Exploring Strange Nonchaotic Attractors through Jacobian Elliptic Functions
ERIC Educational Resources Information Center
Garcia-Hoz, A. Martinez; Chacon, R.
2011-01-01
We demonstrate the effectiveness of Jacobian elliptic functions (JEFs) for inquiring into the reshaping effect of quasiperiodic forces in nonlinear nonautonomous systems exhibiting strange nonchaotic attractors (SNAs). Specifically, we characterize analytically and numerically some reshaping-induced transitions starting from SNAs in the context of…
A Jacobian elliptic single-field inflation
NASA Astrophysics Data System (ADS)
Villanueva, J. R.; Gallo, Emanuel
2015-06-01
In the scenario of single-field inflation, this field is described in terms of Jacobian elliptic functions. This approach provides, when constrained to particular cases, analytic solutions already known in the past, generalizing them to a bigger family of analytical solutions. The emergent cosmology is analyzed using the Hamilton-Jacobi approach and then the main results are contrasted with the recent measurements obtained from the Planck 2015 data.
Fourier Series and Elliptic Functions
ERIC Educational Resources Information Center
Fay, Temple H.
2003-01-01
Non-linear second-order differential equations whose solutions are the elliptic functions "sn"("t, k"), "cn"("t, k") and "dn"("t, k") are investigated. Using "Mathematica", high precision numerical solutions are generated. From these data, Fourier coefficients are determined yielding approximate formulas for these non-elementary functions that are…
Force-free Jacobian equilibria for Vlasov-Maxwell plasmas
Abraham-Shrauner, B.
2013-10-15
New analytic force-free Vlasov-Maxwell equilibria for thin current sheets are presented. The magnetic flux densities are expressed in terms of Jacobian elliptic functions of one Cartesian spatial coordinate. The magnetic flux densities reduce to previously reported hyperbolic functions in one limit and sinusoidal functions in another limit of the modulus k. A much wider class of nonlinear force-free Vlasov-Maxwell equilibria open expanded possibilities for modeling of solar system, astrophysical and laboratory plasmas. Modified Maxwellian distribution functions are determined explicitly in terms of Jacobian elliptic functions. Conditions for double peaked distribution functions that could be unstable are developed.
Elliptic functions and maximal unitarity
NASA Astrophysics Data System (ADS)
Søgaard, Mads; Zhang, Yang
2015-04-01
Scattering amplitudes at loop level can be reduced to a basis of linearly independent Feynman integrals. The integral coefficients are extracted from generalized unitarity cuts which define algebraic varieties. The topology of an algebraic variety characterizes the difficulty of applying maximal cuts. In this work, we analyze a novel class of integrals of which the maximal cuts give rise to an algebraic variety with irrational irreducible components. As a phenomenologically relevant example, we examine the two-loop planar double-box contribution with internal massive lines. We derive unique projectors for all four master integrals in terms of multivariate residues along with Weierstrass' elliptic functions. We also show how to generate the leading-topology part of otherwise infeasible integration-by-parts identities analytically from exact meromorphic differential forms.
Compactified strings as quantum statistical partition function on the Jacobian torus.
Matone, Marco; Pasti, Paolo; Shadchin, Sergey; Volpato, Roberto
2006-12-31
We show that the solitonic contribution of toroidally compactified strings corresponds to the quantum statistical partition function of a free particle living on higher dimensional spaces. In the simplest case of compactification on a circle, the Hamiltonian is the Laplacian on the 2g-dimensional Jacobian torus associated with the genus g Riemann surface corresponding to the string world sheet. T duality leads to a symmetry of the partition function mixing time and temperature. Such a classical-quantum correspondence and T duality shed some light on the well-known interplay between time and temperature in quantum field theory and classical statistical mechanics.
Elliptic Functions with Disconnected Julia Sets
NASA Astrophysics Data System (ADS)
Koss, Lorelei
2016-06-01
In this paper, we investigate elliptic functions of the form fΛ = 1/(1 + (℘Λ)2), where ℘Λ is the Weierstrass elliptic function on a real rhombic lattice. We show that a typical function in this family has a superattracting fixed point at the origin and five other equivalence classes of critical points. We investigate conditions on the lattice which guarantee that fΛ has a double toral band, and we show that this family contains the first known examples of elliptic functions for which the Julia set is disconnected but not Cantor.
NASA Astrophysics Data System (ADS)
Bisetti, Fabrizio
2012-06-01
Recent trends in hydrocarbon fuel research indicate that the number of species and reactions in chemical kinetic mechanisms is rapidly increasing in an effort to provide predictive capabilities for fuels of practical interest. In order to cope with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix. The components of the approach are described in detail and applied to the ignition of stoichiometric methane-air and iso-octane-air mixtures, here described by two widely adopted chemical kinetic mechanisms. The approach is found to be robust even at relatively large time steps and the global error displays a nominal third-order convergence. The performance of the approach is improved by utilising an adaptive algorithm for the selection of the Krylov subspace size, which guarantees an approximation to the matrix exponential within user-defined error tolerance. The Krylov projection of the Jacobian matrix onto a low-dimensional space is interpreted as a local model reduction with a well-defined error control strategy. Finally, the performance of the approach is discussed with regard to the optimal selection of the parameters governing the accuracy of its individual components.
NASA Astrophysics Data System (ADS)
Briane, M.; Casado Díaz, J.
2016-04-01
In this paper a new div-curl result is established in an open set Ω of RN, N ≥ 2, for the product σn ṡηn of two sequences of vector-valued functions σn, ηn such that σn is bounded in Lp(Ω) N, ηn is bounded in Lq(Ω) N, with 1 / p + 1 / q = 1 + 1 / (N - 1), and such that divσn, curlηn are compact in suitable spaces. The new assumption is that the product converges weakly in W - 1 , 1 (Ω). The approach is also new in the topic, and is based on a compactness result for bounded sequences in W 1 , q (Ω) through a suitable selection of annuli on which the gradients are not too high, in the spirit of [26,32] and using the imbedding of W 1 , q into Lp‧ for the unit sphere of RN. The div-curl result is applied to the homogenization of equi-coercive systems whose coefficients are equi-bounded in Lρ (Ω) for some ρ >N - 1/2 if N > 2, or in L1 (Ω) if N = 2. It also allows us to prove a weak continuity result for the Jacobian for bounded sequences in W 1 , N - 1 (Ω) satisfying an alternative assumption to the L∞-strong estimate of [8]. Two examples show the sharpness of the results.
Plane-wave expansion of elliptic cylindrical functions
NASA Astrophysics Data System (ADS)
Santini, Carlo; Frezza, Fabrizio; Tedeschi, Nicola
2015-08-01
Elliptic Cylindrical Waves (ECW), defined as the product of an angular Mathieu function by its corresponding radial Mathieu function, occur in the solution of scattering problems involving two-dimensional structures with elliptic cross sections. In this paper, we explicitly derive the expansion of ECW, along a plane surface, in terms of homogeneous and evanescent plane waves, showing the accuracy of the numerical implementation of the formulas and discussing possible applications of the result.
Jacobi elliptic functions: A review of nonlinear oscillatory application problems
NASA Astrophysics Data System (ADS)
Kovacic, Ivana; Cveticanin, Livija; Zukovic, Miodrag; Rakaric, Zvonko
2016-10-01
This review paper is concerned with the applications of Jacobi elliptic functions to nonlinear oscillators whose restoring force has a monomial or binomial form that involves cubic and/or quadratic nonlinearity. First, geometric interpretations of three basic Jacobi elliptic functions are given and their characteristics are discussed. It is shown then how their different forms can be utilized to express exact solutions for the response of certain free conservative oscillators. These forms are subsequently used as a starting point for a presentation of different quantitative techniques for obtaining an approximate response for free perturbed nonlinear oscillators. An illustrative example is provided. Further, two types of externally forced nonlinear oscillators are reviewed: (i) those that are excited by elliptic-type excitations with different exact and approximate solutions; (ii) those that are damped and excited by harmonic excitations, but their approximate response is expressed in terms of Jacobi elliptic functions. Characteristics of the steady-state response are discussed and certain qualitative differences with respect to the classical Duffing oscillator excited harmonically are pointed out. Parametric oscillations of the oscillators excited by an elliptic-type forcing are considered as well, and the differences with respect to the stability chart of the classical Mathieu equation are emphasized. The adjustment of the Melnikov method to derive the general condition for the onset of homoclinic bifurcations in a system parametrically excited by an elliptic-type forcing is provided and compared with those corresponding to harmonic excitations. Advantages and disadvantages of the use of Jacobi elliptic functions in nonlinear oscillatory application problems are discussed and some suggestions for future work are given.
NASA Astrophysics Data System (ADS)
Cardona, Carlos; Gomez, Humberto
2016-06-01
Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a mathbb{C}{P}^2 space. We show that for the simplest integrand, namely the n - gon, our proposal indeed reproduces the expected result. By using the recently formulated Λ-algorithm, we found a novel recurrence relation expansion in terms of tree level off-shell amplitudes. Our results connect nicely with recent results on the one-loop formulation of the scattering equations. In addition, this new proposal can be easily stretched out to hyperelliptic curves in order to compute higher genus.
A Primer on Elliptic Functions with Applications in Classical Mechanics
ERIC Educational Resources Information Center
Brizard, Alain J.
2009-01-01
The Jacobi and Weierstrass elliptic functions used to be part of the standard mathematical arsenal of physics students. They appear as solutions of many important problems in classical mechanics: the motion of a planar pendulum (Jacobi), the motion of a force-free asymmetric top (Jacobi), the motion of a spherical pendulum (Weierstrass) and the…
Some new addition formulae for Weierstrass elliptic functions
Eilbeck, J. Chris; England, Matthew; Ônishi, Yoshihiro
2014-01-01
We present new addition formulae for the Weierstrass functions associated with a general elliptic curve. We prove the structure of the formulae in n-variables and give the explicit addition formulae for the 2- and 3-variable cases. These new results were inspired by new addition formulae found in the case of an equianharmonic curve, which we can now observe as a specialization of the results here. The new formulae, and the techniques used to find them, also follow the recent work for the generalization of Weierstrass functions to curves of higher genus. PMID:25383018
On the Distance Function Between Two Keplerian Elliptic Orbits
NASA Astrophysics Data System (ADS)
Kholshevnikov, Konstantin V.; Vassiliev, Nikolay N.
1999-10-01
The problem of finding critical points of the distance function between two Keplerian elliptic orbits is reduced to the determination of all real roots of a trigonometric polynomial of degree 8. The coefficients of the polynomial are rational functions of orbital parameters. Using computer algebra methods we show that a polynomial of a smaller degree with such properties does not exist. This fact shows that our result cannot be improved and it allows us to construct an optimal algorithm to find the minimal distance between two Keplerian orbits.
Miniaturized LTCC elliptic-function lowpass filters with side stopbands
Hsieh, Lung -Hwa; Dai, Steve Xunhu
2015-05-28
A compact, high-selectivity, and wide stopband lowpass filter is highly demanded in wireless communication systems to suppress adjacent harmonics and unwanted signals. In this letter, a new miniaturized lowpass filter with elliptic-function frequency response is introduced. The filter is fabricated in multilayer low temperature cofired ceramics. The size of the miniaturized filter is 5.5 × 3.9 × 1.72 mm3. As a result, the measured insertion loss of the filter is better than 0.37 dB from DC to 1.28 GHz and the measured stopband of the filter is great than 22 dB from 2.3 to 7.5 GHz.
Shapes of lipid monolayer domains: Solutions using elliptic functions
NASA Astrophysics Data System (ADS)
Iwamoto, M.; Liu, F.; Ou-Yang, Z. C.
2008-09-01
Solid lipid monolayer domains surrounded by a fluid phase at an air-water interface exhibit complex shapes. These intriguing shapes can be understood in terms of a competition between line tension and long-range dipole-dipole interaction. The dipolar energy has recently been relevant to a negative line tension and a positive curvature energy at the boundary, and a corresponding shape equation was derived by the variation of the approximated domain energy (Phys. Rev. Lett. 93, 206101 (2004)). Here we further incorporate surface pressure into the shape equation and show that the equation can be analytically solved: the curvature of the domain boundary is exactly obtained as an elliptic function of arc-length. We find that a circular domain can grow into bean- and peach-like domains with pressure, i.e., dipping and cuspidal transitions of circle by compression. The comparison with the experimental observation shows nice agreement.
Lin, Lin; Yang, Chao
2013-10-28
We discuss techniques for accelerating the self consistent field (SCF) iteration for solving the Kohn-Sham equations. These techniques are all based on constructing approximations to the inverse of the Jacobian associated with a fixed point map satisfied by the total potential. They can be viewed as preconditioners for a fixed point iteration. We point out different requirements for constructing preconditioners for insulating and metallic systems respectively, and discuss how to construct preconditioners to keep the convergence rate of the fixed point iteration independent of the size of the atomistic system. We propose a new preconditioner that can treat insulating and metallic system in a unified way. The new preconditioner, which we call an elliptic preconditioner, is constructed by solving an elliptic partial differential equation. The elliptic preconditioner is shown to be more effective in accelerating the convergence of a fixed point iteration than the existing approaches for large inhomogeneous systems at low temperature.
Correlation functions and cumulants in elliptic flow analysis
NASA Astrophysics Data System (ADS)
Kovchegov, Yuri V.; Tuchin, Kirill L.
2003-04-01
We consider various methods of flow analysis in heavy ion collisions and compare experimental data on corresponding observables to the predictions of our saturation model proposed earlier [Nucl. Phys. A 708 (2002) 413]. We demonstrate that, due to the nature of the standard flow analysis, azimuthal distribution of particles with respect to reaction plane determined from the second order harmonics should always be proportional to cos2( φ- ΨR) independent of the physical origin of particle correlations (flow or non-flow). The amplitude of this distribution is always physical and proportional to v2. Two-particle correlations analysis is, therefore, a more reliable way of extracting the shape of physical azimuthal anisotropy. We demonstrate that two-particle correlation functions generated in our minijet model of particle production [Nucl. Phys. A 708 (2002) 413] are in good agreement with the data reported by PHENIX. We discuss the role of non-flow correlations in the cumulant flow analysis and demonstrate using a simple example that if the flow is weak, higher order cumulants analysis does not significantly reduce the contribution of non-flow correlations to elliptic flow observable v2 in RHIC data.
Joint inversion of body wave receiver function and Rayleigh wave ellipticity
NASA Astrophysics Data System (ADS)
Chong, J.; Ni, S.; Chu, R.
2015-12-01
In recent years, surface wave dispersion has been used to image lithospheric structure jointly with receiver function, or Rayleigh wave ellipticity (Julia et al., 2000; Lin et al., 2012). Because surface wave dispersion is the total propagation effect of the travel path, the joint inversion relies on dense seismic arrays or high seismicity to obtain local velocity structure. However, both receiver function and Rayleigh wave ellipticity are single station measurements with localized sensitivities and could be combined for joint inversion naturally. In this study we explored the feasibility of the joint inversion of Rayleigh wave ellipticity and receiver function. We performed sensitivity tests with forward modeling, and found that the receiver function is sensitive to sharp velocity interfaces but shows weak sensitivity to long wavelength structure, almost complementary to Rayleigh wave ellipticity. Therefore, joint inversion with two single-station measurements provides tighter constraints on the velocity structure beneath the seismic station. A joint inversion algorithm based on the Fast Simulated Annealing method is developed to invert Rayleigh wave ellipticity and receiver function for the lithospheric structure. Application of the algorithm to the Indian Craton and the Williston Basin in the United States demonstrates its effectiveness in reducing the non-uniqueness of the inversion. However, the joint inversion is not sensitive to average crustal velocity, suggesting the need to combine surface wave dispersion, receiver function and Rayleigh wave ellipticity to more accurately resolve the velocity structure. ReferenceJuliá, J., C. Ammon, R. Herrmann, and A. Correig, 2000. Joint inversion of receiver function and surface wave dispersion observations, Geophys. J. Int., 143(1), 99-112. Lin F.C., Schmandt B. and Tsai V.C., 2012. Joint inversion of Rayleigh wave phase velocity and ellipticity using USArray: constraining velocity and density structure in the upper
Partition function of the elliptic solid-on-solid model as a single determinant
NASA Astrophysics Data System (ADS)
Galleas, W.
2016-07-01
In this Rapid Communication we express the partition function of the integrable elliptic solid-on-solid model with domain-wall boundary conditions as a single determinant. This representation appears naturally as the solution of a system of functional equations governing the model's partition function.
Mao, Shi-Chun; Wu, Zhen-Sen
2008-12-01
An exact solution to the two-dimensional scattering properties of an anisotropic elliptic cylinder for transverse electric polarization is presented. The internal field in an anisotropic elliptic cylinder is expressed as integral representations of Mathieu functions and Fourier series. The coefficients of the series expansion are obtained by imposing boundary conditions on the anisotropic-free-space interface. A matrix is developed to solve the nonorthogonality properties of Mathieu functions at the interface between two different media. Numerical results are given for the bistatic radar cross section and the amplitude of the total magnetic field along the x and y axes. The result is in agreement with that available as expected when an elliptic cylinder degenerates to a circular one.
Dynamically consistent Jacobian inverse for mobile manipulators
NASA Astrophysics Data System (ADS)
Ratajczak, Joanna; Tchoń, Krzysztof
2016-06-01
By analogy to the definition of the dynamically consistent Jacobian inverse for robotic manipulators, we have designed a dynamically consistent Jacobian inverse for mobile manipulators built of a non-holonomic mobile platform and a holonomic on-board manipulator. The endogenous configuration space approach has been exploited as a source of conceptual guidelines. The new inverse guarantees a decoupling of the motion in the operational space from the forces exerted in the endogenous configuration space and annihilated by the dual Jacobian inverse. A performance study of the new Jacobian inverse as a tool for motion planning is presented.
Krasnoperov, R A; Gerasimov, A N
2009-06-01
The article theoretically regards probability density functions (PDFs) for axial ratio (X/Y) of sectioning profiles of elliptical microvessels (MVs) arranged with anisotropy in a biological tissue volume. A technique for the PDF(X/Y) calculations in anisotropy of the elliptical MVs is described. The essence of this technique is introducing anisotropy in PDF(alpha,phi), i.e. the function of the joint distribution of the polar and planar angles alpha and phi, which define mutual orientation of the elliptical MVs and sectioning planes. With the aid of this technique, the anisotropy cases are studied with PDF(alpha,phi) given by pair combinations of the following distributions: (i) a uniform distribution of the angles alpha and/or phi, (ii) the angle alpha distribution with PDF(alpha)=sin alpha(alpha in [0,pi/2]), and (iii) Gaussian distributions of the alpha or phi values. Specifically, PDF(X/Y) curves are obtained for MVs with the true, or three-dimensional, axial ratio X(0)/Y(0)=2.0, and the anisotropy effects on the X/Y expected frequencies are analysed. Conclusions of this analysis, the PDF(X/Y) calculation technique, and the PDF(X/Y) curves obtained are useful for stereological reconstruction of anisotropically organised microcirculatory networks, with an ellipticity of their MVs being taken into consideration. PMID:19318110
Origin of a bottom-heavy stellar initial mass function in elliptical galaxies
Bekki, Kenji
2013-12-10
We investigate the origin of a bottom-heavy stellar initial mass function (IMF) recently observed in elliptical galaxies by using chemical evolution models with a non-universal IMF. We adopt the variable Kroupa IMF with the three slopes (α{sub 1}, α{sub 2}, and α{sub 3}) dependent on metallicities ([Fe/H]) and densities (ρ{sub g}) of star-forming gas clouds and thereby search for the best IMF model that can reproduce (1) the observed steep IMF slope (α{sub 2} ∼ 3, i.e., bottom-heavy) for low stellar masses (m ≤ 1 M {sub ☉}) and (2) the correlation of α{sub 2} with chemical properties of elliptical galaxies in a self-consistent manner. We find that if the IMF slope α{sub 2} depends on both [Fe/H] and ρ{sub g}, then elliptical galaxies with higher [Mg/Fe] can have steeper α{sub 2} (∼3) in our models. We also find that the observed positive correlation of stellar mass-to-light ratios (M/L) with [Mg/Fe] in elliptical galaxies can be quantitatively reproduced in our models with α{sub 2}∝β[Fe/H] + γlog ρ{sub g}, where β ∼ 0.5 and γ ∼ 2. We discuss whether the IMF slopes for low-mass (α{sub 2}) and high-mass stars (α{sub 3}) need to vary independently from each other to explain a number of IMF-related observational results self-consistently. We also briefly discuss why α{sub 2} depends differently on [Fe/H] in dwarf and giant elliptical galaxies.
On the modularity of certain functions from the Gromov–Witten theory of elliptic orbifolds
Bringmann, Kathrin; Rolen, Larry; Zwegers, Sander
2015-01-01
In this paper, we study modularity of several functions which naturally arose in a recent paper of Lau and Zhou on open Gromov–Witten potentials of elliptic orbifolds. They derived a number of examples of indefinite theta functions, and we provide modular completions for several such functions which involve more complicated objects than ordinary modular forms. In particular, we give new closed formulae for special indefinite theta functions of type (1,2) in terms of products of mock modular forms. This formula is also of independent interest. PMID:26715996
Matrix coefficient identification in an elliptic equation with the convex energy functional method
NASA Astrophysics Data System (ADS)
Hinze, Michael; Nhan Tam Quyen, Tran
2016-08-01
In this paper we study the inverse problem of identifying the diffusion matrix in an elliptic PDE from measurements. The convex energy functional method with Tikhonov regularization is applied to tackle this problem. For the discretization we use the variational discretization concept, where the PDE is discretized with piecewise linear, continuous finite elements. We show the convergence of approximations. Using a suitable source condition, we prove an error bound for discrete solutions. For the numerical solution we propose a gradient-projection algorithm and prove the strong convergence of its iterates to a solution of the identification problem. Finally, we present a numerical experiment which illustrates our theoretical results.
Analytical Jacobian Calculation in RT Model Including Polarization Effect
NASA Astrophysics Data System (ADS)
Okabayashi, Y.; Yoshida, Y.; Ota, Y.
2014-12-01
The greenhouse gas observing satellite "GOSAT" launched in January 2009 has been observing global distribution of CO2 and CH4. The TANSO-FTS mounted on GOSAT measures the two polarized components (called "P" and "S") of short wavelength infrared (SWIR) spectrum reflected from the earth's surface. In NIES, column-averaged dry air mole fraction of CO2 and CH4 (XCO2 and XCH4) are retrieved from SWIR spectra. However, the observed polarization information is not effectively utilized in the retrieval process due to the large computational cost of a vector RT model, instead the polarization synthesized spectra and a scalar RT model are used in the operational processing. An optical path length modification due to aerosol scattering is known as the major error source for XCO2 and XCH4 retrieval from SWIR spectra. Because the aerosol scattering changes polarization state of light, more accurate or additional aerosol information is expected by using the observed polarization spectra effectively in the retrieval process, which improves the retrieval accuracy of XCO2 and XCH4. In addition, for information content analysis, sensitivity analysis and error analysis, Jacobian matrix is important onto retrieval algorithm design before analyses for actual observed data. However, in the case of using RT model including polarization effect in retrieval process, the computational cost of Jacobian matrix calculations in maximum a posteriori retrieval is significantly large. Efficient calculation of analytical Jacobian is necessary. As a first step, we are implementing an analytical Jacobian calculation function to the vector RT model "Pstar". RT scheme of Pstar is based on hybrid method comprising the discrete ordinate and matrix operator methods. The reflection/transmission matrices and source vectors are obtained for each vertical layer through the discrete ordinate solution, and the vertically inhomogeneous system is constructed using the matrix operator method. Because the delta
Jacobian conditioning analysis for model validation.
Rivals, Isabelle; Personnaz, Léon
2004-02-01
Our aim is to stress the importance of Jacobian matrix conditioning for model validation. We also comment on Monari and Dreyfus (2002), where, following Rivals and Personnaz (2000), it is proposed to discard neural candidates that are likely to overfit and/or for which quantities of interest such as confidence intervals cannot be computed accurately. In Rivals and Personnaz (2000), we argued that such models are to be discarded on the basis of the condition number of their Jacobian matrix. But Monari and Dreyfus (2002) suggest making the decision on the basis of the computed values of the leverages, the diagonal elements of the projection matrix on the range of the Jacobian, or "hat" matrix: they propose to discard a model if computed leverages are outside some theoretical bounds, pretending that it is the symptom of the Jacobian rank deficiency. We question this proposition because, theoretically, the hat matrix is defined whatever the rank of the Jacobian and because, in practice, the computed leverages of very ill-conditioned networks may respect their theoretical bounds while confidence intervals cannot be estimated accurately enough, two facts that have escaped Monari and Dreyfus's attention. Wealso recall the most accurate way to estimate the leverages and the properties of these estimations. Finally, we make an additional comment concerning the performance estimation in Monari and Dreyfus (2002). PMID:15006102
Perspectives on Intracluster Enrichment and the Stellar Initial Mass Function in Elliptical Galaxies
NASA Technical Reports Server (NTRS)
Lowenstein, Michael
2013-01-01
The amount of metals in the Intracluster Medium (ICM) in rich galaxy clusters exceeds that expected based on the observed stellar population by a large factor. We quantify this discrepancy--which we term the "cluster elemental abundance paradox"--and investigate the required properties of the ICM-enriching population. The necessary enhancement in metal enrichment may, in principle, originate in the observed stellar population if a larger fraction of stars in the supernova-progenitor mass range form from an initial mass function (IMF) that is either bottom-light or top-heavy, with the latter in some conflict with observed ICM abundance ratios. Other alternatives that imply more modest revisions to the IMF, mass return and remnant fractions, and primordial fraction, posit an increase in the fraction of 3-8 solar mass stars that explode as SNIa or assume that there are more stars than conventionally thought--although the latter implies a high star formation efficiency. We discuss the feasibility of these various solutions and the implications for the diversity of star formation, the process of elliptical galaxy formation, and the nature of this hidden source of ICM metal enrichment in light of recent evidence of an elliptical galaxy IMF that, because it is skewed to low masses, deepens the paradox.
Elliptically oscillating classical solution in Higgs potential and the effects on vacuum transitions
NASA Astrophysics Data System (ADS)
Kitadono, Yoshio; Inagaki, Tomohiro
2016-05-01
We investigate oscillating solutions of the equation of motion for the Higgs potential. The solutions are described by Jacobian elliptic functions. Classifying the classical solutions, we evaluate a possible parameter space for the initial conditions. To construct the field theory around the oscillating solutions, quantum fluctuations are introduced. This alternative perturbation method is useful to describe the nontrivial quantum theory around the oscillating state. This perturbation theory reduces to the standard one if we take the solution at the vacuum expectation value. It is shown that the transition probability between the vacuum and multiquanta states is finite as long as the initial field configuration does not start from the true vacuum.
The X-ray Luminosity Function of Point Sources in Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Diehl, Steven; Statler, Thomas
2004-04-01
The sub-arcsecond spatial resolution of Chandra recently revealed that early-type galaxies comprise a significant number of low-mass X-ray binaries (LMXBs). Early studies suggest the existence of a 'knee' in their X-ray luminosity function near the Eddington luminosity of a 1.4 Mo neutron star, indicating a transition from neutron star to black hole binaries. Recent analyses show however that a thorough correction for incompleteness is crucial, and able to remove the need for this break luminosity, leaving single power law fits more suitable for the data. We present luminosity functions of 65 elliptical galaxies in the Chandra archive which represents the largest uniformly reduced sample so far. An iterative Bayesian algorithm takes incompleteness and local background variation into account and generates the unbiased luminosity functions. This new non-parametric approach uncovers the significance of the contribution of unresolved LMXBs to the diffuse emission and the degree to which a break luminosity is required.
NASA Astrophysics Data System (ADS)
Lin, Chris L.; Ordóñez, Carlos R.
2016-10-01
We regulate in Euclidean space the Jacobian under scale transformations for two-dimensional nonrelativistic fermions and bosons interacting via contact interactions and compare the resulting scaling anomalies. For fermions, Grassmannian integration inverts the Jacobian; however, this effect is canceled by the regularization procedure and a result similar to that of bosons is attained. We show the independence of the result with respect to the regulating function, and show the robustness of our methods by comparing the procedure with an effective potential method using both cutoff and ζ -function regularization.
Beyond the excised ensemble: modelling elliptic curve L-functions with random matrices
NASA Astrophysics Data System (ADS)
Cooper, I. A.; Morris, Patrick W.; Snaith, N. C.
2016-02-01
The ‘excised ensemble’, a random matrix model for the zeros of quadratic twist families of elliptic curve L-functions, was introduced by Dueñez et al (2012 J. Phys. A: Math. Theor. 45 115207) The excised model is motivated by a formula for central values of these L-functions in a paper by Kohnen and Zagier (1981 Invent. Math. 64 175-98). This formula indicates that for a finite set of L-functions from a family of quadratic twists, the central values are all either zero or are greater than some positive cutoff. The excised model imposes this same condition on the central values of characteristic polynomials of matrices from {SO}(2N). Strangely, the cutoff on the characteristic polynomials that results in a convincing model for the L-function zeros is significantly smaller than that which we would obtain by naively transferring Kohnen and Zagier’s cutoff to the {SO}(2N) ensemble. In this current paper we investigate a modification to the excised model. It lacks the simplicity of the original excised ensemble, but it serves to explain the reason for the unexpectedly low cutoff in the original excised model. Additionally, the distribution of central L-values is ‘choppier’ than the distribution of characteristic polynomials, in the sense that it is a superposition of a series of peaks: the characteristic polynomial distribution is a smooth approximation to this. The excised model did not attempt to incorporate these successive peaks, only the initial cutoff. Here we experiment with including some of the structure of the L-value distribution. The conclusion is that a critical feature of a good model is to associate the correct mass to the first peak of the L-value distribution.
Superposition of elliptic functions as solutions for a large number of nonlinear equations
Khare, Avinash; Saxena, Avadh
2014-03-15
For a large number of nonlinear equations, both discrete and continuum, we demonstrate a kind of linear superposition. We show that whenever a nonlinear equation admits solutions in terms of both Jacobi elliptic functions cn(x, m) and dn(x, m) with modulus m, then it also admits solutions in terms of their sum as well as difference. We have checked this in the case of several nonlinear equations such as the nonlinear Schrödinger equation, MKdV, a mixed KdV-MKdV system, a mixed quadratic-cubic nonlinear Schrödinger equation, the Ablowitz-Ladik equation, the saturable nonlinear Schrödinger equation, λϕ{sup 4}, the discrete MKdV as well as for several coupled field equations. Further, for a large number of nonlinear equations, we show that whenever a nonlinear equation admits a periodic solution in terms of dn{sup 2}(x, m), it also admits solutions in terms of dn {sup 2}(x,m)±√(m) cn (x,m) dn (x,m), even though cn(x, m)dn(x, m) is not a solution of these nonlinear equations. Finally, we also obtain superposed solutions of various forms for several coupled nonlinear equations.
Mineev, Mark
2008-01-01
The planar elliptic extension of the Laplacian growth is, after a proper parametrization, given in a form of a solution to the equation for areapreserving diffeomorphisms. The infinite set of conservation laws associated with such elliptic growth is interpreted in terms of potential theory, and the relations between two major forms of the elliptic growth are analyzed. The constants of integration for closed form solutions are identified as the singularities of the Schwarz function, which are located both inside and outside the moving contour. Well-posedness of the recovery of the elliptic operator governing the process from the continuum of interfaces parametrized by time is addressed and two examples of exact solutions of elliptic growth are presented.
NASA Astrophysics Data System (ADS)
Tasbozan, Orkun; Çenesiz, Yücel; Kurt, Ali
2016-07-01
In this paper, the Jacobi elliptic function expansion method is proposed for the first time to construct the exact solutions of the time conformable fractional two-dimensional Boussinesq equation and the combined KdV-mKdV equation. New exact solutions are found. This method is based on Jacobi elliptic functions. The results obtained confirm that the proposed method is an efficient technique for analytic treatment of a wide variety of nonlinear conformable time-fractional partial differential equations.
EMG-based facial gesture recognition through versatile elliptic basis function neural network
2013-01-01
Background Recently, the recognition of different facial gestures using facial neuromuscular activities has been proposed for human machine interfacing applications. Facial electromyograms (EMGs) analysis is a complicated field in biomedical signal processing where accuracy and low computational cost are significant concerns. In this paper, a very fast versatile elliptic basis function neural network (VEBFNN) was proposed to classify different facial gestures. The effectiveness of different facial EMG time-domain features was also explored to introduce the most discriminating. Methods In this study, EMGs of ten facial gestures were recorded from ten subjects using three pairs of surface electrodes in a bi-polar configuration. The signals were filtered and segmented into distinct portions prior to feature extraction. Ten different time-domain features, namely, Integrated EMG, Mean Absolute Value, Mean Absolute Value Slope, Maximum Peak Value, Root Mean Square, Simple Square Integral, Variance, Mean Value, Wave Length, and Sign Slope Changes were extracted from the EMGs. The statistical relationships between these features were investigated by Mutual Information measure. Then, the feature combinations including two to ten single features were formed based on the feature rankings appointed by Minimum-Redundancy-Maximum-Relevance (MRMR) and Recognition Accuracy (RA) criteria. In the last step, VEBFNN was employed to classify the facial gestures. The effectiveness of single features as well as the feature sets on the system performance was examined by considering the two major metrics, recognition accuracy and training time. Finally, the proposed classifier was assessed and compared with conventional methods support vector machines and multilayer perceptron neural network. Results The average classification results showed that the best performance for recognizing facial gestures among all single/multi-features was achieved by Maximum Peak Value with 87.1% accuracy
Perspectives on Intracluster Enrichment and the Stellar Initial Mass Function in Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Loewenstein, Michael
2013-01-01
Stars born in galaxy cluster potential wells must be responsible for the high level of enrichment measured in the intracluster medium; however, there is increasing tension between this truism and the parsimonious assumption that the stars in the generally old population studied optically in cluster galaxies emerged from the same formation sites at the same epochs. We show that star formation that produces a stellar population with a canonical IMF and standard efficiency in producing SNIa, and comprises 10% of the current overall cluster baryon content, falls short by a factor of >2 of explaining a typical rich cluster ICM Fe abundance. This is true even for extreme assumptions about the level and relative amount of SNIa and SNII products locked up in the stellar population that conflict with spectroscopic studies of cluster galaxies. We construct and utilize a simple evolutionary model of an old, simple stellar population to quantify the changes in the IMF shape required to bring the ICM and stars into concordance. While in some cases the required departure from the canonical IMF is modest, optical determinations of the IMF from kinematic and population studies in elliptical galaxies are driving the inferred IMF in the opposite direction. This recent evidence of a steep IMF in elliptical galaxies that conflicts with the nucleosynthetic requirements of the ICM may therefore indicate the need for an additional source of enrichment, or a higher stellar fraction than is usually assumed.
JFKengine: A Jacobian and Forward Kinematics Generator
Fischer, K.N.
2003-02-13
During robot path planning and control the equations that describe the robot motions are determined and solved. Historically these expressions were derived analytically off-line. For robots that must adapt to their environment or perform a wide range of tasks, a way is needed to rapidly re-derive these expressions to take into account the robot kinematic changes, such as when a tool is added to the end-effector. The JFKengine software was developed to automatically produce the expressions representing the manipulator arm motion, including the manipulator arm Jacobian and the forward kinematic expressions. Its programming interface can be used in conjunction with robot simulation software or with robot control software. Thus, it helps to automate the process of configuration changes for serial robot manipulators. If the manipulator undergoes a geometric change, such as tool acquisition, then JFKengine can be invoked again from the control or simulation software, passing it parameters for the new arm configuration. This report describes the automated processes that are implemented by JFKengine to derive the kinematic equations and the programming interface by which it is invoked. Then it discusses the tree data structure that was chosen to store the expressions, followed by several examples of portions of expressions as represented in the tree. The C++ classes and their methods that implement the expression differentiation and evaluation operations are described. The algorithms used to construct the Jacobian and forward kinematic equations using these basic building blocks are then illustrated. The activity described in this report is part of a larger project entitled ''Multi-Optimization Criteria-Based Robot Behavioral Adaptability and Motion Planning'' that focuses on the development of a methodology for the generalized resolution of robot motion equations with time-varying configurations, constraints, and task objective criteria. A specific goal of this project is
ADIFOR working note. number sign. 2: Using ADIFOR to compute dense and sparse Jacobians
Bischof, C.; Hovland, P.
1992-01-01
ADIFOR is a source translator that, given a collection of Fortran subroutines for the computation of a function,'' produces Fortran code for the computation of the derivatives of this function. More specifically, ADIFOR produces code to compute the matrix-matrix product JS, where J is the Jacobian of the function'' with respect to the user-defined independent variables, and S is the composition of the derivative objects corresponding to the independent variables. This interface is flexible; by setting S = x, one can compute the matrix-vector product Jx, or by setting S = I, one can compute the whole Jacobian J. Other initializations of S allow one to exploit a known sparsity structure of J. This paper illustrates the proper initialization of ADIFOR-generated derivative codes and the exploitation of a known structure of J.
ADIFOR working note {number_sign}2: Using ADIFOR to compute dense and sparse Jacobians
Bischof, C.; Hovland, P.
1992-01-01
ADIFOR is a source translator that, given a collection of Fortran subroutines for the computation of a ``function,`` produces Fortran code for the computation of the derivatives of this function. More specifically, ADIFOR produces code to compute the matrix-matrix product JS, where J is the Jacobian of the ``function`` with respect to the user-defined independent variables, and S is the composition of the derivative objects corresponding to the independent variables. This interface is flexible; by setting S = x, one can compute the matrix-vector product Jx, or by setting S = I, one can compute the whole Jacobian J. Other initializations of S allow one to exploit a known sparsity structure of J. This paper illustrates the proper initialization of ADIFOR-generated derivative codes and the exploitation of a known structure of J.
Near-infrared line-strengths in elliptical galaxies: evidence for initial mass function variations?
NASA Astrophysics Data System (ADS)
Cenarro, A. J.; Gorgas, J.; Vazdekis, A.; Cardiel, N.; Peletier, R. F.
2003-02-01
We present new relations between recently defined line-strength indices in the near-infrared (CaT*, CaT, PaT, MgI and sTiO) and central velocity dispersion (σ0) for a sample of 35 early-type galaxies, showing evidence for significant anti-correlations between CaII triplet indices (CaT* and CaT) and log σ0. These relations are interpreted in the light of our recent evolutionary synthesis model predictions, suggesting the existence of important Ca underabundances with respect to Fe and/or an increase of the dwarf to giant stars ratio along the mass sequence of elliptical galaxies.
Off-diagonal Jacobian support for Nodal BCs
Peterson, John W.; Andrs, David; Gaston, Derek R.; Permann, Cody J.; Slaughter, Andrew E.
2015-01-01
In this brief note, we describe the implementation of o-diagonal Jacobian computations for nodal boundary conditions in the Multiphysics Object Oriented Simulation Environment (MOOSE) [1] framework. There are presently a number of applications [2{5] based on the MOOSE framework that solve complicated physical systems of partial dierential equations whose boundary conditions are often highly nonlinear. Accurately computing the on- and o-diagonal Jacobian and preconditioner entries associated to these constraints is crucial for enabling ecient numerical solvers in these applications. Two key ingredients are required for properly specifying the Jacobian contributions of nonlinear nodal boundary conditions in MOOSE and nite element codes in general: 1. The ability to zero out entire Jacobian matrix rows after \
Garcia-Botella, Angel; Fernandez-Balbuena, Antonio Alvarez; Bernabeu, Eusebio
2006-10-10
Nonimaging optics is a field devoted to the design of optical components for applications such as solar concentration or illumination. In this field, many different techniques have been used to produce optical devices, including the use of reflective and refractive components or inverse engineering techniques. However, many of these optical components are based on translational symmetries, rotational symmetries, or free-form surfaces. We study a new family of nonimaging concentrators called elliptical concentrators. This new family of concentrators provides new capabilities and can have different configurations, either homofocal or nonhomofocal. Translational and rotational concentrators can be considered as particular cases of elliptical concentrators. PMID:17068595
Elliptical Orbit Performance Computer Program
NASA Technical Reports Server (NTRS)
Myler, T.
1984-01-01
Elliptical Orbit Performance (ELOPE) computer program for analyzing orbital performance of space boosters uses orbit insertion data obtained from trajectory simulation to generate parametric data on apogee and perigee altitudes as function of payload data. Data used to generate presentation plots that display elliptical orbit performance capability of space booster.
NASA Astrophysics Data System (ADS)
Manapova, Aigul
2016-08-01
We consider optimal control problems for second order elliptic equations with non-self-adjoint operators-convection-diffusion problems. Control processes are described by semi-linear convection-diffusion equation with discontinuous data and solutions (states) subject to the boundary interface conditions of imperfect type (i.e., problems with a jump of the coefficients and the solution on the interface; the jump of the solution is proportional to the normal component of the flux). Controls are involved in the coefficients of diffusion and convective transfer. We prove differentiability and Lipshitz continuity of the cost functional, depending on a state of the system and a control. The calculation of the gradients uses the numerical solutions of direct problems for the state and adjoint problems.
Van Dokkum, Pieter G.; Conroy, Charlie
2011-07-01
We recently found that massive cluster elliptical galaxies have strong Na I {lambda}8183, 8195 and FeH {lambda}9916 Wing-Ford band absorption, indicating the presence of a very large population of stars with masses {approx}< 0.3 M{sub sun}. Here we test this result by comparing the elliptical galaxy spectra to those of luminous globular clusters associated with M31. These globular clusters have similar metallicities, abundance ratios, and ages as massive elliptical galaxies but their low dynamical mass-to-light ratios rule out steep stellar initial mass functions (IMFs). From high-quality Keck spectra we find that the dwarf-sensitive absorption lines in globular clusters are significantly weaker than in elliptical galaxies and consistent with normal IMFs. The differences in the Na I and Wing-Ford indices are 0.027 {+-} 0.007 mag and 0.017 {+-} 0.006 mag, respectively. We directly compare the two classes of objects by subtracting the averaged globular cluster spectrum from the averaged elliptical galaxy spectrum. The difference spectrum is well fit by the difference between a stellar population synthesis model with a bottom-heavy IMF and one with a bottom-light IMF. We speculate that the slope of the IMF may vary with velocity dispersion, although it is not yet clear what physical mechanism would be responsible for such a relation.
Dynamics on strata of trigonal Jacobians and some integrable problems of rigid body motion
NASA Astrophysics Data System (ADS)
Braden, H. W.; Enolski, V. Z.; Fedorov, Yu N.
2013-07-01
We present an algebraic geometrical and analytical description of the Goryachev case of rigid body motion. It belongs to a family of systems sharing the same properties: although completely integrable, they are not algebraically integrable, their solution is not meromorphic in the complex time and involves dynamics on the strata of the Jacobian varieties of trigonal curves. Although the strata of hyperelliptic Jacobians have already appeared in the literature in the context of some dynamical systems, the Goryachev case is the first example of an integrable system whose solution involves a more general curve. Several new features (and formulae) are encountered in the solution given in terms of sigma-functions of such a curve.
Algorithmic vs. finite difference Jacobians for infrared atmospheric radiative transfer
NASA Astrophysics Data System (ADS)
Schreier, Franz; Gimeno García, Sebastián; Vasquez, Mayte; Xu, Jian
2015-10-01
Jacobians, i.e. partial derivatives of the radiance and transmission spectrum with respect to the atmospheric state parameters to be retrieved from remote sensing observations, are important for the iterative solution of the nonlinear inverse problem. Finite difference Jacobians are easy to implement, but computationally expensive and possibly of dubious quality; on the other hand, analytical Jacobians are accurate and efficient, but the implementation can be quite demanding. GARLIC, our "Generic Atmospheric Radiation Line-by-line Infrared Code", utilizes algorithmic differentiation (AD) techniques to implement derivatives w.r.t. atmospheric temperature and molecular concentrations. In this paper, we describe our approach for differentiation of the high resolution infrared and microwave spectra and provide an in-depth assessment of finite difference approximations using "exact" AD Jacobians as a reference. The results indicate that the "standard" two-point finite differences with 1 K and 1% perturbation for temperature and volume mixing ratio, respectively, can exhibit substantial errors, and central differences are significantly better. However, these deviations do not transfer into the truncated singular value decomposition solution of a least squares problem. Nevertheless, AD Jacobians are clearly recommended because of the superior speed and accuracy.
Elliptic integrals: Symmetry and symbolic integration
Carlson, B.C. |
1997-12-31
Computation of elliptic integrals, whether numerical or symbolic, has been aided by the contributions of Italian mathematicians. Tricomi had a strong interest in iterative algorithms for computing elliptic integrals and other special functions, and his writings on elliptic functions and elliptic integrals have taught these subjects to many modern readers (including the author). The theory of elliptic integrals began with Fagnano`s duplication theorem, a generalization of which is now used iteratively for numerical computation in major software libraries. One of Lauricella`s multivariate hypergeometric functions has been found to contain all elliptic integrals as special cases and has led to the introduction of symmetric canonical forms. These forms provide major economies in new integral tables and offer a significant advantage also for symbolic integration of elliptic integrals. Although partly expository the present paper includes some new proofs and proposes a new procedure for symbolic integration.
The Matrix Editor for symbolic Jacobians in ALPAL
Painter, J.F.
1991-12-01
ALPAL is a Macsyma-based tool that automatically generates code to solve nonlinear integro-differential equations, given a very high-level specification of the equations to be solved and the numerical methods to be used. The Matrix Editor is a graphical, interactive tool for specifying the handling of Jacobian matrices and linear solvers. It automates such routine but difficult tasks as correctly converting from the data structures used for computing the Jacobian to data structures used by a linear solver. The user specifies what to do only at a high, natural level of abstraction.
NASA Astrophysics Data System (ADS)
Gubbiotti, G.; Carlotti, G.; Okuno, T.; Grimsditch, M.; Giovannini, L.; Montoncello, F.; Nizzoli, F.
2005-11-01
Brillouin light scattering (BLS) spectra have been measured in arrays of cylindrical Permalloy dots with elliptical cross section, 200nm wide, 15nm thick, and eccentricities from 1 to 3. Several spin modes are observed and their frequencies tracked as a function of the direction of the applied 1.5kOe magnetic field H . The experimental data are interpreted within the framework of the recently introduced dynamical matrix method to calculate spin excitations in magnetic particles. We find that the mode frequencies strongly depend on the eccentricity of the dots and on the direction of the applied field. For fields along the principal axes the solutions can be classified into: (i) modes localized near the particle ends, (ii) modes with nodal lines perpendicular to H (backwardlike modes), (iii) modes with nodal lines parallel to H (Damon-Eshbach-like modes) and (iv) modes with both parallel and perpendicular nodal lines. In cases where the frequencies of two modes in different families are similar, some hybridization between the modes is observed. For H along nonsymmetry directions only the modes of type (i) remain reasonably well defined, other modes can at best be described as hybrids of modes in the above categories. Determining which of the modes is active in BLS experiments leads to excellent agreement with the experimental results.
NASA Astrophysics Data System (ADS)
Yu. Moshin, Pavel; Reshetnyak, Alexander A.
2016-07-01
We continue our research1-4 and extend the class of finite BRST-anti-BRST transformations with odd-valued parameters λa, a = 1, 2, introduced in these works. In doing so, we evaluate the Jacobians induced by finite BRST-anti-BRST transformations linear in functionally-dependent parameters, as well as those induced by finite BRST-anti-BRST transformations with arbitrary functional parameters. The calculations cover the cases of gauge theories with a closed algebra, dynamical systems with first-class constraints, and general gauge theories. The resulting Jacobians in the case of linearized transformations are different from those in the case of polynomial dependence on the parameters. Finite BRST-anti-BRST transformations with arbitrary parameters induce an extra contribution to the quantum action, which cannot be absorbed into a change of the gauge. These transformations include an extended case of functionally-dependent parameters that implies a modified compensation equation, which admits nontrivial solutions leading to a Jacobian equal to unity. Finite BRST-anti-BRST transformations with functionally-dependent parameters are applied to the Standard Model, and an explicit form of functionally-dependent parameters λa is obtained, providing the equivalence of path integrals in any 3-parameter Rξ-like gauges. The Gribov-Zwanziger theory is extended to the case of the Standard Model, and a form of the Gribov horizon functional is suggested in the Landau gauge, as well as in Rξ-like gauges, in a gauge-independent way using field-dependent BRST-anti-BRST transformations, and in Rξ-like gauges using transverse-like non-Abelian gauge fields.
On the equivariant algebraic Jacobian for curves of genus two
NASA Astrophysics Data System (ADS)
Athorne, Chris
2012-04-01
We present a treatment of the algebraic description of the Jacobian of a generic genus two plane curve which exploits an SL2(k) equivariance and clarifies the structure of Flynn's 72 defining quadratic relations. The treatment is also applied to the Kummer variety.
Challenges of Inversely Estimating Jacobian from Metabolomics Data.
Sun, Xiaoliang; Länger, Bettina; Weckwerth, Wolfram
2015-01-01
Inferring dynamics of metabolic networks directly from metabolomics data provides a promising way to elucidate the underlying mechanisms of biological systems, as reported in our previous studies (Weckwerth, 2011; Sun and Weckwerth, 2012; Nägele et al., 2014) by a differential Jacobian approach. The Jacobian is solved from an overdetermined system of equations as JC + CJ(T) = -2D, called Lyapunov Equation in its generic form, where J is the Jacobian, C is the covariance matrix of metabolomics data, and D is the fluctuation matrix. Lyapunov Equation can be further simplified as the linear form Ax = b. Frequently, this linear equation system is ill-conditioned, i.e., a small variation in the right side b results in a big change in the solution x, thus making the solution unstable and error-prone. At the same time, inaccurate estimation of covariance matrix and uncertainties in the fluctuation matrix bring biases to the solution x. Here, we first reviewed common approaches to circumvent the ill-conditioned problems, including total least squares, Tikhonov regularization, and truncated singular value decomposition. Then, we benchmarked these methods on several in silico kinetic models with small to large perturbations on the covariance and fluctuation matrices. The results identified that the accuracy of the reverse Jacobian is mainly dependent on the condition number of A, the perturbation amplitude of C, and the stiffness of the kinetic models. Our research contributes a systematical comparison of methods to inversely solve Jacobian from metabolomics data. PMID:26636075
The Effects of Instrumental Elliptical Polarization on Stellar Point Spread Function Fine Structure
NASA Technical Reports Server (NTRS)
Carson, Joseph C.; Kern, Brian D.; Breckinridge, James B.; Trauger, John T.
2005-01-01
We present procedures and preliminary results from a study on the effects of instrumental polarization on the fine structure of the stellar point spread function (PSF). These effects are important to understand because the the aberration caused by instrumental polarization on an otherwise diffraction-limited will likely have have severe consequences for extreme high contrast imaging systems such as NASA's planned Terrestrial Planet Finder (TPF) mission and the proposed NASA Eclipse mission. The report here, describing our efforts to examine these effects, includes two parts: 1) a numerical analysis of the effect of metallic reflection, with some polarization-specific retardation, on a spherical wavefront; 2) an experimental approach for observing this effect, along with some preliminary laboratory results. While the experimental phase of this study requires more fine-tuning to produce meaningful results, the numerical analysis indicates that the inclusion of polarization-specific phase effects (retardation) results in a point spread function (PSF) aberration more severe than the amplitude (reflectivity) effects previously recorded in the literature.
NASA Astrophysics Data System (ADS)
Okumura, Teppei; Jing, Y. P.
2009-03-01
We examine whether the gravitational shear-intrinsic ellipticity (GI) correlation function of the luminous red galaxies (LRGs) can be modeled with the distribution function of a misalignment angle advocated recently by Okumura et al. For this purpose, we have accurately measured the GI correlation for the LRGs in the Data Release 6 (DR6) of the Sloan Digital Sky Survey (SDSS), which confirms the results of Hirata et al. who used the DR4 data. By comparing the GI correlation functions in the simulation and in the observation, we find that the GI correlation can be modeled in the current ΛCDM model if the misalignment follows a Gaussian distribution with a zero mean and a typical misalignment angle σθ = 34.9+1.9 -2.1 degrees. We also find a correlation between the axis ratios and intrinsic alignments of LRGs. This effect should be taken into account in theoretical modeling of the GI and intrinsic ellipticity-ellipticity correlations for weak lensing surveys.
Okura, Yuki; Futamase, Toshifumi E-mail: tof@astr.tohoku.ac.jp
2014-09-10
Highly accurate weak lensing analysis is urgently required for planned cosmic shear observations. For this purpose we have eliminated various systematic noises in the measurement. The point-spread function (PSF) effect is one of them. A perturbative approach for correcting the PSF effect on the observed image ellipticities has been previously employed. Here we propose a new non-perturbative approach for PSF correction that avoids the systematic error associated with the perturbative approach. The new method uses an artificial image for measuring shear which has the same ellipticity as the lensed image. This is done by re-smearing the observed galaxy images and observed star images (PSF) with an additional smearing function to obtain the original lensed galaxy images. We tested the new method with simple simulated objects that have Gaussian or Sérsic profiles smeared by a Gaussian PSF with sufficiently large size to neglect pixelization. Under the condition of no pixel noise, it is confirmed that the new method has no systematic error even if the PSF is large and has a high ellipticity.
Cramer, S.N.
1999-06-01
An analytical study of the solid angle subtended at a point by objects of first and second algebraic order has been made. It is shown that the derived solid angle for all such objects is in the form of a general elliptic integral, which can be written as a linear combination of elliptic integrals of the first and third kind and elementary functions. Many common surfaces and volumes have been investigated, including the conic sections and their volumes of revolution. The principal feature of the study is the manipulation of solid-angle equations into integral forms that can be matched with those found in handbook tables. These integrals are amenable to computer special function library routine analysis requiring no direct interaction with elliptic integrals by the user. The general case requires the solution of a fourth-order equation before specific solid-angle formulations can be made, but for many common geometric objects this equation can be solved by elementary means. Methods for the testing and application of solid-angle equations with Monte Carlo rejection and estimation techniques are presented. Approximate and degenerate forms of the equations are shown, and methods for the evaluation of the solid angle of a torus are outlined.
Ellipticities of Elliptical Galaxies in Different Environments
NASA Astrophysics Data System (ADS)
Chen, Cheng-Yu; Hwang, Chorng-Yuan; Ko, Chung-Ming
2016-10-01
We studied the ellipticity distributions of elliptical galaxies in different environments. From the ninth data release of the Sloan Digital Sky Survey, we selected galaxies with absolute {r}\\prime -band magnitudes between ‑21 and ‑22. We used the volume number densities of galaxies as the criterion for selecting the environments of the galaxies. Our samples were divided into three groups with different volume number densities. The ellipticity distributions of the elliptical galaxies differed considerably in these three groups of different density regions. We deprojected the observed 2D ellipticity distributions into intrinsic 3D shape distributions, and the result showed that the shapes of the elliptical galaxies were relatively spherically symmetric in the high density region (HDR) and that relatively more flat galaxies were present in the low density region (LDR). This suggests that the ellipticals in the HDRs and LDRs have different origins or that different mechanisms might be involved. The elliptical galaxies in the LDR are likely to have evolved from mergers in relatively anisotropic structures, such as filaments and webs, and might contain information on the anisotropic spatial distribution of their parent mergers. By contrast, elliptical galaxies in the HDR might be formed in more isotropic structures, such as galaxy clusters, or they might encounter more torqueing effects compared with galaxies in LDRs, thereby becoming rounder.
Commutative Families of the Elliptic Macdonald Operator
NASA Astrophysics Data System (ADS)
Saito, Yosuke
2014-03-01
In the paper [J. Math. Phys. 50 (2009), 095215, 42 pages], Feigin, Hashizume, Hoshino, Shiraishi, and Yanagida constructed two families of commuting operators which contain the Macdonald operator (commutative families of the Macdonald operator). They used the Ding-Iohara-Miki algebra and the trigonometric Feigin-Odesskii algebra. In the previous paper [arXiv:1301.4912], the present author constructed the elliptic Ding-Iohara-Miki algebra and the free field realization of the elliptic Macdonald operator. In this paper, we show that by using the elliptic Ding-Iohara-Miki algebra and the elliptic Feigin-Odesskii algebra, we can construct commutative families of the elliptic Macdonald operator. In Appendix, we will show a relation between the elliptic Macdonald operator and its kernel function by the free field realization.
A new Jacobian matrix for optimal learning of single-layer neural networks.
Peng, Jian Xun; Li, Kang; Irwin, George W
2008-01-01
This paper investigates the learning of a wide class of single-hidden-layer feedforward neural networks (SLFNs) with two sets of adjustable parameters, i.e., the nonlinear parameters in the hidden nodes and the linear output weights. The main objective is to both speed up the convergence of second-order learning algorithms such as Levenberg-Marquardt (LM), as well as to improve the network performance. This is achieved here by reducing the dimension of the solution space and by introducing a new Jacobian matrix. Unlike conventional supervised learning methods which optimize these two sets of parameters simultaneously, the linear output weights are first converted into dependent parameters, thereby removing the need for their explicit computation. Consequently, the neural network (NN) learning is performed over a solution space of reduced dimension. A new Jacobian matrix is then proposed for use with the popular second-order learning methods in order to achieve a more accurate approximation of the cost function. The efficacy of the proposed method is shown through an analysis of the computational complexity and by presenting simulation results from four different examples. PMID:18269943
Image Ellipticity from Atmospheric Aberrations
de Vries, W H; Olivier, S S; Asztalos, S J; Rosenberg, L J; Baker, K L
2007-03-06
We investigate the ellipticity of the point-spread function (PSF) produced by imaging an unresolved source with a telescope, subject to the effects of atmospheric turbulence. It is important to quantify these effects in order to understand the errors in shape measurements of astronomical objects, such as those used to study weak gravitational lensing of field galaxies. The PSF modeling involves either a Fourier transform of the phase information in the pupil plane or a ray-tracing approach, which has the advantage of requiring fewer computations than the Fourier transform. Using a standard method, involving the Gaussian weighted second moments of intensity, we then calculate the ellipticity of the PSF patterns. We find significant ellipticity for the instantaneous patterns (up to more than 10%). Longer exposures, which we approximate by combining multiple (N) images from uncorrelated atmospheric realizations, yield progressively lower ellipticity (as 1/{radical}N). We also verify that the measured ellipticity does not depend on the sampling interval in the pupil plane using the Fourier method. However, we find that the results using the ray-tracing technique do depend on the pupil sampling interval, representing a gradual breakdown of the geometric approximation at high spatial frequencies. Therefore, ray tracing is generally not an accurate method of modeling PSF ellipticity induced by atmospheric turbulence unless some additional procedure is implemented to correctly account for the effects of high spatial frequency aberrations. The Fourier method, however, can be used directly to accurately model PSF ellipticity, which can give insights into errors in the statistics of field galaxy shapes used in studies of weak gravitational lensing.
Multi-GPU Jacobian Accelerated Computing for Soft Field Tomography
Borsic, A.; Attardo, E. A.; Halter, R. J.
2012-01-01
Image reconstruction in soft-field tomography is based on an inverse problem formulation, where a forward model is fitted to the data. In medical applications, where the anatomy presents complex shapes, it is common to use Finite Element Models to represent the volume of interest and to solve a partial differential equation that models the physics of the system. Over the last decade, there has been a shifting interest from 2D modeling to 3D modeling, as the underlying physics of most problems are three-dimensional. Though the increased computational power of modern computers allows working with much larger FEM models, the computational time required to reconstruct 3D images on a fine 3D FEM model can be significant, on the order of hours. For example, in Electrical Impedance Tomography applications using a dense 3D FEM mesh with half a million elements, a single reconstruction iteration takes approximately 15 to 20 minutes with optimized routines running on a modern multi-core PC. It is desirable to accelerate image reconstruction to enable researchers to more easily and rapidly explore data and reconstruction parameters. Further, providing high-speed reconstructions are essential for some promising clinical application of EIT. For 3D problems 70% of the computing time is spent building the Jacobian matrix, and 25% of the time in forward solving. In the present work, we focus on accelerating the Jacobian computation by using single and multiple GPUs. First, we discuss an optimized implementation on a modern multi-core PC architecture and show how computing time is bounded by the CPU-to-memory bandwidth; this factor limits the rate at which data can be fetched by the CPU. Gains associated with use of multiple CPU cores are minimal, since data operands cannot be fetched fast enough to saturate the processing power of even a single CPU core. GPUs have a much faster memory bandwidths compared to CPUs and better parallelism. We are able to obtain acceleration factors of
NASA Astrophysics Data System (ADS)
Belobo Belobo, D.; Ben-Bolie, G. H.; Kofane, T. C.
2015-04-01
By using the F-expansion method associated with four auxiliary equations, i.e., the Bernoulli equation, the Riccati equation, the Lenard equation, and the hyperbolic equation, we present exact explicit solutions describing the dynamics of matter-wave condensates with time-varying two- and three-body nonlinearities. Condensates are trapped in a harmonic potential and they exchange atoms with the thermal cloud. These solutions include the generalized Jacobi elliptic function solutions, hyperbolic function solutions, and trigonometric function solutions. In addition, we have also found rational function solutions. Solutions constructed here have many free parameters that can be used to manipulate and control some important features of the condensate, such as the position, width, velocity, acceleration, and homogeneous phase. The stability of the solutions is confirmed by their long-time numerical behavior.
Nonlinear Schwarz-Fas Methods for Unstructured Finite Element Elliptic Problems
Jones, J E; Vassilevski, P S; Woodward, C S
2002-09-30
This paper provides extensions of an element agglomeration AMG method to nonlinear elliptic problems discretized by the finite element method on general unstructured meshes. The method constructs coarse discretization spaces and corresponding coarse nonlinear operators as well as their Jacobians. We introduce both standard (fairly quasi-uniformly coarsened) and non-standard (coarsened away) coarse meshes and respective finite element spaces. We use both kind of spaces in FAS type coarse subspace correction (or Schwarz) algorithms. Their performance is illustrated on a number of model problems. The coarsened away spaces seem to perform better than the standard spaces for problems with nonlinearities in the principal part of the elliptic operator.
Isolated elliptical galaxies in the local Universe
NASA Astrophysics Data System (ADS)
Lacerna, I.; Hernández-Toledo, H. M.; Avila-Reese, V.; Abonza-Sane, J.; del Olmo, A.
2016-04-01
Context. We have studied a sample of 89 very isolated, elliptical galaxies at z < 0.08 and compared their properties with elliptical galaxies located in a high-density environment such as the Coma supercluster. Aims: Our aim is to probe the role of environment on the morphological transformation and quenching of elliptical galaxies as a function of mass. In addition, we elucidate the nature of a particular set of blue and star-forming isolated ellipticals identified here. Methods: We studied physical properties of ellipticals, such as color, specific star formation rate, galaxy size, and stellar age, as a function of stellar mass and environment based on SDSS data. We analyzed the blue and star-forming isolated ellipticals in more detail, through photometric characterization using GALFIT, and infer their star formation history using STARLIGHT. Results: Among the isolated ellipticals ≈20% are blue, ≲8% are star forming, and ≈10% are recently quenched, while among the Coma ellipticals ≈8% are blue and just ≲1% are star forming or recently quenched. There are four isolated galaxies (≈4.5%) that are blue and star forming at the same time. These galaxies, with masses between 7 × 109 and 2 × 1010 h-2 M⊙, are also the youngest galaxies with light-weighted stellar ages ≲1 Gyr and exhibit bluer colors toward the galaxy center. Around 30-60% of their present-day luminosity, but only <5% of their present-day mass, is due to star formation in the last 1 Gyr. Conclusions: The processes of morphological transformation and quenching seem to be in general independent of environment since most of elliptical galaxies are "red and dead", although the transition to the red sequence should be faster for isolated ellipticals. In some cases, the isolated environment seems to propitiate the rejuvenation of ellipticals by recent (<1 Gyr) cold gas accretion.
Zhao, Bo; Wang, Lei; Tan, Jiu-Bin
2015-01-01
This paper presents the design and realization of a three degrees of freedom (DOFs) displacement measurement system composed of Hall sensors, which is built for the XYθz displacement measurement of the short stroke stage of the reticle stage of lithography. The measurement system consists of three pairs of permanent magnets mounted on the same plane on the short stroke stage along the Y, Y, X directions, and three single axis Hall sensors correspondingly mounted on the frame of the reticle stage. The emphasis is placed on the decoupling and magnetic field fitting of the three DOFs measurement system. The model of the measurement system is illustrated, and the XY positions and θZ rotation of the short stroke stage can be obtained by decoupling the sensor outputs. A magnetic field fitting by an elliptic function-based compensation method is proposed. The practical field intensity of a permanent magnet at a certain plane height can be substituted for the output voltage of a Hall sensors, which can be expressed by the elliptic function through experimental data as the crucial issue to calculate the three DOFs displacement. Experimental results of the Hall sensor displacement measurement system are presented to validate the proposed three DOFs measurement system. PMID:26370993
Damiano, Diane L; Zampieri, Cristiane; Ge, Jie; Acevedo, Ana; Dsurney, John
2016-08-01
This small clinical trial utilized a novel rehabilitation strategy, rapid-resisted elliptical training, in an effort to increase motor, and thereby cognitive, processing speed in ambulatory individuals with traumatic brain injury (TBI). As an initial step, multimodal functional abilities were quantified and compared in 12 ambulatory adults with and 12 without TBI. After the baseline assessment, the group with TBI participated in an intensive 8-week daily exercise program using an elliptical trainer and was reassessed after completion and at an 8-week follow-up. The focus of training was on achieving a fast movement speed, and once the target was reached, resistance to motion was increased in small increments to increase intensity of muscle activation. Primary outcomes were: High-Level Mobility Assessment Tool (HiMAT), instrumented balance tests, dual-task (DT) performance and neurobehavioral questionnaires. The group with TBI had poorer movement excursion during balance tests and poorer dual-task (DT) performance. After training, balance reaction times improved and were correlated with gains in the HiMAT and DT. Sleep quality also improved and was correlated with improved depression and learning. This study illustrates how brain injury can affect multiple linked aspects of functioning and provides preliminary evidence that intensive rapid-resisted training has specific positive effects on dynamic balance and more generalized effects on sleep quality in TBI.
Zampieri, Cris; Ge, Jie; Acevedo, Ana; Dsurney, John
2016-01-01
This small clinical trial utilized a novel rehabilitation strategy, rapid-resisted elliptical training, in an effort to increase motor, and thereby cognitive, processing speed in ambulatory individuals with traumatic brain injury (TBI). As an initial step, multimodal functional abilities were quantified and compared in 12 ambulatory adults with and 12 without TBI. After the baseline assessment, the group with TBI participated in an intensive 8-week daily exercise program using an elliptical trainer and was reassessed after completion and at an 8-week follow-up. The focus of training was on achieving a fast movement speed, and once the target was reached, resistance to motion was increased in small increments to increase intensity of muscle activation. Primary outcomes were: High-Level Mobility Assessment Tool (HiMAT), instrumented balance tests, dual-task (DT) performance and neurobehavioral questionnaires. The group with TBI had poorer movement excursion during balance tests and poorer dual-task (DT) performance. After training, balance reaction times improved and were correlated with gains in the HiMAT and DT. Sleep quality also improved and was correlated with improved depression and learning. This study illustrates how brain injury can affect multiple linked aspects of functioning and provides preliminary evidence that intensive rapid-resisted training has specific positive effects on dynamic balance and more generalized effects on sleep quality in TBI. PMID:27025506
Zhao, Bo; Wang, Lei; Tan, Jiu-Bin
2015-09-08
This paper presents the design and realization of a three degrees of freedom (DOFs) displacement measurement system composed of Hall sensors, which is built for the XYθz displacement measurement of the short stroke stage of the reticle stage of lithography. The measurement system consists of three pairs of permanent magnets mounted on the same plane on the short stroke stage along the Y, Y, X directions, and three single axis Hall sensors correspondingly mounted on the frame of the reticle stage. The emphasis is placed on the decoupling and magnetic field fitting of the three DOFs measurement system. The model of the measurement system is illustrated, and the XY positions and θZ rotation of the short stroke stage can be obtained by decoupling the sensor outputs. A magnetic field fitting by an elliptic function-based compensation method is proposed. The practical field intensity of a permanent magnet at a certain plane height can be substituted for the output voltage of a Hall sensors, which can be expressed by the elliptic function through experimental data as the crucial issue to calculate the three DOFs displacement. Experimental results of the Hall sensor displacement measurement system are presented to validate the proposed three DOFs measurement system.
Zhao, Bo; Wang, Lei; Tan, Jiu-Bin
2015-01-01
This paper presents the design and realization of a three degrees of freedom (DOFs) displacement measurement system composed of Hall sensors, which is built for the XYθz displacement measurement of the short stroke stage of the reticle stage of lithography. The measurement system consists of three pairs of permanent magnets mounted on the same plane on the short stroke stage along the Y, Y, X directions, and three single axis Hall sensors correspondingly mounted on the frame of the reticle stage. The emphasis is placed on the decoupling and magnetic field fitting of the three DOFs measurement system. The model of the measurement system is illustrated, and the XY positions and θZ rotation of the short stroke stage can be obtained by decoupling the sensor outputs. A magnetic field fitting by an elliptic function-based compensation method is proposed. The practical field intensity of a permanent magnet at a certain plane height can be substituted for the output voltage of a Hall sensors, which can be expressed by the elliptic function through experimental data as the crucial issue to calculate the three DOFs displacement. Experimental results of the Hall sensor displacement measurement system are presented to validate the proposed three DOFs measurement system. PMID:26370993
NASA Astrophysics Data System (ADS)
Muthukumar, K.; Larsson, J. A.
2010-07-01
Endohedral metallofullerenes that encapsulate one or several atoms, or a cluster of atoms have molecular properties making them useful both in technology and in bio-medical applications. Some fullerenes are found to have two metal atoms incarcerated and it has been recently found that two Ce atoms are incorporated into the C78-D3h (78 : 5) cage. In this study, we report calculations on the structural and electronic properties of Ce2@C78 using density functional theory (DFT). While Ce2@C80-Ih (D3d) and La2@C80-Ih (D2h) have different ground state structures, we have found that Ce2@C78 has a D3h ground state structure just as La2@C78. The encapsulated Ce atoms bind strongly to the C78-D3h cage with a binding energy (BE) of 5.925 eV but not as strong as in Ce@C82-C2v nor in Ce2@C80-Ih. The elliptical nature of the cage plays a crucial role and accommodates the two Ce atoms at opposite ends of the C3 axis with a maximized inter atomic distance (4.078 Å). This means that the effect of the additional f-electron repulsion in M2@C78 with M = Ce compared to M = La, is less pronounced than in Ce2@C80 compared to La2@C80. We compare the results to the elliptical M2@C72 (#10611) (M = La, Ce), and with a range of additional Ce and La endohedral fullerenes and explain the role ellipticity has in the preferential binding site of Ce and shed light on the formation mechanism of these nanostructures.
Muthukumar, K; Larsson, J A
2010-07-01
Endohedral metallofullerenes that encapsulate one or several atoms, or a cluster of atoms have molecular properties making them useful both in technology and in bio-medical applications. Some fullerenes are found to have two metal atoms incarcerated and it has been recently found that two Ce atoms are incorporated into the C(78)-D(3h) (78 : 5) cage. In this study, we report calculations on the structural and electronic properties of Ce(2)@C(78) using density functional theory (DFT). While Ce(2)@C(80)-I(h) (D(3d)) and La(2)@C(80)-I(h) (D(2h)) have different ground state structures, we have found that Ce(2)@C(78) has a D(3h) ground state structure just as La(2)@C(78). The encapsulated Ce atoms bind strongly to the C(78)-D(3h) cage with a binding energy (BE) of 5.925 eV but not as strong as in Ce@C(82)-C(2v) nor in Ce(2)@C(80)-I(h). The elliptical nature of the cage plays a crucial role and accommodates the two Ce atoms at opposite ends of the C(3) axis with a maximized inter atomic distance (4.078 A). This means that the effect of the additional f-electron repulsion in M(2)@C(78) with M = Ce compared to M = La, is less pronounced than in Ce(2)@C(80) compared to La(2)@C(80). We compare the results to the elliptical M(2)@C(72) (#10611) (M = La, Ce), and with a range of additional Ce and La endohedral fullerenes and explain the role ellipticity has in the preferential binding site of Ce and shed light on the formation mechanism of these nanostructures.
Liouville Theory and Elliptic Genera
NASA Astrophysics Data System (ADS)
Taormina, A.
The structure and modular properties of N = 4 superconformal characters are reviewed and exploited, in an attempt to construct elliptic genera-like functions by decompactifying K_3. The construction is tested against expressions obtained in the context of strings propagating in background ALE spaces of type A_{N-1}, using the underlying superconformal theory N = 2 minimal ⊗ N = 2 Liouville.
Goudfrooij, Paul; Diederik Kruijssen, J. M. E-mail: kruijssen@mpa-garching.mpg.de
2013-01-10
We report a systematic and statistically significant offset between the optical (g - z or B - I) colors of seven massive elliptical galaxies and the mean colors of their associated massive metal-rich globular clusters (GCs) in the sense that the parent galaxies are redder by {approx}0.12-0.20 mag at a given galactocentric distance. However, spectroscopic indices in the blue indicate that the luminosity-weighted ages and metallicities of such galaxies are equal to that of their averaged massive metal-rich GCs at a given galactocentric distance, to within small uncertainties. The observed color differences between the red GC systems and their parent galaxies cannot be explained by the presence of multiple stellar generations in massive metal-rich GCs, as the impact of the latter to the populations' integrated g - z or B - I colors is found to be negligible. However, we show that this paradox can be explained if the stellar initial mass function (IMF) in these massive elliptical galaxies was significantly steeper at subsolar masses than canonical IMFs derived from star counts in the solar neighborhood, with the GC colors having become bluer due to dynamical evolution, causing a significant flattening of the stellar MF of the average surviving GC.
Goudfrooij, Paul; Kruijssen, J. M. Diederik E-mail: kruijssen@mpa-garching.mpg.de
2014-01-01
Several recent studies have provided evidence for a 'bottom-heavy' stellar initial mass function (IMF) in massive elliptical galaxies. Here we investigate the influence of the IMF shape on the recently discovered color-magnitude relation (CMR) among globular clusters (GCs) in such galaxies. To this end we use calculations of GC mass loss due to stellar and dynamical evolution to evaluate (1) the shapes of stellar mass functions in GCs after 12 Gyr of evolution as a function of current GC mass along with their effects on integrated-light colors and mass-to-light ratios, and (2) their impact on the effects of GC self-enrichment using the 2009 'reference' model of Bailin and Harris. As to the class of metal-poor GCs, we find the observed shape of the CMR (often referred to as the 'blue tilt') to be very well reproduced by Bailin and Harris's reference self-enrichment model once 12 Gyr of GC mass loss is taken into account. The influence of the IMF on this result is found to be insignificant. However, we find that the observed CMR among the class of metal-rich GCs (the 'red tilt') can only be adequately reproduced if the IMF was bottom-heavy (–3.0 ≲ α ≲ –2.3 in dN/dM∝M{sup α}), which causes the stellar mass function at subsolar masses to depend relatively strongly on GC mass. This constitutes additional evidence that the metal-rich stellar populations in giant elliptical galaxies were formed with a bottom-heavy IMF.
NASA Astrophysics Data System (ADS)
Tala-Tebue, E.; Tsobgni-Fozap, D. C.; Kenfack-Jiotsa, A.; Kofane, T. C.
2014-06-01
Using the Jacobi elliptic functions and the alternative ( G'/ G-expansion method including the generalized Riccati equation, we derive exact soliton solutions for a discrete nonlinear electrical transmission line in (2+1) dimension. More precisely, these methods are general as they lead us to diverse solutions that have not been previously obtained for the nonlinear electrical transmission lines. This study seeks to show that it is not often necessary to transform the equation of the network into a well-known differential equation before finding its solutions. The solutions obtained by the current methods are generalized periodic solutions of nonlinear equations. The shape of solutions can be well controlled by adjusting the parameters of the network. These exact solutions may have significant applications in telecommunication systems where solitons are used to codify or for the transmission of data.
Supersonic Elliptical Ramp Inlet
NASA Technical Reports Server (NTRS)
Adamson, Eric E. (Inventor); Fink, Lawrence E. (Inventor); Fugal, Spencer R. (Inventor)
2016-01-01
A supersonic inlet includes a supersonic section including a cowl which is at least partially elliptical, a ramp disposed within the cowl, and a flow inlet disposed between the cowl and the ramp. The ramp may also be at least partially elliptical.
Low-rank Quasi-Newton updates for Robust Jacobian lagging in Newton methods
Brown, J.; Brune, P.
2013-07-01
Newton-Krylov methods are standard tools for solving nonlinear problems. A common approach is to 'lag' the Jacobian when assembly or preconditioner setup is computationally expensive, in exchange for some degradation in the convergence rate and robustness. We show that this degradation may be partially mitigated by using the lagged Jacobian as an initial operator in a quasi-Newton method, which applies unassembled low-rank updates to the Jacobian until the next full reassembly. We demonstrate the effectiveness of this technique on problems in glaciology and elasticity. (authors)
Solving Nonlinear Solid Mechanics Problems with the Jacobian-Free Newton Krylov Method
J. D. Hales; S. R. Novascone; R. L. Williamson; D. R. Gaston; M. R. Tonks
2012-06-01
The solution of the equations governing solid mechanics is often obtained via Newton's method. This approach can be problematic if the determination, storage, or solution cost associated with the Jacobian is high. These challenges are magnified for multiphysics applications with many coupled variables. Jacobian-free Newton-Krylov (JFNK) methods avoid many of the difficulties associated with the Jacobian by using a finite difference approximation. BISON is a parallel, object-oriented, nonlinear solid mechanics and multiphysics application that leverages JFNK methods. We overview JFNK, outline the capabilities of BISON, and demonstrate the effectiveness of JFNK for solid mechanics and solid mechanics coupled to other PDEs using a series of demonstration problems.
Tetrahedral Element Shape Optimization via the Jacobian Determinant and Condition Number
FREITAG,LORI A.; KNUPP,PATRICK
1999-09-27
We present a new shape measure for tetrahedral elements that is optimal in the sense that it gives the distance of a tetrahedron from the set of inverted elements. This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetrahedron with positive volume. We use this shape measure to formulate two optimization objective functions that are differentiated by their goal: the first seeks to improve the average quality of the tetrahedral mesh; the second aims to improve the worst-quality element in the mesh. Because the element condition number is not defined for tetrahedral with negative volume, these objective functions can be used only when the initial mesh is valid. Therefore, we formulate a third objective function using the determinant of the element Jacobian that is suitable for mesh untangling. We review the optimization techniques used with each objective function and present experimental results that demonstrate the effectiveness of the mesh improvement and untangling methods. We show that a combined optimization approach that uses both condition number objective functions obtains the best-quality meshes.
Nakamura, Kunio; Guizard, Nicolas; Fonov, Vladimir S.; Narayanan, Sridar; Collins, D. Louis; Arnold, Douglas L.
2013-01-01
Gray matter atrophy provides important insights into neurodegeneration in multiple sclerosis (MS) and can be used as a marker of neuroprotection in clinical trials. Jacobian integration is a method for measuring volume change that uses integration of the local Jacobian determinants of the nonlinear deformation field registering two images, and is a promising tool for measuring gray matter atrophy. Our main objective was to compare the statistical power of the Jacobian integration method to commonly used methods in terms of the sample size required to detect a treatment effect on gray matter atrophy. We used multi-center longitudinal data from relapsing–remitting MS patients and evaluated combinations of cross-sectional and longitudinal pre-processing with SIENAX/FSL, SPM, and FreeSurfer, as well as the Jacobian integration method. The Jacobian integration method outperformed these other commonly used methods, reducing the required sample size by a factor of 4–5. The results demonstrate the advantage of using the Jacobian integration method to assess neuroprotection in MS clinical trials. PMID:24266007
NASA Technical Reports Server (NTRS)
Janin, G.; Bond, V. R.
1980-01-01
An independent variable different from the time for elliptic orbit integration is used. Such a time transformation provides an analytical step-size regulation along the orbit. An intermediate anomaly (an anomaly intermediate between the eccentric and the true anomaly) is suggested for optimum performances. A particular case of an intermediate anomaly (the elliptic anomaly) is defined, and its relation with the other anomalies is developed.
Elliptic pfaffians and solvable lattice models
NASA Astrophysics Data System (ADS)
Rosengren, Hjalmar
2016-08-01
We introduce and study twelve multivariable theta functions defined by pfaffians with elliptic function entries. We show that, when the crossing parameter is a cubic root of unity, the domain wall partition function for the eight-vertex-solid-on-solid model can be written as a sum of two of these pfaffians. As a limit case, we express the domain wall partition function for the three-colour model as a sum of two Hankel determinants. We also show that certain solutions of the TQ-equation for the supersymmetric eight-vertex model can be expressed in terms of elliptic pfaffians.
Elastohydrodynamic lubrication of elliptical contacts
NASA Technical Reports Server (NTRS)
Hamrock, B. J.
1982-01-01
Fully flooded, elastohydrodynamically lubricated, elliptical contacts are discussed. The relevant equations used in the elastohydrodynamic lubrication (EHL) of elliptical contacts are briefly described. Film thickness equations are developed for materials of high elastic modulus, such as metal, and for materials of low elastic modulus, such as rubber. In addition to the film thickness equations that are developed, plots of pressure and film thickness are presented. A theoretical study of the influence of lubricant starvation on film thickness and pressure in hard and soft elliptical elastohydrodynamic contacts is presented. From the results for both hard and soft EHL contacts a simple and important dimensionless inlet boundary distance is specified. It is also found that the film thickness for a starved condition can be written in dimensionless terms as a function of the inlet distance parameter and the film thickness for a fully flooded condition. contour plots of pressure and film thickness in and around the contact are shown for fully flooded and starved conditions. The theoretical findings are compared directly with results obtained experimentally.
Dana A. Knoll; H. Park; Kord Smith
2011-02-01
The use of the Jacobian-free Newton-Krylov (JFNK) method within the context of nonlinear diffusion acceleration (NDA) of source iteration is explored. The JFNK method is a synergistic combination of Newton's method as the nonlinear solver and Krylov methods as the linear solver. JFNK methods do not form or store the Jacobian matrix, and Newton's method is executed via probing the nonlinear discrete function to approximate the required matrix-vector products. Current application of NDA relies upon a fixed-point, or Picard, iteration to resolve the nonlinearity. We show that the JFNK method can be used to replace this Picard iteration with a Newton iteration. The Picard linearization is retained as a preconditioner. We show that the resulting JFNK-NDA capability provides benefit in some regimes. Furthermore, we study the effects of a two-grid approach, and the required intergrid transfers when the higher-order transport method is solved on a fine mesh compared to the low-order acceleration problem.
Multilevel filtering elliptic preconditioners
NASA Technical Reports Server (NTRS)
Kuo, C. C. Jay; Chan, Tony F.; Tong, Charles
1989-01-01
A class of preconditioners is presented for elliptic problems built on ideas borrowed from the digital filtering theory and implemented on a multilevel grid structure. They are designed to be both rapidly convergent and highly parallelizable. The digital filtering viewpoint allows the use of filter design techniques for constructing elliptic preconditioners and also provides an alternative framework for understanding several other recently proposed multilevel preconditioners. Numerical results are presented to assess the convergence behavior of the new methods and to compare them with other preconditioners of multilevel type, including the usual multigrid method as preconditioner, the hierarchical basis method and a recent method proposed by Bramble-Pasciak-Xu.
NASA Astrophysics Data System (ADS)
Dutton, Aaron A.; Treu, Tommaso
2014-03-01
Recent studies have shown that massive elliptical galaxies have total mass density profiles within an effective radius that can be approximated as ρ_tot∝ r^{-γ^', with mean slope <γ'> = 2.08 ± 0.03 and scatter σ _{γ ^' } }=0.16± 0.02. The small scatter of the slope (known as the bulge-halo conspiracy) is not generic in Λ cold dark matter (ΛCDM) based models and therefore contains information about the galaxy formation process. We compute the distribution of γ' for ΛCDM-based models that reproduce the observed correlations between stellar mass, velocity dispersion, and effective radius of early-type galaxies in the Sloan Digital Sky Survey. The models have a range of stellar initial mass functions (IMFs) and dark halo responses to galaxy formation. The observed distribution of γ' is well reproduced by a model with cosmologically motivated but uncontracted dark matter haloes, and a Salpeter-type IMF. Other models are on average ruled out by the data, even though they may happen in individual cases. Models with adiabatic halo contraction (and lighter IMFs) predict too small values of γ'. Models with halo expansion, or mass-follows-light predict too high values of γ'. Our study shows that the non-homologous structure of massive early-type galaxies can be precisely reproduced by ΛCDM models if the IMF is not universal and if mechanisms, such as feedback from active galactic nuclei, or dynamical friction, effectively on average counterbalance the contraction of the halo expected as a result of baryonic cooling.
Stability of simply supported and clamped elliptical plates
NASA Astrophysics Data System (ADS)
Rao, A. V.; Rao, B. N.; Prasad, K. L.
1992-12-01
Formulas are developed for estimating the elastic stability of an elliptical plate under compressive forces uniformly distributed around the edge of the plate. Then, a Cartesian coordinate system is used to perform the stability analysis of simply supported and clamped elliptical plates by following the Rayleigh-Ritz technique with a three-term deflection function.
NASA Astrophysics Data System (ADS)
Smith, Stuart T.; Badami, Vivek G.; Dale, Jami S.; Xu, Ying
1997-03-01
This paper presents closed form equations based on a modification of those originally derived by Paros and Weisbord in 1965, for the mechanical compliance of a simple monolithic flexure hinge of elliptic cross section, the geometry of which is determined by the ratio ɛ of the major and minor axes. It is shown that these equations converge at ɛ=1 to the Paros and Weisbord equations for a hinge of circular section and at ɛ ⇒∞ to the equations predicted from simple beam bending theory for the compliance of a cantilever beam. These equations are then assessed by comparison with results from finite element analysis over a range of geometries typical of many hinge designs. Based on the finite element analysis, stress concentration factors for the elliptical hinge are also presented. As a further verification of these equations, a number of elliptical hinges were manufactured on a CNC milling machine. Experimental data were produced by applying a bending moment using dead weight loading and measuring subsequent angular deflections with a laser interferometer. In general, it was found that predictions for the compliance of elliptical hinges are likely to be within 12% for a range of geometries with the ratio βx(=t/2ax) between 0.06 and 0.2 and for values of ɛ between 1 and 10.
Using ADIFOR and ADIC to provide Jacobians for the SNES component of PETSc
Wu, Po-Ting; Bischof, C.H.; Hovland, P.D.
1997-11-01
The solution of large-scale nonlinear problems is important to many areas of computational science. The SNES component of PETSc provides a robust and flexible suite of numerical routines for the solving such problems. These routines generally utilize the Jacobian matrix. We present a strategy for using ADIFOR or ADIC to assist in the development of a subroutine for computing this matrix. We illustrate this strategy using one of the PETSc example programs and four different approaches to computing the Jacobian via automatic differentiation.
Vortex dynamics in thin elliptic ferromagnetic nanodisks
NASA Astrophysics Data System (ADS)
Wysin, G. M.
2015-10-01
Vortex gyrotropic motion in thin ferromagnetic nanodisks of elliptical shape is described here for a pure vortex state and for a situation with thermal fluctuations. The system is analyzed using numerical simulations of the Landau-Lifshitz-Gilbert (LLG) equations, including the demagnetization field calculated with a Green's function approach for thin film problems. At finite temperature the thermalized dynamics is found using a second order Heun algorithm for a magnetic Langevin equation based on the LLG equations. The vortex state is stable only within a limited range of ellipticity, outside of which a quasi-single-domain becomes the preferred minimum energy state. A vortex is found to move in an elliptical potential, whose force constants along the principal axes are determined numerically. The eccentricity of vortex motion is directly related to the force constants. Elliptical vortex motion is produced spontaneously by thermal fluctuations. The vortex position and velocity distributions in thermal equilibrium are Boltzmann distributions. The results show that vortex motion in elliptical disks can be described by a Thiele equation.
Elliptical orbit performance computer program
NASA Technical Reports Server (NTRS)
Myler, T. R.
1981-01-01
A FORTRAN coded computer program which generates and plots elliptical orbit performance capability of space boosters for presentation purposes is described. Orbital performance capability of space boosters is typically presented as payload weight as a function of perigee and apogee altitudes. The parameters are derived from a parametric computer simulation of the booster flight which yields the payload weight as a function of velocity and altitude at insertion. The process of converting from velocity and altitude to apogee and perigee altitude and plotting the results as a function of payload weight is mechanized with the ELOPE program. The program theory, user instruction, input/output definitions, subroutine descriptions and detailed FORTRAN coding information are included.
Flux Jacobian matrices and generaled Roe average for an equilibrium real gas
NASA Technical Reports Server (NTRS)
Vinokur, Marcel
1988-01-01
Inviscid flux Jacobian matrices and their properties used in numerical solutions of conservation laws are extended to general, equilibrium gas laws. Exact and approximate generalizations of the Roe average are presented. Results are given for one-dimensional flow, and then extended to three-dimensional flow with time-varying grids.
NASA Astrophysics Data System (ADS)
Chak, Yew-Chung; Varatharajoo, Renuganth
2016-07-01
Many spacecraft attitude control systems today use reaction wheels to deliver precise torques to achieve three-axis attitude stabilization. However, irrecoverable mechanical failure of reaction wheels could potentially lead to mission interruption or total loss. The electrically-powered Solar Array Drive Assemblies (SADA) are usually installed in the pitch axis which rotate the solar arrays to track the Sun, can produce torques to compensate for the pitch-axis wheel failure. In addition, the attitude control of a flexible spacecraft poses a difficult problem. These difficulties include the strong nonlinear coupled dynamics between the rigid hub and flexible solar arrays, and the imprecisely known system parameters, such as inertia matrix, damping ratios, and flexible mode frequencies. In order to overcome these drawbacks, the adaptive Jacobian tracking fuzzy control is proposed for the combined attitude and sun-tracking control problem of a flexible spacecraft during attitude maneuvers in this work. For the adaptation of kinematic and dynamic uncertainties, the proposed scheme uses an adaptive sliding vector based on estimated attitude velocity via approximate Jacobian matrix. The unknown nonlinearities are approximated by deriving the fuzzy models with a set of linguistic If-Then rules using the idea of sector nonlinearity and local approximation in fuzzy partition spaces. The uncertain parameters of the estimated nonlinearities and the Jacobian matrix are being adjusted online by an adaptive law to realize feedback control. The attitude of the spacecraft can be directly controlled with the Jacobian feedback control when the attitude pointing trajectory is designed with respect to the spacecraft coordinate frame itself. A significant feature of this work is that the proposed adaptive Jacobian tracking scheme will result in not only the convergence of angular position and angular velocity tracking errors, but also the convergence of estimated angular velocity to
Starved elastohydrodynamic lubricated elliptical contacts
NASA Technical Reports Server (NTRS)
Hamrock, B. J.
1980-01-01
A theoretical study of the influence of lubricant starvation on film thickness and pressure in hard and soft elliptical elastohydrodynamic contacts is presented. From the results for both hard and soft EHL contacts a simple and important dimensionless inlet boundary distance is specified. This inlet boundary defines whether a fully flooded or a starved condition exists in the contact. Furthermore it is found that the film thickness for a starved condition could be written in dimensionless terms as a function of the inlet distance parameter and the film thickness for a fully flooded condition. Contour plots of pressure and film thickness in and around the contact are shown for fully flooded and starved conditions. The theoretical findings are compared directly with results obtained experimentally.
Bernety, Hossein M; Yakovlev, Alexander B
2015-05-13
In this paper, we present a novel analytical approach for cloaking of dielectric and metallic elliptical cylinders with a graphene monolayer and a nanostructured graphene metasurface at low-terahertz frequencies. The analytical approach is based on the solution of the electromagnetic scattering problem in terms of elliptical waves represented by the radial and angular even and odd Mathieu functions, with the use of sheet impedance boundary conditions at the metasurface. It is shown that scattering cancellation occurs for all incident and observation angles. A special case concerns cloaking of a 2D metallic strip represented by a degenerated ellipse, wherein the focal points of the cloak metasurface correspond to the edges of the strip. The analytical approach has been extended in order to cloak a cluster of elliptical objects for different cases of closely spaced, merging, and overlapping configurations. The results obtained by our analytical approach are validated with full-wave numerical simulations. PMID:25894518
NASA Astrophysics Data System (ADS)
Bernety, Hossein M.; Yakovlev, Alexander B.
2015-05-01
In this paper, we present a novel analytical approach for cloaking of dielectric and metallic elliptical cylinders with a graphene monolayer and a nanostructured graphene metasurface at low-terahertz frequencies. The analytical approach is based on the solution of the electromagnetic scattering problem in terms of elliptical waves represented by the radial and angular even and odd Mathieu functions, with the use of sheet impedance boundary conditions at the metasurface. It is shown that scattering cancellation occurs for all incident and observation angles. A special case concerns cloaking of a 2D metallic strip represented by a degenerated ellipse, wherein the focal points of the cloak metasurface correspond to the edges of the strip. The analytical approach has been extended in order to cloak a cluster of elliptical objects for different cases of closely spaced, merging, and overlapping configurations. The results obtained by our analytical approach are validated with full-wave numerical simulations.
Investigation on computation of elliptical microwave plasma cavity
NASA Astrophysics Data System (ADS)
Liao, Xiaoli; Liu, Hua; Zhang, Kai
2008-12-01
In recent years, the advance of the elliptical resonant cavity and focus cavity is known by many people. There are homogeneous and multipatternal virtues in the focus dimensional microwave field of the elliptical resonant cavity. It is very suitable for applying the low power microwave biological effect equipment. However, when designing the elliptical resonant cavity may meet the problems of complex and huge computation need to be solved. This paper proposed the simple way of approximate processing the Mathieu function. It can greatly simplify the difficulty and decrease the scale of computation. This method can satisfy the requirements of research and development within project permitted precision.
Blue ellipticals in compact groups
NASA Technical Reports Server (NTRS)
Zepf, Stephen E.; Whitmore, Bradley C.
1990-01-01
By studying galaxies in compact groups, the authors examine the hypothesis that mergers of spiral galaxies make elliptical galaxies. The authors combine dynamical models of the merger-rich compact group environment with stellar evolution models and predict that roughly 15 percent of compact group ellipticals should be 0.15 mag bluer in B - R color than normal ellipticals. The published colors of these galaxies suggest the existence of this predicted blue population, but a normal distribution with large random errors can not be ruled out based on these data alone. However, the authors have new ultraviolet blue visual data which confirm the blue color of the two ellipticals with blue B - R colors for which they have their own colors. This confirmation of a population of blue ellipticals indicates that interactions are occurring in compact groups, but a blue color in one index alone does not require that these ellipticals are recent products of the merger of two spirals. The authors demonstrate how optical spectroscopy in the blue may distinguish between a true spiral + spiral merger and the swallowing of a gas-rich system by an already formed elliptical. The authors also show that the sum of the luminosity of the galaxies in each group is consistent with the hypothesis that the final stage in the evolution of compact group is an elliptical galaxy.
Enhanced Elliptic Grid Generation
NASA Technical Reports Server (NTRS)
Kaul, Upender K.
2007-01-01
An enhanced method of elliptic grid generation has been invented. Whereas prior methods require user input of certain grid parameters, this method provides for these parameters to be determined automatically. "Elliptic grid generation" signifies generation of generalized curvilinear coordinate grids through solution of elliptic partial differential equations (PDEs). Usually, such grids are fitted to bounding bodies and used in numerical solution of other PDEs like those of fluid flow, heat flow, and electromagnetics. Such a grid is smooth and has continuous first and second derivatives (and possibly also continuous higher-order derivatives), grid lines are appropriately stretched or clustered, and grid lines are orthogonal or nearly so over most of the grid domain. The source terms in the grid-generating PDEs (hereafter called "defining" PDEs) make it possible for the grid to satisfy requirements for clustering and orthogonality properties in the vicinity of specific surfaces in three dimensions or in the vicinity of specific lines in two dimensions. The grid parameters in question are decay parameters that appear in the source terms of the inhomogeneous defining PDEs. The decay parameters are characteristic lengths in exponential- decay factors that express how the influences of the boundaries decrease with distance from the boundaries. These terms govern the rates at which distance between adjacent grid lines change with distance from nearby boundaries. Heretofore, users have arbitrarily specified decay parameters. However, the characteristic lengths are coupled with the strengths of the source terms, such that arbitrary specification could lead to conflicts among parameter values. Moreover, the manual insertion of decay parameters is cumbersome for static grids and infeasible for dynamically changing grids. In the present method, manual insertion and user specification of decay parameters are neither required nor allowed. Instead, the decay parameters are
NASA Astrophysics Data System (ADS)
Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil
2016-08-01
We develop a new approach for solving the nonlinear Richards' equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioning strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. We also show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.
Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil
2016-04-29
We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioningmore » strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.« less
NASA Technical Reports Server (NTRS)
Abou-Khousa, M. A.
2009-01-01
A novel modulated slot design has been proposed and tested. The proposed slot is aimed to replace the inefficient small dipoles used in conventional MST-based imaging systems. The developed slot is very attractive as MST array element due to its small size and high efficiency/modulation depth. In fact, the developed slot has been successfully used to implement the first prototype of a microwave camera operating at 24 GHZ. It is also being used in the design of the second generation of the camera. Finally, the designed elliptical slot can be used as an electronically controlled waveguide iris for many other purposes (for instance in constructing waveguide reflective phase shifters and multiplexers/switches).
Knupp, P.M.
1999-03-26
Three-dimensional unstructured tetrahedral and hexahedral finite element mesh optimization is studied from a theoretical perspective and by computer experiments to determine what objective functions are most effective in attaining valid, high quality meshes. The approach uses matrices and matrix norms to extend the work in Part I to build suitable 3D objective functions. Because certain matrix norm identities which hold for 2 x 2 matrices do not hold for 3 x 3 matrices. significant differences arise between surface and volume mesh optimization objective functions. It is shown, for example, that the equivalence in two-dimensions of the Smoothness and Condition Number of the Jacobian matrix objective functions does not extend to three dimensions and further. that the equivalence of the Oddy and Condition Number of the Metric Tensor objective functions in two-dimensions also fails to extend to three-dimensions. Matrix norm identities are used to systematically construct dimensionally homogeneous groups of objective functions. The concept of an ideal minimizing matrix is introduced for both hexahedral and tetrahedral elements. Non-dimensional objective functions having barriers are emphasized as the most logical choice for mesh optimization. The performance of a number of objective functions in improving mesh quality was assessed on a suite of realistic test problems, focusing particularly on all-hexahedral ''whisker-weaved'' meshes. Performance is investigated on both structured and unstructured meshes and on both hexahedral and tetrahedral meshes. Although several objective functions are competitive, the condition number objective function is particularly attractive. The objective functions are closely related to mesh quality measures. To illustrate, it is shown that the condition number metric can be viewed as a new tetrahedral element quality measure.
Generalized Harnack Inequality for Nonhomogeneous Elliptic Equations
NASA Astrophysics Data System (ADS)
Julin, Vesa
2015-05-01
This paper is concerned with nonlinear elliptic equations in nondivergence form where F has a drift term which is not Lipschitz continuous. Under this condition the equations are nonhomogeneous and nonnegative solutions do not satisfy the classical Harnack inequality. This paper presents a new generalization of the Harnack inequality for such equations. As a corollary we obtain the optimal Harnack type of inequality for p( x)-harmonic functions which quantifies the strong minimum principle.
MIB Galerkin method for elliptic interface problems.
Xia, Kelin; Zhan, Meng; Wei, Guo-Wei
2014-12-15
Material interfaces are omnipresent in the real-world structures and devices. Mathematical modeling of material interfaces often leads to elliptic partial differential equations (PDEs) with discontinuous coefficients and singular sources, which are commonly called elliptic interface problems. The development of high-order numerical schemes for elliptic interface problems has become a well defined field in applied and computational mathematics and attracted much attention in the past decades. Despite of significant advances, challenges remain in the construction of high-order schemes for nonsmooth interfaces, i.e., interfaces with geometric singularities, such as tips, cusps and sharp edges. The challenge of geometric singularities is amplified when they are associated with low solution regularities, e.g., tip-geometry effects in many fields. The present work introduces a matched interface and boundary (MIB) Galerkin method for solving two-dimensional (2D) elliptic PDEs with complex interfaces, geometric singularities and low solution regularities. The Cartesian grid based triangular elements are employed to avoid the time consuming mesh generation procedure. Consequently, the interface cuts through elements. To ensure the continuity of classic basis functions across the interface, two sets of overlapping elements, called MIB elements, are defined near the interface. As a result, differentiation can be computed near the interface as if there is no interface. Interpolation functions are constructed on MIB element spaces to smoothly extend function values across the interface. A set of lowest order interface jump conditions is enforced on the interface, which in turn, determines the interpolation functions. The performance of the proposed MIB Galerkin finite element method is validated by numerical experiments with a wide range of interface geometries, geometric singularities, low regularity solutions and grid resolutions. Extensive numerical studies confirm the
MIB Galerkin method for elliptic interface problems
Xia, Kelin; Zhan, Meng; Wei, Guo-Wei
2014-01-01
Summary Material interfaces are omnipresent in the real-world structures and devices. Mathematical modeling of material interfaces often leads to elliptic partial differential equations (PDEs) with discontinuous coefficients and singular sources, which are commonly called elliptic interface problems. The development of high-order numerical schemes for elliptic interface problems has become a well defined field in applied and computational mathematics and attracted much attention in the past decades. Despite of significant advances, challenges remain in the construction of high-order schemes for nonsmooth interfaces, i.e., interfaces with geometric singularities, such as tips, cusps and sharp edges. The challenge of geometric singularities is amplified when they are associated with low solution regularities, e.g., tip-geometry effects in many fields. The present work introduces a matched interface and boundary (MIB) Galerkin method for solving two-dimensional (2D) elliptic PDEs with complex interfaces, geometric singularities and low solution regularities. The Cartesian grid based triangular elements are employed to avoid the time consuming mesh generation procedure. Consequently, the interface cuts through elements. To ensure the continuity of classic basis functions across the interface, two sets of overlapping elements, called MIB elements, are defined near the interface. As a result, differentiation can be computed near the interface as if there is no interface. Interpolation functions are constructed on MIB element spaces to smoothly extend function values across the interface. A set of lowest order interface jump conditions is enforced on the interface, which in turn, determines the interpolation functions. The performance of the proposed MIB Galerkin finite element method is validated by numerical experiments with a wide range of interface geometries, geometric singularities, low regularity solutions and grid resolutions. Extensive numerical studies confirm
Analysis of elliptical and circular microstrip antennas using moment method
NASA Technical Reports Server (NTRS)
Bailey, M. C.; Deshpande, M. D.
1985-01-01
A method of calculating the input impedance of either a circular or a slightly elliptical microstrip antenna excited by a coaxial probe is presented. Using the reaction integral equation and the exact dyadic Green's function, the finite substrate thickness is taken into account in the formulation. Good agreement with experimental results for an elliptical patch is obtained and a design procedure for a circularly polarized antenna is presented.
NASA Astrophysics Data System (ADS)
Kaus, B.; Popov, A.
2015-12-01
The analytical expression for the Jacobian is a key component to achieve fast and robust convergence of the nonlinear Newton-Raphson iterative solver. Accomplishing this task in practice often requires a significant algebraic effort. Therefore it is quite common to use a cheap alternative instead, for example by approximating the Jacobian with a finite difference estimation. Despite its simplicity it is a relatively fragile and unreliable technique that is sensitive to the scaling of the residual and unknowns, as well as to the perturbation parameter selection. Unfortunately no universal rule can be applied to provide both a robust scaling and a perturbation. The approach we use here is to derive the analytical Jacobian for the coupled set of momentum, mass, and energy conservation equations together with the elasto-visco-plastic rheology and a marker in cell/staggered finite difference method. The software project LaMEM (Lithosphere and Mantle Evolution Model) is primarily developed for the thermo-mechanically coupled modeling of the 3D lithospheric deformation. The code is based on a staggered grid finite difference discretization in space, and uses customized scalable solvers form PETSc library to efficiently run on the massively parallel machines (such as IBM Blue Gene/Q). Currently LaMEM relies on the Jacobian-Free Newton-Krylov (JFNK) nonlinear solver, which approximates the Jacobian-vector product using a simple finite difference formula. This approach never requires an assembled Jacobian matrix and uses only the residual computation routine. We use an approximate Jacobian (Picard) matrix to precondition the Krylov solver with the Galerkin geometric multigrid. Because of the inherent problems of the finite difference Jacobian estimation, this approach doesn't always result in stable convergence. In this work we present and discuss a matrix-free technique in which the Jacobian-vector product is replaced by analytically-derived expressions and compare results
Model dependence of elliptic flow differences
NASA Astrophysics Data System (ADS)
Cozma, M. D.
2013-02-01
An isospin dependent version of the QMD transport model is used to study the influence of the isovector part of the equation of state of nuclear matter on observables that can be measured in heavy-ion collisions at intermediate energy. The model dependence of neutron-proton elliptic flow difference is studied for AuAu collisions at an incident energy of 400 MeV per nucleon. It is found that the sensitivity to microscopical nucleon-nucleon cross-sections, momentum dependence of the optical potential, compressibility modulus of nuclear matter and width of nucleon wave function are moderate compared to the dependence on the stiffness of the isospin asymmetric part of the equation of state. It is concluded that neutron-proton elliptic flow difference is a suitable observable for setting constraints on the supra-saturation density dependence of symmetry energy.
Modelling elliptically polarised free electron lasers
NASA Astrophysics Data System (ADS)
Henderson, J. R.; Campbell, L. T.; Freund, H. P.; McNeil, B. W. J.
2016-06-01
A model of a free electron laser (FEL) operating with an elliptically polarised undulator is presented. The equations describing the FEL interaction, including resonant harmonic radiation fields, are averaged over an undulator period and generate a generalised Bessel function scaling factor, similar to that of planar undulator FEL theory. Comparison between simulations of the averaged model with those of an unaveraged model show very good agreement in the linear regime. Two unexpected results were found. Firstly, an increased coupling to harmonics for elliptical rather than planar polarisarised undulators. Secondly, and thought to be unrelated to the undulator polarisation, a significantly different evolution between the averaged and unaveraged simulations of the harmonic radiation evolution approaching FEL saturation.
Bounding the elliptic Mahler measure
NASA Astrophysics Data System (ADS)
Pinner, Christopher
1998-11-01
We give a simple inequality relating the elliptic Mahler measure of a polynomial to the traditional Mahler measure (via the length of the polynomial). These bounds are essentially sharp. We also give the corresponding result for polynomials in several variables.
Degenerating the elliptic Schlesinger system
NASA Astrophysics Data System (ADS)
Aminov, G. A.; Artamonov, S. B.
2013-01-01
We study various ways of degenerating the Schlesinger system on the elliptic curve with R marked points. We construct a limit procedure based on an infinite shift of the elliptic curve parameter and on shifts of the marked points. We show that using this procedure allows obtaining a nonautonomous Hamiltonian system describing the Toda chain with additional spin sl(N, ℂ) degrees of freedom.
Extremely Isolated Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Fuse, Christopher R.; Marcum, P.; Fanelli, M.; Aars, C.
2006-06-01
Isolated galaxies provide a means of assessing the evolution of galactic systems. Extremely isolated galaxies define a zero-interaction baseline for comparative studies of galaxy evolution. We present results of a search for isolated elliptical galaxies (IEGs). We utilize the optical imaging data produced by the Sloan Digital Sky Survey (SDSS) to identify candidate galaxies from Release 1-4 of the SDSS. Candidate IEGs meet strict isolation criteria: Any IEG must be separated by at least 2.5 Mpc from any neighboring non-dwarf galaxy having a MV fainter than -16.5 mag. The candidate isolated systems have no non-dwarf neighbors within a distance such that we can insure that the IEGs have never interacted with another existing galaxy since formation.In order to increase the signal-to-noise ratio, we have used the SDSS images in the u,g,r filters to create combined sets of images for each IEG. The stacked images permit a more robust determination of the morphology of the candidate galaxies. Verification that these are spheroidal systems is achieved through a bulge/disk decomposition technique using standard surface photometry. Our preliminary sample of 51 isolated systems defines a complete volume-limited population of extremely isolated early-type galaxies within a distance of 72Mpc
Exact Jacobians in an implicit Newton method for two-phase flow in porous media
NASA Astrophysics Data System (ADS)
Büsing, H.; Clauser, C.
2012-04-01
Geological storage of CO2 is one option for mitigating the effects of CO2 emissions on global warming. Since extensive on-site monitoring of the CO2 plume propagation is expensive, numerical simulations are an attractive alternative for gaining deeper insight in the dynamics of this system. We consider a model for two-phase flow in porous media for representing the injection stage of a CO2 sequestration scenario, when the plume propagation is dominated by advection. The porous medium filled by the two phases CO2 and brine is modelled as an initial-boundary-value problem consisting of two nonlinear, coupled partial differential equations, which are complemented by appropriate boundary and initial conditions. We present a new numerical approach to solve this fully coupled system using exact Jacobians. The method is based on the finite element, finite volume, box method [Huber & Helmig(2000)] for the space discretization and, since stability of the method is one of the main concerns, the fully implicit Euler method for the time discretization. A simple first order upwind method takes into account advective contributions. The resulting system of nonlinear algebraic equations is linearized by Newton's method. The required Jacobians can be obtained elegantly by automatic differentiation (AD) [Griewank & Walther(2008), Rall(1981)], a source code transformation giving exact derivatives of the discretized equations with respect to primary variables. The resulting system of linear equations is then solved by an iterative method (BiCGStab) with ILU0 preconditioning in every Newton step. We compare the forward AD differentiation mode to the standard finite difference method in terms of precision and performance. It turns out that AD performs favourable in both aspects. We also illustrate the advantages of exact Jacobians for two-phase flow in a sequestration scenario investigating the evolution of pressure and saturation.
Unseren, M.A.; Reister, D.B.
1995-07-01
A method for kinematically modeling a constrained rigid body mechanical system and a method for controlling such a system termed input relegation control (IRC) were applied to resolve the kinematic redundancy of a serial link manipulator moving in an open chain configuration in. A set of equations was introduced to define a new vector variable parameterizing the redundant degrees of freedom (DOF) as a linear function of the joint velocities. The new set was combined with the classical kinematic velocity model of manipulator and solved to yield a well specified solution for the joint velocities as a function of the Cartesian velocities of the end effector and of the redundant DOF variable. In the previous work a technique was proposed for selecting the matrix relating the redundant DOF variable to the joint velocities which resulted in it rows being orthogonal to the rows of the Jacobian matrix. The implications for such a selection were not discussed in. In Part 1 of this report a basis for the joint space is suggested which provides considerable insight into why picking the aforementioned matrix to be orthogonal to the Jacobian is advantageous. A second objective of Part 1 is to compare the IRC method to the Extended Jacobian method of Baillieul and Martin and other related methods.
Acceleration of k-Eigenvalue / Criticality Calculations using the Jacobian-Free Newton-Krylov Method
Dana Knoll; HyeongKae Park; Chris Newman
2011-02-01
We present a new approach for the $k$--eigenvalue problem using a combination of classical power iteration and the Jacobian--free Newton--Krylov method (JFNK). The method poses the $k$--eigenvalue problem as a fully coupled nonlinear system, which is solved by JFNK with an effective block preconditioning consisting of the power iteration and algebraic multigrid. We demonstrate effectiveness and algorithmic scalability of the method on a 1-D, one group problem and two 2-D two group problems and provide comparison to other efforts using silmilar algorithmic approaches.
NASA Technical Reports Server (NTRS)
Chen, Yu-Che; Walker, Ian D.; Cheatham, John B., Jr.
1992-01-01
We present a unified formulation for the inverse kinematics of redundant arms, based on a special formulation of the null space of the Jacobian. By extending (appropriately re-scaling) previously used null space parameterizations, we obtain, in a unified fashion, the manipulability measure, the null space projector, and particular solutions for the joint velocities. We obtain the minimum norm pseudo-inverse solution as a projection from any particular solution, and the method provides an intuitive visualization of the self-motion. The result is a computationally efficient, consistent approach to computing redundant robot inverse kinematics.
Assessing the quality of curvilinear coordinate meshes by decomposing the Jacobian matrix
NASA Technical Reports Server (NTRS)
Kerlick, G. D.; Klopfer, G. H.
1982-01-01
An algebraic decomposition of the Jacobian matrix which relates physical and computational variables is presented. This invertible decomposition parameterizes the mesh by the physically intuitive qualities of cell orientation, cell orthogonality, cell volume, and cell aspect ratio. The decomposition can be used to analyze numerically generated curvilinear coordinate meshes and to assess the contribution of the mesh to the truncation error for any specific differential operator and algorithm. This is worked out in detail for Laplace's equation in nonconservative and conservative forms. The analysis is applied to the solution of the full potential code TAIR, showing grid plots, carpet plots, and truncation error for a NACA 0012 airfoil.
ELLIPT2D: A Flexible Finite Element Code Written Python
Pletzer, A.; Mollis, J.C.
2001-03-22
The use of the Python scripting language for scientific applications and in particular to solve partial differential equations is explored. It is shown that Python's rich data structure and object-oriented features can be exploited to write programs that are not only significantly more concise than their counter parts written in Fortran, C or C++, but are also numerically efficient. To illustrate this, a two-dimensional finite element code (ELLIPT2D) has been written. ELLIPT2D provides a flexible and easy-to-use framework for solving a large class of second-order elliptic problems. The program allows for structured or unstructured meshes. All functions defining the elliptic operator are user supplied and so are the boundary conditions, which can be of Dirichlet, Neumann or Robbins type. ELLIPT2D makes extensive use of dictionaries (hash tables) as a way to represent sparse matrices.Other key features of the Python language that have been widely used include: operator over loading, error handling, array slicing, and the Tkinter module for building graphical use interfaces. As an example of the utility of ELLIPT2D, a nonlinear solution of the Grad-Shafranov equation is computed using a Newton iterative scheme. A second application focuses on a solution of the toroidal Laplace equation coupled to a magnetohydrodynamic stability code, a problem arising in the context of magnetic fusion research.
STRUCTURE AND FORMATION OF ELLIPTICAL AND SPHEROIDAL GALAXIES
Kormendy, John; Fisher, David B.; Cornell, Mark E.; Bender, Ralf E-mail: dbfisher@astro.as.utexas.edu E-mail: bender@usm.uni-muenchen.de
2009-05-15
New surface photometry of all known elliptical galaxies in the Virgo cluster is combined with published data to derive composite profiles of brightness, ellipticity, position angle, isophote shape, and color over large radius ranges. These provide enough leverage to show that Sersic log I {proportional_to} r {sup 1/n} functions fit the brightness profiles I(r) of nearly all ellipticals remarkably well over large dynamic ranges. Therefore, we can confidently identify departures from these profiles that are diagnostic of galaxy formation. Two kinds of departures are seen at small radii. All 10 of our ellipticals with total absolute magnitudes M{sub VT} {<=} -21.66 have cuspy cores-'missing light'-at small radii. Cores are well known and naturally scoured by binary black holes (BHs) formed in dissipationless ('dry') mergers. All 17 ellipticals with -21.54 {<=} M{sub VT} {<=} -15.53 do not have cores. We find a new distinct component in these galaxies: all coreless ellipticals in our sample have extra light at the center above the inward extrapolation of the outer Sersic profile. In large ellipticals, the excess light is spatially resolved and resembles the central components predicted in numerical simulations of mergers of galaxies that contain gas. In the simulations, the gas dissipates, falls toward the center, undergoes a starburst, and builds a compact stellar component that, as in our observations, is distinct from the Sersic-function main body of the elliptical. But ellipticals with extra light also contain supermassive BHs. We suggest that the starburst has swamped core scouring by binary BHs. That is, we interpret extra light components as a signature of formation in dissipative ('wet') mergers. Besides extra light, we find three new aspects to the ('E-E') dichotomy into two types of elliptical galaxies. Core galaxies are known to be slowly rotating, to have relatively anisotropic velocity distributions, and to have boxy isophotes. We show that they have
Joseph, Ilon
2014-05-27
Jacobian-free Newton-Krylov (JFNK) algorithms are a potentially powerful class of methods for solving the problem of coupling codes that address dfferent physics models. As communication capability between individual submodules varies, different choices of coupling algorithms are required. The more communication that is available, the more possible it becomes to exploit the simple sparsity pattern of the Jacobian, albeit of a large system. The less communication that is available, the more dense the Jacobian matrices become and new types of preconditioners must be sought to efficiently take large time steps. In general, methods that use constrained or reduced subsystems can offer a compromise in complexity. The specific problem of coupling a fluid plasma code to a kinetic neutrals code is discussed as an example.
An improved nearly-orthogonal structured mesh generation system with smoothness control functions
Technology Transfer Automated Retrieval System (TEKTRAN)
This paper presents an improved nearly-orthogonal structured mesh generation system with a set of smoothness control functions, which were derived based on the ratio between the Jacobian of the transformation matrix and the Jacobian of the metric tensor. The proposed smoothness control functions are...
Energy and the Elliptical Orbit
NASA Astrophysics Data System (ADS)
Nettles, Bill
2009-03-01
In the January 2007 issue of The Physics Teacher, Prentis, Fulton, Hesse, and Mazzino describe a laboratory exercise in which students use a geometrical analysis inspired by Newton to show that an elliptical orbit and an inverse-square law force go hand in hand. The historical, geometrical, and teamwork aspects of the exercise are useful and important. This paper presents an exercise which uses an energy/angular momentum conservation model for elliptical orbits. This exercise can be done easily by an individual student and on regular notebook-sized paper.
Vibration and buckling of super elliptical plates
NASA Astrophysics Data System (ADS)
Wang, C. M.; Wang, L.; Liew, K. M.
1994-03-01
This paper is concerned with the vibration and buckling of a new class of plates, the periphery shape of which is defined by a super elliptical function. Such a plate shape has practical applications, as the advantageous curved corners help to diffuse stress concentrations. The loading considered for the buckling problem is that of in-plane uniform pressure along the periphery. Accurate frequency and buckling factors are tabulated for such plates with either simply supported or clamped edges. The solutions are obtained using the pb - 2 Rayleigh-Ritz method.
Liouville field, modular forms and elliptic genera
NASA Astrophysics Data System (ADS)
Eguchi, Tohru; Sugawara, Yuji; Taormina, Anne
2007-03-01
When we describe non-compact or singular Calabi-Yau manifolds by CFT, continuous as well as discrete representations appear in the theory. These representations mix in an intricate way under the modular transformations. In this article, we propose a method of combining discrete and continuous representations so that the resulting combinations have a simpler modular behavior and can be used as conformal blocks of the theory. We compute elliptic genera of ALE spaces and obtain results which agree with those suggested from the decompactification of K3 surface. Consistency of our approach is assured by some remarkable identity of theta functions whose proof, by D. Zagier, is included in an appendix.
Formation, evolution and properties of isolated field elliptical galaxies
NASA Astrophysics Data System (ADS)
Niemi, Sami-Matias; Heinämäki, Pekka; Nurmi, Pasi; Saar, Enn
2010-06-01
We study the properties, evolution and formation mechanisms of isolated field elliptical (IfE) galaxies. We create a `mock' catalogue of IfE galaxies from the Millennium Simulation Galaxy Catalogue, and trace their merging histories. The formation, identity and assembly redshifts of simulated isolated and non-isolated elliptical galaxies are studied and compared. Observational and numerical data are used to compare age, mass and the colour-magnitude relation. Our results, based on simulation data, show that almost 7 per cent of all elliptical galaxies brighter than -19mag in B band can be classified as IfE galaxies. Results also show that isolated elliptical galaxies have a rather flat luminosity function; a number density of ~3 × 10-6h3Mpc-3mag-1, throughout their B-band magnitudes. IfE galaxies show bluer colours than non-isolated elliptical galaxies and they appear younger, in a statistical sense, according to their mass-weighted age. IfE galaxies also form and assemble at lower redshifts compared to non-isolated elliptical galaxies. About 46 per cent of IfE galaxies have undergone at least one major merging event in their formation history, while the same fraction is only ~33 per cent for non-isolated ellipticals. Almost all (~98 per cent) isolated elliptical galaxies show merging activity during their evolution, pointing towards the importance of mergers in the formation of IfE galaxies. The mean time of the last major merging is at z ~ 0.6 or 6Gyr ago for isolated ellipticals, while non-isolated ellipticals experience their last major merging significantly earlier at z ~ 1.1 or 8Gyr ago. After inspecting merger trees of simulated IfE galaxies, we conclude that three different, yet typical, formation mechanisms can be identified: solitude, coupling and cannibalism. Our results also predict a previously unobserved population of blue, dim and light galaxies that fulfil observational criteria to be classified as IfE galaxies. This separate population comprises
Acoustic scattering by multiple elliptical cylinders using collocation multipole method
NASA Astrophysics Data System (ADS)
Lee, Wei-Ming
2012-05-01
This paper presents the collocation multipole method for the acoustic scattering induced by multiple elliptical cylinders subjected to an incident plane sound wave. To satisfy the Helmholtz equation in the elliptical coordinate system, the scattered acoustic field is formulated in terms of angular and radial Mathieu functions which also satisfy the radiation condition at infinity. The sound-soft or sound-hard boundary condition is satisfied by uniformly collocating points on the boundaries. For the sound-hard or Neumann conditions, the normal derivative of the acoustic pressure is determined by using the appropriate directional derivative without requiring the addition theorem of Mathieu functions. By truncating the multipole expansion, a finite linear algebraic system is derived and the scattered field can then be determined according to the given incident acoustic wave. Once the total field is calculated as the sum of the incident field and the scattered field, the near field acoustic pressure along the scatterers and the far field scattering pattern can be determined. For the acoustic scattering of one elliptical cylinder, the proposed results match well with the analytical solutions. The proposed scattered fields induced by two and three elliptical-cylindrical scatterers are critically compared with those provided by the boundary element method to validate the present method. Finally, the effects of the convexity of an elliptical scatterer, the separation between scatterers and the incident wave number and angle on the acoustic scattering are investigated.
Energy and the Elliptical Orbit
ERIC Educational Resources Information Center
Nettles, Bill
2009-01-01
In the January 2007 issue of "The Physics Teacher," Prentis, Fulton, Hesse, and Mazzino describe a laboratory exercise in which students use a geometrical analysis inspired by Newton to show that an elliptical orbit and an inverse-square law force go hand in hand. The historical, geometrical, and teamwork aspects of the exercise are useful and…
The ESS elliptical cavity cryomodules
Darve, Christine; Bosland, Pierre; Devanz, Guillaume; Renard, Bertrand; Olivier, Gilles; Thermeau, Jean-Pierre
2014-01-29
The European Spallation Source (ESS) is a multi-disciplinary research centre under design and construction in Lund, Sweden. This new facility is funded by a collaboration of 17 European countries and is expected to be up to 30 times brighter than today’s leading facilities and neutron sources. The ESS will enable new opportunities for researchers in the fields of life sciences, energy, environmental technology, cultural heritage and fundamental physics. A 5 MW long pulse proton accelerator is used to reach this goal. The pulsed length is 2.86 ms, the repetition frequency is 14 Hz (4 % duty cycle), and the beam current is 62.5 mA. The superconducting section of the Linac accelerates the beam from 80 MeV to 2.0 GeV. It is composed of one string of spoke cavity cryomodule and two strings of elliptical cavity cryomodules. These cryomodules contain four elliptical Niobium cavities operating at 2 K and at a frequency of 704.42 MHz. This paper introduces the thermo-mechanical design, the prototyping and the expected operation of the ESS elliptical cavity cryomodules. An Elliptical Cavity Cryomodule Technology Demonstrator (ECCTD) will be built and tested in order to validate the ESS series production.
Elliptic curves and primality proving
NASA Astrophysics Data System (ADS)
Atkin, A. O. L.; Morain, F.
1993-07-01
The aim of this paper is to describe the theory and implementation of the Elliptic Curve Primality Proving algorithm. Problema, numeros primos a compositis dignoscendi, hosque in factores suos primos resolvendi, ad gravissima ac utilissima totius arithmeticae pertinere, et geometrarum tum veterum tum recentiorum industriam ac sagacitatem occupavisse, tam notum est, ut de hac re copiose loqui superfluum foret.
The Cores of Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Zeilinger, W. W.
High spatial resolution observations impose stricter constraints on theories on the presence of dark objects in galactic nuclei. Observational evidence suggests that central massive black holes are a common phenomenon in dynamically hot stellar systems such as ellipticals and bulges of spirals.
Wavelength meter having elliptical wedge
Hackel, R.P.; Feldman, M.
1992-12-01
A wavelength meter is disclosed which can determine the wavelength of a laser beam from a laser source within an accuracy range of two parts in 10[sup 8]. The wavelength meter has wedge having an elliptically shaped face to the optical path of the laser source and includes interferometer plates which form a vacuum housing. 7 figs.
Wavelength meter having elliptical wedge
Hackel, Richard P.; Feldman, Mark
1992-01-01
A wavelength meter is disclosed which can determine the wavelength of a laser beam from a laser source within an accuracy range of two parts in 10.sup.8. The wavelength meter has wedge having an elliptically shaped face to the optical path of the laser source and includes interferometer plates which form a vacuum housing.
Jacobian and stiffness analysis of a novel class of six-DOF parallel minimanipulators
Tashmasebi, F.; Tsai, Lung-Wen
1992-08-01
The Jacobian and stiffness matrices of two types of novel, six-DOF parallel minimanipulators are derived. A minimanipulator consists of three inextensible limbs, each of which is driven by a two-DOF driver. Bilinear stepper motors are used as drivers in the first type minimanipulator, whereas five-bar linkages are used as drivers in the second type minimanipulator. All of the minimanipulator actuators are base-mounted. Inextensible limbs (and five-bar linkage drivers in the second type minimanipulator) improve positional resolution and stiffness of the minimanipulators in certain directions. It is shown that, at the central configuration, the stiffness matrix of the first type minimanipulator can be diagonalized (decoupled). It is also shown that the first type minimanipulator can be designed to possess direct or torsional isotropic stiffness properties. Moreover, guidelines for designing the drivers of the second type minimanipulator are established. 20 refs.
Jacobian and stiffness analysis of a novel class of six-DOF parallel minimanipulators
Tashmasebi, F. . Goddard Space Flight Center); Tsai, Lung-Wen . Dept. of Mechanical Engineering)
1992-01-01
The Jacobian and stiffness matrices of two types of novel, six-DOF parallel minimanipulators are derived. A minimanipulator consists of three inextensible limbs, each of which is driven by a two-DOF driver. Bilinear stepper motors are used as drivers in the first type minimanipulator, whereas five-bar linkages are used as drivers in the second type minimanipulator. All of the minimanipulator actuators are base-mounted. Inextensible limbs (and five-bar linkage drivers in the second type minimanipulator) improve positional resolution and stiffness of the minimanipulators in certain directions. It is shown that, at the central configuration, the stiffness matrix of the first type minimanipulator can be diagonalized (decoupled). It is also shown that the first type minimanipulator can be designed to possess direct or torsional isotropic stiffness properties. Moreover, guidelines for designing the drivers of the second type minimanipulator are established. 20 refs.
Radiance and Jacobian Intercomparison of Radiative Transfer Models Applied to HIRS and AMSU Channels
NASA Technical Reports Server (NTRS)
Garand, L.; Turner, D. S.; Larocque, M.; Bates, J.; Boukabara, S.; Brunel, P.; Chevallier, F.; Deblonde, G.; Engelen, R.; Atlas, Robert (Technical Monitor)
2000-01-01
The goals of this study are the evaluation of current fast radiative transfer models (RTMs) and line-by-line (LBL) models. The intercomparison focuses on the modeling of 11 representative sounding channels routinely used at numerical weather prediction centers: seven HIRS (High-resolution Infrared Sounder) and four AMSU (Advanced Microwave Sounding Unit) channels. Interest in this topic was evidenced by the participation of 24 scientists from 16 institutions. An ensemble of 42 diverse atmospheres was used and results compiled for 19 infrared models and 10 microwave models, including several LBL RTMs. For the first time, not only radiances, but also Jacobians (of temperature, water vapor, and ozone) were compared to various LBL models for many channels. In the infrared, LBL models typically agree to within 0.05-0.15 K (standard deviation) in terms of top-of-the-atmosphere brightness temperature (BT). Individual differences up to 0.5 K still exist, systematic in some channels, and linked to the type of atmosphere in others. The best fast models emulate LBL BTs to within 0.25 K, but no model achieves this desirable level of success for all channels. The ozone modeling is particularly challenging. In the microwave, fast models generally do quite well against the LBL model to which they were tuned. However significant differences were noted among LBL models. Extending the intercomparison to the Jacobians proved very useful in detecting subtle and more obvious modeling errors. In addition, total and single gas optical depths were calculated, which provided additional insight on the nature of differences. Recommendations for future intercomparisons are suggested.
Integral formula for elliptic SOS models with domain walls and a reflecting end
NASA Astrophysics Data System (ADS)
Lamers, Jules
2015-12-01
In this paper we extend previous work of Galleas and the author to elliptic SOS models. We demonstrate that the dynamical reflection algebra can be exploited to obtain a functional equation characterizing the partition function of an elliptic SOS model with domain-wall boundaries and one reflecting end. Special attention is paid to the structure of the functional equation. Through this approach we find a novel multiple-integral formula for that partition function.
On the Dirichlet problem for a nonlinear elliptic equation
NASA Astrophysics Data System (ADS)
Egorov, Yu V.
2015-04-01
We prove the existence of an infinite set of solutions to the Dirichlet problem for a nonlinear elliptic equation of the second order. Such a problem for a nonlinear elliptic equation with Laplace operator was studied earlier by Krasnosel'skii, Bahri, Berestycki, Lions, Rabinowitz, Struwe and others. We study the spectrum of this problem and prove the weak convergence to 0 of the sequence of normed eigenfunctions. Moreover, we obtain some estimates for the 'Fourier coefficients' of functions in W^1p,0(Ω). This allows us to improve the preceding results. Bibliography: 8 titles.
Eccentricity and elliptic flow in pp collisions at the LHC
NASA Astrophysics Data System (ADS)
Avsar, E.; Hatta, Y.; Flensburg, C.; Ollitrault, J.-Y.; Ueda, T.
2011-12-01
High-multiplicity proton-proton collisions at the LHC may exhibit collective phenomena such as elliptic flow. We study this issue using DIPSY, a brand-new Monte Carlo event generator which features almost-NLO BFKL dynamics and describes the transverse shape of the proton including all fluctuations. We predict the eccentricity of the collision as a function of the multiplicity and estimate the magnitude of elliptic flow. We suggest that flow can be signaled by a sign change in the four-particle azimuthal correlation.
Calderón's method on an elliptical domain.
Muller, P A; Isaacson, D; Newell, J C; Saulnier, G J
2013-06-01
One possible application for electrical impedance tomography is in medical imaging where lung and heart function may be monitored. One drawback of current algorithms is that they are implemented for use in a circular domain, but a human thorax is more elliptical than circular. In this paper, a reconstruction algorithm based on the work of Calderón (1980 Seminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro) pp 65-75) on the inverse conductivity problem is derived for an elliptical domain. It is explained how this reconstruction algorithm uses a transformed Dirichlet-to-Neumann map. Experimental results from an elliptical tank are given to show how correct domain modelling reduces the artefacts produced by this version of Calderón's reconstruction algorithm.
System Size, Energy, Pseudorapidity, and Centrality Dependence of Elliptic Flow
Alver, B.; Ballintijn, M.; Busza, W.; Decowski, M. P.; Gulbrandsen, K.; Henderson, C.; Kane, J. L.; Kulinich, P.; Li, W.; Loizides, C.; Reed, C.; Roland, C.; Roland, G.; Stephans, G. S. F.; Vale, C.; Nieuwenhuizen, G. J. van; Vaurynovich, S. S.; Verdier, R.; Veres, G. I.; Wenger, E.
2007-06-15
This Letter presents measurements of the elliptic flow of charged particles as a function of pseudorapidity and centrality from Cu-Cu collisions at 62.4 and 200 GeV using the PHOBOS detector at the Relativistic Heavy Ion Collider. The elliptic flow in Cu-Cu collisions is found to be significant even for the most central events. For comparison with the Au-Au results, it is found that the detailed way in which the collision geometry (eccentricity) is estimated is of critical importance when scaling out system-size effects. A new form of eccentricity, called the participant eccentricity, is introduced which yields a scaled elliptic flow in the Cu-Cu system that has the same relative magnitude and qualitative features as that in the Au-Au system.
Free vibration of simply supported and clamped elliptical plates
NASA Astrophysics Data System (ADS)
Prasad, K. L.; Rao, A. V.; Rao, B. N.
1992-10-01
An approximate formulation of a simply supported and clamped elliptical plate is described which is based on the Rayleigh-Ritz technique with a three-term deflection function. A comparison of the fundamental frequency parameters for the case under consideration is presented.
Cold dust in elliptical galaxies.
NASA Astrophysics Data System (ADS)
Wiklind, T.; Henkel, C.
1995-05-01
We have observed the λ1250 µm flux in 8 elliptical galaxies using the MPIfR 7-channel bolometer system attachet to the IRAM 30-m telescope. Five of the galaxies are detected at more than 3σ, two are tentatively detected and for one we obtained an upper limit. For two of the detected galaxies, the CO(2-1) line makes a significant contribution to the measured λ1250 µm flux. A comparison of the λ1250 µm fluxes, corrected for the CO(2-1) line contribution, with IRAS 60 and 100µm data shows that there is a colt dust component (Td~<20K) in two of the ellipticals. The other galaxies have λ1250 µm fluxes consistent with a one-temperature component, with Td typically between 20-30K.
Palczewski, Ari; Ciovati, Gianluigi; Li, Yongming; Geng, Rongli
2013-09-01
Centrifugal barrel polishing (cbp) for SRF application is becoming more wide spread as the technique for cavity surface preparation. CBP is now being used in some form at SRF laboratories around the world including in the US, Europe and Asia. Before the process can become as mature as wet chemistry like eletro-polishing (EP) and buffered chemical polishing (BCP) there are many questions which remain unanswered. One of these topics includes the uniformity of removal as a function of cavity shape and material type. In this presentation we show CBP removal rates for various media types on 1.3 GHz TESLA and 1.5 GHz CEBAF large/fine grain niobium cavities, and 1.3GHz low surface field copper cavity. The data will also include calculated RF frequency shift modeling non-uniform removal as a function of cavity position and comparing them with CBP results.
Do elliptical galaxies have thick disks?
NASA Technical Reports Server (NTRS)
Thomson, R. C.; Wright, A. E.
1990-01-01
The authors discuss new evidence which supports the existence of thick disks in elliptical/SO galaxies. Numerical simulations of weak interactions with thick disk systems produce shell structures very similar in appearance to those observed in many shell galaxies. The authors think this model presents a more plausible explanation for the formation of shell structures in elliptical/SO galaxies than does the merger model and, if correct, supports the existence of thick disks in elliptical/SO galaxies.
NASA Astrophysics Data System (ADS)
Bernardara, M.; Tabuada, G.
2016-06-01
Conjectures of Beilinson-Bloch type predict that the low-degree rational Chow groups of intersections of quadrics are one-dimensional. This conjecture was proved by Otwinowska in [20]. By making use of homological projective duality and the recent theory of (Jacobians of) non-commutative motives, we give an alternative proof of this conjecture in the case of a complete intersection of either two quadrics or three odd-dimensional quadrics. Moreover, we prove that in these cases the unique non-trivial algebraic Jacobian is the middle one. As an application, we make use of Vial's work [26], [27] to describe the rational Chow motives of these complete intersections and show that smooth fibrations into such complete intersections over bases S of small dimension satisfy Murre's conjecture (when \\dim (S)≤ 1), Grothendieck's standard conjecture of Lefschetz type (when \\dim (S)≤ 2), and Hodge's conjecture (when \\dim(S)≤ 3).
A Jacobian-free Newton Krylov method for mortar-discretized thermomechanical contact problems
NASA Astrophysics Data System (ADS)
Hansen, Glen
2011-07-01
Multibody contact problems are common within the field of multiphysics simulation. Applications involving thermomechanical contact scenarios are also quite prevalent. Such problems can be challenging to solve due to the likelihood of thermal expansion affecting contact geometry which, in turn, can change the thermal behavior of the components being analyzed. This paper explores a simple model of a light water reactor nuclear fuel rod, which consists of cylindrical pellets of uranium dioxide (UO 2) fuel sealed within a Zircalloy cladding tube. The tube is initially filled with helium gas, which fills the gap between the pellets and cladding tube. The accurate modeling of heat transfer across the gap between fuel pellets and the protective cladding is essential to understanding fuel performance, including cladding stress and behavior under irradiated conditions, which are factors that affect the lifetime of the fuel. The thermomechanical contact approach developed here is based on the mortar finite element method, where Lagrange multipliers are used to enforce weak continuity constraints at participating interfaces. In this formulation, the heat equation couples to linear mechanics through a thermal expansion term. Lagrange multipliers are used to formulate the continuity constraints for both heat flux and interface traction at contact interfaces. The resulting system of nonlinear algebraic equations are cast in residual form for solution of the transient problem. A Jacobian-free Newton Krylov method is used to provide for fully-coupled solution of the coupled thermal contact and heat equations.
Phenomenological study of irregular cellular automata based on Lyapunov exponents and Jacobians
NASA Astrophysics Data System (ADS)
Baetens, Jan M.; De Baets, Bernard
2010-09-01
Originally, cellular automata (CA) have been defined upon regular tessellations of the n-dimensional Euclidean space, while CA on irregular tessellations have received only little attention from the scientific community, notwithstanding serious shortcomings are associated with the former manner of subdividing Rn. In this paper we present a profound phenomenological study of two-state, two-dimensional irregular CA from a dynamical systems viewpoint. We opted to exploit properly defined quantitative measures instead of resorting to qualitative methods for discriminating between behavioral classes. As such, we employ Lyapunov exponents, measuring the divergence rate of close trajectories in phase space, and Jacobians, formulated using Boolean derivatives and expressing the sensitivity of a cellular automaton to its inputs. Both are stated for two-state CA on irregular tessellations, enabling us to characterize these discrete dynamical systems, and advancing us to propose a classification scheme for this CA family. In addition, a relationship between these quantitative measures is established in extension of the insights already developed for the classical CA paradigm. Finally, we discuss the repercussions on the CA dynamics that arise when the geometric variability of the spatial entities is taken into account during the CA simulation.
Theoretical results for starved elliptical contacts
NASA Technical Reports Server (NTRS)
Hamrock, B. J.; Dowson, D.
1983-01-01
Eighteen cases were used in the theoretical study of the influence of lubricant starvation on film thickness and pressure in elliptical elastohydrodynamic conjunctions. From the results a simple and important critical dimensionless inlet boundary distance at which lubricant starvation becomes significant was specified. This inlet boundary distance defines whether a fully flooded or a starved condition exists in the contact. Furthermore, it was found that the film thickness for a starved condition is written in dimensionless terms as a function of the inlet distance parameter and the film thickness for a fully flooded condition. Contour plots of pressure and film thickness in and around the contact are shown for fully flooded and starved conditions.
Dark matter in elliptical galaxies
NASA Technical Reports Server (NTRS)
Carollo, C. M.; Zeeuw, P. T. DE; Marel, R. P. Van Der; Danziger, I. J.; Qian, E. E.
1995-01-01
We present measurements of the shape of the stellar line-of-sight velocity distribution out to two effective radii along the major axes of the four elliptical galaxies NGC 2434, 2663, 3706, and 5018. The velocity dispersion profiles are flat or decline gently with radius. We compare the data to the predictions of f = f(E, L(sub z)) axisymmetric models with and without dark matter. Strong tangential anisotropy is ruled out at large radii. We conclude from our measurements that massive dark halos must be present in three of the four galaxies, while for the fourth galaxy (NGC 2663) the case is inconclusive.
Ellipticity of Rayleigh waves and crustal structure in northern Italy
NASA Astrophysics Data System (ADS)
Berbellini, Andrea; Morelli, Andrea; Ferreira, Ana M. G.
2016-04-01
Horizontal-to-vertical amplitude ratio of elliptically-polarised ground motion of Rayleigh waves depends on the local crustal structure. Its measurement therefore adds another, seldom used, tool to image shallow earth structure. Frequency-dependent sensitivity kernels are dominated by shear-wave velocity and are rather shallow, so they are a convenient tool to model sedimentary layers that nicely complement surface wave studies. We perform extensive measurements, in the period range between 10 and 110 s, on traces from about 500 globally-distributed earthquakes, occurred in years 2008 ÷ 2014, recorded by 95 stations in northern Italy - - a region including the wide basin of the Po Plain and encircling Alps and northern Apennines. The observations are well correlated with known strucure: high ellipticity correlates well with low seismic velocity (such as in the Po Plain), and low ellipticity corresponds to fast seismic velocity in hard rock environments in correspondence of Alps and Apennines. Comparison between observations and predicted ellipticity from a reference crustal model of the region (Molinari et al., 2015) shows substantial fit. Sensitivity to vS is quite non linear, but inversion is possible and may provide very useful complementary information to, e.g., surface wave phase or group velocity or receiver functions.
Elliptical galaxies kinematics within general relativity with renormalization group effects
Rodrigues, Davi C.
2012-09-01
The renormalization group framework can be applied to Quantum Field Theory on curved space-time, but there is no proof whether the beta-function of the gravitational coupling indeed goes to zero in the far infrared or not. In a recent paper [1] we have shown that the amount of dark matter inside spiral galaxies may be negligible if a small running of the General Relativity coupling G is present (δG/G{sub 0}∼<10{sup −7} across a galaxy). Here we extend the proposed model to elliptical galaxies and present a detailed analysis on the modeling of NGC 4494 (an ordinary elliptical) and NGC 4374 (a giant elliptical). In order to compare our results to a well known alternative model to the standard dark matter picture, we also evaluate NGC 4374 with MOND. In this galaxy MOND leads to a significative discrepancy with the observed velocity dispersion curve and has a significative tendency towards tangential anisotropy. On the other hand, the approach based on the renormalization group and general relativity (RGGR) could be applied with good results to these elliptical galaxies and is compatible with lower mass-to-light ratios (of about the Kroupa IMF type)
Constructing massive blue elliptical galaxies in the local universe
NASA Astrophysics Data System (ADS)
Haines, Tim
Over cosmic time, galaxy mass assembly has transitioned from low-mass, star-forming disk galaxies to massive, quiescent elliptical galaxies. The merger hypothesis for the formation of new elliptical galaxies provides one physical explanation to the observed buildup of this population, a key prediction of which is a brief phase of morphological transformation from highly-disturbed remnant to blue elliptical. We study 12 plausible new ellipticals with varying degrees of morphological peculiarities visually selected from a larger parent sample of nearby (0.01 ≤ z ≤ 0.04), massive (M* ≥ 10 10 M⊙ ), concentrated (Petrosian R90/R50 ≥ 2.6), and optically blue galaxies from the SDSS DR4 catalog. Using integral field spectroscopy, we construct two-dimensional spectra of the stellar populations and azimuthally bin them into concentric annuli to determine the relative ages of the stellar populations as a function of radius. Using this data and conclusions from simulations, we seek to distinguish post-mergers from galaxies undergoing other modes of mass assembly. We find that 1/3 of our sample is consistent with having undergone a recent, gas-rich major merger. Another 1/3 of our sample is consistent with having undergone a 'frosting' of recent star formation. The final 1/3 of our sample is either inconsistent with or inconclusive of having undergone a recent, gas-rich major merger.
Matrix factorizations and elliptic fibrations
NASA Astrophysics Data System (ADS)
Omer, Harun
2016-09-01
I use matrix factorizations to describe branes at simple singularities of elliptic fibrations. Each node of the corresponding Dynkin diagrams of the ADE-type singularities is associated with one indecomposable matrix factorization which can be deformed into one or more factorizations of lower rank. Branes with internal fluxes arise naturally as bound states of the indecomposable factorizations. Describing branes in such a way avoids the need to resolve singularities. This paper looks at gauge group breaking from E8 fibers down to SU (5) fibers due to the relevance of such fibrations for local F-theory GUT models. A purpose of this paper is to understand how the deformations of the singularity are understood in terms of its matrix factorizations. By systematically factorizing the elliptic fiber equation, this paper discusses geometries which are relevant for building semi-realistic local models. In the process it becomes evident that breaking patterns which are identical at the level of the Kodaira type of the fibers can be inequivalent at the level of matrix factorizations. Therefore the matrix factorization picture supplements information which the conventional less detailed descriptions lack.
NASA Astrophysics Data System (ADS)
Rajalingham, C.; Bhat, R. B.
1993-02-01
The axisymmetric vibration of circular plates and its analog in elliptic plates with clamped, simply supported and free boundary conditions are investigated using boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method. Modified polar coordinates are employed to analyze the vibration of elliptical plates, with circular plates as a special case. Axisymmetric vibration of circular plates and its analog in elliptical plates with concentric nodal elipses require only one-dimensional shape functions in the Rayleigh-Ritz method. The first six natural frequencies and the parameters associated with nodal ellipses are tabulated.
Subsuns, Bottlinger's rings, and elliptical halos.
Lynch, D K; Gedzelman, S D; Fraser, A B
1994-07-20
Subsuns, Bottlinger's rings, and elliptical halos are simulated by the use of a Monte Carlo model; reflection of sunlight from almost horizontal ice crystals is assumed. Subsuns are circular or elliptical spots seen at the specular reflection point when one flies over cirrus or cirrostratus clouds. Bottlinger's rings are rare, almost elliptical rings centered about the subsun. Elliptical halos are small rings of light centered around the Sun or the Moon that rarely occur with other halo phenomena. Subsuns and Bottlinger's rings can be explained by reflection from a single crystal, whereas elliptical halos require reflection from two separate crystals. All three phenomena are colorless and vertically elongated with an eccentricity that increases with increasing solar zenith angle. For several cases of Bottlinger's rings the simulations are compared with density scans of photographs. Clouds that consist of large swinging or gyrating plates and dendritic crystals, which form near -15 °C, seem the most likely ca didates to produce the rings and elliptical halos. Meteorological evidence is presented that supports these conditions for elliptical halos. Simulations suggest that the most distinct elliptical halos may be produced by hybrid clouds that contain both horizontal and gyrating crystals.
Uniting old stellar systems: from globular clusters to giant ellipticals
NASA Astrophysics Data System (ADS)
Forbes, Duncan A.; Lasky, Paul; Graham, Alister W.; Spitler, Lee
2008-10-01
Elliptical galaxies and globular clusters (GCs) have traditionally been regarded as physically distinct entities due to their discontinuous distribution in key scaling diagrams involving size, luminosity and velocity dispersion. Recently this distinctness has been challenged by the discovery of stellar systems with mass intermediate between those of GCs and dwarf ellipticals (such as ultracompact dwarfs and dwarf galaxy transition objects). Here we examine the relationship between the virial and stellar mass for a range of old stellar systems, from GCs to giant ellipticals, and including such intermediate-mass objects (IMOs). Improvements on previous work in this area include the use of (i) near-infrared magnitudes from the Two Micron All Sky Survey (2MASS), (ii) aperture corrections to velocity dispersions, (iii) homogeneous half-light radii and (iv) accounting for the effects of non-homology in galaxies. We find a virial-to-stellar mass relation that ranges from ~104Msolar systems (GCs) to ~1012Msolar systems (elliptical galaxies). The lack of measured velocity dispersions for dwarf ellipticals with -16 > MK > -18 (~108Msolar) currently inhibits our ability to determine how, or indeed if, these galaxies connect continuously with GCs in terms of their virial-to-stellar mass ratios. We find elliptical galaxies to have roughly equal fractions of dark and stellar matter within a virial radius; only in the most massive (greater than 1012Msolar) ellipticals does dark matter dominate the virial mass. Although the IMOs reveal slightly higher virial-to-stellar mass ratios than lower mass GCs, this may simply reflect our limited understanding of their initial mass function (and hence their stellar mass-to-light ratios) or structural properties. We argue that most of these IMOs have similar properties to massive GCs, i.e. IMOs are essentially massive star clusters. Only the dwarf spheroidal galaxies exhibit behaviour notably distinct from the other stellar systems examined
Thermopile detector of light ellipticity
Lu, Feng; Lee, Jongwon; Jiang, Aiting; Jung, Seungyong; Belkin, Mikhail A.
2016-01-01
Polarimetric imaging is widely used in applications from material analysis to biomedical diagnostics, vision and astronomy. The degree of circular polarization, or light ellipticity, is associated with the S3 Stokes parameter which is defined as the difference in the intensities of the left- and right-circularly polarized components of light. Traditional way of determining this parameter relies on using several external optical elements, such as polarizers and wave plates, along with conventional photodetectors, and performing at least two measurements to distinguish left- and right-circularly polarized light components. Here we theoretically propose and experimentally demonstrate a thermopile photodetector element that provides bipolar voltage output directly proportional to the S3 Stokes parameter of the incident light. PMID:27703152
Thermopile detector of light ellipticity
NASA Astrophysics Data System (ADS)
Lu, Feng; Lee, Jongwon; Jiang, Aiting; Jung, Seungyong; Belkin, Mikhail A.
2016-10-01
Polarimetric imaging is widely used in applications from material analysis to biomedical diagnostics, vision and astronomy. The degree of circular polarization, or light ellipticity, is associated with the S3 Stokes parameter which is defined as the difference in the intensities of the left- and right-circularly polarized components of light. Traditional way of determining this parameter relies on using several external optical elements, such as polarizers and wave plates, along with conventional photodetectors, and performing at least two measurements to distinguish left- and right-circularly polarized light components. Here we theoretically propose and experimentally demonstrate a thermopile photodetector element that provides bipolar voltage output directly proportional to the S3 Stokes parameter of the incident light.
An experimental analysis of elliptical adhesive contact
NASA Astrophysics Data System (ADS)
Sümer, Bilsay; Onal, Cagdas D.; Aksak, Burak; Sitti, Metin
2010-06-01
The elliptical adhesive contact is studied experimentally utilizing two hemicylinders of elastomeric poly(dimethylsiloxane) (PDMS). Experimental results are compared with the recent approximate Johnson-Kendall-Roberts (JKR) theory for elliptical contacts, and the deviation of the experiments from this theory is discussed in detail. To do this, the cylinders are placed with different skew angles with respect to each other in order to emulate the effect of orientation. The maximum adhesion force and the size of the contact zone are determined experimentally under the action of surface energy. The difference of the maximum adhesion force between experiments and theory is found to increase as the contact area goes from mildly elliptical to slim elliptical contact. Similarly, it is observed that the contact area can be approximated to have elliptical geometry for a wide range of skew angles while a deviation is observed for slim elliptical contacts. Moreover, the reduction in the contact area is observed to be nonself-similar during detachment from an elliptical shape to a circular one.
NASA Astrophysics Data System (ADS)
Tenneti, Ananth; Mandelbaum, Rachel; Di Matteo, Tiziana
2016-11-01
We study the shapes and intrinsic alignments of discs and elliptical galaxies in the MassiveBlack-II (MBII) and Illustris cosmological hydrodynamic simulations, with volumes of (100 h-1 Mpc)3 and (75 h-1 Mpc)3, respectively. We find that simulated disc galaxies are more oblate in shape and more misaligned with the shape of their host dark matter subhalo when compared with ellipticals. The disc major axis is found to be oriented towards the location of nearby elliptical galaxies. We also find that the discs are thinner in MBII and misalignments with dark matter halo orientations are smaller in both discs and ellipticals when compared with Illustris. As a result, the intrinsic alignment correlation functions at fixed mass have a higher amplitude in MBII than in Illustris. Finally, at scales above ˜0.1 h-1 Mpc, the intrinsic alignment two-point correlation functions for disc galaxies in both simulations are consistent with a null detection, unlike those for ellipticals. Despite significant differences in the treatments of hydrodynamics and baryonic physics in the simulations, we find that the wδ + correlation function scales similarly with transverse separation. However, the less massive galaxies show different scale dependence in the ellipticity-direction correlation. This result indicates that, while hydrodynamic simulations are a promising tool to study intrinsic alignments, further study is needed to understand the impact of differences in the implementations of hydrodynamics and baryonic feedback.
Microwave gas breakdown in elliptical waveguides
Koufogiannis, I. D.; Sorolla, E. Mattes, M.
2014-01-15
This paper analyzes the microwave gas discharge within elliptical waveguides excited by the fundamental mode. The Rayleigh-Ritz method has been applied to solve the continuity equation. The eigenvalue problem defined by the breakdown condition has been solved and the effective diffusion length of the elliptical waveguide has been calculated, what is used to find the corona threshold. This paper extends the microwave breakdown model developed for circular waveguides and shows the better corona withstanding capabilities of elliptical waveguides. The corona breakdown electric field threshold obtained with the variational method has been compared with the one calculated with the Finite Elements Method, showing excellent agreement.
HyeongKae Park; Robert R. Nourgaliev; Richard C. Martineau; Dana A. Knoll
2008-09-01
We present high-order accurate spatiotemporal discretization of all-speed flow solvers using Jacobian-free Newton Krylov framework. One of the key developments in this work is the physics-based preconditioner for the all-speed flow, which makes use of traditional semi-implicit schemes. The physics-based preconditioner is developed in the primitive variable form, which allows a straightforward separation of physical phenomena. Numerical examples demonstrate that the developed preconditioner effectively reduces the number of the Krylov iterations, and the efficiency is independent of the Mach number and mesh sizes under a fixed CFL condition.
Pressure algorithm for elliptic flow calculations with the PDF method
NASA Technical Reports Server (NTRS)
Anand, M. S.; Pope, S. B.; Mongia, H. C.
1991-01-01
An algorithm to determine the mean pressure field for elliptic flow calculations with the probability density function (PDF) method is developed and applied. The PDF method is a most promising approach for the computation of turbulent reacting flows. Previous computations of elliptic flows with the method were in conjunction with conventional finite volume based calculations that provided the mean pressure field. The algorithm developed and described here permits the mean pressure field to be determined within the PDF calculations. The PDF method incorporating the pressure algorithm is applied to the flow past a backward-facing step. The results are in good agreement with data for the reattachment length, mean velocities, and turbulence quantities including triple correlations.
Elliptic surface grid generation on minimal and parmetrized surfaces
NASA Technical Reports Server (NTRS)
Spekreijse, S. P.; Nijhuis, G. H.; Boerstoel, J. W.
1995-01-01
An elliptic grid generation method is presented which generates excellent boundary conforming grids in domains in 2D physical space. The method is based on the composition of an algebraic and elliptic transformation. The composite mapping obeys the familiar Poisson grid generation system with control functions specified by the algebraic transformation. New expressions are given for the control functions. Grid orthogonality at the boundary is achieved by modification of the algebraic transformation. It is shown that grid generation on a minimal surface in 3D physical space is in fact equivalent to grid generation in a domain in 2D physical space. A second elliptic grid generation method is presented which generates excellent boundary conforming grids on smooth surfaces. It is assumed that the surfaces are parametrized and that the grid only depends on the shape of the surface and is independent of the parametrization. Concerning surface modeling, it is shown that bicubic Hermite interpolation is an excellent method to generate a smooth surface which is passing through a given discrete set of control points. In contrast to bicubic spline interpolation, there is extra freedom to model the tangent and twist vectors such that spurious oscillations are prevented.
NASA Astrophysics Data System (ADS)
Borazjani, Iman; Asgharzadeh, Hafez
2015-11-01
Flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates with explicit and semi-implicit schemes. Implicit schemes can be used to overcome these restrictions. However, implementing implicit solver for nonlinear equations including Navier-Stokes is not straightforward. Newton-Krylov subspace methods (NKMs) are one of the most advanced iterative methods to solve non-linear equations such as implicit descritization of the Navier-Stokes equation. The efficiency of NKMs massively depends on the Jacobian formation method, e.g., automatic differentiation is very expensive, and matrix-free methods slow down as the mesh is refined. Analytical Jacobian is inexpensive method, but derivation of analytical Jacobian for Navier-Stokes equation on staggered grid is challenging. The NKM with a novel analytical Jacobian was developed and validated against Taylor-Green vortex and pulsatile flow in a 90 degree bend. The developed method successfully handled the complex geometries such as an intracranial aneurysm with multiple overset grids, and immersed boundaries. It is shown that the NKM with an analytical Jacobian is 3 to 25 times faster than the fixed-point implicit Runge-Kutta method, and more than 100 times faster than automatic differentiation depending on the grid (size) and the flow problem. The developed methods are fully parallelized with parallel efficiency of 80-90% on the problems tested.
A transmission line model for propagation in elliptical core optical fibers
Georgantzos, E.; Boucouvalas, A. C.; Papageorgiou, C.
2015-12-31
The calculation of mode propagation constants of elliptical core fibers has been the purpose of extended research leading to many notable methods, with the classic step index solution based on Mathieu functions. This paper seeks to derive a new innovative method for the determination of mode propagation constants in single mode fibers with elliptic core by modeling the elliptical fiber as a series of connected coupled transmission line elements. We develop a matrix formulation of the transmission line and the resonance of the circuits is used to calculate the mode propagation constants. The technique, used with success in the case of cylindrical fibers, is now being extended for the case of fibers with elliptical cross section. The advantage of this approach is that it is very well suited to be able to calculate the mode dispersion of arbitrary refractive index profile elliptical waveguides. The analysis begins with the deployment Maxwell’s equations adjusted for elliptical coordinates. Further algebraic analysis leads to a set of equations where we are faced with the appearance of harmonics. Taking into consideration predefined fixed number of harmonics simplifies the problem and enables the use of the resonant circuits approach. According to each case, programs have been created in Matlab, providing with a series of results (mode propagation constants) that are further compared with corresponding results from the ready known Mathieu functions method.
The noise from supersonic elliptic jets
NASA Technical Reports Server (NTRS)
Morris, Philip J.; Bhat, Thonse R. S.
1992-01-01
This paper presents calculations of the noise radiated by a supersonic elliptic jet. The large scale structures in the jet, that are the predominant source of noise in the downstream direction, are modeled as instability waves. The evolution of the instability waves is determined by a local, linear, inviscid analysis. An expression is derived for the acoustic field outside the jet and the far field directivity associated with each instability wave. Calculations are performed for a Mach 1.5 elliptic jet with aspect ratio 2:1 and a Mach 2.0 elliptic jet with aspect ratio 2:1 and a Mach 2.0 elliptic jet with aspect ratio 3:1. The mean flow development is taken from experimental results. Comparisons are made with far field acoustic measurements.
Elliptic and parabolic equations for measures
NASA Astrophysics Data System (ADS)
Bogachev, Vladimir I.; Krylov, Nikolai V.; Röckner, Michael
2009-12-01
This article gives a detailed account of recent investigations of weak elliptic and parabolic equations for measures with unbounded and possibly singular coefficients. The existence and differentiability of densities are studied, and lower and upper bounds for them are discussed. Semigroups associated with second-order elliptic operators acting in L^p-spaces with respect to infinitesimally invariant measures are investigated. Bibliography: 181 titles.
Elastohydrodynamic lubrication of elliptical contacts
NASA Technical Reports Server (NTRS)
Hamrock, B. J.
1981-01-01
The determination of the minimum film thickness within contact is considered for both fully flooded and starved conditions. A fully flooded conjunction is one in which the film thickness is not significantly changed when the amount of lubricant is increased. The fully flooded results presented show the influence of contact geometry on minimum film thickness as expressed by the ellipticity parameter and the dimensionless speed, load, and materials parameters. These results are applied to materials of high elastic modulus (hard EHL), such as metal, and to materials of low elastic modulus(soft EHL), such as rubber. In addition to the film thickness equations that are developed, contour plots of pressure and film thickness are given which show the essential features of elastohydrodynamically lubricated conjunctions. The crescent shaped region of minimum film thickness, with its side lobes in which the separation between the solids is a minimum, clearly emerges in the numerical solutions. In addition to the 3 presented for the fully flooded results, 15 more cases are used for hard EHL contacts and 18 cases are used for soft EHL contacts in a theoretical study of the influence of lubricant starvation on film thickness and pressure. From the starved results for both hard and soft EHL contacts, a simple and important dimensionless inlet boundary distance is specified. This inlet boundary distance defines whether a fully flooded or a starved condition exists in the contact. Contour plots of pressure and film thickness in and around the contact are shown for conditions.
Elliptical instability in the planetary fluid cores
NASA Astrophysics Data System (ADS)
Moradi, Ali
Elliptical instability may be excited in any rotating flow with elliptically deformed streamlines. Investigating this instability in containers with spheroidal or ellipsoidal boundaries is of geophysical and astrophysical interest as many stars and planets are either rotating ellipsoidal fluid bodies or have substantial fluid cores which are either ellipsoidal, in the absence of a solid inner core, or ellipsoidal shells such as the Earth's fluid core; elliptical instability may be excited in these bodies as a result of the gravitational pull of a secondary body such as a moon or a large asteroid orbiting these bodies. In this thesis, the nonlinear evolution of elliptical instability in an inviscid incompressible rotating triaxial ellipsoid is numerically studied using the least-square finite element method. After validating the method by reproducing some known results, it is applied to other configurations in order to investigate some open questions on this subject, namely, the effects of the oblateness of the ellipsoid and the frequency ratio of the orbital speed of the secondary body on the evolution of the elliptical instability. We have found that if the parameters of the system, i.e. the flattening ratio and the frequency ratio of the background rotation, are in the range of the spin-over instability, a repetitive three-dimensional rigorous motion is maintained indefinitely; otherwise, instability may be excited initially, once the streamlines become elliptical, for certain ranges of the system parameters; however, as time elapses the motion becomes two dimensional with small displacement amplitudes in x- and y- directions.
Luanjing Guo; Chuan Lu; Hai Huang; Derek R. Gaston
2012-06-01
Systems of multicomponent reactive transport in porous media that are large, highly nonlinear, and tightly coupled due to complex nonlinear reactions and strong solution-media interactions are often described by a system of coupled nonlinear partial differential algebraic equations (PDAEs). A preconditioned Jacobian-Free Newton-Krylov (JFNK) solution approach is applied to solve the PDAEs in a fully coupled, fully implicit manner. The advantage of the JFNK method is that it avoids explicitly computing and storing the Jacobian matrix during Newton nonlinear iterations for computational efficiency considerations. This solution approach is also enhanced by physics-based blocking preconditioning and multigrid algorithm for efficient inversion of preconditioners. Based on the solution approach, we have developed a reactive transport simulator named RAT. Numerical results are presented to demonstrate the efficiency and massive scalability of the simulator for reactive transport problems involving strong solution-mineral interactions and fast kinetics. It has been applied to study the highly nonlinearly coupled reactive transport system of a promising in situ environmental remediation that involves urea hydrolysis and calcium carbonate precipitation.
Instability of a supersonic shock free elliptic jet
NASA Technical Reports Server (NTRS)
Baty, Roy S.; Seiner, John M.; Ponton, Michael K.
1990-01-01
This paper presents a comparison of the measured and the computed spatial stability properties of an aspect ratio 2 supersonic shock free elliptic jet. The shock free nature of the elliptic jet provides an ideal test of validity of modeling the large scale coherent structures in the initial mixing region of noncircular supersonic jets with linear hydrodynamic stability theory. Both aerodynamic and acoustic data were measured. The data are used to compute the mean velocity profiles and to provide a description of the spatial composition of pressure waves in the elliptic jet. A hybrid numerical scheme is applied to solve the Rayleigh problem governing the inviscid linear spatial stability of the jet. The measured mean velocity profiles are used to provide a qualitative model for the cross sectional geometry and the smooth velocity profiles used in the stability analysis. Computational results are presented for several modes of instability at two jet cross sections. The acoustic measurements show that a varicose instability is the jet's perferred mode of motion. The stability analysis predicts that the Strouhal number varies linearly as a function of axial distance in the jet's initial mixing region, which is in good qualitative agreement with previous measurements.
Shape measurement biases from underfitting and ellipticity gradients
Bernstein, Gary M.
2010-08-21
With this study, precision weak gravitational lensing experiments require measurements of galaxy shapes accurate to <1 part in 1000. We investigate measurement biases, noted by Voigt and Bridle (2009) and Melchior et al. (2009), that are common to shape measurement methodologies that rely upon fitting elliptical-isophote galaxy models to observed data. The first bias arises when the true galaxy shapes do not match the models being fit. We show that this "underfitting bias" is due, at root, to these methods' attempts to use information at high spatial frequencies that has been destroyed by the convolution with the point-spread function (PSF) and/or by sampling. We propose a new shape-measurement technique that is explicitly confined to observable regions of k-space. A second bias arises for galaxies whose ellipticity varies with radius. For most shape-measurement methods, such galaxies are subject to "ellipticity gradient bias". We show how to reduce such biases by factors of 20–100 within the new shape-measurement method. The resulting shear estimator has multiplicative errors < 1 part in 10^{3} for high-S/N images, even for highly asymmetric galaxies. Without any training or recalibration, the new method obtains Q = 3000 in the GREAT08 Challenge of blind shear reconstruction on low-noise galaxies, several times better than any previous method.
Anisotropic elliptic optical fibers. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Kang, Soon Ahm
1991-01-01
The exact characteristic equation for an anisotropic elliptic optical fiber is obtained for odd and even hybrid modes in terms of infinite determinants utilizing Mathieu and modified Mathieu functions. A simplified characteristic equation is obtained by applying the weakly guiding approximation such that the difference in the refractive indices of the core and the cladding is small. The simplified characteristic equation is used to compute the normalized guide wavelength for an elliptical fiber. When the anisotropic parameter is equal to unity, the results are compared with the previous research and they are in close agreement. For a fixed value normalized cross-section area or major axis, the normalized guide wavelength lambda/lambda(sub 0) for an anisotropic elliptic fiber is small for the larger value of anisotropy. This condition indicates that more energy is carried inside of the fiber. However, the geometry and anisotropy of the fiber have a smaller effect when the normalized cross-section area is very small or very large.
Shape measurement biases from underfitting and ellipticity gradients
Bernstein, Gary M.
2010-08-21
With this study, precision weak gravitational lensing experiments require measurements of galaxy shapes accurate to <1 part in 1000. We investigate measurement biases, noted by Voigt and Bridle (2009) and Melchior et al. (2009), that are common to shape measurement methodologies that rely upon fitting elliptical-isophote galaxy models to observed data. The first bias arises when the true galaxy shapes do not match the models being fit. We show that this "underfitting bias" is due, at root, to these methods' attempts to use information at high spatial frequencies that has been destroyed by the convolution with the point-spread function (PSF)more » and/or by sampling. We propose a new shape-measurement technique that is explicitly confined to observable regions of k-space. A second bias arises for galaxies whose ellipticity varies with radius. For most shape-measurement methods, such galaxies are subject to "ellipticity gradient bias". We show how to reduce such biases by factors of 20–100 within the new shape-measurement method. The resulting shear estimator has multiplicative errors < 1 part in 103 for high-S/N images, even for highly asymmetric galaxies. Without any training or recalibration, the new method obtains Q = 3000 in the GREAT08 Challenge of blind shear reconstruction on low-noise galaxies, several times better than any previous method.« less
Properties of Ellipticity Correlation with Atmospheric Structure from Gemini South
Asztalos, S J; Treadway, T; de Vries, W H; Rosenberg, L J; Burke, D; Claver, C; Saha, A; Puxley, P
2006-12-21
Cosmic shear holds great promise for a precision independent measurement of {Omega}{sub m}, the mass density of the universe relative to the critical density. The signal is expected to be weak, so a thorough understanding of systematic effects is crucial. An important systematic effect is the atmosphere: shear power introduced by the atmosphere is larger than the expected signal. Algorithms exist to extract the cosmic shear from the atmospheric component, though a measure of their success applied to a range of seeing conditions is lacking. To gain insight into atmospheric shear, Gemini South imaging in conjunction with ground condition and satellite wind data were obtained. We find that under good seeing conditions Point-Spread-Function (PSF) correlations persist well beyond the separation typical of high-latitude stars. Under these conditions, ellipticity residuals based on a simple PSF interpolation can be reduced to within a factor of a few of the shot-noise induced ellipticity floor. We also find that the ellipticity residuals are highly correlated with wind direction. Finally, we correct stellar shapes using a more sophisticated procedure and generate shear statistics from stars. Under all seeing conditions in our data set the residual correlations lie everywhere below the target signal level. For good seeing we find that the systematic error attributable to atmospheric turbulence is comparable in magnitude to the statistical error (shape noise) over angular scales relevant to present lensing surveys.
Properties of Ellipticity Correlation with Atmospheric Structure From Gemini South
Asztalos, Stephen J.; de Vries, W.H.; Rosenberg, L.J; Treadway, T.; Burke, D.; Claver, C.; Saha, A.; Puxley, P.; /Gemini Observ., La Serena
2007-01-17
Cosmic shear holds great promise for a precision independent measurement of {Omega}{sub m}, the mass density of the universe relative to the critical density. The signal is expected to be weak, so a thorough understanding of systematic effects is crucial. An important systematic effect is the atmosphere: shear power introduced by the atmosphere is larger than the expected signal. Algorithms exist to extract the cosmic shear from the atmospheric component, though a measure of their success applied to a range of seeing conditions is lacking. To gain insight into atmospheric shear, Gemini South imaging in conjunction with ground condition and satellite wind data were obtained. We find that under good seeing conditions Point-Spread-Function (PSF) correlations persist well beyond the separation typical of high-latitude stars. Under these conditions, ellipticity residuals based on a simple PSF interpolation can be reduced to within a factor of a few of the shot-noise induced ellipticity floor. We also find that the ellipticity residuals are highly correlated with wind direction. Finally, we correct stellar shapes using a more sophisticated procedure and generate shear statistics from stars. Under all seeing conditions in our data set the residual correlations lie everywhere below the target signal level. For good seeing we find that the systematic error attributable to atmospheric turbulence is comparable in magnitude to the statistical error (shape noise) over angular scales relevant to present lensing surveys.
Ultraluminous Infrared Mergers: Elliptical Galaxies in Formation?
NASA Astrophysics Data System (ADS)
Genzel, R.; Tacconi, L. J.; Rigopoulou, D.; Lutz, D.; Tecza, M.
2001-12-01
We report high-quality near-IR spectroscopy of 12 ultraluminous infrared galaxy mergers (ULIRGs). Our new VLT and Keck data provide ~0.5" resolution, stellar and gas kinematics of these galaxies, most of which are compact systems in the last merger stages. We confirm that ULIRG mergers are ``ellipticals in formation.'' Random motions dominate their stellar dynamics, but significant rotation is common. Gasdynamics and stellar dynamics are decoupled in most systems. ULIRGs fall on or near the fundamental plane of hot stellar systems, and especially on its less evolution-sensitive, reff-σ projection. The ULIRG velocity dispersion distribution, their location in the fundamental plane, and their distribution of vrotsini/σ closely resemble those of intermediate-mass (~L*), elliptical galaxies with moderate rotation. As a group ULIRGs do not resemble giant ellipticals with large cores and little rotation. Our results are in good agreement with other recent studies indicating that disky ellipticals with compact cores or cusps can form through dissipative mergers of gas-rich disk galaxies while giant ellipticals with large cores have a different formation history. Based on observations at the European Southern Observatory, Chile (ESO 65.N-0266, 65.N-0289), and on observations at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, The University of California, and the National Aeronautics and Space Administration. The Keck Observatory was made possible by the general financial support by the W. M. Keck Foundation.
An elliptic parameterisation of the Zamolodchikov model
NASA Astrophysics Data System (ADS)
Bazhanov, Vladimir V.; Mangazeev, Vladimir V.; Okada, Yuichiro; Sergeev, Sergey M.
2013-06-01
The Zamolodchikov model describes an exact relativistic factorized scattering theory of straight strings in (2+1)-dimensional space-time. It also defines an integrable 3D lattice model of statistical mechanics and quantum field theory. The three-string S-matrix satisfies the tetrahedron equation which is a 3D analog of the Yang-Baxter equation. Each S-matrix depends on three dihedral angles formed by three intersecting planes, whereas the tetrahedron equation contains five independent spectral parameters, associated with angles of an Euclidean tetrahedron. The vertex weights are given by rather complicated expressions involving square roots of trigonometric function of the spectral parameters, which is quite unusual from the point of view of 2D solvable lattice models. In this paper we consider a particular four-parameter specialisation of the tetrahedron equation when one of its vertices goes to infinity and the tetrahedron itself degenerates into an infinite prism. We show that in this limit all the vertex weights in the tetrahedron equation can be represented as meromorphic functions on an elliptic curve. Moreover we show that a special reduction of the tetrahedron equation in this case leads precisely to an example of the tetrahedral Zamolodchikov algebra, previously constructed by Korepanov. This algebra plays important role for a "layered" construction of the Shastry's R-matrix and the 2D S-matrix appearing in the problem of the ADS/CFT correspondence for N=4 SUSY Yang-Mills theory in four dimensions. Possible applications of our results in this field are briefly discussed.
DISSIPATION AND EXTRA LIGHT IN GALACTIC NUCLEI. II. 'CUSP' ELLIPTICALS
Hopkins, Philip F.; Cox, Thomas J.; Dutta, Suvendra N.; Hernquist, Lars; Kormendy, John; Lauer, Tod R.
2009-03-15
We study the origin and properties of 'extra' or 'excess' central light in the surface brightness profiles of cusp or power-law elliptical galaxies. Dissipational mergers give rise to two-component profiles: an outer profile established by violent relaxation acting on stars already present in the progenitor galaxies prior to the final stages of the merger, and an inner stellar population comprising the extra light, formed in a compact central starburst. By combining a large set of hydrodynamical simulations with data that span a broad range of profiles at various masses, we show that observed cusp ellipticals appear consistent with the predicted 'extra light' structure, and we use our simulations to motivate a two-component description of the observations that allows us to examine how the properties and mass of this component scale with, e.g., the mass, gas content, and other properties of the galaxies. We show how to robustly separate the physically meaningful extra light and outer, violently relaxed profile, and demonstrate that the observed cusps and 'extra light' are reliable tracers of the degree of dissipation in the spheroid-forming merger. We show that the typical degree of dissipation is a strong function of stellar mass, roughly tracing the observed gas fractions of disks of the same mass over the redshift range z {approx} 0-2. We demonstrate a correlation between the strength of this component and effective radius at fixed mass, in the sense that systems with more dissipation are more compact, sufficient to explain the discrepancy in the maximum phase-space and mass densities of ellipticals and their progenitor spirals. We show that the outer shape of the light profile in simulated and observed systems (when fit to properly account for the central light) does not depend on mass, with a mean outer Sersic index {approx}2.5. We also explore how this relates to, e.g., the shapes, kinematic properties, and stellar population gradients of ellipticals. Extra
The Advanced Light Source elliptically polarizing undulator
Marks, S.; Cortopassi, C.; DeVries, J.
1997-05-01
An elliptically polarizing undulator (EPU) for the Advanced Light Source (ALS) has been designed and is currently under construction. The magnetic design is a moveable quadrant pure permanent magnet structure featuring adjustable magnets to correct phase errors and on-axis field integrals. The device is designed with a 5.0 cm period and will produce variably polarized light of any ellipticity, including pure circular and linear. The spectral range at 1.9 GeV for typical elliptical polarization with a degree of circular polarization greater than 0.8 will be from 100 eV to 1,500 eV, using the first, third, and fifth harmonics. The device will be switchable between left and right circular modes at a frequency of up to 0.1 Hz. The 1.95 m long overall length will allow two such devices in a single ALS straight sector.
NASA Astrophysics Data System (ADS)
Morii, Youhi; Terashima, Hiroshi; Koshi, Mitsuo; Shimizu, Taro; Shima, Eiji
2016-10-01
We herein propose a fast and robust Jacobian-free time integration method named as the extended robustness-enhanced numerical algorithm (ERENA) to treat the stiff ordinary differential equations (ODEs) of chemical kinetics. The formulation of ERENA is based on an exact solution of a quasi-steady-state approximation that is optimized to preserve the mass conservation law through use of a Lagrange multiplier method. ERENA exhibits higher accuracy and faster performance in homogeneous ignition simulations compared to existing popular explicit and implicit methods for stiff ODEs such as VODE, MTS, and CHEMEQ2. We investigate the effects of user-specified threshold values in ERENA, to provide trade-off information between the accuracy and the computational cost.
Zou, Ling; Zhao, Haihua; Zhang, Hongbin
2016-08-24
This study presents a numerical investigation on using the Jacobian-free Newton–Krylov (JFNK) method to solve the two-phase flow four-equation drift flux model with realistic constitutive correlations (‘closure models’). The drift flux model is based on Isshi and his collaborators’ work. Additional constitutive correlations for vertical channel flow, such as two-phase flow pressure drop, flow regime map, wall boiling and interfacial heat transfer models, were taken from the RELAP5-3D Code Manual and included to complete the model. The staggered grid finite volume method and fully implicit backward Euler method was used for the spatial discretization and time integration schemes, respectively. Themore » Jacobian-free Newton–Krylov method shows no difficulty in solving the two-phase flow drift flux model with a discrete flow regime map. In addition to the Jacobian-free approach, the preconditioning matrix is obtained by using the default finite differencing method provided in the PETSc package, and consequently the labor-intensive implementation of complex analytical Jacobian matrix is avoided. Extensive and successful numerical verification and validation have been performed to prove the correct implementation of the models and methods. Code-to-code comparison with RELAP5-3D has further demonstrated the successful implementation of the drift flux model.« less
Spontaneous motion of an elliptic camphor particle
NASA Astrophysics Data System (ADS)
Kitahata, Hiroyuki; Iida, Keita; Nagayama, Masaharu
2013-01-01
The coupling between deformation and motion in a self-propelled system has attracted broader interest. In the present study, we consider an elliptic camphor particle for investigating the effect of particle shape on spontaneous motion. It is concluded that the symmetric spatial distribution of camphor molecules at the water surface becomes unstable first in the direction of a short axis, which induces the camphor disk motion in this direction. Experimental results also support the theoretical analysis. From the present results, we suggest that when an elliptic particle supplies surface-active molecules to the water surface, the particle can exhibit translational motion only in the short-axis direction.
Elliptic flow from collision geometry and rescattering
Boeggild, H.; Hansen, Ole; Humanic, T. J.
2009-04-15
Calculations of elliptic flow based on two initial state models of Au+Au collisions at {radical}(s)=200 GeV/n coupled with a hadronic rescattering calculation are presented. The two initial state models used are a thermal model and a partonic model. Results from these calculations are compared with experiments and it is found that both initial state models give satisfactory representations of elliptic flow measurements, provided that the rescattering is started early enough in the collision process. It is also found that the present hadronic model studies do not show the jet suppression observed experimentally.
Vectorial spherical-harmonics representation of an inhomogeneous elliptically polarized plane wave.
Frezza, F; Mangini, F
2015-07-01
In this paper, a generalization of the vectorial spherical-harmonics expansion of an inhomogeneous elliptically polarized plane wave is presented. The solution has been achieved using the Legendre functions generalized via hypergeometric and gamma functions, shifting the difficulty to the determination of only expansion coefficients. In order to validate the presented method, a Matlab code has been implemented. To compare the results a Mie scattering by a sphere is considered, then a truncation criterion for the numerical evaluation of the series is proposed, and the Mie scattering coefficients by perfectly conducting and dielectric spheres excited by an inhomogeneous elliptically polarized plane wave are shown. PMID:26367169
Vectorial spherical-harmonics representation of an inhomogeneous elliptically polarized plane wave.
Frezza, F; Mangini, F
2015-07-01
In this paper, a generalization of the vectorial spherical-harmonics expansion of an inhomogeneous elliptically polarized plane wave is presented. The solution has been achieved using the Legendre functions generalized via hypergeometric and gamma functions, shifting the difficulty to the determination of only expansion coefficients. In order to validate the presented method, a Matlab code has been implemented. To compare the results a Mie scattering by a sphere is considered, then a truncation criterion for the numerical evaluation of the series is proposed, and the Mie scattering coefficients by perfectly conducting and dielectric spheres excited by an inhomogeneous elliptically polarized plane wave are shown.
Effective material properties of thermoelectric composites with elliptical fibers
NASA Astrophysics Data System (ADS)
Wang, Yi-Ze
2015-06-01
In the present work, the effective material properties of thermoelectric composites with elliptical fibers are studied. Explicit solutions are derived by the conformal mapping function and Mori-Tanaka method. Numerical simulations are performed to present the behaviors of normalized effective material constants. From the results, it can be observed that both the effective electric and thermal conductivities can be reduced by increasing the filling ratio and a/ b. Such influences can also be found for the effective thermoelectric figure of merit. But they are different from those on the effective Seebeck and Peltier coefficients.
Cavity modes and their excitations in elliptical plasmonic patch nanoantennas.
Chakrabarty, Ayan; Wang, Feng; Minkowski, Fred; Sun, Kai; Wei, Qi-Huo
2012-05-21
We present experimental and theoretical studies of two dimensional periodic arrays of elliptical plasmonic patch nanoantennas. Experimental and simulation results demonstrate that the azimuthal symmetry breaking of the metal patches leads to the occurrence of even and odd resonant cavity modes and the excitation geometries dependent on their modal symmetries. We show that the cavity modes can be described by the product of radial and angular Mathieu functions with excellent agreements with both simulations and experiments. The effects of the patch periodicity on the excitation of the surface plasmon and its coupling with the cavity modes are also discussed. PMID:22714147
Metallicity Gradients in the Halos of Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Greene, Jenny E.; Ma, Chung-Pei; Goulding, Andrew; McConnell, Nicholas J.; Blakeslee, John P.; Davis, Timothy; Thomas, Jens
2016-08-01
We discuss the stellar halos of massive elliptical galaxies, as revealed by our ambitious integral-field spectroscopic survey MASSIVE. We show that metallicity drops smoothly as a function of radius out to ~ 2.5 Re , while the [α/Fe] abundance ratios stay flat. The stars in the outskirts likely formed rapidly (to explain the high ratio of alpha to Fe) but in a relatively shallow potential (to explain the low metallicities). This is consistent with expectations for a two-phase growth of massive galaxies, in which the second phase involves accretion of small satellites. We also show some preliminary study of the gas content of these most MASSIVE galaxies.
Schlaufman, K
2004-10-11
Atmospheric turbulence can mimic the effects of weak lensing in astronomical images, so it is necessary to understand to what degree turbulence affects weak lensing measurements. In particular, we studied the ellipticity induced upon the point-spread functions (PSFs) of a grid of simulated stars separated by distances (d {approx} 1{prime}) that will be characteristic of Large Synoptic Survey Telescope (LSST) images. We observe that atmospherically induced ellipticity changes on small scales (d < 0.5{prime}) and use linear interpolation between stars separated by d = 0.5{prime} to determine the induced ellipticity everywhere in the field-of-view.
NASA Astrophysics Data System (ADS)
Ahn, Woo Sang; Park, Sung Ho; Jung, Sang Hoon; Choi, Wonsik; Do Ahn, Seung; Shin, Seong Soo
2014-06-01
The purpose of this study is to determine the radial dose function of HDR 192Ir source based on Monte Carlo simulation using elliptic cylindrical phantom, similar to realistic shape of pelvis, in brachytherapy dosimetric study. The elliptic phantom size and shape was determined by analysis of dimensions of pelvis on CT images of 20 patients treated with brachytherapy for cervical cancer. The radial dose function obtained using the elliptic cylindrical water phantom was compared with radial dose functions for different spherical phantom sizes, including the Williamsion's data loaded into conventional planning system. The differences in the radial dose function for the different spherical water phantoms increase with radial distance, r, and the largest differences in the radial dose function appear for the smallest phantom size. The radial dose function of the elliptic cylindrical phantom significantly decreased with radial distance in the vertical direction due to different scatter condition in comparison with the Williamson's data. Considering doses to ICRU rectum and bladder points, doses to reference points can be underestimated up to 1-2% at the distance from 3 to 6 cm. The radial dose function in this study could be used as realistic data for calculating the brachytherapy dosimetry for cervical cancer.
Xia, Kelin; Zhan, Meng; Wan, Decheng; Wei, Guo-Wei
2011-01-01
Mesh deformation methods are a versatile strategy for solving partial differential equations (PDEs) with a vast variety of practical applications. However, these methods break down for elliptic PDEs with discontinuous coefficients, namely, elliptic interface problems. For this class of problems, the additional interface jump conditions are required to maintain the well-posedness of the governing equation. Consequently, in order to achieve high accuracy and high order convergence, additional numerical algorithms are required to enforce the interface jump conditions in solving elliptic interface problems. The present work introduces an interface technique based adaptively deformed mesh strategy for resolving elliptic interface problems. We take the advantages of the high accuracy, flexibility and robustness of the matched interface and boundary (MIB) method to construct an adaptively deformed mesh based interface method for elliptic equations with discontinuous coefficients. The proposed method generates deformed meshes in the physical domain and solves the transformed governed equations in the computational domain, which maintains regular Cartesian meshes. The mesh deformation is realized by a mesh transformation PDE, which controls the mesh redistribution by a source term. The source term consists of a monitor function, which builds in mesh contraction rules. Both interface geometry based deformed meshes and solution gradient based deformed meshes are constructed to reduce the L∞ and L2 errors in solving elliptic interface problems. The proposed adaptively deformed mesh based interface method is extensively validated by many numerical experiments. Numerical results indicate that the adaptively deformed mesh based interface method outperforms the original MIB method for dealing with elliptic interface problems. PMID:22586356
Circular and Elliptic Submerged Impinging Water Jets
NASA Astrophysics Data System (ADS)
Claudey, Eric; Benedicto, Olivier; Ravier, Emmanuel; Gutmark, Ephraim
1999-11-01
Experiments and CFD have been performed to study circular and elliptic jets in a submerged water jet facility. The tests included discharge coefficient measurement to evaluate pressure losses encountered in noncircular nozzles compared to circular ones. Three-dimensional pressure mappings on the impingement surface and PIV measurement of the jet mean and turbulent velocity have been performed at different compound impingement angles relative to the impingement surface and at different stand-off distances. The objective was to investigate the effect of the non-circular geometry on the flow field and on the impact region. The tests were performed in a close loop system in which the water was pumped through the nozzles into a clear Plexiglas tank. The Reynolds numbers were typically in the range of 250000. Discharge coefficients of the elliptic nozzle was somewhat lower than that of the circular jet but spreading rate and turbulence level were higher. Pressure mapping showed that the nozzle exit geometry had an effect on the pressure distribution in the impact region and that high-pressure zones were generated at specific impact points. PIV measurements showed that for a same total exit area, the elliptic jets affected a surface area that is 8the equivalent circular. The turbulence level in the elliptic jet tripled due to the nozzle design. Results of the CFD model were in good agreement with the experimental data.
Nomenclature of polarized light - Elliptical polarization
NASA Technical Reports Server (NTRS)
Clarke, D.
1974-01-01
Alternative handedness and sign conventions for relating the orientation of elliptical polarization are discussed. The discussion proceeds under two headings: (1) snapshot picture, where the emphasis for the convention is contained in the concept of handedness; and (2) angular momentum consideration, where the emphasis for the convention is strongly associated with mathematical convention and the sign of the fourth Stokes parameter.
ELLIPTIC FLOW, INITIAL ECCENTRICITY AND ELLIPTIC FLOW FLUCTUATIONS IN HEAVY ION COLLISIONS AT RHIC.
NOUICER,R.; ALVER, B.; BACK, B.B.; BAKER, M.D.; BALLINTIJN, M.; BARTON, D.S.; ET AL.
2007-02-19
We present measurements of elliptic flow and event-by-event fluctuations established by the PHOBOS experiment. Elliptic flow scaled by participant eccentricity is found to be similar for both systems when collisions with the same number of participants or the same particle area density are compared. The agreement of elliptic flow between Au+Au and Cu+Cu collisions provides evidence that the matter is created in the initial stage of relativistic heavy ion collisions with transverse granularity similar to that of the participant nucleons. The event-by-event fluctuation results reveal that the initial collision geometry is translated into the final state azimuthal particle distribution, leading to an event-by-event proportionality between the observed elliptic flow and initial eccentricity.
NASA Astrophysics Data System (ADS)
Djidel, S.; Bouamar, M.; Khedrouche, D.
2016-04-01
This paper presents a performances study of UWB monopole antenna using half-elliptic radiator conformed on elliptical surface. The proposed antenna, simulated using microwave studio computer CST and High frequency simulator structure HFSS, is designed to operate in frequency interval over 3.1 to 40 GHz. Good return loss and radiation pattern characteristics are obtained in the frequency band of interest. The proposed antenna structure is suitable for ultra-wideband applications, which is, required for many wearable electronics applications.
Optimal impulsive trajectories for orbital rendezvous between elliptic orbits
NASA Astrophysics Data System (ADS)
Cheng, Ching-Wei
1992-01-01
This study uses and extends primer vector theory to obtain a minimum-fuel two or multiple impulse solution for co-planar and non co-planar elliptic-to-elliptic, time-fixed rendezvous. Lawden's conditions for an optimal impulsive trajectory and three additional methods to improve the non-optimal multiple impulse are introduced. To extend a 3-Impulse differential cost function provided by Jezewski and Rozendaal, the general differential cost function for an N-Impulse trajectory is developed. This approach defines the gradient vector for any set of boundary conditions. To determine the number of impulses, times, and locations for multiple-impulse optimal trajectories automatically, a computer program is developed. This software has been thoroughly tested in a wide variety of rendezvous situations. The singularity for a transfer angle of 180 degrees and the singular case of sin I = 0 are also accounted for in the program. Part of this work was accomplished using the Generalized Reduced Gradient method using its associated GRG2 computer code. The effects of inclination between the vehicle and target orbits, the initial positions of the vehicle and target, and the direction of the major axes are considered. Numerical results for several different orbit configurations are produced and discussed. The results are compared with the Hohmann/Hohmann type transfer and/or the optimal, finite, three-impulse transfer.
Elliptic Anomaly in Constructing Long-Term and Short-Term Dynamical Theories
NASA Astrophysics Data System (ADS)
Brumberg, V. A.; Brumberg, E. V.
2001-07-01
The techniques of Brumberg and Brumberg (1999) based on the use of elliptic anomaly are specified in this paper in two aspects. The iteration technique (Broucke, 1969) to construct short-term semi-analytical theories of motion in rectangular coordinates in lines of Encke and Hill is reelaborated in terms of elliptic anomaly resulting in extending this technique for high-eccentricity orbits. In constructing long-term semi-analytical theories the key point is to integrate trigonometric functions of several angular arguments related to time by different differential expressions. This problem is reduced in the paper to linear algebraic recurrence relations admitting efficient solution by iterations.
Elliptic Genera of Two-Dimensional Gauge Theories with Rank-One Gauge Groups
NASA Astrophysics Data System (ADS)
Benini, Francesco; Eager, Richard; Hori, Kentaro; Tachikawa, Yuji
2014-04-01
We compute the elliptic genera of two-dimensional and -gauged linear sigma models via supersymmetric localization, for rank-one gauge groups. The elliptic genus is expressed as a sum over residues of a meromorphic function whose argument is the holonomy of the gauge field along both the spatial and the temporal directions of the torus. We illustrate our formulas by a few examples including the quintic Calabi-Yau, SU(2) and O(2) gauge theories coupled to N fundamental chiral multiplets, and a geometric model.
Nonparaxial elliptic waves and solitary waves in coupled nonlinear Helmholtz equations
NASA Astrophysics Data System (ADS)
Tamilselvan, K.; Kanna, T.; Khare, Avinash
2016-10-01
We obtain a class of elliptic wave solutions of coupled nonlinear Helmholtz (CNLH) equations describing nonparaxial ultra-broad beam propagation in nonlinear Kerr-like media, in terms of the Jacobi elliptic functions and also discuss their limiting forms (hyperbolic solutions). Especially, we show the existence of non-trivial solitary wave profiles in the CNLH system. The effect of nonparaxiality on speed, pulse width and amplitude of the nonlinear waves is analyzed in detail. Particularly, a mechanism for tuning the speed by altering the nonparaxial parameter is proposed. We also identify a novel phase-unlocking behavior due to the presence of nonparaxial parameter.
NeXSPheRIO results on elliptic-flow fluctuations at RHIC
Hama, Y. Andrade, R. P. G.; Grassi, F.; Qian, W.-L.; Osada, T.; Aguiar, C. E.; Kodama, T.
2008-09-15
By using the NeXSPheRIO code, we study the elliptic-flow fluctuations in Au + Au collisions at 200 A GeV. It is shown that, by fixing the parameters of the model to correctly reproduce the charged pseudorapidity and the transverse-momentum distributions, reasonable agreement of
A new method for the identification of non-Gaussian line profiles in elliptical galaxies
NASA Technical Reports Server (NTRS)
Van Der Marel, Roeland P.; Franx, Marijn
1993-01-01
A new parameterization for the line profiles of elliptical galaxies, the Gauss-Hermite series, is proposed. This approach expands the line profile as a sum of orthogonal functions which minimizes the correlations between the errors in the parameters of the fit. This method also make use of the fact that Gaussians provide good low-order fits to observed line profiles. The method yields measurements of the line strength, mean radial velocity, and the velocity dispersion as well as two extra parameters, h3 and h4, that measure asymmetric and symmetric deviations of the line profiles from a Gaussian, respectively. The new method was used to derive profiles for three elliptical galaxies which all have asymmetric line profiles on the major axis with symmetric deviations from a Gaussian. Results confirm that elliptical galaxies have complex structures due to their complex formation history.
Mining the Suzaku Archive for Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Loewenstein, Michael
Despite significant progress, our understanding of the formation and evolution of giant elliptical galaxies is incomplete. Many unresolved details about the star formation and assembly history, dissipation and feedback processes, and how these are connected in space and time relate to complex gasdynamical processes that are not directly observable, but that leave clues in the form of the level and pattern of heavy element enrichment in the hot ISM. The low background and relatively sharp spectral resolution of the Suzaku X-ray Observatory XIS CCD detectors enable one to derive a particularly extensive abundance pattern in the hot ISM out to large galactic radii for bright elliptical galaxies. These encode important clues to the chemical and dynamical history of elliptical galaxies. The Suzaku archive now includes data on many of the most suitable galaxies for these purposes. To date, these have been analyzed in a very heterogeneous manner -- some at an early stage in the mission using instrument calibration and analysis tools that have greatly evolved in the interim. Given the level of maturity of the data archive, analysis software, and calibration, the time is right to undertake a uniform analysis of this sample and interpret the results in the context of a coherent theoretical framework for the first time. We propose to (1) carefully and thoroughly analyze the available X-ray luminous elliptical galaxies in the Suzaku database, employing the techniques we have established in our previous work to measure hot ISM abundance patterns. Their interpretation requires careful deconstruction within the context of physical gasdynamical and chemical evolutionary models. Since we have developed models for elliptical galaxy chemical evolution specifically constructed to place constraints on the history and development of these systems based on hot ISM abundances, we are uniquely positioned to interpret -- as well as to analyze -- X-ray spectra of these objects. (2) We will
The Invertible Double of Elliptic Operators
NASA Astrophysics Data System (ADS)
Booss-Bavnbek, Bernhelm; Lesch, Matthias
2009-02-01
First, we review the Dirac operator folklore about basic analytic and geometrical properties of operators of Dirac type on compact manifolds with smooth boundary and on closed partitioned manifolds and show how these properties depend on the construction of a canonical invertible double and are related to the concept of the Calderón projection. Then we summarize a recent construction of a canonical invertible double for general first order elliptic differential operators over smooth compact manifolds with boundary. We derive a natural formula for the Calderón projection which yields a generalization of the famous Cobordism Theorem. We provide a list of assumptions to obtain a continuous variation of the Calderón projection under smooth variation of the coefficients. That yields various new spectral flow theorems. Finally, we sketch a research program for confining, respectively closing, the last remaining gaps between the geometric Dirac operator type situation and the general linear elliptic case.
The Stellar Halos of Massive Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Greene, Jenny E.; Murphy, Jeremy D.; Comerford, Julia M.; Gebhardt, Karl; Adams, Joshua J.
2012-05-01
We use the Mitchell Spectrograph (formerly VIRUS-P) on the McDonald Observatory 2.7 m Harlan J. Smith Telescope to search for the chemical signatures of massive elliptical galaxy assembly. The Mitchell Spectrograph is an integral-field spectrograph with a uniquely wide field of view (107'' × 107''), allowing us to achieve remarkably high signal-to-noise ratios of ~20-70 pixel-1 in radial bins of 2-2.5 times the effective radii of the eight galaxies in our sample. Focusing on a sample of massive elliptical galaxies with stellar velocity dispersions σ* > 150 km s-1, we study the radial dependence in the equivalent widths (EW) of key metal absorption lines. By twice the effective radius, the Mgb EWs have dropped by ~50%, and only a weak correlation between σ* and Mgb EW remains. The Mgb EWs at large radii are comparable to those seen in the centers of elliptical galaxies that are ~ an order of magnitude less massive. We find that the well-known metallicity gradients often observed within an effective radius continue smoothly to 2.5 Re , while the abundance ratio gradients remain flat. Much like the halo of the Milky Way, the stellar halos of our galaxies have low metallicities and high α-abundance ratios, as expected for very old stars formed in small stellar systems. Our observations support a picture in which the outer parts of massive elliptical galaxies are built by the accretion of much smaller systems whose star formation history was truncated at early times.
Wiener criterion for X-elliptic operators
NASA Astrophysics Data System (ADS)
Tralli, Giulio; Uguzzoni, Francesco
2015-12-01
In this note we prove a Wiener criterion of regularity of boundary points for the Dirichlet problem related to X-elliptic operators in divergence form enjoying the doubling condition and the Poincaré inequality. As a step towards this result, we exhibit some other characterizations of regularity in terms of the capacitary potentials. Finally, we also show that a cone-type criterion holds true in our setting.
Spectral methods for exterior elliptic problems
NASA Technical Reports Server (NTRS)
Canuto, C.; Hariharan, S. I.; Lustman, L.
1984-01-01
Spectral approximations for exterior elliptic problems in two dimensions are discussed. As in the conventional finite difference or finite element methods, the accuracy of the numerical solutions is limited by the order of the numerical farfield conditions. A spectral boundary treatment is introduced at infinity which is compatible with the infinite order interior spectral scheme. Computational results are presented to demonstrate the spectral accuracy attainable. Although a simple Laplace problem is examined, the analysis covers more complex and general cases.
A heterogeneous stochastic FEM framework for elliptic PDEs
Hou, Thomas Y. Liu, Pengfei
2015-01-15
We introduce a new concept of sparsity for the stochastic elliptic operator −div(a(x,ω)∇(⋅)), which reflects the compactness of its inverse operator in the stochastic direction and allows for spatially heterogeneous stochastic structure. This new concept of sparsity motivates a heterogeneous stochastic finite element method (HSFEM) framework for linear elliptic equations, which discretizes the equations using the heterogeneous coupling of spatial basis with local stochastic basis to exploit the local stochastic structure of the solution space. We also provide a sampling method to construct the local stochastic basis for this framework using the randomized range finding techniques. The resulting HSFEM involves two stages and suits the multi-query setting: in the offline stage, the local stochastic structure of the solution space is identified; in the online stage, the equation can be efficiently solved for multiple forcing functions. An online error estimation and correction procedure through Monte Carlo sampling is given. Numerical results for several problems with high dimensional stochastic input are presented to demonstrate the efficiency of the HSFEM in the online stage.
The case against bimodal star formation in elliptical galaxies
NASA Astrophysics Data System (ADS)
Gibson, B. K.
1996-02-01
We consider the present-day photometric and chemical properties of elliptical galaxies, adopting the bimodal star formation scenario of Elbaz, Arnaud & Vangioni-Flam. These models utilize an initial mass function (IMF) biased heavily toward massive stars during the early phases of galactic evolution, leading to early Type II supernovae-driven galactic winds. A subsequent lengthy, milder star formation phase with a normal IMF ensues, supposedly responsible for the stellar population observed today. Based upon chemical evolution arguments alone, this scenario has been invoked to explain the observed metal mass, and their abundance ratios, in the intracluster medium of galaxy clusters. Building upon the recent compilations of metallicity-dependent isochrones for simple stellar populations, we have constructed a coupled photometric and chemical evolution package for composite stellar populations in order to quantify the effects of such a model upon the photochemical properties of the resultant elliptical galaxies. We demonstrate that these predicted properties are incompatible with those observed at the current epoch.
Optimal Lorentz-augmented spacecraft formation flying in elliptic orbits
NASA Astrophysics Data System (ADS)
Huang, Xu; Yan, Ye; Zhou, Yang
2015-06-01
An electrostatically charged spacecraft accelerates as it moves through the Earth's magnetic field due to the induced Lorentz force, providing a new means of propellantless electromagnetic propulsion for orbital maneuvers. The feasibility of Lorentz-augmented spacecraft formation flying in elliptic orbits is investigated in this paper. Assuming the Earth's magnetic field as a tilted dipole corotating with Earth, a nonlinear dynamical model that characterizes the orbital motion of Lorentz spacecraft in the vicinity of arbitrary elliptic orbits is developed. To establish a predetermined formation configuration at given terminal time, pseudospectral method is used to solve the optimal open-loop trajectories of hybrid control inputs consisted of Lorentz acceleration and thruster-generated control acceleration. A nontilted dipole model is also introduced to analyze the effect of dipole tilt angle via comparisons with the tilted one. Meanwhile, to guarantee finite-time convergence and system robustness against external perturbations, a continuous fast nonsingular terminal sliding mode controller is designed and the closed-loop system stability is proved by Lyapunov theory. Numerical simulations substantiate the validity of proposed open-loop and closed-loop control schemes, and the results indicate that an almost propellantless formation establishment can be achieved by choosing appropriate objective function in the pseudospectral method. Furthermore, compared to the nonsingular terminal sliding mode controller, the closed-loop controller presents superior convergence rate with only a bit more control effort. And the proposed controller can be applied in other Lorentz-augmented relative orbital control problems.
Fully flooded elastohydrodynamic lubricated elliptical contacts
NASA Technical Reports Server (NTRS)
Hamrock, B. J.
1980-01-01
Emphasis is on fully flooded, elastohydrodynamic lubricated, elliptical contacts. A fully flooded conjunction is one in which the film thickness is not significantly changed when the amount of lubricant is increased. A brief description of the relevant equations used in the elastohydrodynamic lubrication of elliptical contacts is given. The most important practical aspect of the elastohydrodynamic theory is the determination of the minimum film thickness within the contact. The maintenance of a fluid film of adequate magnitude is an essential feature of the correct operation of lubricated machine elements. The results presented show the influence of contact geometry on minimum film thickness as expressed by the ellipticity parameter and the dimensionless speed, load, and materials parameters. Film thickness equations are developed for materials of high elastic modulus, such as metal, and for materials of low elastic modulus, such as rubber. In addition to the film thickness equations that are developed, plots of pressure and film thickness are presented. These theoretical solutions for film thickness have all the essential features of previously reported experimental observations based on optical interferometry. Correlation between theory and experiments is also presented.
The elliptic model for communication fluxes
NASA Astrophysics Data System (ADS)
Herrera-Yagüe, C.; Schneider, C. M.; Smoreda, Z.; Couronné, T.; Zufiria, P. J.; González, M. C.
2014-04-01
In this paper, a model (called the elliptic model) is proposed to estimate the number of social ties between two locations using population data in a similar manner to how transportation research deals with trips. To overcome the asymmetry of transportation models, the new model considers that the number of relationships between two locations is inversely proportional to the population in the ellipse whose foci are in these two locations. The elliptic model is evaluated by considering the anonymous communications patterns of 25 million users from three different countries, where a location has been assigned to each user based on their most used phone tower or billing zip code. With this information, spatial social networks are built at three levels of resolution: tower, city and region for each of the three countries. The elliptic model achieves a similar performance when predicting communication fluxes as transportation models do when predicting trips. This shows that human relationships are influenced at least as much by geography as is human mobility.
The Abundance Ratio Pattern in Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Worthey, Guy
1995-12-01
Non-solar abundance ratios in elliptical galaxies are readily detectable in a qualitative sense. The elements Mg, Na, and N appear overabundant compared to Ca and Fe. There is a probable variation of (Sc + V)/Ti. Abundance ratio effects are the single most serious barrier to the estimation of mean stellar ages: even more serious than the 35% model-to-model uncertainty. Isochrone grids allowing for the variation of many individual elements (He, O, C, and N at least, in addition to overall Z and alpha elements) are needed to quantitatively estimate the overabundances and mean ages of ellipticals. The tolerances for relative shifts in isochrone temperatures are tight: about 7 K if we hope for 5% accurate ages. The abundance pattern in elliptical galaxies matches neither the disk, nor the halo, nor the bulge our own Galaxy, although the bulge appears to provide the best match. This research was funded by NASA through grant HF-1066.01-94A from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.
Elliptic Solvers for Adaptive Mesh Refinement Grids
Quinlan, D.J.; Dendy, J.E., Jr.; Shapira, Y.
1999-06-03
We are developing multigrid methods that will efficiently solve elliptic problems with anisotropic and discontinuous coefficients on adaptive grids. The final product will be a library that provides for the simplified solution of such problems. This library will directly benefit the efforts of other Laboratory groups. The focus of this work is research on serial and parallel elliptic algorithms and the inclusion of our black-box multigrid techniques into this new setting. The approach applies the Los Alamos object-oriented class libraries that greatly simplify the development of serial and parallel adaptive mesh refinement applications. In the final year of this LDRD, we focused on putting the software together; in particular we completed the final AMR++ library, we wrote tutorials and manuals, and we built example applications. We implemented the Fast Adaptive Composite Grid method as the principal elliptic solver. We presented results at the Overset Grid Conference and other more AMR specific conferences. We worked on optimization of serial and parallel performance and published several papers on the details of this work. Performance remains an important issue and is the subject of continuing research work.
Fluxon Dynamics in Elliptic Annular Josephson Junctions
NASA Astrophysics Data System (ADS)
Monaco, Roberto; Mygind, Jesper
2016-04-01
We analyze the dynamics of a magnetic flux quantum (current vortex) trapped in a current-biased long planar elliptic annular Josephson tunnel junction. The system is modeled by a perturbed sine-Gordon equation that determines the spatial and temporal behavior of the phase difference across the tunnel barrier separating the two superconducting electrodes. In the absence of an external magnetic field, the fluxon dynamics in an elliptic annulus does not differ from that of a circular annulus where the stationary fluxon speed merely is determined by the system losses. The interaction between the vortex magnetic moment and a spatially homogeneous in-plane magnetic field gives rise to a tunable periodic non-sinusoidal potential which is strongly dependent on the annulus aspect ratio. We study the escape of the vortex from a well in the tilted potential when the bias current exceeds the depinning current. The smallest depinning current as well as the lowest sensitivity of the annulus to the external field is achieved when the axes ratio is equal to √{2}. The presented extensive numerical results are in good agreement with the findings of the perturbative approach. We also probe the rectifying properties of an asymmetric potential implemented with an egg-shaped annulus formed by two semi-elliptic arcs.
NASA Astrophysics Data System (ADS)
Lemieux, Jean-François; Price, Stephen F.; Evans, Katherine J.; Knoll, Dana; Salinger, Andrew G.; Holland, David M.; Payne, Antony J.
2011-07-01
We have implemented the Jacobian-free Newton-Krylov (JFNK) method for solving the first-order ice sheet momentum equation in order to improve the numerical performance of the Glimmer-Community Ice Sheet Model (Glimmer-CISM), the land ice component of the Community Earth System Model (CESM). Our JFNK implementation is based on significant re-use of existing code. For example, our physics-based preconditioner uses the original Picard linear solver in Glimmer-CISM. For several test cases spanning a range of geometries and boundary conditions, our JFNK implementation is 1.8-3.6 times more efficient than the standard Picard solver in Glimmer-CISM. Importantly, this computational gain of JFNK over the Picard solver increases when refining the grid. Global convergence of the JFNK solver has been significantly improved by rescaling the equation for the basal boundary condition and through the use of an inexact Newton method. While a diverse set of test cases show that our JFNK implementation is usually robust, for some problems it may fail to converge with increasing resolution (as does the Picard solver). Globalization through parameter continuation did not remedy this problem and future work to improve robustness will explore a combination of Picard and JFNK and the use of homotopy methods.
NASA Astrophysics Data System (ADS)
Fujii, Fumio; Yamakawa, Yuki; Noguchi, Hirohisa
2010-07-01
In the previous publications of the authors, an eigenanalysis-free computational procedure has been proposed to extract the bifurcation buckling mode(s) from the LDL T -decomposed symmetric stiffness matrix in the vicinity of a stability point. Any eigensolver, for instance, inverse iteration or subspace method, is not necessary. The procedure has been verified in numerical examples and well works in multiple and clustered bifurcation problems too. This present paper will extend the eigenanalysis-free procedure to the LDU-decomposed non-symmetric Jacobian matrix, from which both left and right critical eigenvectors relevant to the stability point may be extracted in a similar way. The idea is mathematical and totally independent of the physical problem to be solved, so that it is applicable to any non-symmetric square matrix in stability problems including plasticity with non-associated flow rules, contact and fluid-structure interaction. The linear-algebraic background of non-symmetric eigenvalue problems is firstly described. The present paper will then mention the role play of the left and right critical eigenvectors in stability analysis and the eigenanalysis-free LDU-procedure is proposed. Numerical examples of elastoplastic bifurcation are illustrated for verification and discussion. In APPENDICES, a bench model visualizes the mechanical meaning of the left and right critical singular vectors of a rectangular matrix.
NASA Astrophysics Data System (ADS)
Kordy, M.; Wannamaker, P.; Maris, V.; Cherkaev, E.; Hill, G.
2016-01-01
We have developed an algorithm, which we call HexMT, for 3-D simulation and inversion of magnetotelluric (MT) responses using deformable hexahedral finite elements that permit incorporation of topography. Direct solvers parallelized on symmetric multiprocessor (SMP), single-chassis workstations with large RAM are used throughout, including the forward solution, parameter Jacobians and model parameter update. In Part I, the forward simulator and Jacobian calculations are presented. We use first-order edge elements to represent the secondary electric field (E), yielding accuracy O(h) for E and its curl (magnetic field). For very low frequencies or small material admittivities, the E-field requires divergence correction. With the help of Hodge decomposition, the correction may be applied in one step after the forward solution is calculated. This allows accurate E-field solutions in dielectric air. The system matrix factorization and source vector solutions are computed using the MKL PARDISO library, which shows good scalability through 24 processor cores. The factorized matrix is used to calculate the forward response as well as the Jacobians of electromagnetic (EM) field and MT responses using the reciprocity theorem. Comparison with other codes demonstrates accuracy of our forward calculations. We consider a popular conductive/resistive double brick structure, several synthetic topographic models and the natural topography of Mount Erebus in Antarctica. In particular, the ability of finite elements to represent smooth topographic slopes permits accurate simulation of refraction of EM waves normal to the slopes at high frequencies. Run-time tests of the parallelized algorithm indicate that for meshes as large as 176 × 176 × 70 elements, MT forward responses and Jacobians can be calculated in ˜1.5 hr per frequency. Together with an efficient inversion parameter step described in Part II, MT inversion problems of 200-300 stations are computable with total run times
Elliptic CY3folds and non-perturbative modular transformation
NASA Astrophysics Data System (ADS)
Iqbal, Amer; Shabbir, Khurram
2016-03-01
We study the refined topological string partition function of a class of toric elliptically fibered Calabi-Yau threefolds. These Calabi-Yau threefolds give rise to five dimensional quiver gauge theories and are dual to configurations of M5-M2-branes. We determine the Gopakumar-Vafa invariants for these threefolds and show that the genus g free energy is given by the weight 2 g Eisenstein series. We also show that although the free energy at all genera are modular invariant, the full partition function satisfies the non-perturbative modular transformation property discussed by Lockhart and Vafa in arXiv:1210.5909 and therefore the modularity of free energy is up to non-perturbative corrections.
NASA Astrophysics Data System (ADS)
Asgharzadeh, Hafez; Borazjani, Iman
2014-11-01
Time step-size restrictions and low convergence rates are major bottle necks for implicit solution of the Navier-Stokes in simulations involving complex geometries with moving boundaries. Newton-Krylov method (NKM) is a combination of a Newton-type method for super-linearly convergent solution of nonlinear equations and Krylov subspace methods for solving the Newton correction equations, which can theoretically address both bottle necks. The efficiency of this method vastly depends on the Jacobian forming scheme e.g. automatic differentiation is very expensive and Jacobian-free methods slow down as the mesh is refined. A novel, computationally efficient analytical Jacobian for NKM was developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered curvilinear grids with immersed boundaries. The NKM was validated and verified against Taylor-Green vortex and pulsatile flow in a 90 degree bend and efficiently handles complex geometries such as an intracranial aneurysm with multiple overset grids, pulsatile inlet flow and immersed boundaries. The NKM method is shown to be more efficient than the semi-implicit Runge-Kutta methods and Jabobian-free Newton-Krylov methods. We believe NKM can be applied to many CFD techniques to decrease the computational cost. This work was supported partly by the NIH Grant R03EB014860, and the computational resources were partly provided by Center for Computational Research (CCR) at University at Buffalo.
Luanjing Guo; Hai Huang; Derek Gaston; Cody Permann; David Andrs; George Redden; Chuan Lu; Don Fox; Yoshiko Fujita
2013-03-01
Modeling large multicomponent reactive transport systems in porous media is particularly challenging when the governing partial differential algebraic equations (PDAEs) are highly nonlinear and tightly coupled due to complex nonlinear reactions and strong solution-media interactions. Here we present a preconditioned Jacobian-Free Newton-Krylov (JFNK) solution approach to solve the governing PDAEs in a fully coupled and fully implicit manner. A well-known advantage of the JFNK method is that it does not require explicitly computing and storing the Jacobian matrix during Newton nonlinear iterations. Our approach further enhances the JFNK method by utilizing physics-based, block preconditioning and a multigrid algorithm for efficient inversion of the preconditioner. This preconditioning strategy accounts for self- and optionally, cross-coupling between primary variables using diagonal and off-diagonal blocks of an approximate Jacobian, respectively. Numerical results are presented demonstrating the efficiency and massive scalability of the solution strategy for reactive transport problems involving strong solution-mineral interactions and fast kinetics. We found that the physics-based, block preconditioner significantly decreases the number of linear iterations, directly reducing computational cost; and the strongly scalable algebraic multigrid algorithm for approximate inversion of the preconditioner leads to excellent parallel scaling performance.
The Puzzlingly Small Ca II Triplet Absorption in Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Saglia, R. P.; Maraston, Claudia; Thomas, Daniel; Bender, Ralf; Colless, Matthew
2002-11-01
We measure the central values (within Re/8) of the Ca II triplet line indices CaT* and CaT and the Paschen index PaT at 8600 Å for a 93% complete sample of 75 nearby early-type galaxies with BT<12 mag and Vgal<2490 km s-1. We find that the values of CaT* are constant to within 5% over the range of central velocity dispersions 100 km s-1<=σ<=340 km s-1, while the PaT (and CaT) values are mildly anticorrelated with σ. Using simple and composite stellar population models, we show the following: (1) The measured CaT* and CaT are lower than expected from simple stellar population (SSP) models with Salpeter initial mass functions (IMFs) and with metallicities and ages derived from optical Lick (Fe, Mg, and Hβ) indices. Uncertainties in the calibration, the fitting functions, and the SSP modeling taken separately cannot explain the discrepancy. On average, the observed PaT values are within the range allowed by the models and the large uncertainties in the fitting functions. (2) The steepening of the IMF at low masses required to lower the CaT* and CaT indices to the observed values is incompatible with the measured FeH index at 9916 Å and the dynamical mass-to-light ratios of elliptical galaxies. (3) Composite stellar populations with a low-metallicity component reduce the disagreement, but rather artificial metallicity distributions are needed. Another explanation may be that calcium is indeed underabundant in elliptical galaxies.
Exposing the non-collectivity in elliptic flow
Liao, Jinfeng; Koch, Volker
2009-02-13
We show that backward-forward elliptic asymmetry correlations provide an experimentally accessible observable which distinguishes between collective and non-collective contributions to the observed elliptic asymmetry v2 in relativistic heavy ion collisions. The measurement of this observable will reveal the momentum scale at which collective expansion seizes and where the elliptic asymmetry is dominated by (semi)-hard processes. In addition, the knowledge of the actual magnitude of the collective component of the elliptic asymmetry will be essential for the extraction of the viscosity of the matter created in these collisions.
Elliptic multiple zeta values and one-loop superstring amplitudes
NASA Astrophysics Data System (ADS)
Broedel, Johannes; Mafra, Carlos R.; Matthes, Nils; Schlotterer, Oliver
2015-07-01
We investigate iterated integrals on an elliptic curve, which are a natural genus-one generalization of multiple polylogarithms. These iterated integrals coincide with the multiple elliptic polylogarithms introduced by Brown and Levin when constrained to the real line. At unit argument they reduce to an elliptic analogue of multiple zeta values, whose network of relations we start to explore. A simple and natural application of this framework are one-loop scattering amplitudes in open superstring theory. In particular, elliptic multiple zeta values are a suitable language to express their low energy limit. Similar to the techniques available at tree-level, our formalism allows to completely automatize the calculation.
Classification of isomonodromy problems on elliptic curves
NASA Astrophysics Data System (ADS)
Levin, A. M.; Olshanetsky, M. A.; Zotov, A. V.
2014-02-01
This paper describes isomonodromy problems in terms of flat G-bundles over punctured elliptic curves \\Sigma_\\tau and connections with regular singularities at marked points. The bundles are classified by their characteristic classes, which are elements of the second cohomology group H^2(\\Sigma_\\tau,{\\mathscr Z}(G)), where {\\mathscr Z}(G) is the centre of G. For any complex simple Lie group G and any characteristic class the moduli space of flat connections is defined, and for them the monodromy-preserving deformation equations are given in Hamiltonian form together with the corresponding Lax representation. In particular, they include the Painlevé VI equation, its multicomponent generalizations, and the elliptic Schlesinger equations. The general construction is described for punctured complex curves of arbitrary genus. The Drinfeld-Simpson (double coset) description of the moduli space of Higgs bundles is generalized to the case of the space of flat connections. This local description makes it possible to establish the Symplectic Hecke Correspondence for a wide class of monodromy-preserving problems classified by the characteristic classes of the underlying bundles. In particular, the Painlevé VI equation can be described in terms of \\operatorname{SL}(2,{ C})-bundles. Since {\\mathscr Z}(\\operatorname{SL}(2,{ C}))={ Z}_2, the Painlevé VI equation has two representations related by the Hecke transformation: 1) as the well-known elliptic form of the Painlevé VI equation (for trivial bundles); 2) as the non-autonomous Zhukovsky-Volterra gyrostat (for non-trivial bundles). Bibliography: 123 titles.
Magnetic flux studies in horizontally cooled elliptical superconducting cavities
Martinello, M. Checchin, M.; Grassellino, A. Crawford, A. C.; Melnychuk, O.; Romanenko, A.; Sergatskov, D. A.
2015-07-28
Previous studies on magnetic flux expulsion as a function of cooldown procedures for elliptical superconducting radio frequency (SRF) niobium cavities showed that when the cavity beam axis is placed parallel to the helium cooling flow and sufficiently large thermal gradients are achieved, all magnetic flux could be expelled and very low residual resistance could be achieved. In this paper, we investigate flux trapping for the case of resonators positioned perpendicularly to the helium cooling flow, which is more representative of how SRF cavities are cooled in accelerators and for different directions of the applied magnetic field surrounding the resonator. We show that different field components have a different impact on the surface resistance, and several parameters have to be considered to fully understand the flux dynamics. A newly discovered phenomenon of concentration of flux lines at the cavity top leading to temperature rise at the cavity equator is presented.
Evolution of Hot Gas in Elliptical Galaxies
NASA Technical Reports Server (NTRS)
Mathews, William G.
2004-01-01
This theory grant was awarded to study the curious nature, origin and evolution of hot gas in elliptical galaxies and their surrounding groups. Understanding the properties of this X-ray emitting gas has profound implications over the broad landscape of modern astrophysics: cosmology, galaxy formation, star formation, cosmic metal enrichment, galactic structure and dynamics, and the physics of hot gases containing dust and magnetic fields. One of our principal specific objectives was to interpret the marvelous new observations from the XMM and Chandru satellite X-ray telescopes.
Dynamical friction in pairs of elliptical galaxies
NASA Technical Reports Server (NTRS)
Prugniel, Philippe; Combes, Francoise
1990-01-01
The authors present numerical experiments on dynamical friction in pairs of elliptical galaxies of unequal mass. They confirm that the self-gravity of the response is not important and show the drastic effect of the deformability of the companion which reduces the decay time by more than a factor of 2. Almost the same amount of orbital energy is dissipated within the satellite as within the large galaxy. Finally, the authors discuss the importance of distant encounters for the dynamical evolution of systems of galaxies.
Average-State Jacobians and Implicit Methods for Compressible Viscous and Turbulent Flows
NASA Astrophysics Data System (ADS)
Batten, P.; Leschziner, M. A.; Goldberg, U. C.
1997-10-01
Several new implicit schemes for the solution of the compressible Navier-Stokes equations are presented. These methods are derived from a hierarchy of average-state approximate solutions to the Riemann problem, ranging from the Lax-Friedrichs flux to the exact Riemann-solver flux. In contrast to linearised approximations, these methods will (with certain provisos on the signal velocities) enforce the entropy condition and preserve positivity without the need for additional corrections. The hierarchy also encompasses and explains the origin of many other upwind and centred methods, including the space-time scheme (due to Chang) and the more recent FORCE scheme (due to Toro). Based on an analysis of the above hierarchy, attention is focussed on the development of a new implicit scheme using a positivity-preserving version of Toro et al.'s HLLC scheme, which is the simplest average-state solver capable of exactly preserving isolated shock, contact, and shear waves. Solutions obtained with this method are essentially indistinguishable from those produced with an exact Riemann solver, whilst convergence to the steady state is the most rapid of all the implicit average-stage schemes considered and directly comparable to that of the unmodified Roe scheme. A new two-step implicit method is applied to various test cases, including turbulent flow with shock/boundary-layer interaction. The new time-stepping scheme is composed of two backward Euler steps, but has twice the convergence rate of the backward Euler scheme and alleviates the convergence problems that are often experienced when employing compressive limiter functions.
NASA Astrophysics Data System (ADS)
Hasheminejad, Seyyed M.; Sanaei, Roozbeh
2007-11-01
Interaction of time harmonic fast longitudinal and shear incident plane waves with an elliptical fiber embedded in a porous elastic matrix is studied. The novel features of Biot dynamic theory of poroelasticity along with the classical method of eigen-function expansion and the pertinent boundary conditions are employed to develop a closed form series solution involving Mathieu and modified Mathieu functions of complex arguments. The complications arising due to the non-orthogonality of angular Mathieu functions corresponding to distinct wave numbers in addition to the problems associated with appearance of additional angular dependent terms in the boundary conditions are all avoided by expansion of the angular Mathieu functions in terms of transcendental functions and subsequent integration, leading to a linear set of independent equations in terms of the unknown scattering coefficients. A MATHEMATICA code is developed for computing the Mathieu functions in terms of complex Fourier coefficients which are themselves calculated by numerically solving appropriate sets of eigen-systems. The analytical results are illustrated with numerical examples in which an elastic fiber of elliptic cross section is insonified by a plane fast compressional or shear wave at normal incidence. The effects of fiber cross sectional ellipticity, angle of incidence (fiber two-dimensional orientation), and incident wave polarization (P, SV, SH) on dynamic stress concentrations are studied in a relatively wide frequency range. Limiting cases are considered and fair agreements with well-known solutions are established.
Integrated X-Ray Reflectivity Measurements for Elliptically Curved PET Crystals
Haugh, M J; Ross, P W; Regan, P W; Magoon, J; Shoup, M J; Barrios, M A; Emig, J A; Fournier, K B
2012-04-26
Spectroscopy provides valuable information about the temperature and density of a compressed pellet in a plasma. Elliptically curved pentaerythritol (PET) crystals are used as components for spectrometers. Their elliptical geometry gives several advantages related to spectral energy range, source focus, and spectral image compression.[1] The crystal curvature increases the spectrometer throughput but at the cost of a loss in resolution. Four different crystals are used in a spectrometer at the National Ignition Facility (NIF) target chamber at Lawrence Livermore National Laboratory (LLNL). Figure 1 shows the arrangement of the elliptical PET crystals in the snout of a NIF target diagnostic shown in Figure 2. The spectrum from the crystals is captured by four image plates located behind the crystals. A typical mandrel, the darkened section, upon which the PET crystal is glued, is shown in Figure 3, which also shows the complete ellipse. There are four elliptical segment types, each having the same major axis but a different minor axis. The crystals are 150 mm long in the diffraction direction and 25.4 mm high. Two crystals of each type were calibrated. The throughput for each spectrometer is determined by the integrated reflectivity of the PET crystal.[1] The goal of this effort was to measure the reflectivity curve of the PET curved crystal at several energies and determine the integrated reflectivity and the curve width as a function of the X-ray spectral energy and location on the ellipse where the beam strikes.
On the N={1}^{ast } gauge theory on a circle and elliptic integrable systems
NASA Astrophysics Data System (ADS)
Bourget, Antoine; Troost, Jan
2016-01-01
We continue our study of the N={1}^{ast } supersymmetric gauge theory on R^{2,1}× {S}^1 and its relation to elliptic integrable systems. Upon compactification on a circle, we show that the semi-classical analysis of the massless and massive vacua depends on the classification of nilpotent orbits, as well as on the conjugacy classes of the component group of their centralizer. We demonstrate that semi-classically massless vacua can be lifted by Wilson lines in unbroken discrete gauge groups. The pseudo-Levi subalgebras that play a classifying role in the nilpotent orbit theory are also key in defining generalized Inozemtsev limits of (twisted) elliptic integrable systems. We illustrate our analysis in the N={1}^{ast } theories with gauge algebras su(3), su(4), so(5) and for the exceptional gauge algebra G 2. We map out modular duality diagrams of the massive and massless vacua. Moreover, we provide an analytic description of the branches of massless vacua in the case of the su(3) and the so(5) theory. The description of these branches in terms of the complexified Wilson lines on the circle invokes the Eichler-Zagier technique for inverting the elliptic Weierstrass function. After fine-tuning the coupling to elliptic points of order three, we identify the Argyres-Douglas singularities of the su(3) N={1}^{ast } theory.
Rainbow scattering by a cylinder with a nearly elliptical cross section.
Adler, C L; Lock, J A; Stone, B R
1998-03-20
We both theoretically and experimentally examine the behavior of the first- and the second-order rainbows produced by a normally illuminated glass rod, which has a nearly elliptical cross section, as it is rotated about its major axis. We decompose the measured rainbow angle, taken as a function of the rod's rotation angle, into a Fourier series and find that the rod's refractive index, average ellipticity, and deviation from ellipticity are encoded primarily in the m = 0, 2, 3 Fourier coefficients, respectively. We determine these parameters for our glass rod and, where possible, compare them with independent measurements. We find that the average ellipticity of the rod agrees well with direct measurements, but that the rod's diameter inferred from the spacing of the supernumeraries of the first-order rainbow is significantly larger than that obtained by direct measurement. We also determine the conditions under which the deviation of falling water droplets from an oblate spheroidal shape permits the first few supernumeraries of the second-order rainbow to be observed in a rain shower. PMID:18268746
Properties of Dwarf Ellipticals in Low-Density Environments
NASA Astrophysics Data System (ADS)
Sur, Debnil; Guhathakurta, P.; Toloba, E.
2013-01-01
Dwarf elliptical galaxies have been studied only in dense cluster environments, where they are the most common type of object. While this suggests that their location affects their formation and evolution, the role of distance is not fully understood. Thus, to investigate the physical processes that shape these galaxies, we have conducted a study of dwarf elliptical galaxies (dEs) in low-density environments to compare their properties with those in clusters. Catalogs of such objects have not been created; thus, we have developed a novel objective method to find new dEs through comparing photometric properties with those of galaxies in the Virgo Cluster Catalog. This method utilizes optical colors, surface brightness and ellipticity, and it confirms smoothness through visual classification. In this last step, we found a very low contamination rate, which suggests the procedure’s utility in finding dEs. Through the NSA Sloan Atlas, we have analyzed the spectrophotometric properties of the dE candidates as a function of distance to the nearest massive galaxy, which we refer to as their host. We have found that these dEs are younger and more actively forming stars than dEs in denser regions. This is consistent with a transformation scenario in which low luminosity spiral galaxies are affected by the environment and transformed into quiescent galaxies. This low density regime contains objects in an intermediate state between the spiral galaxy and the classical dE in Virgo, where no star formation is ongoing. The correlation of the studied properties with the distance to the host galaxy provides new evidence that the dEs are created by a process called ram-pressure stripping: the interstellar medium of a host galaxy removes the gas of a smaller star-forming galaxy and provokes its quenching. We are currently analysing Keck/DEIMOS spectroscopy of some of the dE candidates from our catalog to explore in more detail their connection to cluster dEs. Possible similarities
Variational elliptic solver for atmospheric applications
Smolarkiewicz, P.K.; Margolin, L.G.
1994-03-01
We discuss a conjugate gradient type method -- the conjugate residual -- suitable for solving linear elliptic equations that result from discretization of complex atmospheric dynamical problems. Rotation and irregular boundaries typically lead to nonself-adjoint elliptic operators whose matrix representation on the grid is definite but not symmetric. On the other hand, most established methods for solving large sparse matrix equations depend on the symmetry and definiteness of the matrix. Furthermore, the explicit construction of the matrix can be both difficult and computationally expensive. An attractive feature of conjugate gradient methods in general is that they do not require any knowledge of the matrix; and in particular, convergence of conjugate residual algorithms do not rely on symmetry for definite operators. We begin by reviewing some basic concepts of variational algorithms from the perspective of a physical analogy to the damped wave equation, which is a simple alternative to the traditional abstract framework of the Krylov subspace methods. We derive two conjugate residual schemes from variational principles, and prove that either definiteness or symmetry ensures their convergence. We discuss issues related to computational efficiency and illustrate our theoretical considerations with a test problem of the potential flow of a Boussinesq fluid flow past a steep, three-dimensional obstacle.
Thermodynamics of Inozemtsev's elliptic spin chain
NASA Astrophysics Data System (ADS)
Klabbers, Rob
2016-06-01
We study the thermodynamic behaviour of Inozemtsev's long-range elliptic spin chain using the Bethe ansatz equations describing the spectrum of the model in the infinite-length limit. We classify all solutions of these equations in that limit and argue which of these solutions determine the spectrum in the thermodynamic limit. Interestingly, some of the solutions are not selfconjugate, which puts the model in sharp contrast to one of the model's limiting cases, the Heisenberg XXX spin chain. Invoking the string hypothesis we derive the thermodynamic Bethe ansatz equations (TBA-equations) from which we determine the Helmholtz free energy in thermodynamic equilibrium and derive the associated Y-system. We corroborate our results by comparing numerical solutions of the TBA-equations to a direct computation of the free energy for the finite-length hamiltonian. In addition we confirm numerically the interesting conjecture put forward by Finkel and González-López that the original and supersymmetric versions of Inozemtsev's elliptic spin chain are equivalent in the thermodynamic limit.
Anisotropic elliptic PDEs for feature classification.
Wang, Shengfa; Hou, Tingbo; Li, Shuai; Su, Zhixun; Qin, Hong
2013-10-01
The extraction and classification of multitype (point, curve, patch) features on manifolds are extremely challenging, due to the lack of rigorous definition for diverse feature forms. This paper seeks a novel solution of multitype features in a mathematically rigorous way and proposes an efficient method for feature classification on manifolds. We tackle this challenge by exploring a quasi-harmonic field (QHF) generated by elliptic PDEs, which is the stable state of heat diffusion governed by anisotropic diffusion tensor. Diffusion tensor locally encodes shape geometry and controls velocity and direction of the diffusion process. The global QHF weaves points into smooth regions separated by ridges and has superior performance in combating noise/holes. Our method's originality is highlighted by the integration of locally defined diffusion tensor and globally defined elliptic PDEs in an anisotropic manner. At the computational front, the heat diffusion PDE becomes a linear system with Dirichlet condition at heat sources (called seeds). Our new algorithms afford automatic seed selection, enhanced by a fast update procedure in a high-dimensional space. By employing diffusion probability, our method can handle both manufactured parts and organic objects. Various experiments demonstrate the flexibility and high performance of our method. PMID:23929843
JAKEF: a portable symbolic differentiator of functions given by algorithms
Hillstrom, K.E.
1982-08-01
JAKEF is a compiler that accepts as data a single or double precision FORTRAN subroutine program defining an objective function F(x) or a vector function f(x) and produces as output a single or double precision FORTRAN program defining the gradient of F(x) or the jacobian of f(x).
Elliptical Orbit [arrow right] 1/r[superscript 2] Force
ERIC Educational Resources Information Center
Prentis, Jeffrey; Fulton, Bryan; Hesse, Carol; Mazzino, Laura
2007-01-01
Newton's proof of the connection between elliptical orbits and inverse-square forces ranks among the "top ten" calculations in the history of science. This time-honored calculation is a highlight in an upper-level mechanics course. It would be worthwhile if students in introductory physics could prove the relation "elliptical orbit" [arrow right]…
Effect of the earth's ellipticity on the lunar tidal potential
NASA Technical Reports Server (NTRS)
Dahlen, F. A.
1993-01-01
The earth's orbital acceleration about the moon is influenced by its ellipticity. In this paper it shown that the ellipticity affects tidal gravity by contributing directly to the lunar tide-generating potential (in addition to effecting the elastic-gravitational response of the solid earth and oceans to this potential).
The Stability of Orthotropic Elliptic Cylinders in Pure Bending
NASA Technical Reports Server (NTRS)
Heck, O S
1937-01-01
The theoretical critical bending stress of elliptic cylindrical shells is determined on the assumption of infinite shell length and absence of local instability phenomena. The results of the tests on isotropic elliptic cylindrical shells stressed in bending are compared with the theoretical results. The practical applicability of the theory is discussed.
Dynamic susceptibility of onion in ferromagnetic elliptical nanoring
NASA Astrophysics Data System (ADS)
Mu, Congpu; Song, Jiefang; Xu, Jianghong; Wen, Fusheng
2016-06-01
Micromagnetic simulation was performed to investigate the equilibrium state and dynamic susceptibility spectra of magnetic elliptical nanoring. There are two equilibrium states (onion and vortex) obtained in elliptical nanoring. The onion state can be used to record information in MRAM. And it is important to investigate the dynamic susceptibility spectra of onion state, which is closely related to writing and reading speed of magnetic memory devices. Those results show that two or three resonance peaks are found under different thickness of elliptical nanoring with onion state, respectively. The low resonance frequency of two resonance peaks is increasing with the arm width of the elliptical ring, but is decreasing with the thickness. However, the high frequency of two resonance peaks is decreasing with the arm width of the elliptical ring.
Ellipticity of near-threshold harmonics from stretched molecules.
Li, Weiyan; Dong, Fulong; Yu, Shujuan; Wang, Shang; Yang, Shiping; Chen, Yanjun
2015-11-30
We study the ellipticity of near-threshold harmonics (NTH) from aligned molecules with large internuclear distances numerically and analytically. The calculated harmonic spectra show a broad plateau for NTH which is several orders of magnitude higher than that for high-order harmonics. In particular, the NTH plateau shows high ellipticity at small and intermediate orientation angles. Our analyses reveal that the main contributions to the NTH plateau come from the transition of the electron from continuum states to these two lowest bound states of the system, which are strongly coupled together by the laser field. Besides continuum states, higher excited states also play a role in the NTH plateau, resulting in a large phase difference between parallel and perpendicular harmonics and accordingly high ellipticity of the NTH plateau. The NTH plateau with high intensity and large ellipticity provides a promising manner for generating strong elliptically-polarized extreme-ultraviolet (EUV) pulses. PMID:26698731
Far-infrared mapping of dusty elliptical galaxies
NASA Technical Reports Server (NTRS)
Lees, Joanna F.; Harper, D. A.; Rupen, Michael P.; Knapp, G. R.
1994-01-01
Preliminary results from a program to map the thermal far-infrared emission from cool dust in elliptical galaxies using the Yerkes 60-Channel Camera on the Kuiper Airborne Observatory (KAO) are presented. The 160 micron emission from the elliptical NGC 6542 is apparently extended over the optical galaxy whereas the 100 micron emission is unresolved. This implies a dust temperature gradient consistent with that expected for dust with Galactic properties exposed to the general interstellar radiation field of the elliptical galaxy. Observations of the elliptical NGC 5666 and the NGC 7463/4/5 compact group (consisting of the elliptical NGC 7464, the S0 NGC 7465, and the spiral NGC 7463) are also discussed.
How Does Abundance Affect the Strength of UV Emission in Elliptical Galaxies?
NASA Technical Reports Server (NTRS)
Sonneborn, George (Technical Monitor); Brown, Thomas
2005-01-01
This program used the Far Ultraviolet Spectroscopic Explorer (FUSE) to observe elliptical galaxies with the intention of measuring the chemical abundances in their hot stellar populations. It was designed to complement an earlier FUSE program that observed elliptical galaxies with strong UV emission. The current program originally planned observations of two ellipticals with weak UV emission (M32 and M49). Once FUSE encountered pointing control problems in certain regions of the sky (particularly Virgo, which is very unfortunate for the study of ellipticals in general), M49 was replaced with the bulge of M31, which has a similar UV-to-optical flux ratio as the center of M49. As the closest elliptical galaxy and the one with the weakest UV-to-optical flux ratio, M32 was an obvious choice of target, but M49 was the ideal complementary target, because it has a very low reddening (unlike M32). With the inability of FUSE to point at Virgo, nearly all of the best elliptical galaxies (bright galaxies with low foreground extinction) were also lost, and this severely hampered three FUSE programs of the PI, all focused on the hot stellar populations of ellipticals. M31 was the best replacement for M49, but like M32, it suffers from significant foreground reddening. Strong Galactic ISM lines heavily contaminate the FUSE spectra of M31 and M32. These ISM lines are coincident with the photospheric lines from the stellar populations (whereas M49, with little foreground ISM and significant redshift, would not have suffered from this problem). We have reduced the faint (and thus difficult) data for M31 and M32, producing final co-added spectra representing all of the exposures, but we have not yet finished our analysis, due to the complication of the contaminating ISM. The silver lining here is the set of CHI lines at 1175 Angstroms, which are not significantly contaminated by the ISM. A comparison of the M31 spectrum with other galaxies observed by FEE showed a surprising result
Shu, Yu; Buster, Thad W.; Taylor, Adam P.; Nelson, Carl A.
2011-01-01
Background The popularity of elliptical training has grown in rehabilitation, fitness, and home settings as a means for improving fitness and walking, yet many people with physical disabilities and chronic conditions experience difficulties when trying to use elliptical trainers. Objective The purpose of this study was to compare, for people with disabilities and chronic conditions, perceptions of safety, comfort, workout, and usability of 4 elliptical trainers before and after the development of a set of low-cost adaptations. Design This study was a quasi-experimental repeated-measures investigation. Methods Twenty adults with diverse medical conditions and functional abilities evaluated 4 elliptical trainers for safety, comfort, workout, and usability. Barriers to the use of the elliptical trainers and solutions to improve the use of the trainers were identified. Prototype modifications were designed, and participants reassessed the same features after the modifications were made. Results An integrated system (steps, bench, side rails, center rail or handle, deeper foot wells, and 1-handed heart rate monitor) was developed. Although at least 25% of participants required physical assistance to get on or off the elliptical trainers before modification, only one required this after modification. Before modification, only 1 participant was able to mount each device independently; after modification, 6 to 8 participants were able to do so. Up to 25% of participants continued to require assistance to initiate or sustain pedal movement. Compared with participants' ratings of the elliptical trainers before modification, those after modification were higher for safety (55% increase in visual analog scale ratings), comfort (43% higher), ability to achieve a good workout (23% greater), and usability (24% increase). Limitations To date, only 4 elliptical trainers have been studied with a small sample of convenience. Conclusions Elliptical trainers posed access challenges to
THE CARNEGIE-IRVINE GALAXY SURVEY. III. THE THREE-COMPONENT STRUCTURE OF NEARBY ELLIPTICAL GALAXIES
Huang, Song; Ho, Luis C.; Peng, Chien Y.; Li, Zhao-Yu; Barth, Aaron J.
2013-03-20
Motivated by recent developments in our understanding of the formation and evolution of massive galaxies, we explore the detailed photometric structure of a representative sample of 94 bright, nearby elliptical galaxies, using high-quality optical images from the Carnegie-Irvine Galaxy Survey. The sample spans a range of environments and stellar masses, from M{sub *} = 10{sup 10.2} to 10{sup 12.0} M{sub Sun }. We exploit the unique capabilities of two-dimensional image decomposition to explore the possibility that local elliptical galaxies may contain photometrically distinct substructure that can shed light on their evolutionary history. Compared with the traditional one-dimensional approach, these two-dimensional models are capable of consistently recovering the surface brightness distribution and the systematic radial variation of geometric information at the same time. Contrary to conventional perception, we find that the global light distribution of the majority ({approx}>75%) of elliptical galaxies is not well described by a single Sersic function. Instead, we propose that local elliptical galaxies generically contain three subcomponents: a compact (R{sub e} {approx}< 1 kpc) inner component with luminosity fraction f Almost-Equal-To 0.1-0.15; an intermediate-scale (R{sub e} Almost-Equal-To 2.5 kpc) middle component with f Almost-Equal-To 0.2-0.25; and a dominant (f = 0.6), extended (R{sub e} Almost-Equal-To 10 kpc) outer envelope. All subcomponents have average Sersic indices n Almost-Equal-To 1-2, significantly lower than the values typically obtained from single-component fits. The individual subcomponents follow well-defined photometric scaling relations and the stellar mass-size relation. We discuss the physical nature of the substructures and their implications for the formation of massive elliptical galaxies.
First-Order System Least-Squares for Second-Order Elliptic Problems with Discontinuous Coefficients
NASA Technical Reports Server (NTRS)
Manteuffel, Thomas A.; McCormick, Stephen F.; Starke, Gerhard
1996-01-01
The first-order system least-squares methodology represents an alternative to standard mixed finite element methods. Among its advantages is the fact that the finite element spaces approximating the pressure and flux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropriate error measure. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. Ellipticity of an appropriately scaled least-squares bilinear form of the size of the jumps in the coefficients leading to adequate finite element approximation results. The occurrence of singularities at interface corners and cross-points is discussed. and a weighted least-squares functional is introduced to handle such cases. Numerical experiments are presented for two test problems to illustrate the performance of this approach.
Supernumerary spacing of rainbows produced by an elliptical-cross-section cylinder. I. Theory.
Lock, J A
2000-09-20
A sequence of rainbows is produced in light scattering by a particle of high symmetry in the short-wavelength limit, and a supernumerary interference pattern occurs to one side of each rainbow. Using both a ray-tracing procedure and the Debye-series decomposition of first-order perturbation wave theory, I examine the spacing of the supernumerary maxima and minima as a function of the cylinder rotation angle when an elliptical-cross-section cylinder is normally illuminated by a plane wave. I find that the supernumerary spacing depends sensitively on the cylinder-cross-section shape, and the spacing varies sinusoidally as a function of the cylinder rotation angle for small cylinder ellipticity. I also find that relatively large uncertainties in the supernumerary spacing affect the rainbow angle only minimally. PMID:18350103
Exact geometric optics in a Morris-Thorne wormhole spacetime
Mueller, Thomas
2008-02-15
The simplicity of the Morris-Thorne wormhole spacetime permits us to determine null and timelike geodesics by means of elliptic integral functions and Jacobian elliptic functions. This analytic solution makes it possible to find a geodesic which connects two distant events. An exact gravitational lensing, an illumination calculation, and even an interactive visualization become possible.
Free vibrations of laminated composite elliptic plates
NASA Technical Reports Server (NTRS)
Andersen, C. M.; Noor, A. K.
1976-01-01
The free vibrations are studied of laminated anisotropic elliptic plates with clamped edges. The analytical formulation is based on a Mindlin-Reissner type plate theory with the effects of transverse shear deformation, rotary inertia, and bending-extensional coupling included. The frequencies and mode shapes are obtained by using the Rayleigh-Ritz technique in conjunction with Hamilton's principle. A computerized symbolic integration approach is used to develop analytic expressions for the stiffness and mass coefficients and is shown to be particularly useful in evaluating the derivatives of the eigenvalues with respect to certain geometric and material parameters. Numerical results are presented for the case of angle-ply composite plates with skew-symmetric lamination.
Splitting of Forced Elliptic Jets and Flames
NASA Technical Reports Server (NTRS)
Hertzberg, J.; Carlton, J.; Schwieterman, M.; Davis, E.; Bradley, E.; Linne, M.
1997-01-01
The objective of this work is to understand the fluid dynamics in the interaction of large scale, three-dimensional vortex structures and transitional diffusion flames in a microgravity environment. The vortex structures are used to provide a known perturbation of the type used in passive and active shear layer control techniques. 'Passive techniques' refers to manipulation of the system geometry to influence the three dimensional dynamics of vortex structures, and 'active' refers to any technique which adds energy (acoustic or kinetic) to the flow to influence the shear layer vortex dynamics. In this work the passive forcing is provided by an elliptic jet cross-section, and the active forcing is incorporated by perturbing the jet velocity using a loudspeaker in the plenum section.
Mobile communications from highly elliptic orbits - ARCHIMEDES
NASA Astrophysics Data System (ADS)
Stuart, John
1992-03-01
ARCHIMEDES is an ongoing telecommunications program of the European Space Agency which considers the use of Highly Elliptic Orbits (HEO) to provide land mobile voice communications in Europe. To date feasibility studies have been completed which indicate the technical and economic viability of such a project. By using HEO orbits a line of sight path between the mobile user and satellite can be maintained even at northerly latitudes where signal fade and blockage will disrupt transmissions to and from a geostationary satellite. British Aerospace has led all the key studies to date and has most recently been concerned with the extension of the service from land mobile voice communications to include Satellite Sound Broadcast (SSB). This paper presents the main conclusions of the feasibility studies comparing the performance which could be achieved with a GEO alternative.
Magnetic elliptical polarization of Schumann resonances
NASA Technical Reports Server (NTRS)
Sentman, D. D.
1987-01-01
Measurements of orthogonal, horizontal components of the magnetic field in the ELF range obtained during September 1985 show that the Schumann resonance eigenfrequencies determined separately for the north-south and east-west magnetic components differ by as much as 0.5 Hz, suggesting that the underlying magnetic signal is not linearly polarized at such times. The high degree of magnetic ellipticity found suggests that the side multiplets of the Schumann resonances corresponding to azimuthally inhomogeneous normal modes are strongly excited in the highly asymmetric earth-ionosphere cavity. The dominant sense of polarization over the measurement passband is found to be right-handed during local daylight hours, and to be left-handed during local nighttime hours.
Nonlinear, dispersive, elliptically polarized Alfven wavaes
NASA Technical Reports Server (NTRS)
Kennel, C. F.; Buti, B.; Hada, T.; Pellat, R.
1988-01-01
The derivative nonlinear Schroedinger (DNLS) equation is derived by an efficient means that employs Lagrangian variables. An expression for the stationary wave solutions of the DNLS that contains vanishing and nonvanishing and modulated and nonmodulated boundary conditions as subcases is then obtained. The solitary wave solutions for elliptically polarized quasiparallel Alfven waves in the magnetohydrodynamic limit (nonvanishing, unmodulated boundary conditions) are obtained. These converge to the Korteweg-de Vries and the modified Korteweg-de Vries solitons obtained previously for oblique propagation, but are more general. It is shown that there are no envelope solitary waves if the point at infinity is unstable to the modulational instability. The periodic solutions of the DNLS are characterized.
Spectral multigrid methods for elliptic equations
NASA Technical Reports Server (NTRS)
Zang, T. A.; Wong, Y. S.; Hussaini, M. Y.
1981-01-01
An alternative approach which employs multigrid concepts in the iterative solution of spectral equations was examined. Spectral multigrid methods are described for self adjoint elliptic equations with either periodic or Dirichlet boundary conditions. For realistic fluid calculations the relevant boundary conditions are periodic in at least one (angular) coordinate and Dirichlet (or Neumann) in the remaining coordinates. Spectral methods are always effective for flows in strictly rectangular geometries since corners generally introduce singularities into the solution. If the boundary is smooth, then mapping techniques are used to transform the problem into one with a combination of periodic and Dirichlet boundary conditions. It is suggested that spectral multigrid methods in these geometries can be devised by combining the techniques.
Ultrasonic guided waves in elliptical annular cylinders.
Rajagopal, Prabhu; Pattanayak, Roson Kumar
2015-09-01
This paper studies the influence of cross-section ovalness or ellipticity on lower order axisymmetric guided wave modes in thin pipes. The second longitudinal mode L(0,2) and the fundamental torsional mode T(0,1) are studied, as these are of interest to current pipe inspection. The semi-analytical finite element (FE) method is mainly used, with three-dimensional FE simulations for visualization and cross-validation of results. The studies reveal that even a small degree of ovalness can affect mode shapes and velocities. The effect is more pronounced on the L(0,2) mode than on T(0,1) and this may be important for practical inspection applications. PMID:26428836
Ultrasonic guided waves in elliptical annular cylinders.
Rajagopal, Prabhu; Pattanayak, Roson Kumar
2015-09-01
This paper studies the influence of cross-section ovalness or ellipticity on lower order axisymmetric guided wave modes in thin pipes. The second longitudinal mode L(0,2) and the fundamental torsional mode T(0,1) are studied, as these are of interest to current pipe inspection. The semi-analytical finite element (FE) method is mainly used, with three-dimensional FE simulations for visualization and cross-validation of results. The studies reveal that even a small degree of ovalness can affect mode shapes and velocities. The effect is more pronounced on the L(0,2) mode than on T(0,1) and this may be important for practical inspection applications.
Winding light beams along elliptical helical trajectories
NASA Astrophysics Data System (ADS)
Wen, Yuanhui; Chen, Yujie; Zhang, Yanfeng; Chen, Hui; Yu, Siyuan
2016-07-01
Conventional caustic methods in real or Fourier space produced accelerating optical beams only with convex trajectories. We developed a superposition caustic method capable of winding light beams along nonconvex trajectories. We ascertain this method by constructing a one-dimensional (1D) accelerating beam moving along a sinusoidal trajectory, and subsequently extending to two-dimensional (2D) accelerating beams along arbitrarily elliptical helical trajectories. We experimentally implemented the method with a compact and robust integrated optics approach by fabricating micro-optical structures on quartz glass plates to perform the spatial phase and amplitude modulation to the incident light, generating beam trajectories highly consistent with prediction. The theoretical and implementation methods can in principle be extended to the construction of accelerating beams with a wide variety of nonconvex trajectories, thereby opening up a route of manipulating light beams for fundamental research and practical applications.
Products of Independent Elliptic Random Matrices
NASA Astrophysics Data System (ADS)
O'Rourke, Sean; Renfrew, David; Soshnikov, Alexander; Vu, Van
2015-07-01
For fixed , we study the product of independent elliptic random matrices as tends to infinity. Our main result shows that the empirical spectral distribution of the product converges, with probability , to the -th power of the circular law, regardless of the joint distribution of the mirror entries in each matrix. This leads to a new kind of universality phenomenon: the limit law for the product of independent random matrices is independent of the limit laws for the individual matrices themselves. Our result also generalizes earlier results of Götze-Tikhomirov (On the asymptotic spectrum of products of independent random matrices, available at http://arxiv.org/abs/1012.2710) and O'Rourke-Soshnikov (J Probab 16(81):2219-2245, 2011) concerning the product of independent iid random matrices.
Interior models of Mercury with equatorial ellipticity
NASA Astrophysics Data System (ADS)
Dumberry, M.
2012-09-01
The combination of planetary rotation observations and gravity field measurements by the MESSENGER spacecraft can be used to constrain the internal structure of Mercury. A recently published model suggests a mean mantle density of ρm = 3650 ± 225 kg m-3, substantially larger than that expected of a silicate mantle (3300 kg m-3) and possibly hinting at the presence of an FeS-rich layer at the base of the mantle. Here, we show that a large ρm is only required if the core-mantle boundary (CMB) of the planet is assumed axially-symmetric. An equatorial ellipticity of CMB of the order of 2 · 10-5 allows to satisfy gravity and rotation constraints with a mean mantle density typical of silicate material. Possible origin of such topography include past mantle convection, aspherical planetary shrinking, remnant tidal deformation, or a combination thereof.
The outer haloes of massive, elliptical galaxies
NASA Astrophysics Data System (ADS)
Das, Payel; Gerhard, Ortwin; de Lorenzi, Flavio; McNeil, Emily; Churazov, Eugene; Coccato, Lodovico
2010-11-01
The outer haloes of massive elliptical galaxies are dark-matter dominated regions where stellar orbits have longer dynamical timescales than the central regions and therefore better preserve their formation history. Dynamical models out to large radii suffer from a degeneracy between mass and orbital structure, as the outer kinematics are unable to resolve higher moments of the line-of-sight velocity distribution. We mitigate this degeneracy for a sample of quiescent, massive, nearby ellipticals by determining their mass distributions independently using a non-parametric method on X-ray observations of the surrounding hot interstellar medium. We then create dynamical models using photometric and kinematic constraints consisting of integral-eld, long-slit and planetary nebulae (PNe) data extending to ~50 kpc. The rst two galaxies of our sample, NGC 5846 and NGC 1399, were found to have very shallow pro jected light distributions with a power law index of ~1.5 and a dark matter content of 70-80% at 50 kpc. Spherical Jeans models of the data show that, in the outer haloes of both galaxies, the pro jected velocity dispersions are almost inde- pendent of the anisotropy and that the PNe prefer the lower end of the range of mass distributions consistent with the X-ray data. Using the N-body code NMAGIC, we cre- ated axisymmetric models of NGC 5846 using the individual PNe radial velocities in a likelihood method and found them to be more constraining than the binned velocity dispersions. Characterising the orbital structure in terms of spherically averaged proles of the velocity dispersions we nd σψ > σr > σθ.
Discontinuous dual-primal mixed finite elements for elliptic problems
NASA Technical Reports Server (NTRS)
Bottasso, Carlo L.; Micheletti, Stefano; Sacco, Riccardo
2000-01-01
We propose a novel discontinuous mixed finite element formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the element level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed finite element methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.
TRANSVERSE MERCATOR MAP PROJECTION OF THE SPHEROID USING TRANSFORMATION OF THE ELLIPTIC INTEGRAL
NASA Technical Reports Server (NTRS)
Wallis, D. E.
1994-01-01
This program produces the Gauss-Kruger (constant meridional scale) Transverse Mercator Projection which is used to construct the U.S. Army's Universal Transverse Mercator (UTM) Grid System. The method is capable of mapping the entire northern hemisphere of the earth (and, by symmetry of the projection, the entire earth) accurately with respect to a single principal meridian, and is therefore mathematically insensitive to proximity either to the pole or the equator, or to the departure of the meridian from the central meridian. This program could be useful to any map-making agency. The program overcomes the limitations of the "series" method (Thomas, 1952) presently used to compute the UTM Grid, specifically its complicated derivation, non-convergence near the pole, lack of rigorous error analysis, and difficulty of obtaining increased accuracy. The method is based on the principle that the parametric colatitude of a point is the amplitude of the Elliptic Integral of the 2nd Kind, and this (irreducible) integral is the desired projection. Thus, a specification of the colatitude leads, most directly (and with strongest motivation) to a formulation in terms of amplitude. The most difficult problem to be solved was setting up the method so that the Elliptic Integral of the 2nd Kind could be used elsewhere than on the principal meridian. The point to be mapped is specified in conventional geographic coordinates (geodetic latitude and longitudinal departure from the principal meridian). Using the colatitude (complement of latitude) and the longitude (departure), the initial step is to map the point to the North Polar Stereographic Projection. The closed-form, analytic function that coincides with the North Polar Stereographic Projection of the spheroid along the principal meridian is put into a Newton-Raphson iteration that solves for the tangent of one half the parametric colatitude, generalized to the complex plane. Because the parametric colatitude is the amplitude of
NASA Astrophysics Data System (ADS)
Shi, Zhong; Huang, Xuexiang; Hu, Tianjian; Tan, Qian; Hou, Yuzhuo
2016-10-01
Space teleoperation is an important space technology, and human-robot motion similarity can improve the flexibility and intuition of space teleoperation. This paper aims to obtain an appropriate kinematics mapping method of coupled Cartesian-joint space for space teleoperation. First, the coupled Cartesian-joint similarity principles concerning kinematics differences are defined. Then, a novel weighted augmented Jacobian matrix with a variable coefficient (WAJM-VC) method for kinematics mapping is proposed. The Jacobian matrix is augmented to achieve a global similarity of human-robot motion. A clamping weighted least norm scheme is introduced to achieve local optimizations, and the operating ratio coefficient is variable to pursue similarity in the elbow joint. Similarity in Cartesian space and the property of joint constraint satisfaction is analysed to determine the damping factor and clamping velocity. Finally, a teleoperation system based on human motion capture is established, and the experimental results indicate that the proposed WAJM-VC method can improve the flexibility and intuition of space teleoperation to complete complex space tasks.
Dusty Feedback from Massive Black Holes in Two Elliptical Galaxies
NASA Technical Reports Server (NTRS)
Temi, P.; Brighenti, F.; Mathews, W. G.; Amblard, A.; Riguccini, L.
2013-01-01
Far-infrared dust emission from elliptical galaxies informs us about galaxy mergers, feedback energy outbursts from supermassive black holes and the age of galactic stars. We report on the role of AGN feedback observationally by looking for its signatures in elliptical galaxies at recent epochs in the nearby universe. We present Herschel observations of two elliptical galaxies with strong and spatially extended FIR emission from colder grains 5-10 kpc distant from the galaxy cores. Extended excess cold dust emission is interpreted as evidence of recent feedback-generated AGN energy outbursts in these galaxies, visible only in the FIR, from buoyant gaseous outflows from the galaxy cores.
Global variational approach to elliptic transport barriers in three dimensions.
Oettinger, David; Blazevski, Daniel; Haller, George
2016-03-01
We introduce an approach to identify elliptic transport barriers in three-dimensional, time-aperiodic flows. Obtained as Lagrangian Coherent Structures (LCSs), the barriers are tubular non-filamenting surfaces that form and bound coherent material vortices. This extends a previous theory of elliptic LCSs as uniformly stretching material surfaces from two-dimensional to three-dimensional flows. Specifically, we obtain explicit expressions for the normals of pointwise (near-) uniformly stretching material surfaces over a finite time interval. We use this approach to visualize elliptic LCSs in steady and time-aperiodic ABC-type flows. PMID:27036192
Single optical tweezers based on elliptical core fiber
NASA Astrophysics Data System (ADS)
Zhang, Yu; Zhao, Li; Chen, Yunhao; Liu, Zhihai; Zhang, Yaxun; Zhao, Enming; Yang, Jun; Yuan, Libo
2016-04-01
We propose and demonstrate a new single optical tweezers based on an elliptical core fiber, which can realize the trapped yeast cell rotation with a precise and simple control. Due to the elliptical shape of the fiber core, the LP11 mode beam can propagate stably. When we rotate the fiber tip, the LP11 mode beam will also rotate along with the fiber tip, which helps to realize the trapped micro-particle rotation. By using this method, we can easily realize the rotation of the trapped yeast cells, the rotating angle of the yeast cell is same as the elliptical core fiber tip.
Global variational approach to elliptic transport barriers in three dimensions
NASA Astrophysics Data System (ADS)
Oettinger, David; Blazevski, Daniel; Haller, George
2016-03-01
We introduce an approach to identify elliptic transport barriers in three-dimensional, time-aperiodic flows. Obtained as Lagrangian Coherent Structures (LCSs), the barriers are tubular non-filamenting surfaces that form and bound coherent material vortices. This extends a previous theory of elliptic LCSs as uniformly stretching material surfaces from two-dimensional to three-dimensional flows. Specifically, we obtain explicit expressions for the normals of pointwise (near-) uniformly stretching material surfaces over a finite time interval. We use this approach to visualize elliptic LCSs in steady and time-aperiodic ABC-type flows.
New Elliptic Solutions of the Yang-Baxter Equation
NASA Astrophysics Data System (ADS)
Chicherin, D.; Derkachov, S. E.; Spiridonov, V. P.
2016-07-01
We consider finite-dimensional reductions of an integral operator with the elliptic hypergeometric kernel describing the most general known solution of the Yang-Baxter equation with a rank 1 symmetry algebra. The reduced R-operators reproduce at their bottom the standard Baxter's R-matrix for the 8-vertex model and Sklyanin's L-operator. The general formula has a remarkably compact form and yields new elliptic solutions of the Yang-Baxter equation based on the finite-dimensional representations of the elliptic modular double. The same result is also derived using the fusion formalism.
Design of high-order elliptic filter from a versatile mode generic OTA-C structure
NASA Astrophysics Data System (ADS)
Ghosh, K.; Ray, B. N.
2015-03-01
A new synthesis methodology for high-order versatile mode programmable Operational transconductance amplifier and capacitor (OTA-C) generic filter structure is proposed. The structure fulfills the three main criteria of high frequency operation i.e it uses (1) less number of components (2) only single ended input OTAs (3) only grounded capacitors. Any nth order transfer function can be realised from it. Elliptic filter is designed from the generic structure using optimisation technique to reduce the number of OTAs. SPICE simulation with BSIM level 53 model and 0.13 μm process confirms the theoretical analysis. Frequency response of third-order and fourth-order elliptic filter is shown as representative set of simulated result. Sensitivity and non-ideal effect of the designed filter are studied.
Formation Design Strategy for SCOPE High-Elliptic Formation Flying Mission
NASA Technical Reports Server (NTRS)
Tsuda, Yuichi
2007-01-01
The new formation design strategy using simulated annealing (SA) optimization is presented. The SA algorithm is useful to survey a whole solution space of optimum formation, taking into account realistic constraints composed of continuous and discrete functions. It is revealed that this method is not only applicable for circular orbit, but also for high-elliptic orbit formation flying. The developed algorithm is first tested with a simple cart-wheel motion example, and then applied to the formation design for SCOPE. SCOPE is the next generation geomagnetotail observation mission planned in JAXA, utilizing a formation flying techonology in a high elliptic orbit. A distinctive and useful heuristics is found by investigating SA results, showing the effectiveness of the proposed design process.
Hertel, I. V.; Shchatsinin, I.; Laarmann, T.; Zhavoronkov, N.; Ritze, H.-H.; Schulz, C. P.
2009-01-16
Ionization and fragmentation of C{sub 60} fullerenes is studied in elliptically polarized, intense fs laser fields at 797 nm [I=(0.5-4.3)x10{sup 14} W cm{sup -2}] and contrasted with Xe{sup +}, utilizing time-of-flight mass spectrometry. Very pronounced changes of parent and fragment ion yield as a function of ellipticity are observed. At lower intensities reduction of the ion yield for circular polarization establishes a coherent two-photon process connected with the key role of the LUMO+1(t{sub 1g})'doorway state' and multielectron dynamics. Comparison with the behavior at 399 nm corroborates this finding. At high intensities enhanced fragmentation is observed which is tentatively attributed to returning loops of electron trajectories by the combined action of the C{sub 60}{sup +} field and the circular laser field.
Trace Formula for Linear Hamiltonian Systems with its Applications to Elliptic Lagrangian Solutions
NASA Astrophysics Data System (ADS)
Hu, Xijun; Ou, Yuwei; Wang, Penghui
2015-04-01
In the present paper, we build up trace formulas for both the linear Hamiltonian systems and Sturm-Liouville systems. The formula connects the monodromy matrix of a symmetric periodic orbit with the infinite sum of eigenvalues of the Hessian of the action functional. A natural application is to study the non-degeneracy of linear Hamiltonian systems. Precisely, by the trace formula, we can give an estimation for the upper bound such that the non-degeneracy preserves. Moreover, we could estimate the relative Morse index by the trace formula. Consequently, a series of new stability criteria for the symmetric periodic orbits is given. As a concrete application, the trace formula is used to study the linear stability of elliptic Lagrangian solutions of the classical planar three-body problem, which depends on the mass parameter and the eccentricity . Based on the trace formula, we estimate the stable region and hyperbolic region of the elliptic Lagrangian solutions.
Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem
NASA Astrophysics Data System (ADS)
Lakshtanov, E.; Vainberg, B.
2013-10-01
The paper concerns the isotropic interior transmission eigenvalue (ITE) problem. This problem is not elliptic, but we show that, using the Dirichlet-to-Neumann map, it can be reduced to an elliptic one. This leads to the discreteness of the spectrum as well as to certain results on a possible location of the transmission eigenvalues. If the index of refraction \\sqrt{n(x)} is real, then we obtain a result on the existence of infinitely many positive ITEs and the Weyl-type lower bound on its counting function. All the results are obtained under the assumption that n(x) - 1 does not vanish at the boundary of the obstacle or it vanishes identically, but its normal derivative does not vanish at the boundary. We consider the classical transmission problem as well as the case when the inhomogeneous medium contains an obstacle. Some results on the discreteness and localization of the spectrum are obtained for complex valued n(x).
Transition on elliptic cones at Mach 8
NASA Astrophysics Data System (ADS)
Huntley, Mark Bradford
2000-10-01
Flow visualizations of boundary layer transition on two sharp-nosed elliptic cones at Mach 8 are presented. The elliptic cone is a relevant three-dimensional flow field since it represents a generic hypersonic lifting vehicle shape. Experiments utilize carbon dioxide enhanced Filtered Rayleigh scattering to produce planar single-shot and motion picture images. CO2 is injected into the flow upstream of the tunnel stagnation chamber and subsequently condenses into nanoscale clusters during the nozzle expansion process. The clusters sublimate as they enter the hot boundary layer, and Rayleigh images capture the interface that exists between the regions of condensed (freestream) and sublimated (boundary layer) carbon dioxide. Boundary layers ranging from laminar to late-transitional in character are imaged using streamwise, spanwise, and planform laser sheet orientations. Characteristics of observed instabilities are quantified using pdf profiles, power spectrum analysis, and autocorrelation results derived from single-shot images. A new MHz-rate imaging system is also used to produce motion pictures images and volumetric reconstructions of the boundary layer. The pressure gradient and associated crossflow from the major axis to the minor axis of the cone causes increased growth and subsequent early transition of the centerline boundary layer. The convection velocity and temporal evolution of structures appearing on both the centerline and off-axis regions is studied using cross correlation procedures. Volumetric image sets of the centerline reveal hairpin structures characteristic of the early stages of subsonic turbulent spot formation. In the off-axis regions, planform single-shot images reveal a pattern of finger-like crests in the boundary layer. At higher Reynolds numbers the breakdown of these crests involves the formation of a series of chain-like structures. The behavior appears qualitatively similar to visualizations of crossflow vortex breakdown in
Mitri, F G
2016-03-01
This work proposes a formal analytical theory using the partial-wave series expansion (PWSE) method in cylindrical coordinates, to calculate the acoustic backscattering form function as well as the radiation force-per-length on an infinitely long elliptical (non-circular) cylinder in plane progressive waves. The major (or minor) semi-axis of the ellipse coincides with the direction of the incident waves. The scattering coefficients for the rigid elliptical cylinder are determined by imposing the Neumann boundary condition for an immovable surface and solving a resulting system of linear equations by matrix inversion. The present method, which utilizes standard cylindrical (Bessel and Hankel) wave functions, presents an advantage over the solution for the scattering that is ordinarily expressed in a basis of elliptical Mathieu functions (which are generally non-orthogonal). Furthermore, an integral equation showing the direct connection of the radiation force function with the square of the scattering form function in the far-field from the scatterer (applicable for plane waves only), is noted and discussed. An important application of this integral equation is the adequate evaluation of the radiation force function from a bistatic measurement (i.e., in the polar plane) of the far-field scattering from any 2D object of arbitrary shape. Numerical predictions are evaluated for the acoustic backscattering form function and the radiation force function, which is the radiation force per unit length, per characteristic energy density, and per unit cross-sectional surface of the ellipse, with particular emphasis on the aspect ratio a/b, where a and b are the semi-axes, as well as the dimensionless size parameter kb, without the restriction to a particular range of frequencies. The results are particularly relevant in acoustic levitation, acousto-fluidics and particle dynamics applications. PMID:26726146
Mitri, F G
2016-03-01
This work proposes a formal analytical theory using the partial-wave series expansion (PWSE) method in cylindrical coordinates, to calculate the acoustic backscattering form function as well as the radiation force-per-length on an infinitely long elliptical (non-circular) cylinder in plane progressive waves. The major (or minor) semi-axis of the ellipse coincides with the direction of the incident waves. The scattering coefficients for the rigid elliptical cylinder are determined by imposing the Neumann boundary condition for an immovable surface and solving a resulting system of linear equations by matrix inversion. The present method, which utilizes standard cylindrical (Bessel and Hankel) wave functions, presents an advantage over the solution for the scattering that is ordinarily expressed in a basis of elliptical Mathieu functions (which are generally non-orthogonal). Furthermore, an integral equation showing the direct connection of the radiation force function with the square of the scattering form function in the far-field from the scatterer (applicable for plane waves only), is noted and discussed. An important application of this integral equation is the adequate evaluation of the radiation force function from a bistatic measurement (i.e., in the polar plane) of the far-field scattering from any 2D object of arbitrary shape. Numerical predictions are evaluated for the acoustic backscattering form function and the radiation force function, which is the radiation force per unit length, per characteristic energy density, and per unit cross-sectional surface of the ellipse, with particular emphasis on the aspect ratio a/b, where a and b are the semi-axes, as well as the dimensionless size parameter kb, without the restriction to a particular range of frequencies. The results are particularly relevant in acoustic levitation, acousto-fluidics and particle dynamics applications.
Elliptic Solvers with Adaptive Mesh Refinement on Complex Geometries
Phillip, B.
2000-07-24
Adaptive Mesh Refinement (AMR) is a numerical technique for locally tailoring the resolution computational grids. Multilevel algorithms for solving elliptic problems on adaptive grids include the Fast Adaptive Composite grid method (FAC) and its parallel variants (AFAC and AFACx). Theory that confirms the independence of the convergence rates of FAC and AFAC on the number of refinement levels exists under certain ellipticity and approximation property conditions. Similar theory needs to be developed for AFACx. The effectiveness of multigrid-based elliptic solvers such as FAC, AFAC, and AFACx on adaptively refined overlapping grids is not clearly understood. Finally, a non-trivial eye model problem will be solved by combining the power of using overlapping grids for complex moving geometries, AMR, and multilevel elliptic solvers.
Stable equilibria of elliptic roly-poly toys
NASA Astrophysics Data System (ADS)
Hong, Seok-In
2016-11-01
As an instructive (gravitational potential) energy approach, we show that the elliptic roly-poly has a richer and more useful profile (including the tilted configuration) of stable equilibria than conventional spherical or cylindrical roly-polys.
Effect of flow fluctuations and nonflow on elliptic flow methods
Ollitrault, Jean-Yves; Poskanzer, Arthur M.; Voloshin, Sergei A.
2009-04-16
We discuss how the different estimates of elliptic flow are influenced by flow fluctuations and nonflow effects. It is explained why the event-plane method yields estimates between the two-particle correlation methods and the multiparticle correlation methods. It is argued that nonflow effects and fluctuations cannot be disentangled without other assumptions. However, we provide equations where, with reasonable assumptions about fluctuations and nonflow, all measured values of elliptic flow converge to a unique mean v_2,PP elliptic flow in the participant plane and, with a Gaussian assumption on eccentricity fluctuations, can be converted to the mean v_2,RP in the reaction plane. Thus, the 20percent spread in observed elliptic flow measurements from different analysis methods is no longer mysterious.
Iterative methods for elliptic finite element equations on general meshes
NASA Technical Reports Server (NTRS)
Nicolaides, R. A.; Choudhury, Shenaz
1986-01-01
Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included.
Toric elliptic fibrations and F-theory compactifications
NASA Astrophysics Data System (ADS)
Braun, Volker
2013-01-01
The 102,581 flat toric elliptic fibrations over {{{P}}^2} are identified among the Calabi-Yau hypersurfaces that arise from the 473,800,776 reflexive 4-dimensional polytopes. In order to analyze their elliptic fibration structure, we describe the precise relation between the lattice polytope and the elliptic fibration. The fiber-divisor-graph is introduced as a way to visualize the embedding of the Kodaira fibers in the ambient toric fiber. In particular in the case of non-split discriminant components, this description is far more accurate than previous studies. The discriminant locus and Kodaira fibers of all 102,581 elliptic fibrations are computed. The maximal gauge group is SU(27), which would naively be in contradiction with 6-dimensional anomaly cancellation.
21. AN IMAGE OF THE FIRST LARGE, ELLIPTICAL RING ARCH ...
21. AN IMAGE OF THE FIRST LARGE, ELLIPTICAL RING ARCH ON THE WEST END OF THE BRIDGE. THE PARKWAY PASSES BENEATH A MINOR ARCH BEYOND. - Main Street Bridge, Spanning East Fork Whitewater River, Richmond, Wayne County, IN
Elliptical dichroism: operating principle of planar chiral metamaterials.
Zhukovsky, Sergei V; Novitsky, Andrey V; Galynsky, Vladimir M
2009-07-01
We employ a homogenization technique based on the Lorentz electronic theory to show that planar chiral structures (PCSs) can be described by an effective dielectric tensor similar to that of biaxial elliptically dichroic crystals. Such a crystal is shown to behave like a PCS insofar as it exhibits its characteristic optical properties, namely, corotating elliptical polarization eigenstates and asymmetric, direction-dependent transmission for left- or right-handed incident wave polarization.
Scatter of elastic waves by a thin flat elliptical inhomogeneity
NASA Technical Reports Server (NTRS)
Fu, L. S.
1983-01-01
Elastodynamic fields of a single, flat, elliptical inhomogeneity embedded in an infinite elastic medium subjected to plane time harmonic waves are studied. Scattered displacement amplitudes and stress intensities are obtained in series form for an incident wave in an arbitrary direction. The cases of a penny shaped crack and an elliptical crack are given as examples. The analysis is valid for alpha a up to about two, where alpha is longitudinal wave number and a is a typical geometric parameter.
Bifurcations in elliptical, asymmetric non-neutral plasmas
NASA Astrophysics Data System (ADS)
Fajans, Joel; Gilson, Erik
1999-11-01
When subjected to a stationary, l=2 potential perturbation on the wall, a pure electron plasma will deform into an elliptical shape. At first, the plasma's ellipticity is proportional to the strength of the potential perturbation. Once the perturbation is increased beyond a critical value, the plasma equilibrium bifurcates into two off-axis states. This bifurcation has been observed experimentally and will be described in this poster. (see http://socrates.berkeley.edu/ fajans/EquilStab/EllipseBifurcation.avi)
Banana orbits in elliptic tokamaks with hole currents
NASA Astrophysics Data System (ADS)
Martin, P.; Castro, E.; Puerta, J.
2015-03-01
Ware Pinch is a consequence of breaking of up-down symmetry due to the inductive electric field. This symmetry breaking happens, though up-down symmetry for magnetic surface is assumed. In previous work Ware Pinch and banana orbits were studied for tokamak magnetic surface with ellipticity and triangularity, but up-down symmetry. Hole currents appear in large tokamaks and their influence in Ware Pinch and banana orbits are now considered here for tokamaks magnetic surfaces with ellipticity and triangularity.
Beam-beam deflection and signature curves for elliptic beams
Ziemann, V.
1990-10-22
In this note we will present closed expressions for the beam-beam deflection angle for arbitrary elliptic beams including tilt. From these expressions signature curves, i.e., systematic deviations from the round beam deflection curve due to ellipticity or tilt are derived. In the course of the presentation we will prove that it is generally impossible to infer individual beam sizes from beam-beam deflection scans. 3 refs., 2 figs.
Elliptical dichroism: operating principle of planar chiral metamaterials.
Zhukovsky, Sergei V; Novitsky, Andrey V; Galynsky, Vladimir M
2009-07-01
We employ a homogenization technique based on the Lorentz electronic theory to show that planar chiral structures (PCSs) can be described by an effective dielectric tensor similar to that of biaxial elliptically dichroic crystals. Such a crystal is shown to behave like a PCS insofar as it exhibits its characteristic optical properties, namely, corotating elliptical polarization eigenstates and asymmetric, direction-dependent transmission for left- or right-handed incident wave polarization. PMID:19571975
Remarks of Elliptic Curves Derived from Ant Colony Routing
NASA Astrophysics Data System (ADS)
Jung, Sangsu; Kim, Daeyeoul; Singh, Dhananjay
2011-09-01
We deal with an ant colony based routing model for wireless multi-hop networks. Our model adopts an elliptic curve equation, which is beneficial to design pheromone dynamics for load balancing and packet delivery robustness. Due to the attribute of an elliptic curve equation, our model prevents the over-utilization of a specific node, distinctively from conventional ant colony based schemes. Numerical simulations exhibit the characteristics of our model with respect to various parameters.
Depth-resolved measurements with elliptically polarized reflectance spectroscopy
Bailey, Maria J.; Sokolov, Konstantin
2016-01-01
The ability of elliptical polarized reflectance spectroscopy (EPRS) to detect spectroscopic alterations in tissue mimicking phantoms and in biological tissue in situ is demonstrated. It is shown that there is a linear relationship between light penetration depth and ellipticity. This dependence is used to demonstrate the feasibility of a depth-resolved spectroscopic imaging using EPRS. The advantages and drawbacks of EPRS in evaluation of biological tissue are analyzed and discussed. PMID:27446712
Formation and Evolution of Dwarf Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Chilingarian, Igor
2006-11-01
This thesis presents observational studies of evolution of dwarf elliptical galaxies. dE's are numerically dominant population in clusters of galaxies, but their origin and evolution is a matter of debate. Several scenarios of gas removal from dE's exist: galactic winds, ram pressure stripping, gravitaional harassment. We present new method to estimate stellar population parameters and internal kinematics, based on fitting observed spectra in the pixel space by PEGASE.HR synthetic populations. We apply this technique to 3D-spectroscopic observations of dE galaxies in the Virgo cluster and nearby groups and multiobject spectroscopy of several dozens of dE's in the Abell 496 cluster. We present discovery of young nuclei in bright dE galaxies in the Virgo cluster. Based on the analysis of observational data we conclude that: (1) there is an evolutionary connection between dE's and dIrr's, (2) the most probable scenario of gas removal is ram pressure stripping by the intergalactic medium.
Stress Analysis of Composite Cylindrical Shells With an Elliptical Cutout
NASA Technical Reports Server (NTRS)
Nemeth, M. P.; Oterkus, E.; Madenci, E.
2005-01-01
A special-purpose, semi-analytical solution method for determining the stress and deformation fields in a thin laminated-composite cylindrical shell with an elliptical cutout is presented. The analysis includes the effects of cutout size, shape, and orientation; nonuniform wall thickness; oval-cross-section eccentricity; and loading conditions. The loading conditions include uniform tension, uniform torsion, and pure bending. The analysis approach is based on the principle of stationary potential energy and uses Lagrange multipliers to relax the kinematic admissibility requirements on the displacement representations through the use of idealized elastic edge restraints. Specifying appropriate stiffness values for the elastic extensional and rotational edge restraints (springs) allows the imposition of the kinematic boundary conditions in an indirect manner, which enables the use of a broader set of functions for representing the displacement fields. Selected results of parametric studies are presented for several geometric parameters that demonstrate that analysis approach is a powerful means for developing design criteria for laminated-composite shells.
Stress Analysis of Composite Cylindrical Shells with an Elliptical Cutout
NASA Technical Reports Server (NTRS)
Oterkus, E.; Madenci, E.; Nemeth, M. P.
2007-01-01
A special-purpose, semi-analytical solution method for determining the stress and deformation fields in a thin laminated-composite cylindrical shell with an elliptical cutout is presented. The analysis includes the effects of cutout size, shape, and orientation; non-uniform wall thickness; oval-cross-section eccentricity; and loading conditions. The loading conditions include uniform tension, uniform torsion, and pure bending. The analysis approach is based on the principle of stationary potential energy and uses Lagrange multipliers to relax the kinematic admissibility requirements on the displacement representations through the use of idealized elastic edge restraints. Specifying appropriate stiffness values for the elastic extensional and rotational edge restraints (springs) allows the imposition of the kinematic boundary conditions in an indirect manner, which enables the use of a broader set of functions for representing the displacement fields. Selected results of parametric studies are presented for several geometric parameters that demonstrate that analysis approach is a powerful means for developing design criteria for laminated-composite shells.
Eccentricity fluctuations in an integrated hybrid approach: Influence on elliptic flow
Petersen, Hannah; Bleicher, Marcus
2010-04-15
The effects of initial state fluctuations on elliptic flow are investigated within a (3+1)-dimensional Boltzmann+hydrodynamics transport approach. The spatial eccentricity (epsilon{sub RP} and epsilon{sub part}) is calculated for initial conditions generated by a hadronic transport approach (ultrarelativistic quantum molecular dynamics). Elliptic flow results as a function of impact parameter, beam energy, and transverse momentum for two different equations of state and for averaged initial conditions or a full event-by-event setup are presented. These investigations allow the conclusion that in mid-central (b=5-9 fm) heavy-ion collisions the final elliptic flow is independent of the initial state fluctuations and the equation of state. Furthermore, it is demonstrated that most of the v{sub 2} is built up during the hydrodynamic stage of the evolution. Therefore, the use of averaged initial profiles does not contribute to the uncertainties of the extraction of transport properties of hot and dense QCD matter based on viscous hydrodynamic calculations.
Acoustic scattering by elastic cylinders of elliptical cross-section and splitting up of resonances
Ancey, S. Bazzali, E. Gabrielli, P. Mercier, M.
2014-05-21
The scattering of a plane acoustic wave by an infinite elastic cylinder of elliptical cross section is studied from a modal formalism by emphasizing the role of the symmetries. More precisely, as the symmetry is broken in the transition from the infinite circular cylinder to the elliptical one, the splitting up of resonances is observed both theoretically and experimentally. This phenomenon can be interpreted using group theory. The main difficulty stands in the application of this theory within the framework of the vectorial formalism in elastodynamics. This method significantly simplifies the numerical treatment of the problem, provides a full classification of the resonances, and gives a physical interpretation of the splitting up in terms of symmetry breaking. An experimental part based on ultrasonic spectroscopy complements the theoretical study. A series of tank experiments is carried out in the case of aluminium elliptical cylinders immersed in water, in the frequency range 0 ≤ kr ≤ 50, where kr is the reduced wave number in the fluid. The symmetry is broken by selecting various cylinders of increasing eccentricity. More precisely, the greater the eccentricity, the higher the splitting up of resonances is accentuated. The experimental results provide a very good agreement with the theoretical ones, the splitting up is observed on experimental form functions, and the split resonant modes are identified on angular diagrams.
A PAndAS view of the resolved stellar populations in M31 dwarf elliptical satellites
NASA Astrophysics Data System (ADS)
Crnojević, D.; PAndAS Collaboration
We present the first truly global view of the closest elliptical galaxies, the dwarf elliptical (dE) companions of M31 NGC147 and NGC185. We exploit the deep PAndAS photometric dataset in order to investigate the resolved stellar content and structure of these dEs out to larger distances than ever previously probed. From the analysis of their old red giant branch stars, we derive density maps, full surface brightness profiles and metallicity distribution functions. We find that NGC147 shows pronounced tidal tails likely due to its interaction with M31, while NGC185 retains a regular elliptical shape over its entire extent. The two dEs follow a Sersic profile out to ˜5 kpc, and the effective radii derived in this study are a factor of two larger than previous literature values. While NGC185 shows a significant gradient in metallicity (˜-0.05 dex/kpc), this is almost absent in NGC147. The detailed understanding of nearby dEs is crucial for the studies of more distant objects, and we discuss how internal and environmental processes could have influenced the evolution of NGC147 and NGC185 in light of our results.
Bernsen, Erik; Dijkstra, Henk A.; Thies, Jonas; Wubs, Fred W.
2010-10-20
In present-day forward time stepping ocean-climate models, capturing both the wind-driven and thermohaline components, a substantial amount of CPU time is needed in a so-called spin-up simulation to determine an equilibrium solution. In this paper, we present methodology based on Jacobian-Free Newton-Krylov methods to reduce the computational time for such a spin-up problem. We apply the method to an idealized configuration of a state-of-the-art ocean model, the Modular Ocean Model version 4 (MOM4). It is shown that a typical speed-up of a factor 10-25 with respect to the original MOM4 code can be achieved and that this speed-up increases with increasing horizontal resolution.
NASA Astrophysics Data System (ADS)
Holden, B. P.; Franx, M.; Illingworth, G. D.; Postman, M.; van der Wel, A.; Kelson, D. D.; Blakeslee, J. P.; Ford, H.; Demarco, R.; Mei, S.
2009-03-01
We have compiled a sample of early-type cluster galaxies from 0 < z < 1.3 and measured the evolution of their ellipticity distributions. Our sample contains 487 galaxies in 17 z>0.3 clusters with high-quality space-based imaging and a comparable sample of 210 galaxies in 10 clusters at z < 0.05. We select early-type galaxies (elliptical and S0 galaxies) that fall within the cluster R 200, and which lie on the red-sequence in the magnitude range -19.3>MB > - 21, after correcting for luminosity evolution as measured by the fundamental plane. Our ellipticity measurements are made in a consistent manner over our whole sample. We perform extensive simulations to quantify the systematic and statistical errors, and find that it is crucial to use point-spread function (PSF)-corrected model fits; determinations of the ellipticity from Hubble Space Telescope image data that do not account for the PSF "blurring" are systematically and significantly biased to rounder ellipticities at redshifts z>0.3. We find that neither the median ellipticity, nor the shape of the ellipticity distribution of cluster early-type galaxies evolves with redshift from z ~ 0 to z>1 (i.e., over the last ~8 Gyr). The median ellipticity at z>0.3 is statistically identical with that at z < 0.05, being higher by only 0.01 ± 0.02 or 3 ± 6%, while the distribution of ellipticities at z>0.3 agrees with the shape of the z < 0.05 distribution at the 1-2% level (i.e., the probability that they are drawn from the same distribution is 98-99%). These results are strongly suggestive of an unchanging overall bulge-to-disk ratio distribution for cluster early-type galaxies over the last ~8 Gyr from z ~ 1 to z ~ 0. This result contrasts with that from visual classifications which show that the fraction of morphologically-selected disk-dominated early-type galaxies, or S0s, is significantly lower at z>0.4 than at z ~ 0. We find that the median disk-dominated early-type, or S0, galaxy has a somewhat higher
Line-of-Sight Velocity Distributions of Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Bender, R.; Saglia, R. P.; Gerhard, O. E.
1994-08-01
The line-of-sight velocity distributions (LOSVDs) have been measured to > R_e_/2 along the major axes of 44 elliptical galaxies (more than 80 per cent of all ellipticals north of δ = -10^deg^ and brighter than B_T_ = 12.0), together with stellar rotational velocity and velocity dispersion profiles. For 19 of these 44 objects, minor axis profiles are also given. Monte Carlo simulations have been used to estimate errors. LOSVDs are found to deviate from Gaussians by no more than ~10 per cent. If rotation is present, LOSVDs are asymmetric with the prograde wings being always steeper than the retrograde wings. The degree of asymmetry (measured by the H_3_ Gauss-Hermite coefficient) correlates with ν/σ. Round and boxy ellipticals have lower asymmetries than flat and discy ones. On the whole, both types must have intrinsically asymmetric velocity distributions. Symmetric deviations (measured by the H_4_ Gauss-Hermite coefficient) are generally smaller than asymmetric ones. On the basis of the observed LOSVD shapes, the validity of two- integral models can be ruled out for most of the non-discy objects observed here (discy ellipticals require detailed modelling before similar conclusions can be drawn). Discy ellipticals have H_3_ and H_4_ major and minor axis profiles which appear consistent with a bulge+disc superposition. The observed H_4_ profile in M87 argues for radially anisotropic spherical or oblate models. Velocity dispersion profiles show significant individuality, but typically become flat outside R_e_/4. Major and minor axis slopes are mostly correlated one to one. We confirm that, with increasing luminosity, ellipticals become more anisotropic and that discy ellipticals have more rotational support. The Fundamental Plane of elliptical galaxies is tighter if total kinetic energy is used instead of central velocity dispersion. Both the small scatter about the Fundamental Plane and the homogenous and systematic properties of the LOSVDs imply that only a small
Elliptic Cones Alone and with Wings at Supersonic Speed
NASA Technical Reports Server (NTRS)
Jorgensen, Leland H
1958-01-01
To help fill the gap in the knowledge of aerodynamics of shapes intermediate between bodies of revolution and flat triangular wings, force and moment characteristics for elliptic cones have been experimentally determined for Mach numbers of 1.97 and 2.94. Elliptic cones having cross-sectional axis ratios from 1 through 6 and with lengths and base areas equal to circular cones of fineness ratios 3.67 and 5 have been studied for angles of bank of 0 degree and 90 degrees. Elliptic and circular cones in combination with triangular wings of aspect ratios 1 and 1.5 also have been considered. The angle-of-attack range was from 0 degree to about 16 degrees, and the Reynolds number was 8 x 10(6), based on model length. In addition to the forces and moments at angle of attack, pressure distributions for elliptic cones at zero angle of attack have been determined. The results of this investigation indicate that there are distinct aerodynamic advantages to the use of elliptic cones.
Elliptic interface problem solved using the mixed finite element method
NASA Astrophysics Data System (ADS)
Wang, Shuqiang
2007-05-01
The elliptic boundary value/interface problem is very important in many applications, for example, in incompressible flow and MHD. Many methods are used to solve these problems in a complex domain, including the finite volume method, the finite element method and the boundary element method. For a complex computational domain, the better choice of the partition of the computational domain is to use an unstructured grid. However, it is not a straight forward task to implement a mesh generation program. Such a program requires extra computing time and resources (such as computer memory). Thus people like to use a structured mesh if possible, especially a cartesian mesh. Popular methods using structured cartesian grids for the elliptic boundary value/interface problem include the immersed boundary method, the immersed interface method, the ghost fluid method, and the embedded boundary method. This thesis solves the elliptic problem using several versions of the mixed nite element method on an unstructured mesh. The results are compared for speed and accuracy to the embedded boundary method. A ghost fluid method for elliptic boundary value/interface problems is also investigated. Finally, a simple test of the 2D Rayleigh-Taylor instability is performed using the FronTier-Lite package. Key Words. Elliptic Boundary Value, Interface, Mesh Generation, Quadtree, Octree, Front Tracking.
Applications of Elliptically Polarized, Few-Cycle Attosecond Pulses
NASA Astrophysics Data System (ADS)
Starace, Anthony F.
2016-05-01
Use of elliptically-polarized light opens the possibility of investigating effects that are not accessible with linearly-polarized pulses. This talk presents two new physical effects that are predicted for ionization of the helium atom by few-cycle, elliptically polarized attosecond pulses. For double ionization of He by an intense elliptically polarized attosecond pulse, we predict a nonlinear dichroic effect (i.e., the difference of the two-electron angular distributions in the polarization plane for opposite helicities of the ionizing pulse) that is sensitive to the carrier-envelope phase, ellipticity, peak intensity I, and temporal duration of the pulse. For single ionization of He by two oppositely circularly polarized, time-delayed attosecond pulses we predict that the photoelectron momentum distributions in the polarization plane have helical vortex structures that are exquisitely sensitive to the time-delay between the pulses, their relative phase, and their handedness. Both of these effects manifest the ability to control the angular distributions of the ionized electrons by means of the attosecond pulse parameters. Our predictions are obtained numerically by solving the six-dimensional two-electron time-dependent Schrödinger equation for the case of elliptically polarized attosecond pulses. They are interpreted analytically by means of perturbation theory analyses of the two ionization processes. This work is supported in part by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), Award No. DE-FG03-96ER14646.
Linear instability in the wake of an elliptic wing
NASA Astrophysics Data System (ADS)
He, Wei; Tendero, Juan Ángel; Paredes, Pedro; Theofilis, Vassilis
2016-07-01
Linear global instability analysis has been performed in the wake of a low aspect ratio three-dimensional wing of elliptic cross section, constructed with appropriately scaled Eppler E387 airfoils. The flow field over the airfoil and in its wake has been computed by full three-dimensional direct numerical simulation at a chord Reynolds number of Rec=1750 and two angles of attack, {AoA}=0° and 5°. Point-vortex methods have been employed to predict the inviscid counterpart of this flow. The spatial BiGlobal eigenvalue problem governing linear small-amplitude perturbations superposed upon the viscous three-dimensional wake has been solved at several axial locations, and results were used to initialize linear PSE-3D analyses without any simplifying assumptions regarding the form of the trailing vortex system, other than weak dependence of all flow quantities on the axial spatial direction. Two classes of linearly unstable perturbations were identified, namely stronger-amplified symmetric modes and weaker-amplified antisymmetric disturbances, both peaking at the vortex sheet which connects the trailing vortices. The amplitude functions of both classes of modes were documented, and their characteristics were compared with those delivered by local linear stability analysis in the wake near the symmetry plane and in the vicinity of the vortex core. While all linear instability analysis approaches employed have delivered qualitatively consistent predictions, only PSE-3D is free from assumptions regarding the underlying base flow and should thus be employed to obtain quantitative information on amplification rates and amplitude functions in this class of configurations.
NASA Technical Reports Server (NTRS)
Silk, J.; Djorgovski, S.; Wyse, R. F. G.; Bruzual A., G.
1986-01-01
A self-consistent treatment of the heating by supernovae associated with star formation in a spherically symmetric cooling flow in a cluster core or elliptical galaxy is presented. An initial stellar mass function similar to that in the solar neighborhood is adopted. Inferred star-formation rates, within the cooling region - typically the inner 100 kpc around dominant galaxies at the centers of cooling flows in XD clusters - are reduced by about a factor of 2, relative to rates inferred when the heat input from star formation is ignored. Truncated initial mass functions (IMFs) are also considered, in which massive star formation is suppressed in accordance with previous treatments, and colors are predicted for star formation in cooling flows associated with central dominant elliptical galaxies and with isolated elliptical galaxies surrounded by gaseous coronae. The low inferred cooling-flow rates around isolated elliptical galaxies are found to be insensitive to the upper mass cutoff in the IMF, provided that the upper mass cutoff exceeds 2 M solar mass. Comparison with observed colors favors a cutoff in the IMF above 1 M solar mass in at least two well-studied cluster cooling flows, but a normal IMF cannot be excluded definitively. Models for NGC 1275 support a young (less than about 3 Gyr) cooling flow. As for the isolated elliptical galaxies, the spread in colors is consistent with a normal IMF. A definitive test of the IMF arising via star formation in cooling flows requires either UV spectral data or supernova searches in the cooling-flow-centered galaxies.
Elliptic jets, part 2. Dynamics of coherent structures: Pairing
NASA Technical Reports Server (NTRS)
Husain, Hyder S.; Hussain, Fazle
1992-01-01
The dynamics of the jet column mode of vortex pairing in the near field of an elliptic jet was investigated. Hot-wire measurements and flow visualization were used to examine the details of the pairing mechanism of nonplanar vortical elliptic structures and its effect on such turbulence measures as coherent velocities, incoherent turbulence intensities, incoherent and coherent Reynolds, stresses, turbulence production, and mass entrainment. It was found that pairing of elliptic vortices in the jet column does not occur uniformly around the entire perimeter, unlike in a circular jet. Merger occurs only in the initial major-axis plane. In the initial minor-axis plane, the trailing vortex rushes through the leading vortex without pairing and then breaks down violently, producing considerably greater entrainment and mixing than in circular or plane jets.
Dynamical properties of the soft-wall elliptical billiard.
Kroetz, Tiago; Oliveira, Hércules A; Portela, Jefferson S E; Viana, Ricardo L
2016-08-01
Physical systems such as optical traps and microwave cavities are realistically modeled by billiards with soft walls. In order to investigate the influence of the wall softness on the billiard dynamics, we study numerically a smooth two-dimensional potential well that has the elliptical (hard-wall) billiard as a limiting case. Considering two parameters, the eccentricity of the elliptical equipotential curves and the wall hardness, which defines the steepness of the well, we show that (1) whereas the hard-wall limit is integrable and thus completely regular, the soft wall elliptical billiard exhibits chaos, (2) the chaotic fraction of the phase space depends nonmonotonically on the hardness of the wall, and (3) the effect of the hardness on the dynamics depends strongly on the eccentricity of the billiard. We further show that the limaçon billiard can exhibit enhanced chaos induced by wall softness, which suggests that our findings generalize to quasi-integrable systems. PMID:27627309
Dynamical properties of the soft-wall elliptical billiard
NASA Astrophysics Data System (ADS)
Kroetz, Tiago; Oliveira, Hércules A.; Portela, Jefferson S. E.; Viana, Ricardo L.
2016-08-01
Physical systems such as optical traps and microwave cavities are realistically modeled by billiards with soft walls. In order to investigate the influence of the wall softness on the billiard dynamics, we study numerically a smooth two-dimensional potential well that has the elliptical (hard-wall) billiard as a limiting case. Considering two parameters, the eccentricity of the elliptical equipotential curves and the wall hardness, which defines the steepness of the well, we show that (1) whereas the hard-wall limit is integrable and thus completely regular, the soft wall elliptical billiard exhibits chaos, (2) the chaotic fraction of the phase space depends nonmonotonically on the hardness of the wall, and (3) the effect of the hardness on the dynamics depends strongly on the eccentricity of the billiard. We further show that the limaçon billiard can exhibit enhanced chaos induced by wall softness, which suggests that our findings generalize to quasi-integrable systems.
Systematic differences between the field and cluster elliptical galaxies
NASA Technical Reports Server (NTRS)
De Carvalho, R. R.; Djorgovski, S.
1992-01-01
Multivariate statistical techniques and fundamental plane fits are used here to study possible systematic differences between field ellipticals (FEs) and cluster ellipticals (CEs). The FEs show more intrinsic scatter in their properties, especially when stellar population variables are included. Pairwise correlations for the two samples are different; the correlations are systematically better for the cluster sample, meaning that ellipticals in the two samples populate their fundamental planes in different ways. Bivariate correlations are different for the two samples, implying that they have different fundamental planes. This is especially true for the correlations which include the population variables Mg2 and (B-V), which are sensitive both to the enrichment history and the storm formation history.
Cluster flight control for fractionated spacecraft on an elliptic orbit
NASA Astrophysics Data System (ADS)
Xu, Ming; Liang, Yuying; Tan, Tian; Wei, Lixin
2016-08-01
This paper deals with the stabilization of cluster flight on an elliptic reference orbit by the Hamiltonian structure-preserving control using the relative position measurement only. The linearized Melton's relative equation is utilized to derive the controller and then the full nonlinear relative dynamics are employed to numerically evaluate the controller's performance. In this paper, the hyperbolic and elliptic eigenvalues and their manifolds are treated without distinction notations. This new treatment not only contributes to solving the difficulty in feedback of the unfixed-dimensional manifolds, but also allows more opportunities to set the controlled frequencies of foundational motions or to optimize control gains. Any initial condition can be stabilized on a Kolmogorov-Arnold-Moser torus near a controlled elliptic equilibrium. The motions are stabilized around the natural relative trajectories rather than track a reference relative configuration. In addition, the bounded quasi-periodic trajectories generated by the controller have advantages in rapid reconfiguration and unpredictable evolution.
Magnetohydrodynamics equilibrium of a self-confined elliptical plasma ball
Wu, H. P. O. Box 8730, Beijing 100080 and Institute of Mechanics, Academia Sinica, Beijing, People's Republic of China ); Oakes, M.E. )
1991-08-01
A variational principle is applied to the problem of magnetohydrodynamics (MHD) equilibrium of a self-contained elliptical plasma ball, such as elliptical ball lightning. The principle is appropriate for an approximate solution of partial differential equations with arbitrary boundary shape. The method reduces the partial differential equation to a series of ordinary differential equations and is especially valuable for treating boundaries with nonlinear deformations. The calculations conclude that the pressure distribution and the poloidal current are more uniform in an oblate self-confined plasma ball than that of an elongated plasma ball. The ellipticity of the plasma ball is obviously restricted by its internal pressure, magnetic field, and ambient pressure. Qualitative evidence is presented for the absence of sighting of elongated ball lightning.
Interpreting Central Surface Brightness and Color Profiles in Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Silva, David R.; Wise, Michael W.
1996-01-01
Hubble Space Telescope imagery has revealed dust features in the central regions of many (50%--80%) nearby bright elliptical galaxies. If these features are an indication of an underlying smooth diffuse dust distribution, then the interpretation of central surface brightness and color profiles in elliptical galaxies becomes significantly more difficult. In this Letter, diagnostics for constraining the presence of such an underlying central dust distribution are presented. We show that easily detectable central color gradients and flattened central surface brightness profiles can be induced by even small amounts of smoothly distributed dust (~100 M⊙). Conversely, combinations of flat surface brightness profiles and flat color gradients or steep surface brightness profiles and steep color gradients are unlikely to be caused by dust. Taken as a whole, these results provide a simple observational tautology for constraining the existence of smooth diffuse dust distributions in the central regions of elliptical galaxies.
Ball bearing lubrication: The elastohydrodynamics of elliptical contacts
NASA Technical Reports Server (NTRS)
Hamrock, B. J.; Dowson, D.
1981-01-01
The history of ball bearings is examined, taking into account rollers and the wheel in the early civilizations, the development of early forms of rolling-element bearings in the classical civilizations, the Middle Ages, the Industrial Revolution, the emergence of the precision ball bearing, scientific studies of contact mechanics and rolling friction, and the past fifty years. An introduction to ball bearings is presented, and aspects of ball bearing mechanics are explored. Basic characteristics of lubrication are considered along with lubrication equations, the lubrication of rigid ellipsoidal solids, and elastohydrodynamic lubrication theory. Attention is given to the theoretical results for fully flooded elliptical hydrodynamic contacts, the theoretical results for starved elliptical contacts, experimental investigations, the elastohydrodynamics of elliptical contacts for materials of low elastic modulus, the film thickness for different regimes of fluid-film lubrication, and applications.
Evolution of a barotropic shear layer into elliptical vortices.
Guha, Anirban; Rahmani, Mona; Lawrence, Gregory A
2013-01-01
When a barotropic shear layer becomes unstable, it produces the well-known Kelvin-Helmholtz instability (KHI). The nonlinear manifestation of the KHI is usually in the form of spiral billows. However, a piecewise linear shear layer produces a different type of KHI characterized by elliptical vortices of constant vorticity connected via thin braids. Using direct numerical simulation and contour dynamics, we show that the interaction between two counterpropagating vorticity waves is solely responsible for this KHI formation. We investigate the oscillation of the vorticity wave amplitude, the rotation and nutation of the elliptical vortex, and straining of the braids. Our analysis also provides a possible explanation for the formation and evolution of elliptical vortices appearing in geophysical and astrophysical flows, e.g., meddies, stratospheric polar vortices, Jovian vortices, Neptune's Great Dark Spot, and coherent vortices in the wind belts of Uranus. PMID:23410439
Improved linac dose distributions for radiosurgery with elliptically shaped fields.
Serago, C F; Lewin, A A; Houdek, P V; Gonzalez-Arias, S; Abitbol, A A; Marcial-Vega, V A; Pisciotti, V; Schwade, J G
1991-10-01
Stereotactic radiosurgery techniques for a linear accelerator typically use circular radiation fields to produce an essentially spherical radiation distribution with a steep dose gradient. Target volumes are frequently irregular in shape, and circular distributions may irradiate normal tissues to high dose as well as the target volume. Improvements to the dose distribution have been made using multiple target points and optimizing the dose per arc to the target. A retrospective review of 20 radiosurgery patients has suggested that the use of elliptically shaped fields may further improve the match of the radiation distribution to the intended target volume. This hypothesis has been verified with film measurements of the radiation distribution obtained using elliptical radiation beam in a head phantom. Reductions of 40% of the high dose volume have been obtained with elliptical fields compared to circular fields without compromising the dose to the target volume. PMID:1938531
Evolution of a barotropic shear layer into elliptical vortices.
Guha, Anirban; Rahmani, Mona; Lawrence, Gregory A
2013-01-01
When a barotropic shear layer becomes unstable, it produces the well-known Kelvin-Helmholtz instability (KHI). The nonlinear manifestation of the KHI is usually in the form of spiral billows. However, a piecewise linear shear layer produces a different type of KHI characterized by elliptical vortices of constant vorticity connected via thin braids. Using direct numerical simulation and contour dynamics, we show that the interaction between two counterpropagating vorticity waves is solely responsible for this KHI formation. We investigate the oscillation of the vorticity wave amplitude, the rotation and nutation of the elliptical vortex, and straining of the braids. Our analysis also provides a possible explanation for the formation and evolution of elliptical vortices appearing in geophysical and astrophysical flows, e.g., meddies, stratospheric polar vortices, Jovian vortices, Neptune's Great Dark Spot, and coherent vortices in the wind belts of Uranus.
Precession and circularization of elliptical space-tether motion
NASA Technical Reports Server (NTRS)
Chapel, Jim D.; Grosserode, Patrick
1993-01-01
In this paper, we present a simplified analytic model for predicting motion of long space tethers. The perturbation model developed here addresses skip rope motion, where each end of the tether is held in place and the middle of the tether swings with a motion similar to that of a child's skip rope. If the motion of the tether midpoint is elliptical rather than circular, precession of the ellipse complicates the procedures required to damp this motion. The simplified analytic model developed in this paper parametrically predicts the precession of elliptical skip rope motion. Furthermore, the model shows that elliptic skip rope motion will circularize when damping is present in the longitudinal direction. Compared with high-fidelity simulation results, this simplified model provides excellent predictions of these phenomena.
Magnetic field induced by elliptical instability in a rotating spheroid
NASA Astrophysics Data System (ADS)
Lacaze, L.; Herreman, W.; Le Bars, M.; Le Dizès, S.; Le Gal, P.
2006-10-01
The tidal or the elliptical instability of the rotating fluid flows is generated by the resonant interaction of the inertial waves. In a slightly elliptically deformed rotating sphere, the most unstable linear mode is called the spin-over mode, and is a solid body rotation versus an axis aligned with the maximum strain direction. In the non-viscous case, this instability corresponds to the median moment of the inertial instability of the solid rotating bodies. This analogy is furthermore illustrated by an elliptical top experiment, which shows the expected inviscid heteroclinic behaviour. In geophysics, the elliptical instability may appear in the molten liquid cores of the rotating planets, which are slightly deformed by the tidal gravitational effects of the close bodies. It may then participate in the general outer core dynamics and possibly the geodynamo process. In this context, Kerswell and Malkus (Kerswell, R.R. and Malkus, W.V.R., Tidal instability as the source for Io's magnetic signature. Geophys. Res. Lett., 1998, 25, 603 606) showed that the puzzling magnetic field of the Jovian satellite Io may indeed be induced by the elliptically unstable motions of its liquid core that deflect the Jupiter's magnetic field. Our magnetohydrodynamics (MHD) experiment is a toy-experiment of this geophysical situation and demonstrates for the first time the possibility of an induction of a magnetic field by the flow motions due to the elliptical instability. A full analytical calculation of the magnetic dipole induced by the spin-over is presented. Finally, exponential growths of this induced magnetic field in a slightly deformed rotating sphere filled with galinstan liquid metal are measured for different rotating rates. Their growth rates compare well with the theoretical predictions in the limit of a vanishing Lorentz force.
Evolution of an elliptic vortex ring in a viscous fluid
NASA Astrophysics Data System (ADS)
Cheng, M.; Lou, J.; Lim, T. T.
2016-03-01
The evolution of a viscous elliptic vortex ring in an initially quiescent fluid or a linear shear flow is numerically simulated using a lattice Boltzmann method. A wide range of parameters are considered, namely, aspect ratios (AR) (1 ≤ AR ≤ 8), core radius to ring radius ratios (σ0) (0.1 ≤ σ0 ≤ 0.3), Reynolds number (Re) (500 ≤ Re ≤ 3000), and shear rate (K) (0 ≤ K ≤ 0.12). The study aims to fill the gap in the current knowledge of the dynamics of an elliptic vortex ring in a viscous fluid and also to address the issue of whether an elliptic ring undergoes vortex stretching and compression during axis-switching. In a quiescent fluid, results show that for fixed Re and σ0, there exists a critical aspect ratio (ARc), below which an elliptic ring undergoes oscillatory deformation with the period that increases with increasing AR. Above ARc, the vortex ring breaks up into two or three sub-rings after the first half-cycle of oscillation. While higher Reynolds number enhances vortex ring breakup, larger core size has the opposite effect. Contrary to an inviscid theory, an elliptic ring does undergo vortex stretching and compression during oscillatory deformation. In the presence of a linear shear flow, the vortex ring undergoes not only oscillatory deformation and stretching but also tilting as it propagates downstream. The tilting angle increases with the shear rate K and is responsible for inducing a "tail" that consists of a counter-rotating vortex pair (CVP) near the upstream end of the initial major axis after the first half-cycle of oscillation. For a high shear rate, the CVP wraps around the ring and transforms its topological structure from a simple elliptic geometry to a complicated structure that eventually leads to the generation of turbulence.
Implementation of Elliptic Curve Cryptography in Binary Field
NASA Astrophysics Data System (ADS)
Susantio, D. R.; Muchtadi-Alamsyah, I.
2016-04-01
Currently, there is a steadily increasing demand of information security, caused by a surge in information flow. There are many ways to create a secure information channel, one of which is to use cryptography. In this paper, we discuss the implementation of elliptic curves over the binary field for cryptography. We use the simplified version of the ECIES (Elliptic Curve Integrated Encryption Scheme). The ECIES encrypts a plaintext by masking the original message using specified points on the curve. The encryption process is done by separating the plaintext into blocks. Each block is then separately encrypted using the encryption scheme.
Plastic Deformation in Profile-Coated Elliptical KB Mirrors
Liu, Chian; Conley, R.; Qian, J.; Kewish, C. M.; Liu, W.; Assoufid, L.; Macrander, A. T.; Ice, G. E.; Tischler, J. Z.
2012-01-01
Profile coating has been successfully applied to produce elliptical Kirkpatrick-Baez (KB) mirrors using both cylindrical and flat Si substrates. Previously, focusing widths of 70 nm with 15-keV monochromatic and 80 nm with white beam were achieved using a flat Si substrate. Now, precision elliptical KB mirrors with sub-nm figure errors are produced with both Au and Pt coatings on flat substrates. Recent studies of bare Si-, Au-, and Pt-coated KB mirrors under prolonged synchrotron X-ray radiation and low-temperature vacuum annealing will be discussed in terms of film stress relaxation and Si plastic deformation.
Study of medium beta elliptical cavities for CADS
NASA Astrophysics Data System (ADS)
Wen, Liangjian; Zhang, Shenghu; Li, Yongming; Wang, Ruoxu; Guo, Hao; Zhang, Cong; Jia, Huan; Jiang, Tiancai; Li, Chunlong; He, Yuan
2016-02-01
The China Accelerator-Driven Sub-critical System (CADS) is a high intensity proton facility to dispose of nuclear waste and generate electric power. CADS is based on a 1.5 GeV, 10 mA CW superconducting (SC) linac as a driver. The high energy section of the linac is composed of two families of SC elliptical cavities which are designed with geometrical beta 0.63 and 0.82. In this paper, the 650 MHz β=0.63 SC elliptical cavity is studied, including cavity optimization, multipacting, high order modes (HOMs) and generator RF power calculation. Supported by National Natural Science Foundation of China (91426303)
Two confirmed compact elliptical galaxies in the Antlia cluster
NASA Astrophysics Data System (ADS)
Smith Castelli, A. V.; Faifer, F. R.; Bassino, L. P.; Romero, G. A.; Cellone, S. A.; Richtler, T.
We confirm the existence of two compact elliptical (cE) galaxies in the cen- tral region of the Antlia cluster through MAGELLAN-MIKE and GEMINI- GMOS spectra. Only about a dozen galaxies of this rare type are known today up to a distance of 100 Mpc. With this finding, Antlia becomes the nearest galaxy cluster harbouring more than one cE galaxy among its galaxy population. One of these galaxies shows evidence of interaction with one of the giant ellipticals that dominate the central region of the cluster.
Plastic Deformation in Profile-Coated Elliptical KB Mirrors
Liu, Chian; Conley, R.; Qian, J.; Kewish, C. M.; Liu, W.; Assoufid, L.; Macrander, A. T.; Ice, G. E.; Tischler, J. Z.
2012-01-01
Profile coating has been successfully applied to produce elliptical Kirkpatrick-Baez (KB) mirrors using both cylindrical and flat Si substrates. Previously, focusing widths of 70 nm with 15-keV monochromatic and 80 nm with white beam were achieved using a flat Si substrate. Now precision elliptical KB mirrors with sub-nm figure errors are produced with both Au and Pt coatings on flat substrates. Recent studies of bare Si, Au-, and Pt-coated KB mirrors under prolonged synchrotron x-ray radiation and low-temperature vacuum annealing will be discussed in terms of film-stress relaxation and Si plastic deformation.
Homogeneous turbulence subjected to mean flow with elliptic streamlines
NASA Technical Reports Server (NTRS)
Blaisdell, G. A.; Shariff, K.
1994-01-01
Direct numerical simulations are performed for homogeneous turbulence with a mean flow having elliptic streamlines. This flow combines the effects of rotation and strain on the turbulence. Qualitative comparisons are made with linear theory for cases with high Rossby number. The nonlinear transfer process is monitored using a generalized skewness. In general, rotation turns off the nonlinear cascade; however, for moderate ellipticities and rotation rates the nonlinear cascade is turned off and then reestablished. Turbulence statistics of interest in turbulence modeling are calculated, including full Reynolds stress budgets.
Elliptical flux vortices in YBa2Cu3O7
NASA Technical Reports Server (NTRS)
Hickman, H.; Dekker, A. J.; Chen, T. M.
1991-01-01
The most energetically favorable vortex in YBa2Cu3O7 forms perpendicular to an anisotropic plane. This vortex is elliptical in shape and is distinguished by an effective interchange of London penetration depths from one axis of the ellipse to another. By generalizing qualitatively from the isotropic to the anisotropic case, we suggest that the flux flow resistivity for the vortex that forms perpendicular to an anistropic plane should have a preferred direction. Similar reasoning indicates that the Kosterlitz-Thouless transition temperature for a vortex mediated transition should be lower if the vortex is elliptical in shape.
The postbuckling analysis of laminated circular plate with elliptic delamination
NASA Astrophysics Data System (ADS)
Chen, Deliang; Chen, Changping; Fu, Yiming
2011-01-01
Based on the Von Karman plate theory, considering the effect of transverse shear deformation, and using the method of the dissociated three regions, the postbuckling governing equations for the axisymmetric laminated circular plates with elliptical delamination are derived. By using the orthogonal point collocation method, the governing equations, boundary conditions and continuity conditions are transformed into a group of nonlinear algebraically equation and the equations are solved with the alternative method. In the numerical examples, the effects of various elliptical in shape, delamination depth and different material properties on buckling and postbuckling of the laminated circular plates are discussed and the numerical results are compared with available data.
Elliptic flow in Au+Au collisions at RHIC.
Back, B. B.; Baker, M. D.; Ballintijn, M.; Barton, D. S.; Betts, R. R.; George, N.; Wuosmaa, A.; Physics; Massachusetts Inst. of Tech.; BNL; Univ. of Illinois at Chicago
2005-01-01
Elliptic flow is an interesting probe of the dynamical evolution of the dense system formed in the ultrarelativistic heavy ion collisions at the relativistic heavy ion collider (RHIC). The elliptic flow dependences on transverse momentum, centrality and pseudorapidity were measured using data collected by the PHOBOS detector, which offers a unique opportunity to study the azimuthal anisotropies of charged particles over a wide range of pseudorapidity. These measurements are presented, together with an overview of the analysis methods and a discussion of the results.
Event-by-event elliptic flow fluctuations from PHOBOS.
Alver, B.; Back, B. B.; Baker, M. D.; Ballintijn, M.; Barton, D. S.; Physics; BNL; Inst. of Nuclear Physics; Massachusetts Inst. of Tech.; National Central Univ.; Univ. of Maryland; Univ. of Rochester
2009-04-01
Recently PHOBOS has focused on the study of fluctuations and correlations in particle production in heavy-ion collisions at the highest energies delivered by the Relativistic Heavy Ion Collider (RHIC). In this report, we present results on event-by-event elliptic flow fluctuations in Au + Au collisions at {radical}s{sub NN} = 200 GeV. A data-driven method was used to estimate the dominant contribution from non-flow correlations. Over the broad range of collision centralities, the observed large elliptic flow fluctuations are in agreement with the fluctuations in the initial source eccentricity.
Two-mode elliptical-core weighted fiber sensors for vibration analysis
NASA Technical Reports Server (NTRS)
Vengsarkar, Ashish M.; Murphy, Kent A.; Fogg, Brian R.; Miller, William V.; Greene, Jonathan A.; Claus, Richard O.
1992-01-01
Two-mode, elliptical-core optical fibers are demonstrated in weighted, distributed and selective vibration-mode-filtering applications. We show how appropriate placement of optical fibers on a vibrating structure can lead to vibration mode filtering. Selective vibration-mode suppression on the order of 10 dB has been obtained using tapered two-mode, circular-core fibers with tapering functions that match the second derivatives of the modes of vibration to be enhanced. We also demonstrate the use of chirped, two-mode gratings in fibers as spatial modal sensors that are equivalents of shaped piezoelectric sensors.
Durran, Richard; Neate, Andrew; Truman, Aubrey
2008-03-15
We consider the Bohr correspondence limit of the Schroedinger wave function for an atomic elliptic state. We analyze this limit in the context of Nelson's stochastic mechanics, exposing an underlying deterministic dynamical system in which trajectories converge to Keplerian motion on an ellipse. This solves the long standing problem of obtaining Kepler's laws of planetary motion in a quantum mechanical setting. In this quantum mechanical setting, local mild instabilities occur in the Keplerian orbit for eccentricities greater than (1/{radical}(2)) which do not occur classically.
Supernumerary Spacing of Rainbows Produced by an Elliptical-Cross-Section Cylinder. II. Experiment.
Adler, C L; Phipps, D; Saunders, K W; Nash, J K; Lock, J A
2001-05-20
We measured the supernumerary spacing parameter of the first- and second-order rainbows of two glass rods, each having an approximately elliptical cross section, as a function of the rod's rotation angle. We attribute large fluctuations in the supernumerary spacing parameter to small local inhomogeneities in the rod's refractive index. The low-pass filtered first-order rainbow experimental data agree with the prediction of ray-tracing-wave-front modeling to within a few percent, and the second-order rainbow data exhibit additional effects that are due to rod nonellipticity. PMID:18357267
Stellar kinematics of X-ray bright massive elliptical galaxies
NASA Astrophysics Data System (ADS)
Lyskova, N.; Churazov, E.; Moiseev, A.; Sil'chenko, O.; Zhuravleva, I.
2014-07-01
We discuss a simple and fast method for estimating masses of early-type galaxies from optical data and compare the results with X-ray derived masses. The optical method relies only on the most basic observables such as the surface brightness I(R) and the line-of-sight velocity dispersion σp(R) profiles and provides an anisotropy-independent estimate of the galaxy circular speed Vc. The mass-anisotropy degeneracy is effectively overcome by evaluating Vc at a characteristic radius Rsweet defined from local properties of observed profiles. The sweet radius Rsweet is expected to lie close to R2, where I(R) ∝ R-2, and not far from the effective radius Reff. We apply the method to a sample of five X-ray bright elliptical galaxies observed with the 6 m telescope BTA-6 in Russia. We then compare the optical Vc estimate with the X-ray derived value, and discuss possible constraints on the non-thermal pressure in the hot gas and configuration of stellar orbits. We find that the average ratio of the optical Vc estimate to the X-ray one is equal to ≈0.98 with 11 per cent scatter, i.e. there is no evidence for the large non-thermal pressure contribution in the gas at ˜Rsweet. From analysis of the Lick indices Hβ, Mgb, Fe5270 and Fe5335, we calculate the mass of the stellar component within the sweet radius. We conclude that a typical dark matter fraction inside Rsweet in the sample galaxies is ˜60 per cent for the Salpeter initial mass function (IMF) and ˜75 per cent for the Kroupa IMF.
On hyperelliptic abelian functions of genus 3
NASA Astrophysics Data System (ADS)
Nakayashiki, Atsushi
2011-06-01
The affine ring A of the affine Jacobian variety J(X)∖Θ of a hyperelliptic curve of genus 3 is studied as a D module. A conjecture on the minimal D-free resolution previously proposed is proved in this case. As a by-product a linear basis of A is explicitly constructed in terms of derivatives of Klein's hyperelliptic ℘-functions.
Optics ellipticity performance of an unobscured off-axis space telescope.
Zeng, Fei; Zhang, Xin; Zhang, Jianping; Shi, Guangwei; Wu, Hongbo
2014-10-20
With the development of astronomy, more and more attention is paid to the survey of dark matter. Dark matter cannot be seen directly but can be detected by weak gravitational lensing measurement. Ellipticity is an important parameter used to define the shape of a galaxy. Galaxy ellipticity changes with weak gravitational lensing and nonideal optics. With our design of an unobscured off-axis telescope, we implement the simulation and calculation of optics ellipticity. With an accurate model of optics PSF, the characteristic of ellipticity is modeled and analyzed. It is shown that with good optical design, the full field ellipticity can be quite small. The spatial ellipticity change can be modeled by cubic interpolation with very high accuracy. We also modeled the ellipticity variance with time and analyzed the tolerance. It is shown that the unobscured off-axis telescope has good ellipticity performance and fulfills the requirement of dark matter survey.
Four ways to compute the inverse of the complete elliptic integral of the first kind
NASA Astrophysics Data System (ADS)
Boyd, John P.
2015-11-01
The complete elliptic integral of the first kind arises in many applications. This article furnishes four different ways to compute the inverse of the elliptic integral. One motive for this study is simply that the author needed to compute the inverse integral for an application. Another is to develop a case study comparing different options for solving transcendental equations like those in the author's book (Boyd, 2014). A third motive is to develop analytical approximations, more useful to theorists than mere numbers. A fourth motive is to provide robust "black box" software for computing this function. The first solution strategy is "polynomialization" which replaces the elliptic integral by an exponentially convergent series of Chebyshev polynomials. The transcendental equation becomes a polynomial equation which is easily solved by finding the eigenvalues of the Chebyshev companion matrix. (The numerically ill-conditioned step of converting from the Chebyshev to monomial basis is never necessary). The second approximation is a regular perturbation series, accurate where the modulus is small. The third is a power-and-exponential series that converges over the entire range parameter range, albeit only sub-exponentially in the limit of zero modulus. Lastly, Newton's iteration is promoted from a local iteration to a global method by a Never-Failing Newton's Iteration (NFNI) in the form of the exponential of the ratio of a linear function divided by another linear polynomial. A short Matlab implementation is provided, easily translatable into other languages. The Matlab/Newton code is recommended for numerical purposes. The other methods are presented because (i) all are broadly applicable strategies useful for other rootfinding and inversion problems (ii) series and substitutions are often much more useful to theorists than numerical software and (iii) the Never-Failing Newton's Iteration was discovered only after a great deal of messing about with power series
A Galerkin formulation of the MIB method for three dimensional elliptic interface problems
Xia, Kelin; Wei, Guo-Wei
2014-01-01
We develop a three dimensional (3D) Galerkin formulation of the matched interface and boundary (MIB) method for solving elliptic partial differential equations (PDEs) with discontinuous coefficients, i.e., the elliptic interface problem. The present approach builds up two sets of elements respectively on two extended subdomains which both include the interface. As a result, two sets of elements overlap each other near the interface. Fictitious solutions are defined on the overlapping part of the elements, so that the differentiation operations of the original PDEs can be discretized as if there was no interface. The extra coefficients of polynomial basis functions, which furnish the overlapping elements and solve the fictitious solutions, are determined by interface jump conditions. Consequently, the interface jump conditions are rigorously enforced on the interface. The present method utilizes Cartesian meshes to avoid the mesh generation in conventional finite element methods (FEMs). We implement the proposed MIB Galerkin method with three different elements, namely, rectangular prism element, five-tetrahedron element and six-tetrahedron element, which tile the Cartesian mesh without introducing any new node. The accuracy, stability and robustness of the proposed 3D MIB Galerkin are extensively validated over three types of elliptic interface problems. In the first type, interfaces are analytically defined by level set functions. These interfaces are relatively simple but admit geometric singularities. In the second type, interfaces are defined by protein surfaces, which are truly arbitrarily complex. The last type of interfaces originates from multiprotein complexes, such as molecular motors. Near second order accuracy has been confirmed for all of these problems. To our knowledge, it is the first time for an FEM to show a near second order convergence in solving the Poisson equation with realistic protein surfaces. Additionally, the present work offers the
MOND prediction of a new giant shell in the elliptical galaxy NGC 3923
NASA Astrophysics Data System (ADS)
Bílek, M.; Bartošková, K.; Ebrová, I.; Jungwiert, B.
2014-06-01
Context. Stellar shells, which form axially symmetric systems of arcs in some elliptical galaxies, are most likely remnants of radial minor mergers. They are observed up a radius of ~100 kpc. The stars in them oscillate in radial orbits. The radius of a shell depends on the free-fall time at the position of the shell and on the time since the merger. We previously verified the consistency of shell radii in the elliptical galaxy NGC 3923 with its most probable MOND potential. Our results implied that an as yet undiscovered shell exists at the outskirts of the galaxy. Aims: We here extend our study by assuming more general models for the gravitational potential to verify the prediction of the new shell and to estimate its position. Methods: We tested the consistency of the shell radial distribution observed in NGC 3923 with a wide variety of MOND potentials of the galaxy. The potentials differed in the mass-to-light ratio and in distance to the galaxy. We considered different MOND interpolation functions, values of the acceleration constant a0, and density profiles of the galaxy. We verified the functionality of our code on a Newtonian self-consistent simulation of the formation of a shell galaxy. Results: Our method reliably predicts that exactly one new outermost shell exists at a galactocentric radius of about 1900'' (~210 kpc) on the southwestern side of the galaxy. Its estimated surface brightness is about 28 mag arcsec-2 in B - a value accessible by current instruments. This prediction enables a rare test of MOND in an elliptical down to an acceleration of a0/ 10. The predictive power of our method is verified by reconstructing the position of the largest known shell from the distribution of the remaining shells.
NASA Astrophysics Data System (ADS)
Duffy, Brenton
The distinguishing characteristic of the elliptic restricted three-body problem from that of the circular case is a pulsating potential field resulting in non-autonomous and non-integrable spacecraft dynamics, which are difficult to model using classical methods of analysis. The purpose of this study is to harness modern methods of analytical perturbation theory to normalize the system dynamics about the circular restricted three-body problem and about one of the triangular Lagrange points. The normalization is achieved through a canonical transformation of the system Hamiltonian function based on the Lie transform method introduced by Hori and Deprit in the 1960s. The classic method derives a near-identity transformation of a Hamiltonian function expanded about a single parameter such that the transformed system possesses ideal properties of integrability. One of the major contributions of this study is to extend the normalization method to two-parameter expansions and to non-autonomous Hamiltonian systems. The two-parameter extension is used to normalize the system dynamics of the elliptic restricted three-body problem such that the stability of the triangular Lagrange points may be determined using the Kolmogorov-Arnold-Moser theorem. Further dynamical analysis is performed in the transformed phase space in terms of local integrals of motion akin to Jacobi's integral of the circular restricted three-body problem. The local phase space around the Lagrange point is foliated by invariant tori that effectively separate the planar dynamics into qualitative regions of motion. Additional analysis is presented for the incorporation of control into the normalization routine with the goal of eliminating the non-circular secular perturbations. The control method is validated on a test case and applied to the elliptic restricted three-body problem for the purposes of stabilizing the motion around the triangular Lagrange points.
NASA Technical Reports Server (NTRS)
kaul, Upender K.
2008-01-01
A procedure for generating smooth uniformly clustered single-zone grids using enhanced elliptic grid generation has been demonstrated here for the Mars Science Laboratory (MSL) geometries such as aeroshell and canopy. The procedure obviates the need for generating multizone grids for such geometries, as reported in the literature. This has been possible because the enhanced elliptic grid generator automatically generates clustered grids without manual prescription of decay parameters needed with the conventional approach. In fact, these decay parameters are calculated as decay functions as part of the solution, and they are not constant over a given boundary. Since these decay functions vary over a given boundary, orthogonal grids near any arbitrary boundary can be clustered automatically without having to break up the boundaries and the corresponding interior domains into various zones for grid generation.
Towards a cladistics of double Yangians and elliptic algebras*
NASA Astrophysics Data System (ADS)
Arnaudon, D.; Avan, J.; Frappat, L.; Ragoucy, E.; Rossi, M.
2000-09-01
A self-contained description of algebraic structures, obtained by combinations of various limit procedures applied to vertex and face sl(2) elliptic quantum affine algebras, is given. New double Yangian structures of dynamical type are defined. Connections between these structures are established. A number of them take the form of twist-like actions. These are conjectured to be evaluations of universal twists.
Adaptive control and orbit determination for elliptical rendezvous
NASA Astrophysics Data System (ADS)
Xu, Lijia; Hu, Yong; Jiang, Tiantian
2016-10-01
In this paper, we study the control and orbit determination problems for elliptical rendezvous. Autonomous rendezvous is achieved by the proposed adaptive control based on the measurements of relative position and velocity between the chaser and target spacecraft. Moreover, the target orbital elements can be estimated during the rendezvous process. Finally, the effectiveness of the method is illustrated by simulations.
Elliptic cylindrical silicon nanowire hybrid surface plasmon polariton waveguide.
Zhang, Li; Xiong, Qiulin; Li, Xiaopeng; Ma, Junxian
2015-08-10
We researched an elliptic cylindrical silicon nanowire hybrid surface plasmon polariton waveguide and evaluated its mode characteristics using the finite element method software COMSOL. The waveguide consists of three parts: an elliptic cylindrical silicon nanowire, a silver film layer, and a silica covering layer between them. All of the components are surrounded by air. After optimizing the geometrical parameters of the waveguide, we can achieve the waveguide's strong field confinement (ranging from λ^{2}/270 to λ^{2}/27) and long propagation distances (119-485 μm). In order to further understand the impact of the waveguide's architecture on its performance, we also studied the ridge hybrid waveguide. The results show that the ridge waveguide has moderate local field confinement ranging from λ^{2}/190 to λ^{2}/20 and its maximum propagation distance is about 340 μm. We compared the elliptic cylindrical and ridge nanowire hybrid waveguides with the cylindrical hybrid waveguide that we studied before. The elliptic cylindrical waveguide achieves a better trade-off between reasonable mode confinement and maximum propagation length in the three waveguides. The researched hybrid surface plasmon polaritons waveguides are useful to construct devices such as a directional coupler and may find potential applications in photonic integrated circuits or other novel SPP devices.
On the elliptic restricted three-body problem.
NASA Technical Reports Server (NTRS)
Broucke, R.
1972-01-01
This article describes the most important features of the elliptic restricted three-body problem. The methods of numerical integration with recurrent power series are developed for both the equations of motion and the variational equations. The conditions for the existence of periodic orbits and families of periodic orbits are also outlined in detail, and finally illustrated with a family of symmetric periodic orbits.
Elastohydrodynamics of elliptical contacts for materials of low elastic modulus
NASA Technical Reports Server (NTRS)
Hamrock, B. J.; Dowson, D.
1983-01-01
The influence of the ellipticity parameter k and the dimensionless speed U, load W, and materials G parameters on minimum film thickness for materials of low elastic modulus was investigated. The ellipticity parameter was varied from 1 (a ball-on-plane configuration) to 12 (a configuration approaching a line contact); U and W were each varied by one order of magnitude. Seventeen cases were used to generate the minimum- and central-film-thickness relations. The influence of lubricant starvation on minimum film thickness in starved elliptical, elastohydrodynamic configurations was also investigated for materials of low elastic modulus. Lubricant starvation was studied simply by moving the inlet boundary closer to the center of the conjunction in the numerical solutions. Contour plots of pressure and film thickness in and around the contact were presented for both fully flooded and starved lubrication conditions. It is evident from these figures that the inlet pressure contours become less circular and closer to the edge of the Hertzian contact zone and that the film thickness decreases substantially as the serverity of starvation increases. The results presented reveal the essential features of both fully flooded and starved, elliptical, elastohydrodynamic conjunctions for materials of low elastic modulus.
Listening to Elliptic Speech: Pay Attention to Stressed Vowels.
ERIC Educational Resources Information Center
Bond, Z. S.
University students were the subjects of three experiments designed to determine the usefulness of elliptic speech in investigating the perception of the phonological structure of continuous speech. Five naturally spoken and five synthesized paragraphs were recorded in two different randomizations of phonological distortions and at two different…
Elliptical polarization of Saturn Kilometric Radiation observed from high latitudes
NASA Astrophysics Data System (ADS)
Fischer, G.; Cecconi, B.; Lamy, L.; Ye, S.-Y.; Taubenschuss, U.; Macher, W.; Zarka, P.; Kurth, W. S.; Gurnett, D. A.
2009-08-01
The high-inclination orbits of the Cassini spacecraft from autumn 2006 until spring 2007 allowed the Cassini/RPWS (Radio and Plasma Wave Science) instrument to observe Saturn Kilometric Radiation (SKR) from latitudes up to 60° for the first time. This has revealed a surprising new property of SKR: above ˜30° in observational latitude, a significant amount of SKR is strongly elliptically polarized, in marked contrast to previous observations from low latitudes, which showed only circular polarization. There are transitional latitudes where the elliptical polarization occurs in “patches” in the time-frequency spectrograms next to regions of still completely circularly polarized SKR. From ˜45° to 60° in northern latitude, it is found that most of the SKR is elliptically polarized throughout its entire frequency range with an average degree of ˜0.7 in linear polarization. We demonstrate the ellipticity of SKR by using the concept of “apparent polarization” in case of two-antenna measurements, but also show three-antenna measurements from which the polarization can be unambiguously determined. Possible reasons for the variation of SKR polarization with the observer's latitude will be discussed.
Micromagnetic simulation of hysteresis loop of elliptic permalloy nanorings
NASA Astrophysics Data System (ADS)
Mishra, Amaresh Chandra
2016-09-01
Magnetic hysteresis behavior of isotropic permalloy elliptic nanorings of outer semi-major axis length (aout) 100 nm and thickness (t) 20 nm were studied with respect to the variation of two parameters: outer semiminor axis length (bout) and the difference between outer and inner dimensions (r). The outer semiminor axis length (bout) varied from 90 nm to 20 nm which covers from nearly circular nanoring to elliptic nanoring of high aspect ratio. The value of r varied in steps of 10 nm. Micromagnetic simulation of in-plane hysteresis curve of these nanorings revealed that the remanent state of all of these elliptic rings are onion states if the magnetic field is applied along the longer side of the elliptic rings. If the magnetic field is applied along the shorter side, then the remanent states turn out to be vortex state. The hysteresis loss indicated by area of the hysteresis loop was found to be decreasing gradually with the increment of either r or bout. On the other hand, the remanent magnetization increased with increment of r but decreased with the increment of bout. The changes were attributed to three parameters mainly: inner curvature, exchange energy and demagnetization energy. The changes in loop area were discussed in light of variation of these three parameters.
The use of MACSYMA for solving elliptic boundary value problems
NASA Technical Reports Server (NTRS)
Thejll, Peter; Gilbert, Robert P.
1990-01-01
A boundary method is presented for the solution of elliptic boundary value problems. An approach based on the use of complete systems of solutions is emphasized. The discussion is limited to the Dirichlet problem, even though the present method can possibly be adapted to treat other boundary value problems.
Molecular gas in elliptical galaxies with dust lanes
NASA Technical Reports Server (NTRS)
Wang, Zhong; Kenney, Jeffrey D. P.; Ishizuki, Sumio
1992-01-01
We have searched for CO(1-0) line emission in eight dust lane elliptical and lenticular galaxies using the Nobeyama 45 m telescope. Five of the eight galaxies, including the well-studied elliptical NGC 1052, have CO emission at above the 5-sigma level, with inferred molecular gas masses ranging from 10 exp 8 to a few times 10 exp 9 solar masses. Our selection criterion differs from previous surveys in that it does not depend on the FIR fluxes, and thus is less sensitive to the sizes and distances of the host galaxies or to the degree to which dust is heated. The relatively high detection rate of CO in these ellipticals suggests a close correlation between molecular mass and cold dust. Compared with previously studied samples of FIR selected early-type galaxies, our sample has on average four times more CO emission per unit FIR (40-120 microns) luminosity. If the intrinsic gas-to-dust ratio of these galaxies as similar to that of the Milky Way, then only about 5 percent of the dust mass in dust lane ellipticals radiates substantially at 60 and 100 microns, and the remaining dust must be colder than about 30 K.
The infrared emission from the elliptical galaxy NGC 1052
NASA Technical Reports Server (NTRS)
Becklin, E. E.; Tokunaga, A. T.; Wynn-Williams, C. G.
1982-01-01
Multi-aperture IR photometry of the elliptical galaxy NGC 1052 shows that its IR excess is confined to a region smaller than 2 arc sec (300 pc) in diameter coincident with the visible nucleus. It is suggested that the emission in the 5-20 micron range arises from dust heated by the nonthermal source seen at other wavelengths.
Massey products for elliptic curves of rank 1
NASA Astrophysics Data System (ADS)
Kim, Minhyong
2010-07-01
For an elliptic curve over {Q} of rank 1, integral j -invariant, and suitable finiteness in the Tate-Shafarevich group, we use the level-two Selmer variety and secondary cohomology products to find explicit analytic defining equations for global integral points inside the set of p -adic points.
An experimental study on jets issuing from elliptic inclined nozzles
NASA Astrophysics Data System (ADS)
New, T. H.
2009-06-01
This paper reports on an experimental flow visualisation and digital particle image velocimetry investigation on forced jets exhausting from aspect ratio equal to three elliptic nozzles with exits inclined at 30° and 60°. Flow images show that shear layer instabilities and subsequent vortex roll-ups are formed parallel to the inclined nozzle exits at 30° incline and that rapid re-orientation of the vortex roll-ups occurs at 60° incline. Flow observations also show that strong axis-switching occurs in a non-inclined elliptic nozzle. However, 30° and 60° elliptic inclined nozzles produce significant distortions to and suppression of the axis-switching behaviour, respectively. As a result, flow stresses and turbulent kinetic energy distributions become increasingly asymmetric. Their coherency and magnitudes along the shorter nozzle lengths also vary significantly. This can be attributed to the dissimilar formations of vortex roll-ups and rib structures, as well as unequal mutual interactions between them as the incline-angle increases. Lastly, results also show that unlike circular inclined nozzles, elliptic inclined nozzles do not produce serpentine-shaped jet columns nor lead to significant lateral jet-spread at large incline-angles.
Source identification problem for an elliptic-hyperbolic equation
NASA Astrophysics Data System (ADS)
Ashyralyev, Allaberen; Tetikoglu, Fatma Songul Ozesenli; Kahraman, Tulay
2016-08-01
In the present paper, a boundary value problem for the differential equation with parameter in a Hilbert space with self-adjoint definite operator is investigated. The well-posedness of this problem is presented. The stability inequalities for the solution of source identification problem for elliptic-hyperbolic equations are given.
Elliptic cylindrical silicon nanowire hybrid surface plasmon polariton waveguide.
Zhang, Li; Xiong, Qiulin; Li, Xiaopeng; Ma, Junxian
2015-08-10
We researched an elliptic cylindrical silicon nanowire hybrid surface plasmon polariton waveguide and evaluated its mode characteristics using the finite element method software COMSOL. The waveguide consists of three parts: an elliptic cylindrical silicon nanowire, a silver film layer, and a silica covering layer between them. All of the components are surrounded by air. After optimizing the geometrical parameters of the waveguide, we can achieve the waveguide's strong field confinement (ranging from λ^{2}/270 to λ^{2}/27) and long propagation distances (119-485 μm). In order to further understand the impact of the waveguide's architecture on its performance, we also studied the ridge hybrid waveguide. The results show that the ridge waveguide has moderate local field confinement ranging from λ^{2}/190 to λ^{2}/20 and its maximum propagation distance is about 340 μm. We compared the elliptic cylindrical and ridge nanowire hybrid waveguides with the cylindrical hybrid waveguide that we studied before. The elliptic cylindrical waveguide achieves a better trade-off between reasonable mode confinement and maximum propagation length in the three waveguides. The researched hybrid surface plasmon polaritons waveguides are useful to construct devices such as a directional coupler and may find potential applications in photonic integrated circuits or other novel SPP devices. PMID:26368373
Spectroscopic ellipsometer based on direct measurement of polarization ellipticity
Watkins, Lionel R.
2011-06-20
A polarizer-sample-Wollaston prism analyzer ellipsometer is described in which the ellipsometric angles {psi} and {Delta} are determined by direct measurement of the elliptically polarized light reflected from the sample. With the Wollaston prism initially set to transmit p- and s-polarized light, the azimuthal angle P of the polarizer is adjusted until the two beams have equal intensity. This condition yields {psi}={+-}P and ensures that the reflected elliptically polarized light has an azimuthal angle of {+-}45 deg. and maximum ellipticity. Rotating the Wollaston prism through 45 deg. and adjusting the analyzer azimuth until the two beams again have equal intensity yields the ellipticity that allows {Delta} to be determined via a simple linear relationship. The errors produced by nonideal components are analyzed. We show that the polarizer dominates these errors but that for most practical purposes, the error in {psi} is negligible and the error in {Delta} may be corrected exactly. A native oxide layer on a silicon substrate was measured at a single wavelength and multiple angles of incidence and spectroscopically at a single angle of incidence. The best fit film thicknesses obtained were in excellent agreement with those determined using a traditional null ellipsometer.
Stable Bundles on Non-Kähler Elliptic Surfaces
NASA Astrophysics Data System (ADS)
Brînzănescu, Vasile; Moraru, Ruxandra
2005-03-01
In this paper, we study the moduli spaces of stable rank-2 vector bundles on non-Kähler elliptic surfaces, thus giving a classification of these bundles; in the case of Hopf and Kodaira surfaces, these moduli spaces admit the structure of an algebraically completely integrable Hamiltonian system.
The dynamical fingerprint of core scouring in massive elliptical galaxies
Thomas, J.; Saglia, R. P.; Bender, R.; Erwin, P.; Fabricius, M.
2014-02-10
The most massive elliptical galaxies have low-density centers or cores that differ dramatically from the high-density centers of less massive ellipticals and bulges of disk galaxies. These cores have been interpreted as the result of mergers of supermassive black hole binaries, which depopulate galaxy centers by gravitationally slingshotting central stars toward large radii. Such binaries naturally form in mergers of luminous galaxies. Here, we analyze the population of central stellar orbits in 11 massive elliptical galaxies that we observed with the integral field spectrograph SINFONI at the European Southern Observatory Very Large Telescope. Our dynamical analysis is orbit-based and includes the effects of a central black hole, the mass distribution of the stars, and a dark matter halo. We show that the use of integral field kinematics and the inclusion of dark matter is important to conclude on the distribution of stellar orbits in galaxy centers. Six of our galaxies are core galaxies. In these six galaxies, but not in the galaxies without cores, we detect a coherent lack of stars on radial orbits in the core region and a uniform excess of radial orbits outside of it: when scaled by the core radius r{sub b} , the radial profiles of the classical anisotropy parameter β(r) are nearly identical in core galaxies. Moreover, they quantitatively match the predictions of black hole binary simulations, providing the first convincing dynamical evidence for core scouring in the most massive elliptical galaxies.
Reconfigurable Optical Spectra from Perturbations on Elliptical Whispering Gallery Resonances
NASA Technical Reports Server (NTRS)
Mohageg, Makan; Maleki, Lute
2008-01-01
Elastic strain, electrical bias, and localized geometric deformations were applied to elliptical whispering-gallery-mode resonators fabricated with lithium niobate. The resultant perturbation of the mode spectrum is highly dependant on the modal indices, resulting in a discretely reconfigurable optical spectrum. Breaking of the spatial degeneracy of the whispering-gallery modes due to perturbation is also observed.
NASA Technical Reports Server (NTRS)
Briggs, Benjamin R.
1960-01-01
The inverse method, with the shock wave prescribed to be an elliptic cone at a finite angle of incidence, is applied to calculate numerically the supersonic perfect-gas flow past conical bodies not having axial symmetry. Two formulations of the problem are employed, one using a pair of stream functions and the other involving entropy and components of velocity. A number of solutions are presented, illustrating the numerical methods employed, and showing the effects of moderate variation of the initial parameters.
Zou, Ling; Zhao, Haihua; Zhang, Hongbin
2016-03-09
This work represents a first-of-its-kind successful application to employ advanced numerical methods in solving realistic two-phase flow problems with two-fluid six-equation two-phase flow model. These advanced numerical methods include high-resolution spatial discretization scheme with staggered grids (high-order) fully implicit time integration schemes, and Jacobian-free Newton–Krylov (JFNK) method as the nonlinear solver. The computer code developed in this work has been extensively validated with existing experimental flow boiling data in vertical pipes and rod bundles, which cover wide ranges of experimental conditions, such as pressure, inlet mass flux, wall heat flux and exit void fraction. Additional code-to-code benchmark with the RELAP5-3Dmore » code further verifies the correct code implementation. The combined methods employed in this work exhibit strong robustness in solving two-phase flow problems even when phase appearance (boiling) and realistic discrete flow regimes are considered. Transitional flow regimes used in existing system analysis codes, normally introduced to overcome numerical difficulty, were completely removed in this work. As a result, this in turn provides the possibility to utilize more sophisticated flow regime maps in the future to further improve simulation accuracy.« less
Zou, Ling; Zhao, Haihua; Zhang, Hongbin
2015-09-01
The majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many nuclear thermal–hydraulics applications, it is desirable to use higher-order numerical schemes to reduce numerical errors. High-resolution spatial discretization schemes provide high order spatial accuracy in smooth regions and capture sharp spatial discontinuity without nonphysical spatial oscillations. In this work, we adapted an existing high-resolution spatial discretization scheme on staggered grids in two-phase flow applications. Fully implicit time integration schemes were also implemented to reduce numerical errors from operator-splitting types of time integration schemes. The resulting nonlinear system has been successfully solved using the Jacobian-free Newton–Krylov (JFNK) method. The high-resolution spatial discretization and high-order fully implicit time integration numerical schemes were tested and numerically verified for several two-phase test problems, including a two-phase advection problem, a two-phase advection with phase appearance/disappearance problem, and the water faucet problem. Numerical results clearly demonstrated the advantages of using such high-resolution spatial and high-order temporal numerical schemes to significantly reduce numerical diffusion and therefore improve accuracy. Our study also demonstrated that the JFNK method is stable and robust in solving two-phase flow problems, even when phase appearance/disappearance exists.
Salinger, Andy; Evans, Katherine J; Lemieux, Jean-Francois; Holland, David; Payne, Tony; Price, Stephen; Knoll, Dana
2011-01-01
We have implemented the Jacobian-free Newton-Krylov (JFNK) method for solving the rst-order ice sheet momentum equation in order to improve the numerical performance of the Community Ice Sheet Model (CISM), the land ice component of the Community Earth System Model (CESM). Our JFNK implementation is based on signicant re-use of existing code. For example, our physics-based preconditioner uses the original Picard linear solver in CISM. For several test cases spanning a range of geometries and boundary conditions, our JFNK implementation is 1.84-3.62 times more efficient than the standard Picard solver in CISM. Importantly, this computational gain of JFNK over the Picard solver increases when rening the grid. Global convergence of the JFNK solver has been signicantly improved by rescaling the equation for the basal boundary condition and through the use of an inexact Newton method. While a diverse set of test cases show that our JFNK implementation is usually robust, for some problems it may fail to converge with increasing resolution (as does the Picard solver). Globalization through parameter continuation did not remedy this problem and future work to improve robustness will explore a combination of Picard and JFNK and the use of homotopy methods.
van Dalen, K N; Drijkoningen, G G; Smeulders, D M J; Heller, H K J; Glorieux, C; Sarens, B; Verstraeten, B
2011-09-01
The interface-wave impedance and ellipticity are wave attributes that interrelate the full waveforms as observed in different components. For each of the fluid/elastic-solid interface waves, i.e., the pseudo-Rayleigh (pR) and Stoneley (St) waves, the impedance and ellipticity are found to have different functional dependencies on Young's modulus and Poisson's ratio. By combining the attributes in a cost function, unique and stable estimates of these parameters can be obtained, particularly when using the St wave. In a validation experiment, the impedance of the laser-excited pR wave is successfully extracted from simultaneous measurements of the normal particle displacement and the fluid pressure at a water/aluminum interface. The displacement is measured using a laser Doppler vibrometer (LDV) and the pressure with a needle hydrophone. Any LDV measurement is perturbed by refractive-index changes along the LDV beam once acoustic waves interfere with the beam. Using a model that accounts for these perturbations, an impedance decrease of 28% with respect to the plane wave impedance of the pR wave is predicted for the water/aluminum configuration. Although this deviation is different for the experimentally extracted impedance, there is excellent agreement between the observed and predicted pR waveforms in both the particle displacement and fluid pressure.
A new perspective on the integrability of Inozemtsev’s elliptic spin chain
Finkel, Federico; González-López, Artemio
2014-12-15
The aim of this paper is studying from an alternative point of view the integrability of the spin chain with long-range elliptic interactions introduced by Inozemtsev. Our analysis relies on some well-established conjectures characterizing the chaotic vs. integrable behavior of a quantum system, formulated in terms of statistical properties of its spectrum. More precisely, we study the distribution of consecutive levels of the (unfolded) spectrum, the power spectrum of the spectral fluctuations, the average degeneracy, and the equivalence to a classical vertex model. Our results are consistent with the general consensus that this model is integrable, and that it is closer in this respect to the Heisenberg chain than to its trigonometric limit (the Haldane–Shastry chain). On the other hand, we present some numerical and analytical evidence showing that the level density of Inozemtsev’s chain is asymptotically Gaussian as the number of spins tends to infinity, as is the case with the Haldane–Shastry chain. We are also able to compute analytically the mean and the standard deviation of the spectrum, showing that their asymptotic behavior coincides with that of the Haldane–Shastry chain. - Highlights: • Construction of Inozemtsev’s elliptic spin chain using Polychronakos’s freezing trick. • Numerical evidence of the Gaussian character of the level density. • Exact computation and asymptotics of the mean and standard deviation of the spectrum. • Evidence of the chain’s integrability from key statistical properties of its spectrum. • Exact evaluation of finite sums of powers of Weierstrass’s elliptic function.
Effective integration of ultra-elliptic solutions of the focusing nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Wright, O. C.
2016-05-01
An effective integration method based on the classical solution of the Jacobi inversion problem, using Kleinian ultra-elliptic functions and Riemann theta functions, is presented for the quasi-periodic two-phase solutions of the focusing cubic nonlinear Schrödinger equation. Each two-phase solution with real quasi-periods forms a two-real-dimensional torus, modulo a circle of complex-phase factors, expressed as a ratio of theta functions associated with the Riemann surface of the invariant spectral curve. The initial conditions of the Dirichlet eigenvalues satisfy reality conditions which are explicitly parametrized by two physically-meaningful real variables: the squared modulus and a scalar multiple of the wavenumber. Simple new formulas for the maximum modulus and the minimum modulus are obtained in terms of the imaginary parts of the branch points of the Riemann surface.
Vibration and Noise Characteristics of Elliptical Gears due to Non-Uniform Rotation
NASA Astrophysics Data System (ADS)
Liu, Xing; Nagamura, Kazuteru; Ikejo, Kiyotaka
Elliptical gear is a typical non-circular gear, which transmits a variable-ratio rotation and power simultaneously. Due to the non-uniform rotation, the vibration and noise of elliptical gears demonstrate particular characteristics which should be paid attention to in practical application. In this paper, two elliptical gears, which are a single elliptical gear and a double elliptical gear, have been investigated to analyze the vibration and noise characteristics of elliptical gears. The corresponding circular gears for comparison are also investigated. General factors including the torque, the rotation speed, the gear vibration acceleration and the gear noise of the four test gears are measured by running test. The root mean square of the Circumferential Vibration Acceleration (CVA) and the sound pressure level of the noise of elliptical gears are obtained from the measured results and compared with those of circular gears to clarify the vibration and noise characteristics of elliptical gears. Furthermore, the frequency analysis of the CVA of elliptical gears is conducted by Fast Fourier Transform Algorithm (FFT) and compared with that of circular gears. The main vibration component of elliptical gear is uncovered according to the obtained frequency spectra. In addition, the Critical Rotation Speeds of Tooth Separation (CRSTS) of elliptical gear is obtained and its relation with load torque is unveiled.
NASA Astrophysics Data System (ADS)
Kon'kov, A. A.
2014-08-01
We consider non-negative solutions of quasi-linear elliptic inequalities \\operatorname{div}A(x,Du)≥0 in ΩR_0,R_1, 0≤ R_0\\lt R_1≤∞, where ΩR_0,R_1= \\{x\\inΩ\\colon R_0\\lt \\vert x\\vert\\lt R_1\\}, Ω\\subset{ R}^n ( n≥2) is a non-empty open set, and the function A\\colonΩR_0,R_1×{ R}^n\\to{ R}^n satisfies the ellipticity conditions C_1\\vertξ\\vert^p≤ξ A(x,ξ), \\vert A(x,ξ)\\vert≤ C_2\\vertξ\\vertp-1, C_1,C_2\\gt 0, p\\gt 1, for almost all x\\inΩR_0,R_1 and all ξ\\in{ R}^n. Our bounds for solutions take the geometry of Ω into account.
Omidi, Mahboubeh Faizabadi, Edris
2015-03-21
Magnetic susceptibility is investigated in a man-made elliptical quantum ring in the presence of Rashba spin-orbit interactions and the magnetic flux. It is shown that magnetic susceptibility as a function of magnetic flux changes between negative and positive signs periodically. The periodicity of the Aharonov-Bohm oscillations depends on the geometry of the region where magnetic field is applied, the eccentricity, and number of sites in each chain ring (the elliptical ring is composed of chain rings). The magnetic susceptibility sign can be reversed by tuning the Rashba spin-orbit strength as well. Both the magnetic susceptibility strength and sign can be controlled via external spin-orbit interactions, which can be exploited in spintronics and nanoelectronics.
Wireless OAM transmission system based on elliptical microstrip patch antenna.
Chen, Jia Jia; Lu, Qian Nan; Dong, Fei Fei; Yang, Jing Jing; Huang, Ming
2016-05-30
The multiplexing transmission has always been a focus of attention for communication technology. In this paper, the radiation characteristics of circular microstrip patch antenna was firstly analyzed based on cavity model theory, and then spiral beams carrying orbital angular momentum (OAM) were generated, using elliptical microstrip patch antenna, with a single feed probe instead of a standard circular patch with two feedpoints. Moreover, by combining the proposed elliptic microstrip patch antenna with Universal Software Radio Peripheral (USRP), a wireless OAM transmission system was established and the real-time transmission of text, image and video in a real channel environment was realized. Since the wireless OAM transmission has the advantage of good safety and high spectrum utilization efficiency, this work has theoretical significance and potential application. PMID:27410080
Sole Inversion Precomputation for Elliptic Curve Scalar Multiplications
NASA Astrophysics Data System (ADS)
Dahmen, Erik; Okeya, Katsuyuki
This paper presents a new approach to precompute points [3]P, [5]P, ..., [2k-1]P, for some k ≥ 2 on an elliptic curve over \\mathbb{F}_p. Those points are required for the efficient evaluation of a scalar multiplication, the most important operation in elliptic curve cryptography. The proposed method precomputes the points in affine coordinates and needs only one single field inversion for the computation. The new method is superior to all known methods that also use one field inversion, if the required memory is taken into consideration. Compared to methods that require several field inversions for the precomputation, the proposed method is faster for a broad range of ratios of field inversions and field multiplications. The proposed method benefits especially from ratios as they occur on smart cards.
Tailoring the magnetization reversal of elliptical dots using exchange bias.
Sort, J.; Buchanan, K. S.; Pearson, J. E.; Hoffmann, A.; Menendez, E.; Salazar-Alvarez, G.; Baro, M. D.; Miron, M.; Rodamcq, B.; Dieny, B.; ICREA; Univ. Autonoma of Barcelona; Insti. Catala de Nanotecnologia; SPINTEC
2008-01-01
Exchange bias effects have been studied in elliptical dots composed of ferromagnetic Ni{sub 80}Fe{sub 20}-antiferromagnetic Ir{sub 20}Mn{sub 80} bilayers. The magnetization reversal mechanisms and magnetic configurations have been investigated by magneto-optic Kerr effect and magnetic force microscopy. Although the obtained bias fields in these dots are relatively small, the magnetization reversal is found to be influenced by the ferromagnetic-antiferromagnetic coupling. Namely, for some off-axis angles of measurement, the magnetization reversal mechanism of the Ni{sub 80}Fe{sub 20}-Ir{sub 20}Mn{sub 80} ellipses depends on whether exchange bias is induced along the minor or major axis of the ellipses. Hence, exchange bias is shown to be an effective means for tailoring the magnetization reversal of elliptical dots after sample fabrication.
Decoupling antennas in printed technology using elliptical metasurface cloaks
NASA Astrophysics Data System (ADS)
M. Bernety, Hossein; Yakovlev, Alexander B.
2016-01-01
In this paper, we extend the idea of reducing the electromagnetic interactions between transmitting radiators to the case of widely used planar antennas in printed technology based on the concept of mantle cloaking. Here, we show that how lightweight elliptical metasurface cloaks can be engineered to restore the intrinsic properties of printed antennas with strip inclusions. In order to present the novel approach, we consider two microstrip-fed monopole antennas resonating at slightly different frequencies cloaked by confocal elliptical metasurfaces formed by arrays of sub-wavelength periodic elements, partially embedded in the substrate. The presence of the metasurfaces leads to the drastic suppression of mutual near-field and far-field couplings between the antennas, and thus, their radiation patterns are restored as if they were isolated. Moreover, it is worth noting that this approach is not limited to printed radiators and can be applied to other planar structures as well.
Analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems
Bramble, J.H.; Pasciak, J.E.; Xu, J.
1988-10-01
We prove some new estimates for the convergence of multigrid algorithms applied to nonsymmetric and indefinite elliptic boundary value problems. We provide results for the so-called 'symmetric' multigrid schemes. We show that for the variable V-script-cycle and the W-script-cycle schemes, multigrid algorithms with any amount of smoothing on the finest grid converge at a rate that is independent of the number of levels or unknowns, provided that the initial grid is sufficiently fine. We show that the V-script-cycle algorithm also converges (under appropriate assumptions on the coarsest grid) but at a rate which may deteriorate as the number of levels increases. This deterioration for the V-script-cycle may occur even in the case of full elliptic regularity. Finally, the results of numerical experiments are given which illustrate the convergence behavior suggested by the theory.
Propagation of light in a circular array of elliptical fibres
NASA Astrophysics Data System (ADS)
Alexeyev, C. N.; Milione, G.; Pogrebnaya, A. O.; Yavorsky, M. A.
2016-02-01
We have studied transformation of discrete light beams in circular arrays of elliptical fibres, in which the orientation of ellipses' axes linearly depends on the angular position of the fibre in the array and makes an half-integer number p of full rotations while tracing along its contour. We have derived analytical expressions for the spectra and supermodes that allow for evanescent coupling between the fibres in the next-neighbour approximation. We have studied the transformative properties of such an array and shown that it can generate cylindrical vector beams (CVBs) of TE and TM types. We have shown that the type of generated beam depends on the orientation of linear polarization of the incident beam. In this way, the circular array of strongly elliptical fibres enables polarization control over the type of the generated CVB. We have also shown that such arrays can change the topological charge of an incoming discrete optical vortex by the doubled array's index p.
Dynamic separation of nanomagnet sublattices by orientation of elliptical elements
NASA Astrophysics Data System (ADS)
Yahagi, Y.; Berk, C. R.; Harteneck, B. D.; Cabrini, S. D.; Schmidt, H.
2014-04-01
We report the separation of the magnetization dynamics of densely packed nanomagnets depending on their orientation. The arrays consist of interleaved sublattices of identical nickel elliptical disks. By controlling the orientation of the elliptic disks relative to the external field in each sublattice, we simultaneously analyzed the magnetization dynamics in each sublattice using a time-resolved magnetooptic Kerr effect (TR-MOKE) microscopy system. The Fourier spectra showed clearly separated precession modes for sublattices with different orientations. The spectra were shown to be robust against the error in applied field orientation. The sublattice response can be tuned to a single collective frequency by choosing a symmetric field orientation. We analyzed the effect of the interelement coupling with various spacing between nanomagnets and found a relatively weak dependence on dipolar interactions in good agreement with micromagnetic simulations.
Elliptic complexes over C∗-algebras of compact operators
NASA Astrophysics Data System (ADS)
Krýsl, Svatopluk
2016-03-01
For a C∗-algebra A of compact operators and a compact manifold M, we prove that the Hodge theory holds for A-elliptic complexes of pseudodifferential operators acting on smooth sections of finitely generated projective A-Hilbert bundles over M. For these C∗-algebras and manifolds, we get a topological isomorphism between the cohomology groups of an A-elliptic complex and the space of harmonic elements of the complex. Consequently, the cohomology groups appear to be finitely generated projective C∗-Hilbert modules and especially, Banach spaces. We also prove that in the category of Hilbert A-modules and continuous adjointable Hilbert A-module homomorphisms, the property of a complex of being self-adjoint parametrix possessing characterizes the complexes of Hodge type.
Is the Capsular Bag Perimeter Round or Elliptical?
Amigó, Alfredo; Bonaque-González, Sergio
2016-01-01
Purpose: To report findings that could suggest an elliptical shape of the capsular bag. Methods: Five eyes of three patients with axial length greater than 24 mm underwent phacoemulsification cataract surgery with plate-haptic multifocal toric intraocular lens (IOL) implantation oriented in the vertical meridian. Results: In all cases, correct orientation of the IOLs was verified 30 minutes after surgery. After 24 hours, all eyes demonstrated unwanted rotation of the IOLs ranging from 15 to 45 degrees. The IOLs remained stable in the new position in all cases until adhesion of the capsular bag took place. Conclusion: These observations could suggest that the perimeter of the capsular bag has an elliptical shape. Therefore, the IOL tends to become fixated in a meridian of the capsular bag that best fits the diagonal diameter of the IOL. PMID:27413495
Artist concept of Magellan spacecraft in elliptical orbit around Venus
NASA Technical Reports Server (NTRS)
1988-01-01
Magellan spacecraft is shown in elliptical orbit around Venus, collecting data (radar mapping), and then transmitting data back to Earth in this artist concept. When the spacecraft orbit is close to Venus the synthetic aperature radar (SAR) will image a swath between 9 and 15 nautical miles (10 and 17 statute miles), beginning at or near the north pole and continuing to the southern hemisphere. Subsequent swaths will slightly overlap and, during its primary mission, the spacecraft will map most of the planet. When the spacecraft moves into the part of its elliptical orbit farthest from Venus, the spacecraft high-gain antenna will be turned toward Earth and will send the data collected during the imaging to Earth. Magellan, named after the 16th century Portuguese explorer, will orbit Venus about once every three hours, acquiring radar data for 37 minutes of each orbit. Magellan is managed by the Jet Propulsion Laboratory (JPL); Martin Marietta is developing the spacecraft and Hughes Air
Artist concept of Magellan spacecraft in elliptical orbit around Venus
NASA Technical Reports Server (NTRS)
1988-01-01
Magellan spacecraft is shown in elliptical orbit around Venus, collecting data (radar mapping), and then transmitting data back to Earth in this artist concept. When the spacecraft orbit is close to Venus the synthetic aperature radar (SAR) will image a swath between 9 and 15 nautical miles (10 and 17 statute miles) (highlighted in image), beginning at or near the north pole and continuing to the southern hemisphere. Subsequent swaths will slightly overlap and, during its primary mission, the spacecraft will map most of the planet. When the spacecraft moves into the part of its elliptical orbit farthest from Venus, the spacecraft high-gain antenna will be turned toward Earth and will send the data collected during the imaging to Earth. Magellan, named after the 16th century Portuguese explorer, will orbit Venus about once every three hours, acquiring radar data for 37 minutes of each orbit. Magellan is managed by the Jet Propulsion Laboratory (JPL); Martin Marietta is developing the sp
Resonances and bifurcations in systems with elliptical equipotentials
NASA Astrophysics Data System (ADS)
Marchesiello, Antonella; Pucacco, Giuseppe
2013-01-01
We present a general analysis of the orbit structure of 2D potentials with self-similar elliptical equipotentials by applying the method of Lie transform normalization. We study the most relevant resonances and related bifurcations. We find that the 1:1 resonance is associated only with the appearance of the loops and leads to the destabilization of either one or the other normal modes, depending on the ellipticity of equipotentials. Inclined orbits are never present and may appear only when the equipotentials are heavily deformed. The 1:2 resonance determines the appearance of bananas and antibanana orbits: the first family is stable and always appears at a lower energy than the second, which is unstable. The bifurcation sequence also produces the variations in the stability character of the major-axis orbit and is modified only by very large deformations of the equipotentials. Higher order resonances appear at intermediate or higher energies and can be described with good accuracy.
Fast ellipse detection by elliptical arcs extracting and grouping
NASA Astrophysics Data System (ADS)
Li, Yipeng; Zhao, Chunhui
2015-03-01
A novel and simple ellipse detection method is proposed in this paper. First, Canny operator is carried on the gray image to get edge image. Second, all the edge segments are obtained from edge image and output gradients of edge segments for further analysis. According to gradient direction, the edge segments are split into primitive lines and arcs. Then elliptical arcs are extracted from the results of splitting and an efficient grouping strategy is proposed to group elliptical arcs coming from the same ellipse as candidate ellipse. Finally, least-square fitting method is implemented to estimate the parameters of these candidate ellipses. Experiment results show that the proposed method is robust to noise and fast for real-time implementation.
Mott scattering in an elliptically polarized laser field
Attaourti, Y.; Manaut, B.; Taj, S.
2004-08-01
We study Mott scattering in the presence of a strong elliptically polarized field. Using the first Born approximation and the Dirac-Volkov states for the electron, we obtain an analytic formula for the unpolarized differential cross section. This generalizes the results found for the linearly polarized field by Li et al. [ 67, 063409 (2003)] and for the circularly polarized field by Attaourti and Manaut [ 68, 067401 (2003)].
A dearth of dark matter in ordinary elliptical galaxies.
Romanowsky, Aaron J; Douglas, Nigel G; Arnaboldi, Magda; Kuijken, Konrad; Merrifield, Michael R; Napolitano, Nicola R; Capaccioli, Massimo; Freeman, Kenneth C
2003-09-19
The kinematics of the outer parts of three intermediate-luminosity elliptical galaxies were studied with the Planetary Nebula Spectrograph. The galaxies' velocity-dispersion profiles were found to decline with the radius, and dynamical modeling of the data indicates the presence of little if any dark matter in these galaxies' halos. This unexpected result conflicts with findings in other galaxy types and poses a challenge to current galaxy formation theories. PMID:12947033
INFRARED SPECTROSCOPY OF NEARBY RADIO ACTIVE ELLIPTICAL GALAXIES
Mould, Jeremy; Reynolds, Tristan; Readhead, Tony; Matthews, Keith; Floyd, David; Brown, Michael; Jannuzi, Buell; Atlee, David; Cotter, Garret; Ferrarese, Laura
2012-11-15
In preparation for a study of their circumnuclear gas we have surveyed 60% of a complete sample of elliptical galaxies within 75 Mpc that are radio sources. Some 20% of our nuclear spectra have infrared emission lines, mostly Paschen lines, Brackett {gamma}, and [Fe II]. We consider the influence of radio power and black hole mass in relation to the spectra. Access to the spectra is provided here as a community resource.
Resonant phenomenon of elliptical cylinder flows in a subcritical regime
NASA Astrophysics Data System (ADS)
Chen, Shih-Sheng; Yen, Ruey-Hor
2011-11-01
The resonant phenomena in the wake behind a transversely vibrating elliptical cylinder with different axis ratios from Ar = 0.01 to Ar = 2.0 in the subcritical regime is numerically investigated. Navier-Stokes equations are solved by a spectral element code with a triangular mesh. Reynolds numbers range from 15 to 60 and the Roshko numbers range from 0.5 to 8 for different elliptical cylinders. Both the velocity and pressure responses in the wake are measured and analyzed. The investigations of the drag coefficients and the wake streamlines indicate that the cylinder's axis ratio has a minor effect on the resonant frequency, Ron. However, the cylinder's axis ratio is found to have a prominent effect on the resonant amplitude; namely, the smaller the cylinder's axis ratio, the stronger the occurrence of resonant amplitude. The investigations of resonant responses of both the velocity and pressure and the probe locations may provide information for designing a flow meter based on pressure responses in the subcritical regime. It shows that the ratio of velocity and pressure responses poses a great linear relationship against the probe distance behind the vibrating cylinder. Moreover, a resonant method based on the different resonant frequencies at different probed locations in the subcritical regime to predict the critical conditions is examined and verified for different elliptical cylinders. Finally, based on the critical values found, a reduced Reynolds number and a reduced Roshko number are proposed to unify the different linear relationships resulting from different elliptical cylinder flows. The result indicates that the effect of axis ratio can be stripped off in the reduced plane, which may be applied to a more generalized cylinder shape.
Two elliptic closed geodesics on positively curved Finsler spheres
NASA Astrophysics Data System (ADS)
Duan, Huagui
2016-06-01
In this paper, we prove that for every Finsler n-dimensional sphere (Sn , F) with reversibility λ and flag curvature K satisfying (λ/1+λ) 2 < K ≤ 1, either there exist infinitely many closed geodesics, or there exist at least two elliptic closed geodesics and each linearized Poincaré map has at least one eigenvalue of the form e √{ - 1 } θ with θ being an irrational multiple of π.
The p-Dirichlet-to-Neumann operator with applications to elliptic and parabolic problems
NASA Astrophysics Data System (ADS)
Hauer, Daniel
2015-10-01
In this paper, we investigate the Dirichlet-to-Neumann operator associated with second order quasi-linear operators of p-Laplace type for 1 < p < ∞, which acts on the boundary of a bounded Lipschitz domain in Rd for d ≥ 2. We establish well-posedness and Hölder-continuity with uniform estimates of weak solutions of some elliptic boundary-value problems involving the Dirichlet-to-Neumann operator. By employing these regularity results of weak solutions of elliptic problems, we show that the semigroup generated by the negative Dirichlet-to-Neumann operator on Lq enjoys an Lq -C 0, α-smoothing effect and the negative Dirichlet-to-Neumann operator on the set of continuous functions on the boundary of the domain generates a strongly continuous and order-preserving semigroup. Moreover, we establish convergence in large time with decay rates of all trajectories of the semigroup, and in the singular case (1 + ε) ∨ 2 d/d + 2 ≤/p < 2 for some ε > 0, we give upper estimates of the finite time of extinction.
A Low-Power VHDL Design for an Elliptic Curve Digital Signature Chip
SCHROEPPEL, RICHARD C.; BEAVER, CHERYL L.; DRAELOS, TIMOTHY J.; GONZALES, RITA A.; MILLER, RUSSELL D.
2002-09-01
The authors present a VHDL design that incorporates optimizations intended to provide digital signature generation with as little power, space, and time as possible. These three primary objectives of power, size, and speed must be balanced along with other important goals, including flexibility of the hardware and ease of use. The highest-level function doffered by their hardware design is Elliptic Curve Optimal El Gamal digital signature generation. The parameters are defined over the finite field GF(2{sup 178}), which gives security that is roughly equivalent to that provided by 1500-bit RSA signatures. The optimizations include using the point-halving algorithm for elliptic curves, field towers to speed up the finite field arithmetic in general, and further enhancements of basic finite field arithmetic operations. The result is a synthesized VHDL digital signature design (using a CMOS 0.5{micro}m, 5V, 25 C library) of 191,000 gates that generates a signature in 4.4 ms at 20 MHz.
A new weak Galerkin finite element method for elliptic interface problems
Mu, Lin; Wang, Junping; Ye, Xiu; Zhao, Shan
2016-08-26
We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments inmore » order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.« less
NASA Astrophysics Data System (ADS)
Jourabian, Mahmoud; Farhadi, Mousa; Rabienataj Darzi, Ahmad Ali
2016-07-01
In this study, the melting process of ice as a phase-change material (PCM) saturated with a nickel-steel porous matrix inside a horizontal elliptical tube is investigated. Due to the low thermal conductivity of the PCM, it is motivated to augment the heat transfer performance of the system simultaneously by finding an optimum value of the aspect ratio and impregnating a metallic porous matrix into the base PCM. The lattice Boltzmann method with a double distribution function formulated based on the enthalpy method, is applied at the representative elementary volume scale under the local thermal equilibrium assumption between the PCM and porous matrix in the composite. While reducing or increasing the aspect ratio of the circular tubes leads to the expedited melting, the 90° inclination of each elliptical tube in the case of the pure PCM melting does not affect the melting rate. With the reduction in the porosity, the effective thermal conductivity and melting rate in all tubes promoted. Although the natural convection is fully suppressed due to the significant flow blockage in the porous structure, the melting rates are generally increased in all cases.
A new weak Galerkin finite element method for elliptic interface problems
NASA Astrophysics Data System (ADS)
Mu, Lin; Wang, Junping; Ye, Xiu; Zhao, Shan
2016-11-01
A new weak Galerkin (WG) finite element method is introduced and analyzed in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. Extensive numerical experiments have been conducted to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.
A substantial population of low-mass stars in luminous elliptical galaxies.
van Dokkum, Pieter G; Conroy, Charlie
2010-12-16
The stellar initial mass function (IMF) describes the mass distribution of stars at the time of their formation and is of fundamental importance for many areas of astrophysics. The IMF is reasonably well constrained in the disk of the Milky Way but we have very little direct information on the form of the IMF in other galaxies and at earlier cosmic epochs. Here we report observations of the Na (I) doublet and the Wing-Ford molecular FeH band in the spectra of elliptical galaxies. These lines are strong in stars with masses less than 0.3M(⊙) (where M(⊙) is the mass of the Sun) and are weak or absent in all other types of stars. We unambiguously detect both signatures, consistent with previous studies that were based on data of lower signal-to-noise ratio. The direct detection of the light of low-mass stars implies that they are very abundant in elliptical galaxies, making up over 80% of the total number of stars and contributing more than 60% of the total stellar mass. We infer that the IMF in massive star-forming galaxies in the early Universe produced many more low-mass stars than the IMF in the Milky Way disk, and was probably slightly steeper than the Salpeter form in the mass range 0.1M(⊙) to 1M(⊙).
NASA Astrophysics Data System (ADS)
Spyratou, E.; Makropoulou, M.; Serafetinides, A. A.
2011-07-01
In this work optical tweezers with elliptical beam profiles have been developed in order to examine the effect of optical force on fresh red blood cells (RBC) in isotonic, hypertonic and hypotonic buffer solutions. Considering that the optical force depends essentially on the cell surface and the cytoplasmic refractive index, it is obvious that biochemical modifications associated with different states of the cell will influence its behaviour in the optical trap. Line optical tweezers were used to manipulate simultaneously more than one red blood cell. After we have been manipulated a RBC with an elliptical laser beam profile in an isotonic or hypertonic buffer, we noticed that it rotates by itself when gets trapped by optical tweezers and undergoes folding. Further shape deformations can be observed attributed to the competition between alignment and rotational torque which are transferred by laser light to the cell. In hypotonic buffer RBCs become spherical and do not rotate or fold since the resultant force due to rays emerging from diametrically opposite points of the cell leads to zero torque. Manipulation of fresh red blood cells in isotonic solution by line optical tweezers leads to folding and elongation of trapped RBCs. Membrane elasticity properties such as bending modulus can be estimated by measuring RBC's folding time in function with laser power.
Theoretical results for fully flooded, elliptical hydrodynamic contacts
NASA Technical Reports Server (NTRS)
Hamrock, B. J.; Dowson, D.
1982-01-01
The influence of the ellipticity parameter and the dimensionless speed, load, and materials parameters on minimum film thickness was investigated. The ellipticity parameter was varied from 1 (a ball-on-plate configuration) to 8 (a configuration approaching a line contact). The dimensionless speed parameter was varied over a range of nearly two orders of magnitude. Conditions corresponding to the use of solid materials of bronze, steel, and silicon nitride and lubricants of praffinic and naphthemic mineral oils were considered in obtaining the exponent in the dimensionless materials parameter. Thirty-four different cases were used in obtaining the minimum film thickness formula H min = 3.63U to the 0.68 power G to the 0.49 power W to the -0.073 power 1-e to the 0.68K power). A simplified expression for the ellipticity parameter was found where k = 1.03 (r(y)/r(x)) to the 0.64 power. Contour plots were also shown which indicate in detail the pressure spike and two side lobes in which the minimum film thickness occurs. These theoretical solutions of film thickness have all the essential features of the previously reported experimental observations based upon optical interferometry.
Fast magnetohydrodynamic oscillations in an elliptical coronal arcade
NASA Astrophysics Data System (ADS)
Díaz, A. J.
2006-09-01
Aims.A model of a elliptically shaped coronal arcade with piecewise constant density is discussed to explore the effects of curvature on radially polarised fast modes. It is important to test whether the main results in the straight and cylindrical geometries can be extrapolated to these more complex equilibria. Methods: .An equilibrium model for a force-free, line-tied elliptical arcade is introduced and a partial differential equation is derived for the velocity perturbation of the fast modes, which is solved analytically. The properties of the modes are studied in terms of the dispersion relation, which depends on the eccentricity, the arcade width, and the density contrast. Results: .Modes mainly contained in the cavity below the arcade are also present, and have avoided crossings with the modes of the arcade. Even the fundamental mode becomes leaky due to curvature. Approximated relations are deduced for the frequency of the modes and the spatial structure is discussed, focusing on the different families through which a rich mode spectrum can be classified. Conclusions: .The different types of modes of the spectrum are described and its relevance to observations is discussed. The periods obtained in Cartesian geometry provide a reasonable approximation, but this geometry lacks some other key ingredients: the damping rates are different and some types of modes present in the elliptical geometry are not sustained in the straight slab.
Tunnel Point Cloud Filtering Method Based on Elliptic Cylindrical Model
NASA Astrophysics Data System (ADS)
Zhua, Ningning; Jiaa, Yonghong; Luo, Lun
2016-06-01
The large number of bolts and screws that attached to the subway shield ring plates, along with the great amount of accessories of metal stents and electrical equipments mounted on the tunnel walls, make the laser point cloud data include lots of non-tunnel section points (hereinafter referred to as non-points), therefore affecting the accuracy for modeling and deformation monitoring. This paper proposed a filtering method for the point cloud based on the elliptic cylindrical model. The original laser point cloud data was firstly projected onto a horizontal plane, and a searching algorithm was given to extract the edging points of both sides, which were used further to fit the tunnel central axis. Along the axis the point cloud was segmented regionally, and then fitted as smooth elliptic cylindrical surface by means of iteration. This processing enabled the automatic filtering of those inner wall non-points. Experiments of two groups showed coincident results, that the elliptic cylindrical model based method could effectively filter out the non-points, and meet the accuracy requirements for subway deformation monitoring. The method provides a new mode for the periodic monitoring of tunnel sections all-around deformation in subways routine operation and maintenance.
Major and minor axis kinematics of 22 ellipticals
NASA Astrophysics Data System (ADS)
Franx, Marijn; Illingworth, Garth; Heckman, Timothy
1989-09-01
Rotation curves and velocity dispersion profiles have been determined for the major and the minor axes of 22 elliptical galaxies. Rotation was detected in all but one galaxy, even though the sample was biased toward round ellipticals. Minor axis rotation larger than major axis rotation was measured in two galaxies, NGC 4406 and NGC 7507. Roughly 10 percent of ellipticals may show large minor axis velocities relative to those on the major axis. A simple model is used to derive a rotational axis from the observed minor and major axis velocities to a typical accuracy of 6 deg. The rotational and photometric minor axes aligned to better than 10 deg for 60 percent of the sample, implying that the direction of the angular momentum is related to the orientation of the figure of the galaxy. IC 1459 has a kinematically distinct core with its angular momentum opposite to the angular momentum of the outer parts, and NGC 4406 has a core with its angular momentum perpendicular to that of the outer parts.
Coherent effects in the field of elliptically polarized light
NASA Astrophysics Data System (ADS)
Andreeva, Ch.; Biancalana, Valerio; Cartaleva, Stefka S.; Dancheva, Yordanka V.; Karaulanov, Todor S.; Mariotti, E.; Moi, L.; Nasyrov, K. A.
2004-06-01
In the present communication we report on the investigation of the effect of elliptically polarized laser light exciting the Fg=3 Cs D2 absorption line. Coherent resonances in Cs have been studied, obtained in Hanle configuration by scanning of magnetic field parallel to the light propagation direction. The resonances were investigated depending on the polarization of the irradiating light field. It has been observed that for linear polarization dark resonances in the fluorescence are registered, while for circularly polarized light, bright resonances are obtained, probably due to stray orthogonal magnetic field. For elliptical polarization a narrow peak appears superimposed on a broader dip. Theoretical description has been made, which shows that at elliptical polarization and orthogonal magnetic field in the case of weak light fields, a single peak in the excited state population is observed, while strong fields lead to the splitting of this peak into two peaks. The presence of both weak and strong light fields, probably due to reflection of the light beam on the cell walls, could lead to the experimentally observed fluorescence behaviour.
Elliptically polarized terahertz radiation from a chiral oxide
Takeda, R.; Kida, N. Sotome, M.; Okamoto, H.
2015-09-28
Polarization control of terahertz wave is a challenging subject in terahertz science and technology. Here, we report a simple method to control polarization state of the terahertz wave in terahertz generation process. At room temperature, terahertz radiation from a noncentrosymmetric and chiral oxide, sillenite Bi{sub 12}GeO{sub 20}, is observed by the irradiation of linearly polarized femtosecond laser pulses at 800 nm. The polarization state of the emitted terahertz wave is found to be elliptic with an ellipticity of ∼0.37 ± 0.10. Furthermore, the ellipticity was altered to a nearly zero (∼0.01 ± 0.01) by changing the polarization of the incident linearly polarized femtosecond laser pulses. Such a terahertz radiation characteristic is attributable to variation of the polarization state of the emitted terahertz waves, which is induced by retardation due to the velocity mismatch between the incident femtosecond laser pulse and generated terahertz wave and by the polarization tilting due to the optical activity at 800 nm.
Lost and found dark matter in elliptical galaxies
NASA Astrophysics Data System (ADS)
Dekel, A.; Stoehr, F.; Mamon, G. A.; Cox, T. J.; Novak, G. S.; Primack, J. R.
2005-09-01
There is strong evidence that the mass of the Universe is dominated by dark matter, which exerts gravitational attraction but whose exact nature is unknown. In particular, all galaxies are believed to be embedded in massive haloes of dark matter. This view has recently been challenged by the observation of surprisingly low random stellar velocities in the outskirts of ordinary elliptical galaxies, which has been interpreted as indicating a lack of dark matter. Here we show that the low velocities are in fact compatible with galaxy formation in dark-matter haloes. Using numerical simulations of disk-galaxy mergers, we find that the stellar orbits in the outer regions of the resulting ellipticals are very elongated. These stars were torn by tidal forces from their original galaxies during the first close passage and put on outgoing trajectories. The elongated orbits, combined with the steeply falling density profile of the observed tracers, explain the observed low velocities even in the presence of large amounts of dark matter. Projection effects when viewing a triaxial elliptical can lead to even lower observed velocities along certain lines of sight.
Hydrodynamical model for J/{psi} suppression and elliptic flow
Chaudhuri, A. K.
2009-10-15
In a hydrodynamic model, we have studied J/{psi} suppression and elliptic flow in Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC) energy {radical}(s)=200 GeV. At the initial time, J/{psi}'s are randomly distributed in the fluid. As the fluid evolves in time, the free-streaming J/{psi}'s are dissolved if the local fluid temperature exceeds a melting temperature T{sub J/{psi}}. Sequential melting of charmonium states ({chi}{sub c}, {psi}{sup '}, and J/{psi}), with melting temperatures T{sub {chi}{sub c}}=T{sub {psi}{sup '}}{approx_equal}1.2T{sub c} and T{sub J/{psi}}{approx_equal}2T{sub c} and a feed-down fraction F{approx_equal}0.3, is consistent with the PHENIX data on J/{psi} suppression and near-zero elliptic flow for J/{psi}'s. It is also shown that the model will require substantial regeneration of charmonium if the charmonium states dissolve at a temperature close to the critical temperatures, T{sub {chi}{sub c}}=T{sub {psi}{sup '}}{<=}T{sub c} and T{sub J/{psi}}{approx_equal}1.2T{sub c}. The regenerated charmonium will have positive elliptic flow.
Application of Analytic Solution in Relative Motion to Spacecraft Formation Flying in Elliptic Orbit
NASA Astrophysics Data System (ADS)
Cho, Hancheol; Park, Sang-Young; Choi, Kyu-Hong
2008-09-01
The current paper presents application of a new analytic solution in general relative motion to spacecraft formation flying in an elliptic orbit. The calculus of variations is used to analytically find optimal trajectories and controls for the given problem. The inverse of the fundamental matrix associated with the dynamic equations is not required for the solution in the current study. It is verified that the optimal thrust vector is a function of the fundamental matrix of the given state equations. The cost function and the state vector during the reconfiguration can be analytically obtained as well. The results predict the form of optimal solutions in advance without having to solve the problem. Numerical simulation shows the brevity and the accuracy of the general analytic solutions developed in the current paper.
Elliptic integral evaluations of Bessel moments
Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Glasser, M.L.
2008-01-06
We record what is known about the closed forms for variousBessel function moments arising in quantum field theory, condensed mattertheory and other parts of mathematical physics. More generally, wedevelop formulae for integrals of products of six or fewer Besselfunctions. In consequence, we are able to discover and prove closed formsfor c(n,k) := Int_0 inf tk K_0 n(t) dt, with integers n = 1, 2, 3, 4 andk greater than or equal to 0, obtaining new results for the even momentsc3,2k and c4,2k . We also derive new closed forms for the odd momentss(n,2k+1) := Int_0 inf t(2k+1) I_0(t) K_0n(t) dt,with n = 3, 4 and fort(n,2k+1) := Int_0 inf t(2k+1) I_02(t) K_0(n-2) dt, with n = 5, relatingthe latter to Green functions on hexagonal, diamond and cubic lattices.We conjecture the values of s(5,2k+1), make substantial progress on theevaluation of c(5,2k+1), s(6,2k+1) and t(6,2k+1) and report more limitedprogress regarding c(5,2k), c(6,2k+1) and c(6,2k). In the process, weobtain 8 conjectural evaluations, each of which has been checked to 1200decimal places. One of these lies deep in 4-dimensional quantum fieldtheory and two are probably provable by delicate combinatorics. Thereremains a hard core of five conjectures whose proofs would be mostinstructive, to mathematicians and physicists alike.
NASA Astrophysics Data System (ADS)
Plana, H.; Boulesteix, J.; Amram, Ph.; Carignan, C.; Mendes de Oliveira, C.
1998-02-01
For the last ten years faint ionized gas detection has been carried out for elliptical galaxies with success. The kinematics is essential to understand galaxy gas origin and fate. Here we present a sample of 11 elliptical and lenticular galaxies observed with the ``Cigale" scanning Perot-Fabry instrument. For each galaxy monochromatic and velocity map of ionized gas is presented. Geometrical properties such as viewing angles and axis ratios are also derived from observations. Double gaseous components are found in 3 galaxies of our sample, implying an external origin for at least part of the observed gas. % Based on observations collected with the S.A.O. 6 m telescope located in Nizhnij Arkhyz (Russia), the 3.6 m CFH telescope and the 3.6 m telescope at ESO.
Degenerate elliptic inequalities with critical growth
NASA Astrophysics Data System (ADS)
Fang, Ming
This article is motivated by the fact that very little is known about variational inequalities of general principal differential operators with critical growth. The concentration compactness principle of P.L. Lions [P.L. Lions, The concentration compactness principle in the calculus of variation. The limit case I, Rev. Mat. Iberoamericana 1 (1) (1985) 145-201; P.L. Lions, The concentration compactness principle in the calculus of variation. The limit case II, Rev. Mat. Iberoamericana 1 (2) (1985) 45-121] is a widely applied technique in the analysis of Palais-Smale sequences. For critical growth problems involving principal differential operators Laplacian or p-Laplacian, much has been accomplished in recent years, whereas very little has been done for problems involving more general main differential operators since a nonlinearity is observed between the corresponding functional I(u) and measure μ introduced in the concentration compactness method. In this paper, we investigate a Leray-Lions type operator and behaviors of its ( sequence.
Quasilinear Elliptic Equations Involving Variable Exponents
NASA Astrophysics Data System (ADS)
Mihǎilescu, Mihai; Moroşanu, Gheorghe
2008-09-01
Consider the boundary value problem -Σi = N∂xi(|∂xiu|pi(x)-2∂xiu) = λ(x)|u|q(x)-2u in Ω, u = 0 on ∂Ω, where Ω is a bounded domain in RN with smooth boundary ∂Ω, while p1,…,pN,q are continuous functions and q(x)>1,pi(x)⩾2 for all x∈Ω¯, i = 1,⋯,N. Combining the mountain pass theorem of Ambrosetti and Rabinowitz [1] and Ekeland's variational principle [7] we show that under suitable conditions the above problem has two nontrivial weak solutions. We also consider the eigenvalue problem corresponding to the case when λ in the above equation is a positive constant. We assume that there exist j,k∈{1,…,N} with j≠k such that pj ≡ q in Ω¯, and q is independent of xj with maxΩ¯q
Burnfield, Judith M; Irons, Sonya L; Buster, Thad W; Taylor, Adam P; Hildner, Gretchen A; Shu, Yu
2014-01-01
Individuals with walking limitations often experience challenges engaging in functionally relevant exercise. An adapted elliptical trainer (motor to assist pedal movement, integrated body weight harness, ramps/stairs, and grab rails) has been developed to help individuals with physical disabilities and chronic conditions regain/retain walking capacity and fitness. However, limited published studies are available to guide therapeutic interventions. This repeated measures study examined the influence of motor-assisted elliptical training speed on lower extremity muscle demands at four body weight support (BWS) levels commonly used therapeutically for walking. Electromyography (EMG) and pedal trajectory data were recorded as ten individuals without known disability used the motor-assisted elliptical trainer at three speeds [20,40, 60 revolutions per minute (RPM)] during each BWS level (0%, 20%, 40%, 60%). Overall, the EMG activity (peak, mean, duration) in key stabilizer muscles (i.e., gluteus medius, gluteus maximus, vastus lateralis, medial gastrocnemius and soleus) recorded at 60 RPM exceeded those at 40 RPM, which were higher than values at 20 RPM in all but three situations (gluteus medius mean at 0% BWS, vastus lateralis mean at 20% BWS, soleus duration at 40% BWS); however, these differences did not always achieve statistical significance. Slower motor-assisted speeds can be used to accommodate weakness of gluteus medius, gluteus maximus, vastus lateralis, medial gastrocnemius and soleus. As strength improves, training at faster motor-assisted speeds may provide a means to progressively challenge key lower extremity stabilizers.
NASA Technical Reports Server (NTRS)
Pan, Y. S.
1978-01-01
A three dimensional, partially elliptic, computer program was developed. Without requiring three dimensional computer storage locations for all flow variables, the partially elliptic program is capable of predicting three dimensional combustor flow fields with large downstream effects. The program requires only slight increase of computer storage over the parabolic flow program from which it was developed. A finite difference formulation for a three dimensional, fully elliptic, turbulent, reacting, flow field was derived. Because of the negligible diffusion effects in the main flow direction in a supersonic combustor, the set of finite-difference equations can be reduced to a partially elliptic form. Only the pressure field was governed by an elliptic equation and requires three dimensional storage; all other dependent variables are governed by parabolic equations. A numerical procedure which combines a marching integration scheme with an iterative scheme for solving the elliptic pressure was adopted.
Rotation and conversion of transmission mode based on a rotatable elliptical core ring resonator
NASA Astrophysics Data System (ADS)
Liu, Bin; Liu, Yun-Feng; Li, Shu-Jing; He, Xing-Dao
2016-06-01
A compact plasmonic waveguide system consisting of a rotating elliptical core ring (ECR) coupled two metal-insulator-metal (MIM) waveguides is proposed. Influences of the eccentricity and rotation angle of the elliptical core on the transmission characteristics are studied in detail, by using Finite-Difference Time-Domain (FDTD) method. Compared with circular core in ring resonator, the elliptical core will lead to the asymmetric field distributions of intrinsic mode. Based on this, a 1×2 splitter is designed, in which the beam-splitting ratio can be adjusted by changing the eccentricity of the elliptical core. In addition, we find that the intrinsic mode of ECR rotate with elliptical core and gradually convert to its orthogonal mode. Separation of the pair orthogonal modes increases with growth of the eccentricity of the elliptical core. And, the higher order intrinsic mode corresponds to the shorter rotation angle of mode conversion.
Elliptical metasurfaces for cloaking and antenna applications at microwave and terahertz frequencies
NASA Astrophysics Data System (ADS)
Mehrpourbernety, Hossein
microwave frequencies. In this work, we propose a novel approach to reduce the mutual coupling between two closely spaced strip dipole antennas with the elliptical metasurfaces formed by conformal printed arrays of sub-wavelength periodic elements. We show that by covering each strip with the metasurface cloak, the antennas become invisible to each other and their radiation patterns are restored as if they were isolated. The electromagnetic scattering analysis pertained to the case of antennas with the frequencies far from each other is shown to be as a good approximation of a 2-D metallic strip scattering cancellation problem solved by expressing the incident and scattered fields in terms of radial and angular Mathieu functions, with the use of sheet impedance boundary conditions at the metasurface. In addition, we extend the novel approach based on the concept of mantle cloaking in order to reduce the mutual near-field and far-field coupling between planar antennas in printed technology. To present the idea, we consider two microstrip-fed monopole antennas resonating at slightly different frequencies and show that by cloaking the radiating part of each antenna, the antennas become invisible to each other, and thus, the mutual coupling between the antennas is suppressed drastically. The cloak structure is realized by a conformal elliptical metasurface formed by confocal printed arrays of sub-wavelength periodic elements, partially embedded in the substrate. The presence of the metasurfaces leads to the restoration of the radiation patterns of the antennas as if they were isolated.
The demagnetizing energies of a uniformly magnetized cylinder with an elliptic cross-section
NASA Astrophysics Data System (ADS)
Goode, D. A.; Rowlands, G.
2003-12-01
Analytic expressions for the demagnetizing energies are obtained in the form of partial series, for long elliptic cylinders and for squat ones where the ellipticity of the cross-section is unrestrained. This leaves just a small range where the demagnetizing energies are not well defined. It is found that by replacing the elliptic cylinders with rectangular blocks, a good approximation to the demagnetizing energy may be made in this small range.
Excess ellipticity of hot and cold spots in the WMAP data?
Berntsen, Eirik; Hansen, Frode K. E-mail: frodekh@astro.uio.no
2013-12-10
We investigate claims of excess ellipticity of hot and cold spots in the Wilkinson Microwave Anisotropy Probe (WMAP) data. Using the cosmic microwave background (CMB) data from 7 yr of observations by the WMAP satellite, we find, contrary to previous claims of a 10σ detection of excess ellipticity in the 3 yr data, that the ellipticity of hot and cold spots is perfectly consistent with simulated CMB maps based on the concordance cosmology. We further test for excess obliquity and excess skewness/kurtosis of ellipticity and obliquity and find the WMAP7 data consistent with Gaussian simulated maps.
Andrade, R.; Grassi, F.; Hama, Y.; Kodama, T.; Socolowski, O. Jr.
2006-11-17
Elliptic flow at BNL RHIC is computed event by event with NeXSPheRIO. We show that when symmetry of the particle distribution in relation to the reaction plane is assumed, as usually done in the experimental extraction of elliptic flow, there is a disagreement between the true and reconstructed elliptic flows (15%-30% for {eta}=0, 30% for p{sub perpendicular}=0.5 GeV). We suggest a possible way to take into account the asymmetry and get good agreement between these elliptic flows.
Multigrid lattice Boltzmann method for accelerated solution of elliptic equations
NASA Astrophysics Data System (ADS)
Patil, Dhiraj V.; Premnath, Kannan N.; Banerjee, Sanjoy
2014-05-01
A new solver for second-order elliptic partial differential equations (PDEs) based on the lattice Boltzmann method (LBM) and the multigrid (MG) technique is presented. Several benchmark elliptic equations are solved numerically with the inclusion of multiple grid-levels in two-dimensional domains at an optimal computational cost within the LB framework. The results are compared with the corresponding analytical solutions and numerical solutions obtained using the Stone's strongly implicit procedure. The classical PDEs considered in this article include the Laplace and Poisson equations with Dirichlet boundary conditions, with the latter involving both constant and variable coefficients. A detailed analysis of solution accuracy, convergence and computational efficiency of the proposed solver is given. It is observed that the use of a high-order stencil (for smoothing) improves convergence and accuracy for an equivalent number of smoothing sweeps. The effect of the type of scheduling cycle (V- or W-cycle) on the performance of the MG-LBM is analyzed. Next, a parallel algorithm for the MG-LBM solver is presented and then its parallel performance on a multi-core cluster is analyzed. Lastly, a practical example is provided wherein the proposed elliptic PDE solver is used to compute the electro-static potential encountered in an electro-chemical cell, which demonstrates the effectiveness of this new solver in complex coupled systems. Several orders of magnitude gains in convergence and parallel scaling for the canonical problems, and a factor of 5 reduction for the multiphysics problem are achieved using the MG-LBM.
Direct Detections of Young Stars in Nearby Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Ford, H. Alyson; Bregman, Joel N.
2013-06-01
Small amounts of star formation in elliptical galaxies are suggested by several results: surprisingly young ages from optical line indices, cooling X-ray gas, and mid-infrared dust emission. Such star formation has previously been difficult to directly detect, but using ultraviolet Hubble Space Telescope Wide Field Camera 3 imaging, we have identified individual young stars and star clusters in four nearby ellipticals. Ongoing star formation is detected in all galaxies, including three ellipticals that have previously exhibited potential signposts of star-forming conditions (NGC 4636, NGC 4697, and NGC 4374), as well as the typical "red and dead" NGC 3379. The current star formation in our closest targets, where we are most complete, is between 2.0 and 9.8 × 10-5 M ⊙ yr-1. The star formation history was roughly constant from 0.5 to 1.5 Gyr (at (3-5) × 10-4 M ⊙ yr-1), but decreased by a factor of several in the past 0.3 Gyr. Most star clusters have a mass between 102 and 104 M ⊙. The specific star formation rates of ~10-16 yr-1 (at the present day) or ~10-14 yr-1 (when averaging over the past Gyr) imply that a fraction 10-8 of the stellar mass is younger than 100 Myr and 10-5 is younger than 1 Gyr, quantifying the level of frosting of recent star formation over the otherwise passive stellar population. There is no obvious correlation between either the presence or spatial distribution of postulated star formation indicators and the star formation we detect. Based on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with program 11583.
Orbital structure and mass distribution in elliptical galaxies
NASA Astrophysics Data System (ADS)
Kronawitter, Andi; Saglia, R. P.; Gerhard, Ortwin; Bender, Ralf
2000-05-01
We report on a homogeneous dynamical analysis of a sample of 21 round (17 E0/E1, 4 E2) elliptical galaxies. We present new kinematic data for eight of these galaxies and new photometry for one object. The remaining kinematic and photometric data and the required distance information are taken from the literature. The analysis uses non-parametric spherical models and takes into account line profile information as well as velocity dispersions. We present model fits to the kinematic data and the derived radial profiles of orbital anisotropy and B-band mass-to-light ratio, including confidence intervals. The circular velocity curves resulting from our model fits are all consistent with being flat outside R~ 0.3 R_e. Generally, the M/L ratio profiles show an outward increase, although models based on luminous matter are ruled out at 95% confidence only for three galaxies (NGC 2434, NGC 7507, NGC 7626). For NGC 1399, NGC 4472, NGC 4486, and NGC 4636, where X-ray observations are available, the mass profiles of the best fit models match the ones derived from the X-ray analysis. The best models for most galaxies are isotropic to slightly radially anisotropic, with typical beta <~0.3, in a few cases beta <~0 .5 at R_e/2. We discuss the generally small effects of flattening along the line-of-sight (the expected
DIRECT DETECTIONS OF YOUNG STARS IN NEARBY ELLIPTICAL GALAXIES
Ford, H. Alyson; Bregman, Joel N.
2013-06-20
Small amounts of star formation in elliptical galaxies are suggested by several results: surprisingly young ages from optical line indices, cooling X-ray gas, and mid-infrared dust emission. Such star formation has previously been difficult to directly detect, but using ultraviolet Hubble Space Telescope Wide Field Camera 3 imaging, we have identified individual young stars and star clusters in four nearby ellipticals. Ongoing star formation is detected in all galaxies, including three ellipticals that have previously exhibited potential signposts of star-forming conditions (NGC 4636, NGC 4697, and NGC 4374), as well as the typical ''red and dead'' NGC 3379. The current star formation in our closest targets, where we are most complete, is between 2.0 and 9.8 Multiplication-Sign 10{sup -5} M{sub Sun} yr{sup -1}. The star formation history was roughly constant from 0.5 to 1.5 Gyr (at (3-5) Multiplication-Sign 10{sup -4} M{sub Sun} yr{sup -1}), but decreased by a factor of several in the past 0.3 Gyr. Most star clusters have a mass between 10{sup 2} and 10{sup 4} M{sub Sun }. The specific star formation rates of {approx}10{sup -16} yr{sup -1} (at the present day) or {approx}10{sup -14} yr{sup -1} (when averaging over the past Gyr) imply that a fraction 10{sup -8} of the stellar mass is younger than 100 Myr and 10{sup -5} is younger than 1 Gyr, quantifying the level of frosting of recent star formation over the otherwise passive stellar population. There is no obvious correlation between either the presence or spatial distribution of postulated star formation indicators and the star formation we detect.
Classical description of strong-field double ionization by elliptical laser pulses
NASA Astrophysics Data System (ADS)
Zhou, Yueming; Zhang, Qingbin; Huang, Cheng; Lu, Peixiang
2012-10-01
Sequential double ionization of argon induced by elliptically polarized laser pulses at the over-the-barrier ionization regime is investigated with a fully classical model. We provide futher detail beyond that found in our previous paper [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.109.053004 109, 053004 (2012)] and show that all of the experimental observations, including the evolution of the ion momentum spectra as a function of laser intensity, the intensity-dependent ratio for the parallel and antiparallel electron emissions, and the release times of both electrons for various laser pulses, are excellently reproduced by our classical model. Our results indicate that the classical treatment is very valid and accurate in describing strong-field ionization, providing a simple and intuitive way to investigate the complex electron correlations in strong-field double and multiple ionizations.
Effect of bulk viscosity on elliptic flow near the QCD phase transition
Denicol, G. S.; Kodama, T.; Mota, Ph.; Koide, T.
2009-12-15
In this work, we examine the effect of bulk viscosity on elliptic flow, taking into account the critical behavior of the equation of state and transport coefficients near the QCD phase transition. We found that the p{sub T} dependence of v{sub 2} is quantitatively changed by the presence of the QCD phase transition. Within reasonable values of the transport coefficients, v{sub 2} decreases by a factor of 15% at small p{sub T} values (<1 GeV). However, for larger values of p{sub T} (>2 GeV), the interplay between the velocity of sound and transport coefficient near the QCD phase transition enhances v{sub 2}. We point out that Grad's 14-moment approximation cannot be applied for the calculation of the one-particle distribution function at the freeze-out.
Multigrid method applied to the solution of an elliptic, generalized eigenvalue problem
Alchalabi, R.M.; Turinsky, P.J.
1996-12-31
The work presented in this paper is concerned with the development of an efficient MG algorithm for the solution of an elliptic, generalized eigenvalue problem. The application is specifically applied to the multigroup neutron diffusion equation which is discretized by utilizing the Nodal Expansion Method (NEM). The underlying relaxation method is the Power Method, also known as the (Outer-Inner Method). The inner iterations are completed using Multi-color Line SOR, and the outer iterations are accelerated using Chebyshev Semi-iterative Method. Furthermore, the MG algorithm utilizes the consistent homogenization concept to construct the restriction operator, and a form function as a prolongation operator. The MG algorithm was integrated into the reactor neutronic analysis code NESTLE, and numerical results were obtained from solving production type benchmark problems.
Drew, L.J.
1979-01-01
In this study the selection of the optimum type of drilling pattern to be used when exploring for elliptical shaped targets is examined. The rhombic pattern is optimal when the targets are known to have a preferred orientation. Situations can also be found where a rectangular pattern is as efficient as the rhombic pattern. A triangular or square drilling pattern should be used when the orientations of the targets are unknown. The way in which the optimum hole spacing varies as a function of (1) the cost of drilling, (2) the value of the targets, (3) the shape of the targets, (4) the target occurrence probabilities was determined for several examples. Bayes' rule was used to show how target occurrence probabilities can be revised within a multistage pattern drilling scheme. ?? 1979 Plenum Publishing Corporation.
Behavior of three modes of decay channels and their self-energies of elliptic dielectric microcavity
NASA Astrophysics Data System (ADS)
Park, Kyu-Won; Kim, Jaewan; Jeong, Kabgyun
2016-09-01
The Lamb shift (self-energy) of an elliptic dielectric microcavity is studied. We show that the size of the Lamb shift, which is a small energy shift due to the system-environment coupling in the quantum regime, is dependent on the geometry of the boundary conditions. It shows a global transition depending on the eccentricity of the ellipsis. These transitions can be classified into three types of decay channels known as whispering-gallery modes, stable-bouncing-ball modes, and unstable-bouncing-ball modes. These modes are manifested through the Poincaré surface of section with the Husimi distribution function in classical phase space. It is found that the similarity (measured in Bhattacharyya distance) between the Husimi distributions below critical lines of two different modes increases as the difference of their self-energies decreases when the quality factors of the modes are on the same order of magnitude.
Effective Numerical Methods for Solving Elliptical Problems in Strengthened Sobolev Spaces
NASA Technical Reports Server (NTRS)
D'yakonov, Eugene G.
1996-01-01
Fourth-order elliptic boundary value problems in the plane can be reduced to operator equations in Hilbert spaces G that are certain subspaces of the Sobolev space W(sub 2)(exp 2)(Omega) is identical with G(sup (2)). Appearance of asymptotically optimal algorithms for Stokes type problems made it natural to focus on an approach that considers rot w is identical with (D(sub 2)w - D(sub 1)w) is identical with vector of u as a new unknown vector-function, which automatically satisfies the condition div vector of u = 0. In this work, we show that this approach can also be developed for an important class of problems from the theory of plates and shells with stiffeners. The main mathematical problem was to show that the well-known inf-sup condition (normal solvability of the divergence operator) holds for special Hilbert spaces. This result is also essential for certain hydrodynamics problems.
Rapidity and pt dependence of identified-particle elliptic flow at RHIC
NASA Astrophysics Data System (ADS)
Sanders, S. J.; BRAHMS Collaboration
2007-08-01
Elliptic flow has been measured by the BRAHMS experiment as a function of transverse momentum and pseudorapidity for the Au+Au reaction at \\sqrt{s_{NN}} = 200 GeV. Identified-particle v2(η, pt) values were obtained with the two BRAHMS spectrometers at pseudorapidities ηap 0, 1 and 3.4. The results show that the differential v2(η, pt) values for a given particle type are essentially constant over the covered pseudorapidity range. It is suggested that the dominant cause of the observed fall-off of the integral v2 values going away from mid-rapidity is a corresponding softening of the particle spectra.
Transport ac loss of elliptical thin strips with a power-law E(J) relation
NASA Astrophysics Data System (ADS)
Jia, Chen-Xi; Chen, Du-Xing; Li, Shuo; Fang, Jin
2015-10-01
The transport ac loss Q of an elliptical thin strip of critical current I c with a power-law relation E\\propto {J}n is accurately computed as a function of current amplitude I m and frequency f. The resulting Q({I}m) is normalized to q({i}m) following the Norris critical-state formula, and converted to {q}*({i}m*) at a critical frequency f c based on a transport scaling law. Having a set of {q}*({i}m*) at several values of n as a base, a general expression of {q}*({i}m*,n) is obtained, which can be used to easily calculate q({i}m) for any practical purposes.
Lipschitz Regularity for Elliptic Equations with Random Coefficients
NASA Astrophysics Data System (ADS)
Armstrong, Scott N.; Mourrat, Jean-Christophe
2016-01-01
We develop a higher regularity theory for general quasilinear elliptic equations and systems in divergence form with random coefficients. The main result is a large-scale L ∞-type estimate for the gradient of a solution. The estimate is proved with optimal stochastic integrability under a one-parameter family of mixing assumptions, allowing for very weak mixing with non-integrable correlations to very strong mixing (for example finite range of dependence). We also prove a quenched L 2 estimate for the error in homogenization of Dirichlet problems. The approach is based on subadditive arguments which rely on a variational formulation of general quasilinear divergence-form equations.
Nonlinear Eigenvalue Problems in Elliptic Variational Inequalities: a local study
Conrad, F.; Brauner, C.; Issard-Roch, F.; Nicolaenko, B.
1985-01-01
The authors consider a class of Nonlinear Eigenvalue Problems (N.L.E.P.) associated with Elliptic Variational Inequalities (E.V.I.). First the authors introduce the main tools for a local study of branches of solutions; the authors extend the linearization process required in the case of equations. Next the authors prove the existence of arcs of solutions close to regular vs singular points, and determine their local behavior up to the first order. Finally, the authors discuss the connection between their regularity condition and some stability concept. 37 references, 6 figures.
Chopper z-scan technique for elliptic Gaussian beams.
Dávila-Pintle, J A; Reynoso-Lara, E; Bravo-García, Y E
2016-09-01
This paper reports an improvement to the chopper z-scan technique for elliptic Gaussian beams. This improvement results in a higher sensitivity by measuring the ratio of eclipsing time to rotating period (duty cycle) of a chopper that eclipses the beam along the main axis. It is shown that the z-scan curve of the major axis is compressed along the z-axis. This compression factor is equal to the ratio between the minor and major axes. It was found that the normalized peak-valley difference with respect to the linear value does not depend on the axis along which eclipsing occurs. PMID:27607713
Chopper z-scan technique for elliptic Gaussian beams.
Dávila-Pintle, J A; Reynoso-Lara, E; Bravo-García, Y E
2016-09-01
This paper reports an improvement to the chopper z-scan technique for elliptic Gaussian beams. This improvement results in a higher sensitivity by measuring the ratio of eclipsing time to rotating period (duty cycle) of a chopper that eclipses the beam along the main axis. It is shown that the z-scan curve of the major axis is compressed along the z-axis. This compression factor is equal to the ratio between the minor and major axes. It was found that the normalized peak-valley difference with respect to the linear value does not depend on the axis along which eclipsing occurs.
Some fast elliptic solvers on parallel architectures and their complexities
NASA Technical Reports Server (NTRS)
Gallopoulos, E.; Saad, Y.
1989-01-01
The discretization of separable elliptic partial differential equations leads to linear systems with special block tridiagonal matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconstant coefficients. A method was recently proposed to parallelize and vectorize BCR. In this paper, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational compelxity lower than that of parallel BCR.
On an Elliptic Equation Arising from Composite Materials
NASA Astrophysics Data System (ADS)
Dong, Hongjie; Zhang, Hong
2016-10-01
In this paper, we derive an interior Schauder estimate for the divergence form elliptic equation D_i (a(x)D_iu) = D_i f_i in R^2,where {a(x)} and {f_i (x)} are piecewise Hölder continuous in a domain containing two touching balls as subdomains. When {f_i ≡ 0} and a is piecewise constant, we prove that u is piecewise smoothwith bounded derivatives.This completely answers a question raised by Li andVogelius (Arch Ration Mech Anal 153(2):91-151, 2000) in dimension 2.
Some fast elliptic solvers on parallel architectures and their complexities
NASA Technical Reports Server (NTRS)
Gallopoulos, E.; Saad, Youcef
1989-01-01
The discretization of separable elliptic partial differential equations leads to linear systems with special block triangular matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconsistant coefficients. A method was recently proposed to parallelize and vectorize BCR. Here, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches, including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational complexity lower than that of parallel BCR.
Differential Spectral Synthesis of Low-Luminosity Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Jones, Lewis Alexander
In this thesis, a study of the spectral variations in the integrated light of eight low-luminosity elliptical galaxies is presented. The unique opportunity provided by low-luminosity elliptical galaxies to study integrated spectra at high line definition is the motivation behind the observational approach for this study. A long wavelength baseline is sacrificed in favor of working at high resolution (~2 Å FWHM) with a large variety of narrow absorption features in a smaller wave-length window. A new spectral library has been developed with this approach in mind. The library consists of spectra of 684 stars all observed with the Coudé Feed Telescope and Spectrograph at the Kitt Peak National Observatory, covering the spectral ranges 3820-4500 Å and 4780-5450 Å and at a spectral resolution of ~2 Å FWHM. The coverage of the library is complete for spectral types A-K and luminosity classes I-V, in the range -2.5 <= FeH; <= +0.5, while the O, B, and M stars are near solar. The empirical investigation of the galaxy spectra in reference to the stellar sequences of the spectral library yields several key results. (1) There is a spread in the mean spectral types of the low-luminosity ellliptical galaxies. (2) The galaxies are similar in evolved star content, Fe line strengths, and their evolved star light is dominated by solar type giants. (3) Five of the eight galaxies are shown to contain less than a 5% hot star contribution, which is inconsistent with the prediction of ~10% from the simple model of chemical evolution (Worthey, Dorman, and Jones 1996). (4) From variations in the balance of dwarf and giant light in the galaxy spectra it is claimed that there is a spread in the mean stellar ages of the low-luminosity elliptical galaxies. These results are interpreted in the context of the evolutionary synthesis models of Worthey (1994). The main result from the comparison of the galaxies and models is that the low-luminosity elliptical galaxies show a large spread in
The construction of preconditioners for elliptic problems by substructuring, IV
Bramble, J.H.; Pasciak, J.E.; Schatz, A.H.
1987-06-01
We consider the problem of solving the algebraic system of equations which result from the discretization of elliptic boundary value problems defined on three dimensional Euclidean space. We develop preconditioners for such systems based on substructuring (also known as domain decomposition). The resulting algorithms are well suited to emerging parallel computing architectures. We describe two techniques for developing these precondictioners. A theory for the analysis of the condition number for the resulting preconditioned system is given and the results of supporting numerical experiments are presented. 16 refs., 2 tabs.
The construction of preconditioners for elliptic problems by substructuring, IV
Bramble, J.H.; Pasciak, J.E.; Schatz, A.H.
1989-07-01
We consider the problem of solving the algebraic system of equations which result from the discretization of elliptic boundary value problems defined on three-dimensional Euclidean space. We develop preconditioners for such systems based on substructuring (also known as domain decomposition). The resulting algorithms are well suited to emerging parallel computing architectures. We describe two techniques for developing these preconditioners. A theory for the analysis of the condition number for the resulting preconditioned system is given and the results of supporting numerical experiments are presented.
Iterative method for elliptic problems on regions partitioned into substructures
Bramble, J.H.; Pasciak, J.E.; Schatz, A.H.
1986-04-01
Some new preconditioners for discretizations of elliptic boundary problems are studied. With these preconditioners, the domain under consideration is broken into subdomains and preconditioners are defined which only require the solution of matrix problems on the subdomains. Analytic estimates are given which guarantee that under appropriate hypotheses, the preconditioned iterative procedure converges to the solution of the discrete equations with a rate per iteration that is independent of the number of unknowns. Numerical examples are presented which illustrate the theoretically predicted iterative convergence rates.
Construction of preconditioners for elliptic problems by substructuring. II
Bramble, J.H.; Pasciak, J.E.; Schatz, A.H.
1987-07-01
We give a method for constructing preconditioners for the discrete systems arising in the approximation of solutions of elliptic boundary value problems. These preconditioners are based on domain decomposition techniques and lead to algorithms which are well suited for parallel computing environments. The method presented in this paper leads to a preconditioned system with condition number proportional to d/h where d is the subdomain size and h is the mesh size. These techniques are applied to singularly perturbed problems and problems in the three dimensions. The results of numerical experiments illustrating the performance of the method on problems in two and three dimensions are given.
Iterative schemes for nonsymmetric and indefinite elliptic boundary value problems
Bramble, J.H.; Leyk, Z.; Pasciak, J.E.
1993-01-01
The purpose of this paper is twofold. The first is to describe some simple and robust iterative schemes for nonsymmetric and indefinite elliptic boundary value problems. The schemes are based in the Sobolev space H ([Omega]) and require minimal hypotheses. The second is to develop algorithms utilizing a coarse-grid approximation. This leads to iteration matrices whose eigenvalues lie in the right half of the complex plane. In fact, for symmetric indefinite problems, the iteration is reduced to a well-conditioned symmetric positive definite system which can be solved by conjugate gradient interation. Applications of the general theory as well as numerical examples are given. 20 refs., 8 tabs.
Liouville properties and critical value of fully nonlinear elliptic operators
NASA Astrophysics Data System (ADS)
Bardi, Martino; Cesaroni, Annalisa
2016-10-01
We prove some Liouville properties for sub- and supersolutions of fully nonlinear degenerate elliptic equations in the whole space. Our assumptions allow the coefficients of the first order terms to be large at infinity, provided they have an appropriate sign, as in Ornstein-Uhlenbeck operators. We give two applications. The first is a stabilization property for large times of solutions to fully nonlinear parabolic equations. The second is the solvability of an ergodic Hamilton-Jacobi-Bellman equation that identifies a unique critical value of the operator.
Using elliptical best fits to characterize dental shapes.
Bauer, Catherine C; Bons, Paul D; Benazzi, Stefano; Harvati, Katerina
2016-02-01
A variety of geometric morphometric methods have recently been used to describe dental shape variation in human evolutionary studies. However, the applicability of these methods is limited when teeth are worn or are difficult to orient accurately. Here we show that elliptical best fits on outlines of dental tissues below the crown provide basic size- and orientation-free shape descriptors. Using the dm(2) and M(3) as examples, we demonstrate that these descriptors can be used for taxonomic purposes, such as distinguishing between Neanderthal and recent modern human teeth. We propose that this approach can be a useful alternative to existing methodology. PMID:26381860
A new CY elliptic fibration and tadpole cancellation
NASA Astrophysics Data System (ADS)
Cacciatori, Sergio L.; Cattaneo, Andrea; van Geemen, Bert
2011-10-01
Tadpole cancellation in Sen limits in F-theory was recently studied by Aluffi and Esole. We extend their results, generalizing the elliptic fibrations they used and obtaining a new case of universal tadpole cancellation, at least numerically. We could not find an actual Sen limit having the correct brane content, and we argue that such a limit may not exist. We also give a uniform description of the fibrations used by Aluffi and Esole as well as a new, simple, fibration which has non-Kodaira type fibers.
Incomplete block factorization preconditioning for indefinite elliptic problems
Guo, Chun-Hua
1996-12-31
The application of the finite difference method to approximate the solution of an indefinite elliptic problem produces a linear system whose coefficient matrix is block tridiagonal and symmetric indefinite. Such a linear system can be solved efficiently by a conjugate residual method, particularly when combined with a good preconditioner. We show that specific incomplete block factorization exists for the indefinite matrix if the mesh size is reasonably small. And this factorization can serve as an efficient preconditioner. Some efforts are made to estimate the eigenvalues of the preconditioned matrix. Numerical results are also given.
Optical observation of supernova remnant in elliptical galaxy NGC 185
NASA Astrophysics Data System (ADS)
Vučetić, M.; Arbutina, B.; Pavlovic, M. Z.; Ciprijanovic, A.; Urosevic, D.; Petrov, N.; Onić, D.; Trcka, A.
2016-06-01
In this paper we discuss the previously known optical supernova remnant (SNR) in NGC 185 galaxy, a dwarf elliptical companion of the Andromeda galaxy, in order to gain more information about its properties and evolutionary status. To this end, we observed a central portion of NGC 185, through the narrowband Hα and [SII]} filters, on a 2m RCC-telescope at National astronomical observatory Rozhen, Bulgaria. Also, we performed MHD simulations using the Pluto code, for the case of low environmental density and high pressure, in order to discuss evolution of a SNR in a gas poor dwarf galaxy.
On the integrable elliptic cylindrical Kadomtsev-Petviashvili equation.
Khusnutdinova, K R; Klein, C; Matveev, V B; Smirnov, A O
2013-03-01
There exist two versions of the Kadomtsev-Petviashvili (KP) equation, related to the Cartesian and cylindrical geometries of the waves. In this paper, we derive and study a new version, related to the elliptic cylindrical geometry. The derivation is given in the context of surface waves, but the derived equation is a universal integrable model applicable to generic weakly nonlinear weakly dispersive waves. We also show that there exist nontrivial transformations between all three versions of the KP equation associated with the physical problem formulation, and use them to obtain new classes of approximate solutions for water waves.
NASA Astrophysics Data System (ADS)
Barakat, R.; Sandler, B. H.
1992-10-01
The authors outline a method for the determination of the unknown wave-front aberration function of an optical system from noisy measurements of the corresponding point-spread function. The problem is cast as a nonlinear unconstrained minimization problem, and trust region techniques are employed for its solution in conjunction with analytic evaluations of the Jacobian and Hessian matrices governing slope and curvature information. Some illustrative numerical results are presented and discussed.
New Traveling Wave Solutions for a Class of Nonlinear Evolution Equations
NASA Astrophysics Data System (ADS)
Bai, Cheng-Jie; Zhao, Hong; Xu, Heng-Ying; Zhang, Xia
The deformation mapping method is extended to solve a class of nonlinear evolution equations (NLEEs). Many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, and Jacobian elliptic function solutions, are obtained by a simple algebraic transformation relation between the solutions of the NLEEs and those of the cubic nonlinear Klein-Gordon (NKG) equation.
Okura, Yuki; Futamase, Toshifumi E-mail: tof@astr.tohoku.ac.jp
2013-07-01
This is the third paper on the improvement of systematic errors in weak lensing analysis using an elliptical weight function, referred to as E-HOLICs. In previous papers, we succeeded in avoiding errors that depend on the ellipticity of the background image. In this paper, we investigate the systematic error that depends on the signal-to-noise ratio of the background image. We find that the origin of this error is the random count noise that comes from the Poisson noise of sky counts. The random count noise makes additional moments and centroid shift error, and those first-order effects are canceled in averaging, but the second-order effects are not canceled. We derive the formulae that correct this systematic error due to the random count noise in measuring the moments and ellipticity of the background image. The correction formulae obtained are expressed as combinations of complex moments of the image, and thus can correct the systematic errors caused by each object. We test their validity using a simulated image and find that the systematic error becomes less than 1% in the measured ellipticity for objects with an IMCAT significance threshold of {nu} {approx} 11.7.
NASA Astrophysics Data System (ADS)
Roediger, E.; Kraft, R. P.; Nulsen, P. E. J.; Forman, W. R.; Machacek, M.; Randall, S.; Jones, C.; Churazov, E.; Kokotanekova, R.
2015-06-01
Elliptical cluster galaxies are progressively stripped of their atmospheres due to their motion through the intracluster medium (ICM). Deep X-ray observations reveal the fine-structure of the galaxy’s remnant atmosphere and its gas tail and wake. This fine-structure depends on dynamic conditions (galaxy potential, initial gas contents, orbit through the host cluster), orbital stage (early infall, pre-/post-pericenter passage), and ICM plasma properties (thermal conductivity, viscosity, magnetic field structure). We aim to disentangle dynamic and plasma effects in order to use stripped ellipticals as probes of ICM plasma properties. This first paper of a series investigates the hydrodynamics of progressive gas stripping by means of inviscid hydrodynamical simulations. We distinguish a long-lasting initial relaxation phase and a quasi-steady stripping phase. During quasi-steady stripping, the ICM flow around the remnant atmosphere resembles the flow around solid bodies, including a “deadwater” region in the near wake. Gas is stripped from the remnant atmosphere predominantly at its sides via Kelvin-Helmholtz instabilities. The downstream atmosphere is largely shielded from the ICM wind and thus shaped into a tail. Observationally, both this “remnant tail” and the stripped gas in the wake can appear as a “tail”, but only in the wake can galactic gas mix with the ambient ICM. While the qualitative results are generic, the simulations presented here are tailored to the Virgo elliptical galaxy M89 (NGC 4552) for the most direct comparison to observations. Papers II and III of this series describe the effect of viscosity and compare to Chandra and XMM-Newton observations, respectively.
Roediger, E.; Kraft, R. P.; Nulsen, P. E. J.; Forman, W. R.; Machacek, M.; Randall, S.; Jones, C.; Kokotanekova, R.
2015-06-10
Elliptical cluster galaxies are progressively stripped of their atmospheres due to their motion through the intracluster medium (ICM). Deep X-ray observations reveal the fine-structure of the galaxy’s remnant atmosphere and its gas tail and wake. This fine-structure depends on dynamic conditions (galaxy potential, initial gas contents, orbit through the host cluster), orbital stage (early infall, pre-/post-pericenter passage), and ICM plasma properties (thermal conductivity, viscosity, magnetic field structure). We aim to disentangle dynamic and plasma effects in order to use stripped ellipticals as probes of ICM plasma properties. This first paper of a series investigates the hydrodynamics of progressive gas stripping by means of inviscid hydrodynamical simulations. We distinguish a long-lasting initial relaxation phase and a quasi-steady stripping phase. During quasi-steady stripping, the ICM flow around the remnant atmosphere resembles the flow around solid bodies, including a “deadwater” region in the near wake. Gas is stripped from the remnant atmosphere predominantly at its sides via Kelvin–Helmholtz instabilities. The downstream atmosphere is largely shielded from the ICM wind and thus shaped into a tail. Observationally, both this “remnant tail” and the stripped gas in the wake can appear as a “tail”, but only in the wake can galactic gas mix with the ambient ICM. While the qualitative results are generic, the simulations presented here are tailored to the Virgo elliptical galaxy M89 (NGC 4552) for the most direct comparison to observations. Papers II and III of this series describe the effect of viscosity and compare to Chandra and XMM-Newton observations, respectively.
Rovniak, Liza S.; Denlinger, LeAnn; Duveneck, Ellen; Sciamanna, Christopher N.; Kong, Lan; Freivalds, Andris; Ray, Chester A.
2013-01-01
Objectives This study aimed to evaluate the feasibility of using a compact elliptical device to increase energy expenditure during sedentary activities. A secondary aim was to evaluate if two accelerometers attached to the elliptical device could provide reliable and valid assessments of participants’ frequency and duration of elliptical device use. Design Physically inactive adults (n = 32, age range = 25–65) were recruited through local advertisements and selected using stratified random sampling based on sex, body mass index (BMI), and age. Methods Indirect calorimetry was used to assess participants’ energy expenditure while seated and while using the elliptical device at a self-selected intensity level. Participants also self-reported their interest in using the elliptical device during sedentary activities. Two Actigraph GT3X accelerometers were attached to the elliptical device to record time-use patterns. Results Participants expended a median of 179.1 kilocalories per hour while using the elliptical device (range = 108.2–269.0), or a median of 87.9 more kilocalories (range = 19.7–178.6) than they would expend per hour of sedentary sitting. Participants reported high interest in using the elliptical device during TV watching and computer work, but relatively low interest in using the device during office meetings. Women reported greater interest in using the elliptical device than men. The two accelerometers recorded identical time-use patterns on the elliptical device and demonstrated concurrent validity with time-stamped computer records. Conclusions Compact elliptical devices could increase energy expenditure during sedentary activities, and may provide proximal environmental cues for increasing energy expenditure across multiple life domains. PMID:24035273
The Globular Cluster System of the Virgo Dwarf Elliptical Galaxy VCC 1087
NASA Astrophysics Data System (ADS)
Beasley, Michael A.; Strader, Jay; Brodie, Jean P.; Cenarro, A. Javier; Geha, M.
2006-02-01
We present an analysis of the globular cluster (GC) system of the nucleated dwarf elliptical galaxy VCC 1087 in the Virgo Cluster based on Keck LRIS spectroscopy and archival Hubble Space Telescope Advanced Camera for Surveys imaging. We estimate that VCC 1087 hosts a total population of 77+/-19 GCs, which corresponds to a relatively high V-band specific frequency of 5.8+/-1.4. The g475-z850 color distribution of the GCs shows a blue (metal-poor) peak with a tail of redder (metal-rich) clusters similar in color to those seen in luminous elliptical galaxies. The luminosity function of the GCs is lognormal and peaks at MTOg475=-7.2+/-0.3, MTOz850=-8.1+/-0.2. These peak positions are consistent with those found for luminous Virgo elliptical galaxies, suggesting either the lack of or, surprisingly similarly, the dynamical destruction processes of GCs among dwarf and giant galaxies. Spectroscopy of a subsample of 12 GCs suggests that the GC system is old and coeval (>~10 Gyr), with a fairly broad metallicity distribution (-1.8<~[M/H]<~-0.8). In contrast, an integrated spectrum of the underlying galaxy starlight reveals that its optical luminosity is dominated by metal-rich, intermediate-age stars. The radial velocities of the GCs suggest rotation close to the major axis of the galaxy, and this rotation is dynamically significant with (vrot/σlos)*>1. A compilation of the kinematics of the GC systems of nine early-type galaxies shows surprising diversity in the (vrot/σlos) parameter for GC systems. In this context, the GC system of VCC 1087 exhibits the most significant rotation-to-velocity dispersion signature. Dynamical mass modeling of the velocity dispersion profile of the GCs and galaxy stars suggests fairly constant mass-to-light ratios of ~3 out to 6.5 kpc. The present observations can entertain both baryonic and nonbaryonic solutions, and GC velocities at larger radii would be most valuable with regard to this issue. Finally, we discuss the evolution of VCC 1087
Elliptic flow in heavy-ion collisions at NICA energies
NASA Astrophysics Data System (ADS)
B. Ivanov, Yu.; Soldatov, A. A.
2016-08-01
The transverse-momentum-integrated elliptic flow of charged particles at midrapidity, v2 (charged), and that of identified hadrons from Au+Au collisions are analyzed in the range of incident energies relevant to the Nuclotron-based Ion Collider Facility (NICA). Simulations are performed within a three-fluid model employing three different equations of state (EoSs): a purely hadronic EoS and two versions of the EoS involving the deconfinement transition-a first-order phase transition and a smooth crossover one. The present simulations demonstrate low sensitivity of v2 (charged) to the EoS. All considered scenarios equally well reproduce recent STAR data on v2 (charged) for mid-central Au+Au collisions and properly describe its change of sign at the incident energy decrease below √{s_{NN}} ≈ 3.5 GeV. The predicted integrated elliptic flow of various species exhibits a stronger dependence on the EoS. A noticeable sensitivity to the EoS is found for anti-protons and, to a lesser extent, for K- mesons. Presently there are no experimental data that could verify these predictions. Future experiments at NICA could corroborate these findings.
The density profile of the elliptical planetary nebula NGC 3242
NASA Technical Reports Server (NTRS)
Soker, Noam; Zucker, Daniel B.; Balick, Bruce
1992-01-01
We present the three-dimensional density structure of the elliptical planetary nebula NGC 3242, deconvolved from its H-alpha image. Using the simplistic assumptions that each mass element preserves its original velocity, which is radial and depends only on latitude, we deduce from this density profile the variation of mass-loss rate from the progenitor of NGC 3242 with latitude and time. The resulting somewhat qualitative mass-loss geometry and history are used to constrain models for the formation of the elliptical structure of NGC 3242. We argue that a triple system, with a very close brown dwarf companion and a more massive distant tertiary star, is compatible with the morphology of NGC 3242. In this model the brown dwarf, of about 0.01 solar mass, shared a common envelope with the progenitor star, and spun up the envelope through deposition of angular momentum. The oblate rotating envelope blew an axisymmetrical wind. We suggest that the presence of a third star, with a mass of about 1 solar mass and an orbital period of about 4000 years, could have caused the large scale deviation from axial symmetry seen in the density structure.
On the distribution of galaxy ellipticity in clusters
NASA Astrophysics Data System (ADS)
D'Eugenio, F.; Houghton, R. C. W.; Davies, R. L.; Dalla Bontà, E.
2015-07-01
We study the distribution of projected ellipticity n(ɛ) for galaxies in a sample of 20 rich (Richness ≥ 2) nearby (z < 0.1) clusters of galaxies. We find no evidence of differences in n(ɛ), although the nearest cluster in the sample (the Coma Cluster) is the largest outlier (P(same) < 0.05). We then study n(ɛ) within the clusters, and find that ɛ increases with projected cluster-centric radius R (hereafter the ɛ-R relation). This trend is preserved at fixed magnitude, showing that this relation exists over and above the trend of more luminous galaxies to be both rounder and more common in the centres of clusters. The ɛ-R relation is particularly strong in the subsample of intrinsically flattened galaxies (ɛ > 0.4), therefore it is not a consequence of the increasing fraction of round slow rotator galaxies near cluster centers. Furthermore, the ɛ-R relation persists for just smooth flattened galaxies and for galaxies with de Vaucouleurs-like light profiles, suggesting that the variation of the spiral fraction with radius is not the underlying cause of the trend. We interpret our findings in light of the classification of early type galaxies (ETGs) as fast and slow rotators. We conclude that the observed trend of decreasing ɛ towards the centres of clusters is evidence for physical effects in clusters causing fast rotator ETGs to have a lower average intrinsic ellipticity near the centres of rich clusters.
Two high-velocity encounters of elliptical galaxies
NASA Technical Reports Server (NTRS)
Balcells, Marc; Borne, Kirk D.; Hoessel, John G.
1989-01-01
This paper describes results obtained on a simulation of two high-velocity encounters of NGC 4782/4783 and NGC 2672/2673 binary elliptical galaxies which differ substantially in mass ratio (about 1 for the first pair, and about 10 for the second). CCD images and velocities obtained from digital spectra were used to constrain simulations of the galaxy collisions. The binary orbital elements, the orientation of the orbit in the sky, the time since pericenter, and the dynamical mass of the pair were derived. Results suggested that the dumb-bell galaxy NGC 4782/4783 is not a supermassive galaxy, as was claimed earlier on the basis of the high relative velocity and high central dispersion, but has a moderate mass to luminosity ratio M/L(B) of about 10. It was concluded that its trajectory changed from hyperbolic to elliptical as a result of energy lost during the collision. It was found that the NGC 2672/2673 also has a moderate M/L(B) of about 7.
Development of an innovative device for ultrasonic elliptical vibration cutting.
Zhou, Ming; Hu, Linhua
2015-07-01
An innovative ultrasonic elliptical vibration cutting (UEVC) device with 1st resonant mode of longitudinal vibration and 3rd resonant mode of bending vibration was proposed in this paper, which can deliver higher output power compared to previous UEVC devices. Using finite element method (FEM), resonance frequencies of the longitudinal and bending vibrations were tuned to be as close as possible in order to excite these two vibrations using two-phase driving voltages at a single frequency, while wave nodes of the longitudinal and bending vibrations were also adjusted to be as coincident as possible for mounting the device at a single fixed point. Based on the simulation analysis results a prototype device was fabricated, then its vibration characteristics were evaluated by an impedance analyzer and a laser displacement sensor. With two-phase sinusoidal driving voltages both of 480 V(p-p) at an ultrasonic frequency of 20.1 kHz, the developed prototype device achieved an elliptical vibration with a longitudinal amplitude of 8.9 μm and a bending amplitude of 11.3 μm. The performance of the developed UEVC device is assessed by the cutting tests of hardened steel using single crystal diamond tools. Experimental results indicate that compared to ordinary cutting process, the tool wear is reduced significantly by using the proposed device.
Guiding mode in elliptical core microstructured polymer optical fiber
NASA Astrophysics Data System (ADS)
Zhang, Yani; Ren, Liyong; Li, Kang; Wang, Hanyi; Zhao, Wei; Wang, Lili; Miao, Runcai; Large, Maryanne C. J.; van Eijkelenborg, Martijn A.
2007-04-01
A kind of microstructured polymer optical fiber with elliptical core has been fabricated by adopting in-situ chemical polymerization technology and the secondary sleeving draw-stretching technique. Microscope photography demonstrates the clear hole-structure retained in the fiber. Though the holes distortion is visible, initial laser experiment indicates that light can be strongly confined in the elliptical core region, and the mode field is split obviously and presents the multi-mode characteristic. Numerical modeling is carried out for the real fiber with the measured parameters, including the external diameter of 150 microns, the average holes diameter of 3.3 microns, and the average hole spacing of 6.3 microns by using full-vector plane wave method. The guided mode fields of the numerical simulation are consistent with the experiment result. This fiber shows the strong multi-mode and weak birefringence in the visible and near-infrared band, and has possibility for achieving the fiber mode convertors, mode selective couplers and so on.
Experimental study of elliptical jet from sub to supercritical conditions
Muthukumaran, C. K.; Vaidyanathan, Aravind
2014-04-15
The jet mixing at supercritical conditions involves fluid dynamics as well as thermodynamic phenomena. All the jet mixing studies at critical conditions to the present date have focused only on axisymmetric jets. When the liquid jet is injected into supercritical environment, the thermodynamic transition could be well understood by considering one of the important fluid properties such as surface tension since it decides the existence of distinct boundary between the liquid and gaseous phase. It is well known that an elliptical liquid jet undergoes axis-switching phenomena under atmospheric conditions due to the presence of surface tension. The experimental investigations were carried out with low speed elliptical jet under supercritical condition. Investigation of the binary component system with fluoroketone jet and N{sub 2} gas as environment shows that the surface tension force dominates for a large downstream distance, indicating delayed thermodynamic transition. The increase in pressure to critical state at supercritical temperature is found to expedite the thermodynamic transition. The ligament like structures has been observed rather than droplets for supercritical pressures. However, for the single component system with fluoroketone jet and fluoroketone environment shows that the jet disintegrates into droplets as it is subjected to the chamber conditions even for the subcritical pressures and no axis switching phenomenon is observed. For a single component system, as the pressure is increased to critical state, the liquid jet exhibits gas-gas like mixing behavior and that too without exhibiting axis-switching behavior.
NASA Astrophysics Data System (ADS)
Kryuchkov, S. V.; Kukhar', E. I.; Zav'yalov, D. V.
2015-06-01
It has been shown that the linewidth of cyclotron absorption in band-gap graphene is nonzero even in the absence of electron scattering. The functional temperature dependence of the cyclotron absorption linewidth, which is applicable to band-gap graphene in the absence of collisions, has been analytically determined. The power of the elliptically polarized electromagnetic wave absorbed by graphene in the presence of a dc magnetic field has been numerically calculated. The Monte Carlo numerical experiment has confirmed the analytical calculations based on the Boltzmann equation.
NASA Technical Reports Server (NTRS)
Vo, San C.; Biegel, Bryan (Technical Monitor)
2001-01-01
Scalar multiplication is an essential operation in elliptic curve cryptosystems because its implementation determines the speed and the memory storage requirements. This paper discusses some improvements on two popular signed window algorithms for implementing scalar multiplications of an elliptic curve point - Morain-Olivos's algorithm and Koyarna-Tsuruoka's algorithm.
Lateral Migration and Rotational Motion of Elliptic Particles in Planar Poiseuille Flow
NASA Technical Reports Server (NTRS)
Qi, Dewei; Luo, Li-Shi; Aravamuthan, Raja; Strieder, William; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
Simulations of elliptic particulate suspensions in the planar Poiseuille flow are performed by using the lattice Boltzmann equation. Effects of the multi-particle on the lateral migration and rotational motion of both neutrally and non-neutrally buoyant elliptic particles are investigated. Low and intermediate total particle volume fraction f(sub a) = 13%, 15%, and 40% are considered in this work.
Lensing measurements of the ellipticity of luminous red galaxies dark matter haloes
NASA Astrophysics Data System (ADS)
Clampitt, Joseph; Jain, Bhuvnesh
2016-04-01
Lensing measurements of the shapes of dark matter haloes can provide tests of gravity theories and possible dark matter interactions. We measure the quadrupole weak lensing signal from the elliptical haloes of 70 000 Sloan Digital Sky Survey luminous red galaxies. We use a new estimator that nulls the spherical halo lensing signal, isolating the shear due to anisotropy in the dark matter distribution. One of the two Cartesian components of our estimator is insensitive to the primary systematic, a spurious alignment of lens and source ellipticities, allowing us to make robust measurements of halo ellipticity. Our best-fitting value for the ellipticity of the surface mass density is 0.24 ± 0.06, which translates to an axis ratio of 0.78. We rule out the hypothesis of no ellipticity at the 4σ confidence level, and ellipticity <0.12 (axis ratio >0.89) at the 2σ level. We discuss how our measurements of halo ellipticity are revised to higher values using estimates of the misalignment of mass and light from simulations. Finally, we apply the same techniques to a smaller sample of redMaPPer galaxy clusters and obtain a 3σ measurement of cluster ellipticity. We discuss how the improved signal-to-noise ratio properties of our estimator can enable studies of halo shapes for different galaxy populations with upcoming surveys.
Short Foucault Pendulum: A Way to Eliminate the Precession Due to Ellipticity.
ERIC Educational Resources Information Center
Crane, H. Richard
1981-01-01
Discusses the problem of ellipticity in the motion of the ordinary Foucault pendulum and the error caused by it. Presents a simple method of slightly modifying the force-displacement relation in such a way that precession does not result from ellipticity. (Author/SK)
On the index of noncommutative elliptic operators over C*-algebras
Savin, Anton Yu; Sternin, Boris Yu
2010-05-11
We consider noncommutative elliptic operators over C*-algebras, associated with a discrete group of isometries of a manifold. The main result of the paper is a formula expressing the Chern characters of the index (Connes invariants) in topological terms. As a corollary to this formula a simple proof of higher index formulae for noncommutative elliptic operators is obtained. Bibliography: 36 titles.
NASA Astrophysics Data System (ADS)
Scheunert, M.; Ullmann, A.; Afanasjew, M.; Börner, R.-U.; Siemon, B.; Spitzer, K.
2016-06-01
We present an inversion concept for helicopter-borne frequency-domain electromagnetic (HEM) data capable of reconstructing 3-D conductivity structures in the subsurface. Standard interpretation procedures often involve laterally constrained stitched 1-D inversion techniques to create pseudo-3-D models that are largely representative for smoothly varying conductivity distributions in the subsurface. Pronounced lateral conductivity changes may, however, produce significant artifacts that can lead to serious misinterpretation. Still, 3-D inversions of entire survey data sets are numerically very expensive. Our approach is therefore based on a cut-&-paste strategy whereupon the full 3-D inversion needs to be applied only to those parts of the survey where the 1-D inversion actually fails. The introduced 3-D Gauss-Newton inversion scheme exploits information given by a state-of-the-art (laterally constrained) 1-D inversion. For a typical HEM measurement, an explicit representation of the Jacobian matrix is inevitable which is caused by the unique transmitter-receiver relation. We introduce tensor quantities which facilitate the matrix assembly of the forward operator as well as the efficient calculation of the Jacobian. The finite difference forward operator incorporates the displacement currents because they may seriously affect the electromagnetic response at frequencies above 100. Finally, we deliver the proof of concept for the inversion using a synthetic data set with a noise level of up to 5%.
New schemes in the adjustment of bendable elliptical mirrors using a long trace profiler
NASA Astrophysics Data System (ADS)
Rah, Seung Y.; Locklin, Scott C.; Irick, Steven C.; Howells, Malcolm R.
1997-11-01
The Long Trace Profiler, an instrument for measuring the slope profile of long X-ray mirrors, has been used for adjusting bendable mirrors. Often an elliptical profile is desired for the mirror surface, since many synchrotron applications involve imaging a point source to a point image. Several techniques have been used in the past for adjusting the profile measured in height or slope of a bendable mirror. Underwood et al. have used collimated X- rays for achieving a desired surface shape for bent glass optics. Nonlinear curve fitting sing the simplex algorithm was later used to determine the best fit ellipse to the surface under test. A more recent method uses a combination of least squares polynomial fitting to the measured slope function in order to enable rapid adjustment to the desired shape. The mirror has mechanical adjustments corresponding to the first and second order terms of the desired slope polynomial, which correspond to defocus and coma, respectively. The higher order terms are realized by shaping the width of the mirror to produce the optimal elliptical surface when bent. The difference between desired and measured surface slope profiles allows us to make methodical adjustments to the bendable mirror based on changes in the signs and magnitudes of the polynomial coefficients. This technique gives rapid convergence to the desired shape of the measured surface, even when we have no information about the bender, other than the desired shape of the optical surface. Nonlinear curve fitting can be used at the end of the process for fine adjustments, and to determine the over all best fit parameters of the surface. This technique cold be generalized to other shapes such as toroids.
Acoustic radiation force on a rigid elliptical cylinder in plane (quasi)standing waves
NASA Astrophysics Data System (ADS)
Mitri, F. G.
2015-12-01
The acoustic radiation force on a 2D elliptical (non-circular) cylinder centered on the axis of wave propagation of plane quasi-standing and standing waves is derived, based on the partial-wave series expansion (PWSE) method in cylindrical coordinates. A non-dimensional acoustic radiation force function, which is the radiation force per unit length, per characteristic energy density and per unit cross-sectional surface of the ellipse, is defined in terms of the scattering coefficients that are determined by applying the Neumann boundary condition for an immovable surface. A system of linear equations involving a single numerical integration procedure is solved by matrix inversion. Numerical simulations showing the transition from the quasi-standing to the (equi-amplitude) standing wave behaviour are performed with particular emphasis on the aspect ratio a/b, where a and b are the ellipse semi-axes, as well as the dimensionless size parameter kb (where k is the wavenumber), without the restriction to a particular range of frequencies. It is found that at high kb values > 1, the radiation force per length with broadside incidence is larger, whereas the opposite situation occurs in the long-wavelength limit (i.e., kb < 1). The results are particularly relevant in acoustic levitation of elliptical cylinders, the acoustic stabilization of liquid columns in a host medium, acousto-fluidics devices, and other particle dynamics applications to name a few. Moreover, the formalism presented here may be effectively applied to compute the acoustic radiation force on other 2D surfaces of arbitrary shape such as super-ellipses, Chebyshev cylindrical particles, or other non-circular geometries.
The Puzzlingly Large Ca II Triplet Absorption in Dwarf Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Michielsen, D.; De Rijcke, S.; Dejonghe, H.; Zeilinger, W. W.; Hau, G. K. T.
2003-11-01
We present central CaT, PaT, and CaT* indices for a sample of 15 dwarf elliptical galaxies (dE's). Twelve of these have CaT*~7 Å and extend the negative correlation between the CaT* index and the central velocity dispersion σ, which was derived for bright elliptical galaxies (E's), down to 20 km s-1 < σ < 55 km s-1. For five dE's, we have independent age and metallicity estimates. Four of these have CaT*~7 Å, much higher than expected from their low metallicities (-1.5<[Z/H]<-0.5). The observed anticorrelation of CaT* as a function of σ or Z is in flagrant disagreement with theory. We discuss some of the amendments that have been proposed to bring the theoretical predictions into agreement with the observed CaT* values of bright E's and how they can be extended to incorporate the observed CaT* values of dE's as well. Moreover, three dE's in our sample have CaT*~5 Å, as would be expected for metal-poor stellar systems. Any theory for dE evolution will have to be able to explain the coexistence of low-CaT* and high-CaT* dE's at a given mean metallicity. This could be the first direct evidence that the dE population is not homogeneous and that different evolutionary paths led to morphologically and kinematically similar but chemically distinct objects. Based on observations collected at the European Southern Observatory, Paranal, Chile (ESO Large Program 165.N 0115).
Acoustic radiation force on a rigid elliptical cylinder in plane (quasi)standing waves
Mitri, F. G.
2015-12-07
The acoustic radiation force on a 2D elliptical (non-circular) cylinder centered on the axis of wave propagation of plane quasi-standing and standing waves is derived, based on the partial-wave series expansion (PWSE) method in cylindrical coordinates. A non-dimensional acoustic radiation force function, which is the radiation force per unit length, per characteristic energy density and per unit cross-sectional surface of the ellipse, is defined in terms of the scattering coefficients that are determined by applying the Neumann boundary condition for an immovable surface. A system of linear equations involving a single numerical integration procedure is solved by matrix inversion. Numerical simulations showing the transition from the quasi-standing to the (equi-amplitude) standing wave behaviour are performed with particular emphasis on the aspect ratio a/b, where a and b are the ellipse semi-axes, as well as the dimensionless size parameter kb (where k is the wavenumber), without the restriction to a particular range of frequencies. It is found that at high kb values > 1, the radiation force per length with broadside incidence is larger, whereas the opposite situation occurs in the long-wavelength limit (i.e., kb < 1). The results are particularly relevant in acoustic levitation of elliptical cylinders, the acoustic stabilization of liquid columns in a host medium, acousto-fluidics devices, and other particle dynamics applications to name a few. Moreover, the formalism presented here may be effectively applied to compute the acoustic radiation force on other 2D surfaces of arbitrary shape such as super-ellipses, Chebyshev cylindrical particles, or other non-circular geometries.
New schemes in the adjustment of bendable, elliptical mirrors using a long trace profiler
Rah, S.
1997-08-01
The Long Trace Profiler (LTP), an instrument for measuring the slope profile of long X-ray mirrors, has been used for adjusting bendable mirrors. Often an elliptical profile is desired for the mirror surface, since many synchrotron applications involve imaging a point source to a point image. Several techniques have been used in the past for adjusting the profile measured in height or slope of a bendable mirror. Underwood et al. have used collimated X-rays for achieving desired surface shape for bent glass optics. Non linear curve fitting using the simplex algorithm was later used to determine the best fit ellipse to the surface under test. A more recent method uses a combination of least squares polynomial fitting to the measured slope function in order to enable rapid adjustment to the desired shape. The mirror has mechanical adjustments corresponding to the first and second order terms of the desired slope polynomial, which correspond to defocus and coma, respectively. The higher order terms are realized by shaping the width of the mirror to produce the optimal elliptical surface when bent. The difference between desired and measured surface slope profiles allows us to make methodical adjustments to the bendable mirror based on changes in the signs and magnitudes of the polynomial coefficients. This technique gives rapid convergence to the desired shape of the measured surface, even when we have no information about the bender, other than the desired shape of the optical surface. Nonlinear curve fitting can be used at the end of the process for fine adjustments, and to determine the over all best fit parameters of the surface. This technique could be generalized to other shapes such as toroids.
Controlling the excitation process of free electrons by a femtosecond elliptically polarized laser
NASA Astrophysics Data System (ADS)
Gao, Lili; Wang, Feng; Jiang, Lan; Qu, Liangti; Lu, Yongfeng
2015-11-01
This paper is focused on the excitation rates of free electrons of an aluminum (Al) bulk irradiated by an elliptically polarized laser in simulation, using time-dependent density functional theory (TDDFT). The polarized 400 nm, 10 fs laser pulse consisted of two elementary sinusoidal beams, and is adjusted by changing the phase difference φ and the intersection angle θ of the polarization directions between the two beams. The simulation includes cases of φ = π/2 with θ = 30°, θ = 45°, θ = 60°, θ = 90°, θ = 120°, θ = 135°, θ = 150°, and cases of θ = 90° with φ = π/4, φ = π/3, φ = π/2, φ = 2π/3, φ = 3π/4. The absorbed energy, the excitation rates and the density distributions of free electrons after laser termination are investigated. At the given power intensity (1×1014Wcm-2), pulse width (10 fs) and wavelength (400 nm) of each elementary laser beam, computational results indicate that the excitation rate of free electrons is impacted by three major factors: the long axis direction of the laser projected profile, the amplitude difference of the first main oscillation (1st AD), and the total amplitude difference of main oscillations (TAD) of the external electric field. Among the aforementioned three factors for the excitation rate of free electrons, the direction of long axis plays the most significant role. The screen effect is crucial to compare the importance of the remaining two factors. The analysis approach to investigate the electron dynamics under an elliptically polarized laser is both pioneering and effective.
NASA Astrophysics Data System (ADS)
Yu, Chih-Jen; Chou, Chien
2011-03-01
An equivalence theory based on a unitary optical system of a generalized elliptical phase retarder was derived. Whereas the elliptical phase retarder can be treated as the combination of a linear phase retarder and a polarization rotator equivalently. Three fundamental parameters, including the elliptical phase retardation, the azimuth angle and the ellipticity angle of the fast elliptical eigen-polarization state were derived. All parameters of a generalized elliptical phase retarder can be determined from the analytical solution of the characteristic parameters of the optical components: linear phase retardation and fast axis angle of the equivalently linear phase retarder respectively, and polarization rotation angle of an equivalent polarization rotator. In this study, the experimental verification was demonstrated by testing a twisted nematic liquid crystal device (TNLCD) treated as a generalized elliptical phase retarder. A dual-frequency heterodyne ellipsometer was setup and the experimental result demonstrates the capability of the equivalent theory on elliptical birefringence measurement at high sensitivity by using heterodyne technique.
NASA Astrophysics Data System (ADS)
Chae, Kyu-Hyun; Gong, In-Taek
2015-08-01
Modified Newtonian dynamics (MOND) proposed by Milgrom provides a paradigm alternative to dark matter (DM) that has been successful in fitting and predicting the rich phenomenology of rotating disc galaxies. There have also been attempts to test MOND in dispersion-supported spheroidal early-type galaxies, but it remains unclear whether MOND can fit the various empirical properties of early-type galaxies for the whole ranges of mass and radius. As a way of rigorously testing MOND in elliptical galaxies we calculate the MOND-predicted velocity dispersion profiles (VDPs) in the inner regions of ˜2000 nearly round Sloan Digital Sky Survey elliptical galaxies under a variety of assumptions on velocity dispersion (VD) anisotropy, and then compare the predicted distribution of VDP slopes with the observed distribution in 11 ATLAS3D galaxies selected with essentially the same criteria. We find that the MOND model parametrized with an interpolating function that works well for rotating galaxies can also reproduce the observed distribution of VDP slopes based only on the observed stellar mass distribution without DM or any other galaxy-to-galaxy varying factor. This is remarkable in view that Newtonian dynamics with DM requires a specific amount and/or profile of DM for each galaxy in order to reproduce the observed distribution of VDP slopes. When we analyse non-round galaxy samples using the MOND-based spherical Jeans equation, we do not find any systematic difference in the mean property of the VDP slope distribution compared with the nearly round sample. However, in line with previous studies of MOND through individual analyses of elliptical galaxies, varying MOND interpolating function or VD anisotropy can lead to systematic change in the VDP slope distribution, indicating that a statistical analysis of VDPs can be used to constrain specific MOND models with an accurate measurement of VDP slopes or a prior constraint on VD anisotropy.
Violent Relaxation, Dynamical Instabilities and the Formation of Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Aguilar, L. A.
1990-11-01
RESUMEN: El problema de la formaci6n de galaxias elfpticas por medjo de colapso gravitacional sin disipaci6n de energfa es estudiado usando un gran numero de simulaciones numericas. Se muestra que este tipo de colapsos, partiendo de condiciones iniciales frfas donde la energfa cinetica inicial representa s6lo un 5%, 0 , de a potencial inicial, produce sistemas relajados de forma triaxial muy similares a las galaxias elfpticas reales en sus formas y perfiles de densidad en proyecci6i . La forina triaxial resulta de la acci6n de una inestabilidad dinamica que aparece en sistemas 'inicos dominados por movimientos radiales, mientras que el perfil de densidad final Cs debido al llamado relajamiento violento que tiende a producir una distribuci6n en espacio fase unica. Estos dos fen6menos tienden a borrar los detalles particulares sobre las condiciones iniciales y dan lugar a una evoluci6n convergente hacia sistemas realistas, esto innecesario el uso de condiciones iniciales especiales (excepto por Ia condici6i de que estas deben ser frfas). Las condiciones iniciales frfas producen los movimientos radiales y fluctuaciones de la energfa potencial requeridos por ambos fen6menos. ABSTRACT: The problem of formation of elliptical galaxies via dissipationless collapse is studied using a large set of numerical simulations. It is shown that dissipationless collapses from cold initial conditions, where the total initial kinetic energy is less than 5% ofthe initial potential energy, lead to relaxed triaxial systems ery similar to real elliptical galaxies ii projected shape and density profiles. The triaxial shape is due to the of a dynamical instability that appears on systems dominated by radial orbits, while final density profile is due to violent relaxation that tends to produce a unique distribution iii space. These two phenomena erase memory of the initial prodtice a convergent evolution toward realistic systems, thus making unnecessary use o[special initial conditions (other
Dark matter deprivation in the field elliptical galaxy NGC 7507
NASA Astrophysics Data System (ADS)
Lane, Richard R.; Salinas, Ricardo; Richtler, Tom
2015-02-01
Context. Previous studies have shown that the kinematics of the field elliptical galaxy NGC 7507 do not necessarily require dark matter. This is troubling because, in the context of ΛCDM cosmologies, all galaxies should have a large dark matter component. Aims: Our aims are to determine the rotation and velocity dispersion profile out to larger radii than do previous studies, and, therefore, more accurately estimate of the dark matter content of the galaxy. Methods: We use penalised pixel-fitting software to extract velocities and velocity dispersions from GMOS slit mask spectra. Using Jeans and MONDian modelling, we then produce models with the goal of fitting the velocity dispersion data. Results: NGC 7507 has a two-component stellar halo, with the outer halo counter rotating with respect to the inner halo, with a kinematic boundary at a radius of ~110'' (~12.4 kpc). The velocity dispersion profile exhibits an increase at ~70'' (~7.9 kpc), reminiscent of several other elliptical galaxies. Our best fit models are those under mild anisotropy, which include ~100 times less dark matter than predicted by ΛCDM, although mildly anisotropic models that are completely dark matter free fit the measured dynamics almost equally well. Our MONDian models, both isotropic and anisotropic, systematically fail to reproduce the measured velocity dispersions at almost all radii. Conclusions: The counter-rotating outer halo implies a merger remnant, as does the increase in velocity dispersion at ~70''. From simulations it seems plausible that the merger that caused the increase in velocity dispersion was a spiral-spiral merger. Our Jeans models are completely consistent with a no dark matter scenario, however, some dark matter can be accommodated, although at much lower concentrations than predicted by ΛCDM simulations. This indicates that NGC 7507 may be a dark matter free elliptical galaxy. Regardless of whether NGC 7507 is completely dark matter free or very dark matter poor
NASA Technical Reports Server (NTRS)
Keyes, David E.; Smooke, Mitchell D.
1987-01-01
A parallelized finite difference code based on the Newton method for systems of nonlinear elliptic boundary value problems in two dimensions is analyzed in terms of computational complexity and parallel efficiency. An approximate cost function depending on 15 dimensionless parameters is derived for algorithms based on stripwise and boxwise decompositions of the domain and a one-to-one assignment of the strip or box subdomains to processors. The sensitivity of the cost functions to the parameters is explored in regions of parameter space corresponding to model small-order systems with inexpensive function evaluations and also a coupled system of nineteen equations with very expensive function evaluations. The algorithm was implemented on the Intel Hypercube, and some experimental results for the model problems with stripwise decompositions are presented and compared with the theory. In the context of computational combustion problems, multiprocessors of either message-passing or shared-memory type may be employed with stripwise decompositions to realize speedup of O(n), where n is mesh resolution in one direction, for reasonable n.
Multilevel methods for elliptic problems on unstructured grids
NASA Technical Reports Server (NTRS)
Chan, Tony F.; Go, Susie; Zikatanov, Ludmil
1997-01-01
Multilevel methods on unstructured grids for elliptic problems are reviewed. The advantages of these techniques are the flexible approximation of the boundaries of complicated physical domains and the ability to adapt the grid to the resolution of fine scaled structures. Multilevel methods, which include multigrid methods and domain decomposition methods, depend on the correct splitting of appropriate finite element spaces. The standard splittings used in the structured grid case cannot be directly extended to unstructured grids due to their requirement for a hierarchical grid structure. Issues related to the application of multilevel methods to unstructured grids are discussed, including how the coarse spaces and transfer operators are defined and how different types of boundary conditions are treated. An obvious way to generate a coarse mesh is to regrid the physical domain several times. Several alternatives are proposed and discussed: node nested coarse spaces, agglomerated coarse spaces and algebraically generated coarse spaces.
Optimal least-squares finite element method for elliptic problems
NASA Technical Reports Server (NTRS)
Jiang, Bo-Nan; Povinelli, Louis A.
1991-01-01
An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.
Dust and ionized gas in active radio elliptical galaxies
NASA Technical Reports Server (NTRS)
Forbes, D. A.; Sparks, W. B.; Macchetto, F. D.
1990-01-01
The authors present broad and narrow bandwidth imaging of three southern elliptical galaxies which have flat-spectrum active radio cores (NGC 1052, IC 1459 and NGC 6958). All three contain dust and extended low excitation optical line emission, particularly extensive in the case of NGC 1052 which has a large H alpha + (NII) luminosity. Both NGC 1052 and IC 1459 have a spiral morphology in emission-line images. All three display independent strong evidence that a merger or infall event has recently occurred, i.e., extensive and infalling HI gas in NGC 1052, a counter-rotating core in IC 1459 and Malin-Carter shells in NGC 6958. This infall event is the most likely origin for the emission-line gas and dust, and the authors are currently investigating possible excitation mechanisms (Sparks et al. 1990).
NASA Technical Reports Server (NTRS)
Matossian, Mark G.
1994-01-01
The Archimedes Project is a joint effort of the European Space Agency (ESA) and the National Space Development Agency of Japan (NASDA). The primary goal of the Archimedes project is to perform a technical feasibility analysis and preliminary design of a highly inclined multisatellite constellation for direct broadcast and mobile communications services for Europe, Japan and much of North America. This report addresses one aspect of this project, specifically an analysis of continuous satellite coverage using multiregional highly elliptical orbits (M-HEO's). The analysis methodology and ensuing software tool, named SPIFF, were developed specifically for this project by the author during the summer of 1992 under the STA/NSF Summer Institute in Japan Program at Tsukuba Space Center.
Construction of preconditioners for elliptic problems by substructuring, III
Bramble, J.H.; Pasciak, J.E.; Schatz, A.H.
1988-10-01
In earlier parts of this series of papers, we constructed preconditioners for the discrete systems of equations arising from the numerical approximation of elliptic boundary value problems. The resulting algorithms are well suited for implementation on computers with parallel architecture. In this paper, we will develop a technique which utilizes these earlier methods to derive even more efficient preconditioners. The iterative algorithms using these new preconditioners converge to the solution of the discrete equations with a rate that is independent of the number of unknowns. These preconditioners involve an incomplete Chebyshev iteration for boundary interface conditions which results in a negligible increase in the amount of computational work. Theoretical estimates and the results of numerical experiments are given which demonstrate the effectiveness of the methods.
Construction of preconditioners for elliptic problems by substructuring. I
Bramble, J.H.; Pasciak, J.E.; Schatz, A.H.
1986-07-01
We consider the problem of solving the algebraic system of equations which arise from the discretization of symmetric elliptic boundary value problems via finite element methods. A new class of preconditioners for the discrete system is developed based on substructuring (also known as domain decomposition). The resulting preconditioned algorithms are well suited to emerging parallel computing architectures. The proposed methods are applicable to problems on general domains involving differential operators with rather general coefficients. A basic theory for the analysis of the condition number of the preconditioned system (which determines the iterative convergence rate of the algorithm) is given. Techniques for applying the theory and algorithms to problems with irregular geometry are discussed and the results of extensive numerical experiments are reported.
A Robust Measure of Dark Matter Halo Ellipticities
NASA Astrophysics Data System (ADS)
Evslin, Jarah
2016-08-01
In simulations of the standard cosmological model (ΛCDM), dark matter halos are aspherical. However, so far the asphericity of an individual galaxy’s halo has never been robustly established. We use the Jeans equations to define a quantity that robustly characterizes a deviation from rotational symmetry. This quantity is essentially the gravitational torque and it roughly provides the ellipticity projected along the line of sight. We show that the Thirty Meter Telescope (TMT), with a single epoch of observations combined with those of the Gaia Space Telescope, can distinguish the ΛCDM value of the torque from zero for each Sculptor-like dwarf galaxy with a confidence between 0 and 5σ, depending on the orientation of each halo. With two epochs of observations, TMT will achieve a 5σ discovery of torque and thus asphericity for most such galaxies, thus providing a new and powerful test of the ΛCDM model.
Isolated elliptical galaxies, their globular cluster systems, and LCDM
NASA Astrophysics Data System (ADS)
Lane, Richard; Salinas, Ricardo; Richtler, Tom
2015-08-01
The globular cluster (GC) systems of isolated elliptical galaxies (IEs) have only recently begun to be studied in detail, and may exhibit morphological connections to the evolutionary histories of their hosts. In fact evidence is mounting that the GC systems of massive galaxies in clusters are largely assembled by infall/accretion processes. IEs are their counterparts in low density environments and a comparison of their GC systems should directly highlight environmental effects. Are GCs the answer to unlocking the evolution of isolated galaxies? In addition, the GC systems of reasonably nearby galaxies are detectable out to large radii, making them useful tracers for producing dynamical models of their hosts. How much dark matter is contained within IEs? Very little it seems, at least in some cases. GCs are, therefore, also one of the most important tools we have for testing Lambda CDM models observationally.
Spatial potential of a weakly compressed elliptical disk
NASA Astrophysics Data System (ADS)
Kondratyev, B. P.
2016-07-01
The problem of expanding spatial potential in terms of eccentricity e accurate to e 2 has been formulated and solved for a homogeneous gravitating (or charged with static electric charge) elliptical disk. An original method that makes it possible to obtain the desired result using the superposition of a perturbation layer and a circular disk has been developed. The potential of such a layer has been derived. The first term of the expansion of the potential (zero power of parameter e) coincides with the potential of a homogeneous circular disk and the coefficient of the first power of the parameter e is zero. The main term of the expansion of the potential proportional to e 2 is analytically derived. The resulting expression makes it possible to determine the potential in the entire space, including the inner region of the disk.
Semi-orthogonal wavelets for elliptic variational problems
Hardin, D.P.; Roach, D.W.
1998-04-01
In this paper the authors give a construction of wavelets which are (a) semi-orthogonal with respect to an arbitrary elliptic bilinear form a({center_dot},{center_dot}) on the Sobolev space H{sub 0}{sup 1}((0, L)) and (b) continuous and piecewise linear on an arbitrary partition of [0, L]. They illustrate this construction using a model problem. They also construct alpha-orthogonal Battle-Lemarie type wavelets which fully diagonalize the Galerkin discretized matrix for the model problem with domain IR. Finally they describe a hybrid basis consisting of a combination of elements from the semi-orthogonal wavelet basis and the hierarchical Schauder basis. Numerical experiments indicate that this basis leads to robust scalable Galerkin discretizations of the model problem which remain well-conditioned independent of {epsilon}, L, and the refinement level K.
Nonperturbative signatures in pair production for general elliptic polarization fields
NASA Astrophysics Data System (ADS)
Li, Z. L.; Lu, D.; Xie, B. S.; Shen, B. F.; Fu, L. B.; Liu, J.
2015-06-01
The momentum signatures in nonperturbative multiphoton pair production for general elliptic polarization electric fields are investigated by employing the real-time Dirac-Heisenberg-Wigner formalism. For a linearly polarized electric field we find that the positions of the nodes in momentum spectra of created pairs depend only on the electric-field frequency. The polarization of external fields could not only change the node structures or even make the nodes disappear but also change the thresholds of pair production. The momentum signatures associated to the node positions in which the even-number photon pair creation process is forbidden could be used to distinguish the orbital angular momentum of created pairs on the momentum spectra. These distinguishable momentum signatures could be relevant for providing the output information of created particles and also the input information of ultrashort laser pulses.
S-DARS broadcast from inclined, elliptical orbits
NASA Astrophysics Data System (ADS)
Briskman, Robert D.; Prevaux, Robert J.
2004-04-01
The first Sirius spacecraft was launched on July 1, 2000. Exactly 5 months later, on December 1, the third spacecraft was launched, completing the three satellite S-DARS (Satellite Digital Audio Radio Service) constellation. The three satellites are deployed in inclined, elliptical, geosynchronous orbits, which allow seamless broadcast coverage to mobile users in the contiguous US. Terrestrial broadcast repeaters provide service in urban cores. The system is in operation, providing the first ever S-DARS service. The constellation design results in satellite ground tracks over North America with two satellites always above the equator. High elevation look angles from the mobile ground terminals to the satellites minimize performance degradation due to blockage, foliage attenuation and multi-path. The spacecraft were built by Space Systems/Loral using the 1300 bus modified for operation in high inclination orbits. Each spacecraft was launched using a dedicated Russian Proton booster. The satellite payload is a bent pipe repeater using 7.1 GHz for the uplink and 2.3 GHz for the broadcast transmission. The repeater high-power amplification stage consists of 32 Traveling Wave Tube Amplifiers phase combined to yield a total radio frequency output power of nearly 4 kW at saturated operation. The satellite antennas are mechanically steered to maintain the transmit beam centered on the Contiguous United States and the receive beam centered on the uplink earth station located in Vernon Valley, New Jersey. The satellite payload design and performance are described. The principal spacecraft bus systems are described with emphasis on improvements made for operation in the inclined, elliptical geosynchronous orbits.
High order methods for elliptic problems in plasma physics
NASA Astrophysics Data System (ADS)
Pataki, Andras
In this dissertation, we develop fast high order solvers for two elliptic problems in plasma physics. The first is the Grad-Shafranov equation, a nonlinear elliptic PDE that describes the magnetohydrodynamic equilibrium of three dimensional, axisymmetric plasmas. A high order solver is desirable to ensure the accurate evaluation of derivatives, required both for the computation of physical quantities and for studying perturbations near equilibrium. Using suitable scaling, we transform the problem from cylindrical coordinates to a nonlinear Poisson problem in Cartesian coordinates. We compute the conformal map from the original domain to the unit circle where we build a separation of variables based solver to obtain a high order, accurate solution. A fixed point or eigenvalue outer iteration is used to solve the nonlinear equation. Our second problem is the computation of the Coulomb collision operator that arises in kinetic models of plasmas. The collision operator can be written in terms of two Rosenbluth potentials obtained by solving a Poisson and a biharmonic problem in the velocity variables. For these PDEs we describe a new class of fast solvers in cylindrical coordinates with free-space radiation conditions. By combining integral equation methods in the radial variable with Fourier methods in the angular and z directions, we show that high-order accuracy can be achieved in both the solution and its derivatives. A weak singularity arises in the Fourier transform with respect to z that is handled with special purpose quadratures. Such solvers are ideally suited to the Rosenbluth potentials, since the collision operator is expressed in terms of up to fourth derivatives of the potentials, placing stringent demands on the computational order. Also, since axisymmetry is generally assumed in the velocity variables, the use of cylindrical coordinates reduces the three dimensional problem to a two dimensional computation.
Radial Motions in Disk Stars: Ellipticity or Secular Flows?
NASA Astrophysics Data System (ADS)
López-Corredoira, M.; González-Fernández, C.
2016-06-01
Average stellar orbits of the Galactic disk may have some small intrinsic ellipticity which breaks the exact axisymmetry and there may also be some migration of stars inwards or outwards. Both phenomena can be detected through kinematic analyses. We use the red clump stars selected spectroscopically from the APO Galactic Evolution Experiment, with known distances and radial velocities, to measure the radial component of the Galactocentric velocities within 5 kpc < R < 16 kpc, | b| \\lt 5^\\circ , and within 20° from the Sun–Galactic center line. The average Galactocentric radial velocity is VR = (1.48 ± 0.35)[R(kpc) ‑ (8.8 ± 2.7)] km s‑1 outwards in the explored range, with a higher contribution from stars below the Galactic plane. Two possible explanations can be given for this result: (i) the mean orbit of the disk stars is intrinsically elliptical with a Galactocentric radial gradient of eccentricity around 0.01 kpc‑1 or (ii) there is a net secular expansion of the disk, in which stars within R ≈ 9–11 kpc are migrating to the region R ≳ 11 kpc at the rate of ∼2 M⊙ yr‑1, and stars with R ≲ 9 kpc are falling toward the center of the Galaxy. This migration ratio would be unattainable for a long time and should decelerate, otherwise the Galaxy would fade away in around 1 Gyr. At present, both hypotheses are speculative and one would need data on the Galactocentric radial velocities for other azimuths different to the center or anticenter in order to confirm one of the scenarios.
Underexpanded Screeching Jets From Circular, Rectangular, and Elliptic Nozzles
NASA Technical Reports Server (NTRS)
Panda, J.; Raman, G.; Zaman, K. B. M. Q.
2004-01-01
The screech frequency and amplitude, the shock spacing, the hydrodynamic-acoustic standing wave spacing, and the convective velocity of large organized structures are measured in the nominal Mach number range of 1.1 less than or = Mj less that or = l0.9 for supersonic, underexpanded jets exhausting from a circular, a rectangular and an elliptic nozzle. This provides a carefully measured data set useful in comparing the importance of various physical parameters in the screech generation process. The hydrodynamic-acoustic standing wave is formed between the potential pressure field of large turbulent structures and the acoustic pressure field of the screech sound. It has been demonstrated earlier that in the currently available screech frequency prediction models replacement of the shock spacing by the standing wave spacing provides an exact expression. In view of this newly found evidence, a comparison is made between the average standing wavelength and the average shock spacing. It is found that there exists a small, yet important, difference, which is dependent on the azimuthal screech mode. For example, in the flapping modes of circular, rectangular, and elliptic jets, the standing wavelength is slightly longer than the shock spacing, while for the helical screech mode in a circular jet the opposite is true. This difference accounts for the departure of the existing models from predicting the exact screech frequency. Another important parameter, necessary in screech prediction, is the convective velocity of the large organized structures. It is demonstrated that the presence of the hydrodynamic-acoustic standing wave, even inside the jet shear layer, becomes a significant source of error in the convective velocity data obtained using the conventional methods. However, a new relationship, using the standing wavelength and screech frequency is shown to provide more accurate results.
Radial Motions in Disk Stars: Ellipticity or Secular Flows?
NASA Astrophysics Data System (ADS)
López-Corredoira, M.; González-Fernández, C.
2016-06-01
Average stellar orbits of the Galactic disk may have some small intrinsic ellipticity which breaks the exact axisymmetry and there may also be some migration of stars inwards or outwards. Both phenomena can be detected through kinematic analyses. We use the red clump stars selected spectroscopically from the APO Galactic Evolution Experiment, with known distances and radial velocities, to measure the radial component of the Galactocentric velocities within 5 kpc < R < 16 kpc, | b| \\lt 5^\\circ , and within 20° from the Sun-Galactic center line. The average Galactocentric radial velocity is VR = (1.48 ± 0.35)[R(kpc) - (8.8 ± 2.7)] km s-1 outwards in the explored range, with a higher contribution from stars below the Galactic plane. Two possible explanations can be given for this result: (i) the mean orbit of the disk stars is intrinsically elliptical with a Galactocentric radial gradient of eccentricity around 0.01 kpc-1 or (ii) there is a net secular expansion of the disk, in which stars within R ≈ 9-11 kpc are migrating to the region R ≳ 11 kpc at the rate of ˜2 M⊙ yr-1, and stars with R ≲ 9 kpc are falling toward the center of the Galaxy. This migration ratio would be unattainable for a long time and should decelerate, otherwise the Galaxy would fade away in around 1 Gyr. At present, both hypotheses are speculative and one would need data on the Galactocentric radial velocities for other azimuths different to the center or anticenter in order to confirm one of the scenarios.