric to symmetric self-renewal kinetics for attainment of the high cell production rate necessary to form clinically significant tumors within a human lifespan. Overlooking this ninth hallmark costs opportunities for discovery of more selective molecular targets for development of improved cancer therapeutics and missing cancer stem cell biomarkers of greater specificity. Here, the biological basis for the ninth hallmark of cancer is considered toward highlighting its importance in human carcinogenesis and, as such, its potential for revealing unique molecules for targeting cancer diagnostics and therapeutics.
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.
Twofold symmetric angular distributions in multiphoton ionization with elliptically polarized light
Basile, S.; Trombetta, F.; Ferrante, G.
1988-11-21
The angular distributions of electrons in multiphoton multichannel ionization of hydrogen for the case of elliptically polarized laser light are calculated within a nonperturbative theoretical model taking into account the Coulomb interaction in the final state. It is found that the ellipticity of the radiation not only modifies the shape but also lowers the fourfold rotational symmetry occurring in linear polarization to a twofold one.
NASA Astrophysics Data System (ADS)
Pavlov, A. I.
1983-02-01
The limit distribution of the number of solutions of the equation x^k = a as n \\to \\infty is investigated for a fixed integer k \\geq 2, where a is in the symmetric group S_n of degree n.Bibliography: 2 titles.
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.
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.
Ellipsoidal Guaranteed Estimation Method for Satellite Collision Avoidance
NASA Astrophysics Data System (ADS)
Kim, Y.; Lee, J.; Ovseevich, A.
2012-01-01
The article represents a new guaranteed approach to determine a small area of deviations around Earth orbiting satellite nominal Keplerian orbit position, caused by a set of acting external disturbing forces and initial conditions. Only very restricted information is assumed about the disturbances: maximum values with no assumptions about the law of their distribution of probability density. The area of satellite deviations achievability is approximated by a state vector ellipsoid that can include satellite position and the velocity as the vector components. Mathematical equations that allow one to find the ellipsoid are developed on the base of linear Euler-Hill equations of satellite orbital motion. The approach can be considered and applied to various problems of satellite collision avoidance with other satellite or space debris, as well as for establishing potentially safe space traffic control norms. In particular, in CSA it is considering for planning collision avoidance manoeuvres of Earth observation satellite family RADARSAT, SCISAT and newly developing satellites. Originally general approach of ellipsoidal estimation was developed by Russian scientist academician .F. Chernousko. Considered in the article problem was studied by his followers and some of them participated in the method development together with the founder.
The octapolic ellipsoidal term in magnetoencephalography
NASA Astrophysics Data System (ADS)
Dassios, George; Hadjiloizi, Demetra; Kariotou, Fotini
2009-01-01
The forward problem of magnetoencephalography (MEG) in ellipsoidal geometry has been studied by Dassios and Kariotou ["Magnetoencephalography in ellipsoidal geometry," J. Math. Phys. 44, 220 (2003)] using the theory of ellipsoidal harmonics. In fact, the analytic solution of the quadrupolic term for the magnetic induction field has been calculated in the case of a dipolar neuronal current. Nevertheless, since the quadrupolic term is only the leading nonvanishing term in the multipole expansion of the magnetic field, it contains not enough information for the construction of an effective algorithm to solve the inverse MEG problem, i.e., to recover the position and the orientation of a dipole from measurements of the magnetic field outside the head. For this task, the next multipole of the magnetic field is also needed. The present work provides exactly this octapolic contribution of the dipolar current to the expansion of the magnetic induction field. The octapolic term is expressed in terms of the ellipsoidal harmonics of the third degree, and therefore it provides the highest order terms that can be expressed in closed form using long but reasonable analytic and algebraic manipulations. In principle, the knowledge of the quadrupolic and the octapolic terms is enough to solve the inverse problem of identifying a dipole inside an ellipsoid. Nevertheless, a simple inversion algorithm for this problem is not yet known.
Asteroid lightcurve inversion using Lommel-Seeliger ellipsoids
NASA Astrophysics Data System (ADS)
Muinonen, K.; Wilkman, O.; Wang, X.; Cellino, A.
2014-07-01
The rotational period, pole orientation, and convex three-dimensional shape of an asteroid can be derived from photometric lightcurves observed in a number of apparitions with varying illumination and observation geometries (e.g., Kaasalainen et al. 2001, Torppa et al. 2008, Durech et al. 2009). It is customary to estimate the rotational period with a simplified shape model and a small number of trial pole orientations. Once the period is available, the pole orientation can be refined with a general convex shape model represented by the spherical harmonics expansion for the Gaussian surface density. Once the Gaussian surface density is available, the actual convex shape is constructed as a solution of the Minkowski problem. We focus on the initial derivation of the rotational period and pole orientation with the help of the Lommel-Seeliger ellipsoid (LS-ellipsoid), a triaxial ellipsoid with a Lommel-Seeliger surface scattering law. The disk-integrated photometric brightness for the LS-ellipsoid is available in a closed form (Muinonen and Lumme, in preparation), warranting efficient direct computation of lightcurves. With modern computers and the LS-ellipsoid, the rotation period, pole orientation, and ellipsoidal shape can be derived, in principle, simultaneously (see Cellino et al., present meeting). However, here we choose to proceed systematically as follows. First, the rotation period is scanned systematically across its relevant range with a resolution of P_0^2/2T dictated by a tentative period estimate P_0 and the time interval spanned by the photometric data T. This is typically carried out for a small number of pole orientations distributed uniformly on a unit sphere. For each pole orientation, the ellipsoid pole orientation, rotational phase, and axial ratios are optimized with the help of the Nelder-Mead downhill simplex method. Although the shape optimization can suffer from getting stuck in local minima, overall, the rotation period is fairly accurately
Diffusion of Ellipsoids in Bacterial Suspensions.
Peng, Yi; Lai, Lipeng; Tai, Yi-Shu; Zhang, Kechun; Xu, Xinliang; Cheng, Xiang
2016-02-12
Active fluids such as swarming bacteria and motile colloids exhibit exotic properties different from conventional equilibrium materials. As a peculiar example, a spherical tracer immersed inside active fluids shows an enhanced translational diffusion, orders of magnitude stronger than its intrinsic Brownian motion. Here, rather than spherical tracers, we investigate the diffusion of isolated ellipsoids in a quasi-two-dimensional bacterial bath. Our study shows a nonlinear enhancement of both translational and rotational diffusions of ellipsoids. More importantly, we uncover an anomalous coupling between particles' translation and rotation that is strictly prohibited in Brownian diffusion. The coupling reveals a counterintuitive anisotropic particle diffusion, where an ellipsoid diffuses fastest along its minor axis in its body frame. Combining experiments with theoretical modeling, we show that such an anomalous diffusive behavior arises from the generic straining flow of swimming bacteria. Our work illustrates an unexpected feature of active fluids and deepens our understanding of transport processes in microbiological systems.
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.
AirMSPI PODEX Rosamond Ellipsoid Images
Atmospheric Science Data Center
2013-12-13
... Images from the PODEX 2013 Campaign Rosamond target (Rosamond, California) 01/31/2013 Ellipsoid-projected ... central observation tttt: Target name aaa: Mean viewing angle (reported to the ...
Primary fabric ellipsoids in sandstones: implications for depositional processes and strain analysis
NASA Astrophysics Data System (ADS)
Paterson, Scott R.; Yu, Hao
1994-04-01
When measuring strains in deformed clastic rocks, geologists usually assume one or more of the following: (1) objects were initially circular; (2) objects were initially non-circular but had uniform orientations; (3) object populations initially had a fabric, but that this fabric had a symmetrical relationship to bedding; or that (4) initial fabrics are recognizable even after straining. To evaluate these assumptions, we measured 43 fabric ellipsoids in non-strained, poorly sorted sandstones from four depositional settings: DSDP core 174 (fan and abyssal plain deposits off the coast of Oregon); the Cretaceous Great Valley sequence, California (fore-arc deposits): the Cretaceous Pigeon Point Formation, California (accreted and slumped turbidites); and crossbedded sandstones from intracontinental basins in California and Australia. Our results indicate the following: (1) in two-dimensional cuts, individual grains have variable but usually small axial ratios (<3/1) and grains with larger axial ratios are more often, but not always, oriented at small angles to bedding; (2) averaged ratios and orientations of populations of grains in three dimensions define non-spherical fabric ellipsoids, but with small axial ratios (average principal ratios = 1.31:1.14:1); (3) these fabric ellipsoids show a wide range of shapes; and (4) orientations of fabric ellipsoid XY planes have highly variable orientations and are not parallel to bedding or cross-bedding. These results indicate that fabric ellipsoids measured in deformed sandstones must be corrected for the presence of primary fabrics when attempting to calculate strains. However, because of the variable orientations and shapes of the primary fabric ellipsoids and lack of relationship to bedding, strains can, at best, only be bracketed by multiplying final ellipsoids measured in strained samples by reciprocal primary fabric ellipsoids having a variety of orientations and shapes. These data and microstructures in grains and
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.
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.
Cellular dosimetry of diagnostic radionuclides for spherical and ellipsoidal geometry
NASA Astrophysics Data System (ADS)
Nettleton, Jo S.; Lawson, Richard S.
1996-09-01
Radionuclides which emit Auger electrons are widely used in diagnostic nuclear medicine. Studies have shown possible uptake of these in developing germ cells within the testes. In addition, mature sperm within the reproductive tract may be subject to uptake of radionuclides from the circulating blood pool. Though much work has been carried out concerning cellular dosimetry applied to spherical sources, such an approach may lead to significant errors when considering spermatids and spermatozoa, which are almost ellipsoidal in shape (with the long axis twice the short). A numerical method for determining geometrical reduction factors has been developed and used in conjunction with experimentally determined range - energy relationships for electrons, to determine dose gradients and S factors for homogeneous distributions of four commonly used diagnostic radionuclides (, , and ) throughout source regions of both spherical and ellipsoidal geometry at typical cellular dimensions. The results indicate that assumption of spherical geometry is acceptable when determining S factors for late-type germ cells, but introduces error into calculations of dose distribution towards the edge of the cell.
Inertial modes in a rotating triaxial ellipsoid
Vantieghem, S.
2014-01-01
In this work, we present an algorithm that enables computation of inertial modes and their corresponding frequencies in a rotating triaxial ellipsoid. The method consists of projecting the inertial mode equation onto finite-dimensional bases of polynomial vector fields. It is shown that this leads to a well-posed eigenvalue problem, and hence, that eigenmodes are of polynomial form. Furthermore, these results shed new light onto the question whether the eigenmodes form a complete basis, i.e. whether any arbitrary velocity field can be expanded in a sum of inertial modes. Finally, we prove that two intriguing integral properties of inertial modes in rotating spheres and spheroids also extend to triaxial ellipsoids. PMID:25104908
ABJM on ellipsoid and topological strings
NASA Astrophysics Data System (ADS)
Hatsuda, Yasuyuki
2016-07-01
It is known that the large N expansion of the partition function in ABJM theory on a three-sphere is completely determined by the topological string on local Hirzebruch surface {F}_0 . In this note, we investigate the ABJM partition function on an ellipsoid, which has a conventional deformation parameter b. Using 3d mirror symmetry, we find a remarkable relation between the ellipsoid partition function for b 2 = 3 (or b 2 = 1 /3) in ABJM theory at k = 1 and a matrix model for the topological string on another CalabiYau threefold, known as local {P}^2 . As in the case of b = 1, we can compute the full large N expansion of the partition function in this case. This is the first example of the complete large N solution in ABJM theory on the squashed sphere. Using the obtained results, we also analyze the supersymmetric Rényi entropy.
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
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.
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 polarizable ellipsoidal force field for halogen bonds.
Du, Likai; Gao, Jun; Bi, Fuzhen; Wang, Lili; Liu, Chengbu
2013-09-01
The anisotropic effects and short-range quantum effects are essential characters in the formation of halogen bonds. Since there are an array of applications of halogen bonds and much difficulty in modeling them in classical force fields, the current research reports solely the polarizable ellipsoidal force field (PEff) for halogen bonds. The anisotropic charge distribution was represented with the combination of a negative charged sphere and a positively charged ellipsoid. The polarization energy was incorporated by the induced dipole model. The resulting force field is "physically motivated," which includes separate, explicit terms to account for the electrostatic, repulsion/dispersion, and polarization interaction. Furthermore, it is largely compatible with existing, standard simulation packages. The fitted parameters are transferable and compatible with the general AMBER force field. This PEff model could correctly reproduces the potential energy surface of halogen bonds at MP2 level. Finally, the prediction of the halogen bond properties of human Cathepsin L (hcatL) has been found to be in excellent qualitative agreement with the cocrystal structures.
Expansion of the gravitational potential in triaxial ellipsoidal harmonics
NASA Astrophysics Data System (ADS)
Panou, G.; Delikaraoglou, D.
2012-04-01
Spherical harmonics have been extensively used in geodesy because they are relatively simple and the shape of the earth is nearly spherical. However, since the shape of the earth is closer to an ellipsoid of revolution, spheroidal harmonics have also been used. In modern geodesy, the triaxial ellipsoid as a generalization of the ellipsoid of revolution will have a significant role to play in studying the figure of the earth. In the era of outer space explorations, small bodies of the solar system are becoming the target of current and forthcoming space missions. These bodies have irregular shapes and the triaxial ellipsoid, being a genuine three-dimensional shape, provides a very good approximation. Thus, it might be expected that ellipsoidal harmonics, which are defined in a way similar to that of the spheroidal harmonics, would be even more suitable for the representation of the gravitational field of the earth, asteroids and comets. The purpose of the presentation is to discuss the theory of ellipsoidal harmonics and the basic background required to solve Dirichlet's boundary-value problem for a triaxial ellipsoid. We introduce triaxial ellipsoidal coordinates and we express Laplace's equation in these coordinates. By applying the method of separation of variables to Laplace's equation, the solution is obtained by solving Lamé's differential equation. For this reason, we present Lamé's functions in some detail. Using these functions, we formulate the ellipsoidal harmonics expansion of the gravitational potential in the exterior of a triaxial ellipsoid. Also, we show that the spherical and spheroidal harmonics can be produced as degenerated cases of the ellipsoidal harmonics. In spite of the fact that ellipsoidal harmonics are more complicated than spherical or spheroidal harmonics, they can be used in certain special cases which nevertheless are important, such as in modeling, for instance, the gravity field of a level triaxial ellipsoid.
Nonlinear neutral inclusions: assemblages of coated ellipsoids
Bolaños, Silvia Jiménez; Vernescu, Bogdan
2015-01-01
The problem of determining nonlinear neutral inclusions in (electrical or thermal) conductivity is considered. Neutral inclusions, inserted in a matrix containing a uniform applied electric field, do not disturb the field outside the inclusions. The well-known Hashin-coated sphere construction is an example of a neutral inclusion. In this paper, we consider the problem of constructing neutral inclusions from nonlinear materials. In particular, we discuss assemblages of coated ellipsoids. The proposed construction is neutral for a given applied field. PMID:26064633
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.
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.
The Hamiltonian description of incompressible fluid ellipsoids
Morrison, P.J. Lebovitz, Norman R.; Biello, Joseph A.
2009-08-15
We construct the noncanonical Poisson bracket associated with the phase space of first order moments of the velocity field and quadratic moments of the density of a fluid with a free-boundary, constrained by the condition of incompressibility. Two methods are used to obtain the bracket, both based on Dirac's procedure for incorporating constraints. First, the Poisson bracket of moments of the unconstrained Euler equations is used to construct a Dirac bracket, with Casimir invariants corresponding to volume preservation and incompressibility. Second, the Dirac procedure is applied directly to the continuum, noncanonical Poisson bracket that describes the compressible Euler equations, and the moment reduction is applied to this bracket. When the Hamiltonian can be expressed exactly in terms of these moments, a closure is achieved and the resulting finite-dimensional Hamiltonian system provides exact solutions of Euler's equations. This is shown to be the case for the classical, incompressible Riemann ellipsoids, which have velocities that vary linearly with position and have constant density within an ellipsoidal boundary. The incompressible, noncanonical Poisson bracket differs from its counterpart for the compressible case in that it is not of Lie-Poisson form.
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.
On a plasmon resonance in ellipsoidal nanoparticles
Oraevsky, A A; Oraevsky, Anatolii N
2002-01-31
The dependence of the plasmon resonance frequency of metal ellipsoids of revolution on their eccentricity is calculated. The plasmon resonance shifts to the red with increasing eccentricity and its intensity increases. The resonance intensity increases with decreasing the imaginary part of the dielectric constant of a metal. The plasmon resonance frequency in a suspension of randomly oriented prolate nanoparticles (with a large eccentricity) almost exactly coincides with that in a suspension of oriented particles. These features permit the efficient improvement of the sensitivity and resolving power of optoacoustic tomography by introducing prolate metal nanoparticles into the region of an object under study. The possibility of plasmon resonance narrowing by introducing metal nanoparticles into an amplifying medium is pointed out. (laser applications and other topics in quantum electronics)
Ellipsoid-conic radiation collector and method
Brunsting, A.; Hogg, W.R.
1980-02-19
Disclosed is a radiation collector apparatus and method primarily for counting and analyzing a flow of dilute particulate material, such as blood cells, sperm cells and the like, through the use of light detection. The radiation collector apparatus comprises a reflector chamber having an ellipsoidal reflector surface with a pair of elipsoidal foci defining a first focus, f11, and second focus, f12, and a second reflector surface with a primary focus, f21, positioned at the same point as focus f12, and a secondary focus, f22. The second reflector surface has the configuration of one of the conic sections of revolution. In operation the radiation collector apparatus is provided with an intensifed beam of light and a stream of particulate material aligned to intersect the intensifed beam of light at focus f11. Detectable light signals, after two reflections, are received in a focused beam by a photosensitive detector.
Indentation of Ellipsoidal and Cylindrical Elastic Shells
NASA Astrophysics Data System (ADS)
Vella, Dominic; Ajdari, Amin; Vaziri, Ashkan; Boudaoud, Arezki
2012-10-01
Thin shells are found in nature at scales ranging from viruses to hens’ eggs; the stiffness of such shells is essential for their function. We present the results of numerical simulations and theoretical analyses for the indentation of ellipsoidal and cylindrical elastic shells, considering both pressurized and unpressurized shells. We provide a theoretical foundation for the experimental findings of Lazarus et al. [following paper, Phys. Rev. Lett. 109, 144301 (2012)PRLTAO0031-9007] and for previous work inferring the turgor pressure of bacteria from measurements of their indentation stiffness; we also identify a new regime at large indentation. We show that the indentation stiffness of convex shells is dominated by either the mean or Gaussian curvature of the shell depending on the pressurization and indentation depth. Our results reveal how geometry rules the rigidity of shells.
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
NASA Astrophysics Data System (ADS)
Barmenkov, Yu O.; Kir'yanov, A. V.; Pérez-Millán, P.; Cruz, J. L.; Andrés, M. V.
2008-05-01
We report an experimental study of a symmetrically-pumped distributed feed-back (DFB) Erbium-doped fiber laser (EFL) with a tunable phase shift induced in the center of the laser cavity. The tunable phase shift is produced using a magnetostrictive transducer. We demonstrate that lasing is observed in our experimental arrangement at any value of the phase shift that is owing to a noticeable birefringence induced by the latter. The laser wavelength is shown to periodically change with increasing pump power due to the fiber heating, which stems from the Stokes loss, the excited state absorption and Auger up-conversion in Erbium, and high thermal expansion coefficient of the magnetostrictive transducer.
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.
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.
NASA Astrophysics Data System (ADS)
Crisanto-Neto, J. C.; da Luz, M. G. E.; Raposo, E. P.; Viswanathan, G. M.
2016-09-01
In practice, the Lévy α-stable distribution is usually expressed in terms of the Fourier integral of its characteristic function. Indeed, known closed form expressions are relatively scarce given the huge parameters space: 0\\lt α ≤slant 2 ({{L\\'{e}vy}} {{index}}), -1≤slant β ≤slant 1 ({{skewness}}),σ \\gt 0 ({{scale}}), and -∞ \\lt μ \\lt ∞ ({{shift}}). Hence, systematic efforts have been made towards the development of proper methods for analytically solving the mentioned integral. As a further contribution in this direction, here we propose a new way to tackle the problem. We consider an approach in which one first solves the Fourier integral through a formal (thus not necessarily convergent) series representation. Then, one uses (if necessary) a pertinent sum-regularization procedure to the resulting divergent series, so as to obtain an exact formula for the distribution, which is amenable to direct numerical calculations. As a concrete study, we address the centered, symmetric, unshifted and unscaled distribution (β =0, μ =0, σ =1), with α ={α }M=2/M, M=1,2,3\\ldots . Conceivably, the present protocol could be applied to other sets of parameter values.
NASA Astrophysics Data System (ADS)
Crisanto-Neto, J. C.; da Luz, M. G. E.; Raposo, E. P.; Viswanathan, G. M.
2016-09-01
In practice, the Lévy α-stable distribution is usually expressed in terms of the Fourier integral of its characteristic function. Indeed, known closed form expressions are relatively scarce given the huge parameters space: 0\\lt α ≤slant 2 ({{L\\'{e}vy}} {{index}}), -1≤slant β ≤slant 1 ({{skewness}}),σ \\gt 0 ({{scale}}), and -∞ \\lt μ \\lt ∞ ({{shift}}). Hence, systematic efforts have been made towards the development of proper methods for analytically solving the mentioned integral. As a further contribution in this direction, here we propose a new way to tackle the problem. We consider an approach in which one first solves the Fourier integral through a formal (thus not necessarily convergent) series representation. Then, one uses (if necessary) a pertinent sum-regularization procedure to the resulting divergent series, so as to obtain an exact formula for the distribution, which is amenable to direct numerical calculations. As a concrete study, we address the centered, symmetric, unshifted and unscaled distribution (β =0, μ =0, σ =1), with α ={α }M=2/M, M=1,2,3\\ldots . Conceivably, the present protocol could be applied to other sets of parameter values.
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
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.
Simulation of Rings about Ellipsoidal Bodies
NASA Astrophysics Data System (ADS)
Gupta, Akash; Nadkarni-Ghosh, Sharvari; Sharma, Ishan
2016-10-01
Recent discovery of rings around Chariklo, a centaur orbiting the Sun (F. Braga-Ribas et al., 2014) and speculations of rings around minor planet, Chiron (Ortiz et al., 2015), Saturn's satellites, Rhea (Jones et al., 2008; Schenk et al., 2011), Iapetus (Ip, 2006) or exoplanets, suggest that rings about non-spherical bodies is perhaps a more general phenomenon than anticipated. As a first step towards understanding such systems, we examine the dynamical behavior of rings around similar bodies using N-body simulations. Our code employs the `local simulation method' (Wisdom & Tremaine, 1988; Salo, 1995) and accounts for particle interactions via collisions using Discrete Element Method (Cundall & Strack, 1978; Bhateja et al., 2016) and mutual gravitation. The central body has been modeled as an axisymmetric ellipsoid characterized by its axis ratio, or defined via characteristic frequencies (circular, vertical and epicyclic frequency) representing the gravitational field of an axisymmetric body. We vary the central body's characterizing parameter and observe the change in various ring properties like the granular temperature, impact frequency, radial width and vertical thickness. We also look into the effect on ring properties upon variation in the size of the central body-ring system. Further, we investigate the role of characteristic frequencies in dictating the ring dynamics, and how this could help in qualitatively estimating the ring dynamics about any arbitrary central body with symmetry about the equatorial plane and the axis normal to it.
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) ...
NASA Astrophysics Data System (ADS)
Akhmadeev, Albert A.; Salakhov, Myakzyum Kh
2016-10-01
In this work we develop an approach of automatic recognition of ellipsoidal particles on the atomic force microscopy (AFM) image and determination of their size, which is based on image segmentation and the surface approximation by ellipsoids. In addition to the comparative simplicity and rapidity of processing, this method allows us to determine the size of particles, the surface of which is not completely visible on the image. The proposed method showed good results on simulated images including noisy ones. Using this algorithm the size distributions of silica particles on experimental AFM images have been determined.
Thermal analysis of resin composites with ellipsoidal filler considering thermal boundary resistance
NASA Astrophysics Data System (ADS)
Asakuma, Yusuke; Yamamoto, Tsuyoshi
2016-10-01
The effective thermal conductivity of composites with ellipsoidal fillers is analyzed by using a homogenization method that is able to represent the microstructure precisely. In this study, various parameters such as the volume fraction, shape, and distribution of the filler are quantitatively estimated to understand the mechanisms of heat transfer in the composite. First, thermal boundary resistance between resin and filler is important for obtaining composites with higher thermal conductivity. Second, the anisotropy of the effective thermal conductivity arises from contact between filler in the case of ellipsoidal filler and produces lower thermal resistance. Finally, the filler network and thermal resistance are essential for the heat transfer in composites because the path of thermal conduction is improved by contact between neighboring filler particles.
NASA Technical Reports Server (NTRS)
Fu, L. S. W.
1982-01-01
The scattering of a single ellipsoidal inhomogeneity is studied via an eigenstrain approach. The displacement field is given in terms of volume integrals that involve eigenstrains that are related to mismatch in mass density and that in elastic moduli. The governing equations for these unknown eigenstrains are derived. Agreement with other approaches for the scattering problem is shown. The formulation is general and both the inhomogeneity and the host medium can be anisotrophic. The axisymmetric scattering of an ellipsoidal inhomogeneity in a linear elastic isotropic medium is given as an example. The angular and frequency dependence of the scattered displacement field, the differential and total cross sections are formally given in series expansions for the case of uniformly distributed eigenstrains.
Wave-optical assessment of alignment tolerances in nano-focusing with ellipsoidal mirror
NASA Astrophysics Data System (ADS)
Yumoto, Hirokatsu; Koyama, Takahisa; Matsuyama, Satoshi; Yamauchi, Kazuto; Ohashi, Haruhiko
2016-01-01
High-precision ellipsoidal mirrors, which can efficiently focus X-rays to the nanometer dimension with a mirror, have not been realized because of the difficulties in the fabrication process. The purpose of our study was to develop nano-focusing ellipsoidal mirrors in the hard X-ray region. We developed a wave-optical focusing simulator for investigating alignment tolerances in nano-focusing with a designed ellipsoidal mirror, which produce a diffraction-limited focus size of 30 × 35 nm2 in full width at half maximum at an X-ray energy of 7 keV. The simulator can calculate focusing intensity distributions around the focal point under conditions of misalignment. The wave-optical simulator enabled the calculation of interference intensity distributions, which cannot be predicted by the conventional ray-trace method. The alignment conditions with a focal length error of ≲ ±10 µm, incident angle error of ≲ ±0.5 µrad, and in-plane rotation angle error of ≲ ±0.25 µrad must be satisfied for nano-focusing.
Ellipsoidal Polyaspartamide Polymersomes with Enhanced Cell-Targeting Ability.
Lai, Mei-Hsiu; Jeong, Jae Hyun; Devolder, Ross J; Brockman, Christopher; Schroeder, Charles; Kong, Hyunjoon
2012-08-01
Nano-sized polymersomes functionalized with peptides or proteins are being increasingly studied for targeted delivery of diagnostic and therapeutic molecules. Earlier computational studies have suggested that ellipsoidal nanoparticles, compared to spherical ones, display enhanced binding efficiency with target cells, but this has not yet been experimentally validated. We hypothesize that hydrophilic polymer chains coupled to vesicle-forming polymers would result in ellipsoidal polymersomes. In addition, ellipsoidal polymersomes modified with cell adhesion peptides bind with target cells more actively than spherical ones. We examine this hypothesis by substituting polyaspartamide with octadecyl chains and varying numbers of poly(ethylene glycol) (PEG) chains. Increasing the degree of substitution of PEG from 0.5 to 1.0 mol% drives the polymer to self-assemble into an ellipsoidal polymersome with an aspect ratio of 2.1. Further modification of these ellipsoidal polymersomes with peptides containing an Arg-Gly-Asp sequence (RGD peptides) lead to a significant increase in the rate of association and decrease in the rate of dissociation with a substrate coated with αvβ3 integrins. In addition, in a circulation-mimicking flow, the ellipsoidal polymersomes linked with RGD peptides adhere to target tissues more favorably than their spherical equivalents do. Overall, the results of this study will greatly serve to improve the efficiency of targeted delivery of a wide array of polymersomes loaded with various biomedical modalities.
Needlelike motion of prolate ellipsoids in the sea of spheres
NASA Astrophysics Data System (ADS)
Vasanthi, R.; Ravichandran, S.; Bagchi, Biman
2001-05-01
Molecular dynamics simulations of translational motion of isolated prolate ellipsoids in the sea of spheres have been carried out for several different values of the aspect ratio (κ), obtained by changing either the length or the diameter of the ellipsoids, at several different solvent densities. The interaction among the spheres is given by the Lennard-Jones pair potential while that between spheres and ellipsoids is given by a modified Gay-Berne potential. Both the mean-square displacements of the center of mass of the ellipsoids and their orientational time correlation function have been calculated. It is found that at short to intermediate times, the motion of ellipsoids is anisotropic and primarily needlelike—the molecules prefer to move parallel to their long axis. The ratio of these two diffusion constants (D∥ and D⊥) approaches κ, suggesting a decoupling of D∥ from the length of the ellipsoid. The diffusion becomes isotropic in the long time with the total diffusion coefficient given by D∥+2D⊥. The crossover from the anisotropic to the isotropic diffusion is surprisingly sharp and clear in most cases.
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.
Volume of confidence ellipsoid: a technique for quantifying trunk sway during stance.
Kutilek, Patrik; Cakrt, Ondrej; Socha, Vladimir; Hana, Karel
2015-04-01
The position of the trunk can be negatively affected by many diseases. This work focuses on a noninvasive method of quantifying human postural stability and identifying defects in balance and coordination as a result of the nervous system pathology. We used a three-degree-of-freedom orientation tracker (Xsens MTx unit) placed on a patient's trunk and measured three-dimensional (3-D) data (pitch, roll, and yaw) during quiet stance. The principal component analysis was used to analyze the data and to determine the volume of 3-D 95% confidence ellipsoid. Using this method, we were able to model the distribution of the measured 3-D data (pitch, roll, and yaw). Eight patients with degenerative cerebellar disease and eight healthy subjects in this study were measured during stance, with eyes open and eyes closed, and statistical analysis was performed. The results of the new method based on the 3-D confidence ellipsoid show that the volumes related to the patients are significantly larger than the volumes related to the healthy subjects. The concept of confidence ellipsoid volume, although known to the biomechanics community, has not been used before to study the postural balance problems. The method can also be used to study, for example, head and pelvis movements or alignments during stance. PMID:25720031
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.
Thermal analysis of porous medium with ellipsoidal pores using a homogenization method
NASA Astrophysics Data System (ADS)
Asakuma, Yusuke; Yamamoto, Tsuyoshi
2016-10-01
Effective thermal conductivity including radiation is analyzed using a homogenization method. This method can precisely represent the microstructure of a porous medium with ellipsoidal pores. Here, the effects of parameters such as porosity, pore shape, pore distribution, and temperature of the porous medium on the conductivity are estimated to clarify the mechanisms in complex pore structures. For example, heat transfer by radiation does not dominate if the medium has pores of less than 1 mm in size. Moreover, the anisotropy of the effective thermal conductivity is found to depend on temperature, pore shape, pore size, and pore distribution.
Ellipsoid ART and ARTMAP for incremental unsupervised and supervised learning
NASA Astrophysics Data System (ADS)
Anagnostopoulos, Georgios C.; Georgiopoulos, Michael
2001-03-01
We introduce Ellipsoid-ART, EA and Ellipsoid-ARTMAP, EAM as a generalization of Hyper-sphere ART and Hypersphere-ARTMAP respectively. Our novel archetectures are based on ideas rooted on Fuzzy-ART, FA and Fuzzy-ARTMAP, FAM. While FA/FAM summarize input data using hyper-rectangles, EA/EAM utilize hyper-ellipsoids for the same purpose. Due to their learning rules, EA and EAM share virtually all properties and characteristics of their FA/FAM counterparts. Preliminary experimentation implies that EA and EAM are to be viewed as good alternatives to FA and FAM for data clustering and classification tasks. Extensive pseudo-code is provided in the appendices for computationally efficient implementations of EA/EAM training and performance phases.
Chambler, A. F.; Chapman-Sheath, P. J.; Pearse, M. F.; Hollingdale, J.
1997-01-01
Chronic recurrent multifocal osteomyelitis is often confused with symmetrical Brodie's abscess as it has a similar pathogenesis. We report an otherwise healthy 17-year-old boy presenting with a true symmetrical Brodie's abscess. We conclude that a symmetrical Brodie's abscess presenting in an otherwise healthy patient is a separate clinical condition with a different management protocol. Images Figure 1 Figure 2 PMID:9497984
Chambler, A F; Chapman-Sheath, P J; Pearse, M F; Hollingdale, J
1997-10-01
Chronic recurrent multifocal osteomyelitis is often confused with symmetrical Brodie's abscess as it has a similar pathogenesis. We report an otherwise healthy 17-year-old boy presenting with a true symmetrical Brodie's abscess. We conclude that a symmetrical Brodie's abscess presenting in an otherwise healthy patient is a separate clinical condition with a different management protocol.
Ellipsoidal geometry in asteroid thermal models - The standard radiometric model
NASA Technical Reports Server (NTRS)
Brown, R. H.
1985-01-01
The major consequences of ellipsoidal geometry in an othewise standard radiometric model for asteroids are explored. It is shown that for small deviations from spherical shape a spherical model of the same projected area gives a reasonable aproximation to the thermal flux from an ellipsoidal body. It is suggested that large departures from spherical shape require that some correction be made for geometry. Systematic differences in the radii of asteroids derived radiometrically at 10 and 20 microns may result partly from nonspherical geometry. It is also suggested that extrapolations of the rotational variation of thermal flux from a nonspherical body based solely on the change in cross-sectional area are in error.
Underwater shock wave focusing in an ellipsoidal cavity
NASA Astrophysics Data System (ADS)
Takayama, K.; Saito, K.; Obara, T.; Kameshima, N.
1990-07-01
A primary study was made experimentally and numerically of spherical underwater shock wave focusing and high pressure generation in an ellipsoidal cavity. Spherical shock waves were produced by microexplosion of silver azide or PETN of 10 to 100 mg. The ellipsoidal cavity has major and minor axes of 700 and 500 mm, respectively. The focused pressure was measured along the major axis by PVDF pressure gauges. By exploding a 100 mg PETN pellet the peak pressure at 8 kbar was obtained near the second focal point. The TVD finite difference numerical simulation was also conducted. Good agreement was obtained between the experiment and simulation.
Stationary solutions for the ellipsoidal BGK model in a slab
NASA Astrophysics Data System (ADS)
Bang, Jeaheang; Yun, Seok-Bae
2016-11-01
We address the boundary value problem for the ellipsoidal BGK model of the Boltzmann equation posed in a bounded interval. The existence of a unique mild solution is established under the assumption that the inflow boundary data does not concentrate too much around the zero velocity, and the gas is sufficiently rarefied.
AirMSPI PODEX LaJolla Ellipsoid Images
Atmospheric Science Data Center
2013-12-13
... Images from the PODEX 2013 Campaign La Jolla target (La Jolla, California) 01/14/2013 Ellipsoid-projected ... central observation tttt: Target name aaa: Mean viewing angle (reported to the ...
Dynamics of ellipsoidal tracers in swimming algal suspensions
NASA Astrophysics Data System (ADS)
Yang, Ou; Peng, Yi; Liu, Zhengyang; Tang, Chao; Xu, Xinliang; Cheng, Xiang
2016-10-01
Enhanced diffusion of passive tracers immersed in active fluids is a universal feature of active fluids and has been extensively studied in recent years. Similar to microrheology for equilibrium complex fluids, the unusual enhanced particle dynamics reveal intrinsic properties of active fluids. Nevertheless, previous studies have shown that the translational dynamics of spherical tracers are qualitatively similar, independent of whether active particles are pushers or pullers—the two fundamental classes of active fluids. Is it possible to distinguish pushers from pullers by simply imaging the dynamics of passive tracers? Here, we investigated the diffusion of isolated ellipsoids in algal C. reinhardtii suspensions—a model for puller-type active fluids. In combination with our previous results on pusher-type E. coli suspensions [Peng et al., Phys. Rev. Lett. 116, 068303 (2016), 10.1103/PhysRevLett.116.068303], we showed that the dynamics of asymmetric tracers show a profound difference in pushers and pullers due to their rotational degree of freedom. Although the laboratory-frame translation and rotation of ellipsoids are enhanced in both pushers and pullers, similar to spherical tracers, the anisotropic diffusion in the body frame of ellipsoids shows opposite trends in the two classes of active fluids. An ellipsoid diffuses fastest along its major axis when immersed in pullers, whereas it diffuses slowest along the major axis in pushers. This striking difference can be qualitatively explained using a simple hydrodynamic model. In addition, our study on algal suspensions reveals that the influence of the near-field advection of algal swimming flows on the translation and rotation of ellipsoids shows different ranges and strengths. Our work provides not only new insights into universal organizing principles of active fluids, but also a convenient tool for detecting the class of active particles.
Olivares, Alberto; Ruiz-Garcia, Gonzalo; Olivares, Gonzalo; Górriz, Juan Manuel; Ramirez, Javier
2013-01-01
Ellipsoid fitting algorithms are widely used to calibrate Magnetic Angular Rate and Gravity (MARG) sensors. These algorithms are based on the minimization of an error function that optimizes the parameters of a mathematical sensor model that is subsequently applied to calibrate the raw data. The convergence of this kind of algorithms to a correct solution is very sensitive to input data. Input calibration datasets must be properly distributed in space so data can be accurately fitted to the theoretical ellipsoid model. Gathering a well distributed set is not an easy task as it is difficult for the operator carrying out the maneuvers to keep a visual record of all the positions that have already been covered, as well as the remaining ones. It would be then desirable to have a system that gives feedback to the operator when the dataset is ready, or to enable the calibration process in auto-calibrated systems. In this work, we propose two different algorithms that analyze the goodness of the distributions by computing four different indicators. The first approach is based on a thresholding algorithm that uses only one indicator as its input and the second one is based on a Fuzzy Logic System (FLS) that estimates the calibration error for a given calibration set using a weighted combination of two indicators. Very accurate classification between valid and invalid datasets is achieved with average Area Under Curve (AUC) of up to 0.98. PMID:24013490
Translational viscous drags of an ellipsoid straddling an interface between two fluids.
Boniello, Giuseppe; Stocco, Antonio; Gross, Michel; In, Martin; Blanc, Christophe; Nobili, Maurizio
2016-07-01
We study the dynamics of individual polystyrene ellipsoids of different aspect ratios trapped at the air-water interface. Using particle tracking and in situ vertical scanning interferometry techniques we are able to measure translational drags and the protrusion in air of the ellipsoids. We report that translational drags on the ellipsoid are unexpectedly enhanced: despite the fact that a noticeable part of the ellipsoid is in air, drags are found larger than the bulk one in water. PMID:27575174
Translational viscous drags of an ellipsoid straddling an interface between two fluids
NASA Astrophysics Data System (ADS)
Boniello, Giuseppe; Stocco, Antonio; Gross, Michel; In, Martin; Blanc, Christophe; Nobili, Maurizio
2016-07-01
We study the dynamics of individual polystyrene ellipsoids of different aspect ratios trapped at the air-water interface. Using particle tracking and in situ vertical scanning interferometry techniques we are able to measure translational drags and the protrusion in air of the ellipsoids. We report that translational drags on the ellipsoid are unexpectedly enhanced: despite the fact that a noticeable part of the ellipsoid is in air, drags are found larger than the bulk one in water.
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)
Effects of dipole magnet inhomogeneities on the beam ellipsoid
Tsoupas, N.; Colman, J.; Levine, M.; McKenzie-Wilson, R.; Ward, T.; Grand, P.
1986-01-01
The RAYTRACE computer code has been modified to accept magnetic fields measured in the median plane of a dipole magnet. This modification allows one to study the effects of a non-ideal dipole magnet on the beam ellipsoid (as defined by the TRANSPORT code manual). The effects on the beam ellipsoid are due to: field inhomogeneities in the interior region of the dipole, and discrepancies from design conditions of the magnetic field values in the fringe field region. The results of the RAYTRACE code calculations based on experimentally measured fields will be compared with the results derived using both an ideal (no inhomogeneities) dipole with SCOFF boundaries and an ideal dipole with perfect (according to design) fringe fields.
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.
Instabilities around a rotating ellipsoid in a stratified fluid
NASA Astrophysics Data System (ADS)
Miquel, Benjamin; Meunier, Patrice; Le Dizes, Stephane
2014-11-01
Geosismic observations have revealed the stacking of horizontal layers of water with different densities in the ocean, particularly above and beneath lens-shaped eddies. We present a simplified model together with an experimental setup to reproduce and identify the mechanism responsible for this layering phenomenon: we consider the stably stratified flow around a rotating, solid ellipsoid. Experimentally, a flat oblate rotating ellipsoid reproduces faithfully the boundary condition of an oceanic eddy, whereas the case of a rotating sphere provides an analytically tractable base flow, suitable for a numerical linear analysis. Two instabilities are witnessed experimentally and numerically. The first instability is the classical, inviscid, strato-inertial instability that tends to develop at the equator of the ellipsoid independently of the value of the Schmidt number. The second instability is localised in the vicinity of the poles and appears only if the Schmidt number differs from one. Hence, this instability is reminiscent of the double-diffusive McIntyre instability, a valuable candidate to explain layering in oceanic eddies. Funded by ANR OLA.
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
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.
Volume monogamy of quantum steering ellipsoids for multiqubit systems
NASA Astrophysics Data System (ADS)
Cheng, Shuming; Milne, Antony; Hall, Michael J. W.; Wiseman, Howard M.
2016-10-01
The quantum steering ellipsoid can be used to visualize 2-qubit states, and thus provides a generalization of the Bloch picture for the single qubit. Recently, a monogamy relation for the volumes of steering ellipsoids has been derived for pure 3-qubit states and shown to be stronger than the celebrated Coffman-Kundu-Wootters inequality. We first demonstrate the close connection between this volume monogamy relation and the classification of pure 3-qubit states under stochastic local operations and classical communication. We then show that this monogamy relation does not hold for general mixed 3-qubit states and derive a weaker monogamy relation that does hold for such states. We also prove a volume monogamy relation for pure 4-qubit states (further conjectured to hold for the mixed case), and generalize our 3-qubit inequality to n qubits. Finally, we study the effect of noise on the quantum steering ellipsoid and find that the volume of any 2-qubit state is nonincreasing when the state is exposed to arbitrary local noise. This implies that any volume monogamy relation for a given class of multiqubit states remains valid under the addition of local noise. We investigate this quantitatively for the experimentally relevant example of isotropic noise.
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
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
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.
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.
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.
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
NASA Astrophysics Data System (ADS)
Dunajewski, Adam; Dusza, Jacek J.; Rosado Muñoz, Alfredo
2014-11-01
The article presents a proposal for the description of human gait as a periodic and symmetric process. Firstly, the data for researches was obtained in the Laboratory of Group SATI in the School of Engineering of University of Valencia. Then, the periodical model - Mean Double Step (MDS) was made. Finally, on the basis of MDS, the symmetrical models - Left Mean Double Step and Right Mean Double Step (LMDS and RMDS) could be created. The method of various functional extensions was used. Symmetrical gait models can be used to calculate the coefficients of asymmetry at any time or phase of the gait. In this way it is possible to create asymmetry, function which better describes human gait dysfunction. The paper also describes an algorithm for calculating symmetric models, and shows exemplary results based on the experimental data.
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.
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.
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.
Dipolar Rings of Microscopic Ellipsoids: Magnetic Manipulation and Cell Entrapment
NASA Astrophysics Data System (ADS)
Martinez-Pedrero, Fernando; Cebers, Andrejs; Tierno, Pietro
2016-09-01
We study the formation and the dynamics of dipolar rings composed by microscopic ferromagnetic ellipsoids, which self-assemble in water by switching the direction of the applied field. We show how to manipulate these fragile structures and control their shape via the application of external static and oscillating magnetic fields. We introduce a theoretical framework which describes the ring deformation under an applied field, allowing us to understand the underlying physical mechanism. Our microscopic rings are finally used to capture, entrap, and later release a biological cell via a magnetic command, i.e., performing a simple operation which can be implemented in other microfluidic devices which make use of ferromagnetic particles.
Eigenmodes of triaxial ellipsoidal acoustical cavities with mixed boundary conditions
NASA Astrophysics Data System (ADS)
Willatzen, M.; Lew Yan Voon, L. C.
2004-12-01
The linear acoustics problem of resonant vibrational modes in a triaxial ellipsoidal acoustic cavity with walls of arbitrary acoustic impedance has been quasi-analytically solved using the Frobenius power-series expansion method. Eigenmode results are presented for the lowest two eigenmodes in cases with pressure-release, rigid-wall, and lossy-wall boundary conditions. A mode crossing is obtained as a function of the specific acoustic impedance of the wall; the degeneracy is not symmetry related. Furthermore, the damping of the wave is found to be maximal near the crossing. .
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.
NASA Astrophysics Data System (ADS)
Yang, Lei Ming
The GEA method is employed to study light scattering by dielectric spheroids and ellipsoids with either fixed or random orientations. A simple formula is obtained for a dielectric ellipsoid. The results from a dielectric spheroid with fixed or random orientations are compared numerically and found to agree well with the T-matrix method for small angle scattering. The numerical results for an ellipsoid are obtained. The validity region for the equal-volume sphere method for a dielectric spheroid and equal-volume spheroid method for a dielectric ellipsoid are also discussed.
Asymptotic solutions for the case of nearly symmetric gravitational lens systems
NASA Astrophysics Data System (ADS)
Wertz, O.; Pelgrims, V.; Surdej, J.
2012-08-01
Gravitational lensing provides a powerful tool to determine the Hubble parameter H0 from the measurement of the time delay Δt between two lensed images of a background variable source. Nevertheless, knowledge of the deflector mass distribution constitutes a hurdle. We propose in the present work interesting solutions for the case of nearly symmetric gravitational lens systems. For the case of a small misalignment between the source, the deflector and the observer, we first consider power-law (ɛ) axially symmetric models for which we derive an analytical relation between the amplification ratio and source position which is independent of the power-law slope ɛ. According to this relation, we deduce an expression for H0 also irrespective of the value ɛ. Secondly, we consider the power-law axially symmetric lens models with an external large-scale gravitational field, the shear γ, resulting in the so-called ɛ-γ models, for which we deduce simple first-order equations linking the model parameters and the lensed image positions, the latter being observable quantities. We also deduce simple relations between H0 and observables quantities only. From these equations, we may estimate the value of the Hubble parameter in a robust way. Nevertheless, comparison between the ɛ-γ and singular isothermal ellipsoid (SIE) models leads to the conclusion that these models remain most often distinct. Therefore, even for the case of a small misalignment, use of the first-order equations and precise astrometric measurements of the positions of the lensed images with respect to the centre of the deflector enables one to discriminate between these two families of models. Finally, we confront the models with numerical simulations to evaluate the intrinsic error of the first-order expressions used when deriving the model parameters under the assumption of a quasi-alignment between the source, the deflector and the observer. From these same simulations, we estimate for the case of the
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.
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
An analytical model for porous single crystals with ellipsoidal voids
NASA Astrophysics Data System (ADS)
Mbiakop, A.; Constantinescu, A.; Danas, K.
2015-11-01
A rate-(in)dependent constitutive model for porous single crystals with arbitrary crystal anisotropy (e.g., FCC, BCC, HCP, etc.) containing general ellipsoidal voids is developed. The proposed model, denoted as modified variational model (MVAR), is based on the nonlinear variational homogenization method, which makes use of a linear comparison porous material to estimate the response of the nonlinear porous single crystal. Periodic multi-void finite element simulations are used in order to validate the MVAR for a large number of parameters including cubic (FCC, BCC) and hexagonal (HCP) crystal anisotropy, various creep exponents (i.e., nonlinearity), several stress triaxiality ratios, general void shapes and orientations and various porosity levels. The MVAR model, which involves a priori no calibration parameters, is found to be in good agreement with the finite element results for all cases considered in the rate-dependent context. The model is then used in a predictive manner to investigate the complex response of porous single crystals in several cases with strong coupling between the anisotropy of the crystal and the (morphological) anisotropy induced by the shape and orientation of the voids. Finally, a simple way of calibrating the MVAR with just two adjustable parameters is depicted in the rate-independent context so that an excellent agreement with the FE simulation results is obtained. In this last case, this proposed model can be thought as a generalization of the Gurson model in the context of porous single crystals and general ellipsoidal void shapes and orientations.
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.
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).
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.
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.
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.
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.
Polynomial shape of an inclined ellipsoid with rotational symmetry about its major axis.
Castañeda-Escobar, Lizbeth A; Malacara-Hernández, Daniel
2006-08-01
We present the approximate polynomial expression for an ellipsoid with rotational symmetry about its major axis, which is on the y-z plane and at angle theta with respect to the z axis. These expressions have many possible useful applications in optics as shown. The main optical properties of these types of inclined ellipsoidal surface will be reviewed.
Liu, Chang; Wang, Guofeng; Xie, Qinglu; Zhang, Yanchao
2014-06-16
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.
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
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.
Finite volume simulations of dynamos in ellipsoidal planets
NASA Astrophysics Data System (ADS)
Ernst-Hullermann, J.; Harder, H.; Hansen, U.
2013-12-01
So far, numerical simulations have mostly considered buoyancy as the driving mechanism of the dynamo process. However, also precession can drive a dynamo, as first suggested by Bullard in 1949. We investigate the properties of precession-driven dynamos in ellipsoidal planets by the use of a finite volume code. In planets, it is much more effective to drive a precessional flow by the pressure differences induced by the topography of the precessing body rather than by viscous coupling to the walls. Numerical simulations are the only method offering the possibility to investigate the influence of the topography since laboratory experiments normally are constrained by the predetermined geometry of the vessel. We discuss how ellipticity of the planets can be included in our simulations by the use of a non-orthogonal grid. Here, we will present some first results and conclude that laminar precession-driven flows can drive kinematic dynamos.
NASA Astrophysics Data System (ADS)
Chen, Yan; Feng, Huijuan; Ma, Jiayao; Peng, Rui; You, Zhong
2016-06-01
The traditional waterbomb origami, produced from a pattern consisting of a series of vertices where six creases meet, is one of the most widely used origami patterns. From a rigid origami viewpoint, it generally has multiple degrees of freedom, but when the pattern is folded symmetrically, the mobility reduces to one. This paper presents a thorough kinematic investigation on symmetric folding of the waterbomb pattern. It has been found that the pattern can have two folding paths under certain circumstance. Moreover, the pattern can be used to fold thick panels. Not only do the additional constraints imposed to fold the thick panels lead to single degree of freedom folding, but the folding process is also kinematically equivalent to the origami of zero-thickness sheets. The findings pave the way for the pattern being readily used to fold deployable structures ranging from flat roofs to large solar panels.
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.
Explicit excluded volume of cylindrically symmetric convex bodies.
Piastra, Marco; Virga, Epifanio G
2015-06-01
We represent explicitly the excluded volume V(e){B(1),B(2)} of two generic cylindrically symmetric, convex rigid bodies, B(1) and B(2), in terms of a family of shape functionals evaluated separately on B(1) and B(2). We show that V(e){B(1),B(2)} fails systematically to feature a dipolar component, thus making illusory the assignment of any shape dipole to a tapered body in this class. The method proposed here is applied to cones and validated by a shape-reconstruction algorithm. It is further applied to spheroids (ellipsoids of revolution), for which it shows how some analytic estimates already regarded as classics should indeed be emended. PMID:26172727
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.
A conditioned visual orientation requires the ellipsoid body in Drosophila.
Guo, Chao; Du, Yifei; Yuan, Deliang; Li, Meixia; Gong, Haiyun; Gong, Zhefeng; Liu, Li
2014-01-01
Orientation, the spatial organization of animal behavior, is an essential faculty of animals. Bacteria and lower animals such as insects exhibit taxis, innate orientation behavior, directly toward or away from a directional cue. Organisms can also orient themselves at a specific angle relative to the cues. In this study, using Drosophila as a model system, we established a visual orientation conditioning paradigm based on a flight simulator in which a stationary flying fly could control the rotation of a visual object. By coupling aversive heat shocks to a fly's orientation toward one side of the visual object, we found that the fly could be conditioned to orientate toward the left or right side of the frontal visual object and retain this conditioned visual orientation. The lower and upper visual fields have different roles in conditioned visual orientation. Transfer experiments showed that conditioned visual orientation could generalize between visual targets of different sizes, compactness, or vertical positions, but not of contour orientation. Rut-Type I adenylyl cyclase and Dnc-phosphodiesterase were dispensable for visual orientation conditioning. Normal activity and scb signaling in R3/R4d neurons of the ellipsoid body were required for visual orientation conditioning. Our studies established a visual orientation conditioning paradigm and examined the behavioral properties and neural circuitry of visual orientation, an important component of the insect's spatial navigation.
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.
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.
Application of polarizable ellipsoidal force field model to pnicogen bonds.
Liu, Fang; Du, Likai; Gao, Jun; Wang, Lili; Song, Bo; Liu, Chengbu
2015-03-15
Noncovalent interactions, such as hydrogen bonds and halogen bonds, are frequently used in drug designing and crystal engineering. Recently, a novel noncovalent pnicogen bonds have been identified as an important driving force in crystal structures with similar bonding mechanisms as hydrogen bond and halogen bond. Although the pnicogen bond is highly anisotropic, the pnicogen bond angles range from 160° to 180° due to the complicated substituent effects. To understand the anisotropic characters of pnicogen bond, a modification of the polarizable ellipsoidal force field (PEff) model previously used to define halogen bonds was proposed in this work. The potential energy surfaces (PESs) of mono- and polysubstituted PH3 -NH3 complexes were calculated at CCSD(T), MP2, and density functional theory levels and were used to examine the modified PEff model. The results indicate that the modified PEff model can precisely characterize pnicogen bond. The root mean squared error of PES obtained with PEff model is less than 0.5 kcal/mol, compared with MP2 results. In addition, the modified PEff model may be applied to other noncovalent bond interactions, which is important to understand the role of intermolecular interactions in the self-assembly structures.
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.
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.
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.
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
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.
Field-enhanced magnetic moment in ellipsoidal nano-hematite
NASA Astrophysics Data System (ADS)
Malik, Vikash; Sen, Somaditya; Gelting, David R.; Gajdardziska-Josifovska, Marija; Schmidt, Marius; Guptasarma, Prasenjit
2014-04-01
Bulk hematite is a canted antiferromagnet at room temperature and displays weak magnetic coercivity above the Morin transition temperature T M ˜ 262 K. Below T M, hematite displays traditional antiferromagnetic behavior, with no net magnetic moment or magnetic hysteresis. Here, we report that ellipsoidal nanocrystals of hematite (ENH) display a significant field-enhanced magnetic moment (FEMM) upon being poled by a magnetic field. This poled moment displays a giant coercive field of nearly 6000 Oe at low temperature. Atomic resolution transmission electron microscopy indicates that the nanocrystals are single crystalline, and that the surfaces are bulk-terminated. The apical terminations include the <001> sets of planes, which are implicated in possible formation of FM-arrangements near the surface. We tentatively suggest that FEMM in ENH could also arise from uncompensated surface spins or a shell of ordered spins oriented and pinned near the surface by a magnetic field. The gradual loss of magnetic moment with increasing temperature could arise as a result of competition between surface pinning energy, and kT. The large coercive field points toward possible applications for ENH in digital magnetic recording.
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
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.
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.
The impact of ellipsoidal particle shape on pebble breakage in gravel
Tuitz, Christoph; Exner, Ulrike; Frehner, Marcel; Grasemann, Bernhard
2012-01-01
We have studied the influence of particle shape and consequently loading configuration on the breakage load of fluvial pebbles. Unfortunately, physical strength tests on pebbles, i.e., point-load tests, can only be conducted under one specific stable loading configuration. Therefore, the physical uniaxial strength tests performed in this study were extended by a two-dimensional finite-element stress analysis, which is capable of investigating those scenarios that are not possible in physical tests. Breakage load, equivalent to that measured in unidirectional physical tests, was determined from the results of the stress analysis by a maximum tensile stress-based failure criterion. Using this assumption, allows the determination of breakage load for a range of different kind of synthetic loading configurations and its comparison with the natural breakage load distribution of the physical strength tests. The results of numerical modelling indicated that the configuration that required the least breakage load corresponded with the minor principal axis of the ellipsoidal pebbles. In addition, most of the simulated gravel-hosted loading configurations exceeded the natural breakage load distribution of fluvial pebbles obtained from the physical strength tests. PMID:26321870
Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation
Yang, Jaw-Yen; Yan, Chin-Yuan; Huang, Juan-Chen; Li, Zhihui
2014-01-01
Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidal-statistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied. PMID:25104904
Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation.
Yang, Jaw-Yen; Yan, Chin-Yuan; Huang, Juan-Chen; Li, Zhihui
2014-08-01
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
Study of electron trapping by a transversely ellipsoidal bubble in the laser wake-field acceleration
Cho, Myung-Hoon; Kim, Young-Kuk; Hur, Min Sup
2013-09-15
We present electron trapping in an ellipsoidal bubble which is not well explained by the spherical bubble model by [Kostyukov et al., Phys. Rev. Lett. 103, 175003 (2009)]. The formation of an ellipsoidal bubble, which is elongated transversely, frequently occurs when the spot size of the laser pulse is large compared to the plasma wavelength. First, we introduce the relation between the bubble size and the field slope inside the bubble in longitudinal and transverse directions. Then, we provide an ellipsoidal model of the bubble potential and investigate the electron trapping condition by numerical integration of the equations of motion. We found that the ellipsoidal model gives a significantly less restrictive trapping condition than that of the spherical bubble model. The trapping condition is compared with three-dimensional particle-in-cell simulations and the electron trajectory in test potential simulations.
MERIDIONAL TILT OF THE STELLAR VELOCITY ELLIPSOID DURING BAR BUCKLING INSTABILITY
Saha, Kanak; Pfenniger, Daniel; Taam, Ronald E.
2013-02-20
The structure and evolution of the stellar velocity ellipsoid play an important role in shaping galaxies undergoing bar-driven secular evolution and the eventual formation of a boxy/peanut bulge such as is present in the Milky Way. Using collisionless N-body simulations, we show that during the formation of such a boxy/peanut bulge, the meridional shear stress of stars, which can be measured by the meridional tilt of the velocity ellipsoid, reaches a characteristic peak in its time evolution. It is shown that the onset of a bar buckling instability is closely connected to the maximum meridional tilt of the stellar velocity ellipsoid. Our findings bring a new insight to this complex gravitational instability of the bar which complements the buckling instability studies based on orbital models. We briefly discuss the observed diagnostics of the stellar velocity ellipsoid during such a phenomenon.
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
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.
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.
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.
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.
{PT}-symmetric optical superlattices
NASA Astrophysics Data System (ADS)
Longhi, Stefano
2014-04-01
The spectral and localization properties of {PT}-symmetric optical superlattices, either infinitely extended or truncated at one side, are theoretically investigated, and the criteria that ensure a real energy spectrum are derived. The analysis is applied to the case of superlattices describing a complex ( {PT}-symmetric) extension of the Harper Hamiltonian in the rational case.
Bimodal symmetric fission observed in the heaviest elements
Hulet, E.K.; Wild, J.F.; Dougan, R.J.; Lougheed, R.W.; Landrum, J.H.; Dougan, A.D.; Schadel, M.; Hahn, R.L.; Baisden, P.A.; Henderson, C.M.
1986-01-27
We measured the mass and kinetic-energy partitioning in the spontaneous fission of /sup 258/Fm, /sup 259/Md, /sup 260/Md, /sup 258/No, and /sup 260/(104). All fissioned with mass distributions that were symmetric. Total-kinetic-energy distributions peaked near either 200 or 235 MeV. Surprisingly, these energy distributions were skewed upward or downward from the peak in each case, except for /sup 260/(104), indicating a composite of two energy distributions. We interpret this as a mixture of liquid-drop-like and fragment-shell directed symmetric fission, although theory had not anticipated this phenomenon.
Design of spherical symmetric gradient index lenses
NASA Astrophysics Data System (ADS)
Miñano, Juan C.; Grabovičkić, Dejan; Benítez, Pablo; González, Juan C.; Santamaría, Asunción
2012-10-01
Spherical symmetric refractive index distributions also known as Gradient Index lenses such as the Maxwell-Fish-Eye (MFE), the Luneburg or the Eaton lenses have always played an important role in Optics. The recent development of the technique called Transformation Optics has renewed the interest in these gradient index lenses. For instance, Perfect Imaging within the Wave Optics framework has recently been proved using the MFE distribution. We review here the design problem of these lenses, classify them in two groups (Luneburg moveable-limits and fixed-limits type), and establish a new design techniques for each type of problem.
Highly-dispersive electromagnetic induced transparency in planar symmetric metamaterials.
Lu, Xiqun; Shi, Jinhui; Liu, Ran; Guan, Chunying
2012-07-30
We propose, design and experimentally demonstrate highly-dispersive electromagnetically induced transparency (EIT) in planar symmetric metamaterials actively switched and controlled by angles of incidence. Full-wave simulation and measurement results show EIT phenomena, trapped-mode excitations and the associated local field enhancement of two symmetric metamaterials consisting of symmetrically split rings (SSR) and a fishscale (FS) metamaterial pattern, respectively, strongly depend on angles of incidence. The FS metamaterial shows much broader spectral splitting than the SSR metamaterial due to the surface current distribution variation.
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
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.
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.
NASA Astrophysics Data System (ADS)
Luongo, Annamaria; Amoruso, Antonella; Crescentini, Luca
2015-04-01
Volcanic unrests can be studied through the induced surface deformation; one limiting factor however is the small number of available deformation source models. Till 2011, the only available (approximate or exact) expressions for finite expansion sources referred to spheres, prolate spheroids, and horizontal circular cracks embedded in a homogeneous half-space. Cervelli (2013) derived more general approximate expressions for displacement from a finite spheroid of arbitrary orientation and aspect ratio, embedded in a homogeneous half-space. The only approximate expressions for displacements and stresses from the inflation of a finite pressurized tri-axial ellipsoid in a (possibly heterogeneous) half-space were published by Amoruso and Crescentini (2011). Starting from the equivalence (exact for an infinite elastic medium) between the external displacement field due to a pressurized ellipsoidal cavity and the displacement field given by a uniform distribution of seismic moments, Amoruso and Crescentini (2011) accounted for source finiteness by using an approach similar to the multipole expansion of the gravitational potential outside a mass distribution. The dipole term is null because of symmetry; terms to quadrupole order are kept. The resulting expressions can be evaluated by combining the effects of seven moment tensors (SMT model) and are approximately valid also for a heterogeneous half-space. In case of a layered half-space, the appropriate displacement Green functions can be evaluated analitically and the SMT model has already been used to invert ground deformation data of the Campi Flegrei Caldera, Italy. In case of a heterogeneous medium, the appropriate displacement Green functions can be computed, once and for all, using FEM, so that the SMT model still allows fast forward computations and can be included into inversion codes. Amoruso and Crescentini (2011) could test the goodness of their approach only in case of spherical and prolate spheroidal cavities
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.
Free vibration of symmetric and sigmoid functionally graded nanobeams
NASA Astrophysics Data System (ADS)
Hamed, M. A.; Eltaher, M. A.; Sadoun, A. M.; Almitani, K. H.
2016-09-01
The objective of this paper was the investigation of vibration characteristics of both nonlinear symmetric power and sigmoid functionally graded nonlocal nanobeams. The volume fractions of metal and ceramic are assumed to be distributed through a beam thickness by sigmoid law distribution and symmetric power function. Structures with symmetric distribution with mid-plane such as ceramic-metal-ceramic and metal-ceramic-metal are proposed. Nonlocal differential Eringen's elasticity is exploited to incorporate size dependency of nanobeam. The kinematic relations of Euler-Bernoulli beam are proposed, with the assumption of a small strain. A nonlocal equation of motion of nanobeam is derived by using principle of virtual work and then discretized by finite element method to obtain numerical solution. Numerical results show the effects of the function distribution, gradient index and nonlocal parameter on natural frequencies of macro- and nanobeam. This model is helpful in the mechanical design of nanoelectromechanical systems manufactured from FGM.
On Higgs branch localization of Seiberg-Witten theories on an ellipsoid
NASA Astrophysics Data System (ADS)
Chen, Heng-Yu; Tsai, Tsung-Hsuan
2016-01-01
In this note, we consider so-called "Higgs branch localization" for four-dimensional N=2 field theories on a 4D ellipsoid. We find a new set of saddle point equations arising from the additional Higgs branch deformation term, whose solutions include both Higgs branch and BPS instanton-vortex mixed configurations. By evaluating the contour integral, we also demonstrate that the ellipsoid partition almost factorizes into purely b- and b^{-1}-dependent parts, using SQCD as an explicit example. We identify various factorized parts with the ellipsoid partition function of two-dimensional N=(2,2) SQCDA, which is precisely the vortex world volume theory. We also give a physical interpretation for the non-factorizable parts and discuss future directions.
Second harmonic generation in composites of ellipsoidal particles with core-shell structure
NASA Astrophysics Data System (ADS)
Zhang, Wen; Liu, De-Hua
2009-01-01
We study the enhancement of the second-harmonic generation (SHG) coefficient in a random composite consisting of ellipsoidal particles with a core-shell structure in a linear dielectric host. The material making up the ellipsoidal core is assumed to be dielectric, but with a nonlinear susceptibility for SHG. The coating material is assumed to be metallic with a linear susceptibility. The effective SHG coefficient is derived and its expression is related to various local field factors. The numerical calculations of the effective SHG response per unit volume of nonlinear material can be greatly enhanced at certain frequencies. For coated ellipsoidal particles, the core-shell structure and the particle shape allow for tuning of the resonance through the choice of material parameters and/or the ratio of the core to shell volume fraction and the depolarization factor of the particles.
From Spheres to Ellipsoids: The Story of the Density of States
NASA Astrophysics Data System (ADS)
Zeravcic, Zorana; Xu, Ning; Nagel, Sidney R.; Liu, Andrea J.
2009-03-01
Packings of frictionless ellipsoids have not only captured the imagination of the public, but also bring up a number of fundamental issues regarding the properties of jammed media. For instance, the average contact number Z of such packings at jamming varies continuously between the spherical isostatic value Ziso=6 and the value Ziso=10 for ellipsoids of revolution if the ellipticity ɛ-1 is turned on. Here we study the vibrational spectra of soft ellipsoids both as a function of density and ɛ. Our spectra show a two-band structure. For small aspect ratios there is first a rotational band, then a gap and then a second band of translational character. As we increase the aspect ratio, the gap closes and the remaining band has a mixed character. We discuss various surprising features of the spectrum in detail and show how the changes in the gap are related with the change of Z with ɛ.
Self-diffusion of Colloidal Spheres and Ellipsoids in Nematic Phases of fd-virus
NASA Astrophysics Data System (ADS)
Zhang, J.
2005-03-01
We report on the self-diffusion of micron sized colloidal spheres and ellipsoids in nematic phases of fd-virus. The mean square displacements (MSDs) of the spheres are diffusive along the nematic director, with the diffusion coefficients displaying an inverse dependence on sphere radius. Displacements perpendicular to the nematic director, however, are markedly slower and are sub-diffusive. The colloidal ellipsoids align with their long axis along the nematic director and also exhibit diffusive motion along the nematic director and a sub-diffusive motion perpendicular to the nematic director. The rotational motions of the ellipsoids are sub-diffusive at short time, and exhibit caged behavior at long times. We examine these motions as a function of nematic order parameter, and compare our results to theories of hindered tracer dynamics. This work has been partially supported by the NSF through MRSEC Grants DMR 00-79909 and DMR-0203378, and by NASA Grant NAG8-2172.
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.
NASA Technical Reports Server (NTRS)
Turmon, Michael
2004-01-01
We consider mixture density estimation under the symmetry constraint x = Az for an orthogonal matrix A. This distributional constraint implies a corresponding constraint on the mixture parameters. Focusing on the gaussian case, we derive an expectation-maximization (EM) algorithm to enforce the constraint and show results for modeling of image feature vectors.
Classical solutions for the ellipsoidal BGK model with fixed collision frequency
NASA Astrophysics Data System (ADS)
Yun, Seok-Bae
2015-12-01
We establish the existence of global in time smooth solutions for the ellipsoidal BGK model, which is a variant of the BGK model for the Boltzmann equation designed to yield the correct Prandtl number in the hydrodynamic approximation at the Navier-Stokes level. For this, we carefully design a function space which captures the growth of the solution in a weighted Sobolev norm, and show that the ellipsoidal relaxation operator is Lipschitz continuous in the induced metric. This approach is restricted to the case when the collision frequency does not depend on the macroscopic field, but no smallness on the initial data is required.
Laser pulse shaping for generating uniform three-dimensional ellipsoidal electron beams.
Li, Y.; Chmnerisov, S.; Lewellen, J. W.
2009-02-01
A scheme of generating a uniform ellipsoidal laser pulse for high-brightness photoinjectors is discussed. The scheme is based on the chromatic aberration of a dispersive lens. Fourier optics simulation reveals the interplay of group velocity delay and dispersion in the scheme, as well as diffractions. Particle tracking simulation shows that the beam generated by such a laser pulse approaches the performance of that by an ideal ellipsoidal laser pulse and represents a significant improvement from the traditionally proposed cylindrical beam geometry. The scheme is tested in an 800-nm, optical proof-of-principle experiment at lower peak power with excellent agreement between the measurement and simulation.
X-ray tomography study of the random packing structure of ellipsoids.
Xia, Chengjie; Zhu, Kuan; Cao, Yixin; Sun, Haohua; Kou, Binquan; Wang, Yujie
2014-02-21
We present an X-ray tomography study for the random packing of ellipsoids. The local structure displays short-range correlations. In addition to the contact number Z, we introduce ρshell, the average contact radius of curvature for contacting neighbors, as an additional parameter to characterize the local orientational geometry. In general, the local free volume w is affected by both Z and ρshell. We believe that the particle asphericity induces a polydispersity effect to influence the packing properties. A model is introduced which explicitly maps the ellipsoid packing onto a polydispersed sphere one, and it reproduces most of the experimental observations.
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.
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.
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.
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.
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…
Recovery of orthometric heights from ellipsoidal heights using offsets method over Japan
NASA Astrophysics Data System (ADS)
Odera, Patroba Achola; Fukuda, Yoichi
2015-08-01
One of the most important applications of a geoid model is a recovery of orthometric heights from ellipsoidal heights (normally obtained from GNSS). The application of the geoid model for recovering orthometric heights from ellipsoidal heights is normally achieved by fitting the geoid model to a local vertical datum. The fitting procedure is usually accomplished by least squares collocation (LSC), using planar or spherical covariance functions. This procedure warps the gravimetric geoid model onto the local vertical datum, hence the local geoid model derived by this procedure, though convenient for local applications, it is not an equipotential surface. We propose offsets method for practical orthometric height recovery from a geoid model. The proposed procedure is more realistic because it does not constrain the local geoid to be coincident to the local vertical datum. We compare the performance of plannar fitting and offsets methods over Japan using a cross-validation procedure. Results show that offsets method performs better than the normally used planar fitting in the recovery of orthometric heights from ellipsoidal heights using a geoid model. The standard deviations of the differences between established and converted orthometric heights at randomly selected GPS/levelling test points over Japan are ±4 and ±3 cm for planar fitting and offsets methods, respectively. The offsets method is therefore more appropriate for converting ellipsoidal heights to orthometric heights than the planar fitting in the area of study.
Cauchy problem for the ellipsoidal-BGK model of the Boltzmann equation
NASA Astrophysics Data System (ADS)
Park, Sa Jun; Yun, Seok-Bae
2016-08-01
Ellipsoidal BGK model (ES-BGK) is a generalized version of the original BGK model designed to reproduce the physically correct Prandtl number in the Navier-Stokes limit. In this paper, we study the Cauchy problem for the ES-BGK model under the condition of finite initial mass, energy, and entropy. Equivalence type estimates for the temperature tensor are crucially used.
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.
Interpolation via symmetric exponential functions
NASA Astrophysics Data System (ADS)
Bezubik, Agata; Pošta, Severin
2013-11-01
Complex valued functions on the Euclidean space Bbb Rn, symmetric or antisymmetric with respect to the permutation group Sn, are often dealt with in various branches of physics, such as quantum theory or theory of integrable systems. One often needs to approximate such functions with series consisting of various special functions which satisfy nice properties. Questions of uniform convergence of such approximations are crucial for applications. In this article a family of special functions called the symmetric exponential functions are used for such approximation and the uniform convergence of their sums is considered.
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.
Fault-tolerant symmetrically-private information retrieval
NASA Astrophysics Data System (ADS)
Wang, Tian-Yin; Cai, Xiao-Qiu; Zhang, Rui-Ling
2016-08-01
We propose two symmetrically-private information retrieval protocols based on quantum key distribution, which provide a good degree of database and user privacy while being flexible, loss-resistant and easily generalized to a large database similar to the precedent works. Furthermore, one protocol is robust to a collective-dephasing noise, and the other is robust to a collective-rotation noise.
Davies, Gary B; Krüger, Timm; Coveney, Peter V; Harting, Jens; Bresme, Fernando
2014-09-21
Manufacturing new soft materials with specific optical, mechanical and magnetic properties is a significant challenge. Assembling and manipulating colloidal particles at fluid interfaces is a promising way to make such materials. We use lattice-Boltzmann simulations to investigate the response of magnetic ellipsoidal particles adsorbed at liquid-liquid interfaces to external magnetic fields. We provide further evidence for the first-order orientation phase transition predicted by Bresme and Faraudo [Journal of Physics: Condensed Matter, 2007, 19, 375110]. We show that capillary interface deformations around the ellipsoidal particle significantly affect the tilt-angle of the particle for a given dipole-field strength, altering the properties of the orientation transition. We propose scaling laws governing this transition, and suggest how to use these deformations to facilitate particle assembly at fluid-fluid interfaces. PMID:25069609
Davies, Gary B; Krüger, Timm; Coveney, Peter V; Harting, Jens; Bresme, Fernando
2014-09-21
Manufacturing new soft materials with specific optical, mechanical and magnetic properties is a significant challenge. Assembling and manipulating colloidal particles at fluid interfaces is a promising way to make such materials. We use lattice-Boltzmann simulations to investigate the response of magnetic ellipsoidal particles adsorbed at liquid-liquid interfaces to external magnetic fields. We provide further evidence for the first-order orientation phase transition predicted by Bresme and Faraudo [Journal of Physics: Condensed Matter, 2007, 19, 375110]. We show that capillary interface deformations around the ellipsoidal particle significantly affect the tilt-angle of the particle for a given dipole-field strength, altering the properties of the orientation transition. We propose scaling laws governing this transition, and suggest how to use these deformations to facilitate particle assembly at fluid-fluid interfaces.
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.
The Newtonian potential and the demagnetizing factors of the general ellipsoid
NASA Astrophysics Data System (ADS)
Di Fratta, Giovanni
2016-06-01
The objective of this paper is to present a modern and concise new derivation for the explicit expression of the interior and exterior Newtonian potential generated by homogeneous ellipsoidal domains in RN (with N≥3). The very short argument is essentially based on the application of Reynold's transport theorem in connection with the Green-Stokes integral representation formula for smooth functions on bounded domains of RN, which permits to reduce the N-dimensional problem to a one-dimensional one. Owing to its physical relevance, a separate section is devoted to the the derivation of the demagnetizing factors of the general ellipsoid which are one of the most fundamental quantities in ferromagnetism.
Symmetric States Requiring System Asymmetry.
Nishikawa, Takashi; Motter, Adilson E
2016-09-01
Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the complete synchronization of the entire network is the state inheriting the system symmetry. As in other systems subject to symmetry breaking, such symmetric states are not always stable. Here, we report on the discovery of the converse of symmetry breaking-the scenario in which complete synchronization is not stable for identically coupled identical oscillators but becomes stable when, and only when, the oscillator parameters are judiciously tuned to nonidentical values, thereby breaking the system symmetry to preserve the state symmetry. Aside from demonstrating that diversity can facilitate and even be required for uniformity and consensus, this suggests a mechanism for convergent forms of pattern formation in which initially asymmetric patterns evolve into symmetric ones. PMID:27661690
Symmetric States Requiring System Asymmetry
NASA Astrophysics Data System (ADS)
Nishikawa, Takashi; Motter, Adilson E.
2016-09-01
Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the complete synchronization of the entire network is the state inheriting the system symmetry. As in other systems subject to symmetry breaking, such symmetric states are not always stable. Here, we report on the discovery of the converse of symmetry breaking—the scenario in which complete synchronization is not stable for identically coupled identical oscillators but becomes stable when, and only when, the oscillator parameters are judiciously tuned to nonidentical values, thereby breaking the system symmetry to preserve the state symmetry. Aside from demonstrating that diversity can facilitate and even be required for uniformity and consensus, this suggests a mechanism for convergent forms of pattern formation in which initially asymmetric patterns evolve into symmetric ones.
Plethystic algebras and vector symmetric functions.
Rota, G C; Stein, J A
1994-01-01
An isomorphism is established between the plethystic Hopf algebra Pleth(Super[L]) and the algebra of vector symmetric functions. The Hall inner product of symmetric function theory is extended to the Hopf algebra Pleth(Super[L]). PMID:11607504
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.
Robe's restricted problem of 2+2 bodies when the bigger primary is a Roche ellipsoid
NASA Astrophysics Data System (ADS)
Kaur, Bhavneet; Aggarwal, Rajiv
2013-08-01
In the problem of 2 + 2 bodies in Robe's setup, one of the primaries of mass m1 is a Roche ellipsoid filled with a homogeneous incompressible fluid of density ρ1. The smaller primary of mass m2 is a point mass outside the ellipsoid. The third and the fourth bodies (of mass m3 and m4, respectively), supposed moving inside the ellipsoid, are small solid spheres of density ρ3 and ρ4, respectively, with the assumption that the mass and the radius of the third and the fourth bodies are infinitesimal. We assume that m2 is describing a circle around m1. The masses m3 and m4 mutually attract each other, do not influence the motions of m1 and m2 but are influenced by them. Robe's restricted three body problem is extended to 2 + 2 body problem under the assumption that the fluid body assumes the shape of the Roche ellipsoid (Chandrashekhar [2]). We take 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 m2, and (iii) that arising from the centrifugal force. In this paper, equilibrium solutions of m3 and m4 and their linear stability are analysed. We have proved that there exist only six equilibrium solutions of the system. In a system where the primaries are considered as earth-moon and m3 ,m4 as submarines, the equilibrium solutions thus obtained are unstable.
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].
MISR Level 1B2 Ellipsoid Data (MI1B2E_V1)
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=250 meters - < 500 meters; Temporal_Resolution=about 15 orbits/day; Temporal_Resolution_Range=about 15 orbits/day].
MISR Level 1B2 Ellipsoid Data (MI1B2E_V3)
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. [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); Temporal_Resolution=about 15 orbits/day; Temporal_Resolution_Range=about 15 orbits/day].
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.
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
2016-05-19
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.
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
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
Retrieval of dust particle refractive index from scattering data using ellipsoid ensembles
NASA Astrophysics Data System (ADS)
Kemppinen, Osku; Nousiainen, Timo; Merikallio, Sini; Räisänen, Petri
2016-04-01
Retrieval of aerosol microphysical properties, such as dust particle refractive index, from remote sensing data is a key problem. Even when full scattering matrix data is available, the problem is challenging to solve due to the large number of possible particle property combinations, and the non-linear response of scattering data to changes in these properties. One approach is to perform a mathematical fit of a pre-defined shape class, such as ellipsoids, varying the free parameter, and evaluating the goodness of the fit for each free parameter value. It is known that a shape ensemble of ellipsoids can replicate dust particle scattering data with good accuracy, but it is less known if the good match guarantees that the microphysical properties used in the ensemble correspond to those of the real particle. Essentially, it is unclear if a small fit residue guarantees that the parameter is retrieved accurately. In this work, we test how accurate the refractive index retrieval with shape ensembles of ellipsoids is by using computational scattering data. Using the computational data allows us to know with certainty what is the true refractive index of the particle in question, and thus to quantify the retrieval accuracy. We test multiple realistic dust-like particle shapes that have been inverted from real dust particles by using electron microscopy stereogrammetry.
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
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)].
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.
Sambudi, Nonni Soraya; Kim, Minjeong G; Park, Seung Bin
2016-03-01
The electrospun fibers consist of backbone fibers and nano-branch network are synthesized by loading of ellipsoidal calcium carbonate in the mixture of chitosan/poly(vinyl alcohol) (PVA) followed by electrospinning. The synthesized ellipsoidal calcium carbonate is in submicron size (730.7±152.4 nm for long axis and 212.6±51.3 nm for short axis). The electrospun backbone fibers experience an increasing in diameter by loading of calcium carbonate from 71.5±23.4 nm to 281.9±51.2 nm. The diameters of branch fibers in the web-network range from 15 nm to 65 nm with most distributions of fibers are in 30-35 nm. Calcium carbonate acts as reinforcing agent to improve the mechanical properties of fibers. The optimum value of Young's modulus is found at the incorporation of 3 wt.% of calcium carbonate in chitosan/PVA fibers, which is enhanced from 15.7±3 MPa to 432.4±94.3 MPa. On the other hand, the ultimate stress of fibers experiences a decrease. This result shows that the fiber network undergoes changes from flexible to more stiff by the inclusion of calcium carbonate. The thermal analysis results show that the crystallinity of polymer is changed by the existence of calcium carbonate in the fiber network. The immersion of fibers in simulated body fluid (SBF) results in the formation of apatite on the surface of fibers.
Sambudi, Nonni Soraya; Kim, Minjeong G; Park, Seung Bin
2016-03-01
The electrospun fibers consist of backbone fibers and nano-branch network are synthesized by loading of ellipsoidal calcium carbonate in the mixture of chitosan/poly(vinyl alcohol) (PVA) followed by electrospinning. The synthesized ellipsoidal calcium carbonate is in submicron size (730.7±152.4 nm for long axis and 212.6±51.3 nm for short axis). The electrospun backbone fibers experience an increasing in diameter by loading of calcium carbonate from 71.5±23.4 nm to 281.9±51.2 nm. The diameters of branch fibers in the web-network range from 15 nm to 65 nm with most distributions of fibers are in 30-35 nm. Calcium carbonate acts as reinforcing agent to improve the mechanical properties of fibers. The optimum value of Young's modulus is found at the incorporation of 3 wt.% of calcium carbonate in chitosan/PVA fibers, which is enhanced from 15.7±3 MPa to 432.4±94.3 MPa. On the other hand, the ultimate stress of fibers experiences a decrease. This result shows that the fiber network undergoes changes from flexible to more stiff by the inclusion of calcium carbonate. The thermal analysis results show that the crystallinity of polymer is changed by the existence of calcium carbonate in the fiber network. The immersion of fibers in simulated body fluid (SBF) results in the formation of apatite on the surface of fibers. PMID:26706559
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.
Novel design for centrifugal counter-current chromatography: VI. Ellipsoid column
Gu, Dongyu; Yang, Yi; Xin, Xuelei; Aisa, Haji Akber; Ito, Yoichiro
2014-01-01
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
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.
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
Field enhancement factor and field emission from a hemi-ellipsoidal metallic needle.
Pogorelov, Evgeny G; Zhbanov, Alexander I; Chang, Yia-Chung
2009-03-01
We present an exact solution for the electrostatic field between a metallic hemi-ellipsoidal needle on a plate (as a cathode) and a flat anode. The basic idea is to replace the cathode by a linearly charged thread in a uniform electric field and to use a set of "image" charges to reproduce the anode. We calculate the field enhancement factor on the needle surface and ponderomotive force acting on the needle. Using the Fowler-Nordheim theory we obtain an exact analytical formula for the total current. PMID:19232831
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.
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
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.
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.
Symmetric blanket nuclear fuel assembly
Penkrot, J.A.
1986-08-19
This patent describes a fuel assembly having spaced-apart fuel rods, the combination comprising: (a) a first group of the fuel rods containing natural uranium only; and (b) a second group of the fuel rods constituting the remainder therof containing enriched uranium only; (c) the fuel rods of the first group being surrounded by the fuel rods of the second group in a predetermined symmetrical relationship; (d) the first group of the fuel rods forming an inner, centrally-located, generally squared pattern wherein the only fuel rods present in the inner squared pattern are the fuel rods of the first group; (e) the second group of the fuel rods forming an outer, peripherally-located, generally squared annular pattern which surrounds the first group wherein the only fuel rods present in the outer squared pattern are the fuel rods of the second group.
Computing symmetric colorings of the dihedral group
NASA Astrophysics Data System (ADS)
Zelenyuk, Yuliya
2016-06-01
A symmetry on a group G is a mapping G ∋ x ↦ gx-1 g ∈ G, where g ∈ G. A subset A ⊆ G is symmetric if it is invariant under some symmetry, that is, A = gA-1g. The notion of symmetry has interesting relations to enumerative combinatorics. A coloring is symmetric if χ(gx-1g) = χ(x) for some g ∈ G. We discuss an approach how to compute the number of symmetric r-colorings for any finite group. Using this approach we derive the formula for the number of symmetric r-colorings of the dihedral group D3.
Instabilities of pancake vortices modelled by rotating ellipsoids in a stratified fluid
NASA Astrophysics Data System (ADS)
Meunier, Patrice
2012-11-01
It is now well known that oceans contain very energetic vortices with a long lifetime. However, it is still unclear how these vortices destabilise and how much energy and mixing they can provide at different scales. We investigate here the destabilisation of an axisymmetric vortex in a stratified and non-rotating environment. The vortex is modeled by a rotating ellipsoid with various diameters and heights. The flow is visualised by shadowgraph, synthetic schlieren and Particle Image Velocimetry. Two types of instabilities have been observed, one being located on the side of the ellipsoid and the other being located at the top and bottom. The first instability is linked to the radiative instability, which is well known in the case of a rotating cylinder, and which emits internal waves with an azimuthal wave number equal to 1. The second instability generates an axisymmetric layering pattern which is reminiscent of the double diffusive instability (between angular momentum and density), observed and described theoretically in a rotating environment. This second instability might be responsible for the layering pattern found above oceanic vortices, which probably leads to a large localised mixing. ANR Grant OLA.
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)
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.
NASA Astrophysics Data System (ADS)
Pan, Y.; Weng, G. J.; Meguid, S. A.; Bao, W. S.; Zhu, Z.-H.; Hamouda, A. M. S.
2011-12-01
An explicit, analytical theory for the percolation threshold, percolation saturation, and effective conductivity of a two-component system involving randomly oriented ellipsoidal inclusions is proposed. The ellipsoids may take the shape of a needle, prolate or oblate spheroid, sphere, or disk. This theory is based upon consideration of Ponte Castañeda--Willis [P. Ponte Castañeda and J. R. Willis, J. Mech. Phys. Solids 43, 1919 (1995)] microstructure in conjunction with Hashin--Shtrikman [Z. Hashin and S. Shtrikman, J. Appl. Phys. 33, 3125 (1962)] upper bound. Two critical volume concentrations, c* and c**, that represent the respective percolation threshold at which the conductive network begins to develop, and the percolation saturation, are identified. During this very short range of concentration, the electrical conductivity of the composite is found to exhibit a very sharp increase, while over the entire range, the calcutilated conductivity exhibits the widely reported sigmoidal shape. Comparison with measurement on a multi-walled carbon nanotube/alumina composite indicates that the theory could capture the major features of the experimentally observed trends sufficiently well.
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.
THE ANALYTICAL STRUCTURE OF THE PRIMARY INTERSTELLAR HELIUM DISTRIBUTION FUNCTION IN THE HELIOSPHERE
Lee, Martin A.; Möbius, Eberhard; Leonard, Trevor W.
2015-10-15
A new analytical model based on the previous work of Lee et al. is presented for the distribution of interstellar helium in the heliosphere. The model is tailored for comparison with the IBEX-Lo observations in order to determine the bulk velocity and temperature of helium in the local interstellar cloud. The model includes solar gravity, spherically symmetric stationary ionization rates, transformation to the Earth/IBEX frame of reference, the IBEX viewing geometry with small spin-axis tilt, and integration of the atom differential intensity over energy and the instrument collimator solid angle. The analysis employs an expansion of the count rate about the peak of the velocity distribution to second order in the magnitudes of several small quantities: the ratio of the helium thermal speed to its bulk speed, the angle between the bulk velocity and the ecliptic, the two angles describing the tilt of the IBEX spin-axis away from Sun-pointing, the collimator angular width, and the angular difference between the observing longitude and the longitude where the projection of the bulk velocity onto the ecliptic is tangential to Earth's orbit. The model reveals the evolving ellipsoidal shape of the helium distribution as it moves along its average hyperbolic orbit. For specified interstellar parameters, the model predicts the latitudinal and longitudinal structure of the helium distribution. The model is in reasonable agreement with IBEX observations and the predictions of the other available models.
Allaire, S; Jacq, J J; Burdin, V; Roux, Ch
2007-01-01
This paper addresses the ellipsoid-type-specified fitting of quadratic surfaces, in the scope of model-based global feature extraction within scattered 3D point clouds. At characterizing articular bone surfaces, the quadrics estimated indicate useful overall-symmetry-related intrinsic centers and axes in joints. A constrained weighted least-squares minimization of algebraic residuals is used, with a robust and bias-corrected metric. With only one quadratic constraint involved, every step produces closed-form eigenvector solutions. To guarantee that an ellipsoid is output, we originally exploit a 2D representation called the Quadric Shape Map (QSM) by carrying out a visual study of the influence of shape constraints. The identified ellipsoid guarantee is needed to extract the center and axes in a wrist joint data stemming from 3D medical images.
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
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.
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.
Symmetrical thalamic lesions in infants.
Eicke, M; Briner, J; Willi, U; Uehlinger, J; Boltshauser, E
1992-01-01
Clinical observations and findings on imaging are reported in six newborns with symmetrical thalamic lesions (STL). In three cases the diagnosis was confirmed by postmortem examination. Characteristic observations in this series and 17 previously reported cases include no evidence of perinatal asphyxia, high incidence of polyhydramnios, absent suck and swallow, absent primitive reflexes, appreciable spasticity at or within days of birth, lack of psychomotor development, and death within days or months. Characteristic pathological findings include loss of neurons, astrogliosis, and 'incrusted' neurons particularly in the thalamus. In two thirds of cases the basal ganglia and brain stem are involved as well. A hypoxic-ischaemic event occurring two to four weeks before birth is most likely responsible for STL. Bilateral thalamic calcification can often, but not always, be demonstrated in the newborn period by computed tomography and/or cranial ultrasound. The presence of these calcifications and the observation of spasticity at birth imply that the responsible insult occurred at least two to four weeks earlier. The small number of published cases with STL suggest that it may be easily missed. Images Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 PMID:1536580
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.
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.
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.
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.
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.
NMR structural inference of symmetric homo-oligomers.
Chandola, Himanshu; Yan, Anthony K; Potluri, Shobha; Donald, Bruce R; Bailey-Kellogg, Chris
2011-12-01
Symmetric homo-oligomers represent a majority of proteins, and determining their structures helps elucidate important biological processes, including ion transport, signal transduction, and transcriptional regulation. In order to account for the noise and sparsity in the distance restraints used in Nuclear Magnetic Resonance (NMR) structure determination of cyclic (C(n)) symmetric homo-oligomers, and the resulting uncertainty in the determined structures, we develop a Bayesian structural inference approach. In contrast to traditional NMR structure determination methods, which identify a small set of low-energy conformations, the inferential approach characterizes the entire posterior distribution of conformations. Unfortunately, traditional stochastic techniques for inference may under-sample the rugged landscape of the posterior, missing important contributions from high-quality individual conformations and not accounting for the possible aggregate effects on inferred quantities from numerous unsampled conformations. However, by exploiting the geometry of symmetric homo-oligomers, we develop an algorithm that provides provable guarantees for the posterior distribution and the inferred mean atomic coordinates. Using experimental restraints for three proteins, we demonstrate that our approach is able to objectively characterize the structural diversity supported by the data. By simulating spurious and missing restraints, we further demonstrate that our approach is robust, degrading smoothly with noise and sparsity. PMID:21718128
Symmetric Monotone Venn Diagrams with Seven Curves
NASA Astrophysics Data System (ADS)
Cao, Tao; Mamakani, Khalegh; Ruskey, Frank
An n-Venn diagram consists of n curves drawn in the plane in such a way that each of the 2 n possible intersections of the interiors and exteriors of the curves forms a connected non-empty region. A k-region in a diagram is a region that is in the interior of precisely k curves. A n-Venn diagram is symmetric if it has a point of rotation about which rotations of the plane by 2π/n radians leaves the diagram fixed; it is polar symmetric if it is symmetric and its stereographic projection about the infinite outer face is isomorphic to the projection about the innermost face. A Venn diagram is monotone if every k-region is adjacent to both some (k - 1)-region (if k > 0) and also to some k + 1 region (if k < n). A Venn diagram is simple if at most two curves intersect at any point. We prove that the "Grünbaum" encoding uniquely identifies monotone simple symmetric n-Venn diagrams and describe an algorithm that produces an exhaustive list of all of the monotone simple symmetric n-Venn diagrams. There are exactly 23 simple monotone symmetric 7-Venn diagrams, of which 6 are polar symmetric.
The symmetric extendibility of quantum states
NASA Astrophysics Data System (ADS)
Nowakowski, Marcin L.
2016-09-01
Studies on the symmetric extendibility of quantum states have become particularly important in the context of the analysis of one-way quantum measures of entanglement, and the distillability and security of quantum protocols. In this paper we analyze composite systems containing a symmetric extendible part, with particular attention devoted to the one-way security of such systems. Further, we introduce a new one-way entanglement monotone based on the best symmetric approximation of a quantum state and the extendible number of a quantum state. We underpin these results with geometric observations about the structures of multi-party settings which posses substantial symmetric extendible components in their subspaces. The impossibility of reducing the maximal symmetric extendibility by means of the one-way local operations and classical communication method is pointed out on multiple copies. Finally, we state a conjecture linking symmetric extendibility with the one-way distillability and security of all quantum states, analyzing the behavior of a private key in the neighborhood of symmetric extendible states.
A Stable Self-Similar Singularity of Evaporating Drops: Ellipsoidal Collapse to a Point
NASA Astrophysics Data System (ADS)
Fontelos, Marco A.; Hong, Seok Hyun; Hwang, Hyung Ju
2015-08-01
We study the problem of evaporating drops contracting to a point. Going back to Maxwell and Langmuir, the existence of a spherical solution for which evaporating drops collapse to a point in a self-similar manner is well established in the physical literature. The diameter of the drop follows the so-called D 2 law: the second power of the drop-diameter decays linearly in time. In this study we provide a complete mathematical proof of this classical law. We prove that evaporating drops which are initially small perturbations of a sphere collapse to a point and the shape of the drop converges to a self-similar ellipsoid whose center, orientation, and semi-axes are determined by the initial shape.
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
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.
Free Energy Calculations for DNA Near Surfaces Using an Ellipsoidal Geometry
Ambia-Garrido, J.; Pettitt, B. Montgomery
2009-01-01
The change in some thermodynamic quantities such as Gibbs' free energy, entropy and enthalpy of the binding of two DNA strands (forming a double helix), while one is tethered to a surface and are analytically calculated. These particles are submerged in an electrolytic solution; the ionic strength of the media allows the linearized version of the Poisson-Boltzmann equation (from the theory of the double layer interaction) to properly describe the interactions [13]. There is experimental and computational evidence that an ion penetrable ellipsoid is an adequate model for the single strand and the double helix [22–25]. The analytic solution provides simple calculations useful for DNA chip design. The predicted electrostatic effects suggest the feasibility of electronic control and detection of DNA hybridization in the fast growing area of DNA recognition. PMID:20011625
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.
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.
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
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).
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.
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.
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.
Single-camera method to determine the optical axis position of ellipsoidal drops.
Jones, B K; Saylor, J R; Bliven, L F
2003-02-20
The sizing of droplets by optical imaging typically requires a small depth of field so that variations in the magnification ratio are minimized. However, if the location of the drop along the optical axis can be determined, a variable magnification ratio can be imposed on each imaged drop, and the depth of field can be increased. Previous research suggested that droplet location can be determined with a characteristic of droplet images that is obtained when the droplet is illuminated from behind. In this prior research, the method was demonstrated with spherical glass objects to simulate raindrops. Raindrop are known to deviate significantly from a spherical shape, especially when the drop size is large. We demonstrate the ability to locate the position of objects that deviate from sphericity. Deformed water drops and glass ellipsoids are tested, along with glass spheres. The role of refractive index is also discussed.
Energies and densities of electrons confined in elliptical and ellipsoidal quantum dots
NASA Astrophysics Data System (ADS)
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.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Maeso, M. J.; Solana, J. R.
An analytical equation of state for hard ellipsoids-of-revolution fluids is derived from a generalization of the Carnahan-Starling method for obtaining the equation of state of the hard-sphere fluid. The results are in very good agreement with existing simulation data.
Martingale Rosenthal inequalities in symmetric spaces
Astashkin, S V
2014-12-31
We establish inequalities similar to the classical Rosenthal inequalities for sequences of martingale differences in general symmetric spaces; a central role is played here by the predictable quadratic characteristic of a martingale. Bibliography: 26 titles.
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.
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 ) .
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.
Chen Lin; Zhu Huangjun; Wei, Tzu-Chieh
2011-01-15
We study the geometric measure of entanglement (GM) of pure symmetric states related to rank 1 positive-operator-valued measures (POVMs) and establish a general connection with quantum state estimation theory, especially the maximum likelihood principle. Based on this connection, we provide a method for computing the GM of these states and demonstrate its additivity property under certain conditions. In particular, we prove the additivity of the GM of pure symmetric multiqubit states whose Majorana points under Majorana representation are distributed within a half sphere, including all pure symmetric three-qubit states. We then introduce a family of symmetric states that are generated from mutually unbiased bases and derive an analytical formula for their GM. These states include Dicke states as special cases, which have already been realized in experiments. We also derive the GM of symmetric states generated from symmetric informationally complete POVMs (SIC POVMs) and use it to characterize all inequivalent SIC POVMs in three-dimensional Hilbert space that are covariant with respect to the Heisenberg-Weyl group. Finally, we describe an experimental scheme for creating the symmetric multiqubit states studied in this article and a possible scheme for measuring the permanence of the related Gram matrix.
Coacervation in Symmetric Mixtures of Oppositely Charged Rodlike Polyelectrolytes
NASA Astrophysics Data System (ADS)
Kumar, Rajeev; Fredrickson, Glenn
2010-03-01
Phase separation in the salt-free symmetric mixtures of oppositely charged rodlike polyelectrolytes is studied using quasi-analytical calculations. Stability analyses for the isotropic-isotropic and the isotropic-nematic phase transitions in the symmetric mixtures are carried out. It is shown that electrostatics favor nematic ordering. Also, the coexistence curves for the symmetric mixtures are computed, and the effects of the linear charge density and the electrostatic interaction strength on the phase boundaries are studied. It is found that the counterions are uniformly distributed in the coexisting phases for low electrostatic interaction strengths characterized by the linear charge density of the polyelectrolytes and the Bjerrum's length. However, the counterions also phase separate along with the rodlike polyelectrolytes with an increase in the electrostatic interaction strength. It is shown that the number density of the counterions is higher in the concentrated (or coacervate) phase than in the dilute (or supernatant) phase. In contrast to the rodlike mixtures, flexible polyelectrolyte mixtures can undergo only isotropic-isotropic phase separation. A comparison of the coexistence curves for the weakly charged rodlike with the flexible polyelectrolyte mixtures reveals that the electrostatic driving force for the isotropic-isotropic phase separation is stronger in the flexible mixtures.
Symmetric neutralized ion beams: Production, acceleration, propagation, and applications
NASA Astrophysics Data System (ADS)
Hicks, Nathaniel Kenneth
This dissertation presents the first integrated experimental, computational, and theoretical research program on symmetric neutralized ion beams. A beam of this type is composed of positive and negative ions having equal charge-to-mass ratios, such that the beam has overall charge neutrality and its constituent ions respond symmetrically to electromagnetic forces. Under the right conditions, these beams may propagate undeflected across transverse magnetic fields due to beam polarization. Such propagation is studied here computationally, using a three-dimensional particle-in-cell code. Also, key theoretical differences between the propagation ability of these beams and that of beams consisting of positive ions and electrons are elucidated. An experimental method of producing a symmetric neutralized ion beam by merging together separate beams of positive and negative ions is demonstrated, and prototype collector hardware to diagnose the composition and energy distribution of the beam is developed. The ability of radio frequency quadrupole accelerators to simultaneously confine and accelerate the positive and negative ions of such a beam is demonstrated computationally and is confirmed experimentally, and a method to reestablish local charge neutrality in the beam after acceleration is conceived and simulated. The favorable scaling of such accelerators to small size and high frequency is illustrated. Finally, applications of the research to magnetic confinement fusion and topics for future study are presented.
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.
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.
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 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.
The Dynamics of Cumulative Step Size Adaptation on the Ellipsoid Model.
Beyer, Hans-Georg; Hellwig, Michael
2016-01-01
The behavior of the [Formula: see text]-Evolution Strategy (ES) with cumulative step size adaptation (CSA) on the ellipsoid model is investigated using dynamic systems analysis. At first a nonlinear system of difference equations is derived that describes the mean value evolution of the ES. This system is successively simplified to finally allow for deriving closed-form solutions of the steady state behavior in the asymptotic limit case of large search space dimensions. It is shown that the system exhibits linear convergence order. The steady state mutation strength is calculated, and it is shown that compared to standard settings in [Formula: see text] self-adaptive ESs, the CSA control rule allows for an approximately [Formula: see text]-fold larger mutation strength. This explains the superior performance of the CSA in non-noisy environments. The results are used to derive a formula for the expected running time. Conclusions regarding the choice of the cumulation parameter c and the damping constant D are drawn.
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.
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.
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
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.
Bailey, M R; Blackstock, D T; Cleveland, R O; Crum, L A
1999-08-01
Dramatically different cavitation was produced by two separate acoustic pulses that had different shapes but similar duration, frequency content, and peak positive and negative pressure. Both pulses were produced by a Dornier HM-3 style lithotripter: one pulse when the ellipsoidal reflector was rigid, the other when the reflector was pressure release. The cavitation, or bubble action, generated by the conventional rigid-reflector pulse was nearly 50 times longer lived and 3-13 times stronger than that produced by the pressure-release-reflector pulse. Cavitation durations measured by passive acoustic detection and high-speed video agreed with calculations based on the Gilmore equation. Cavitation intensity, or destructive potential, was judged (1) experimentally by the size of pits in aluminum foil detectors and (2) numerically by the calculated amplitude of the shock wave emitted by a collapsing bubble. The results indicate that the trailing positive spike in the pressure-release-reflector waveform stifles bubble growth and mitigates the collapse, whereas the trough after the positive spike in the rigid-reflector waveform triggers inertially driven growth and collapse. The two reflectors therefore provide a tool to compare effects in weakly and strongly cavitating fields and thereby help assess cavitation's role in lithotripsy.
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].
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.
Thompson, Alex J; Mastria, Eric M; Eniola-Adefeso, Omolola
2013-07-01
Particle shape is becoming increasingly recognized as an important parameter for the development of vascular-targeted carriers (VTCs) for disease treatment and diagnosis. However, limited research exists that investigates how particle shape coupled with hemodynamics affects VTC margination (localization and adhesion). In this study, we investigate the effects of particle shape parameters (volume, aspect ratio, axis length) on the margination efficacy of targeted spheres and prolate ellipsoids (rods) to an inflamed endothelial wall from human blood flow in an in vitro model of human vasculature. Overall, particles with 2 μm equivalent spherical diameters (ESD) display higher margination than particles with either 1 μm or 500 nm ESDs. Interestingly, rod-shaped microparticles (1 μm or 2 μm ESD) with high aspect ratios display significantly improved margination compared to spheres of equal volume, particularly under high shear rates and disturbed flow profiles. Nanorods (500 nm ESD), even with high aspect ratio, do not display enhanced margination compared to that of equivalent spheres, which suggests that nanorods, like nanospheres, display minimal margination due to their inability to effectively localize to the vessel wall in the presence of RBCs.
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.
Maswiwat, Kanokkan; Wachner, Derk; Gimsa, Jan
2008-11-01
The transmembrane potential (Deltaphi) induced by external electric fields is important both in biotech applications and in new medical therapies. We analyzed the effects of AC field frequency and cell orientation for cells of a general ellipsoidal shape. Simplified equations were derived for the membrane surface points where the maximum Deltaphi is induced. The theoretical results were confirmed in experiments with three-axial chicken red blood cells (a:b:c=6.66 microm:4.17 microm:1.43 microm). Propidium iodide (PI) staining and cell lysis were detected after an AC electropermeabilization (EP) pulse. The critical field strength for both effects increased when the shorter axis of a cell was parallel to the field, as well as at higher field frequency and for shorter pulse durations. Nevertheless, data analysis based on our theoretical description revealed that the Deltaphi required is lower for the shorter axis, i.e. for smaller membrane curvatures. The critical Deltaphi was independent of the field frequency for a given axis, i.e. the field strength had to be increased with frequency to compensate for the membrane dispersion effect. Comparison of the critical field strengths of PI staining in a linear field aligned along semi-axis a (142 kV m(-1)) and a field rotating in the a-b plane (115 kV m(-1)) revealed the higher EP efficiency of rotating fields.
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.
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 Astrophysics Data System (ADS)
Ravichandran, S.; Bagchi, B.
1999-10-01
Detailed molecular dynamics simulations of the rotational and the translational motions of Gay-Berne ellipsoids in a sea of Lennard-Jones spheres have been carried out. It is found that while the translational motion of an ellipsoid is isotropic at low density, it becomes increasingly anisotropic with density until the ratio of the parallel to the perpendicular diffusion coefficients becomes nearly equal to the value of the aspect ratio at high density. The latter is in agreement with the prediction of Navier-Stokes hydrodynamics with slip boundary condition. The product of the translational diffusion coefficient and the rotational correlation time also attains a hydrodynamic-like density independent behavior only at high density. The reorientational correlation function becomes nonexponential at high density and low temperature where it also develops a slow decay. The perpendicular component of the velocity time correlation function exhibits a clear double minimum, only at high density, which becomes more pronounced as the aspect ratio is increased.
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.
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
Radiative corrections in symmetrized classical electrodynamics
Van Meter JR; Kerman; Chen; Hartemann
2000-12-01
The physics of radiation reaction for a point charge is discussed within the context of classical electrodynamics. The fundamental equations of classical electrodynamics are first symmetrized to include magnetic charges: a double four-potential formalism is introduced, in terms of which the field tensor and its dual are employed to symmetrize Maxwell's equations and the Lorentz force equation in covariant form. Within this framework, the symmetrized Dirac-Lorentz equation is derived, including radiation reaction (self-force) for a particle possessing both electric and magnetic charge. The connection with electromagnetic duality is outlined, and an in-depth discussion of nonlocal four-momentum conservation for the wave-particle system is given.
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.
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
Symmetric States on the Octonionic Bloch Ball
NASA Astrophysics Data System (ADS)
Graydon, Matthew
2012-02-01
Finite-dimensional homogeneous self-dual cones arise as natural candidates for convex sets of states and effects in a variety of approaches towards understanding the foundations of quantum theory in terms of information-theoretic concepts. The positive cone of the ten-dimensional Jordan-algebraic spin factor is one particular instantiation of such a convex set in generalized frameworks for quantum theory. We consider a projection of the regular 9-simplex onto the octonionic projective line to form a highly symmetric structure of ten octonionic quantum states on the surface of the octonionic Bloch ball. A uniform subnormalization of these ten symmetric states yields a symmetric informationally complete octonionic quantum measurement. We discuss a Quantum Bayesian reformulation of octonionic quantum formalism for the description of two-dimensional physical systems. We also describe a canonical embedding of the octonionic Bloch ball into an ambient space for states in usual complex quantum theory.
NASA Astrophysics Data System (ADS)
Buote, David A.; Humphrey, Philip J.
2012-04-01
This is the second of two papers investigating the spherical averaging of ellipsoidal galaxy clusters in the context of X-ray and Sunyaev-Zel'dovich (SZ) observations. In the present study, we quantify the orientation-average bias and scatter in observables that result from spherically averaging clusters described by either ellipsoidal generalizations of the Navarro-Frenk-White (NFW) profile or a nearly scale-free logarithmic potential. Although the mean biases are small and mostly <1 per cent, the flattest cluster models generally have a significant mean bias; i.e. averaging over all orientations does not always eliminate projection biases. Substantial biases can result from different viewing orientations, where the integrated Compton-y parameter (YSZ) and the concentration have the largest scatter (as large as σ˜ 10 per cent for YSZ), and the emission-weighted temperature (TX) has the smallest (σ≲ 0.5 per cent). The very small scatter for TX leads to YX and Mgas having virtually the same orientation biases. Substantial scatter is expected for individual clusters (up to σ˜ 8 per cent) in the correlation between YSZ and YX in comparison to the small mean bias (σ≲ 1 per cent) applicable to a random sample of clusters of sufficient size. For ellipsoidal NFW models, we show that the orientation bias for the total cluster mass attains a minimum near the radius r2500 so that the spherically averaged mass computed at this radius is always within ≈0.5 per cent of the true value for any orientation. Finally, to facilitate the accounting for orientation bias in X-ray and SZ cluster studies, we provide cubic polynomial approximations to the mean orientation bias and 1σ scatter for each cluster observable as a function of axial ratio for the ellipsoidal NFW models.
Symmetric extensions of normal discrete velocity models
NASA Astrophysics Data System (ADS)
Bobylev, A. V.; Vinerean, M. C.
2012-11-01
In this paper we discuss a general problem related to spurious conservation laws for discrete velocity models (DVMs) of the classical (elastic) Boltzmann equation. Models with spurious conservation laws appeared already at the early stage of the development of discrete kinetic theory. The well-known theorem of uniqueness of collision invariants for the continuous velocity space very often does not hold for a set of discrete velocities. In our previous works we considered the general problem of the construction of normal DVMs, we found a general algorithm for the construction of all such models and presented a complete classification of normal DVMs with small number n of velocities (n<11). Even if we have a general method to classify all normal discrete kinetic models (and in particular DVMs), the existing method is relatively slow and the amount of possible cases to check increases rapidly with n. We remarked that many of our normal DVMs appear to be axially symmetric. In this paper we consider a connection between symmetric transformations and normal DVMs. We first develop a new inductive method that, starting with a given normal DVM, leads by symmetric extensions to a new normal DVM. This method can produce very fast many new normal DVMs with larger number of velocities, showing that the class of normal DVMs contains a large subclass of symmetric models. We finally apply the method to several normal DVMs and construct new models that are not only normal, but also symmetric relatively to more and more axes. We hope that such symmetric velocity sets can be used for DSMC methods of solving Boltzmann equation.
On symmetric and upwind TVD schemes
NASA Technical Reports Server (NTRS)
Yee, H. C.
1986-01-01
The performance of the upwind and symmetric total variation diminishing (TVD) schemes in viscous and inviscid airfoil steady-state calculations is considered, and the extension of the implicit second-order-accurate TVD scheme for hyperbolic systems of conservative laws in curvilinear coordinates is discussed. For two-dimensional steady-state applications, schemes are implemented in a conservative noniterative alternating direction implicit form, and results illustrate that the algorithm produces a fairly good solution for an RAE2822 airfoil calculation. The study demonstrates that the symmetric TVD scheme is as accurate as the upwind TVD scheme, while requiring less computational effort than it.
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.
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.
The rhomboidal symmetric four-body problem
NASA Astrophysics Data System (ADS)
Waldvogel, Jörg
2012-05-01
We consider the planar symmetric four-body problem with two equal masses m 1 = m 3 > 0 at positions (± x 1( t), 0) and two equal masses m 2 = m 4 > 0 at positions (0, ± x 2( t)) at all times t, referred to as the rhomboidal symmetric four-body problem. Owing to the simplicity of the equations of motion this problem is well suited to study regularization of the binary collisions, periodic solutions, chaotic motion, as well as the four-body collision and escape manifolds. Furthermore, resonance phenomena between the two interacting rectilinear binaries play an important role.
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.
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).
NASA Astrophysics Data System (ADS)
Xu, W. X.; Chen, H. S.
2013-01-01
The determination of the volume fraction of interfacial layers is very significant for assessing the quantitative relationship between the microstructure and macroscopic physical properties of complex multiphase materials. In this work, based on a three-phase composite structure, an approximate analytical model for the volume fraction of interfacial layers around ellipsoidal aggregate particles is presented in detail. To verify the accuracy and reliability of the derived analytical model, a numerical model is introduced by means of random packing of polydispersed ellipsoidal aggregate particles, in which the relative spatial position between an arbitrary point and an ellipsoidal particle is precisely and conveniently determined. With the analytical and numerical models applied, the dependence of the volume fraction of interfacial layers on various factors, such as the particle shape, the volume fraction and the maximum particle size of aggregates, and the thickness of the interfacial layers, is evaluated. Furthermore, the results from the analytical model and the numerical model with these factors are compared. It is found that the theoretical results are favorably consistent with the simulated results.
NASA Astrophysics Data System (ADS)
Nakashima, Yoshito; Kamiya, Susumu; Nakano, Tsukasa
2008-12-01
Water molecules and contaminants migrate in water-saturated porous strata by diffusion in systems with small Péclet numbers. Natural porous rocks possess the anisotropy for diffusive transport along the percolated pore space. An X-ray computed tomography (CT) based approach is presented to quickly characterize anisotropic diffusion in porous rocks. High-resolution three-dimensional (3-D) pore images were obtained for a pumice and three sandstones by microfocus X-ray CT and synchrotron microtomography systems. The cluster-labeling process was applied to each image set to extract the 3-D image of a single percolated pore cluster through which diffusing species can migrate a long distance. The nonsorbing lattice random walk simulation was performed on the percolated pore cluster to obtain the mean square displacement. The self-diffusion coefficient along each direction in the 3-D space was calculated by taking the time derivative of the mean square displacement projected on the corresponding direction. A diffusion ellipsoid (i.e., polar representation of the direction-dependent normalized self-diffusivity) with three orthogonal principal axes was obtained for each rock sample. The 3-D two-point autocorrelation was also calculated for the percolated pore cluster of each rock sample to estimate the pore diameter anisotropy. The autocorrelation ellipsoids obtained by the ellipsoid fitting to the high correlation zone were prolate or oblate in shape, presumably depending on the eruption-induced deformation of magma and regional stress during sandstone diagenesis. The pore network anisotropy was estimated by calculating the diffusion ellipsoid for uniaxially elongated or compressed rock images. The degree and direction of the geological deformation of the samples estimated by the pore diameter anisotropy analysis agreed well with those estimated by the pore network anisotropy analysis. We found that the direction of the geological deformation coincided with the direction
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
NASA Astrophysics Data System (ADS)
Bhartia, Mini; Chatterjee, Arun Kumar
2015-04-01
A 2D model for the potential distribution in silicon film is derived for a symmetrical double gate MOSFET in weak inversion. This 2D potential distribution model is used to analytically derive an expression for the subthreshold slope and threshold voltage. A drain current model for lightly doped symmetrical DG MOSFETs is then presented by considering weak and strong inversion regions including short channel effects, series source to drain resistance and channel length modulation parameters. These derived models are compared with the simulation results of the SILVACO (Atlas) tool for different channel lengths and silicon film thicknesses. Lastly, the effect of the fixed oxide charge on the drain current model has been studied through simulation. It is observed that the obtained analytical models of symmetrical double gate MOSFETs are in good agreement with the simulated results for a channel length to silicon film thickness ratio greater than or equal to 2.
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.
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.
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…
Matching a static cylindrically symmetric elastic spacetime
NASA Astrophysics Data System (ADS)
Brito, I.; Carot, J.; Mena, F. C.; Vaz, E. G. L. R.
2012-07-01
We consider a static cylindrically symmetric spacetime with elastic matter and study the matching problem of this spacetime with a suitable exterior. For the exterior, we take the Levi-Civita spacetime and its generalization including a cosmological constant, the Linet-Tian spacetime. We show that the matching is only possible with the Linet-Tian solution.
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.
The growth and coalescence of ellipsoidal voids in plane strain under combined shear and tension
NASA Astrophysics Data System (ADS)
Scheyvaerts, F.; Onck, P. R.; Tekogˇlu, C.; Pardoen, T.
2011-02-01
New extensions of a model for the growth and coalescence of ellipsoidal voids based on the Gurson formalism are proposed in order to treat problems involving shear and/or voids axis not necessarily aligned with the main loading direction, under plane strain loading conditions. These extensions are motivated and validated using 3D finite element void cell calculations with overall plane strain enforced in one direction. The starting point is the Gologanu model dealing with spheroidal void shape. A void rotation law based on homogenization theory is coupled to this damage model. The predictions of the model closely agree with the 3D cell calculations, capturing the effect of the initial void shape and orientation on the void rotation rate. An empirical correction is also introduced for the change of the void aspect ratio in the plane transverse to the main axis of the void departing from its initially circular shape. This correction is needed for an accurate prediction of the onset of coalescence. Next, a new approach is proposed to take strain hardening into account within the Thomason criterion for internal necking, avoiding the use of strain hardening-dependent fitting parameters. The coalescence criterion is generalized to any possible direction of the coalescence plane and void orientation. Finally, the model is supplemented by a mathematical description of the final drop of the stress carrying capacity during coalescence. The entire model is developed for plane strain conditions, setting the path to a 3D extension. After validation of the model, a parametric study addresses the effect of shear on the ductility of metallic alloys for a range of microstructural and flow parameters, under different stress states. In general, the presence of shear, for identical stress triaxiality, decreases the ductility, partly explaining recent experimental results obtained in the low stress triaxiality regime.
Fabrication of an 8:1 ellipsoidal mirror for a synchrotron x-ray microprobe
Jones, K.W.; Takacs, P.Z.; Hastings, J.B.; Casstevens, J.M.; Pionke, C.D.
1987-01-11
The fabrication of an 8:1 demagnifying ellipsoidal mirror to be used for an x-ray microprobe at the National Synchrotron Light Source X-26 beam port is described. The design aim was to produce a mirror that could be used over the photon energy range from about 3 to 17 keV. The 300-mm long mirror was required to operate at a grazing angle of 5 mr. The semimajor axis was 4500 mm and the semiminor axis 14.142 mm. Surface roughness of 1 nm or less and slope errors of 1 arc second parallel to the long axis and 200 arc seconds parallel to the short direction were specified. Production of the first electroless nickel-coated aluminum mirror using a diamond-turning technique has been completed. The mirror meets the 1 arc sec surface figure specification except for areas near the ends of the mirror. The reasons for these deviations arise from subtle details of the diamond-turning process which have not been fully incorporated in to the computer program that controls the diamond-turning machines. Further work in computer correction of repeatable errors of the diamond-turning machine can eliminate the waviness at the ends of the mirror. The diamond-turned mirror surface was not fully polished under this effort and therefore does not meet the roughness specification; however, surface smoothness of a fully polished cylindrical mirror manufactured using the same techniques does not meet the specification. It can be concluded that it is now technically feasible to meet the required specifications for the mirror and that the x-ray microprobe based on its use can be achieved.
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.; 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.
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.
Saadat, Fatemeh; Birman, Victor; Thomopoulos, Stavros; Genin, Guy M.
2016-01-01
Estimates of the effective stiffness of a composite containing multiple types of inclusions are needed for the design and study of functionally graded 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 complex systems with multiple types of inclusions. For example, three-point parameters are known for only a few inclusion shapes and orientations. 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 lie outside of 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. PMID:26973356
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.
Cylindrically symmetric inhomogeneous cosmological models with viscous fluid and varying Λ
NASA Astrophysics Data System (ADS)
Pradhan, Anirudh; Singh, Prashant Kumar; Jotania, R. Kanti
2006-06-01
Cylindrically symmetric non-static cosmological models representing a bulk viscous fluid distribution have been obtained which are inhomogeneous and anisotropic. Without assuming any adhoc law, we obtain a cosmological constant as a decreasing function of time. Various physical and geometrical features of the models are also discussed.
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
Symmetric scalar constraint for loop quantum gravity
NASA Astrophysics Data System (ADS)
Lewandowski, Jerzy; Sahlmann, Hanno
2015-02-01
In the framework of loop quantum gravity, we define a new Hilbert space of states which are solutions of a large number of components of the diffeomorphism constraint. On this Hilbert space, using the methods of Thiemann, we obtain a family of gravitational scalar constraints. They preserve the Hilbert space for every choice of lapse function. Thus adjointness and commutator properties of the constraint can be investigated in a straightforward manner. We show how the space of solutions of the symmetrized constraint can be defined by spectral decomposition, and the Hilbert space of physical states by subsequently fully implementing the diffeomorphism constraint. The relationship of the solutions to those resulting from a proposal for a symmetric constraint operator by Thiemann remains to be elucidated.
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.
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
Braneworld gravity in a symmetric space bulk
NASA Astrophysics Data System (ADS)
Yilmaz, Nejat T.
2010-07-01
By considering the p-brane motion in a G/K symmetric space bulk we identify the G-invariant bulk metric in the solvable Lie algebra gauge of the brane action. After calculating the Levi-Civita connection of this bulk metric we use it in the Gauss equation to compute the braneworld curvature in terms of the bulk coordinates. Finally, by making use of the Gauss equation in the braneworld Einstein equation we present a geometrical method of implementing the first fundamental form in the gravitating brane dynamics for the specially chosen symmetric space bulk case leading to an Einstein equation expressed solely in terms of the bulk coordinates of the braneworld.
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.
Symmetrical Peripheral Gangrene Following Snake Bite
Shastri, Minal; Parikh, Mital; Patel, Dwijal; Chudasma, Ketan
2014-01-01
SPG (Symmetrical peripheral gangrene) is defined as symmetrical distal ischemic damage at two or more sites in the absence of large vessels obstruction. It has been ascribed to a number of infectious and non infectious conditions including connective tissue, cardiovascular, neoplastic and iatrogenic causes. We report a unique case of SPG in a 35-year-old Indian female who developed spontaneous gangrene of the distal phalanges of the right and left index, middle, ring and little fingers and the distal phalanges of all toes of the right and left foot following a snake bite. There have been very few cases of peripheral gangrene and acute renal failure associated with snake bite in literature. PMID:25386476
Intensity-symmetric accelerating caustic beams.
Ren, Zhijun; Jin, Hongzhen; Peng, Baojin; Shi, Yile
2016-09-20
We construct and generate symmetric accelerating caustic beams (ACBs) by using 3/2-order phase-only masks with elliptical contour based on optical caustics and diffraction theory. The symmetric ACBs are a type of bimodal accelerating caustic beam with two quasi-constant intensity peaks, very similar to the combination of two face-to-face Airy-like beams judging by appearance. Their fundamental optical morphology and force properties of particles in ACBs are subsequently provided. The unique optical properties of ACBs can be exploited for practical uses, such as accelerating electrons and clearing micrometer-sized particles as a laser micrometer-sized "water pump" instead of a laser micrometer-sized "snowblower" of accelerating Airy beams. PMID:27661599
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
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.
Solitons in PT-symmetric nonlinear lattices
Abdullaev, Fatkhulla Kh.; Konotop, Vladimir V.; Zezyulin, Dmitry A.; Kartashov, Yaroslav V.
2011-04-15
The existence of localized modes supported by the PT-symmetric nonlinear lattices is reported. The system considered reveals unusual properties: unlike other typical dissipative systems, it possesses families (branches) of solutions, which can be parametrized by the propagation constant; relatively narrow localized modes appear to be stable, even when the conservative nonlinear lattice potential is absent; and finally, the system supports stable multipole solutions.
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.
NASA Astrophysics Data System (ADS)
Paterson, Scott R.; Tobisch, Othmar T.
1993-06-01
Paterson, S.R. and Tobisch, O.T. 1993. Pre-lithification structures, deformation mechanisms, and fabric ellipsoids in slumped turbidites from the Pigeon Point Formation, California. Tectonophysics, 222: 135-149. Quantitative fabric, structural, and microstructural analyses of pre-lithification folds, foliations, and lineations formed by slumping of turbidite sequences in the Cretaceous Pigeon Point Formation, California, provide a useful comparison with strain and microstructures developed in lithified and tectonically deformed turbidites. Our results indicate the following: (1) multiple generations of folds, cleavages, and lineations can develop prior to any post-lithification tectonic deformation (2) individual grains in sandstones have variable axial ratios, but the ratios and orientations of large populations of grains define fabric ellipsoids with small axial ratios ( ave. = 1.25:1.13:1) (3) phyllosilicate grains define moderate flattening fabrics (reflecting 20-40% shortening or volume loss), with the intensity of alignment partly controlled by the percent of quartz and feldspar grains (4) the fabric ellipsoids in sand-rich layers largely reflect deposition and slumping: pre- and post-slump compactions did not occur, in sand-rich units but did align clay particles in mud-siltstone units, and (5) intra-grain microstructures in quartz and feldspar (e.g., undulose extinction, subgrains) are inherited or recycled features rather than representing effects of post-lithification strains. Our data also suggest that prelithification slumping occurred by pervasive grain rotation and grain boundary sliding in saturated sands with some local movement of material along bedding horizons. A likely model for the folding and associated fabrics is that buckling and fold-hinge flattening drove fluid expulsion, which in turn caused local grain-scale realignment, transposition of bedding, and the development of an axial planar cleavage in the hinge zones. Continued fluid flow was
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.
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.
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.
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.
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.
14 CFR 23.331 - Symmetrical flight conditions.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 14 Aeronautics and Space 1 2014-01-01 2014-01-01 false Symmetrical flight conditions. 23.331... Flight Loads § 23.331 Symmetrical flight conditions. (a) The appropriate balancing horizontal tail load... inertia loads corresponding to any of the symmetrical flight conditions specified in §§ 23.333 through...
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
Low-threshold nanowire laser based on composition-symmetric semiconductor nanowires.
Guo, Pengfei; Zhuang, Xiujuan; Xu, Jinyou; Zhang, Qinglin; Hu, Wei; Zhu, Xiaoli; Wang, Xiaoxia; Wan, Qiang; He, Pengbin; Zhou, Hong; Pan, Anlian
2013-03-13
Low-threshold nanoscale lasers are attractive for their promising applications in highly integrated photonic devices and systems. Here we report the controllable growth of composition-symmetric CdS(x)Se(1-x) nanowires by using a multistep thermal evaporation route with moving sources. Microstructure analyses reveal the obtained wires are high-quality single crystals with the composition gradually changed from the center toward their both ends. Under laser illumination, these wires exhibit symmetrical color distribution along the length direction, with red at the center and green at the both ends. Optically pumped lasing is realized at room temperature using these composition-symmetric nanowires, with the threshold several times lower than that of composition-homogeneous wires. This new nanowire structure will have potential applications as low-threshold nanoscale lasers in integrated nanophotonics.
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).
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.
A differential equation for Lerch's transcendent and associated symmetric operators in Hilbert space
Kaplitskii, V M
2014-08-01
The function Ψ(x,y,s)=e{sup iy}Φ(−e{sup iy},s,x), where Φ(z,s,v) is Lerch's transcendent, satisfies the following two-dimensional formally self-adjoint second-order hyperbolic differential equation, where s=1/2+iλ. The corresponding differential expression determines a densely defined symmetric operator (the minimal operator) on the Hilbert space L{sub 2}(Π), where Π=(0,1)×(0,2π). We obtain a description of the domains of definition of some symmetric extensions of the minimal operator. We show that formal solutions of the eigenvalue problem for these symmetric extensions are represented by functional series whose structure resembles that of the Fourier series of Ψ(x,y,s). We discuss sufficient conditions for these formal solutions to be eigenfunctions of the resulting symmetric differential operators. We also demonstrate a close relationship between the spectral properties of these symmetric differential operators and the distribution of the zeros of some special analytic functions analogous to the Riemann zeta function. Bibliography: 15 titles.
Spherically symmetric random walks. I. Representation in terms of orthogonal polynomials
Bender, C.M.; Cooper, F.; Meisinger, P.N.
1996-07-01
It is shown that, in general, a connection exists between orthogonal polynomials and semibounded random walks. This connection allows one to view a random walk as taking place on the set of integers that index the orthogonal polynomials. An illustration is provided by the case of spherically symmetric random walks. The correspondence between orthogonal polynomials and random walks enables one to express random-walk probabilities as weighted inner products of the polynomials. This correspondence is exploited to construct and analyze spherically symmetric random walks in {ital D}-dimensional space, where {ital D} is {ital not} restricted to be an integer. Such random walks can be described in terms of Gegenbauer (ultraspherical) polynomials. For example, Legendre polynomials can be used to represent the special case of two-dimensional spherically symmetric random walks. The weighted inner-product representation is used to calculate exact closed-form spatial and temporal moments of the probability distribution associated with the random walk. The polynomial representation of spherically symmetric random walks is then used to calculate the two-point Green{close_quote}s function for a rotationally symmetric free scalar quantum field theory. {copyright} {ital 1996 The American Physical Society.}
Averaged Eigenvalue Spectrum of Large Symmetric Random Matrix
NASA Astrophysics Data System (ADS)
Takano, Fumihiko; Takano, Hiroshi
1984-09-01
The averaged eigenvalue spectrum of a large symmetric random matrix, in which each element is an independent random variable with the Gaussian distribution, is calculated by using the diagram technique. Compared with the methods used by Edwards and Jones and by Mehta, the present method is very simple and can be used in other calculations. Leading terms in N (the dimension of the matrix) and next leading terms are calculated exactly. It is shown that the term proportional to N gives the semi-circular law obtained by Edwards and Jones. Next leading terms, which is of the order of unity, give three δ-functions as well as the corrections to the semi-circular law. One of the three δ-functions is the same as that of Edwards and Jones and other two are located at the band edges of the semi-circular law. The physical meanings of these results are discussed.
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.
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
Symmetric and Asymmetric Tendencies in Stable Complex Systems
NASA Astrophysics Data System (ADS)
Tan, James P. L.
2016-08-01
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.
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
NASA Astrophysics Data System (ADS)
Martinez, F. J.; Cisneros, J.; Montalvo, D.
1990-06-01
RESUMEN Se demuestra la existencia de figuras de equilibrio para un cuerpo fluido, autogravitante y libre de presi6n externa, que consiste de dos elipsoides confocales de distiiita densidad que giran con velocidad angular comun. El analisis muestra que a cada valor asignado a la densidad relativa del cuerpo, le corresponde un solo grado de achatamiento, es decir, no puede existir una sene. Otra conclusi6n es que Ia densidad relativa posee un inferior (tal que la densidad del elipsoide interior es ligeramente mayor que el doble de Ia del exterior) y al respecto se ofrece una explicaci6n semicualitativa. Se asume que el flufdo es ideal e incompresible. ABSTRACT For a self-gravitating free from external pressure fluid body, consisting of two homogeneous Co nfo cal ellipsoids of different density rotating with common angular velocity, we demonstrate the existence of equilibrium figures. No senes is possible, however, since the rotating body attains, for given values of its relative density, a unique degree of flattening. In addition, the analysis shows that there is a lower limit to the relative density (in which case the density of the interior ellipsoid is only slightly larger than twice the density of the exterior one) and a semi-qualitative explanation on the subject is offered. The fluids are assumed ideal and incompressible. Key words: HYDRODYNAMICS
NASA Astrophysics Data System (ADS)
Holota, Petr; Nesvadba, Otakar
2014-05-01
In physical geodesy mathematical tools applied for solving problems of potential theory are often essentially associated with the concept of the so-called spherical approximation (interpreted as a mapping). The same holds true for the method of analytical (harmonic) continuation which is frequently considered as a means suitable for converting the ground gravity anomalies or disturbances to corresponding values on the level surface that is close to the original boundary. In the development and implementation of this technique the key role has the representation of a harmonic function by means of the famous Poisson's formula and the construction of a radial derivative operator on the basis of this formula. In this contribution an attempt is made to avoid spherical approximation mentioned above and to develop mathematical tools that allow implementation of the concept of analytical continuation also in a more general case, in particular for converting the ground gravity anomalies or disturbances to corresponding values on the surface of an oblate ellipsoid of revolution. The respective integral kernels are constructed with the aid of series of ellipsoidal harmonics and their summation, but also the mathematical nature of the boundary date is discussed in more details.
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
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 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
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.
Cruz, Alejandro; Padilla-Martínez, Itzia I; García-Báez, Efrén V
2012-08-24
Symmetric and non-symmetric 2-(N-H, N-methyl, N-ethylenyl and N-aryl)guanidinebenzothiazoles were synthesized from the reaction of ammonia, methylamine, pyrrolidine and aniline with dimethyl benzo[d]thiazol-2-yl-carbonodithioimidate as intermediate. The products were characterized by ¹H-, ¹³C-NMR spectroscopy and three of them by X-ray diffraction analysis. HN-phenyl protons formed intramolecular hydrogen bonds that assist the stereochemistry of the second substituent, whereas the HN-alkyl protons were involved in intermolecular hydrogen bonding.
Mishra, Chandan K; Ganapathy, Rajesh
2015-05-15
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.
Expanding symmetric multiprocessor capability through gang scheduling
Jette, M.A.
1998-03-01
Symmetric Multiprocessor (SMP) systems normally provide both space- sharing and time-sharing to insure high system utilization and good responsiveness. However the prevailing lack of concurrent scheduling for parallel programs precludes SMP use in addressing many large-scale problems. Tightly synchronized communications are impractical and normal time-sharing reduces the benefit of cache memory. Evidence gathered at Lawrence Livermore National Laboratory (LLNL) indicates that gang scheduling can increase the capability of SMP systems and parallel program performance without adverse impact upon system utilization or responsiveness.
Characterisation of an AGATA symmetric prototype detector
NASA Astrophysics Data System (ADS)
Nelson, L.; Dimmock, M. R.; Boston, A. J.; Boston, H. C.; Cresswell, J. R.; Nolan, P. J.; Lazarus, I.; Simpson, J.; Medina, P.; Santos, C.; Parisel, C.
2007-04-01
The Advanced GAmma Tracking Array (AGATA) symmetric prototype detector has been tested at the University of Liverpool. A 137Ce source, collimated to a 2 mm diameter, was scanned across the front face of the detector and data were acquired utilising digital electronics. Pulse shapes from a selection of well-defined photon interaction positions have been analysed to investigate the position sensitivity of the detector. Furthermore, the application of the electric field simulation software, Multi Geometry Simulation (MGS) to generate theoretical pulse shapes for AGATA detectors has been presented.
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.
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.
Pelizzo, Maria-Guglielmina; Da Deppo, Vania; Naletto, Giampiero; Ragazzoni, Roberto; Novi, Andrea
2006-08-20
The design of a quasi-null lens system for the fabrication of an aspheric oblate convex ellipsoidal mirror is presented. The Performance and tolerance of the system have been analyzed. The system has been applied successfully for the fabrication of the primary mirror of the Wide Angle Camera (WAC), the imaging system onboard the Rosetta, the European Space Agency cornerstone mission dedicated to the exploration of a comet. The WAC is based on an off-axis two-mirror configuration, in which the primary mirror is an oblate convex ellipsoid with a significant conic constant.
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.
Analysis of non-symmetrical flapping airfoils
NASA Astrophysics Data System (ADS)
Tay, W. B.; Lim, K. B.
2009-08-01
Simulations have been done to assess the lift, thrust and propulsive efficiency of different types of non-symmetrical airfoils under different flapping configurations. The variables involved are reduced frequency, Strouhal number, pitch amplitude and phase angle. In order to analyze the variables more efficiently, the design of experiments using the response surface methodology is applied. Results show that both the variables and shape of the airfoil have a profound effect on the lift, thrust, and efficiency. By using non-symmetrical airfoils, average lift coefficient as high as 2.23 can be obtained. The average thrust coefficient and efficiency also reach high values of 2.53 and 0.61, respectively. The lift production is highly dependent on the airfoil’s shape while thrust production is influenced more heavily by the variables. Efficiency falls somewhere in between. Two-factor interactions are found to exist among the variables. This shows that it is not sufficient to analyze each variable individually. Vorticity diagrams are analyzed to explain the results obtained. Overall, the S1020 airfoil is able to provide relatively good efficiency and at the same time generate high thrust and lift force. These results aid in the design of a better ornithopter’s wing.
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.
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.
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.
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
Wang, Jieqiong; Yang, Sen; Gong, Junfeng; Xu, Minwei; Adil, Murtaza; Wang, Yu; Zhang, Yin; Song, Xiaoping; Zeng, Hao
2015-04-21
Recently, magnetic nanotubes have attracted great attention owing to the advantages of tubular geometry. Of all the physical properties of magnetic nanotubes, the magnetic behavior plays a pivotal role in potential applications, particularly in biotechnology. Modeling magnetic nanotubes provides an effective way to determine the geometry dependent magnetic properties. In the present article, we model the nanotube as a chain of ellipsoid-rings; thus the magnetic behavior of nanotubes is simulated by the fanning rotation of magnetic moments. Based on this model, we further discuss the influence of tubular geometric parameters on the magnetic properties. The calculated magnetic properties of Fe, Co, Ni, Fe3O4 and CoFe2O4 nanotubes are all consistent with their experimental data. Consequently, our model provides an easy and general approach to magnetic nanotubes.
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.
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.
VACUUM calculation in azimuthally symmetric geometry
Chance, M.S.
1996-11-01
A robustly accurate and effective method is presented to solve Laplace`s equation in general azimuthally symmetric geometry for the magnetic scalar potential in the region surrounding a plasma discharge which may or may not contain external conducting shells. These shells can be topologically toroidal or spherical, and may have toroidal gaps in them. The solution is incorporated into the various MHD stability codes either through the volume integrated perturbed magnetic energy in the vacuum region or through the continuity requirements for the normal component of the perturbed magnetic field and the total perturbed pressure across the unperturbed plasma-vacuum boundary. The method is based upon using Green`s second identity and the method of collocation. As useful byproducts, the eddy currents and the simulation of Mirnov loop measurements are calculated.
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.
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
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.
Minimal Left-Right Symmetric Dark Matter.
Heeck, Julian; Patra, Sudhanwa
2015-09-18
We show that left-right symmetric models can easily accommodate stable TeV-scale dark matter particles without the need for an ad hoc stabilizing symmetry. The stability of a newly introduced multiplet either arises accidentally as in the minimal dark matter framework or comes courtesy of the remaining unbroken Z_{2} subgroup of B-L. Only one new parameter is introduced: the mass of the new multiplet. As minimal examples, we study left-right fermion triplets and quintuplets and show that they can form viable two-component dark matter. This approach is, in particular, valid for SU(2)×SU(2)×U(1) models that explain the recent diboson excess at ATLAS in terms of a new charged gauge boson of mass 2 TeV.
Implications of nonlinearity for spherically symmetric accretion
NASA Astrophysics Data System (ADS)
Sen, Sourav; Ray, Arnab K.
2014-03-01
We subject the steady solutions of a spherically symmetric accretion flow to a time-dependent radial perturbation. The equation of the perturbation includes nonlinearity up to any arbitrary order and bears a form that is very similar to the metric equation of an analogue acoustic black hole. Casting the perturbation as a standing wave on subsonic solutions, and maintaining nonlinearity in it up to the second order, we get the time dependence of the perturbation in the form of a Liénard system. A dynamical systems analysis of the Liénard system reveals a saddle point in real time, with the implication that instabilities will develop in the accreting system when the perturbation is extended into the nonlinear regime. The instability of initial subsonic states also adversely affects the temporal evolution of the flow toward a final and stable transonic state.
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.
Hamiltonian theory of symmetric optical network transforms
NASA Astrophysics Data System (ADS)
Törmä, Päivi; Stenholm, Stig
1995-12-01
We discuss the theory of extracting an interaction Hamiltonian from a preassigned unitary transformation of quantum states. Such a procedure is of significance in quantum computations and other optical information processing tasks. We particularize the problem to the construction of totally symmetric 2N ports as introduced by Zeilinger and his collaborators [A. Zeilinger, M. Zukowski, M. A. Horne, H. J. Bernstein, and D. M. Greenberger, in Fundamental Aspects of Quantum Theory, edited by J. Anandan and J. J. Safko (World Scientific, Singapore, 1994)]. These are realized by the discrete Fourier transform, which simplifies the construction of the Hamiltonian by known methods of linear algebra. The Hamiltonians found are discussed and alternative realizations of the Zeilinger class transformations are presented. We briefly discuss the applicability of the method to more general devices.
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.
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.
Entanglement equivalence of N-qubit symmetric states
NASA Astrophysics Data System (ADS)
Mathonet, P.; Krins, S.; Godefroid, M.; Lamata, L.; Solano, E.; Bastin, T.
2010-05-01
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.
Integrable nonlinear parity-time-symmetric optical oscillator.
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.
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.
Integrable nonlinear parity-time-symmetric optical oscillator.
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. PMID:27176305
Ramesh, Nivarthi; Sarangi, Nirod Kumar; Patnaik, Archita
2013-05-01
Soft molecular ellipsoids conceived from 3,4-di(dodecyloxy)benzoic acid (DDBA) amphiphile draw attention to monomer structure design, intramolecular -COOH headgroup twist (ϕ°) and cyclic-acyclic dimer switching through facial H-bond torsion (ψ°). Generically, precipitation in hydrogen bonded systems has been the prime phenomenon once the critical aggregation concentrations were reached in the bulk solution. DDBA was no exception to this generalization. It formed precipitates in chloroform and methanol with no specific geometry but with cyclic dimer motifs in them. On the contrary, surface pressure modulated interfacial aggregation with ellipsoidal geometry followed acyclic dimerization (catemer motif) with various levels of headgroup torsion, established through real-time polarization modulated infrared reflection-absorption spectroscopy (IRRAS) and density functional theory (DFT) calculations, that estimated the energy costs for these unexplored pathways. The reaction coordinates ϕ° and ψ° in consonance with 2D surface pressure modulation thus directed the shape anisotropy during the dynamic self-assembly of DDBA. Changes in subphase pH and metal ionic environment had a derogatory effect on the ellipsoid formation, the structural requirement for which strictly followed a stringent need for twin alkyl chains in an asymmetric unit cell, as 4-dodecyloxybenzoic acid (MABA) with a single alkyl chain formed exclusively spherical assemblies with no dimer modulation. The investigation thus reports unexplored energy pathways toward ellipsoidal geometry of the amphiphile in the course of its interfacial aggregation.
NASA Astrophysics Data System (ADS)
Madou, Komlanvi; Leblond, Jean-Baptiste
2012-05-01
Gurson (1977)'s famous model of the behavior of porous ductile solids, initially developed for spherical cavities, was extended by Gologanu et al. (1993, 1994, 1997) to spheroidal, both prolate and oblate voids. The aim of this work is to further extend it to general (non-spheroidal) ellipsoidal cavities, through approximate homogenization of some representative elementary porous cell. As a first step, we perform in the present Part I a limit-analysis of such a cell, namely an ellipsoidal volume made of some rigid-ideal-plastic von Mises material and containing a confocal ellipsoidal void, loaded arbitrarily under conditions of homogeneous boundary strain rate. This analysis provides an estimate of the overall plastic dissipation based on a family of trial incompressible velocity fields recently discovered by Leblond and Gologanu (2008), satisfying conditions of homogeneous strain rate on all ellipsoids confocal with the void and the outer boundary. The asymptotic behavior of the integrand in the expression of the global plastic dissipation is studied both far from and close to the void. The results obtained suggest approximations leading to explicit approximate expressions of the overall dissipation and yield function. These expressions contain parameters the full determination of which will be the object of Part II.
Huang, Guoyong; Xu, Shengming; Xu, Zhenghe; Sun, Hongyu; Li, Linyan
2014-12-10
In this study, novel core-shell ellipsoidal MnCo2O4 powders with desired micro/nano-structure and a unique concentration gradient have been synthesized as anode material for Li-ion batteries. The special porous ellipsoid (2.5-4.5 μm in the long axis, 1.5-2.5 μm in the short axis, 200-300 nm in the thickness of shell) is built up by irregular nanoparticles attached to each other, and corresponding to the ellipsoid with concentration gradient, the Co/Mn atomic ratios of core and shell are about 1.76:1 and 2.34:1, respectively. The good performance, including high initial discharge capacities (1433.3 mAhg(-1) at 0.1 Ag(-1) and 1248.4 mAhg(-1) at 0.4 Ag(-1)), advanced capacity retention (∼900.0 mAhg(-1) after 60 cycles at 0.1 Ag(-1)), and fair rate performance (∼620.0 mAhg(-1) after 50 cycles at 0.4 Ag(-1)) has been measured by the battery test. Remarkably, the ellipsoidal shape and core-shell microstructure with concentration gradient are still maintained after 70 cycles of charge/discharge at 0.1 Ag(-1).
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
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.
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.
On the Symmetric Space σ-MODEL Kinematics
NASA Astrophysics Data System (ADS)
Yilmaz, Nejat T.
The solvable Lie algebra parametrization of the symmetric spaces is discussed. Based on the solvable Lie algebra gauge two equivalent formulations of the symmetric space sigma model are studied. Their correspondence is established by inspecting the normalization conditions and deriving the field transformation laws.
Bilateral Symmetrical Congenital Giant Becker's Nevus: A Rare Presentation
Rao, Angoori Gnaneshwar
2015-01-01
Becker's nevus is a focal epidermal hypermelanotic disorder. It morphologically presents as unilateral, hyperpigmented, hypertrichotic patch on upper trunk, proximal upper extremities and arms. However, Becker's nevus presenting as bilateral, symmetrical patches is rare. Herein, we report a rare case of giant Becker's nevus with bilateral symmetrical presentation in an adult male. PMID:26538733
47 CFR 51.711 - Symmetrical reciprocal compensation.
Code of Federal Regulations, 2010 CFR
2010-10-01
... 47 Telecommunication 3 2010-10-01 2010-10-01 false Symmetrical reciprocal compensation. 51.711... (CONTINUED) INTERCONNECTION Reciprocal Compensation for Transport and Termination of Telecommunications Traffic § 51.711 Symmetrical reciprocal compensation. (a) Rates for transport and termination...
14 CFR 23.331 - Symmetrical flight conditions.
Code of Federal Regulations, 2010 CFR
2010-01-01
... Flight Loads § 23.331 Symmetrical flight conditions. (a) The appropriate balancing horizontal tail load must be accounted for in a rational or conservative manner when determining the wing loads and linear inertia loads corresponding to any of the symmetrical flight conditions specified in §§ 23.333 through...
14 CFR 23.331 - Symmetrical flight conditions.
Code of Federal Regulations, 2011 CFR
2011-01-01
... Flight Loads § 23.331 Symmetrical flight conditions. (a) The appropriate balancing horizontal tail load must be accounted for in a rational or conservative manner when determining the wing loads and linear inertia loads corresponding to any of the symmetrical flight conditions specified in §§ 23.333 through...
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...
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.
Doskolovich, L L; Borisova, K V; Moiseev, M A; Kazanskiy, N L
2016-02-01
A method for the design of reflecting surfaces generating prescribed continuous illuminance distributions in two-dimensional domains is proposed. The mirror surface is represented as an envelope of a two-parameter family of ellipsoids. The first focus of each ellipsoid coincides with the point light source, while the second one is located at the illuminated domain. This surface representation can be interpreted as a limiting case of a segmented surface used in the supporting quadric method for focusing onto a set of points. The envelope equation depends on the function defining the lengths of the major axes of the ellipsoids of the family. The calculation of this function is performed using a continuous approximation of a discrete function obtained from the solution of a discrete problem of focusing onto a set of points. High efficiency of the proposed method is illustrated by the designed examples of mirrors for generating uniform illuminance distributions in areas of different shapes. PMID:26836069
Doskolovich, L L; Borisova, K V; Moiseev, M A; Kazanskiy, N L
2016-02-01
A method for the design of reflecting surfaces generating prescribed continuous illuminance distributions in two-dimensional domains is proposed. The mirror surface is represented as an envelope of a two-parameter family of ellipsoids. The first focus of each ellipsoid coincides with the point light source, while the second one is located at the illuminated domain. This surface representation can be interpreted as a limiting case of a segmented surface used in the supporting quadric method for focusing onto a set of points. The envelope equation depends on the function defining the lengths of the major axes of the ellipsoids of the family. The calculation of this function is performed using a continuous approximation of a discrete function obtained from the solution of a discrete problem of focusing onto a set of points. High efficiency of the proposed method is illustrated by the designed examples of mirrors for generating uniform illuminance distributions in areas of different shapes.
Analysis of Non-symmetrical Flapping Airfoils
NASA Astrophysics Data System (ADS)
Beng Tay, Wee; Lim, Kah Bin
2007-11-01
Simulations have been done to assess the performance of different types of non-symmetrical airfoils on lift, thrust and propulsive efficiency under different flapping configurations at a Reynolds number of 10,000. The variables studied include the Stroudal number, reduced frequency, pitch angle and phase angle difference. In order to analyze the variables more efficiently, the Design of Experiments using the response surface methodology is applied. The simulation results show that besides the flapping configuration, airfoil shape also has a profound effect on the efficiency, thrust and lift production. The 4 factors have different levels of significance on the responses, indicating the shape of the airfoil plays a part as well. Thrust production depends more heavily on these parameters, rather than the shape of the airfoil. On the other hand, lift production is primarily dominated by its airfoil shape. Efficiency falls somewhere in between. Two-factor interactions among the variables also exist in efficiency and thrust production. Vorticity plots are analyzed to explain some of the results. Overall, the s1020 airfoil is able to provide relatively good efficiency and at the same time generate high thrust and lift force. These results can be used to help in the design of a better ornithopter's wing.
Phase Behavior of Symmetric Sulfonated Block Copolymers
Park, Moon Jeong; Balsara, Nitash P.
2008-08-21
Phase behavior of poly(styrenesulfonate-methylbutylene) (PSS-PMB) block copolymers was studied by varying molecular weight, sulfonation level, and temperature. Molecular weights of the copolymers range from 2.9 to 117 kg/mol. Ordered lamellar, gyroid, hexagonally perforated lamellae, and hexagonally packed cylinder phases were observed in spite of the fact that the copolymers are nearly symmetric with PSS volume fractions between 0.45 and 0.50. The wide variety of morphologies seen in our copolymers is inconsistent with current theories on block copolymer phase behavior such as self-consistent field theory. Low molecular weight PSS-PMB copolymers (<6.2 kg/mol) show order-order and order-disorder phase transitions as a function of temperature. In contrast, the phase behavior of high molecular weight PSS-PMB copolymers (>7.7 kg/mol) is independent of temperature. Due to the large value of Flory-Huggins interaction parameter, x, between the sulfonated and non-sulfonated blocks, PSS-PMB copolymers with PSS and PMB molecular weights of 1.8 and 1.4 kg/mol, respectively, show the presence of an ordered gyroid phase with a 2.5 nm diameter PSS network. A variety of methods are used to estimate x between PSS and PMB chains as a function of sulfonation level. Some aspects of the observed phase behavior of PSS-PMB copolymers can be rationalized using x.
Spherically symmetric conformal gravity and ''gravitational bubbles''
Berezin, V.A.; Dokuchaev, V.I.; Eroshenko, Yu.N. E-mail: dokuchaev@inr.ac.ru
2016-01-01
The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson-Walker metrics. One of them we called the ''gravitational bubbles'', which is compact and with zero Weyl tensor. Thus, we obtained the pure vacuum curved space-times (without any material sources, including the cosmological constant) what is absolutely impossible in General Relativity. Such a phenomenon makes it easier to create the universe from ''nothing''. The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family. It appears that it can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We also investigated the general structure of the energy-momentum tensor in the spherical conformal gravity and constructed the vectorial equation that reveals clearly some features of non-vacuum solutions. Two of them are explicitly written, namely, the metrics à la Vaidya, and the electrovacuum space-time metrics.
Coscheduling Technique for Symmetric Multiprocessor Clusters
Yoo, A B; Jette, M A
2000-09-18
Coscheduling is essential for obtaining good performance in a time-shared symmetric multiprocessor (SMP) cluster environment. However, the most common technique, gang scheduling, has limitations such as poor scalability and vulnerability to faults mainly due to explicit synchronization between its components. A decentralized approach called dynamic coscheduling (DCS) has been shown to be effective for network of workstations (NOW), but this technique is not suitable for the workloads on a very large SMP-cluster with thousands of processors. Furthermore, its implementation can be prohibitively expensive for such a large-scale machine. IN this paper, they propose a novel coscheduling technique based on the DCS approach which can achieve coscheduling on very large SMP-clusters in a scalable, efficient, and cost-effective way. In the proposed technique, each local scheduler achieves coscheduling based upon message traffic between the components of parallel jobs. Message trapping is carried out at the user-level, eliminating the need for unsupported hardware or device-level programming. A sending process attaches its status to outgoing messages so local schedulers on remote nodes can make more intelligent scheduling decisions. Once scheduled, processes are guaranteed some minimum period of time to execute. This provides an opportunity to synchronize the parallel job's components across all nodes and achieve good program performance. The results from a performance study reveal that the proposed technique is a promising approach that can reduce response time significantly over uncoordinated time-sharing and batch scheduling.
Drift waves in helically symmetric stellarators
Rafiq, T.; Hegna, C.
2005-11-15
The local linear stability of electron drift waves and ion temperature gradient modes (ITG) is investigated in a quasihelically symmetric (QHS) stellarator and a conventional asymmetric (Mirror) stellarator. The geometric details of the different equilibria are emphasized. Eigenvalue equations for the models are derived using the ballooning mode formalism and solved numerically using a standard shooting technique in a fully three-dimensional stellarator configuration. While the eigenfunctions have a similar shape in both magnetic geometries, they are slightly more localized along the field line in the QHS case. The most unstable electron drift modes are strongly localized at the symmetry points (where stellarator symmetry is present) and in the regions where normal curvature is unfavorable and magnitude of the local magnetic shear and magnetic field is minimum. The presence of a large positive local magnetic shear in the bad curvature region is found to be destabilizing. Electron drift modes are found to be more affected by the normal curvature than by the geodesic curvature. The threshold of stability of the ITG modes in terms of {eta}{sub i} is found to be 2/3 in this fluid model consistent with the smallest threshold for toroidal geometry with adiabatic electrons. Optimization to favorable drift wave stability has small field line curvature, short connection lengths, the proper combination of geodesic curvature and local magnetic shear, large values of local magnetic shear, and the compression of flux surfaces in the unfavorable curvature region.
Symmetric Quartic Map in natural canonical coordinates
NASA Astrophysics Data System (ADS)
Baldwin, Danielle; Jones, Bilal; Settle, Talise; Ali, Halima; Punjabi, Alkesh
2015-11-01
The generating function for the simple map is modified by replacing the cubic term in canonical momentum by a quartic term. New parameters are introduced in the modified generating function to control the height and the width of ideal separatrix surface and the poloidal magnetic flux inside ideal separatrix. The new generating function is the generating function for the Symmetric Quartic Map (SQM). The new parameters in the generating function are chosen such that the height, width, elongation, and the poloidal flux inside the separatrix for the SQM are same as the simple map. The resulting generating function for the SQM is then transformed from the physical coordinates to the natural canonical coordinates. The equilibrium separatrix of the SQM is calculated in the natural canonical coordinates. The purpose of this research is to calculate the homoclinic tangle of the SQM and compare with the simple map. The separatrix of the simple map is open and unbounded; while the separatrix of the SQM is closed and compact. Motivation is to see what role the topology of the separatrix plays in its homoclinic tangle in single-null divertor tokamaks. This work is supported by grants DE-FG02-01ER54624, DE-FG02-04ER54793, and DE-FG02-07ER54937.
Hydroelastic dynamic characteristics of a slender axis-symmetric body
NASA Astrophysics Data System (ADS)
Chen, Weimin; Li, Min; Zheng, Zhongqin; Zhang, Liwu
2010-07-01
The slender axis-symmetric submarine body moving in the vertical plane is the object of our investigation. A coupling model is developed where displacements of a solid body as a Euler beam (consisting of rigid motions and elastic deformations) and fluid pressures are employed as basic independent variables, including the interaction between hydrodynamic forces and structure dynamic forces. Firstly the hydrodynamic forces, depending on and conversely influencing body motions, are taken into account as the governing equations. The expressions of fluid pressure are derived based on the potential theory. The characteristics of fluid pressure, including its components, distribution and effect on structure dynamics, are analyzed. Then the coupling model is solved numerically by means of a finite element method (FEM). This avoids the complicacy, combining CFD (fluid) and FEM (structure), of direct numerical simulation, and allows the body with a non-strict ideal shape so as to be more suitable for practical engineering. An illustrative example is given in which the hydroelastic dynamic characteristics, natural frequencies and modes of a submarine body are analyzed and compared with experimental results. Satisfactory agreement is observed and the model presented in this paper is shown to be valid.
On the Symmetric Collinear Four-Body Problem
NASA Astrophysics Data System (ADS)
Sekiguchi, Masayoshi; Tanikawa, Kiyotaka
2004-02-01
The global geometry of the phase structure in a special case of the general Newtonian four-body problem was studied both analytically and numerically in the case of negative energy. Our method consists of blow-up of total collision by McGehee's coordinates. and representation of orbits by symbol sequences. The analytical study for arbitrary masses clarifies the macroscopic behavior in phase space: escape motion, vortical motion around vertical lines along which the escape motion occurs, and vertical convective flow. We numerically examined a distribution of the symbol sequences on a surface of section in the case of equal masses. The result has clarified that there never exist orbits whose symbol sequences contain special words: un-realizable words. On the other hand, the existence of oscillatory motions are shown under a reasonable assumption. We semi-analytically obtained the initial conditions leading to escape using escape criteria established in the present study. Additionally, we established a way to find the fastest capture-escape orbits, the ejection-collision orbits besides the homothetic solution, the capture-collision orbits, and the ejection-escape orbits. Moreover, quasi-periodic orbits containing a Schubart-like orbit, and unstable periodic orbits were found. The result displays a similarity between the symmetric collinear four-body problem and the collinear three-body problem.
Pradhan, D.; Schlegel, R.A. ); Williamson, P. )
1991-08-06
Two mechanisms have been proposed for maintenance of transbilayer phospholipid asymmetry in the erythrocyte plasma membrane, one involving specific interactions between the aminophospholipids of the inner leaflet of the bilayer and the cytoskeleton, particularly spectrin, and the other involving the aminophospholipid translocase. If the former mechanism is correct, then erythrocytes which have lost their asymmetric distribution of phospholipids should display altered bilayer/cytoskeleton interactions. To test this possibility, normal erythrocytes, erythrocytes from patients with chronic myelogenous leukemia or sickle disease, and lipid-symmetric and -asymmetric erythrocyte ghosts were labeled with the radioactive photoactivable analogue of phosphatidylethanolamine, 2-(2-azido-4-nitrobenzoyl)-1-acyl-sn-glycero-3-phospho({sup 14}C) ethanolamine (({sup 14}C)AzPE), previously shown to label cytoskeletal proteins from the bilayer. The labeling pattern of cytoskeletal proteins in pathologic erythrocytes and lipid-asymmetric erythrocyte ghosts was indistinguishable from normal erythrocytes, indicating that the probe detects no differences in bilayer/cytoskeleton interactions in these cells. In contrast, in lipid-symmetric erythrocyte ghosts, labeling of bands 4.1 and 4.2 and actin, and to a lesser extent ankyrin, by ({sup 14}C)AzPE was considerably reduced. Significantly, however, labeling of spectrin was unaltered in the lipid-symmetric cells. These results do not support a model in which spectrin is involved in the maintenance of an asymmetric distribution of phospholipids in erythrocytes.
Recent advances in symmetric and network dynamics.
Golubitsky, Martin; Stewart, Ian
2015-09-01
We summarize some of the main results discovered over the past three decades concerning symmetric dynamical systems and networks of dynamical systems, with a focus on pattern formation. In both of these contexts, extra constraints on the dynamical system are imposed, and the generic phenomena can change. The main areas discussed are time-periodic states, mode interactions, and non-compact symmetry groups such as the Euclidean group. We consider both dynamics and bifurcations. We summarize applications of these ideas to pattern formation in a variety of physical and biological systems, and explain how the methods were motivated by transferring to new contexts René Thom's general viewpoint, one version of which became known as "catastrophe theory." We emphasize the role of symmetry-breaking in the creation of patterns. Topics include equivariant Hopf bifurcation, which gives conditions for a periodic state to bifurcate from an equilibrium, and the H/K theorem, which classifies the pairs of setwise and pointwise symmetries of periodic states in equivariant dynamics. We discuss mode interactions, which organize multiple bifurcations into a single degenerate bifurcation, and systems with non-compact symmetry groups, where new technical issues arise. We transfer many of the ideas to the context of networks of coupled dynamical systems, and interpret synchrony and phase relations in network dynamics as a type of pattern, in which space is discretized into finitely many nodes, while time remains continuous. We also describe a variety of applications including animal locomotion, Couette-Taylor flow, flames, the Belousov-Zhabotinskii reaction, binocular rivalry, and a nonlinear filter based on anomalous growth rates for the amplitude of periodic oscillations in a feed-forward network. PMID:26428565
Recent advances in symmetric and network dynamics
NASA Astrophysics Data System (ADS)
Golubitsky, Martin; Stewart, Ian
2015-09-01
We summarize some of the main results discovered over the past three decades concerning symmetric dynamical systems and networks of dynamical systems, with a focus on pattern formation. In both of these contexts, extra constraints on the dynamical system are imposed, and the generic phenomena can change. The main areas discussed are time-periodic states, mode interactions, and non-compact symmetry groups such as the Euclidean group. We consider both dynamics and bifurcations. We summarize applications of these ideas to pattern formation in a variety of physical and biological systems, and explain how the methods were motivated by transferring to new contexts René Thom's general viewpoint, one version of which became known as "catastrophe theory." We emphasize the role of symmetry-breaking in the creation of patterns. Topics include equivariant Hopf bifurcation, which gives conditions for a periodic state to bifurcate from an equilibrium, and the H/K theorem, which classifies the pairs of setwise and pointwise symmetries of periodic states in equivariant dynamics. We discuss mode interactions, which organize multiple bifurcations into a single degenerate bifurcation, and systems with non-compact symmetry groups, where new technical issues arise. We transfer many of the ideas to the context of networks of coupled dynamical systems, and interpret synchrony and phase relations in network dynamics as a type of pattern, in which space is discretized into finitely many nodes, while time remains continuous. We also describe a variety of applications including animal locomotion, Couette-Taylor flow, flames, the Belousov-Zhabotinskii reaction, binocular rivalry, and a nonlinear filter based on anomalous growth rates for the amplitude of periodic oscillations in a feed-forward network.
Symmetric coordinates in solids: magnetic Bloch oscillations
NASA Astrophysics Data System (ADS)
Zak, Joshua
2015-04-01
There has recently been a revival of the Bloch theory of energy bands in solids. This revival was caused, on one hand, by the discovery of topological insulators and the discovery of graphene, and, on the other end, by a very efficient new technique that was developed for creating artificial solids. These are the cold atoms in optical lattices. Last year geometric phases were measured in energy bands of cold atoms in a one-dimensional optical lattice by using Bloch oscillations. These phases are related to the Wyckoff positions, or the symmetry centers in the Bravais lattice. In this lecture a theoretical frame is developed for magnetic Bloch oscillations, meaning oscillations in the presence of a magnetic field. The theory is based on the kq-representation and the symmetric coordinates in solids. It is shown that for a Bloch electron in a magnetic field the orbit quasi-center is a conserved quantity. This is similar to the conservation of the quasi-momentum for an electron in a periodic potential. When an electric field is turned on, the orbit quasi-center oscillates in a similar way to the Bloch oscillations in the absence of a magnetic field. But there is a difference because the magnetic Brillouin zone is different. It depends on the strength of the magnetic field. An analogy is drawn between Bloch oscillations and magnetic Bloch oscillations. By using the magnetic translations it is indicated that a magnetic Wannier-Stark ladder appears in the spectrum of a Bloch electron in crossed magnetic and electric fields. The geometric phases for magnetic Bloch oscillations should be magnetic field dependent.
Comparison of eigensolvers for symmetric band matrices
Moldaschl, Michael; Gansterer, Wilfried N.
2014-01-01
We compare different algorithms for computing eigenvalues and eigenvectors of a symmetric band matrix across a wide range of synthetic test problems. Of particular interest is a comparison of state-of-the-art tridiagonalization-based methods as implemented in Lapack or Plasma on the one hand, and the block divide-and-conquer (BD&C) algorithm as well as the block twisted factorization (BTF) method on the other hand. The BD&C algorithm does not require tridiagonalization of the original band matrix at all, and the current version of the BTF method tridiagonalizes the original band matrix only for computing the eigenvalues. Avoiding the tridiagonalization process sidesteps the cost of backtransformation of the eigenvectors. Beyond that, we discovered another disadvantage of the backtransformation process for band matrices: In several scenarios, a lot of gradual underflow is observed in the (optional) accumulation of the transformation matrix and in the (obligatory) backtransformation step. According to the IEEE 754 standard for floating-point arithmetic, this implies many operations with subnormal (denormalized) numbers, which causes severe slowdowns compared to the other algorithms without backtransformation of the eigenvectors. We illustrate that in these cases the performance of existing methods from Lapack and Plasma reaches a competitive level only if subnormal numbers are disabled (and thus the IEEE standard is violated). Overall, our performance studies illustrate that if the problem size is large enough relative to the bandwidth, BD&C tends to achieve the highest performance of all methods if the spectrum to be computed is clustered. For test problems with well separated eigenvalues, the BTF method tends to become the fastest algorithm with growing problem size. PMID:26594079
Symmetric inertial confinement fusion implosions at ultra-high laser energies
Glenzer, S H; MacGowan, B J; Michel, P; Meezan, N B; Suter, L J; Dixit, S N; Kline, J L; Kyrala, G A; Callahan, D A; Dewald, E L; Divol, L; Dzenitis, E; Edwards, J; Hamza, A V; Haynam, C A; Hinkel, D E; Kalantar, D H; Kilkenny, J D; Landen, O L; Lindle, J D; LePape, S; Moody, J D; Nikroo, A; Parham, T; Schneider, M B; Town, R J; Wegner, P; Widmann, K; Whitman, P; Young, B F; Van Wonterghem, B; Atherton, J E; Moses, E I
2009-12-03
The first indirect-drive hohlraum experiments at the National Ignition Facility have demonstrated symmetric capsule implosions at unprecedented laser drive energies of 0.7 MJ. 192 simultaneously fired laser beams heat ignition hohlraums to radiation temperatures of 3.3 million Kelvin compressing 1.8-millimeter capsules by the soft x rays produced by the hohlraum. Self-generated plasma-optics gratings on either end of the hohlraum tune the laser power distribution in the hohlraum producing symmetric x-ray drive as inferred from capsule self-emission measurements. These experiments indicate conditions suitable for compressing deuterium-tritium filled capsules with the goal to achieve burning fusion plasmas and energy gain in the laboratory.
Cutting Force Predication Based on Integration of Symmetric Fuzzy Number and Finite Element Method
Wang, Zhanli; Hu, Yanjuan; Wang, Yao; Dong, Chao; Pang, Zaixiang
2014-01-01
In the process of turning, pointing at the uncertain phenomenon of cutting which is caused by the disturbance of random factors, for determining the uncertain scope of cutting force, the integrated symmetric fuzzy number and the finite element method (FEM) are used in the prediction of cutting force. The method used symmetric fuzzy number to establish fuzzy function between cutting force and three factors and obtained the uncertain interval of cutting force by linear programming. At the same time, the change curve of cutting force with time was directly simulated by using thermal-mechanical coupling FEM; also the nonuniform stress field and temperature distribution of workpiece, tool, and chip under the action of thermal-mechanical coupling were simulated. The experimental result shows that the method is effective for the uncertain prediction of cutting force. PMID:24790556
NASA Astrophysics Data System (ADS)
Reiss, Robert; Barton, Oscar; Thigpen, Lewis; Aung, Win; Qian, Bo
A new closed-form approximation for the fundamental frequency of symmetric rectangular laminates subject to all combinations of hinged and clamped boundary conditions is presented. The distributed parameter eigenvalue equation is cast in an equivalent infinitely-dimensional discrete form. The stiffness and mass matrices are each decomposed into the sum of two matrices, one of which is diagonal while the other contains zero diagonal elements. Design sensitivity analysis is used to expand the desired eigenfrequency in a Maclaurin series of the zero diagonal matrices. The general formula thus obtained is then specialized to rectangular symmetric laminated plates. The remarkable accuracy of this new formula is established by numerical comparisons of results calculated from it to those obtained from the conventional Rayleigh-Ritz method.
Li, Zheng; Borner, Arnaud; Levin, Deborah A
2014-06-14
Homogeneous water condensation and ice formation in supersonic expansions to vacuum for stagnation pressures from 12 to 1000 mbar are studied using the particle-based Ellipsoidal-Statistical Bhatnagar-Gross-Krook (ES-BGK) method. We find that when condensation starts to occur, at a stagnation pressure of 96 mbar, the increase in the degree of condensation causes an increase in the rotational temperature due to the latent heat of vaporization. The simulated rotational temperature profiles along the plume expansion agree well with measurements confirming the kinetic homogeneous condensation models and the method of simulation. Comparisons of the simulated gas and cluster number densities, cluster size for different stagnation pressures along the plume centerline were made and it is found that the cluster size increase linearly with respect to stagnation pressure, consistent with classical nucleation theory. The sensitivity of our results to cluster nucleation model and latent heat values based on bulk water, specific cluster size, or bulk ice are examined. In particular, the ES-BGK simulations are found to be too coarse-grained to provide information on the phase or structure of the clusters formed. For this reason, molecular dynamics simulations of water condensation in a one-dimensional free expansion to simulate the conditions in the core of a plume are performed. We find that the internal structure of the clusters formed depends on the stagnation temperature. A larger cluster of average size 21 was tracked down the expansion, and a calculation of its average internal temperature as well as a comparison of its radial distribution functions (RDFs) with values measured for solid amorphous ice clusters lead us to conclude that this cluster is in a solid-like rather than liquid form. In another molecular-dynamics simulation at a much lower stagnation temperature, a larger cluster of size 324 and internal temperature 200 K was extracted from an expansion plume and
Li, Zheng; Borner, Arnaud; Levin, Deborah A
2014-06-14
Homogeneous water condensation and ice formation in supersonic expansions to vacuum for stagnation pressures from 12 to 1000 mbar are studied using the particle-based Ellipsoidal-Statistical Bhatnagar-Gross-Krook (ES-BGK) method. We find that when condensation starts to occur, at a stagnation pressure of 96 mbar, the increase in the degree of condensation causes an increase in the rotational temperature due to the latent heat of vaporization. The simulated rotational temperature profiles along the plume expansion agree well with measurements confirming the kinetic homogeneous condensation models and the method of simulation. Comparisons of the simulated gas and cluster number densities, cluster size for different stagnation pressures along the plume centerline were made and it is found that the cluster size increase linearly with respect to stagnation pressure, consistent with classical nucleation theory. The sensitivity of our results to cluster nucleation model and latent heat values based on bulk water, specific cluster size, or bulk ice are examined. In particular, the ES-BGK simulations are found to be too coarse-grained to provide information on the phase or structure of the clusters formed. For this reason, molecular dynamics simulations of water condensation in a one-dimensional free expansion to simulate the conditions in the core of a plume are performed. We find that the internal structure of the clusters formed depends on the stagnation temperature. A larger cluster of average size 21 was tracked down the expansion, and a calculation of its average internal temperature as well as a comparison of its radial distribution functions (RDFs) with values measured for solid amorphous ice clusters lead us to conclude that this cluster is in a solid-like rather than liquid form. In another molecular-dynamics simulation at a much lower stagnation temperature, a larger cluster of size 324 and internal temperature 200 K was extracted from an expansion plume and
NASA Astrophysics Data System (ADS)
Wang, Li-Hua; Li, Ji-Tao; Li, Shao-Feng; Liu, Quan-Tao
2016-06-01
We study a (3+1)-dimensional variable-coefficient nonlinear Schrödinger equation with different diffractions and power-law nonlinearity in PT-symmetric potentials. Considering different PT-symmetric potentials, we obtain two kinds of analytical sech-type localized soliton solutions. From these solutions, we analytically discuss the powers and power-flow densities. Moreover, we study compression and expansion of localized structures in the periodic distributed amplification system.
(M-theory-)Killing spinors on symmetric spaces
Hustler, Noel; Lischewski, Andree
2015-08-15
We show how the theory of invariant principal bundle connections for reductive homogeneous spaces can be applied to determine the holonomy of generalised Killing spinor covariant derivatives of the form D = ∇ + Ω in a purely algebraic and algorithmic way, where Ω : TM → Λ{sup ∗}(TM) is a left-invariant homomorphism. Specialising this to the case of symmetric M-theory backgrounds (i.e., (M, g, F) with (M, g) an eleven-dimensional Lorentzian (locally) symmetric space and F an invariant closed 4-form), we derive several criteria for such a background to preserve some supersymmetry and consequently find all supersymmetric symmetric M-theory backgrounds.
Experimental scheme for unambiguous discrimination of linearly independent symmetric states
Jimenez, O.; Burgos-Inostroza, E.; Delgado, A.; Saavedra, C.; Sanchez-Lozano, X.
2007-12-15
We propose an experimental setup for discriminating four linearly independent nonorthogonal symmetric quantum states. The setup is based on linear optics only and can be configured to implement both optimal unambiguous state discrimination [Chefles and Barnett, Phys. Lett. A 250, 223 (1998)] and minimum error discrimination. In both cases, the setup is characterized by an optimal success probability. The experimental setup can be generalized to the case of discrimination among N linearly nonorthogonal symmetric quantum states. We also study the discrimination between two incoherent superpositions of symmetric states. In this case, the setup also achieves an optimal success probability in the case of unambiguous discrimination as well as minimum error discrimination.
Weyl symmetric representation of SU(3) gluodynamics in abelian projection
NASA Astrophysics Data System (ADS)
Koma, Y.; Takayama, M.; Toki, H.; Ebert, D.
2001-10-01
The dual Ginzburg-Landau (DGL) theory corresponding to the SU(3) gluodynamics in Abelian projection is formulated in a Weyl symmetric way. The Weyl symmetric DGL theory can be regarded as the sum of three types of the U(1) dual Abelian Higgs (DAH) model. As an application of this approach, the hadronic flux-tube solution corresponding to the baryonic state is investigated adopting the similar techniques used in the U(1) DAH model. The string representation of the DGL theory is also discussed in a Weyl symmetric way.
Chirally Symmetric but Confined Hadrons at Finite Density
NASA Astrophysics Data System (ADS)
Ya. Glozman, L.; Wagenbrunn, R. F.
At a critical finite chemical potential and low temperature QCD undergoes the chiral restoration phase transition. The folklore tradition is that simultaneously hadrons are deconfined and there appears the quark matter. We demonstrate that it is possible to have confined but chirally symmetric hadrons at a finite chemical potential and hence beyond the chiral restoration point at a finite chemical potential and low temperature there could exist a chirally symmetric matter consisting of chirally symmetric but confined hadrons. If it does happen in QCD, then the QCD phase diagram should be reconsidered with obvious implications for heavy ion programs and astrophysics.
(M-theory-)Killing spinors on symmetric spaces
NASA Astrophysics Data System (ADS)
Hustler, Noel; Lischewski, Andree
2015-08-01
We show how the theory of invariant principal bundle connections for reductive homogeneous spaces can be applied to determine the holonomy of generalised Killing spinor covariant derivatives of the form D = ∇ + Ω in a purely algebraic and algorithmic way, where Ω : TM → Λ∗(TM) is a left-invariant homomorphism. Specialising this to the case of symmetric M-theory backgrounds (i.e., (M, g, F) with (M, g) an eleven-dimensional Lorentzian (locally) symmetric space and F an invariant closed 4-form), we derive several criteria for such a background to preserve some supersymmetry and consequently find all supersymmetric symmetric M-theory backgrounds.
Reconstruction of symmetric Dirac-Maxwell equations using nonassociative algebra
NASA Astrophysics Data System (ADS)
Kalauni, Pushpa; Barata, J. C. A.
2015-01-01
In the presence of sources, the usual Maxwell equations are neither symmetric nor invariant with respect to the duality transformation between electric and magnetic fields. Dirac proposed the existence of magnetic monopoles for symmetrizing the Maxwell equations. In the present work, we obtain the fully symmetric Dirac-Maxwell's equations (i.e. with electric and magnetic charges and currents) as a single equation by using 4 × 4 matrix presentation of fields and derivative operators. This matrix representation has been derived with the help of the algebraic properties of quaternions and octonions. Such description gives a compact representation of electric and magnetic counterparts of the field in a single equation.
Garcia-Aguirre, Gerardo; Schwartz, Shulamit
2014-01-01
Purpose. Pathophysiology of macular hole (MH) is not yet well defined but the advances of spectral domain optical coherence tomography (SD-OCT) give us access to further detailed imaging. We report a case with macular inner segment ellipsoid (ISe) band loss and cone outer segment tips (COST) line changes seen in SD-OCT preceding MH appearance in a young patient. Methods. 21-year-old woman presented with a partial central scotoma, metamorphopsia, and a 20/25 vision in her right eye. Past medical history was positive for laser assisted in situ keratomileusis (LASIK) surgery 7 months ago with no complications. Macular SD-OCT showed ISe band loss and COST line elevation. She was followed a month later with visual acuity deteriorating to 20/200 and a full thickness MH. Results. The patient underwent a pars plana vitrectomy with internal limiting membrane peeling. Her visual acuity 2 months later was 20/20. Conclusion. SD-OCT can identify preliminary changes, yet to be described, preceding MH formation. Our patient demonstrated ISe band loss and COST abnormalities on SD-OCT a month prior to MH development. SD-OCT should be considered in young patients with subtle visual symptoms and mild changes in visual acuity that are not readily explained by ophthalmological exam. PMID:25548697
NASA Astrophysics Data System (ADS)
Zlinszky, András; Ressl, Camillo; Timár, Gábor; Weber, Robert; Székely, Balázs; Briese, Christian; Pfeifer, Norbert
2013-04-01
The geoid is the theoretical model of the Earth, defined as an equipotential surface. Typically it corresponds to a mean ocean surface and is extended through the continents. Elevations are measured above "sea level" based on the fact that the surface of water in equilibrium closely follows this equipotential surface. On dry land, the geoid can be determined from gravimetric measurements, and interpolation methods are used to represent variations of gravity in a regular grid model. For practical reasons, these are represented as geoid undulation, which is the difference of the ellipsoidal height and the height of the equipotential surface. In his work Principia, Isaac Newton proposed the thought experiment of connecting the North Pole and the Equator through a "canal" filled with water in order to determine gravitational flattening of the Earth. It was also Newton's idea to use the level of water in a global network of canals and wells to survey the geoid. Of course, these experiments are impossible at a global scale, but a sufficiently large lake and an accurate method for measuring elevation independently from the geoid can be used to prove the concept. Our objective was to measure the ellipsoidal water surface elevation of Lake Balaton in Hungary with high spatial resolution and accuracy and compare these measurements with the gravimetrically determined local geoid model. Airborne laser scanning (ALS, also known as airborne LIDAR) is a remote sensing technique capable of delivering a large number of points with elevations and horizontal positions accurate to a few centimetres. Laser pulses are emitted in a scan pattern from an airborne sensor, and are reflected from the illuminated terrain (or water) surface. Based on the position and orientation of the aircraft (typically observed by GNSS and an inertial navigation system), the scan angle and the travel time of the laser pulse, the exact position of each measurement point is calculated. In this particular case
NASA Astrophysics Data System (ADS)
Cellino, A.; Muinonen, K.; Hestroffer, D.; Carbognani, A.
2015-12-01
The inversion of sparse photometric data of asteroids to derive from them information about the spin and shape properties of the objects is a hot topic in the era of the Gaia space mission. We have used a rigorous analytical treatment of the Lommel-Seeliger light-scattering law computed for the particular case of bodies having the shapes of ideal triaxial ellipsoids, and we have implemented this in the software developed for the treatment of Gaia photometric data for asteroids. In a set of numerical simulations, the performances of the photometry inversion code improve significantly with respect to the case in which purely geometric scattering is taken into account. When applied to real photometric data of asteroids obtained in the past by the Hipparcos satellite, however, we do not see any relevant improvement of the performances, due to the poor accuracy of these measurements. These results suggest that the role played by the light-scattering properties of asteroid surfaces is indeed relevant. On the other hand, any refined treatment of light-scattering effects cannot improve the reliability of photometric inversion when the quantity and quality of available data are much worse than what we expect to obtain from Gaia.
Barbier, Michaël; Jaensch, Steffen; Cornelissen, Frans; Vidic, Suzana; Gjerde, Kjersti; de Hoogt, Ronald; Graeser, Ralph; Gustin, Emmanuel; Chong, Yolanda T.
2016-01-01
In oncology, two-dimensional in-vitro culture models are the standard test beds for the discovery and development of cancer treatments, but in the last decades, evidence emerged that such models have low predictive value for clinical efficacy. Therefore they are increasingly complemented by more physiologically relevant 3D models, such as spheroid micro-tumor cultures. If suitable fluorescent labels are applied, confocal 3D image stacks can characterize the structure of such volumetric cultures and, for example, cell proliferation. However, several issues hamper accurate analysis. In particular, signal attenuation within the tissue of the spheroids prevents the acquisition of a complete image for spheroids over 100 micrometers in diameter. And quantitative analysis of large 3D image data sets is challenging, creating a need for methods which can be applied to large-scale experiments and account for impeding factors. We present a robust, computationally inexpensive 2.5D method for the segmentation of spheroid cultures and for counting proliferating cells within them. The spheroids are assumed to be approximately ellipsoid in shape. They are identified from information present in the Maximum Intensity Projection (MIP) and the corresponding height view, also known as Z-buffer. It alerts the user when potential bias-introducing factors cannot be compensated for and includes a compensation for signal attenuation. PMID:27303813
Harasawa, Mariana; Quiroz-Mercado, Hugo; Salcedo-Villanueva, Guillermo; Garcia-Aguirre, Gerardo; Schwartz, Shulamit
2014-01-01
Purpose. Pathophysiology of macular hole (MH) is not yet well defined but the advances of spectral domain optical coherence tomography (SD-OCT) give us access to further detailed imaging. We report a case with macular inner segment ellipsoid (ISe) band loss and cone outer segment tips (COST) line changes seen in SD-OCT preceding MH appearance in a young patient. Methods. 21-year-old woman presented with a partial central scotoma, metamorphopsia, and a 20/25 vision in her right eye. Past medical history was positive for laser assisted in situ keratomileusis (LASIK) surgery 7 months ago with no complications. Macular SD-OCT showed ISe band loss and COST line elevation. She was followed a month later with visual acuity deteriorating to 20/200 and a full thickness MH. Results. The patient underwent a pars plana vitrectomy with internal limiting membrane peeling. Her visual acuity 2 months later was 20/20. Conclusion. SD-OCT can identify preliminary changes, yet to be described, preceding MH formation. Our patient demonstrated ISe band loss and COST abnormalities on SD-OCT a month prior to MH development. SD-OCT should be considered in young patients with subtle visual symptoms and mild changes in visual acuity that are not readily explained by ophthalmological exam. PMID:25548697
NASA Astrophysics Data System (ADS)
Madou, Komlanvi; Leblond, Jean-Baptiste
2012-05-01
The aim of this paper is to fully determine the parameters of the approximate homogenized yield criterion for porous ductile solids containing arbitrary ellipsoidal cavities proposed in Part I. This is done through improvements of the limit-analysis of some representative hollow cell presented there. The improvements are of two kinds. For hydrostatic loadings, the limit-analysis is refined by performing micromechanical finite element computations in a number of significant cases, so as to replace Leblond and Gologanu (2008)'s trial velocity field representing the expansion of the void by the exact, numerically determined one. For deviatoric loadings, limit-analysis is dropped and direct use is made of some general rigorous results for nonlinear composites derived by Ponte-Castaneda (1991), Willis (1991) and Michel and Suquet (1992) using the earlier work of Willis (1977) and the concept of "linear comparison material". This hybrid approach is thought to lead to the best possible expressions of the yield criterion parameters. The criterion proposed reduces to (variants of) classical approximate criteria proposed by Gurson (1977) and Gologanu et al. (1993, 1994, 1997) in the specific cases of spherical or spheroidal, prolate or oblate cavities. An overview of the validation of this criterion through micromechanical finite element computations is finally presented.
Yin, Ligeng; Lodge, Timothy P; Hillmyer, Marc A
2012-11-26
Micellar polymorphism from block copolymers has been well documented, but most attention has focused on noncrystalline hydrophobic systems. We have investigated the micellization in water of model diblock copolymers with semicrystalline polyethylene (PE) as the core-forming component. Poly(N,N-dimethylacrylamide)–polyethylene (AE) diblock copolymers were synthesized by a combination of anionic and RAFT polymerizations. The bulk nanostructures were probed by small-angle X-ray scattering (SAXS) and AE diblock copolymers were found to be moderately segregated at 140 °C. Dispersions of AE amphiphiles in water were prepared by direct dissolution at 120 °C (i.e., above the melting transition of PE) followed by cooling to 25 °C. By manipulating the composition of AE diblock copolymers, discrete structures with oblate ellipsoidal, cylindrical, and bilayer morphologies were produced, as evidenced in cryogenic transmission electron microscopy (cryo-TEM). The self-assembled aggregates were also studied by small-angle neutron scattering (SANS) and dilute solution rheology. The semicrystalline nature of the nanostructures was further revealed by differential scanning calorimetry (DSC) and wide-angle X-ray scattering (WAXS). A stepwise “micellization–crystallization” process was proposed as the micelle formation mechanism, as supported by the existence of similar nanostructures at 120 °C using SANS. This strategy holds promise for a general protocol toward the production of giant wormlike micelles and vesicles with semicrystalline polymeric cores.
One-loop omega-potential of quantum fields with ellipsoid constant-energy surface dispersion law
NASA Astrophysics Data System (ADS)
Kazinski, P. O.; Shipulya, M. A.
2011-10-01
Rapidly convergent expansions of a one-loop contribution to the partition function of quantum fields with ellipsoid constant-energy surface dispersion law are derived. The omega-potential is naturally decomposed into three parts: the quasiclassical contribution, the contribution from the branch cut of the dispersion law, and the oscillating part. The low- and high-temperature expansions of the quasiclassical part are obtained. An explicit expression and a relation of the contribution from the cut with the Casimir term and vacuum energy are established. The oscillating part is represented in the form of the Chowla-Selberg expansion of the Epstein zeta function. Various resummations of this expansion are considered. The general procedure developed is then applied to two models: massless particles in a box both at zero and nonzero chemical potential, and electrons in a thin metal film. Rapidly convergent expansions of the partition function and average particle number are obtained for these models. In particular, the oscillations of the chemical potential of conduction electrons in graphene and a thin metal film due to a variation of size of the crystal are described.
Barbier, Michaël; Jaensch, Steffen; Cornelissen, Frans; Vidic, Suzana; Gjerde, Kjersti; de Hoogt, Ronald; Graeser, Ralph; Gustin, Emmanuel; Chong, Yolanda T
2016-01-01
In oncology, two-dimensional in-vitro culture models are the standard test beds for the discovery and development of cancer treatments, but in the last decades, evidence emerged that such models have low predictive value for clinical efficacy. Therefore they are increasingly complemented by more physiologically relevant 3D models, such as spheroid micro-tumor cultures. If suitable fluorescent labels are applied, confocal 3D image stacks can characterize the structure of such volumetric cultures and, for example, cell proliferation. However, several issues hamper accurate analysis. In particular, signal attenuation within the tissue of the spheroids prevents the acquisition of a complete image for spheroids over 100 micrometers in diameter. And quantitative analysis of large 3D image data sets is challenging, creating a need for methods which can be applied to large-scale experiments and account for impeding factors. We present a robust, computationally inexpensive 2.5D method for the segmentation of spheroid cultures and for counting proliferating cells within them. The spheroids are assumed to be approximately ellipsoid in shape. They are identified from information present in the Maximum Intensity Projection (MIP) and the corresponding height view, also known as Z-buffer. It alerts the user when potential bias-introducing factors cannot be compensated for and includes a compensation for signal attenuation. PMID:27303813
NASA Astrophysics Data System (ADS)
Zlinszky, András; Ressl, Camillo; Timár, Gábor; Weber, Robert; Székely, Balázs; Briese, Christian; Pfeifer, Norbert
2013-04-01
The geoid is the theoretical model of the Earth, defined as an equipotential surface. Typically it corresponds to a mean ocean surface and is extended through the continents. Elevations are measured above "sea level" based on the fact that the surface of water in equilibrium closely follows this equipotential surface. On dry land, the geoid can be determined from gravimetric measurements, and interpolation methods are used to represent variations of gravity in a regular grid model. For practical reasons, these are represented as geoid undulation, which is the difference of the ellipsoidal height and the height of the equipotential surface. In his work Principia, Isaac Newton proposed the thought experiment of connecting the North Pole and the Equator through a "canal" filled with water in order to determine gravitational flattening of the Earth. It was also Newton's idea to use the level of water in a global network of canals and wells to survey the geoid. Of course, these experiments are impossible at a global scale, but a sufficiently large lake and an accurate method for measuring elevation independently from the geoid can be used to prove the concept. Our objective was to measure the ellipsoidal water surface elevation of Lake Balaton in Hungary with high spatial resolution and accuracy and compare these measurements with the gravimetrically determined local geoid model. Airborne laser scanning (ALS, also known as airborne LIDAR) is a remote sensing technique capable of delivering a large number of points with elevations and horizontal positions accurate to a few centimetres. Laser pulses are emitted in a scan pattern from an airborne sensor, and are reflected from the illuminated terrain (or water) surface. Based on the position and orientation of the aircraft (typically observed by GNSS and an inertial navigation system), the scan angle and the travel time of the laser pulse, the exact position of each measurement point is calculated. In this particular case
{ P }{ T }-symmetric transport in non-{ P }{ T }-symmetric bi-layer optical arrays
NASA Astrophysics Data System (ADS)
Ramirez-Hernandez, J.; Izrailev, F. M.; Makarov, N. M.; Christodoulides, D. N.
2016-09-01
We study transport properties of an array created by alternating (a, b) layers with balanced loss/gain characterized by the key parameter γ. It is shown that for non-equal widths of (a, b) layers, i.e., when the corresponding Hamiltonian is non-{ P }{ T }-symmetric, the system exhibits the scattering properties similar to those of truly { P }{ T }-symmetric models provided that without loss/gain the structure presents the matched quarter stack. The inclusion of the loss/gain terms leads to an emergence of a finite number of spectral bands characterized by real values of the Bloch index. Each spectral band consists of a central region where the transmission coefficient {T}N≥slant 1, and two side regions with {T}N≤slant 1. At the borders between these regions the unidirectional reflectivity occurs. Also, the set of Fabry–Perot resonances with T N = 1 are found in spite of the presence of loss/gain.
{ P }{ T }-symmetric transport in non-{ P }{ T }-symmetric bi-layer optical arrays
NASA Astrophysics Data System (ADS)
Ramirez-Hernandez, J.; Izrailev, F. M.; Makarov, N. M.; Christodoulides, D. N.
2016-09-01
We study transport properties of an array created by alternating (a, b) layers with balanced loss/gain characterized by the key parameter γ. It is shown that for non-equal widths of (a, b) layers, i.e., when the corresponding Hamiltonian is non-{ P }{ T }-symmetric, the system exhibits the scattering properties similar to those of truly { P }{ T }-symmetric models provided that without loss/gain the structure presents the matched quarter stack. The inclusion of the loss/gain terms leads to an emergence of a finite number of spectral bands characterized by real values of the Bloch index. Each spectral band consists of a central region where the transmission coefficient {T}N≥slant 1, and two side regions with {T}N≤slant 1. At the borders between these regions the unidirectional reflectivity occurs. Also, the set of Fabry-Perot resonances with T N = 1 are found in spite of the presence of loss/gain.
NASA Astrophysics Data System (ADS)
Hu, Xuanyu; Jekeli, Christopher
2015-02-01
We present a comprehensive numerical analysis of spherical, spheroidal, and ellipsoidal harmonic series for gravitational field modeling near small moderately irregular bodies, such as the Martian moons. The comparison of model performances for these bodies is less intuitive and distinct than for a highly irregular object, such as Eros. The harmonic series models are each associated with a distinct surface, i.e., the Brillouin sphere, spheroid, or ellipsoid, which separates the regions of convergence and possible divergence for the parent infinite series. In their convergence regions, the models are subject only to omission errors representing the residual field variations not accounted for by the finite degree expansions. In the regions inside their respective Brillouin surfaces, the models are susceptible to amplification of omission errors and possible divergence effects, where the latter can be discerned if the error increases with an increase in the maximum degree of the model. We test the harmonic series models on the Martian moons, Phobos and Deimos, with moderate oblateness of 0.4. The possible divergence effects and amplified omission errors of the models are illustrated and quantified. The three models yield consistent results on a bounding sphere of Phobos in their common convergence region, with relative errors in potential of 0.01 and 0.001 % for expansions up to degree 10 and degree 20 respectively. On the surface of Phobos, the spherical and spheroidal models up to degree 10 both have maximum relative errors of 1 % in potential and 100 % in acceleration due ostensibly to divergence effect. Their performances deteriorate more severely on the more irregular Deimos. The ellipsoidal model exhibits much less distinct divergence behavior and proves more reliable in modeling both potential and acceleration, with respective maximum relative errors of 1 and 10 %, on both bodies. Our results show that for the Martian moons and other such moderately irregular
Agnihotri, Deepak; Verma, Kesari; Tripathi, Priyanka
2016-01-01
The contiguous sequences of the terms (N-grams) in the documents are symmetrically distributed among different classes. The symmetrical distribution of the N-Grams raises uncertainty in the belongings of the N-Grams towards the class. In this paper, we focused on the selection of most discriminating N-Grams by reducing the effects of symmetrical distribution. In this context, a new text feature selection method named as the symmetrical strength of the N-Grams (SSNG) is proposed using a two pass filtering based feature selection (TPF) approach. Initially, in the first pass of the TPF, the SSNG method chooses various informative N-Grams from the entire extracted N-Grams of the corpus. Subsequently, in the second pass the well-known Chi Square (χ(2)) method is being used to select few most informative N-Grams. Further, to classify the documents the two standard classifiers Multinomial Naive Bayes and Linear Support Vector Machine have been applied on the ten standard text data sets. In most of the datasets, the experimental results state the performance and success rate of SSNG method using TPF approach is superior to the state-of-the-art methods viz. Mutual Information, Information Gain, Odds Ratio, Discriminating Feature Selection and χ(2). PMID:27386386
Flow-separation patterns on symmetric forebodies
NASA Technical Reports Server (NTRS)
Keener, Earl R.
1986-01-01
Flow-visualization studies of ogival, parabolic, and conical forebodies were made in a comprehensive investigation of the various types of flow patterns. Schlieren, vapor-screen, oil-flow, and sublimation flow-visualization tests were conducted over an angle-of-attack range from 0 deg. to 88 deg., over a Reynolds-number range from 0.3X10(6) to 2.0X10(6) (based on base diameter), and over a Mach number range from 0.1 to 2. The principal effects of angle of attack, Reynolds number, and Mach number on the occurrence of vortices, the position of vortex shedding, the principal surface-flow-separation patterns, the magnitude of surface-flow angles, and the extent of laminar and turbulent flow for symmetric, asymmetric, and wake-like flow-separation regimes are presented. It was found that the two-dimensional cylinder analogy was helpful in a qualitative sense in analyzing both the surface-flow patterns and the external flow field. The oil-flow studies showed three types of primary separation patterns at the higher Reynolds numbers owing to the influence of boundary-layer transition. The effect of angle of attack and Reynolds number is to change the axial location of the onset and extent of the primary transitional and turbulent separation regions. Crossflow inflectional-instability vortices were observed on the windward surface at angles of attack from 5 deg. to 55 deg. Their effect is to promote early transition. At low angles of attack, near 10 deg., an unexpected laminar-separation bubble occurs over the forward half of the forebody. At high angles of attack, at which vortex asymmetry occurs, the results support the proposition that the principal cause of vortex asymmetry is the hydrodynamic instability of the inviscid flow field. On the other hand, boundary-layer asymmetries also occur, especially at transitional Reynolds numbers. The position of asymmetric vortex shedding moves forward with increasing angle of attack and with increasing Reynolds number, and moves
NASA Astrophysics Data System (ADS)
Sebera, Josef; Bezděk, Aleš; Kostelecký, Jan; Pešek, Ivan; Shum, C. K.
2016-01-01
The most important high-resolution geopotential models such as EGM96 and EGM2008 have been released approximately once per decade. In light of the ability of modern satellite, airborne or terrestrial techniques to provide new data sets every year (e.g., in polar and ocean areas), these data can be readily included in existing models without waiting for a new release. In this article, we present a novel ellipsoidal approach for updating high-resolution models over the oceans with new gridded data. The problem is demonstrated using the EGM2008 model updated with DTU10 geoid and gravity grids that provide additional signal over the Arctic oceans. The result of the procedure are the ellipsoidal and the spherical harmonic coefficients up to degree 4320 and 4400, respectively. These coefficients represent the input data set to within 0.08 mGal globally, with the largest differences located at the land-ocean boundaries, which is two orders of magnitude less than real accuracy of gravity data from satellite altimetry. Along with the harmonic coefficients a detailed map of the second vertical derivative of the anomalous potential (or vertical gravitational gradient) on 1 arc-min grid is anticipated to improve or complement the original DTU10 geoid model. Finally, an optimized set of Jekeli's functions is provided as they allow for computing oblate ellipsoidal harmonics up to a very high degree and order (>10,000) in terms of the hypergeometric formulation.
NASA Astrophysics Data System (ADS)
Marques, F. G.; Cobbold, P. R.
1995-04-01
The three-dimensional development of strongly non-cylindrical folds around competent ellipsoidal inclusions in bulk simple shear regimes is studied in experiments and natural examples. Examples from the Continental Allochthonous Terrane of the Bragança Nappe Complex (NE Portugal) show rim folds and sheath folds associated with different parts of rigid ellipsoidal boudins. Experimental work has been carried out with models made from analogue materials (silicone putty and plasticine) and deformed in a simple shear machine. We have considered three different models to simulate natural examples, and the results show that fold morphology depends on the shape of the inclusion and position around the inclusion. Although the bulk deformation regime is layer parallel homogeneous simple shear, we can distinguish local deformation regimes responsible for the folding associated with different parts of the rigid body. Flow and strain patterns must therefore be complex around inclusions or populations of inclusions. Prolate to oblate strain ellipsoids can be expected in different positions close to the rigid inclusion. In our experiments, the competent inclusions do not rotate synthetically with the applied bulk simple shear (e.g. clockwise rotation of inclusion in dextral shear). Instead, they back-rotate, early in the shearing history, and keep this position throughout the experiment. This is the result of the size relationship between the inclusion and the finite width of the shear zone. The fold pattern around rigid inclusions may be used as a shear sense criterion.
Local existence of symmetric spinor potentials for symmetric (3,1)-spinors in Einstein space-times
NASA Astrophysics Data System (ADS)
Andersson, F.; Edgar, S. B.
2001-03-01
We investigate the possibility of existence of a symmetric potential HABA' B' = H( AB)( A' B') for a symmetric (3,1)-spinor LABCA' , e.g., a Lanczos potential of the Weyl spinor, as defined by the equation LABCA' =∇ ( AB' HBC) A' B' . We prove that in all Einstein space-times such a symmetric potential HABA' B' exists. Potentials of this type have been found earlier in investigations of some very special spinors in restricted classes of space-times. A tensor version of this result is also given. We apply similar ideas and results by Illge to Maxwell's equations in a curved space-time.
Propagation of electromagnetic waves in P T -symmetric hyperbolic structures
NASA Astrophysics Data System (ADS)
Shramkova, O. V.; Tsironis, G. P.
2016-07-01
We investigate theoretically and numerically the propagation of electromagnetic waves in P T -symmetric periodic stacks composed of hyperbolic metamaterial layers separated by dielectric media with balanced loss and gain. We derive the characteristic frequencies governing the dispersion properties of the eigenwaves of P T -symmetric semiconductor-dielectric stacks. By tuning the loss/gain level and thicknesses of the layers, we study the evolution of the dispersion dependencies. We show that the effective-medium approach does not adequately describe the propagating waves in the P T -symmetric hypercrystals, even for wavelengths that are about 100 times larger than the period of the stack. We demonstrate the existence of anisotropic transmission resonances and above-unity reflection in P T -symmetric hyperbolic systems. The P T -symmetry-breaking transition of the scattering matrix is strongly influenced by the constitutive and geometrical parameters of the layers and the angles of wave incidence.
Symmetric Space σ-MODEL Dynamics:. Current Formalism
NASA Astrophysics Data System (ADS)
Yilmaz, Nejat T.
After explicitly constructing the symmetric space sigma model Lagrangian in terms of the coset scalars of the solvable Lie algebra gauge in the current formalism, we derive the field equations of the theory.
A parallel algorithm for the non-symmetric eigenvalue problem
Dongarra, J.; Sidani, M. |
1991-12-01
This paper describes a parallel algorithm for computing the eigenvalues and eigenvectors of a non-symmetric matrix. The algorithm is based on a divide-and-conquer procedure and uses an iterative refinement technique.
TRMM Satellite Sees an Non-symmetric Hurricane Cristobal
TRMM satellite passed over Cristobal on Aug. 27 at 8:16 a.m. EDT. Cristobal didn't appear round and symmetric in either clouds or rainfall which suggests that the hurricane is being battered by sou...
14 CFR 23.331 - Symmetrical flight conditions.
Code of Federal Regulations, 2012 CFR
2012-01-01
... inertia loads corresponding to any of the symmetrical flight conditions specified in §§ 23.333 through 23... angular inertia of the airplane in a rational or conservative manner. (c) Mutual influence of...
14 CFR 23.331 - Symmetrical flight conditions.
Code of Federal Regulations, 2013 CFR
2013-01-01
... inertia loads corresponding to any of the symmetrical flight conditions specified in §§ 23.333 through 23... angular inertia of the airplane in a rational or conservative manner. (c) Mutual influence of...
Systems of Differential Equations with Skew-Symmetric, Orthogonal Matrices
ERIC Educational Resources Information Center
Glaister, P.
2008-01-01
The solution of a system of linear, inhomogeneous differential equations is discussed. The particular class considered is where the coefficient matrix is skew-symmetric and orthogonal, and where the forcing terms are sinusoidal. More general matrices are also considered.
Noise Suppression Using Symmetric Exchange Gates in Spin Qubits.
Martins, Frederico; Malinowski, Filip K; Nissen, Peter D; Barnes, Edwin; Fallahi, Saeed; Gardner, Geoffrey C; Manfra, Michael J; Marcus, Charles M; Kuemmeth, Ferdinand
2016-03-18
We demonstrate a substantial improvement in the spin-exchange gate using symmetric control instead of conventional detuning in GaAs spin qubits, up to a factor of six increase in the quality factor of the gate. For symmetric operation, nanosecond voltage pulses are applied to the barrier that controls the interdot potential between quantum dots, modulating the exchange interaction while maintaining symmetry between the dots. Excellent agreement is found with a model that separately includes electrical and nuclear noise sources for both detuning and symmetric gating schemes. Unlike exchange control via detuning, the decoherence of symmetric exchange rotations is dominated by rotation-axis fluctuations due to nuclear field noise rather than direct exchange noise. PMID:27035316
Symmetric polynomials in information theory: Entropy and subentropy
Jozsa, Richard; Mitchison, Graeme
2015-06-15
Entropy and other fundamental quantities of information theory are customarily expressed and manipulated as functions of probabilities. Here we study the entropy H and subentropy Q as functions of the elementary symmetric polynomials in the probabilities and reveal a series of remarkable properties. Derivatives of all orders are shown to satisfy a complete monotonicity property. H and Q themselves become multivariate Bernstein functions and we derive the density functions of their Levy-Khintchine representations. We also show that H and Q are Pick functions in each symmetric polynomial variable separately. Furthermore, we see that H and the intrinsically quantum informational quantity Q become surprisingly closely related in functional form, suggesting a special significance for the symmetric polynomials in quantum information theory. Using the symmetric polynomials, we also derive a series of further properties of H and Q.
Symmetrical ilial pseudofractures: A complication of chronic renal failure
Griffin, C.N. Jr.
1982-08-01
A patient with chronic renal failure and progressive symmetrical ilial pseudofractures (Looser zones, Milkman's syndrome) is presented. The literature is reviewed in light of the findings in this patient, and possible mechanisms of pseudofracture formation are discussed.
Optical aberration coefficients: FORTRAN subroutines for symmetrical systems.
Andersen, T B
1981-09-15
FORTRAN computer subroutines for the automatic computation of the optical aberration functions S, T, V, W, and K to the 15th order for rotationally symmetric systems are presented. The routines may be conveniently extended toward higher orders.
Noise Suppression Using Symmetric Exchange Gates in Spin Qubits
NASA Astrophysics Data System (ADS)
Martins, Frederico; Malinowski, Filip K.; Nissen, Peter D.; Barnes, Edwin; Fallahi, Saeed; Gardner, Geoffrey C.; Manfra, Michael J.; Marcus, Charles M.; Kuemmeth, Ferdinand
2016-03-01
We demonstrate a substantial improvement in the spin-exchange gate using symmetric control instead of conventional detuning in GaAs spin qubits, up to a factor of six increase in the quality factor of the gate. For symmetric operation, nanosecond voltage pulses are applied to the barrier that controls the interdot potential between quantum dots, modulating the exchange interaction while maintaining symmetry between the dots. Excellent agreement is found with a model that separately includes electrical and nuclear noise sources for both detuning and symmetric gating schemes. Unlike exchange control via detuning, the decoherence of symmetric exchange rotations is dominated by rotation-axis fluctuations due to nuclear field noise rather than direct exchange noise.
Rindler-like Horizon in Spherically Symmetric Spacetime
NASA Astrophysics Data System (ADS)
Yang, Jinbo; He, Tangmei; Zhang, Jingyi
2016-07-01
In this paper, the Rindler-like horizon in a spherically symmetric spacetime is proposed. It is showed that just like the Rindler horizon in Minkowski spacetimes, there is also a Rindler-like horizon to a family of special observers in general spherically symmetric spacetimes. The entropy of this type of horizon is calculated with the thin film brick-wall model. The significance of entropy is discussed. Our results imply some connection between Bekeinstein-Hawking entropy and entanglement entropy.
On projective invariants of spherically symmetric Finsler spaces in Rn
NASA Astrophysics Data System (ADS)
Sadeghzadeh, Nasrin; Hesamfar, Maedeh
2015-05-01
In this paper, we study projective invariants of spherically symmetric Finsler metrics in Rn. We find the necessary and sufficient conditions for the metrics to be Weyl, Douglas and generalized Douglas-Weyl (GDW) types. In particular, we find the necessary and sufficient condition for the metrics to be of scalar flag curvature. Also we show that two classes of GDW and Douglas spherically symmetric Finsler metrics coincide.
Symmetric and antisymmetric forms of the Pauli master equation
NASA Astrophysics Data System (ADS)
Klimenko, A. Y.
2016-07-01
When applied to matter and antimatter states, the Pauli master equation (PME) may have two forms: time-symmetric, which is conventional, and time-antisymmetric, which is suggested in the present work. The symmetric and antisymmetric forms correspond to symmetric and antisymmetric extensions of thermodynamics from matter to antimatter — this is demonstrated by proving the corresponding H-theorem. The two forms are based on the thermodynamic similarity of matter and antimatter and differ only in the directions of thermodynamic time for matter and antimatter (the same in the time-symmetric case and the opposite in the time-antisymmetric case). We demonstrate that, while the symmetric form of PME predicts an equibalance between matter and antimatter, the antisymmetric form of PME favours full conversion of antimatter into matter. At this stage, it is impossible to make an experimentally justified choice in favour of the symmetric or antisymmetric versions of thermodynamics since we have no experience of thermodynamic properties of macroscopic objects made of antimatter, but experiments of this kind may become possible in the future.
Symmetric and antisymmetric forms of the Pauli master equation
Klimenko, A. Y.
2016-01-01
When applied to matter and antimatter states, the Pauli master equation (PME) may have two forms: time-symmetric, which is conventional, and time-antisymmetric, which is suggested in the present work. The symmetric and antisymmetric forms correspond to symmetric and antisymmetric extensions of thermodynamics from matter to antimatter — this is demonstrated by proving the corresponding H-theorem. The two forms are based on the thermodynamic similarity of matter and antimatter and differ only in the directions of thermodynamic time for matter and antimatter (the same in the time-symmetric case and the opposite in the time-antisymmetric case). We demonstrate that, while the symmetric form of PME predicts an equibalance between matter and antimatter, the antisymmetric form of PME favours full conversion of antimatter into matter. At this stage, it is impossible to make an experimentally justified choice in favour of the symmetric or antisymmetric versions of thermodynamics since we have no experience of thermodynamic properties of macroscopic objects made of antimatter, but experiments of this kind may become possible in the future. PMID:27440454
Robustness of differentiation cascades with symmetric stem cell division.
Sánchez-Taltavull, Daniel; Alarcón, Tomás
2014-06-01
Stem cells (SCs) perform the task of maintaining tissue homeostasis by both self-renewal and differentiation. While it has been argued that SCs divide asymmetrically, there is also evidence that SCs undergo symmetric division. Symmetric SC division has been speculated to be key for expanding cell numbers in development and regeneration after injury. However, it might lead to uncontrolled growth and malignancies such as cancer. In order to explore the role of symmetric SC division, we propose a mathematical model of the effect of symmetric SC division on the robustness of a population regulated by a serial differentiation cascade and we show that this may lead to extinction of such population. We examine how the extinction likelihood depends on defining characteristics of the population such as the number of intermediate cell compartments. We show that longer differentiation cascades are more prone to extinction than systems with less intermediate compartments. Furthermore, we have analysed the possibility of mixed symmetric and asymmetric cell division against invasions by mutant invaders in order to find optimal architecture. Our results show that more robust populations are those with unfrequent symmetric behaviour.
NASA Astrophysics Data System (ADS)
Rexer, Moritz; Hirt, Christian; Claessens, Sten; Tenzer, Robert
2016-08-01
Global forward modelling of the Earth's gravitational potential, a classical problem in geophysics and geodesy, is relevant for a range of applications such as gravity interpretation, isostatic hypothesis testing or combined gravity field modelling with high and ultra-high resolution. This study presents spectral forward modelling with volumetric mass layers to degree 2190 for the first time based on two different levels of approximation. In spherical approximation, the mass layers are referred to a sphere, yielding the spherical topographic potential. In ellipsoidal approximation where an ellipsoid of revolution provides the reference, the ellipsoidal topographic potential (ETP) is obtained. For both types of approximation, we derive a mass layer concept and study it with layered data from the Earth2014 topography model at 5-arc-min resolution. We show that the layer concept can be applied with either actual layer density or density contrasts w.r.t. a reference density, without discernible differences in the computed gravity functionals. To avoid aliasing and truncation errors, we carefully account for increased sampling requirements due to the exponentiation of the boundary functions and consider all numerically relevant terms of the involved binominal series expansions. The main outcome of our work is a set of new spectral models of the Earth's topographic potential relying on mass layer modelling in spherical and in ellipsoidal approximation. We compare both levels of approximations geometrically, spectrally and numerically and quantify the benefits over the frequently used rock-equivalent topography (RET) method. We show that by using the ETP it is possible to avoid any displacement of masses and quantify also the benefit of mapping-free modelling. The layer-based forward modelling is corroborated by GOCE satellite gradiometry, by in-situ gravity observations from recently released Antarctic gravity anomaly grids and degree correlations with spectral models of