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.
Gravity modeling: the Jacobian function and its approximation
NASA Astrophysics Data System (ADS)
Strykowski, G.; Lauritsen, N. L. B.
2012-04-01
In mathematics, the elements of a Jacobian matrix are the first-order partial derivatives of a scalar function or a vector function with respect to another vector. In inversion theory of geophysics the elements of a Jacobian matrix are a measure of the change of the output signal caused by a local perturbation of a parameter of a given (Earth) model. The elements of a Jacobian matrix can be determined from the general Jacobian function. In gravity modeling this function consists of the "geometrical part" (related to the relative location in 3D of a field point with respect to the source element) and the "source-strength part" (related to the change of mass density of the source element). The explicit (functional) expressions for the Jacobian function can be quite complicated and depend both on the coordinates used (Cartesian, spherical, ellipsoidal) and on the mathematical parametrization of the source (e.g. the homogenous rectangular prism). In practice, and irrespective of the exact expression for the Jacobian function, its value on a computer will always be rounded to a finite number of digits. In fact, in using the exact formulas such finite representation may cause numerical instabilities. If the Jacobian function is smooth enough, it is an advantage to approximate it by a simpler function, e.g. a piecewise-polynomial, which numerically is more robust than the exact formulas and which is more suitable for the subsequent integration. In our contribution we include a whole family of the Jacobian functions which are associated with all the partial derivatives of the gravitational potential of order 0 to 2, i.e. including all the elements of the gravity gradient tensor. The quality of the support points for the subsequent polynomial approximation of the Jacobian function is ensured by using the exact prism formulas in quadruple precision. We will show some first results. Also, we will discuss how such approximated Jacobian functions can be used for large scale
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…
Determination of caustic surfaces using point spread function and ray Jacobian and Hessian matrices.
Lin, Psang Dain
2014-09-10
Existing methods for determining caustic surfaces involve computing either the flux density singularity or the center of curvature of the wavefront. However, such methods rely rather heavily on ray tracing and finite difference methods for estimating the first- and second-order derivative matrices (i.e., Jacobian and Hessian matrices) of a ray. The main reason is that previously the analytical expressions of these two matrices have been tedious or even impossible. Accordingly, the present study proposes a robust numerical method for determining caustic surfaces based on a point spread function and the established analytical Jacobian and Hessian matrices of a ray by our group. It is shown that the proposed method provides a convenient and computationally straightforward means of determining the caustic surfaces of both simple and complex optical systems without the need for analytical equations, and is substantially different from the two existing methods. PMID:25321667
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.
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.
Elliptic Functions and Integrals with Real Modulus in Fluid Mechanics
NASA Technical Reports Server (NTRS)
Legendre, Robert
1958-01-01
Advantage of the elliptic functions and of the more general functions of Schwarz for fluid mechanics. Flows outside and inside polygons. Application to the calculation of an elbow diffuser for a wind tunnel. Properties of the elliptic integrals of the first kind and of the elliptic functions. Properties of the theta functions and decomposition of the elliptic functions into products of theta functions. Properties of the zeta functions. Decomposition of the elliptic functions into sums of zeta functions and calculations of the elliptic integrals. Applications to the calculation of wing profiles, of compressor profiles, and to the study of the vibrations of airplane wings and of compressor vanes. The manuscript of the present paper was checked by Mr. Eichelbrenner who corrected several imperfections and suggested numerous improvements to make reading of the paper easier. However, the limited subject does not permit filling in more than an incomplete knowledge of the properties of analytic functions.
Modified Elliptic Gamma Functions and 6d Superconformal Indices
NASA Astrophysics Data System (ADS)
Spiridonov, Vyacheslav P.
2014-04-01
We construct a modified double elliptic gamma function which is well defined when one of the base parameters lies on the unit circle. A model consisting of 6d hypermultiplets coupled to a gauge field theory living on a 4d defect is proposed whose superconformal index uses the double elliptic gamma function and obeys W( E 7)-group symmetry.
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…
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.
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
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.
A giant elliptical galaxy with a lightweight initial mass function
NASA Astrophysics Data System (ADS)
Smith, Russell J.; Lucey, John R.
2013-09-01
We present new observations of the closest known strong-lensing galaxy, the σ ≈ 330 km s- 1 giant elliptical ESO325-G004, made with the ESO Very Large Telescope. The low redshift of the lens (zl = 0.035) results in arcs being formed at a small fraction of the effective radius (REin = 2.85 arcsec ≈ Reff/4). At such small radii, stars dominate the lensing mass, so that lensing provides a direct probe of the stellar mass-to-light ratio, with only small corrections needed for dark matter. However, the redshift of the galaxy lensed by ESO325-G004 was unknown until now, so the lensing mass was not securely determined. Using X-SHOOTER, we have detected multiple spectral lines, from two bright parts of the arc system, and measured a source redshift of zs = 2.141. Combined with lens modelling constraints, this yields a total mass inside the Einstein radius of 1.50 ± 0.06 × 1011 M⊙. We estimate the range of possible contribution of dark matter to the lensing mass, using halo profile statistics from cosmological N-body simulations. Subtracting this component yields a stellar mass-to-light ratio for the lens of M*/LF814W = 3.14^{+0.24}_{-0.42} (M/L)_{{odot }, F814W}. Using VIMOS, we have also obtained very high signal-to-noise spectroscopy for the lens galaxy. Fitting models to this spectrum confirms that ESO325-G004 has a very old stellar population. For a Milky-Way-like (Kroupa) initial mass function (IMF), the stellar population fit yields a predicted stellar mass-to-light ratio of ΥMW = 3.01 ± 0.25 (M/L)⊙, F814W. Hence, the mass attributable to stars with a Kroupa IMF is consistent with the lensing estimate. By contrast, a Salpeter (or heavier) IMF is disfavoured at the 99.8 per cent confidence level. A `heavyweight' IMF, with a mass twice as large as the Kroupa case, is firmly excluded for this galaxy. Such an IMF has been proposed for more distant elliptical lenses, and also to explain strong dwarf-star-sensitive spectral features, in particular the Na I
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.
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.
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.
Swarm formation control utilizing elliptical surfaces and limiting functions.
Barnes, Laura E; Fields, Mary Anne; Valavanis, Kimon P
2009-12-01
In this paper, we present a strategy for organizing swarms of unmanned vehicles into a formation by utilizing artificial potential fields that were generated from normal and sigmoid functions. These functions construct the surface on which swarm members travel, controlling the overall swarm geometry and the individual member spacing. Nonlinear limiting functions are defined to provide tighter swarm control by modifying and adjusting a set of control variables that force the swarm to behave according to set constraints, formation, and member spacing. The artificial potential functions and limiting functions are combined to control swarm formation, orientation, and swarm movement as a whole. Parameters are chosen based on desired formation and user-defined constraints. This approach is computationally efficient and scales well to different swarm sizes, to heterogeneous systems, and to both centralized and decentralized swarm models. Simulation results are presented for a swarm of 10 and 40 robots that follow circle, ellipse, and wedge formations. Experimental results are included to demonstrate the applicability of the approach on a swarm of four custom-built unmanned ground vehicles (UGVs). PMID:19447722
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 connection of the quadratic Lienard equation with an equation for the elliptic functions
NASA Astrophysics Data System (ADS)
Kudryashov, Nikolay A.; Sinelshchikov, Dmitry I.
2015-07-01
The quadratic Lienard equation is widely used in many applications. A connection between this equation and a linear second-order differential equation has been discussed. Here we show that the whole family of quadratic Lienard equations can be transformed into an equation for the elliptic functions. We demonstrate that this connection can be useful for finding explicit forms of general solutions of the quadratic Lienard equation. We provide several examples of application of our approach.
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
NASA Astrophysics Data System (ADS)
Spurr, Robert; Christi, Matt
2014-07-01
The linearized radiative transfer models VLIDORT and LIDORT will deliver profile weighting functions (Jacobians) with respect to layer optical properties. We derive transformation rules for the conversion of layer Jacobian output to weighting functions defined for level (layer boundary) quantities such as volume mixing ratio, temperature and pressure. In a related development, we discuss the derivation of bulk-property atmospheric Jacobians with respect to quantities such as the temperature shift, the surface pressure and scaling parameters for constituent profiles. We also present some rules for calculating Jacobians for parameters characterizing aerosol loading regimes. An appendix contains linearization (with respect to temperature and pressure) of the trace species cross-sections derived from the HITRAN line spectroscopy data base.
NASA Astrophysics Data System (ADS)
Quaas, Alexander; Xia, Aliang
2016-06-01
In this article, we prove the existence and multiplicity of positive solutions for the following fractional elliptic equation with sign-changing weight functions: (-Δ)^α u= a_λ(x)|u|^{q-2}u+b(x)|u|^{2^*_α-1}u &in Ω, u=0&in {R}^N{setminus} Ω, where {0 < α < 1}, {Ω} is a bounded domain with smooth boundary in {{R}^N} with {N > 2 α} and {2^*_{α}=2N/(N-2α)} is the fractional critical Sobolev exponent. Our multiplicity results are based on studying the decomposition of the Nehari manifold and the Lusternik-Schnirelmann category.
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.
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.
PERSPECTIVES ON INTRACLUSTER ENRICHMENT AND THE STELLAR INITIAL MASS FUNCTION IN ELLIPTICAL GALAXIES
Loewenstein, Michael
2013-08-10
Stars formed in galaxy cluster potential wells must be responsible for the high level of enrichment measured in the intracluster medium (ICM); 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 construct a phenomenological cluster enrichment model to demonstrate that ICM elemental abundances are underestimated by a factor >2 for standard assumptions about the stellar population-a discrepancy we call the ''cluster elemental abundance paradox''. Recent evidence of an elliptical galaxy initial mass function (IMF) skewed to low masses deepens the paradox. We quantify the adjustments to the star formation efficiency and IMF, and Type Ia supernovae (SNIa) production efficiency, required to resolve this while being consistent with the observed ICM abundance pattern. 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 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 M{sub Sun} 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 in the universe, the process of elliptical galaxy formation, and the origin of this ''hidden'' source of ICM metal enrichment.
A function space approach to state and model error estimation for elliptic systems
NASA Technical Reports Server (NTRS)
Rodriguez, G.
1983-01-01
An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal esimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed. While this paper focuses on theoretical developments, applications arising in the area of large structure static shape determination are contained in a closely related paper (Rodriguez and Scheid, 1982).
A function space approach to state and model error estimation for elliptic systems
NASA Technical Reports Server (NTRS)
Rodriguez, G.
1983-01-01
An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed.
Efficient time-symmetric simulation of torqued rigid bodies using Jacobi elliptic functions
NASA Astrophysics Data System (ADS)
Celledoni, E.; Säfström, N.
2006-05-01
If the three moments of inertia are distinct, the solution to the Euler equations for the free rigid body is given in terms of Jacobi elliptic functions. Using the arithmetic-geometric mean algorithm (Abramowitz and Stegun 1992 Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (New York: Dover)), these functions can be calculated efficiently and accurately. Compared to standard numerical ODE and Lie-Poisson solvers, the overall approach yields a faster and more accurate numerical solution to the Euler equations. This approach is designed for mass asymmetric rigid bodies. In the case of symmetric bodies, the exact solution is available in terms of trigonometric functions, see Dullweber et al (1997 J. Chem. Phys. 107 5840-51), Reich (1996 Fields Inst. Commun. 10 181-91) and Benettin et al (2001 SIAM J. Sci. Comp. 23 1189-203) for details. In this paper, we consider the case of asymmetric rigid bodies subject to external forces. We consider a strategy similar to the symplectic splitting method proposed in Reich (1996 Fields Inst. Commun. 10 181-91) and Dullweber et al (1997 J. Chem. Phys. 107 5840-51). The method proposed here is time-symmetric. We decompose the vector field of our problem into a free rigid body (FRB) problem and another completely integrable vector field. The FRB problem consists of the Euler equations and a differential equation for the 3 × 3 orientation matrix. The Euler equations are integrated exactly while the matrix equation is approximated using a truncated Magnus series. In our experiments, we observe that the overall numerical solution benefits greatly from the very accurate solution of the Euler equations. We apply the method to the heavy top and the simulation of artificial satellite attitude dynamics.
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.
Milne, Stephen C.
1996-01-01
In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others. PMID:11038532
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
NASA Astrophysics Data System (ADS)
Zhang, Xiaofeng
2012-03-01
Image formation in fluorescence diffuse optical tomography is critically dependent on construction of the Jacobian matrix. For clinical and preclinical applications, because of the highly heterogeneous characteristics of the medium, Monte Carlo methods are frequently adopted to construct the Jacobian. Conventional adjoint Monte Carlo method typically compute the Jacobian by multiplying the photon density fields radiated from the source at the excitation wavelength and from the detector at the emission wavelength. Nonetheless, this approach assumes that the source and the detector in Green's function are reciprocal, which is invalid in general. This assumption is particularly questionable in small animal imaging, where the mean free path length of photons is typically only one order of magnitude smaller than the representative dimension of the medium. We propose a new method that does not rely on the reciprocity of the source and the detector by tracing photon propagation entirely from the source to the detector. This method relies on the perturbation Monte Carlo theory to account for the differences in optical properties of the medium at the excitation and the emission wavelengths. Compared to the adjoint methods, the proposed method is more valid in reflecting the physical process of photon transport in diffusive media and is more efficient in constructing the Jacobian matrix for densely sampled configurations.
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
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.
Okura, Yuki; Futamase, Toshifumi E-mail: tof@astr.tohoku.ac.jp
2012-04-01
We developed a new method (E-HOLICs) of estimating gravitational shear by adopting an elliptical weight function to measure background galaxy images in our previous paper. Following the previous paper, in which an isotropic point-spread function (PSF) correction is calculated, in this paper we consider an anisotropic PSF correction in order to apply E-HOLICs to real data. As an example, E-HOLICs is applied to Subaru data of the massive and compact galaxy cluster A370 and is able to detect double peaks in the central region of the cluster consistent with the analysis of strong lensing. We also study the systematic error in E-HOLICs using STEP2 simulation. In particular, we consider the dependences of the signal-to-noise ratio (S/N) of background galaxies in the shear estimation. Although E-HOLICs does improve the systematic error due to the ellipticity dependence as shown in Paper I, a systematic error due to the S/N dependence remains, namely, E-HOLICs underestimates shear when background galaxies with low S/N objects are used. We discuss a possible improvement of the S/N dependence.
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.
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 \
Analytical Jacobian and its application to tilted-wave interferometry.
Fortmeier, Ines; Stavridis, Manuel; Wiegmann, Axel; Schulz, Michael; Osten, Wolfgang; Elster, Clemens
2014-09-01
Tilted-wave interferometry (TWI) is a novel optical measurement principle for the measurement of aspherical surfaces. For the reconstruction of the wavefront and the surface under test, respectively, perturbation methods are applied, which require the calculation of the Jacobian matrix. For the practical use of the instrument, a fast and exact calculation of the Jacobian matrices is crucial, since this strongly influences the calculation times of the TWI. By applying appropriate approaches in optical perturbation methods we are able to calculate the required Jacobian matrices analytically when the nominal optical path through the system is given. As a result, calculation times for the TWI can be considerably reduced. We finally illustrate the improved TWI procedure and apply methods of optimal design to determine optimal positions of the surface under test. For such applications the fast calculation of the Jacobian matrices is essential. PMID:25321510
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.
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.
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.
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.
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.
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 + CJT = −2D, called Lyapunov Equation in its generic form,1 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.
Semistable modifications of families of curves and compactified Jacobians
NASA Astrophysics Data System (ADS)
Esteves, Eduardo; Pacini, Marco
2016-04-01
Given a family of nodal curves, a semistable modification of it is another family made up of curves obtained by inserting chains of rational curves of any given length at certain nodes of certain curves of the original family. We give comparison theorems between torsion-free, rank-1 sheaves in the former family and invertible sheaves in the latter. We apply them to show that there are functorial isomorphisms between the compactifications of relative Jacobians of families of nodal curves constructed through Caporaso's approach and those constructed through Pandharipande's approach.
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.
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.
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
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. PMID:27025506
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
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
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.
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.
Inversion without Explicit Jacobian Calculations in Electrical Impedance Tomography
NASA Astrophysics Data System (ADS)
Fouchard, A.; Bonnet, S.; Hervé, L.; David, O.
2014-10-01
Electrical impedance tomography (EIT) is the inverse problem of finding the internal conductivity distribution of a medium given boundary electrical measurements performed via an electrode array onto its surface. Conventional inversion schemes adopt Tikhonov regularized Newton-type methods. Following a transport back-transport approach, we develop in this work an adjoint approach which allows reducing computational burden in enabling inversion without explicit Jacobian calculation. Forward and back-projection operators are defined from potential gradients, along with their efficient implementation. These derivations allow the transparent use of inversion algorithms. We first check the implementation of operators. We then evaluate how reconstructions perform on simulated noisy data using a preconditioned conjugate gradient. We eventually practice our inversion framework on experimental data acquired in vitro from a saline phantom.
NASA Astrophysics Data System (ADS)
Dimitrov, Dimitar
2014-09-01
The present investigation encloses the started in the earlier papers [3] and [4] analytical evaluations of some kinds definite integrals. These solutions are necessary steps towards the revealing the mathematical structure of the dynamical equation, governing the properties of the stationary elliptical accretion discs, which apse lines of all orbits are in line with each other[5]. Though the considered here task, at first glance, may seem as a purely mathematical one, there are some restrictions of physical nature on the variables, entering as arguments into the integrals. In this paper we resolve analytically the following two definite integrals, including into their nominators (as a factor) the logarithmic function ln(1 + ecosφ). Concretely, we find in an explicit form the solutions of the integrals Li(e,ė) ≡ 2 π ≡ ∫[ln(1 + ecosφ)](1 + ecosφ) – 1[1 + (e – ė)cosφ] – i dφ, (i = 0,…, 3), 0 2 π and Kj(e,ė) ≡ ∫[ln(1 + ecosφ)] [1 +(e – ė)cosφ] – j dφ, (j = 1, …, 5). 0 Here we have used the following notations: φ is the azimutal angle. The integration over φ from 0 to 2π means an averaging over the whole trajectory for each disc particle. Each such particle spirals inward to the center of the disc, moving on (quasi-) elliptical orbits with focal parameters p. These parameters p are allowed to vary for different elliptical orbits.In the our approach of computations, we treat e(u) and ė(u) as independent variables. The physically imposed restrictions (which, to some extend, lead to simplifications of the problems) are |e(u)| < 1,|ė(u)| < 1 and |e(u) – ė(u)| < 1 for all admitted values of u. That is to say, between the innermost and outermost orbits of the disc. Consequently, the established in this paper analytical solutions for the integrals Li(e,ė), (i = 0,…, 3) and Kj(e,ė), (j = 1, …, 5), are, probably, not the most general ones, even in the domain of the real analysis. But nevertheless, they are sufficient for our
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.
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)
Tetrahedral element shape optimization via the Jacobian determinant and condition number.
Freitag, L. A.; Knupp, P. M.
1999-07-30
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.
NASA Astrophysics Data System (ADS)
Kim, Dong-Woo
2005-10-01
We propose deep XMM-Newton observations of two young, post-merger elliptical galaxies, NGC 3377 and NGC 5018. Because their X-ray to optical luminosity ratios are the lowest among ellipticals and their stellar populations are significantly metal-enriched, they are the best candidates to address two biggest unsolved problems of the X-ray study of elliptical galaxies: large L_X/L_B scatter and ISM Fe discrepancy. Our XMM-Newton data, in conjunction with the existing Chandra data will allow us to accurately determine Fe and alpha-elements abundances. We will then address the origin of the large L_X/L_B scatter in terms of ISM removal mechanisms by merger-induced galactic winds.
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.
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.
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.
A Unified Microwave Radiative Transfer Model with Jacobian for General Stratified Media
NASA Astrophysics Data System (ADS)
Tian, Miao
A unified microwave radiative transfer (UMRT) model is developed for rapid, stable and accurate level-centric calculation of the thermal radiation emitted from any geophysical medium comprised of planar layers of either densely or tenuously distributed, moderately sized spherical scatterers. The formulation includes rapid calculation of the tangent linear relationship (i.e., Jacobian) between the observed brightness temperature and any relevant radiative and geophysical layer parameters, such as the scattering and absorption coefficients, temperature, temperature lapse rate, and medium layer thickness. UMRT employs a rapid multistream scattering-based discrete ordinate eigenanalysis solution with a layer-adding algorithm stabilized by incorporating symmetrization of the discretized differential radiative transfer equations and analytical diagonalization and factorization of the resulting symmetric and positive definite matrices. It is based on the discrete ordinate tangent linear radiative transfer model of Voronovich et al. (2004), but extended to include both Mie and dense media scattering theories and employ refractive layers. Other nontrivial extensions are: 1) exact modeling of linearized temperature profiles and resulting radiation streams across medium layers, 2) compensation for refracted radiation streams using Snell's law, the Fresnel reflectivity and transmissivity coefficients, and a cubic spline interpolation matrix, and 3) seamless calculation of associated Jacobians for both sparse and dense medium parameters. Details of the UMRT Jacobian formulation are presented. The entire formulation has been programmed in Matlab and validated through both energy conservation and numerical Jacobian intercomparisons. Comparisons of the upwelling brightness temperatures over dry snow and ice from simulations and field measurements are presented and discussed.
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
Optimizing elliptic curve scalar multiplication for small scalars
NASA Astrophysics Data System (ADS)
Giorgi, Pascal; Imbert, Laurent; Izard, Thomas
2009-08-01
On an elliptic curve, the multiplication of a point P by a scalar k is defined by a series of operations over the field of definition of the curve E, usually a finite field Fq. The computational cost of [k]P = P + P + ...+ P (k times) is therefore expressed as the number of field operations (additions, multiplications, inversions). Scalar multiplication is usually computed using variants of the binary algorithm (double-and-add, NAF, wNAF, etc). If s is a small integer, optimized formula for [s]P can be used within a s-ary algorithm or with double-base methods with bases 2 and s. Optimized formulas exists for very small scalars (s <= 5). However, the exponential growth of the number of field operations makes it a very difficult task when s > 5. We present a generic method to automate transformations of formulas for elliptic curves over prime fields in various systems of coordinates. Our method uses a directed acyclic graph structure to find possible common subexpressions appearing in the formula and several arithmetic transformations. It produces efficient formulas to compute [s]P for a large set of small scalars s. In particular, we present a faster formula for [5]P in Jacobian coordinates. Moreover, our program can produce code for various mathematical software (Magma) and libraries (PACE).
A new weak lensing shear analysis method using ellipticity defined by 0th order moments
NASA Astrophysics Data System (ADS)
Okura, Yuki; Futamase, Toshifumi
2015-04-01
We developed a new method that uses ellipticity defined by 0th order moments (0th-ellipticity) for weak gravitational lensing shear analysis. Although there is a strong correlation between the ellipticity calculated using this approach and the usual ellipticity defined by the 2nd order moment, the ellipticity calculated here has a higher signal-to-noise ratio because it is weighted to the central region of the image. These results were confirmed using data for Abell 1689 from the Subaru telescope. For shear analysis, we adopted the ellipticity of re-smeared artificial image method for point spread function correction, and we tested the precision of this 0th-ellipticity with simple simulation, then we obtained the same level of precision with the results of ellipticity defined by quadrupole moments. Thus, we can expect that weak lensing analysis using 0 shear will be improved in proportion to the statistical error.
The size-frequency distribution of elliptical impact craters
NASA Astrophysics Data System (ADS)
Collins, G. S.; Elbeshausen, D.; Davison, T. M.; Robbins, S. J.; Hynek, B. M.
2011-10-01
Impact craters are elliptical in planform if the impactor's trajectory is below a threshold angle of incidence. Laboratory experiments and 3D numerical simulations demonstrate that this threshold angle decreases as the ratio of crater size to impactor size increases. According to impact cratering scaling laws, this implies that elliptical craters occur at steeper impact angles as crater size or target strength increases. Using a standard size-frequency distribution for asteroids impacting the terrestrial planets we estimate the fraction of elliptical craters as a function of crater size on the Moon, Mars, Earth, Venus and Mercury. In general, the expected fraction of elliptical craters is ~ 2-4% for craters between 5 and 100-km in diameter, consistent with the observed population of elliptical craters on Mars. At larger crater sizes both our model and observations suggest a dramatic increase in the fraction of elliptical craters with increasing crater diameter. The observed fraction of elliptical craters larger than 100-km diameter is significantly greater than our model predictions, which may suggest that there is an additional source of large elliptical craters other than oblique impact.
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 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 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.
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.
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
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
C1,1 regularity for degenerate elliptic obstacle problems
NASA Astrophysics Data System (ADS)
Daskalopoulos, Panagiota; Feehan, Paul M. N.
2016-03-01
The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate-elliptic partial differential operator, where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. In mathematical finance, solutions to the obstacle problem for the elliptic Heston operator correspond to value functions for perpetual American-style options on the underlying asset. With the aid of weighted Sobolev spaces and weighted Hölder spaces, we establish the optimal C 1 , 1 regularity (up to the boundary of the half-plane) for solutions to obstacle problems for the elliptic Heston operator when the obstacle functions are sufficiently smooth.
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).
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
Knupp, P.M.
1999-01-18
Structured mesh quality optimization methods are extended to optimization of unstructured triangular, quadrilateral, and mixed finite element meshes. N"ew interpretations of well-known nodally-bssed objective functions are made possible using matrices and matrix norms. The matrix perspective also suggests several new objective functions. Particularly significant is the interpretation of the Oddy metric and the Smoothness objective functions in terms of the condition number of the metric tensor and Jacobian matrix, respectively. Objective functions are grouped according to dimensionality to form weighted combinations. A simple unconstrained local optimum is computed using a modiiied N-ewton iteration. The optimization approach was implemented in the CUBIT mesh generation code and tested on several problems. Results were compared against several standard element-based quaIity measures to demonstrate that good mesh quality can be achieved with nodally-based objective functions.
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
Rotating convection in elliptical geometries
NASA Astrophysics Data System (ADS)
Evonuk, M.
2014-12-01
Tidal interactions between hot jupiter planets and their host stars are likely to result in non-spherical geometries. These elliptical instabilities may have interesting effects on interior fluid convective patterns, which in turn influence the nature of the magnetic dynamo within these planets. Simulations of thermal convection in the 2D rotating equatorial plane are conducted to determine to first order the effect of ellipticity on convection for varying density contrasts with differing convective vigor and rotation rate. This survey is conducted in two dimensions in order to simulate a broad range of ellipticities and to maximize the parameter space explored.
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.
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.
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.
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.
Mapping Elliptical Orbits Around Europa
NASA Astrophysics Data System (ADS)
Vilhena de Moraes, Rodolpho; Prado, Antonio; Carvalho, Jean Paulo; Cardoso dos Santos, Josué
Due to specifics scientific purposes space missions has been proposed to explore natural satellites, comets and asteroids sending artificial satellites orbiting around these bodies. The planning of such missions must be taken into account a good choice for the orbits that reduces the cost related to station-keeping and the increasing the duration of the mission. The present research has the objective of using a new concept to map with respect the station-keeping maneuvers to study elliptical orbits around Europa. This concept is based in the integral of the perturbing forces over the time. This value can estimate the total variation of velocity received by the spacecraft from the perturbations forces acting on it. The value of this integral is a characteristic of the perturbations considered and the orbit chosen for the spacecraft. Numerical simulations are made showing the value of this integral for orbits around Europa as a function of the eccentricity and semi-major axis of the orbits. An important application of the present research is in the search for frozen orbits.
Jacobian variety and integrable system — after Mumford, Beauville and Vanhaecke
NASA Astrophysics Data System (ADS)
Inoue, Rei; Konishi, Yukiko; Yamazaki, Takao
2007-02-01
Beauville [A. Beauville, Jacobiennes des courbes spectrales et systèmes hamiltoniens complètement intégrables, Acta. Math. 164 (1990) 211-235] introduced an integrable Hamiltonian system whose general level set is isomorphic to the complement of the theta divisor in the Jacobian of the spectral curve. This can be regarded as a generalization of the Mumford system [D. Mumford, Tata Lectures on Theta II, Birkhäuser, 1984]. In this article, we construct a variant of Beauville's system whose general level set is isomorphic to the complement of the intersection of the translations of the theta divisor in the Jacobian. A suitable subsystem of our system can be regarded as a generalization of the even Mumford system introduced by Vanhaecke [P. Vanhaecke, Linearising two-dimensional integrable systems and the construction of action-angle variables, Math. Z. 211 (1992) 265-313; P. Vanhaecke, Integrable systems in the realm of algebraic geometry, in: Lecture Notes in Mathematics, vol. 1638, 2001].
Extending the Belavin-Knizhnik "wonderful formula" by the characterization of the Jacobian
NASA Astrophysics Data System (ADS)
Matone, Marco
2012-10-01
A long-standing question in string theory is to find the explicit expression of the bosonic measure, a crucial issue also in determining the superstring measure. Such a measure was known up to genus three. Belavin and Knizhnik conjectured an expression for genus four which has been proved in the framework of the recently introduced vector-valued Teichmüller modular forms. It turns out that for g ≥ 4 the bosonic measure is expressed in terms of such forms. In particular, the genus four Belavin-Knizhnik "wonderful formula" has a remarkable extension to arbitrary genus whose structure is deeply related to the characterization of the Jacobian locus. Furthermore, it turns out that the bosonic string measure has an elegant geometrical interpretation as generating the quadrics in ℙ g-1 characterizing the Riemann surface. All this leads to identify forms on the Siegel upper half-space that, if certain conditions related to the characterization of the Jacobian are satisfied, express the bosonic measure as a multiresidue in the Siegel upper half-space. We also suggest that it may exist a super analog on the super Siegel half-space.
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.
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.
STELLAR POPULATIONS OF ELLIPTICAL GALAXIES IN THE LOCAL UNIVERSE
Zhu Guangtun; Blanton, Michael R.; Moustakas, John E-mail: michael.blanton@nyu.ed
2010-10-10
We study the stellar populations of 1923 elliptical galaxies at z < 0.05 selected from the Sloan Digital Sky Survey as a function of velocity dispersion, {sigma}, and environment. Our sample constitutes among the largest high-fidelity samples of elliptical galaxies with uniform imaging and optical spectroscopy assembled to date. Confirming previous studies, we find that elliptical galaxies dominate at high luminosities ({approx}>L*), and that the highest-{sigma} ellipticals favor high-density environments. We construct average, high signal-to-noise spectra in bins of {sigma} and environment and find the following: (1) lower-{sigma} galaxies have a bluer optical continuum and stronger (but still weak) emission lines; (2) at fixed {sigma}, field ellipticals have a slightly bluer stellar continuum, especially at wavelengths {approx}<4000 A, and have stronger (but still weak) emission lines compared with their group counterparts, although this environmental dependence is strongest for low-{sigma} ellipticals and the highest-{sigma} ellipticals are much less affected. Based on Lick indices measured from both the individual and average spectra, we find that (1) at a given {sigma}, elliptical galaxies in groups have systematically weaker Balmer absorption than their field counterparts, although this environmental dependence is most pronounced at low {sigma}; (2) there is no clear environmental dependence of (Fe), while the {alpha}-element absorption indices such as Mg b are only slightly stronger in galaxies belonging to rich groups. An analysis based on simple stellar populations (SSPs) reveals that more massive elliptical galaxies are older, more metal-rich, and more strongly {alpha}-enhanced. We also find that (1) the SSP-equivalent ages of galaxies in rich groups are, on average, {approx}1 Gyr older than in the field, although once again this effect is strongest at low {sigma}; (2) galaxies in rich groups have slightly lower [Fe/H] and are marginally more strongly
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.
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
NASA Astrophysics Data System (ADS)
Lin, J.; Lin, C. C.; Lo, H.-S.
2009-10-01
Interest in complex robotic systems is growing in new application areas. An example of such a robotic system is a dexterous manipulator mounted on an oscillatory base. In literature, such systems are known as macro/micro systems. This work proposes pseudo-inverse Jacobian feedback control laws and applies grey relational analysis for tuning outer-loop PID control parameters of Cartesian computed-torque control law for robotic manipulators mounted on oscillatory bases. The priority when modifying controller parameters should be the top ranking importance among parameters. Grey relational grade is utilized to investigate the sensitivity of tuning the auxiliary signal PID of the Cartesian computed-torque law to achieve desired performance. Results of this study can be feasible to numerous mechanical systems, such as mobile robots, gantry cranes, underwater robots, and other dynamic systems mounted on oscillatory bases, for moving the end-effector to a desired Cartesian position.
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.
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.
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.
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.
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…
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.
The ESS elliptical cavity cryomodules
NASA Astrophysics Data System (ADS)
Darve, Christine; Bosland, Pierre; Devanz, Guillaume; Olivier, Gilles; Renard, Bertrand; Thermeau, Jean-Pierre
2014-01-01
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.
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.
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.
System Size, Energy, Pseudorapidity, and Centrality Dependence of Elliptic Flow
NASA Astrophysics Data System (ADS)
Alver, B.; Back, B. B.; Baker, M. D.; Ballintijn, M.; Barton, D. S.; Betts, R. R.; Bickley, A. A.; Bindel, R.; Busza, W.; Carroll, A.; Chai, Z.; Chetluru, V.; Decowski, M. P.; García, E.; Gburek, T.; George, N.; Gulbrandsen, K.; Halliwell, C.; Hamblen, J.; Harnarine, I.; Hauer, M.; Henderson, C.; Hofman, D. J.; Hollis, R. S.; Hołyński, R.; Holzman, B.; Iordanova, A.; Johnson, E.; Kane, J. L.; Khan, N.; Kulinich, P.; Kuo, C. M.; Li, W.; Lin, W. T.; Loizides, C.; Manly, S.; Mignerey, A. C.; Nouicer, R.; Olszewski, A.; Pak, R.; Reed, C.; Richardson, E.; Roland, C.; Roland, G.; Sagerer, J.; Seals, H.; Sedykh, I.; Smith, C. E.; Stankiewicz, M. A.; Steinberg, P.; Stephans, G. S. F.; Sukhanov, A.; Szostak, A.; Tonjes, M. B.; Trzupek, A.; Vale, C.; van Nieuwenhuizen, G. J.; Vaurynovich, S. S.; Verdier, R.; Veres, G. I.; Walters, P.; Wenger, E.; Willhelm, D.; Wolfs, F. L. H.; Wosiek, B.; Woźniak, K.; Wyngaardt, S.; Wysłouch, B.
2007-06-01
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.
Elliptic surface grid generation on minimal and parametrized surfaces
NASA Technical Reports Server (NTRS)
Spekreijse, S. P.; Nijhuis, G. H.; Boerstoel, J. W.
1995-01-01
An elliptic grid generation method, which generates boundary conforming grids in a two dimensional physical space, is presented. The method is based on the composition of an algebraic and elliptic transformation. The composite mapping obeys the Poisson grid generation system with control functions specified by the algebraic transformation. It is shown that the grid generation on a minimal surface in a three dimensional space is equivalent to the grid generation in a two dimensional domain in physical space. A second elliptic grid generation method, which generates boundary conforming grids on smooth surfaces, is presented. Concerning surface modeling, it is shown that bicubic Hermit interpolation is an excellent method to generate a smooth surface crossing a discrete set of control points.
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.
Instability of low viscosity elliptic jets with varying aspect ratio
NASA Astrophysics Data System (ADS)
Kulkarni, Varun
2011-11-01
In this work an analytical description of capillary instability of liquid elliptic jets with varying aspect ratio is presented. Linear stability analysis in the long wave approximation with negligible gravitational effects is employed. Elliptic cylindrical coordinate system is used and perturbation velocity potential substituted in the Laplace equation to yield Mathieu and Modified Mathieu differential equations. The dispersion relation for elliptical orifices of any aspect ratio is derived and validated for axisymmetric disturbances with m = 0, in the limit of aspect ratio, μ = 1 , i.e. the case of a circular jet. As Mathieu functions and Modified Mathieu function solutions converge to Bessel's functions in this limit the Rayleigh-Plateau instability criterion is met. Also, stability of solutions corresponding to asymmetric disturbances for the kink mode, m = 1 and flute modes corresponding to m >= 2 is discussed. Experimental data from earlier works is used to compare observations made for elliptical orifices with μ ≠ 1 . This novel approach aims at generalizing the results pertaining to cylindrical jets with circular cross section leading to better understanding of breakup in liquid jets of various geometries.
Phenomenological study of irregular cellular automata based on Lyapunov exponents and Jacobians.
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. PMID:20887052
Qin, Jin; Trudeau, Matthieu; Buchholz, Bryan; Katz, Jeffrey N; Xu, Xu; Dennerlein, Jack T
2014-04-01
Upper extremity kinematics during keyboard use is associated with musculoskeletal health among computer users; however, specific kinematics patterns are unclear. This study aimed to determine the dynamic roles of the shoulder, elbow, wrist and metacarpophalangeal (MCP) joints during a number entry task. Six subjects typed in phone numbers using their right index finger on a stand-alone numeric keypad. The contribution of each joint of the upper extremity to the fingertip movement during the task was calculated from the joint angle trajectory and the Jacobian matrix of a nine-degree-of-freedom kinematic representation of the finger, hand, forearm and upper arm. The results indicated that in the vertical direction where the greatest fingertip movement occurred, the MCP, wrist, elbow (including forearm) and shoulder joint contributed 10.2%, 55.6%, 27.7% and 6.5%, respectively, to the downward motion of the index finger averaged across subjects. The results demonstrated that the wrist and elbow contribute the most to the fingertip vertical movement, indicating that they play a major role in the keying motion and have a dynamic load beyond maintaining posture. PMID:24144858
NASA Astrophysics Data System (ADS)
Jazi, B.; Rahmani, Z.; Heidari-Semiromi, E.; Abdoli-Arani, A.
2012-10-01
The dispersion relation of guided electromagnetic waves propagating in an elliptical metallic waveguide with a dielectric rod driven by relativistic elliptical electron beam (REEB) is investigated. The electric field profiles and the growth rates of the waves are numerically calculated by using Mathieu functions. The effects of relative permittivity constant of dielectric rod, accelerating voltage, and current density of REEB on the growth rate are presented.
Jazi, B.; Rahmani, Z.; Abdoli-Arani, A.; Heidari-Semiromi, E.
2012-10-15
The dispersion relation of guided electromagnetic waves propagating in an elliptical metallic waveguide with a dielectric rod driven by relativistic elliptical electron beam (REEB) is investigated. The electric field profiles and the growth rates of the waves are numerically calculated by using Mathieu functions. The effects of relative permittivity constant of dielectric rod, accelerating voltage, and current density of REEB on the growth rate are presented.
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.
Fast algorithms for computing isogenies between elliptic curves
NASA Astrophysics Data System (ADS)
Bostan, A.; Morain, F.; Salvy, B.; Schost, E.
2008-09-01
We survey algorithms for computing isogenies between elliptic curves defined over a field of characteristic either 0 or a large prime. We introduce a new algorithm that computes an isogeny of degree ell ( ell different from the characteristic) in time quasi-linear with respect to ell E This is based in particular on fast algorithms for power series expansion of the Weierstrass wp -function and related functions.
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.
Horizon complementarity in elliptic de Sitter space
NASA Astrophysics Data System (ADS)
Hackl, Lucas; Neiman, Yasha
2015-02-01
We study a quantum field in elliptic de Sitter space dS4/Z2—the spacetime obtained from identifying antipodal points in dS4. We find that the operator algebra and Hilbert space cannot be defined for the entire space, but only for observable causal patches. This makes the system into an explicit realization of the horizon complementarity principle. In the absence of a global quantum theory, we propose a recipe for translating operators and states between observers. This translation involves information loss, in accordance with the fact that two observers see different patches of the spacetime. As a check, we recover the thermal state at the de Sitter temperature as a state that appears the same to all observers. This thermal state arises from the same functional that, in ordinary dS4, describes the Bunch-Davies vacuum.
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.
Analytical solutions of cracks emanating from an elliptic hole in an infinite plate under tension
NASA Astrophysics Data System (ADS)
Liu, Shuhong; Duan, Shijie
2014-09-01
It is a common phenomenon that the cracks originating from a hole can cause structural damage in engineering. However, the fracture mechanics studies of hole edge crack problems are not sufficient. The problem of an elliptical hole with two collinear edge cracks of unequal length in an infinite plate under uniform tension at infinity is investigated. Based on the complex variable method, the analytical solutions of stress functions and stress intensity factors are provided. The stress distribution along the axes and the edge of the elliptical hole is given graphically. The numerical results show that there is obvious stress concentration near the hole and cracks, and the stresses tend to applied loads at distances far from the defect, which conform to Saint-Venant's principle. Hence, the stress functions are proved to be right. Under special conditions, the present configuration becomes the Griffith crack, two symmetrical cracks emanating from an elliptical hole, two cracks of unequal length emanating from a circular hole, a crack at the edge of a circular hole, or a crack emanating from an elliptical hole. Compared with available results, stress intensity factors for these special shapes of ellipses and cracks show good coincidence. The stress intensity factor for two cracks of unequal length at the edge of an elliptical hole increases with the crack length and the major-to-minor axis ratio of the elliptical hole. The stress distribution in an infinite plate containing an elliptic hole with unsymmetrical cracks is given for the first time.
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.
Advanced Light Source elliptical wiggler
Hoyer, E.; Akre, J.; Humphries, D.; Marks, S.; Minamihara, Y.; Pipersky, P.
1994-07-01
A 3.5m long elliptical wiggler, optimized to produce elliptically polarized light in the 50 eV to 10 keV range, is currently under design and construction at the Advanced Light Source (ALS) at Lawrence Berkeley Laboratory. Calculations of spectral performance show that the flux of circularly polarized photons exceeds 10{sup 13} photons/sec over the 50 eV to 10 keV operating range for current of 0.4 amps and 1.5 GeV electron energy. This device features vertical and horizontal magnetic structures of 14 and 14{1/2} periods respectively. The period length is 20.0 cm. The vertical structure is a hybrid permanent magnet design with tapered pole tips that produce a peak field of 2.0 T. The horizontal structure is an iron core electromagnetic design, shifted longitudinally {1/4} period, that is tucked between the upper and lower vertical magnetic structure sections. A maximum peak oscillating field of 0.095 T at a frequency up to 1 Hz will be achieved by excitation of the horizontal poles with a trapezoidal current waveform. The vacuum chamber is an unconventional design that is removable from the magnetic structure, after magnetic measurements, for UHV processing. The chamber is fabricated from non-magnetic stainless steel to minimize the effects of eddy currents. Device design is presented.
Shaping the beam profile of an elliptical Gaussian beam by an elliptical phase aperture
NASA Astrophysics Data System (ADS)
Wen, Wei; Wu, Gaofeng; Song, Kehui; Dong, Yiming
2013-03-01
Based on the generalized Collins integral formula, an analytical paraxial propagation formula for an elliptical Gaussian beam (EGB) passing through an astigmatic ABCD optical system with an elliptical phase aperture is derived by use of a tensor method. As an application example, we study the propagation properties of an EGB passing through an elliptical aperture in free space. It is found that the elliptical phase aperture can be used for shaping the beam profile of an EGB, which is useful in many applications, such as free space optical communication and material thermal processing. The elliptical phase aperture induced changes of the propagation factors of an EGB are also analyzed.
Centrality dependence of multiplicity, transverse energy, and elliptic flow from hydrodynamics
Kolb, Peter F.; Heinz, Ulrich; Huovinen, Pasi; Eskola, Kari J.; Tuominen, Kimmo
2001-03-21
The centrality dependence of the charged multiplicity, transverse energy, and elliptic flow coefficient is studied in a hydrodynamic model, using a variety of different initializations which model the initial energy or entropy production process as a hard or soft process, respectively. While the charged multiplicity depends strongly on the chosen initialization, the p{sub T}-integrated elliptic flow for charged particles as a function of charged particle multiplicity and the p{sub T}-differential elliptic flow for charged particles in minimum bias events turn out to be almost independent of the initialization.
ELLIPTIC FLOW FROM COLOR GLASS CONDENSATE.
KRASNITZ,A.; NARA,Y.; VENUGOPALAN,R.
2002-07-18
We show that an observable fraction of the measured elliptic flow may originate in classical gluon fields at the initial stage of a peripheral high-energy nuclear collision. This mechanism complements the contribution of late stage mechanisms, such as those described by hydrodynamics, to the observed elliptic flow.
Elliptic solitons in optical fiber media
NASA Astrophysics Data System (ADS)
Fandio Jubgang, Défi, Jr.; Dikandé, Alain M.; Sunda-Meya, A.
2015-11-01
We examine the evolution of a time-varying perturbation signal pumped into a monomode fiber in the anomalous dispersion regime. We establish analytically that the perturbation evolves into a conservative pattern of periodic pulses whose structures and profiles share a close similarity with the so-called soliton-crystal states recently observed in fiber media [see, e.g., A. Haboucha et al., Phys. Rev. A 78, 043806 (2008), 10.1103/PhysRevA.78.043806; D. Y. Tang et al., Phys. Rev. Lett. 101, 153904 (2008), 10.1103/PhysRevLett.101.153904; F. Amrani et al., Opt. Express 19, 13134 (2011), 10.1364/OE.19.013134]. We derive mathematically and generate numerically a crystal of solitons using time-division multiplexing of identical pulses. We suggest that at very fast pumping rates, the pulse signals overlap and create an unstable signal that is modulated by the fiber nonlinearity to become a periodic lattice of pulse solitons that can be described by elliptic functions. We carry out a linear stability analysis of the soliton-crystal structure and establish that the correlation of centers of mass of interacting pulses broadens their internal-mode spectrum, some modes of which are mutually degenerate. While it has long been known that high-intensity periodic pulse trains in optical fibers are generated from the phenomenon of modulational instability of continuous waves, the present study provides evidence that they can also be generated via temporal multiplexing of an infinitely large number of equal-intensity single pulses to give rise to stable elliptic solitons.
Structure and Formation of Elliptical and Spheroidal Galaxies
NASA Astrophysics Data System (ADS)
Kormendy, John; Fisher, David B.; Cornell, Mark E.; Bender, Ralf
2009-05-01
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 Sérsic log I vprop r 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 MVT <= -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 <= MVT <= -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 Sérsic 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 Sérsic-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 Sérsic indices n > 4 uncorrelated
Euler characteristics and elliptic curves.
Coates, J; Howson, S
1997-10-14
Let E be a modular elliptic curve over [symbol, see text], without complex multiplication; let p be a prime number where E has good ordinary reduction; and let Finfinity be the field obtained by adjoining [symbol, see text] to all p-power division points on E. Write Ginfinity for the Galois group of Finfinity over [symbol, see text]. Assume that the complex L-series of E over [symbol, see text] does not vanish at s = 1. If p >/= 5, we make a precise conjecture about the value of the Ginfinity-Euler characteristic of the Selmer group of E over Finfinity. If one makes a standard conjecture about the behavior of this Selmer group as a module over the Iwasawa algebra, we are able to prove our conjecture. The crucial local calculations in the proof depend on recent joint work of the first author with R. Greenberg. PMID:11607752
The elliptical multipole wiggler project
Gluskin, E.; Frachon, D.; Ivanov, P.M.
1995-06-01
The elliptical multipole wiggler (EMW) has been designed, constructed, and installed in the X13 straight section of the NSLS X-ray Ring. The EMW generates circularly polarized photons in the energy range of 0.1-10 keV with AC modulation of polarization helicity. The vertical magnetic field of 0.8 T is produced by a hybrid permanent magnet structure with a period of 16 cm. The horizontal magnetic field of 0.22 T is generated by an electromagnet, the core of which is fabricated from laminated iron to operate with a switching frequency up to 100 Hz. There are dynamic compensation trim magnets at the wiggler ends to control the first and second field integrals with very high accuracy throughout the AC cycle. The residual closed orbit motion due to the electromagnet AC operation is discussed.
The augmented Lagrangian method for parameter estimation in elliptic systems
NASA Technical Reports Server (NTRS)
Ito, Kazufumi; Kunisch, Karl
1990-01-01
In this paper a new technique for the estimation of parameters in elliptic partial differential equations is developed. It is a hybrid method combining the output-least-squares and the equation error method. The new method is realized by an augmented Lagrangian formulation, and convergence as well as rate of convergence proofs are provided. Technically the critical step is the verification of a coercivity estimate of an appropriately defined Lagrangian functional. To obtain this coercivity estimate a seminorm regularization technique is used.
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.
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.
Establishing the Metallicity Distribution in Normal Giant Ellipticals
NASA Astrophysics Data System (ADS)
Harris, William
2003-07-01
NGC 3377 and 3379, the Leo Group ellipticals at d=11 Mpc, are the nearest E galaxies commonly regarded to be structually"normal", and as such, they are keystone objects for understanding the evolution and early star formation history of large ellipticals. The ACS/WFC camera now gives us the ability to obtain the metallicity distribution function {MDF} of their stellar population by direct resolution and photometry of their halo stars. To do this, we will follow the same highly successful techniques we have previously used for NGC 5128 with WFPC2 {V, I} imaging: the {V-I} colors of the brightest red-giant stars are highly sensitive to metallicity, and their locations in the color-magnitude diagram can be used for direct construction of the MDF. This will be a major step forward to understanding the formation history of these cosmologically dominant galaxies.
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.
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.
A transmission line model for propagation in elliptical core optical fibers
NASA Astrophysics Data System (ADS)
Georgantzos, E.; Papageorgiou, C.; Boucouvalas, A. C.
2015-12-01
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.
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.
NASA Astrophysics Data System (ADS)
Snellings, Raimond
2011-05-01
One of the fundamental questions in the field of subatomic physics is the question of what happens to matter at extreme densities and temperatures as may have existed in the first microseconds after the Big Bang and exists, perhaps, in the core of dense neutron stars. The aim of heavy-ion physics is to collide nuclei at very high energies and thereby create such a state of matter in the laboratory. The experimental program began in the 1990s with collisions made available at the Brookhaven Alternating Gradient Synchrotron (AGS) and the CERN Super Proton Synchrotron (SPS), and continued at the Brookhaven Relativistic Heavy-Ion Collider (RHIC) with the maximum center-of-mass energies of \\sqrt{s_{NN}} = 4.75 , 17.2 and 200 GeV, respectively. Collisions of heavy ions at the unprecedented energy of 2.76 TeV recently became available at the LHC collider at CERN. In this review, I give a brief introduction to the physics of ultrarelativistic heavy-ion collisions and discuss the current status of elliptic flow measurements.
Age and metallicity gradients in fossil ellipticals
NASA Astrophysics Data System (ADS)
Eigenthaler, P.; Zeilinger, W. W.
2013-05-01
Context. Fossil galaxy groups are speculated to be old and highly evolved systems of galaxies that formed early in the universe and had enough time to deplete their L∗ galaxies through successive mergers of member galaxies, building up one massive central elliptical, but retaining the group X-ray halo. Aims: Considering that fossils are the remnants of mergers in ordinary groups, the merger history of the progenitor group is expected to be imprinted in the fossil central galaxy (FCG). We present for the first time radial gradients of single-stellar population (SSP) ages and metallicites in a sample of FCGs to constrain their formation scenario. We also measure line-strength gradients for the strongest absorption features in these galaxies. Methods: We took deep spectra with the long-slit spectrograph ISIS at the William Herschel Telescope (WHT) for six FCGs. The obtained spectra are fit with Pegase HR SSP models within the full-spectrum fitting package ULySS yielding SSP ages and metallicities of the stellar populations. We measure radial gradients of SSP ages and metallicities along the major axes. Lick indices are measured for the strongest absorption features to determine line-strength gradients and compare with the full-spectrum fitting results. Results: Our sample comprises some of the most massive galaxies in the universe exhibiting an average central velocity dispersion of σ0 = 271 ± 28 km s-1. Metallicity gradients are throughout negative with comparatively flat slopes of ∇[Fe/H] = -0.19 ± 0.08 while age gradients are found to be insignificant (∇age = 0.00 ± 0.05). All FCGs lie on the fundamental plane, suggesting that they are virialised systems. We find that gradient strengths and central metallicities are similar to those found in cluster ellipticals of similar mass. Conclusions: The comparatively flat metallicity gradients with respect to those predicted by monolithic collapse (∇Z = -0.5) suggest that fossils are indeed the result of
Anomaly cancelling terms from the elliptic genus
NASA Astrophysics Data System (ADS)
Lerche, W.; Nilsson, B. E. W.; Schellekens, A. N.; Warner, N. P.
1988-03-01
We calculate the heterotic string one-loop diagram in 2n + 2 dimensions with one external Bμν and n external gravitons and/or gauge bosons. The result is a modular integral over the weight zero terms of the character valued partition function (or elliptic genus) of the theory, and can be directly expressed in terms of the factor which multiplies TrF2 - TrR2 in the field theory anomaly. The integrands have a non-trivial dependence on the modular parameter τ, reflecting contributions not only from the physical massless states but also from an infinity of ``unphysical'' modes. Some of them are identical to integrands which have been discussed recently in relation with Atkin-Lehner symmetry and the cosmological constant. As a corollary we find a method to compute these integrals without using Atkin-Lehner transformations. On leave of absence from: Department of Mathematics, Massachusetts Institute of Technology, Cambridge MA 02139, USA. Work supported in part by National Science Foundation Grant #84-07109.
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.
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.
Instability of a supersonic shock free elliptic jet
Baty, R.S. ); Seiner, J.M.; Ponton, M.K. . Langley Research Center)
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. 18 refs., 18 figs., 1 tab.
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.
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, 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.
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.
The Stellar Population Histories of Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Trager, Scott Charles
1997-08-01
This dissertation sets out to probe the stellar population histories of local field and distant cluster elliptical galaxies. Absorption-line strengths of the centers of 381 early-type galaxies and 38 globular clusters measured from the Lick Image Dissector Scanner (Lick/IDS) are presented. Error estimation and corrections for velocity-dispersion broadening are described in detail. Monte Carlo simulations show that the Lick/IDS data are not accurate enough to infer ages and abundances of individual ellipticals with confidence. The excellent data of Gonzalez (1993) are therefore used to infer the stellar population ages and abundances of the centers of local field ellipticals. Elliptical galaxy nuclei follow three relations in this sample. (1) The t-Z relation. Elliptical nuclei have an age-abundance relation at fixed velocity dispersion σ that follows the Worthey (1994) '3/2 rule.' Ellipticals therefore have fixed color and metal-line strengths at fixed σ. (2) The σ-Z relation. The abundance zeropoint of the t-Z relation increases with increasing σ. Taken together, (1) and (2) predict scaling relations like the Mg2-σ and color-magnitude relations. (3) The σ- (Mg/Fe) relation. The abundance ratio (Mg/Fe) increases with increasing σ, as the σ-Z relation for Mg has twice the slope of the σ-Z relation for Fe. Relations (1)-(3) can be expressed as a pair of planes in t-Z-σ space, one for Fe and one for Mg, with similar age dependences but different σ-dependences. Scenarios for the possible origins of these relations are presented. Absorption-line strengths of eighteen early-type galaxies in two rich clusters at z = 0.41 (CL0939 + 4713) and z = 0.76 (CL1322 + 3027) have been measured from Keck LRIS spectra. The Balmer-line strengths of ellipticals at z = 0.41 are consistent with passive evolution of local field ellipticals but seem too metal-rich. Both Balmer- and metal-line strengths of ellipticals at z = 0.76 are consistent with passive evolution of local
Intrinsic shapes of elliptical galaxy: NGC 1052 using modified prior
NASA Astrophysics Data System (ADS)
Kumar Singh, Arun; Chakraborty, D. K.
Determination of intrinsic shapes of the individual elliptical galaxies using photometry is an important problem because the number of galaxies with good photometry is many more than those with good kinematics. We determine the intrinsic shapes of the light distribution of elliptical galaxies by combining the profiles of photometric data from the literature with triaxial models. We use ensembles of models so that the shape estimates are largely model independent. We follow the methodology as described in Statler (1994) which is modified to suit our requirements. We find that short to long axial ratios at very small radii and at very large radii, and the absolute value of the triaxiality difference are the best constrained shape parameters. Using a flat prior, the shapes of elliptical galaxies are reported by Chakraborty et al (2008) and Singh & Chakraborty (2009). The flat prior of 20 galaxies are superimposed over EAC-Ph other to obtain the distribution. This distribution is regarded as a prior (a modified prior) and shapes of 20 galaxies are again recalculated by using such modified prior. We determine the intrinsic shapes of the elliptical galaxy NGC 1052 using modified prior should be more reliable. These results are compared with the previous estimates which are determined by using flat prior. The plot shows the intrinsic shapes of the NGC 1052 as a function of (q0,q∞) for two dimensional shapes and (q0,q∞, |Td|) for three dimensional shapes, where q0 and q∞(=q) are the short to long axial ratios at small and at large radii and |Td| is the absolute values of the triaxiality difference, defined as |Td|= |T∞ - T0|. The probability is shown in the dark gray region: darker is the region higher is the probability. We find that the galaxy NGC 1052 is flatter inside and flatter outside.
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
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.
Elastodynamics and resonances in elliptical geometry
NASA Astrophysics Data System (ADS)
Ancey, S.; Bazzali, E.; Gabrielli, P.; Mercier, M.
2013-11-01
The resonant modes of two-dimensional elastic elliptical objects are studied from a modal formalism by emphasizing the role of the symmetries of the objects. More precisely, as the symmetry is broken in the transition from the circular disc to the elliptical one, the splitting up of resonances and level crossings are observed. From the mathematical point of view, this observation can be explained by the broken invariance of the continuous symmetry group { {O}(2)} associated with the circular disc. The elliptical disc is however invariant under the finite group { {C}}_{2v} and the resonances are classified and associated with a given irreducible representation of this group. The main difficulty arises in the application of the group theory in elastodynamics where the vectorial formalism is used to express the physical quantities (elastic displacement and stress) involved in the boundary conditions. However, this method significantly simplifies the numerical treatment of the problem which is uncoupled over the four irreducible representations of { {C} }_{2v}. This provides a full classification of the resonances. They are tagged and tracked as the eccentricity of the elliptical disc increases. Then, the splitting up of resonances, which occurs in the transition from the circular disc to the elliptic one, is emphasized. The computation of displacement normal modes also highlights the mode splittings. A physical interpretation of resonances in terms of geometrical paths is provided.
NASA Astrophysics Data System (ADS)
Büsing, Henrik
2013-04-01
Two-phase flow in porous media occurs in various settings, such as the sequestration of CO2 in the subsurface, radioactive waste management, the flow of oil or gas in hydrocarbon reservoirs, or groundwater remediation. To model the sequestration of CO2, we consider a fully coupled formulation of the system of nonlinear, partial differential equations. For the solution of this system, we employ the Box method after Huber & Helmig (2000) for the space discretization and the fully implicit Euler method for the time discretization. After linearization with Newton's method, it remains to solve a linear system in every Newton step. We compare different iterative methods (BiCGStab, GMRES, AGMG, c.f., [Notay (2012)]) combined with different preconditioners (ILU0, ASM, Jacobi, and AMG as preconditioner) for the solution of these systems. The required Jacobians can be obtained elegantly with automatic differentiation (AD) [Griewank & Walther (2008)], a source code transformation providing exact derivatives. We compare the performance of the different iterative methods with their respective preconditioners for these linear systems. Furthermore, we analyze linear systems obtained by approximating the Jacobian with finite differences in terms of Newton steps per time step, steps of the iterative solvers and the overall solution time. Finally, we study the influence of heterogeneities in permeability and porosity on the performance of the iterative solvers and their robustness in this respect. References [Griewank & Walther(2008)] Griewank, A. & Walther, A., 2008. Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, SIAM, Philadelphia, PA, 2nd edn. [Huber & Helmig(2000)] Huber, R. & Helmig, R., 2000. Node-centered finite volume discretizations for the numerical simulation of multiphase flow in heterogeneous porous media, Computational Geosciences, 4, 141-164. [Notay(2012)] Notay, Y., 2012. Aggregation-based algebraic multigrid for convection
BINARY COMPACT OBJECT COALESCENCE RATES: THE ROLE OF ELLIPTICAL GALAXIES
O'Shaughnessy, R.; Kalogera, V.; Belczynski, Krzysztof E-mail: vicky@northwestern.ed
2010-06-10
In this paper, we estimate binary compact object merger detection rates for LIGO, including the potentially significant contribution from binaries that are produced in elliptical galaxies near the epoch of peak star formation. Specifically, we convolve hundreds of model realizations of elliptical- and spiral-galaxy population syntheses with a model for elliptical- and spiral-galaxy star formation history as a function of redshift. Our results favor local merger rate densities of 4 x 10{sup -3} Mpc{sup -3} Myr{sup -1} for binary black holes (BHs), 3 x 10{sup -2} Mpc{sup -3} Myr{sup -1} for binary neutron stars (NSs), and 10{sup -2} Mpc{sup -3} Myr{sup -1} for BH-NS binaries. We find that mergers in elliptical galaxies are a significant fraction of our total estimate for BH-BH and BH-NS detection rates; NS-NS detection rates are likely dominated by the contribution from spiral galaxies. Limiting attention to elliptical-galaxy plus only those spiral-galaxy models that reproduce current observations of Galactic NS-NS, we find slightly higher rates for NS-NS and largely similar ranges for BH-NS and BH-BH binaries. Assuming a detection signal-to-noise ratio threshold of 8 for a single detector (in practice as part of a network, to reduce its noise), corresponding to radii D {sub bns} of the effective volume inside of which a single LIGO detector could observe the inspiral of two 1.4 M {sub sun} NSs of 14 Mpc and 197 Mpc, for initial and advanced LIGO, we find event rates of any merger type of 2.9 x 10{sup -2}-0.46 and 25-400 yr{sup -1} (at 90% confidence level), respectively. We also find that the probability P {sub detect} of detecting one or more mergers with this single detector can be approximated by (1) P {sub detect} {approx_equal} 0.4 + 0.5 log(T/0.01 yr), assuming D {sub bns} = 197 Mpc and it operates for T yr, for T between 2 days and 0.1 yr, or by (2) P {sub detect} {approx_equal} 0.5 + 1.5 log(D {sub bns}/32 Mpc), for 1 yr of operation and for D {sub bns
Far-infrared emission from dusty ellipticals
NASA Technical Reports Server (NTRS)
Walsh, Duncan; Knapp, Jill
1990-01-01
The incidence of dust lanes in elliptical galaxies has been estimated at approx. 40 percent by Sadler and Gerhard (1985), although the observed fraction is lower because of inclination effects. A similar percentage of ellipticals has been detected by the Infrared Astronomy Satellite (IRAS) at 100 microns (Knapp et al. 1989); these have far-infrared colors expected for emission from cool dust (S sub 60 micron/S sub 100 micron approx. 1/3). For the far-infrared detected galaxies, neither L sub 100 microns/L sub B nor L sub 60 microns/L sub 100 microns are very dependent on dust content, suggesting that the source of the infrared luminosity is the same in both cases; and hence that dust is responsible even when not detected optically. Despite this indication, L sub 100 microns does not prove to be a good indicator of the quantity of cool interstellar matter in elliptical galaxies, as measured by the mass of neutral hydrogen. There even exist several examples of ellipticals with dust, strong 100 micron flux density and sensitive limits on HI mass (Walsh et al. in preparation). Chief reasons for the lack of correlation include the existence of other important sources of far-IR power in ellipticals, such as nonthermal continuum emission extending from longer wavelengths in flat spectrum radio sources (Golombek, Miley and Neugebauer 1988); and the fact that far-infrared luminosity per unit dust mass is extremely sensitive to the temperature of the ambient radiation field, which is not accurately known. In addition to having their appearance distorted by dust, several ellipticals also show such features as shells, box-shaped isophotes or inner disks. These may be signatures of past mergers, which could also add to the ISM content of the system.
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
Elliptically polarized bursty radio emissions from Jupiter
NASA Technical Reports Server (NTRS)
Reiner, M. J.; Desch, M. D.; Kaiser, M. L.; Manning, R.; Fainberg, J.; Stone, R. G.
1995-01-01
We report a new component of Jovian radio emission observed by the Ulysses spacecraft when Ulysses was at high Jovigraphic latitudes (greater than or approximately = 30 deg north or south of the Jovian magnetic equator). This bursty high-latitude emission is elliptically polarized in the right-hand sense when observed from northern latitudes and in the left-hand sense when observed from southern latitudes, consistent with extraordinary mode. The orientation of the polarization ellipse is observed to systematically vary with time relative to the observer. It is argued that the elliptically-polarized nature of the emission is intrinsic to the source region.
Three-dimensional instability of elliptical flow
NASA Astrophysics Data System (ADS)
Bayly, B. J.
1986-10-01
A clarification of the physical and mathematical nature of Pierrhumbert's (1986) three-dimensional short-wave inviscid instability of simple two-dimensional elliptical flow is presented. The instabilities found are independent of length scale, extending Pierrhumbert's conclusion that the structures of the instabilities are independent of length scale in the limit of large wave number. The fundamental modes are exact solutions of the nonlinear equations, and they are plane waves whose wave vector rotates elliptically around the z axis with a period of 2(pi)/Omega. The growth rates are shown to be the exponents of a matrix Floquet problem, and good agreement is found with previous results.
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.
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.
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.
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
The motion of elliptic cylinder under free surface
NASA Astrophysics Data System (ADS)
Kostikov, V. K.; Makarenko, N. I.
2016-06-01
A problem on generation of unsteady nonlinear waves on the surface of an infinitely deep ideal fluid due to the motion of a submerged elliptical cylinder is considered. It is supposed that the cylinder can rotate in addition to translational two-dimensional motion. The initial formulation of the problem is reduced to an integrodifferential system of equations for the functions defining the free surface shape, the normal and tangential components of velocity on the free boundary. The small-time asymptotics of the solution is constructed in the case of the cylinder that moves with a constant acceleration from rest.
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.
Buckling of elliptical rings under uniform external pressure
Tang, Y.
1991-04-03
A thin, elastic elliptical ring is subjected to uniform external pressure. The lowest critical pressure is computed and presented for various ratio of the major axis to the minor axis of the elliptical ring. It is found that the critical pressure for an elliptical ring is higher than that for the circular ring whose diameter is equal to the major axis of the elliptical ring. It can be shown that under the same external pressure, the axial force developed in the elliptical ring is less than that developed in the corresponding circular ring. Thus, a higher pressure is required to buckle the elliptical rings. Therefore, by changing the shape of the ring from circular to elliptical, the capability of the ring to sustain the external pressure can be increased substantially. The results of this study can be useful in the design of elliptical reinforcing rings and thin-walled tubes subjected to external pressure.
Xia, Kelin; Zhan, Meng; Wan, Decheng; Wei, Guo-Wei
2012-02-01
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 L(2) 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
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
Elliptic genera from multi-centers
NASA Astrophysics Data System (ADS)
Gaddam, Nava
2016-05-01
I show how elliptic genera for various Calabi-Yau threefolds may be understood from supergravity localization using the quantization of the phase space of certain multi-center configurations. I present a simple procedure that allows for the enumeration of all multi-center configurations contributing to the polar sector of the elliptic genera — explicitly verifying this in the cases of the quintic in {P} 4, the sextic in {W}{P} (2,1,1,1,1), the octic in {W}{P} (4,1,1,1,1) and the dectic in {W}{P} (5,2,1,1,1). With an input of the corresponding `single-center' indices (Donaldson-Thomas invariants), the polar terms have been known to determine the elliptic genera completely. I argue that this multi-center approach to the low-lying spectrum of the elliptic genera is a stepping stone towards an understanding of the exact microscopic states that contribute to supersymmetric single center black hole entropy in {N} = 2 supergravity.
Body tides on an elliptical rotating earth
NASA Technical Reports Server (NTRS)
Wahr, J. M.
1978-01-01
The complete tidal response of an elliptical, rotating, elastic Earth is found to contain small displacements which do not fit into the conventional Love number framework. Corresponding observable tidal quantities (gravity, tilt, strain, Eulerian potential, etc.) are modified by the addition of small latitude dependent terms.
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.
Transverse Mercator Projection Via Elliptic Integrals
NASA Technical Reports Server (NTRS)
Wallis, David E.
1992-01-01
Improved method of construction of U.S. Army's universal transverse Mercator grid system based on Gauss-Kruger transverse Mercator projection and on use of elliptic integrals of second kind. Method can be used to map entire northern or southern hemisphere with respect to single principal meridian.
On the rotation of elliptical galaxies
NASA Technical Reports Server (NTRS)
Binney, J.
1978-01-01
The tensor virial theorem is applied to models of early-type galaxies. First the theorem is applied to rotating elliptical galaxies whose constant-density surfaces are similar ellipsoids. A relationship is obtained between the observed rotations and the forms of generally triaxial galaxies. By applying the results of Robert (1962) to the evaluation of the components of the Chandrasekhar tensor which occurs in this relationship, it is found that the form of a galaxy that lacks global velocity anisotropy uniquely determines the ratio of its rotational and random kinetic energies independently of the radial density profile of that galaxy. A distribution of three-dimensional prolate spheroids is derived which accounts for the observed distribution of ellipticities reported by Sandage, Freeman, and Stokes (1970). This is then used to derive curves giving the expected frequency of occurrence of galaxies of given rotational velocities for each of a number of different apparent elongations on the sky. It is found that if elliptical galaxies are prolate, there should be little correlation between apparent ellipticity and rotation velocity.
Elliptic Flow, Initial Eccentricity and Elliptic Flow Fluctuations in Heavy Ion Collisions at RHIC
NASA Astrophysics Data System (ADS)
Nouicer, Rachid; Alver, B.; Back, B. B.; Baker, M. D.; Ballintijn, M.; Barton, D. S.; Betts, R. R.; Bickley, A. A.; Bindel, R.; Busza, W.; Carroll, A.; Chai, Z.; Decowski, M. P.; García, E.; Gburek, T.; George, N.; Gulbrandsen, K.; Halliwell, C.; Hamblen, J.; Hauer, M.; Henderson, C.; Hofman, D. J.; Hollis, R. S.; Holzman, B.; Iordanova, A.; Kane, J. L.; Khan, N.; Kulinich, P.; Kuo, C. M.; Li, W.; Lin, W. T.; Loizides, C.; Manly, S.; Mignerey, A. C.; Nouicer, R.; Olszewski, A.; Pak, R.; Reed, C.; Roland, C.; Roland, G.; Sagerer, J.; Seals, H.; Sedykh, I.; Smith, C. E.; Stankiewicz, M. A.; Steinberg, P.; Stephans, G. S. F.; Sukhanov, A.; Tonjes, M. B.; Trzupek, A.; Vale, C.; van Nieuwenhuizen, G. J.; Vaurynovich, S. S.; Verdier, R.; Veres, G. I.; Walters, P.; Wenger, E.; Wolfs, F. L. H.; Wosiek, B.; Woźniak, K.; Wysłouch, B.
2008-12-01
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.
Application of rectangular and elliptical dielcore feed horns to elliptical reflector antennas
NASA Astrophysics Data System (ADS)
Lier, Erik; Rahmat-Samii, Yahya; Rengarajan, Sembiam R.
1991-11-01
The pattern characteristics of elliptical reflector antennas are investigated when they are fed by rectangular and elliptical horns partially filled with a dielectric. The bandwidth characteristics of these dielcore horns are superior to those of their corrugated horn counterparts. Representative reflector patterns are computed to properly demonstrate the utility of these feeds for reflector antennas with elliptical apertures. This reflector antenna exhibits high efficiency and low cross polarization, and may be suitable for radar and satellite antenna applications. The antenna configuration may become useful in relatively small antennas where more than 10 percent cross-polar bandwidth is required. The efficient dielcore horns may also be used as feeds for elliptical nonshaped dual-reflector antennas.
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.
The Ellipticity Distribution of Ambiguously Blended Objects
NASA Astrophysics Data System (ADS)
Dawson, William A.; Schneider, Michael D.; Tyson, J. Anthony; Jee, M. James
2016-01-01
Using overlapping fields with space-based Hubble Space Telescope and ground-based Subaru Telescope imaging we identify a population of blended galaxies that are blended to such a large degree that they are detected as single objects in the ground-based monochromatic imaging, which we label “ambiguous blends.” For deep imaging data, such as the depth targeted with the Large Synoptic Survey Telescope (LSST), the ambiguous blend population is both large (∼14%) and has a distribution of ellipticities that is different from that of unblended objects in a way that will likely be important for weak lensing measurements. Most notably, for a limiting magnitude of i ∼ 27 we find that ambiguous blending results in a ∼14% increase in shear noise (or an ∼12% decrease in the effective projected number density of lensed galaxies; neff) due to (1) larger intrinsic ellipticity dispersion, and (2) a scaling with the galaxy number density Ngal that is shallower than 1/\\sqrt{{N}{gal}}. For the LSST Gold Sample (i < 25.3) there is a ∼7% increase in shear noise (or ∼7% decrease in neff). More importantly than these increases in the shear noise, we find that the ellipticity distribution of ambiguous blends has an rms that is 13% larger than that of non-blended galaxies. Given the need of future weak lensing surveys to constrain the ellipticity distribution of galaxies to better than a percent in order to mitigate cosmic shear multiplicative biases, if it is unaccounted for, the different ellipticity distribution of ambiguous blends could be a dominant systematic.
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
Elliptic Genus of Phases of N = 2 Theories
NASA Astrophysics Data System (ADS)
Libgober, Anatoly
2015-12-01
We discuss an algebro-geometric description of Witten's phases of N = 2 theories and propose a definition of their elliptic genus provided some conditions on singularities of the phases are met. For Landau-Ginzburg phase one recovers elliptic genus of LG models proposed in physics literature in early 1990s. For certain transitions between phases we derive invariance of elliptic genus from an equivariant form of McKay correspondence for elliptic genus. As special cases one obtains Landau-Giznburg/Calabi-Yau correspondence for elliptic genus of weighted homogeneous potentials as well as certain hybrid/CY correspondences.
Multilevel elliptic smoothing of large three-dimensional grids
NASA Technical Reports Server (NTRS)
Mastin, C. Wayne
1995-01-01
Elliptic grid generation methods have been used for many years to smooth and improve grids generated by algebraic interpolation schemes. However, the elliptic system that must be solved is nonlinear and convergence is generally very slow for large grids. In an attempt to make elliptic methods practical for large three-dimensional grids, a two-stage implementation is developed where the overall grid point locations are set using a coarse grid generated by the elliptic system. The coarse grid is then interpolated to generate a finer grid which is smoothed using only a few iterations of the elliptic system.
Jacobi-Bessel Analysis Of Antennas With Elliptical Apertures.
NASA Technical Reports Server (NTRS)
Rahmat-Samii, Y.
1989-01-01
Coordinate transformation improves convergence pattern analysis of elliptical-aperture antennas. Modified version of Jacobi-Bessel expansion for vector diffraction analysis of reflector antennas uses coordinate transformation to improve convergence with elliptical apertures. Expansion converges rapidly for antennas with circular apertures, but less rapidly for elliptical apertures. Difference in convergence behavior between circular and elliptical Jacobi-Bessel algorithms indicated by highest values of indices m, n, and p required to achieve same accuracy in computed radiation pattern of offset paraboloidal antenna with elliptical aperture.
Symmetry classification and joint invariants for the scalar linear (1 + 1) elliptic equation
NASA Astrophysics Data System (ADS)
Mahomed, F. M.; Johnpillai, A. G.; Aslam, A.
2015-08-01
The equations for the classification of symmetries of the scalar linear (1 + 1) elliptic partial differential equation (PDE) are obtained in terms of Cotton's invariants. New joint differential invariants of the scalar linear elliptic (1 + 1) PDE in two independent variables are derived in terms of Cotton's invariants by application of the infinitesimal method. Joint differential invariants of the scalar linear elliptic equation are also deduced from the basis of the joint differential invariants of the scalar linear (1 + 1) hyperbolic equation under the application of the complex linear transformation. We also find a basis of joint differential invariants for such type of equations by utilization of the operators of invariant differentiation. The other invariants are functions of the basis elements and their invariant derivatives. Examples are given to illustrate our results.
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.
Scattering of shear waves by an elliptical cavity in a radially inhomogeneous isotropic medium
NASA Astrophysics Data System (ADS)
Hei, Baoping; Yang, Zailin; Chen, Zhigang
2016-03-01
Complex function and general conformal mapping methods are used to investigate the scattering of elastic shear waves by an elliptical cylindrical cavity in a radially inhomogeneous medium. The conformal mappings are introduced to solve scattering by an arbitrary cavity for the Helmholtz equation with variable coefficient through the transformed standard Helmholtz equation with a circular cavity. The medium density depends on the distance from the origin with a power-law variation and the shear elastic modulus is constant. The complex-value displacements and stresses of the inhomogeneous medium are explicitly obtained and the distributions of the dynamic stress for the case of an elliptical cavity are discussed. The accuracy of the present approach is verified by comparing the present solution results with the available published data. Numerical results demonstrate that the wave number, inhomogeneous parameters and different values of aspect ratio have significant influence on the dynamic stress concentration factors around the elliptical cavity.
Comparison principles for viscosity solutions of elliptic equations via fuzzy sum rule
NASA Astrophysics Data System (ADS)
Luo, Yousong; Eberhard, Andrew
2005-07-01
A comparison principle for viscosity sub- and super-solutions of second order elliptic partial differential equations is derived using the "fuzzy sum rule" of non-smooth calculus. This method allows us to weaken the assumptions made on the function F when the equation F(x,u,=u,=2u)=0 is under consideration.
NASA Astrophysics Data System (ADS)
Coleman, Thomas F.; Santosa, Fadil; Verma, Arun
2000-01-01
Wave propagational inverse problems arise in several applications including medical imaging and geophysical exploration. In these problems, one is interested in obtaining the parameters describing the medium from its response to excitations. The problems are characterized by their large size, and by the hyperbolic equation which models the physical phenomena. The inverse problems are often posed as a nonlinear data-fitting where the unknown parameters are found by minimizing the misfit between the predicted data and the actual data. In order to solve the problem numerically using a gradient-type approach, one must calculate the action of the Jacobian and its adjoint on a given vector. In this paper, we explore the use of automatic differentiation (AD) to develop codes that perform these calculations. We show that by exploiting structure at 2 scales, we can arrive at a very efficient code whose main components are produced by AD. In the first scale we exploite the time-stepping nature of the hyperbolic solver by using the “Extended Jacobian” framework. In the second (finer) scale, we exploit the finite difference stencil in order to make explicit use of the sparsity in the dependence of the output variables to the input variables. The main ideas in this work are illustrated with a simpler, one-dimensional version of the problem. Numerical results are given for both one- and two- dimensional problems. We present computational templates that can be used in conjunction with optimization packages to solve the inverse problem.
Roberts, R.G.; Repperger, D.W.
1999-01-01
This article presents some results on the closed-form, singular-value decomposition of the orientational Jacobian for three- and four-degree-of-freedom wristlike mechanisms. These results are used to study the kinematics of a centrifuge simulator, and to determine the centrifuge`s limitations in achieving maximum angular velocities. Also, the issue of fault tolerance for a redundant wrist is addressed.
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
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.
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.
Blue star-forming isolated elliptical galaxies
NASA Astrophysics Data System (ADS)
Lacerna, I.; Hernández-Toledo, H. M.; Avila-Reese, V.; Abonza-Sane, J.; del Olmo, A.
2016-06-01
The isolated environment seems to favor the formation of blue, star-forming galaxies that are not observed in a high-density environment such as the Coma supercluster. These galaxies, with masses between 7 × 10^9 and 2 × 10^10 h‑2 Msun, are also the youngest galaxies from a sample of isolated elliptical 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. The color and star-formation activity in these galaxies could be explained by rejuvenation of ellipticals by recent (<1 Gyr) cold gas accretion.
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
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'' Multiplication-Sign 107''), allowing us to achieve remarkably high signal-to-noise ratios of {approx}20-70 pixel{sup -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 {sigma}{sub *} > 150 km s{sup -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 {approx}50%, and only a weak correlation between {sigma}{sub *} and Mgb EW remains. The Mgb EWs at large radii are comparable to those seen in the centers of elliptical galaxies that are {approx} 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 R{sub e} , 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 {alpha}-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.
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.
The superconformal index and an elliptic algebra of surface defects
NASA Astrophysics Data System (ADS)
Bullimore, Mathew; Fluder, Martin; Hollands, Lotte; Richmond, Paul
2014-10-01
In this paper we continue the study of the superconformal index of four-dimensional =2 theories of class in the presence of surface defects. Our main result is the construction of an algebra of difference operators, whose elements are labeled by irreducible representations of A N -1. For the fully antisymmetric tensor representations these difference operators are the Hamiltonians of the elliptic Ruijsenaars-Schneider system. The structure constants of the algebra are elliptic generalizations of the Littlewood-Richardson coefficients. In the Macdonald limit, we identify the difference operators with local operators in the two-dimensional TQFT interpretation of the superconformal index. We also study the dimensional reduction to difference operators acting on the three-sphere partition function, where they characterize supersymmetric defects supported on a circle, and show that they are transformed to supersymmetric Wilson loops under mirror symmetry. Finally, we compare to the difference operators that create 't Hooft loops in the four-dimensional =2* theory on a four-sphere by embedding the three-dimensional theory as an S-duality domain wall.
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.
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.
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.
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.
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.
Elliptical instability of compressible flow in ellipsoids
NASA Astrophysics Data System (ADS)
Clausen, N.; Tilgner, A.
2014-02-01
Context. Elliptical instability is due to a parametric resonance of two inertial modes in a fluid velocity field with elliptical streamlines. This flow is a simple model of the motion in a tidally deformed, rotating body. Elliptical instability typically leads to three-dimensional turbulence. The associated turbulent dissipation together with the dissipation of the large scale mode may be important for the synchronization process in stellar and planetary binary systems. Aims: In order to determine the influence of the compressibility on the stability limits of tidal flows in stars or planets, we calculate the growth rates of perturbations in flows with elliptical streamlines within ellipsoidal boundaries of small ellipticity. In addition, the influence of the orbiting frequency of the tidal perturber ΩP and the viscosity of the fluid are taken into account. Methods: We studied the linear stability of the flow to determine the growth rates. We solved the Euler equation and the continuity equation. The viscosity was introduced heuristically in our calculations. We assumed a power law for the radial dependence of the background density. Together with the use of the anelastic approximation, this enabled us to use semi-analytical methods to solve the equations. Results: It is found that the growth rate of a certain mode combination depends on the compressibility. However, the influence of the compressibility is negligible for the growth rate maximized over all possible modes if viscous bulk damping effects can be neglected. The growth rate maximized over all possible modes determines the stability of the flow. The stability limit for the compressible fluid confined to an ellipsoid is the same as for incompressible fluid in an unbounded domain. Depending on the ratio ΩP/ΩF, with ΩF the spin rate of the central object in the frame of the rotating tidal perturber, certain pairs of modes resonate with each other. The size of the bulk damping term depends on the modes
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.
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.
Scattering of a Gaussian beam by an elliptical cylinder using the vectorial complex ray model.
Jiang, Keli; Han, Xiang'e; Ren, Kuan Fang
2013-08-01
The scattered waves of a shaped beam by an infinite cylinder in the far field are, stricto sensu, neither cylindrical nor spherical, so the asymptotic form of special functions involved in the theories based on the rigorous solution of Maxwell equations cannot be used to evaluate scattered intensities, even in the most simple case of Gaussian beam scattering by an infinite circular cylinder. Thus, although theories exist for the scattering of a shaped beam by infinite cylinders with circular and elliptical sections, the numerical calculations are limited to the near field. The vectorial complex ray model (VCRM) developed by Ren et al. describes waves by rays with a new property: the curvature of the wavefront. It is suitable to deal with the scattering of an arbitrarily shaped beam by a particle with a smooth surface of any form. In this paper, we apply this method to the scattering of an infinite elliptical cylinder illuminated by a Gaussian beam at normal incidence with an arbitrary position and orientation relative to the symmetric axis of the elliptical section of the cylinder. The method for calculating the curvature of an arbitrary surface is given and applied in the determination of the two curvature radii of the Gaussian beam wavefront at any point. Scattered intensities for different parameters of the beam and the particle as well as observation distance are presented to reveal the scattering properties and new phenomena observed in the beam scattering by an infinite elliptical cylinder. PMID:24323213
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.
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
NASA Astrophysics Data System (ADS)
Yang, J. S.; Chen, K. W.
1989-10-01
It was known from a complete model analysis1,2 that the wake potential in the pill-box cavity is predominantly determined by a few longitudinal modes counting from the fundamental longitudinal mode. An approach to find the longitudinal modes of an elliptical cavity is developed by means of the coordinate transformation method. It is found that the field configuration and eigenfrequencies of the elliptical cavity can be expressed in a closed form in terms of Mathieu functions. Inserting the closed form solution of modes into the previous analytical formula for the wake field, the wake field is expressed too in a closed form solution, which is convenient for numerical calculation. Thus, a numerical method to calculate expediently the wake field is developed, and a model calculation is presented.
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
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.
The acetabular component: an elliptical monoblock alternative.
Sculco, Thomas P
2002-06-01
The major failure mode of cemented or noncemented acetabular fixation is osteolysis produced by biologic reaction to polyethylene and metallic debris. A monoblock acetabular noncemented component offers advantages in reducing the failure mechanism of acetabular cups. First, there is no extra-articular back surface polyethylene wear. Second, locking rings that may generate metallic debris are eliminated. Third, screw-holes, which decrease the surface area for ingrowth, are not needed, and pelvic entrance points for wear debris are eliminated. Fourth, an elliptical configuration allows better coaptation of the shell to the dome of the acetabulum. I have implanted >2,400 elliptical monoblock acetabular cups with a short-term follow-up of 6.5 years, with >4 years of follow-up in 840 hips. There have been no mechanical failures requiring revision. Four patients have been revised for recurrent hip instability, and one has been revised for infection. The need to convert to an acetabular component with screw fixation because of poor press-fit is <1%. PMID:12068420
Flow around a helically twisted elliptic cylinder
NASA Astrophysics Data System (ADS)
Kim, Woojin; Lee, Jungil; Choi, Haecheon
2016-05-01
In the present study, we conduct unsteady three-dimensional simulations of flows around a helically twisted elliptic (HTE) cylinder at the Reynolds numbers of 100 and 3900, based on the free-stream velocity and square root of the product of the lengths of its major and minor axes. A parametric study is conducted for Re = 100 by varying the aspect ratio (AR) of the elliptic cross section and the helical spanwise wavelength (λ). Depending on the values of AR and λ, the flow in the wake contains the characteristic wavelengths of λ, 2λ, 6λ, or even longer than 60λ, showing a wide diversity of flows in the wake due to the shape change. The drag on the optimal (i.e., having lowest drag) HTE cylinder (AR = 1.3 and λ = 3.5d) is lower by 18% than that of the circular cylinder, and its lift fluctuations are zero owing to complete suppression of vortex shedding in the wake. This optimal HTE configuration reduces the drag by 23% for Re = 3900 where the wake is turbulent, showing that the HTE cylinder reduces the mean drag and lift fluctuations for both laminar and turbulent flows.
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.
Prospects of Elliptic Flow Studies at NICA/MPD
NASA Astrophysics Data System (ADS)
Geraksiev, Nikolay
2016-01-01
As a key observable, anisotropic flow presents a unique insight into heavy ion collision physics. The presented poster reveals the prospects of studying elliptic flow at the NICA/MPD facility through the UrQMD model. Here, results for the elliptic flow of simulated and reconstructed hadrons at the planned NICA energy range are presented.
Working charts for the stress analysis of elliptic rings
NASA Technical Reports Server (NTRS)
Burke, Walter F
1933-01-01
This report presents charts which reduce the stress analysis of circular and elliptic rings of uniform cross section subjected to balanced systems of concentrated loads from a statically indeterminate problem to a statically determinate one. To demonstrate the use of the charts in the stress analysis of elliptic rings, an illustrative problem is included.
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]…
Radial and elliptic flow at RHIC: Further predictions
Huovinen, Pasi; Kolb, Peter F.; Heinz, Ulrich; Ruuskanen, P.V.; Voloshin, Sergei A.
2001-01-30
Using a hydrodynamic model, we predict the transverse momentum dependence of the spectra and the elliptic flow for different hadrons in Au+Au collisions at sqrt(s)=130 AGeV. The dependence of the differential and p{_}t-integrated elliptic flow on the hadron mass, equation of state and freeze-out temperature is studied both numerically and analytically.
Elliptic cylinder geometry for distinguishability analysis in impedance tomography.
Saka, Birsen; Yilmaz, Atila
2004-01-01
Electrical impedance tomography (EIT) is a technique that computes the cross-sectional impedance distribution within the body by using current and voltage measurements made on the body surface. It has been reported that the image reconstruction is distorted considerably when the boundary shape is considered to be more elliptical than circular as a more realistic shape for the measurement boundary. This paper describes an alternative framework for determining the distinguishability region with a finite measurement precision for different conductivity distributions in a body modeled by elliptic cylinder geometry. The distinguishable regions are compared in terms of modeling error for predefined inhomogeneities with elliptical and circular approaches for a noncircular measurement boundary at the body surface. Since most objects investigated by EIT are noncircular in shape, the analytical solution for the forward problem for the elliptical cross section approach is shown to be useful in order to reach a better assessment of the distinguishability region defined in a noncircular boundary. This paper is concentrated on centered elliptic inhomogeneity in the elliptical boundary and an analytic solution for this type of forward problem. The distinguishability performance of elliptical cross section with cosine injected current patterns is examined for different parameters of elliptical geometry. PMID:14723501
Strelkov, V. V.
2006-07-15
We present a quantum-mechanical theory of xuv generation by an elliptically polarized intense laser field. Our approach is valid when the Keldysh parameter {gamma} is about unity or less, and the driving ellipticity is less than {radical}(2){gamma}. After the photoionization the motion of the electronic wave packet along the major axis of the driving field polarization ellipse is described quasiclassically, whereas the motion in the transverse direction is considered fully quantum mechanically; we also find the condition that allows the reduction of the motion description to a quantum orbit in the polarization plane of the laser field. We use the ionization rate calculated via numerical solution of the three-dimensional Schroedinger equation (TDSE), and take into account the Coulomb modification of the free electronic wave packet. The predictions of our theory for xuv emission agree well with numerical and experimental results. We study the high harmonic intensities and phases as functions of the driving intensity and ellipticity, and also the ellipticity and the rotation angle of the harmonic field polarization ellipse as functions of the driving ellipticity. The atomic response is decomposed into the contributions of different quantum paths. This allows finding a straightforward explanation for the observed dependencies.
Non-elliptic wavevector anisotropy for magnetohydrodynamic turbulence
NASA Astrophysics Data System (ADS)
Narita, Y.
2015-11-01
A model of non-elliptic wavevector anisotropy is developed for the inertial-range spectrum of magnetohydrodynamic turbulence and is presented in the two-dimensional wavevector domain spanning the directions parallel and perpendicular to the mean magnetic field. The non-elliptic model is a variation of the elliptic model with different scalings along the parallel and the perpendicular components of the wavevectors to the mean magnetic field. The non-elliptic anisotropy model reproduces the smooth transition of the power-law spectra from an index of -2 in the parallel projection with respect to the mean magnetic field to an index of -5/3 in the perpendicular projection observed in solar wind turbulence, and is as competitive as the critical balance model to explain the measured frequency spectra in the solar wind. The parameters in the non-elliptic spectrum model are compared with the solar wind observations.
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.
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
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.
NASA Astrophysics Data System (ADS)
Okumura, Teppei; Jing, Y. P.; Li, Cheng
2009-03-01
We investigate the orientation correlation of giant elliptical galaxies by measuring the intrinsic ellipticity correlation function of 83,773 luminous red galaxies (LRGs) at redshifts 0.16-0.47 from the Sloan Digital Sky Survey. We have accurately determined the correlation up to 30 h-1 Mpc. Luminosity dependence of the ellipticity correlation is also detected although the error bars are large, while no evidence is found for its redshift evolution between z = 0.2 and z = 0.4. Then we use a cosmological N-body simulation to examine misalignment between the central LRGs and their parent dark matter halos. Central and satellite galaxies are assigned to simulated halos by employing a halo occupation distribution model for the LRGs. The ellipticity correlation is predicted to have the same shape as, but an amplitude about four times higher than, our observation if the central LRGs are perfectly aligned with their host halos. This indicates that the central LRG galaxies are preferentially but not perfectly aligned with their host halos. With the assumption that there is a misalignment angle between a central LRG and its host halo which follows a Gaussian distribution with a zero mean and a width σθ, we obtain a tight constraint on the misalignment parameter, σθ = 35.4+4.0 -3.3 deg. This type of intrinsic ellipticity correlation, if not corrected, can lead to contamination at 5% level to the shear power spectrum in weak lensing surveys of limiting magnitude RAB = 24.5 if the source central galaxies follow the same misalignment distribution as the LRGs.
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.
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.
Crushing characteristics of composite tubes with 'near-elliptical' cross sections
NASA Technical Reports Server (NTRS)
Farley, Gary L.; Jones, Robert M.
1992-01-01
An experimental investigation was conducted to determine whether the energy-absorption capability of near-elliptical cross-section composite tubular specimens is a function of included angle. Each half of the near-elliptical cross-section tube is a segment of a circle. The included angle is the angle created by radial lines extending from the center of the circular segment to the ends of the circular segment. Graphite- and Kevlar-reinforced epoxy material was used to fabricate specimens. Tube internal diameters were 2.54, 3.81, and 7.62 cm, and included angles were 180, 160, 135, and 90 degrees. Based upon the test results from these tubes, energy-absorption capability increased between 10 and 30 percent as included angle decreased between 180 and 90 degrees for the materials evaluated. Energy-absorption capability was a decreasing nonlinear function of the ratio of tube internal diameter to wall thickness.
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
Subregions of Motion and Elliptic Halo Orbits in the Elliptic Restricted Three-Body Problem
NASA Technical Reports Server (NTRS)
Campagnola, Stefano; Lo, Martin; Newton, Paul
2008-01-01
In this paper we present regions of motion and periodic orbits in the spatial elliptic restricted three body problem (ER3BP). Periodic orbits and regions of motion are fundamental keys to understand any dynamical system; for this reason the Hill's surfaces or the families of halo orbits have been extensively studied in the frame of the circular restricted three body problem. It is our opinion that their natural extensions to the ER3BP have not been studied enough. We divide the position space into forbidden subregions, subregions of motion and low-velocity subregions.We use these notions to define necessary condition for a transfer trajectory in the ER3BP. Also we compute branches of elliptic halo orbits bifurcating from halo orbits in the circular restricted three body problem. The new periodic orbits have principal periods and stability properties different from those of the originating halo orbit.
Crack-face displacements for embedded elliptic and semi-elliptical surface cracks
NASA Technical Reports Server (NTRS)
Raju, I. S.
1989-01-01
Analytical expressions for the crack-face displacements of an embedded elliptic crack in infinite solid subjected to arbitrary tractions are obtained. The tractions on the crack faces are assumed to be expressed in a polynomial form. These displacements expressions complete the exact solution of Vijayakumar and Atluri, and Nishioki and Atluri. For the special case of an embedded crack in an infinite solid subjected to uniform pressure loading, the present displacements agree with those by Green and Sneddon. The displacement equations derived were used with the finite-element alternating method (FEAM) for the analysis of a semi-elliptic surface crack in a finite solid subjected to remote tensile loading. The maximum opening displacements obtained with FEAM are compared to those with the finite-element method with singularity elements. The maximum crack opening displacements by the two methods showed good agreement.
The elliptic billiard: subtleties of separability
NASA Astrophysics Data System (ADS)
van Zon, R.; Ruijgrok, Th W.
1998-01-01
Some of the subtleties of the integrability of the elliptic quantum billiard are discussed. Considering a well known classical constant of the motion in the quantum case, we find that a naive calculation of the commutator with the Hamiltonian does not show whether or not it is zero. It is shown how this problem can be solved. A geometric picture is given that reveals why levels of a separable system cross. It is shown that the repulsions found by Ayant and Arvieu are computational effects and that the method used by Traiber et al is related to the present picture which explains the crossings they find. An asymptotic formula for the energy levels is derived and it is found that the statistical quantities of the spectrum P(s) and 0143-0807/19/1/011/img1 have the form expected for an integrable system.
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.
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.
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.
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.
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.
Magnetic elliptical polarization of Schumann resonances
Sentman, D.D.
1987-08-01
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. 16 references.
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.
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
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.
Unbounded sets of solutions of non-cooperative elliptic systems on spheres
NASA Astrophysics Data System (ADS)
Rybicki, Sławomir; Stefaniak, Piotr
2015-10-01
The aim of this paper is to show that any continuum of nontrivial solutions of a non-cooperative system of elliptic equations on the sphere S n - 1, bifurcating from the set of trivial solutions, is unbounded. Moreover, we characterize bifurcation points of this system at which the global symmetry-breaking phenomenon occurs. As the main tool we use the degree for SO (2)-invariant strongly indefinite functionals defined in [13].
On the solution of elliptic partial differential equations on regions with corners
NASA Astrophysics Data System (ADS)
Serkh, Kirill; Rokhlin, Vladimir
2016-01-01
In this paper we investigate the solution of boundary value problems on polygonal domains for elliptic partial differential equations. We observe that when the problems are formulated as the boundary integral equations of classical potential theory, the solutions are representable by series of elementary functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.
Elliptical Undulators HU256 for Synchrotron SOLEIL
Batrakov, A.; Churkin, I.; Ilyin, I.; Kolokolnikov, Yu.; Rouvinski, E.; Semenov, E.; Steshov, A.; Vobly, P.; Briquez, F.; Chubar, O.; Dael, A.; Marcouile, O.; Marteau, F.; Roux, G.; Valleau, M.
2007-01-19
Three elliptical undulators HU256 of electromagnetic type were produced, tested and magnetically measured by the Budker Institute of Nuclear Physics (Russia) for Synchrotron Soleil (France). The undulators have a new design of a Bx and Bz closed structure for insertion vacuum chamber. In the elliptical undulator HU256 with period of the magnetic fields of 256 mm, the vertical magnetic field (Bzmax=0.44 T) formed by 27 Bz laminated dipole magnets is symmetric, and the horizontal magnetic field (Bxmax=0.33 T) formed by 28 Bx laminated dipole magnets is asymmetric. The undulator can work in standard mode as well as in a quasi-periodical mode. The vertical magnetic field may be modulated by switching on the modulation coils placed on the Bz dipoles. Two power supply systems allow us to modulate the horizontal magnetic field, and change the radiation spectrum. The magnetic calculations of the individual dipoles and dipoles in ''undulator'' environment were executed by means of Mermaid 3D Code. The magnetic measurements of the individual dipoles had confirmed the magnetic calculations. On basis of semiempirical dependences from the mechanical characteristics the estimates of the magnetic parameters for all dipoles were calculated. Sorting of dipoles in the undulators have been done, and it has improved the magnetic parameters of the assembled undulators in comparison with the statistical estimations. The magnetic measurements of the undulators HU256 were carried out at Budker INP by Hall probes and at Soleil by Hall probes and Stretched Wire. Now the 1st undulator HU256 is installed at Soleil Storage Ring.
Elliptical Undulators HU256 for Synchrotron SOLEIL
NASA Astrophysics Data System (ADS)
Batrakov, A.; Briquez, F.; Chubar, O.; Churkin, I.; Dael, A.; Ilyin, I.; Kolokolnikov, Yu.; Marcouile, O.; Marteau, F.; Roux, G.; Rouvinski, E.; Semenov, E.; Steshov, A.; Valleau, M.; Vobly, P.
2007-01-01
Three elliptical undulators HU256 of electromagnetic type were produced, tested and magnetically measured by the Budker Institute of Nuclear Physics (Russia) for Synchrotron Soleil (France). The undulators have a new design of a Bx & Bz closed structure for insertion vacuum chamber. In the elliptical undulator HU256 with period of the magnetic fields of 256 mm, the vertical magnetic field (Bzmax=0.44 T) formed by 27 Bz laminated dipole magnets is symmetric, and the horizontal magnetic field (Bxmax=0.33 T) formed by 28 Bx laminated dipole magnets is asymmetric. The undulator can work in standard mode as well as in a quasi-periodical mode. The vertical magnetic field may be modulated by switching on the modulation coils placed on the Bz dipoles. Two power supply systems allow us to modulate the horizontal magnetic field, and change the radiation spectrum. The magnetic calculations of the individual dipoles and dipoles in "undulator" environment were executed by means of Mermaid 3D Code. The magnetic measurements of the individual dipoles had confirmed the magnetic calculations. On basis of semiempirical dependences from the mechanical characteristics the estimates of the magnetic parameters for all dipoles were calculated. Sorting of dipoles in the undulators have been done, and it has improved the magnetic parameters of the assembled undulators in comparison with the statistical estimations. The magnetic measurements of the undulators HU256 were carried out at Budker INP by Hall probes and at Soleil by Hall probes and Stretched Wire. Now the 1st undulator HU256 is installed at Soleil Storage Ring.
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
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
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.
New Elliptic Solutions of the Yang-Baxter Equation
NASA Astrophysics Data System (ADS)
Chicherin, D.; Derkachov, S. E.; Spiridonov, V. P.
2016-02-01
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.
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.
Jacobi-Bessel analysis of reflector antennas with elliptical apertures
NASA Technical Reports Server (NTRS)
Rahmat-Samii, Yahya
1987-01-01
Although many reflector antennas possess circular projected apertures, there are recent satellite and ground antenna applications for which it is desirable to employ reflectors with elliptical apertures. Here a modification of the Jacobi-Bessel expansion is presented for the diffraction analysis of reflectors with elliptical apertures. A comparative study is also performed between this modified Jacobi-Bessel algorithm and the one which uses the Jacobi-Bessel expansion over a circumscribing circular region. Numerical results are presented for offset reflectors with elliptical and circular apertures and the improved convergence properties of the modified algorithm are highlighted.
Laplacian growth, elliptic growth, and singularities of the Schwarz potential
NASA Astrophysics Data System (ADS)
Lundberg, Erik
2011-04-01
The Schwarz function has played an elegant role in understanding and in generating new examples of exact solutions to the Laplacian growth (or 'Hele-Shaw') problem in the plane. The guiding principle in this connection is the fact that 'non-physical' singularities in the 'oil domain' of the Schwarz function are stationary, and the 'physical' singularities obey simple dynamics. We give an elementary proof that the same holds in any number of dimensions for the Schwarz potential, introduced by Khavinson and Shapiro (1989 Technical Report TRITA-MAT-1989-36 Royal Institute of Technology, Stockholm). An extension is also given for the so-called elliptic growth problem by defining a generalized Schwarz potential. New exact solutions are constructed, and we solve inverse problems of describing the driving singularities of a given flow. We demonstrate, by example, how {C}^n-techniques can be used to locate the singularity set of the Schwarz potential. One of our methods is to prolong available local extension theorems by constructing 'globalizing families'.
Tracing of the chemical evolution of the massive elliptical galaxy NGC 3377 using a merger scenario
NASA Astrophysics Data System (ADS)
Nykytyuk, T.
2015-05-01
Mergers are thought to play a significant role in the formation of galaxies in clusters. The chemical evolution of the halo of the massive elliptical galaxy NGC 3377, a member of the Leo cluster, is considered in the framework of such a merger scenario. An open chemical evolution model is set up to calculate the metallicity distributions of pre-merging fragments. The model assumes that pristine gas was accreted onto the fragments during their whole evolution before their merger. The metallicity distribution resulting from the overlay of a variable number of fragments is then compared to observational data for NGC 3377. It was found that the observed metallicity distribution function of this elliptical galaxy is reproduced by merging at least five fragments from two different groups, namely low-and high-metallicity fragments.
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.
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.
NASA Astrophysics Data System (ADS)
Biskup, M.; Salvi, M.; Wolff, T.
2014-06-01
Given a resistor network on with nearest-neighbor conductances, the effective conductance in a finite set with a given boundary condition is the minimum of the Dirichlet energy over functions with the prescribed boundary values. For shift-ergodic conductances, linear (Dirichlet) boundary conditions and square boxes, the effective conductance scaled by the volume of the box converges to a deterministic limit as the box-size tends to infinity. Here we prove that, for i.i.d. conductances with a small ellipticity contrast, also a (non-degenerate) central limit theorem holds. The proof is based on the corrector method and the Martingale Central Limit Theorem; a key integrability condition is furnished by the Meyers estimate. More general domains, boundary conditions and ellipticity contrasts will be addressed in a subsequent paper.
Old and new results in regularity theory for diagonal elliptic systems via blowup techniques
NASA Astrophysics Data System (ADS)
Beck, Lisa; Bulíček, Miroslav; Frehse, Jens
2015-12-01
We consider quasilinear diagonal elliptic systems in bounded domains subject to Dirichlet, Neumann or mixed boundary conditions. The leading elliptic operator is assumed to have only measurable coefficients, and the nonlinearities (Hamiltonians) are allowed to be of quadratic (critical) growth in the gradient variable of the unknown. These systems appear in many applications, in particular in differential geometry and stochastic differential game theory. We impose on the Hamiltonians structural conditions developed between 1972-2002 and also a new condition (sum coerciveness) introduced in recent years (in the context of the pay off functional in stochastic game theory). We establish existence, Hölder continuity, Liouville properties, W 2, q estimates, etc. for solutions, via a unified approach through the blow-up method. The main novelty of the paper is the introduction of a completely new technique, which in particular leads to smoothness of the solution also for dimensions d ≥ 3.
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
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.
Design and fabrication of embedded two elliptical cores hollow fiber
NASA Astrophysics Data System (ADS)
Tian, Fengjun; Yuan, Libo; Dai, Qian; Liu, Zhihai
2011-11-01
We propose a novel embedded two elliptical cores fiber with a hollow air hole, and demonstrate the fabrication of the embedded two elliptical cores hollow fiber (EECHF). By using a suspended core-in-tube technique, the fibers are drawn from the preform utilizing a fiber drawing system with a pressure controller. The fiber have a 60μm diameter hollow air hole centrally, a 125μm diameter cladding, two 7.2μm /3.0μm (major axis/minor axis) elliptical cores, and a 3μm thickness silica cladding between core layer and air hole. The EECHF has a great potential for PMFs, high sensitivity in-fiber interferometers, poling fiber and Bio-sensor based on evanescent wave field. The fabrication technology is simple and versatile, and can be easily utilized to fabricate multi-core fiber with any desired aspect ratio elliptical core.
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.
Elliptical varied line-space (EVLS) gratings
NASA Astrophysics Data System (ADS)
Thomas, Roger J.
2004-10-01
Imaging spectroscopy at wavelengths below 2000 Å offers an especially powerful method for studying many extended high-temperature astronomical objects, like the Sun and its outer layers. But the technology to make such measurements is also especially challenging, because of the poor reflectance of all standard materials at these wavelengths, and because the observation must be made from above the absorbing effects of the Earth's atmosphere. To solve these problems, single-reflection stigmatic spectrographs for XUV wavelengths have bee flown on several space missions based on designs with toroidal uniform line-space (TULS) or spherical varied line-space (SVLS) gratings that operate at near normal-incidence. More recently, three solar EUV/UV instruments have been selected that use toroidal varied line-space (TVLS) gratings; these are SUMI and RAISE, both sounding rocket payloads, and NEXUS, a SMEX satellite-mission. The next logical extension to such designs is the use of elliptical surfaces for varied line-space (EVLS) rulings. In fact, EVLS designs are found to provide superior imaging even at very large spectrograph magnifications and beam-speeds, permitting extremely high-quality performance in remarkably compact instrument packages. In some cases, such designs may be optimized even further by using a hyperbolic surface for the feeding telescope. The optical characteristics of two solar EUV spectrometers based on these concepts are described: EUS and EUI, both being developed as possible instruments for ESA's Solar Orbiter mission by consortia led by RAL and by MSSL, respectively.
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.
Elliptical acoustic particle motion in underwater waveguides.
Dall'Osto, David R; Dahl, Peter H
2013-07-01
Elliptical particle motion, often encountered in acoustic fields containing interference between a source signal and its reflections, can be quantified by the degree of circularity, a vector quantity formulated from acoustic particle velocity, or vector intensity measurements. Acoustic analysis based on the degree of circularity is expected to find application in ocean waveguides as its spatial dependence relates to the acquisition geometry, water column sound speed, surface conditions, and bottom properties. Vector sensor measurements from a laboratory experiment are presented to demonstrate the depth dependence of both the degree of circularity and an approximate formulation based on vertical intensity measurements. The approximation is applied to vertical intensity field measurements made in a 2006 experiment off the New Jersey coast (in waters 80 m deep) to demonstrate the effect of sediment structure on the range dependence of the degree of circularity. The mathematical formulation presented here establishes the framework to readily compute the degree of circularity from experimental measurements; the experimental examples are provided as evidence of the spatial and frequency dependence of this fundamental vector property. PMID:23862789
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.
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
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
Interference of multiplane wings having elliptical lift distribution
NASA Technical Reports Server (NTRS)
Von Sanden, H
1924-01-01
In calculating the self-induction of a wing surface, elliptical lift distribution is assumed, while in calculating the mutual induction or interference of two wing surfaces, a uniform distribution of the lift along the wing has hitherto been assumed. Whether the results of these calculations are substantially altered by assuming an elliptical lift distribution (which is just as probable as uniform distribution) is examined here.
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)
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.
Quasar Radio-Loudness and the Elliptical Core Problem
NASA Astrophysics Data System (ADS)
Hamilton, Timothy S.
2010-01-01
The dichotomy between radio-loud and radio-quiet QSOs is not simply one of host morphology. While radio-louds are almost always found in elliptical hosts, radio-quiets are known to reside in both elliptical and spiral galaxies. We find that what determines whether a given elliptical galaxy will host either a radio-loud or radio-quiet QSO is a combination of accretion rate and host scale. QSOs with high x-ray luminosities (above 10e44.9 erg/s at 0.5 keV) are nearly all found to be radio-loud. But those with low luminosities divide fairly neatly along the Kormendy law, the correlation between re and μe. Those larger than about 10 kpc are radio-loud, while smaller ones are radio-quiet. It has recently been found that core and coreless ellipticals are also divided at about this limit. This implies that for low-luminosity QSOs, radio-louds are found in core ellipticals, while radio-quiets are in coreless ellipticals and spirals. This segregation shows up particularly strongly for low-redshift objects. Since the presence or absence of a core may be tied to the galactic merger history, we have an evolutionary explanation for the differences between radio-loud and radio-quiet QSOs.
Forward-backward elliptic anisotropy correlations in parton cascades
NASA Astrophysics Data System (ADS)
Han, L. X.; Ma, G. L.; Ma, Y. G.; Cai, X. Z.; Chen, J. H.; Zhang, S.; Zhong, C.
2011-04-01
A potential experimental probe, the forward-backward elliptic anisotropy correlation (CFB), has been proposed by Liao and Koch to distinguish the jet and true elliptic flow contribution to the measured elliptic flow (v2) in relativistic heavy-ion collisions. The jet and flow fluctuation contribution to elliptic flow is investigated within the framework of a multiphase transport model using the CFB probe. We find that the CFB correlation is remarkably different from, and about two times that, proposed by Liao and Koch. It originates from the correlation between fluctuation of forward and that of backward elliptic flow at a low transverse momentum, which is mainly caused by the initial correlation between fluctuation of forward and that of backward eccentricity. This results in an amendment of the CFB by a term related to the correlation between fluctuation of forward and that of backward elliptic flow. Our results suggest that a suitable rapidity gap for CFB correlation studies is about ±3.5.
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)
Viallet, M.; Goffrey, T.; Baraffe, I.; Folini, D.; Geroux, C.; Popov, M. V.; Pratt, J.; Walder, R.
2016-02-01
This work is a continuation of our efforts to develop an efficient implicit solver for multidimensional hydrodynamics for the purpose of studying important physical processes in stellar interiors, such as turbulent convection and overshooting. We present an implicit solver that results from the combination of a Jacobian-free Newton-Krylov method and a preconditioning technique tailored to the inviscid, compressible equations of stellar hydrodynamics. We assess the accuracy and performance of the solver for both 2D and 3D problems for Mach numbers down to 10-6. Although our applications concern flows in stellar interiors, the method can be applied to general advection and/or diffusion-dominated flows. The method presented in this paper opens up new avenues in 3D modeling of realistic stellar interiors allowing the study of important problems in stellar structure and evolution.
NASA Astrophysics Data System (ADS)
Bernsen, Erik; Dijkstra, Henk A.; Thies, Jonas; Wubs, Fred W.
2010-10-01
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.
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.
Liquid sloshing in half-full horizontal elliptical tanks
NASA Astrophysics Data System (ADS)
Hasheminejad, Seyyed M.; Aghabeigi, Mostafa
2009-07-01
A two dimensional hydrodynamic analysis based on the linear potential theory is introduced to study the natural sloshing frequencies of transverse modes in a half-filled non-deformable horizontal cylindrical container of elliptical cross section, without or with a pair of inflexible horizontal longitudinal side baffles of arbitrary extension positioned at the free liquid surface. Successive conformal coordinate transformations in conjunction with the method of separation of variables and the relevant boundary conditions are employed to obtain standard truncated matrix eigen-value problems which are then solved numerically for the resonance eigen-frequencies. The Gauss-Laguerre quadrature formula is used to approximate the integral eigen-problem obtained in the unbaffled case. Plots of the sloshing frequencies as functions of the container aspect ratio and baffle extension are presented and discussed for the three lowest antisymmetric and symmetric transverse oscillation modes. A convergence study is performed to demonstrate the fast convergence and remarkably small computational cost of the Fourier series approach used for the baffled container, and the effects of tank geometry and baffle length on the convergence are also examined. Limiting cases are considered and good agreements with available analytic and numerical solutions as well as experimental data are obtained, demonstrating the accuracy of proposed models.
Multiple solutions for a singular quasilinear elliptic system.
Chen, Lin; Chen, Caisheng; Xiu, Zonghu
2013-01-01
We consider the multiplicity of nontrivial solutions of the following quasilinear elliptic system -div(|x|(-ap)|∇u|(p-2)∇u) + f₁(x)|u|(p-2) u = (α/(α + β))g(x)|u| (α-2) u|v| (β) + λh₁(x)|u| (γ-2) u + l₁(x), -div(|x|(-ap) |∇v| (p-2)∇v) + f₂(x)|v| (p-2) v = (β/(α + β))g(x)|v|(β-2) v|u|(α) + μh 2(x)|v|(γ-2)v + l 2(x), u(x) > 0, v(x) > 0, x ∈ ℝ(N), where λ, μ > 0, 1 < p < N, 1 < γ < p < α + β < p* = Np/(N-pd), 0 ≤ a < (N - p)/p, a ≤ b < a + 1, d = a + 1 - b > 0. The functions f₁(x), f₂(x), g(x), h₁(x), h₂(x), l₁(x), and l₂(x) satisfy some suitable conditions. We will prove that the problem has at least two nontrivial solutions by using Mountain Pass Theorem and Ekeland's variational principle. PMID:24282377
Spatiotemporal representation of 3D hand trajectory based on beta-elliptic models.
Boubaker, Houcine; Rezzoug, Nasser; Kherallah, Monji; Gorce, Philippe; Alimi, Adel M
2015-01-01
The aim of this paper was to model the hand trajectory during grasping by an extension in 3D of the 2D written language beta-elliptic model. The interest of this model is that it takes into account both geometric and velocity information. The method relies on the decomposition of the task space trajectories in elementary bricks. The latter is characterized by a velocity profile modelled with beta functions and a geometry modelled with elliptic shapes. A data base of grasping movements has been constructed and the errors of reconstruction were assessed (distance and curvature) considering two variations of the beta-elliptic model ('quarter ellipse' and 'two tangents points' method). The results showed that the method based on two tangent points outperforms the quarter ellipse method with average and maximum relative errors of 2.73% and 8.62%, respectively, and a maximum curvature error of 9.26% for the former. This modelling approach can find interesting application to characterize the improvement due to a rehabilitation or teaching process by a quantitative measurement of hand trajectory parameters. PMID:25199025
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.
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 numerical solution of a Cauchy problem for an elliptic equation by Krylov subspaces
NASA Astrophysics Data System (ADS)
Eldén, Lars; Simoncini, Valeria
2009-06-01
We study the numerical solution of a Cauchy problem for a self-adjoint elliptic partial differential equation uzz - Lu = 0 in three space dimensions (x, y, z), where the domain is cylindrical in z. Cauchy data are given on the lower boundary and the boundary values on the upper boundary are sought. The problem is severely ill-posed. The formal solution is written as a hyperbolic cosine function in terms of the two-dimensional elliptic operator L (via its eigenfunction expansion), and it is shown that the solution is stabilized (regularized) if the large eigenvalues are cut off. We suggest a numerical procedure based on the rational Krylov method, where the solution is projected onto a subspace generated using the operator L-1. This means that in each Krylov step, a well-posed two-dimensional elliptic problem involving L is solved. Furthermore, the hyperbolic cosine is evaluated explicitly only for a small symmetric matrix. A stopping criterion for the Krylov recursion is suggested based on the relative change of an approximate residual, which can be computed very cheaply. Two numerical examples are given that demonstrate the accuracy of the method and the efficiency of the stopping criterion.
Yousefi, T.; Paknezhad, M.; Ashjaee, M.; Yazdani, S.
2009-09-15
Steady state two-dimensional natural convection heat transfer from the vertical array of five horizontal isothermal elliptic cylinders with vertical major axis which confined between two adiabatic walls has been studied experimentally. Experiments were carried out using a Mach-Zehnder interferometer. The Rayleigh number based on cylinder major axis was in the range 10{sup 3}{<=}Ra{<=}2.5 x 10{sup 3}, and dimensionless wall spacing 1.5{<=} t/b{<=}9 and infinity. The effect of wall spacing and Rayleigh number on the heat transfer from the individual cylinder and the array were investigated. Experiments are performed for ratio wall spacing to major diameter t/b = 1.5, 2, 2.5, 3, 3.5, 4, 5, 6, 7, 8, 9 and infinity. A correlation based on the experimental data for the average Nusselt number of the array as a function of Ra and t/b is presented in the aforementioned ranges. A relation has been derived for optimum wall spacing at which the Nusselt number of the array attains its maximum value. At optimum wall spacing, approximately 10% increase in the heat transfer from the confined array of elliptic cylinders has been observed as compared to the unconfined case. Also, a heat transfer correlation has been proposed for a single elliptic cylinder with vertical major axis and has been compared with earlier works. (author)
NASA Astrophysics Data System (ADS)
Zhuravlev, V. M.
2016-03-01
We discuss an extension of the theory of multidimensional second-order equations of the elliptic and hyperbolic types related to multidimensional quasilinear autonomous first-order partial differential equations. Calculating the general integrals of these equations allows constructing exact solutions in the form of implicit functions. We establish a connection with hydrodynamic equations. We calculate the number of free functional parameters of the constructed solutions. We especially construct and analyze implicit solutions of the Laplace and d'Alembert equations in a coordinate space of arbitrary finite dimension. In particular, we construct generalized Penrose-Rindler solutions of the d'Alembert equation in 3+1 dimensions.
Elliptical accretion disks in active galactic nuclei
NASA Technical Reports Server (NTRS)
Eracleous, Michael; Livio, Mario; Halpern, Jules P.; Storchi-Bergmann, Thaisa
1995-01-01
We present a calculation of the profiles of emission lines originating in a relativistic, eccentric disk, and show examples of the resulting model profiles. Our calculations are motivated by the fact that in about one-quarter of the double-peaked emission lines observed in radio-loud active galactic nuclei (and in the mildly active nucleus of NGC 1097), the red peak is stronger than the blue peak, which is contrary to the prediction of relativistic, circular disk models. Using the eccentric disk model we fit some of the observed profiles that cannot be fitted with a circular disk model. We propose two possible scenarios for the formation of an eccentric disk in an active galactic nucleus: (a) tidal perturbation of the disk around a supermassive black hole by a smaller binary companion, and (b) formation of an elliptical disk from the debris resulting from the tidal disruption of a star by the central black hole. In the former case we show that the eccentricity can be long-lived because of the presence of the binary companion. In the latter case, although the inner parts of the disk may circularize quickly, we estimate that the outer parts will maintain their eccentricity for times much longer than the local viscous time. We suggest that it may be possible to detect profile variability on much shorter timescales than those ranging from a decade to several centuries by comparing the evolution of the line profile with detailed model predictions. We argue that line-profile variability may also be the most promising discriminant among competing models for the origin of asymmetric, double-peaked emission lines.
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.
On the spectral accuracy of a fictitious domain method for elliptic operators in multi-dimensions
NASA Astrophysics Data System (ADS)
Le Penven, Lionel; Buffat, Marc
2012-10-01
This work is a continuation of the authors efforts to develop high-order numerical methods for solving elliptic problems with complex boundaries using a fictitious domain approach. In a previous paper, a new method was proposed, based on the use of smooth forcing functions with identical shapes, mutually disjoint supports inside the fictitious domain and whose amplitudes play the role of Lagrange multipliers in relation to a discrete set of boundary constraints. For one-dimensional elliptic problems, this method shows spectral accuracy but its implementation in two dimensions seems to be limited to a fourth-order algebraic convergence rate. In this paper, a spectrally accurate formulation is presented for multi-dimensional applications. Instead of being specified locally, the forcing function is defined as a convolution of a mollifier (smooth bump function) and a Lagrange multiplier function (the amplitude of the bump). The multiplier function is then approximated by Fourier series. Using a Fourier Galerkin approximation, the spectral accuracy is demonstrated on a two-dimensional Laplacian problem and on a Stokes flow around a periodic array of cylinders. In the latter, the numerical solution achieves the same high-order accuracy as a Stokes eigenfunction expansion and is much more accurate than the solution obtained with a classical third order finite element approximation using the same number of degrees of freedom.
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.
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.
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
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.
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.
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.
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.
Cluster flight control for fractionated spacecraft on an elliptic orbit
NASA Astrophysics Data System (ADS)
Xu, Ming; Liang, Yuying; Tan, Tian; Wei, Lixin
2016-04-01
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.
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.
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
Numerical solutions of nonlinear STIFF initial value problems by perturbed functional iterations
NASA Technical Reports Server (NTRS)
Dey, S. K.
1982-01-01
Numerical solution of nonlinear stiff initial value problems by a perturbed functional iterative scheme is discussed. The algorithm does not fully linearize the system and requires only the diagonal terms of the Jacobian. Some examples related to chemical kinetics are presented.
Questions on Pure Luminosity Evolution for Elliptical Galaxies
NASA Astrophysics Data System (ADS)
He, Ping; Zhang, Yuan-Zhong
1999-02-01
The explanation for the existence of an excess population of faint blue galaxies (FBGs) has been a mystery for nearly two decades and remains one of the grand astronomical issues to date. Existing models cannot explain all of the observational data, such as galaxy number counts in the optical and infrared passbands and the redshift distributions of galaxies. Here, by modeling the morphological number counts derived from the Hubble Space Telescope, as well as the number counts in optical and infrared passbands and the redshift and color distributions of galaxies obtained from ground-based observations, we show that the ``FBG problem'' cannot be resolved if elliptical galaxies are assumed to have formed in an instantaneous burst of star formation at high redshift with no subsequent star formation events, which is the conventional scenario for formation and evolution of ellipticals. There exist great discrepancies between the observed B-K color distribution and the predicted distribution for ellipticals by such a pure luminosity evolution (PLE) model in the context of the conventional scenario. Neither can the mild evolution (i.e., the star formation events have lasted for a longer time than those of the instantaneous burst and passive evolution since the formation of galaxies) for ellipticals be accepted in the context of PLE assumption. The introduction of dust extinction also cannot save the PLE models. This conclusion holds for each of the three cosmological models under consideration: flat, open, and Λ-dominated. Hence, our investigation suggests that PLE assumption for elliptical galaxies is questionable, and number evolution may be essential for ellipticals.
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.
Modifications of bundles, elliptic integrable systems, and related problems
NASA Astrophysics Data System (ADS)
Zotov, A. V.; Smirnov, A. V.
2013-10-01
We describe a construction of elliptic integrable systems based on bundles with nontrivial characteristic classes, especially attending to the bundle-modification procedure, which relates models corresponding to different characteristic classes. We discuss applications and related problems such as the Knizhnik-Zamolodchikov-Bernard equations, classical and quantum R-matrices, monopoles, spectral duality, Painlevé equations, and the classical-quantum correspondence. For an SL(N,ℂ)-bundle on an elliptic curve with nontrivial characteristic classes, we obtain equations of isomonodromy deformations.
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)
Event-by-Event Elliptic Flow Fluctuations from PHOBOS
NASA Astrophysics Data System (ADS)
Wosiek, B.; Alver, B.; Back, B. B.; Baker, M. D.; Ballintijn, M.; Barton, D. S.; Betts, R. R.; Bickley, A. A.; Bindel, R.; Busza, W.; Carroll, A.; Chai, Z.; Chetluru, V.; Decowski, M. P.; García, E.; Gburek, T.; George, N.; Gulbrandsen, K.; Halliwell, C.; Hamblen, J.; Harnarine, I.; Hauer, M.; Henderson, C.; Hofman, D. J.; Hollis, R. S.; Hołyński, R.; Holzman, B.; Iordanova, A.; Johnson, E.; Kane, J. L.; Khan, N.; Kulinich, P.; Kuo, C. M.; Li, W.; Lin, W. T.; Loizides, C.; Manly, S.; Mignerey, A. C.; Nouicer, R.; Olszewski, A.; Pak, R.; Reed, C.; Richardson, E.; Roland, C.; Roland, G.; Sagerer, J.; Seals, H.; Sedykh, I.; Smith, C. E.; Stankiewicz, M. A.; Steinberg, P.; Stephans, G. S. F.; Sukhanov, A.; Szostak, A.; Tonjes, M. B.; Trzupek, A.; Vale, C.; van Nieuwenhuizen, G. J.; Vaurynovich, S. S.; Verdier, R.; Veres, G. I.; Walters, P.; Wenger, E.; Willhelm, D.; Wolfs, F. L. H.; Woźniak, K.; Wyngaardt, S.; Wysłouch, B.
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 sqrt {sNN}=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.
Elliptic flow in Au+Au collisions at RHIC
NASA Astrophysics Data System (ADS)
Vale, Carla M.; PHOBOS Collaboration; Back, B. B.; Baker, M. D.; Ballintijn, M.; Barton, D. S.; Betts, R. R.; Bickley, A. A.; Bindel, R.; Budzanowski, A.; Busza, W.; Carroll, A.; Decowski, M. P.; García, E.; George, N.; Gulbrandsen, K.; Gushue, S.; Halliwell, C.; Hamblen, J.; Heintzelman, G. A.; Henderson, C.; Hofman, D. J.; Hollis, R. S.; Holynski, R.; Holzman, B.; Iordanova, A.; Johnson, E.; Kane, J. L.; Katzy, J.; Khan, N.; Kucewicz, W.; Kulinich, P.; Kuo, C. M.; Lin, W. T.; Manly, S.; McLeod, D.; Mignerey, A. C.; Ngyuen, M.; Nouicer, R.; Olszewski, A.; Pak, R.; Park, I. C.; Pernegger, H.; Reed, C.; Remsberg, L. P.; Reuter, M.; Roland, C.; Roland, G.; Rosenberg, L.; Sagerer, J.; Sarin, P.; Sawicki, P.; Skulski, W.; Steinberg, P.; Stephans, G. S. F.; Sukhanov, A.; Tang, J.-L.; Tonjes, M. B.; Trzupek, A.; van Nieuwenhuizen, G. J.; Verdier, R.; Veres, G.; Wolfs, F. L. H.; Wosiek, B.; Wozniak, K.; Wuosmaa, A. H.; Wyslouch, B.
2005-04-01
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.
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.
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.
Two-dimensional subsonic compressible flow past elliptic cylinders
NASA Technical Reports Server (NTRS)
Kaplan, Carl
1938-01-01
The method of Poggi is used to calculate, for perfect fluids, the effect of compressibility upon the flow on the surface of an elliptic cylinder at zero angle of attack and with no circulation. The result is expressed in a closed form and represents a rigorous determination of the velocity of the fluid at the surface of the obstacle insofar as the second approximation is concerned. Comparison is made with Hooker's treatment of the same problem according to the method of Janzen and Rayleight and it is found that, for thick elliptic cylinders, the two methods agree very well. The labor of computation is considerably reduced by the present solution.
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.
Analysis of surface pressure distributions on two elliptic missile configurations
NASA Technical Reports Server (NTRS)
Allen, J. M.; Pittman, J. L.
1983-01-01
The state-of-the-art methods for predicting missile aerodynamic characteristics do not accurately predict the loads of missile configurations with bodies of elliptic cross section. An investigation of this problem found significant nonlinear flow disturbance on the windward surface of a 3:1 elliptic body at Mach 2.50 in addition to the nonlinear vortical flows which develop on the leeside. A nonlinear full-potential flow method (NCOREL) was found to provide extremely accurate pressure estimates for attached-flow conditions and the vortex prediction method contained in the state-of-the-art method (NOSEVTX) was shown to accurately calculate body vortices and leeside pressures.
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, Wenjun; Assoufid, Lahsen; Macrander, Albert T.; Ice, Gene E; Tischler, Jonathan
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.
Centaurus A galaxy, type EO peculiar elliptical, also radio source
NASA Technical Reports Server (NTRS)
2002-01-01
Centaurus A galaxy, type EO peculiar elliptical, also radio source. CTIO 4-meter telescope, 1975. NGC 5128, a Type EO peculiar elliptical galaxy in the constellation Centaurus. This galaxy is one of the most luminous and massive galaxies known and is a strong source of both radio and X-ray radiation. Current theories suggest that the nucleus is experiencing giant explosions involving millions of stars and that the dark band across the galactic disk is material being ejected outward. Cerro Toloto 4-meter telescope photo. Photo credit: National Optical Astronomy Observatories
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.
Montoncello, F.; Giovannini, L.; Nizzoli, F.; Vavassori, P.; Grimsditch, M.; Materials Science Division; Univ. di Ferrara; CNISM; CNR-INFM; CIC nanoGUNE Res. Ctr.
2008-06-01
We study the magnetization reversal in elliptical nanodots with the external field applied exactly along the minor (hard) axis. By varying the magnitude of the applied field, several first and second order transitions take place and the system proceeds through magnetic configurations characterized by different symmetry properties. The dynamical matrix method is used to calculate the spin excitations as function of the applied field. This model system allows us to investigate the relationship between the singularities of the magnetization, the presence of soft spin excitations, and the symmetry properties of the static and dynamic magnetization fields. Rules that govern the transitions are formulated.
Wavelength-dependent optical force on elliptical silver cylinders at plasmon resonance.
Rockstuhl, Carsten; Herzig, Hans Peter
2004-09-15
We use rigorous diffraction theory to analyze the force on elliptical cylinders made from silver as a function of the elongation. We find that, when the wires are illuminated at the plasmon wavelength and placed in a highly focused Gaussian beam, they are attracted toward the optical axis if the waist of the laser is behind the wire and repelled if the waist is before the wire. Also, the force distributions of illumination wavelengths smaller and larger than the plasmon wavelength are analyzed. PMID:15460895
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.
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.
NASA Astrophysics Data System (ADS)
Chen, Jeng-Tzong; Lee, Jia-Wei
2013-09-01
In this paper, we focus on the water wave scattering by an array of four elliptical cylinders. The null-field boundary integral equation method (BIEM) is used in conjunction with degenerate kernels and eigenfunctions expansion. The closed-form fundamental solution is expressed in terms of the degenerate kernel containing the Mathieu and the modified Mathieu functions in the elliptical coordinates. Boundary densities are represented by using the eigenfunction expansion. To avoid using the addition theorem to translate the Mathieu functions, the present approach can solve the water wave problem containing multiple elliptical cylinders in a semi-analytical manner by introducing the adaptive observer system. Regarding water wave problems, the phenomena of numerical instability of fictitious frequencies may appear when the BIEM/boundary element method (BEM) is used. Besides, the near-trapped mode for an array of four identical elliptical cylinders is observed in a special layout. Both physical (near-trapped mode) and mathematical (fictitious frequency) resonances simultaneously appear in the present paper for a water wave problem by an array of four identical elliptical cylinders. Two regularization techniques, the combined Helmholtz interior integral equation formulation (CHIEF) method and the Burton and Miller approach, are adopted to alleviate the numerical resonance due to fictitious frequency.
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. PMID:25401561
A Galerkin formulation of the MIB method for three dimensional elliptic interface problems.
Xia, Kelin; Wei, Guo-Wei
2014-10-01
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
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
Three-dimensional elliptic grid generation with fully automatic boundary constraints
NASA Astrophysics Data System (ADS)
Kaul, Upender K.
2010-08-01
A new procedure for generating smooth uniformly clustered three-dimensional structured elliptic grids is presented here which formulates three-dimensional boundary constraints by extending the two-dimensional counterpart presented by the author earlier. This fully automatic procedure obviates the need for manual specification of decay parameters over the six bounding surfaces of a given volume grid. The procedure has been demonstrated here for the Mars Science Laboratory (MSL) geometries such as aeroshell and canopy, as well as the Inflatable Aerodynamic Decelerator (IAD) geometry and a 3D analytically defined geometry. The new procedure also enables generation of single-block grids for such geometries because the automatic boundary constraints permit the decay parameters to evolve as part of the solution to the elliptic grid system of equations. These decay parameters are no longer just constants, as specified in the conventional approach, but functions of generalized coordinate variables over a given bounding surface. Since these decay functions vary over a given boundary, orthogonal grids around any arbitrary simply-connected boundary can be clustered automatically without having to break up the boundaries and the corresponding interior or exterior domains into various blocks for grid generation. The new boundary constraints are not limited to the simply-connected regions only, but can also be formulated around multiply-connected and isolated regions in the interior. The proposed method is superior to other methods of grid generation such as algebraic and hyperbolic techniques in that the grids obtained here are C2 continuous, whereas simple elliptic smoothing of algebraic or hyperbolic grids to enforce C2 continuity destroys the grid clustering near the boundaries. US patent 7231329.
The generalized Dirichlet-Neumann map for linear elliptic PDEs and its numerical implementation
NASA Astrophysics Data System (ADS)
Sifalakis, A. G.; Fokas, A. S.; Fulton, S. R.; Saridakis, Y. G.
2008-09-01
A new approach for analyzing boundary value problems for linear and for integrable nonlinear PDEs was introduced in Fokas [A unified transform method for solving linear and certain nonlinear PDEs, Proc. Roy. Soc. London Ser. A 53 (1997) 1411-1443]. For linear elliptic PDEs, an important aspect of this approach is the characterization of a generalized Dirichlet to Neumann map: given the derivative of the solution along a direction of an arbitrary angle to the boundary, the derivative of the solution perpendicularly to this direction is computed without solving on the interior of the domain. This is based on the analysis of the so-called global relation, an equation which couples known and unknown components of the derivative on the boundary and which is valid for all values of a complex parameter k. A collocation-type numerical method for solving the global relation for the Laplace equation in an arbitrary bounded convex polygon was introduced in Fulton et al. [An analytical method for linear elliptic PDEs and its numerical implementation, J. Comput. Appl. Math. 167 (2004) 465-483]. Here, by choosing a different set of the "collocation points" (values for k), we present a significant improvement of the results in Fulton et al. [An analytical method for linear elliptic PDEs and its numerical implementation, J. Comput. Appl. Math. 167 (2004) 465-483]. The new collocation points lead to well-conditioned collocation methods. Their combination with sine basis functions leads to a collocation matrix whose diagonal blocks are point diagonal matrices yielding efficient implementation of iterative methods; numerical experimentation suggests quadratic convergence. The choice of Chebyshev basis functions leads to higher order convergence, which for regular polygons appear to be exponential.
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
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 Astrophysics Data System (ADS)
Liu, Michael C.; Charlot, Stéphane; Graham, James R.
2000-11-01
We compute theoretical predictions for surface brightness fluctuations (SBFs) of single-burst stellar populations (SSPs) using models optimized for this purpose. We present results over a wide range of ages (from 1 to 17 Gyr) and metallicities (from 1/200 to 2.5 times solar) and for a comprehensive set of ground-based and space-based optical and infrared bandpasses. Our models agree well with existing SBF observations of Milky Way globular clusters and elliptical galaxies. Our results also provide refined theoretical calibrations and k-corrections that are needed to use SBFs as standard candles. We suggest that SBF distance measurements can be improved by (1) using a filter around 1 μm to minimize the influence of stellar population variations, and (2) using the integrated V-K galaxy color instead of V-Ic to calibrate I-band SBF distances. In addition, we show that available SBF observations set useful constraints on current population synthesis models, and we suggest SBF-based tests for future models. The existing SBF data favor particular choices of stellar evolutionary tracks and spectral libraries among the several choices allowed by comparisons based on only the integrated properties of galaxies. Also, the tightness of the empirical I-band SBF calibration as a function of V-Ic galaxy color is a useful constraint. It suggests that the model uncertainties in the lifetimes of the post-main-sequence evolutionary phases are probably less than +/-50% and that the initial mass function in elliptical galaxies is probably not much steeper than that in the solar neighborhood. Finally, we analyze the potential of SBFs for probing unresolved stellar populations in elliptical galaxies. Since SBFs depend on the second moment of the stellar luminosity function, they are sensitive to the brightest giant stars and provide complementary information to commonly used integrated light and spectra. In particular, we find that optical/near-infrared SBFs are much more sensitive to
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.
Adamczyk, L; Adkins, J K; Agakishiev, G; Aggarwal, M M; Ahammed, Z; Alekseev, I; Alford, J; Aparin, A; Arkhipkin, D; Aschenauer, E C; Averichev, G S; Banerjee, A; Bellwied, R; Bhasin, A; Bhati, A K; Bhattarai, P; Bielcik, J; Bielcikova, J; Bland, L C; Bordyuzhin, I G; Bouchet, J; Brandin, A V; Bunzarov, I; Burton, T P; Butterworth, J; Caines, H; Calderón de la Barca Sánchez, M; Campbell, J M; Cebra, D; Cervantes, M C; Chakaberia, I; Chaloupka, P; Chang, Z; Chattopadhyay, S; Chen, J H; Chen, X; Cheng, J; Cherney, M; Christie, W; Contin, G; Crawford, H J; Das, S; De Silva, L C; Debbe, R R; Dedovich, T G; Deng, J; Derevschikov, A A; di Ruzza, B; Didenko, L; Dilks, C; Dong, X; Drachenberg, J L; Draper, J E; Du, C M; Dunkelberger, L E; Dunlop, J C; Efimov, L G; Engelage, J; Eppley, G; Esha, R; Evdokimov, O; Eyser, O; Fatemi, R; Fazio, S; Federic, P; Fedorisin, J; Feng, Z; Filip, P; Fisyak, Y; Flores, C E; Fulek, L; Gagliardi, C A; Garand, D; Geurts, F; Gibson, A; Girard, M; Greiner, L; Grosnick, D; Gunarathne, D S; Guo, Y; Gupta, S; Gupta, A; Guryn, W; Hamad, A; Hamed, A; Haque, R; Harris, J W; He, L; Heppelmann, S; Heppelmann, S; Hirsch, A; Hoffmann, G W; Hofman, D J; Horvat, S; Huang, H Z; Huang, B; Huang, X; Huck, P; Humanic, T J; Igo, G; Jacobs, W W; Jang, H; Jiang, K; Judd, E G; Kabana, S; Kalinkin, D; Kang, K; Kauder, K; Ke, H W; Keane, D; Kechechyan, A; Khan, Z H; Kikola, D P; Kisel, I; Kisiel, A; Koetke, D D; Kollegger, T; Kosarzewski, L K; Kotchenda, L; Kraishan, A F; Kravtsov, P; Krueger, K; Kulakov, I; Kumar, L; Kycia, R A; Lamont, M A C; Landgraf, J M; Landry, K D; Lauret, J; Lebedev, A; Lednicky, R; Lee, J H; Li, W; Li, Y; Li, C; Li, N; Li, Z M; Li, X; Li, X; Lisa, M A; Liu, F; Ljubicic, T; Llope, W J; Lomnitz, M; Longacre, R S; Luo, X; Ma, L; Ma, R; Ma, Y G; Ma, G L; Magdy, N; Majka, R; Manion, A; Margetis, S; Markert, C; Masui, H; Matis, H S; McDonald, D; Meehan, K; Minaev, N G; Mioduszewski, S; Mohanty, B; Mondal, M M; Morozov, D A; Mustafa, M K; Nandi, B K; Nasim, Md; Nayak, T K; Nigmatkulov, G; Nogach, L V; Noh, S Y; Novak, J; Nurushev, S B; Odyniec, G; Ogawa, A; Oh, K; Okorokov, V; Olvitt, D L; Page, B S; Pak, R; Pan, Y X; Pandit, Y; Panebratsev, Y; Pawlik, B; Pei, H; Perkins, C; Peterson, A; Pile, P; Planinic, M; Pluta, J; Poljak, N; Poniatowska, K; Porter, J; Posik, M; Poskanzer, A M; Pruthi, N K; Putschke, J; Qiu, H; Quintero, A; Ramachandran, S; Raniwala, S; Raniwala, R; Ray, R L; Ritter, H G; Roberts, J B; Rogachevskiy, O V; Romero, J L; Roy, A; Ruan, L; Rusnak, J; Rusnakova, O; Sahoo, N R; Sahu, P K; Sakrejda, I; Salur, S; Sandweiss, J; Sarkar, A; Schambach, J; Scharenberg, R P; Schmah, A M; Schmidke, W B; Schmitz, N; Seger, J; Seyboth, P; Shah, N; Shahaliev, E; Shanmuganathan, P V; Shao, M; Sharma, B; Sharma, M K; Shen, W Q; Shi, S S; Shou, Q Y; Sichtermann, E P; Sikora, R; Simko, M; Skoby, M J; Smirnov, D; Smirnov, N; Song, L; Sorensen, P; Spinka, H M; Srivastava, B; Stanislaus, T D S; Stepanov, M; Stock, R; Strikhanov, M; Stringfellow, B; Sumbera, M; Summa, B J; Sun, X; Sun, X M; Sun, Z; Sun, Y; Surrow, B; Svirida, D N; Szelezniak, M A; Tang, Z; Tang, A H; Tarnowsky, T; Tawfik, A N; Thomas, J H; Timmins, A R; Tlusty, D; Tokarev, M; Trentalange, S; Tribble, R E; Tribedy, P; Tripathy, S K; Trzeciak, B A; Tsai, O D; Ullrich, T; Underwood, D G; Upsal, I; Van Buren, G; van Nieuwenhuizen, G; Vandenbroucke, M; Varma, R; Vasiliev, A N; Vertesi, R; Videbaek, F; Viyogi, Y P; Vokal, S; Voloshin, S A; Vossen, A; Wang, F; Wang, Y; Wang, H; Wang, J S; Wang, Y; Wang, G; Webb, G; Webb, J C; Wen, L; Westfall, G D; Wieman, H; Wissink, S W; Witt, R; Wu, Y F; Xiao, Z; Xie, W; Xin, K; Xu, Y F; Xu, N; Xu, Z; Xu, Q H; Xu, H; Yang, Y; Yang, Y; Yang, C; Yang, S; Yang, Q; Ye, Z; Yepes, P; Yi, L; Yip, K; Yoo, I-K; Yu, N; Zbroszczyk, H; Zha, W; Zhang, X P; Zhang, J B; Zhang, J; Zhang, Z; Zhang, S; Zhang, Y; Zhang, J L; Zhao, F; Zhao, J; Zhong, C; Zhou, L; Zhu, X; Zoulkarneeva, Y; Zyzak, M
2015-06-26
We present measurements of π(-) and π(+) elliptic flow, v(2), at midrapidity in Au+Au collisions at √[s(NN)]=200, 62.4, 39, 27, 19.6, 11.5, and 7.7 GeV, as a function of event-by-event charge asymmetry, A(ch), based on data from the STAR experiment at RHIC. We find that π(-) (π(+)) elliptic flow linearly increases (decreases) with charge asymmetry for most centrality bins at √[s(NN)]=27 GeV and higher. At √[s(NN)]=200 GeV, the slope of the difference of v(2) between π(-) and π(+) as a function of A(ch) exhibits a centrality dependence, which is qualitatively similar to calculations that incorporate a chiral magnetic wave effect. Similar centrality dependence is also observed at lower energies. PMID:26197122
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.
NASA Astrophysics Data System (ADS)
Adamczyk, L.; Adkins, J. K.; Agakishiev, G.; Aggarwal, M. M.; Ahammed, Z.; Alekseev, I.; Alford, J.; Aparin, A.; Arkhipkin, D.; Aschenauer, E. C.; Averichev, G. S.; Banerjee, A.; Bellwied, R.; Bhasin, A.; Bhati, A. K.; Bhattarai, P.; Bielcik, J.; Bielcikova, J.; Bland, L. C.; Bordyuzhin, I. G.; Bouchet, J.; Brandin, A. V.; Bunzarov, I.; Burton, T. P.; Butterworth, J.; Caines, H.; Calderón de la Barca Sánchez, M.; Campbell, J. M.; Cebra, D.; Cervantes, M. C.; Chakaberia, I.; Chaloupka, P.; Chang, Z.; Chattopadhyay, S.; Chen, J. H.; Chen, X.; Cheng, J.; Cherney, M.; Christie, W.; Contin, G.; Crawford, H. J.; Das, S.; De Silva, L. C.; Debbe, R. R.; Dedovich, T. G.; Deng, J.; Derevschikov, A. A.; di Ruzza, B.; Didenko, L.; Dilks, C.; Dong, X.; Drachenberg, J. L.; Draper, J. E.; Du, C. M.; Dunkelberger, L. E.; Dunlop, J. C.; Efimov, L. G.; Engelage, J.; Eppley, G.; Esha, R.; Evdokimov, O.; Eyser, O.; Fatemi, R.; Fazio, S.; Federic, P.; Fedorisin, J.; Feng, Z.; Filip, P.; Fisyak, Y.; Flores, C. E.; Fulek, L.; Gagliardi, C. A.; Garand, D.; Geurts, F.; Gibson, A.; Girard, M.; Greiner, L.; Grosnick, D.; Gunarathne, D. S.; Guo, Y.; Gupta, S.; Gupta, A.; Guryn, W.; Hamad, A.; Hamed, A.; Haque, R.; Harris, J. W.; He, L.; Heppelmann, S.; Heppelmann, S.; Hirsch, A.; Hoffmann, G. W.; Hofman, D. J.; Horvat, S.; Huang, H. Z.; Huang, B.; Huang, X.; Huck, P.; Humanic, T. J.; Igo, G.; Jacobs, W. W.; Jang, H.; Jiang, K.; Judd, E. G.; Kabana, S.; Kalinkin, D.; Kang, K.; Kauder, K.; Ke, H. W.; Keane, D.; Kechechyan, A.; Khan, Z. H.; Kikola, D. P.; Kisel, I.; Kisiel, A.; Koetke, D. D.; Kollegger, T.; Kosarzewski, L. K.; Kotchenda, L.; Kraishan, A. F.; Kravtsov, P.; Krueger, K.; Kulakov, I.; Kumar, L.; Kycia, R. A.; Lamont, M. A. C.; Landgraf, J. M.; Landry, K. D.; Lauret, J.; Lebedev, A.; Lednicky, R.; Lee, J. H.; Li, W.; Li, Y.; Li, C.; Li, N.; Li, Z. M.; Li, X.; Li, X.; Lisa, M. A.; Liu, F.; Ljubicic, T.; Llope, W. J.; Lomnitz, M.; Longacre, R. S.; Luo, X.; Ma, L.; Ma, R.; Ma, Y. G.; Ma, G. L.; Magdy, N.; Majka, R.; Manion, A.; Margetis, S.; Markert, C.; Masui, H.; Matis, H. S.; McDonald, D.; Meehan, K.; Minaev, N. G.; Mioduszewski, S.; Mohanty, B.; Mondal, M. M.; Morozov, D. A.; Mustafa, M. K.; Nandi, B. K.; Nasim, Md.; Nayak, T. K.; Nigmatkulov, G.; Nogach, L. V.; Noh, S. Y.; Novak, J.; Nurushev, S. B.; Odyniec, G.; Ogawa, A.; Oh, K.; Okorokov, V.; Olvitt, D. L.; Page, B. S.; Pak, R.; Pan, Y. X.; Pandit, Y.; Panebratsev, Y.; Pawlik, B.; Pei, H.; Perkins, C.; Peterson, A.; Pile, P.; Planinic, M.; Pluta, J.; Poljak, N.; Poniatowska, K.; Porter, J.; Posik, M.; Poskanzer, A. M.; Pruthi, N. K.; Putschke, J.; Qiu, H.; Quintero, A.; Ramachandran, S.; Raniwala, S.; Raniwala, R.; Ray, R. L.; Ritter, H. G.; Roberts, J. B.; Rogachevskiy, O. V.; Romero, J. L.; Roy, A.; Ruan, L.; Rusnak, J.; Rusnakova, O.; Sahoo, N. R.; Sahu, P. K.; Sakrejda, I.; Salur, S.; Sandweiss, J.; Sarkar, A.; Schambach, J.; Scharenberg, R. P.; Schmah, A. M.; Schmidke, W. B.; Schmitz, N.; Seger, J.; Seyboth, P.; Shah, N.; Shahaliev, E.; Shanmuganathan, P. V.; Shao, M.; Sharma, B.; Sharma, M. K.; Shen, W. Q.; Shi, S. S.; Shou, Q. Y.; Sichtermann, E. P.; Sikora, R.; Simko, M.; Skoby, M. J.; Smirnov, D.; Smirnov, N.; Song, L.; Sorensen, P.; Spinka, H. M.; Srivastava, B.; Stanislaus, T. D. S.; Stepanov, M.; Stock, R.; Strikhanov, M.; Stringfellow, B.; Sumbera, M.; Summa, B. J.; Sun, X.; Sun, X. M.; Sun, Z.; Sun, Y.; Surrow, B.; Svirida, D. N.; Szelezniak, M. A.; Tang, Z.; Tang, A. H.; Tarnowsky, T.; Tawfik, A. N.; Thomas, J. H.; Timmins, A. R.; Tlusty, D.; Tokarev, M.; Trentalange, S.; Tribble, R. E.; Tribedy, P.; Tripathy, S. K.; Trzeciak, B. A.; Tsai, O. D.; Ullrich, T.; Underwood, D. G.; Upsal, I.; Van Buren, G.; van Nieuwenhuizen, G.; Vandenbroucke, M.; Varma, R.; Vasiliev, A. N.; Vertesi, R.; Videbaek, F.; Viyogi, Y. P.; Vokal, S.; Voloshin, S. A.; Vossen, A.; Wang, F.; Wang, Y.; Wang, H.; Wang, J. S.; Wang, Y.; Wang, G.; Webb, G.; Webb, J. C.; Wen, L.; Westfall, G. D.; Wieman, H.; Wissink, S. W.; Witt, R.; Wu, Y. F.; Xiao, Z.; Xie, W.; Xin, K.; Xu, Y. F.; Xu, N.; Xu, Z.; Xu, Q. H.; Xu, H.; Yang, Y.; Yang, Y.; Yang, C.; Yang, S.; Yang, Q.; Ye, Z.; Yepes, P.; Yi, L.; Yip, K.; Yoo, I.-K.; Yu, N.; Zbroszczyk, H.; Zha, W.; Zhang, X. P.; Zhang, J. B.; Zhang, J.; Zhang, Z.; Zhang, S.; Zhang, Y.; Zhang, J. L.; Zhao, F.; Zhao, J.; Zhong, C.; Zhou, L.; Zhu, X.; Zoulkarneeva, Y.; Zyzak, M.; STAR Collaboration
2015-06-01
We present measurements of π- and π+ elliptic flow, v2, at midrapidity in Au +Au collisions at √{sNN }=200 , 62.4, 39, 27, 19.6, 11.5, and 7.7 GeV, as a function of event-by-event charge asymmetry, Ach, based on data from the STAR experiment at RHIC. We find that π- (π+) elliptic flow linearly increases (decreases) with charge asymmetry for most centrality bins at √{sNN }=27 GeV and higher. At √{sNN }=200 GeV , the slope of the difference of v2 between π- and π+ as a function of Ach exhibits a centrality dependence, which is qualitatively similar to calculations that incorporate a chiral magnetic wave effect. Similar centrality dependence is also observed at lower energies.
Dwarf Elliptical Galaxies in the Coma Cluster Core
NASA Astrophysics Data System (ADS)
Secker, Jeff
1995-12-01
I have analyzed deep R- and B-band CCD images of the central ~ 700 arcmin(2) of the Coma cluster (Abell 1656, v = 7000 km/s, richness-class 2), using a statistically rigorous and automated method for the detection, photometry and classification of faint objects on digital images. The dwarf elliptical (dE) galaxies are confined to a well-defined sequence in the color range given by 0.7 <= (B-R) <= 1.9 mag; within this interval and complete to R = 22.5 mag, there are 2535 dE candidates in the cluster core, and 694 objects on the associated control field (2.57x less area). I detected a significant metallicity gradient in the radial distribution of dE galaxies, which goes as Z ~ R(-0.32) outwards from the cluster center at NGC 4874. As well, there is a strong color-luminosity correlation, in the sense that more luminous dE galaxies are redder in the mean. These observations are consistent with a model in which the intracluster gas exerted a confinement pressure (greatest near the cluster core), impeding the outflow of supernovae-driven metal-rich gas from the young dE galaxies. The spatial distribution of faint dEs is well fit by a standard King model with a core radius R_c = 18.7 arcmin ( =~ 0.44 Mpc), significantly larger than found for the brightest dEs and giant cluster galaxies, and consistent with tidal disruption of faint dEs in the dense cluster core. The composite luminosity function for Coma galaxies was modeled as the sum of a log-normal distribution for the giant galaxies and a Schechter function for the dE galaxies. Decomposing the galaxy luminosity function in this manner, I found that the early-type dwarf-to-giant ratio (EDGR) for the Coma cluster core is identical with that of the Virgo cluster. I proposed that the presence of substructure is an important factor in determining the cluster's EDGR, since during the merger of two or more richness-class 1 galaxy clusters, the total number of dwarf and giant galaxies will be conserved. Thus, this low EDGR
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.
Numerical Investigation of Viscous Dissipation in Elliptic Microducts
NASA Astrophysics Data System (ADS)
Vocale, P.; Puccetti, G.; Morini, G. L.; Spiga, M.
2014-11-01
In this work a numerical analysis of heat transfer in elliptical microchannels heated at constant and uniform heat flux is presented. A gaseous flow has been considered, in laminar steady state condition, in hydrodynamically and thermally fully developed forced convection, accounting for the rarefaction effects. The velocity and temperature distributions have been determined in the elliptic cross section, for different values of aspect ratio, Knudsen number and Brinkman number, solving the Navier-Stokes and energy equations within the Comsol Multiphysics® environment. The numerical procedure has been validated resorting to data available in literature for slip flow in elliptic cross sections with Br =0 and for slip flow in circular ducts with Br > 0. The comparison between numerical results and data available in literature shows a perfect agreement. The velocity and temperature distributions thus found have been used to calculate the average Nusselt number in the cross section. The numerical results for Nusselt number are presented in terms of rarefaction degree (Knudsen number), of viscous dissipation (Brinkman number), and of the aspect ratio. The results point out that the thermal fluid behavior is significantly affected by the viscous dissipation for low rarefaction degrees and for aspect ratios of the elliptic cross-section higher than 0.2.
Elliptic instability in a Rankine vortex with axial flow
NASA Astrophysics Data System (ADS)
Lacaze, Laurent; Birbaud, Anne-Laure; Le Dizès, Stéphane
2005-01-01
The elliptic instability of a Rankine vortex with axial flow subject to a weak strain field perpendicular to its axis is analyzed by asymptotic methods in the limit of small strain rate. General unstable modes associated with resonant Kelvin modes of arbitrary azimuthal wavenumbers are considered. Both the effects of axial flow and viscosity are analyzed in details.
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 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.
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.
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.
Triangularity effects on the collisional diffusion for elliptic tokamaks
NASA Astrophysics Data System (ADS)
Martín, Pablo; Castro, Enrique
2015-09-01
The effect of ellipticity and triangularity will be analyzed for axisymmetric tokamak in the collisional regime. Analytic forms for the magnetic field cross sections are taken from those derived recently by other authors. Analytic results can be obtained in elliptic plasmas with triangularity by using an special system of tokamak coordinates previously published. Our results show that triangularities smaller than 0.6 increase confinement for ellipticities in the range 1.2-2. This behavior happens for negative and positive triangularities, however this effect is stronger for negative than for positive triangularities. The maximum diffusion velocity is not obtained for zero triangularity, but for small negative triangularities. Ellipticity is also very important in confinement, but the effect of triangularity seems to be more important. High electric inductive fields increase confinement, though this field is difficult to modify once the tokamak has been built. The analytic form of the current produced by this field is like that of a weak Ware pinch with an additional factor, which weakens the effect by an order of magnitude. The dependence of the triangularity effect with the Shafranov shift is also analyzed.
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.
Shielding of elliptic guides with direct sight to the moderator
NASA Astrophysics Data System (ADS)
Böni, P.; Grünauer, F.; Schanzer, C.
2010-12-01
With the invention of elliptic guides, the neutron flux at instruments can be increased significantly even without sacrificing resolution. In addition, the phase space homogeneity of the delivered neutrons is improved. Using superpolished metal substrates that are coated with supermirror, it is now possible to install neutron guides close to the moderator thus decreasing the illumination losses of the guide and reducing the background because the entrance window of the elliptic guide can be decreased significantly. We have performed Monte Carlo simulations using the program package MCNP5 to calculate the shielding requirements for an elliptic guide geometry assuming that the initial guide section elements are composed of Al substrates. We show that shielding made from heavy concrete shields the neutron and γ-radiation effectively to levels below 1 μSv/h. It is shown that the elliptic geometry allows to match the phase space of the transported neutrons easily to the needs of the instruments to be installed. In particular it is possible to maintain a compact phase space during the transport of the neutrons because the reflection losses are strongly reduced.
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.
The elliptic wing based on the potential theory
NASA Technical Reports Server (NTRS)
Krienes, Klaus
1941-01-01
This article is intended as a contribution to the theory of the lifting surface. The aerodynamics of the elliptic wing in straight and oblique flow are explored on the basis of potential theory. The foundation of the calculation is the linearized theory of the acceleration potential in which all small quantities of higher order are disregarded.
Buckling characteristic of multi-laminated composite elliptical cylindrical shells
NASA Astrophysics Data System (ADS)
Kassegne, Samuel Kinde; Chun, Kyoung-Sik
2015-03-01
Fiber-reinforced composite materials continue to experience increased adoption in aerospace, marine, automobile, and civil structures due to their high specific strength, high stiffness, and light weight. This increased use has been accompanied by applications involving non-traditional configurations such as compression members with elliptical cross-sections. To model such shapes, we develop and report an improved generalized shell element called 4EAS-FS through a combination of enhanced assumed strain and the substitute shear strain fields. A flat shell element has been developed by combining a membrane element with drilling degree-of-freedom and a plate bending element. We use the element developed to determine specifically buckling loads and mode shapes of composite laminates with elliptical cross-section including transverse shear deformations. The combined influence of shell geometry and elliptical cross-sectional parameters, fiber angle, and lay-up on the buckling loads of an elliptical cylinder is examined. It is hoped that the critical buckling loads and mode shapes presented here will serve as a benchmark for future investigations.
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.
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
Reconfigurable optical spectra from perturbations on elliptical whispering gallery resonances.
Mohageg, Makan; Maleki, Lute
2008-02-01
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. PMID:18542283
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.
Line Strength Gradients in Elliptical and Brightest Cluster Galaxies
NASA Astrophysics Data System (ADS)
Fisher, David; Franx, Marijn; Illingworth, Garth
1995-07-01
Line strengths and their gradients in Mg, Fe, and Hβ have been determined for seven elliptical and nine brightest cluster galaxies (BCGs) in order to study their stellar populations and investigate their relationship to one another. We find that BCGs follow the same relationship between central Mg b line strength and central velocity dispersion found for elliptical galaxies. Brightest cluster galaxies are in agreement with the known trend toward more massive elliptical galaxies having larger [Mg/Fe] ratios, while the internal gradients within our BCG and E galaxies are consistent with a roughly constant [Mg/Fe] ratio. We find that a correlation exists between the central [Mg/Fe] ratio and average Hβ line strength in the sense that both BCG and elliptical galaxies with larger [Mg/Fe] ratios have lower
MIB method for elliptic equations with multi-material interfaces.
Xia, Kelin; Zhan, Meng; Wei, Guo-Wei
2011-06-01
Elliptic partial differential equations (PDEs) are widely used to model real-world problems. Due to the heterogeneous characteristics of many naturally occurring materials and man-made structures, devices, and equipments, one frequently needs to solve elliptic PDEs with discontinuous coefficients and singular sources. The development of high-order elliptic interface schemes has been an active research field for decades. However, challenges remain in the construction of high-order schemes and particularly, for nonsmooth interfaces, i.e., interfaces with geometric singularities. The challenge of geometric singularities is amplified when they are originated from two or more material interfaces joining together or crossing each other. High-order methods for elliptic equations with multi-material interfaces have not been reported in the literature to our knowledge. The present work develops matched interface and boundary (MIB) method based schemes for solving two-dimensional (2D) elliptic PDEs with geometric singularities of multi-material interfaces. A number of new MIB schemes are constructed to account for all possible topological variations due to two-material interfaces. The geometric singularities of three-material interfaces are significantly more difficult to handle. Three new MIB schemes are designed to handle a variety of geometric situations and topological variations, although not all of them. The performance of the proposed new MIB schemes is validated by numerical experiments with a wide range of coefficient contrasts, geometric singularities, and solution types. Extensive numerical studies confirm the designed second order accuracy of the MIB method for multi-material interfaces, including a case where the derivative of the solution diverges. PMID:21691433
From Flat Substrate to Elliptical KB Mirror by Profile Coating
Liu Chian; Conley, R.; Assoufid, L.; Cai, Z.; Qian, J.; Macrander, A.T.
2004-05-12
For microfocusing x-ray mirrors, an elliptical shape is essential for aberration-free optics. However, it is difficult to polish elliptical mirrors to x-ray-quality smoothness. Profile coatings have been applied on both cylindrical and flat Si substrates to make the desired elliptical shape. In a profile-coating process, the sputter source power is kept constant, while the substrate is passed over a contoured mask at a constant speed to obtain a desired profile along the direction perpendicular to the substrate-moving direction. The shape of the contour was derived from a desired profile and the thickness distribution of the coating material at the substrate level. The thickness distribution was measured on films coated on Si wafers using a spectroscopic ellipsometer with computer-controlled X-Y translation stages. The mirror coating profile is determined from the difference between the ideal surface figure of a focusing ellipse and the surface figure obtained from a long trace profiler measurement on the substrate. The number of passes and the moving speed of the substrate are determined according to the required thickness and the growth-rate calibration of a test run. A KB mirror pair was made using Au as a coating material and cylindrically polished mirrors as substrates. Synchrotron x-ray results using this KB mirror pair showed a focused spot size of 0.4 x 0.4 {mu}m2. This technique has also been applied for making elliptical KB mirrors from flat Si substrates. The challenges and solutions associated with elliptical profile coating on flat substrates will be discussed.
Optimization of an inclined elliptic impinging jet with cross flow for enhancing heat transfer
NASA Astrophysics Data System (ADS)
Heo, Man-Woong; Lee, Ki-Don; Kim, Kwang-Yong
2011-06-01
This work presents a parametric study and optimization of a single impinging jet with cross flow to enhance heat transfer with two design variables. The fluid flow and heat transfer have been analyzed using three-dimensional compressible Reynolds-averaged Navier-Stokes equations with a uniform heat flux condition being applied to the impingement plate. The aspect ratio of the elliptic jet hole and the angle of inclination of the jet nozzle are chosen as the two design variables, and the area-averaged Nusselt number on a limited target plate is set as the objective function. The effects of the design variables on the heat transfer performance have been evaluated, and the objective function has been found to be more sensitive to the angle of inclination of the jet nozzle than to the aspect ratio of the elliptic jet hole. The optimization has been performed by using the radial basis neural network model. Through the optimization, the area-averaged Nusselt number increased by 7.89% compared to that under the reference geometry.
Hubble Space Telescope Photometry for the Halo Stars in the Leo Elliptical NGC 3377
NASA Astrophysics Data System (ADS)
Harris, William E.; Harris, Gretchen L. H.; Layden, Andrew C.; Stetson, Peter B.
2007-07-01
We have used the ACS camera on HST to obtain (V,I) photometry for 57,000 red giant stars in the halo of the Leo elliptical NGC 3377, an intermediate-luminosity elliptical. We use this sample of stars to derive the metallicity distribution function (MDF) for its halo field stars and comment on its chemical evolution history compared with both larger and smaller E galaxies. Our ACS WFC field spans a radial range extending from 4 to 18 kpc projected distance from the center of NGC 3377 and thus covers a significant portion of this galaxy's halo. We find that the MDF is broad, reaching a peak at log(Z/Zsolar)~=-0.6, but containing virtually no stars more metal-poor than log(Z/Zsolar)=-1.5. It may, in addition, have relatively few stars more metal-rich than log(Z/Zsolar)~=-0.3, although interpretation of the high-metallicity end of the MDF is limited by photometric completeness that affects the detection of the reddest, most metal-rich stars. NGC 3377 appears to have an enrichment history intermediate between those of normal dwarf ellipticals and the much larger giants. As yet, we find no clear evidence that the halo of NGC 3377 contains a significant population of ``young'' (<3 Gyr) stars. 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 9811. Support for this work was provided in part by NASA through grant HST-GO-09811.01-A from the Space Telescope Science Institute, under NASA contract NAS 5-26555.
Hubble Space Telescope Counts of Elliptical Galaxies: Constraints on Cosmological Models?
NASA Astrophysics Data System (ADS)
Driver, Simon P.; Windhorst, Rogier A.; Phillipps, Steven; Bristow, Paul D.
1996-04-01
The interpretation of galaxy number counts in terms of cosmological models is fraught with difficulty because of uncertainties in the overall galaxy population (mix of morphological types, luminosity functions, etc.) and in the observations (loss of low surface brightness images, image blending, etc.). Many of these can be overcome if we use deep high- resolution imaging of a single class of high surface brightness galaxies, whose evolution is thought to be fairly well understood. This is now possible by selecting elliptical and S0 galaxies using Hubble Space Telescope images from the Medium Deep Survey and other ultradeep Wide Field and Planetary Camera 2 images. In the present paper, we examine whether such data can be used to discriminate between open and closed universes, or between conventional cosmological models and those dominated by a cosmological constant. We find, based on the currently available data, that unless elliptical galaxies undergo very strong merging since z ~ 1 (and/or very large errors exist in the morphological classifications), then flat models dominated by a cosmological constant are ruled out. However, both an Einstein-de Sitter ({OMEGA}_0_ = 1) model with standard passive stellar evolution and an open ({OMEGA}_0_ = 0.05) model with no net evolution (i.e., canceling stellar and dynamical evolution) predict virtually identical elliptical and S0 galaxy counts. Based on these findings and the recent reportings of H_0_ ~ 80 km s^- 1^ Mpc^-1^, we find that the maximum acceptable age of the universe is 13.3 Gyr, and a value of <= 9 Gyr is favored. A flat ({LAMBDA} not equal to 0) universe is therefore not a viable solution to the H_0_/globular cluster age problem.
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.
NASA Technical Reports Server (NTRS)
Thames, F. C.
1982-01-01
A three-dimensional elliptic solver technique is utilized to generate surface-fitted coordinates about wing/wing-tip configurations. The method is applicable to wings of arbitrary section profile and camber, leading-edge sweep, taper ratio, and spanwise thickness variation. The basic theory of three-dimensional elliptic mappings is developed along with a method to compute interior coordinate control functions. Examples of grids generated about several wing/wing-tip geometries are given. A 49 x 33 x 17 grid requires about 3 minutes of CPU time on a CYBER 203 computer.
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.
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.
The distance to the giant elliptical galaxy NGC 5128
NASA Astrophysics Data System (ADS)
Rejkuba, M.
2004-01-01
The distance to NGC 5128, the central galaxy of the Centaurus group and the nearest giant elliptical to us, has been determined using two independent distance indicators: the Mira period-luminosity (PL) relation and the luminosity of the tip of the red giant branch (RGB). The data were taken at two different locations in the halo of NGC 5128 with the ISAAC near-IR array on ESO VLT. From more than 20 hours of observations with ISAAC a very deep Ks-band luminosity function was constructed. The tip of the RGB is detected at Ks=21.24 ± 0.05 mag. Using an empirical calibration of the K-band RGB tip magnitude, and assuming a mean metallicity of [M/ H]=-0.4 dex and reddening of E(B-V)=0.11, a distance modulus of NGC 5128 of (m-M)0=27.87 ± 0.16 was derived. The comparison of the H-band RGB tip magnitude in NGC 5128 and the Galactic Bulge implies a distance modulus of NGC 5128 of (m-M)0=27.9 ± 0.2 in good agreement with the K-band RGB tip measurement. The inner halo field has larger photometric errors, brighter completeness limits and a larger number of blends. Thus the RGB tip feature is not as sharp as in the outer halo field. The population of stars above the tip of the RGB amounts to 2176 stars in the outer halo field (Field 1) and 6072 stars in the inner halo field (Field 2). The large majority of these sources belong to the asymptotic giant branch (AGB) population in NGC 5128 with numerous long period variables. Mira variables were used to determine the distance of NGC 5128 from a period-luminosity relation calibrated using the Hipparcos parallaxes and LMC Mira period-luminosity relation in the K-band. This is the first Mira period-luminosity relation outside the Local Group. A distance modulus of 27.96 ± 0.11 was derived, adopting the LMC distance modulus of 18.50 ± 0.04. The mean of the two methods yields a distance modulus to NGC 5128 of 27.92 ± 0.19 corresponding to D=3.84 ± 0.35 Mpc. Based on observations collected at the European Southern Observatory
Near-field structure of underexpanded elliptic jets
NASA Astrophysics Data System (ADS)
Mitchell, Daniel M.; Honnery, Damon R.; Soria, Julio
2013-07-01
Quantitative measurements of velocity for a low aspect ratio underexpanded elliptical jet are presented. Four jets at nozzle pressure ratios NPR = [2.2, 2.6, 3.4, 4.2] are studied for a smoothly contoured elliptical nozzle with an aspect ratio a/ b = 2. High-resolution planar particle image velocimetry is used to extract information about the velocity fields and turbulent statistics. All four jets display the expected axis switching phenomenon, with the axis switching gaining strength with increasing pressure ratio. Evidence of regular reflection is seen for jets at pressure ratios of 2.6 and above. Measurements of fluctuating velocity indicate an oscillatory flapping mode in the minor axis plane for all but the highest pressure ratio. At the highest pressure ratio of NPR = 4.2, there is evidence of a cut-and-connect vortex bifurcation previously only observed for jets with higher aspect ratio.
A New Elliptical Model for Device-Free Localization.
Lei, Qian; Zhang, Haijian; Sun, Hong; Tang, Linling
2016-01-01
Device-free localization (DFL) based on wireless sensor networks (WSNs) is expected to detect and locate a person without the need for any wireless devices. Radio tomographic imaging (RTI) has attracted wide attention from researchers as an emerging important technology in WSNs. However, there is much room for improvement in localization estimation accuracy. In this paper, we propose a geometry-based elliptical model and adopt the orthogonal matching pursuit (OMP) algorithm. The new elliptical model uses not only line-of-sight information, but also non-line-of-sight information, which divides one ellipse into several areas with different weights. Meanwhile the OMP, which can eliminate extra bright spots in image reconstruction, is used to derive an image estimator. The experimental results demonstrate that the proposed algorithm could improve the accuracy of positioning by up to 23.8% for one person and 33.3% for two persons over some state-of-the-art RTI methods. PMID:27110788
Parallel computation with adaptive methods for elliptic and hyperbolic systems
Benantar, M.; Biswas, R.; Flaherty, J.E.; Shephard, M.S.
1990-01-01
We consider the solution of two dimensional vector systems of elliptic and hyperbolic partial differential equations on a shared memory parallel computer. For elliptic problems, the spatial domain is discretized using a finite quadtree mesh generation procedure and the differential system is discretized by a finite element-Galerkin technique with a piecewise linear polynomial basis. Resulting linear algebraic systems are solved using the conjugate gradient technique with element-by-element and symmetric successive over-relaxation preconditioners. Stiffness matrix assembly and linear system solutions are processed in parallel with computations scheduled on noncontiguous quadrants of the tree in order to minimize process synchronization. Determining noncontiguous regions by coloring the regular finite quadtree structure is far simpler than coloring elements of the unstructured mesh that the finite quadtree procedure generates. We describe linear-time complexity coloring procedures that use six and eight colors.
Isothermal elastohydrodynamic lubrication of point contacts. II - Ellipticity parameter results
NASA Technical Reports Server (NTRS)
Hamrock, B. J.; Dowson, D.
1975-01-01
A numerical solution of the isothermal elastohydrodynamic problem for point contacts has been presented which reproduces all the essential features of the previously reported experimental observations based upon optical interferometry. In particular, the two 'side lobes' in which minimum film thickness regions occur are shown to emerge in the theoretical solutions. The influence of the ellipticity parameter upon solutions to the point contact problem has been explored in the present paper. The ellipticity parameter (k) was varied from one (a ball on a plate) to eight (a configuration approaching line contact), and it has been shown that both the central and minimum film thicknesses can be related to the well known line contact solutions by remarkably simple expressions involving either (k) or the effective radius of curvature ratio (Ry/Rx).
The Multi-Talented Elliptical Galaxy NGC1052
NASA Astrophysics Data System (ADS)
Irwin, Jimmy
2004-09-01
We propose to observe the nearby elliptical galaxy NGC1052 for 60 ksec with Chandra to address a variety of issues. First, we will study the interaction between the hot X-ray gas and radio jets/lobes present in this galaxy. A previous short (2 ksec) Chandra observation indicated extended soft emission at the location of the radio emission. Second, NGC1052 is the prototypical LINER galaxy, and this Chandra observation will constrain competing spectral models for the origin of LINER X-ray emission. Finally, we will constrain the X-ray binary--globular cluster connection in elliptical galaxies. NGC1052 contains a large number of globular clusters per unit light, and will be quite useful for determining if all X-ray binaries are formed within globular clusters.
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
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
The missing mass in clusters of galaxies and elliptical galaxies
NASA Technical Reports Server (NTRS)
Mushotzky, Richard F.
1991-01-01
We review the available data for the existence of dark matter in clusters of galaxies and elliptical galaxies. While the amount of dark matter in clusters is not well determined, both the X-ray and optical data show that more than 50 percent of the total mass must be dark. There is in general fair agreement in the binding mass estimates between the X-ray and optical techniques, but there is not detailed agreement on the form of the potential or the distribution of dark matter. The X-ray spectral and spatial observations of elliptical galaxies demonstrate that dark matter is also required in these objects and that it must be considerably more extended than the stellar distribution.
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.
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.
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
A New Elliptical Model for Device-Free Localization
Lei, Qian; Zhang, Haijian; Sun, Hong; Tang, Linling
2016-01-01
Device-free localization (DFL) based on wireless sensor networks (WSNs) is expected to detect and locate a person without the need for any wireless devices. Radio tomographic imaging (RTI) has attracted wide attention from researchers as an emerging important technology in WSNs. However, there is much room for improvement in localization estimation accuracy. In this paper, we propose a geometry-based elliptical model and adopt the orthogonal matching pursuit (OMP) algorithm. The new elliptical model uses not only line-of-sight information, but also non-line-of-sight information, which divides one ellipse into several areas with different weights. Meanwhile the OMP, which can eliminate extra bright spots in image reconstruction, is used to derive an image estimator. The experimental results demonstrate that the proposed algorithm could improve the accuracy of positioning by up to 23.8% for one person and 33.3% for two persons over some state-of-the-art RTI methods. PMID:27110788
Two-center black holes, qubits, and elliptic curves
NASA Astrophysics Data System (ADS)
Lévay, Péter
2011-07-01
We relate the U-duality invariants characterizing two-center extremal black-hole solutions in the stu, st2, and t3 models of N=2, d=4 supergravity to the basic invariants used to characterize entanglement classes of four-qubit systems. For the elementary example of a D0D4-D2D6 composite in the t3 model we illustrate how these entanglement invariants are related to some of the physical properties of the two-center solution. Next we show that it is possible to associate elliptic curves to charge configurations of two-center composites. The hyperdeterminant of the hypercube, a four-qubit polynomial invariant of order 24 with 2 894 276 terms, is featuring the j invariant of the elliptic curve. We present some evidence that this quantity and its straightforward generalization should play an important role in the physics of two-center solutions.
Elliptical x-ray microprobe mirrors by differential deposition
Ice, Gene E.; Chung, Jin-Seok; Tischler, Jonathan Z.; Lunt, Andrew; Assoufid, Lahsen
2000-07-01
A differential coating method is described for fabricating high-performance x-ray microfocusing mirrors. With this method, the figure of ultrasmooth spherical mirrors can be modified to produce elliptical surfaces with low roughness and low figure errors. Submicron focusing is demonstrated with prototype mirrors. The differential deposition method creates stiff monolithic mirrors which are compact, robust, and easy to cool and align. Prototype mirrors have demonstrated gains of more than 10{sup 4} in beam intensity while maintaining submilliradian divergence on the sample. This method of producing elliptical mirrors is well matched to the requirements of an x-ray microdiffraction Kirkpatrick-Baez focusing system. (c) 2000 American Institute of Physics.
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.
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.
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)].
Nonexistence results for elliptic equations with gradient terms
NASA Astrophysics Data System (ADS)
Alarcón, S.; Burgos-Pérez, M. Á.; García-Melián, J.; Quaas, A.
2016-01-01
We consider the elliptic problem - Δu +| ∇u | q = λf (u) in exterior domains of RN. Here q > 1, f is a nondecreasing, continuous and positive nonlinearity defined in (0, + ∞) and λ > 0 is a parameter. Under suitable assumptions on f near zero or infinity, we obtain some nonexistence results for positive supersolutions, depending on the relative values of q and N/N-1 and on the parameter λ.
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.
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.
Towards a theory of automated elliptic mesh generation
NASA Technical Reports Server (NTRS)
Cordova, J. Q.
1992-01-01
The theory of elliptic mesh generation is reviewed and the fundamental problem of constructing computational space is discussed. It is argued that the construction of computational space is an NP-Complete problem and therefore requires a nonstandard approach for its solution. This leads to the development of graph-theoretic, combinatorial optimization and integer programming algorithms. Methods for the construction of two dimensional computational space are presented.
NASA Astrophysics Data System (ADS)
Wang, H. N.; Utili, S.; Jiang, M. J.; He, P.
2015-09-01
Time dependency in tunnel excavation is mainly due to the rheological properties of rock and sequential excavation. In this paper, analytical solutions for deeply buried tunnels with elliptical cross-section excavated in linear viscoelastic media are derived accounting for the process of sequential excavation. For this purpose, an extension of the principle of correspondence to solid media with time varying boundaries is formulated for the first time. An initial anisotropic stress field is assumed. To simulate realistically the process of tunnel excavation, solutions are developed for a time-dependent excavation process with the major and minor axes of the elliptical tunnel changing from zero until a final value according to time-dependent functions specified by the designers. In the paper, analytical expressions in integral form are obtained assuming the incompressible generalized Kelvin viscoelastic model for the rheology of the rock mass, with Maxwell and Kelvin models solved as particular cases. An extensive parametric analysis is then performed to investigate the effects of various excavation methods and excavation rates. Also the distribution of displacements and stresses in space at different times is illustrated. Several dimensionless charts for ease of use of practitioners are provided.
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.
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.
Elliptic flow and shear viscosity of the shattered color glass condensate
NASA Astrophysics Data System (ADS)
Ruggieri, Marco; Scardina, Francesco; Plumari, Salvatore; Greco, Vincenzo
2014-07-01
In this contribution, we report on our results about the computation of the elliptic flow of the quark-gluon-plasma produced in relativistic heavy ion collisions, simulating the expansion of the fireball by solving the relativistic Boltzmann equation for the parton distribution function tuned at a fixed shear viscosity to entropy density ratio η/s. We emphasize the role of saturation in the initial gluon spectrum modelling the shattering of the color glass condensate, causing the initial distribution to be out of equilibrium. We find that the saturation reduces the efficiency in building-up the elliptic flow, even if the thermalization process is quite fast τtherm ≈ 0.8fm/c. and the pressure isotropization even faster τisotr ≈ 0.3fm/c. The impact of the initial non-equilibrium manifests for non-central collisions and can modify the estimate of the viscosity respect to the assumption of full thermalization in pT-space.
Wave-optical simulation of hard-x-ray nanofocusing by precisely figured elliptical mirrors.
Kewish, Cameron M; Assoufid, Lahsen; Macrander, Albert T; Qian, Jun
2007-04-10
Computer simulations of nanofocusing by elliptical mirrors are presented wherein the diffraction and propagation of coherent hard x rays are predicted using wave-optical calculations. Surface height data acquired via microstitching interferometry were used to calculate the complex pupil function of a mirror, taking into account the Fresnel reflectivity and treating the surface topography as an aberration to a perfect elliptical mirror. The reflected wave-field amplitude and phase downstream of the mirror were obtained by numerically evaluating the Fresnel-Kirchhoff diffraction integral. Simulated intensity profiles and contours (isophotes) around the focal plane are presented for coherent illumination by a 15 keV point source, which indicate nearly diffraction-limited focusing at the 40 nm level. The effect of high spatial frequency microroughness on nanofocusing was investigated by low-pass filtering the Fourier spectrum of the residual height profile. Simulations using the filtered metrology data confirmed that roughness length scales shorter than 0.1 mm have a minor effect on the focal spot size and intensity. PMID:17384715
Wave-optical simulation of hard-x-ray nanofocusing by precisely figured elliptical mirrors
Kewish, Cameron M.; Assoufid, Lahsen; Macrander, Albert T.; Qian Jun
2007-04-10
Computer simulations of nanofocusing by elliptical mirrors are presented wherein the diffraction and propagation of coherent hard x rays are predicted using wave-optical calculations. Surface height data acquired via microstitching interferometry were used to calculate the complex pupil function of a mirror, taking into account the Fresnel reflectivity and treating the surface topography as an aberration to a perfect elliptical mirror. The reflected wave-field amplitude and phase downstream of the mirror were obtained by numerically evaluating the Fresnel-Kirchhoff diffraction integral. Simulated intensity profiles and contours (isophotes) around the focal plane are presented for coherent illumination by a15 keV point source, which indicate nearly diffraction-limited focusing at the40 nm level. The effect of high spatial frequency microroughness on nanofocusing was investigated by low-pass filtering the Fourier spectrum of the residual height profile. Simulations using the filtered metrology data confirmed that roughness length scales shorter than0.1 mm have a minor effect on the focal spot size and intensity.
Hot gas metallicity and the history of supernova activity in elliptical galaxies
NASA Technical Reports Server (NTRS)
Loewenstein, Michael; Mathews, William G.
1991-01-01
Calculations of the dynamical evolution of the hot interstellar medium (ISM) in a massive elliptical galaxy are described, with a variety of past variations of the SN rate being assumed. The investigation focuses on iron enrichment in the ISM. The equivalent widths of the 6.7-keV iron line are calculated as a function of redshift and of galactic projected radius. The present-day interstellar gas in elliptical galaxies contains a fossil record of past SN activity that can be determined from measurements of iron line equivalent widths at several projected radii in the galaxy. It is proposed that the ISM iron abundance is likely to be quite inhomogeneous. The hydrogen-free ejecta of type Ia SN also result in pronounced ISM abundance inhomogeneities that probably eventually cool and move in pressure equilibrium with the local ISM flow velocity. The 6.7-keV iron line emission is greater if the iron is confined to ionized regions of pure iron.
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.
On the distribution of scalar k for elliptic scalar multiplication
NASA Astrophysics Data System (ADS)
Ajeena, Ruma Kareem K.; Kamarulhaili, Hailiza
2015-10-01
In this study, we introduce the probability distribution of the elliptic curve scalar multiplication through finding the probability distribution of the secret key, namely, the scalar k of the scalar multiplication kP of a point P which has a large prime order n lying on elliptic curve group E(Fp) over a finite prime field Fp. To determine this distribution of k, we use the integer sub-decomposition (ISD) approach that inspired from Gallant, Lambert and Vanstone (GLV) idea. In ISD approach, the distribution of the values of scalars k lie outside the range ±√{n } on the interval [1, n - 1]. This distribution determines the successful rate to compute a scalar multiplication kP, on ISD approach, in comparison with the original GLV method. The conception of the ISD approach depends on the sub- decomposition of the scalar k to compute the scalar multiplication kP which uses efficiently computable endomorphisms Ψ1 and Ψ2 of elliptic curve E over Fp. The ISD sub-decomposition can be defined by k P =k11P +k12ψ1(P )+k21P +k22ψ2(P ), with max{ | k11 | ,| k12 | } and max{ | k21 | ,| k22 | } ≤C √{n }, for some explicit constant C > 0. Furthermore, this study compares between the GLV and ISD approaches on the basis of the probability distribution of the scalar k in the interval [1, n - 1], where n is a large prime number.
Determining spatial orientation of axes of elliptical magnetic field
NASA Astrophysics Data System (ADS)
Rudnitskiy, L. M.; Frumin, V. L.; Guyetskiy, B. A.; Klimov, N. Z.
1984-11-01
The rotating magnetic field in induction motors is often elliptical, because of asymmetry of the polyphase line voltages or structural asymmetry in the machine. For an accurate analysis of electromechanical energy conversion in such a machine, one must then take into account the ellipticity of the magnetic field with the attendant nonuniformity of saturation. A generalized two field model of an induction motor is proposed for this purpose, with superposition of two mutually orthogonal elliptical pulsating fields in stator coordinates. The self inductances and the mutual inductances can be subsequently calculated on this basis. The spatial orientation of the two ellipses, specifically of their axes, needs to be determined first and this is done here for the most general case of an asymmetric machine with m stator phases and n rotor phases under asymmetric input voltages. The magnetizing force of any stator phase and any rotor phase is calculated accordingly, then the resultant magnetizing force and its space distribution. The major axis and the minor axis of the resultant ellipse correspond to the direction of the respectively maximum and minimum magnetizing force. Numerical results converging after six iterations are shown for a machine with m 3 stator phases and n = 2 rotor phases.
Intrinsic momentum transport in tokamaks with tilted elliptical flux surfaces
NASA Astrophysics Data System (ADS)
Ball, Justin; Parra, Felix; Barnes, Michael; Dorland, William; Hammett, Gregory; Rodrigues, Paulo; Loureiro, Nuno
2014-10-01
Recent work demonstrated that breaking the up-down symmetry of tokamaks removes a constraint limiting intrinsic momentum transport, and hence toroidal rotation, to be small. We show, through MHD analysis, that ellipticity is most effective at introducing up-down asymmetry throughout the plasma. Using GS2, a local δf gyrokinetic code that self-consistently calculates momentum transport, we simulate tokamaks with tilted elliptical poloidal cross-sections and a Shafranov shift. These simulations show both the magnitude and poloidal dependence of nonlinear momentum transport. The results are consistent with TCV experimental measurements and suggest that this mechanism can generate rotation with an Alfven Mach number of several percent in a tilted elliptical ITER-like machine. It appears that rotation generated with up-down asymmetry may be sufficient to stabilize the resistive wall mode in reactor-sized devices. J.R.B. and F.I.P. were partially supported by the RCUK Energy Programme (grant number EP/I501045) and the European Unions Horizon 2020 research and innovation programme.
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.
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.
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.
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.
Near-infrared properties of asymptotic giant branch stars in nearby dwarf elliptical galaxy NGC 205
NASA Astrophysics Data System (ADS)
Jung, M. Y.; Ko, J.; Kim, J.-W.; Chun, S.-H.; Kim, H.-I.; Sohn, Y.-J.
2012-07-01
Aims: We investigated the distribution of resolved asymptotic giant branch (AGB) stars over a much larger area than covered by previous near-infrared studies in the nearby dwarf elliptical galaxy NGC 205. Methods: Using data obtained with the WIRCam near-infrared imager of the CFHT, we selected the AGB stars in the JHKs color - magnitude diagrams, and separated the C stars from M-giant stars in the JHKs color - color diagram. Results: We identified 1,550 C stars in NGC 205 with a mean absolute magnitude of ⟨ MKs ⟩ = -7.49 ± 0.54, and colors of ⟨ (J - Ks)0 ⟩ = 1.81 ± 0.41 and ⟨ (H - Ks)0 ⟩ = 0.76 ± 0.24. The ratio of C stars to M-giant stars was estimated to be 0.15 ± 0.01 in NGC 205, and the local C/M ratios for the southern region are somewhat lower than those for the northern region. The (J - Ks) color distributions of AGB stars contain the main peak of the M-giant stars and the red tail of the C stars. A comparison of the theoretical isochrone models with the observed color distribution indicates that most of the bright M-giant stars in NGC 205 were formed at log (tyr) ~ 9.0-9.7. The logarithmic slope of the MKs luminosity function for M-giant stars was estimated to be 0.84 ± 0.01, which is comparable with dwarf elliptical galaxies NGC 147 and NGC 185. Furthermore, we found that the logarithmic slopes of the MKs luminosity function for C and M-giant stars are different to places, implying a different star formation history within NGC 205. The bolometric luminosity function for M-giant stars extends to Mbol = -6.0 mag, and that for C stars spans -5.6 < Mbol < -3.0. The bolometric luminosity function of C stars is unlikely to be a Gaussian distribution and the mean bolometric magnitude of C stars is estimated to be Mbol = -4.24 ± 0.55, which is consistent with our results for dwarf elliptical galaxies NGC 147 and NGC 185. Based on observations carried out at the Canada-France-Hawaii Telescope, operated by the National Research Council of Canada
Krasnoperov, R A; Gerasimov, A N
2003-01-01
In transmission electron microscopy, microvessels (MVs) are studied as profiles on ultrathin sections. To determine MV sizes from measurements made on MV profiles, an assumption must be made about MV shape, a circular cylinder being used to approximate the latter on limited lengths. However, this model is irrelevant in case MVs have some flatness. The elliptical cylinder model is preferable, although relationships between the cylinder profile (two-dimensional; 2D) and its true (three-dimensional; 3D) sizes are not yet known. We have obtained the 2D/3D functions that express the relationships between such profile sizes as the minor radius (Y), major radius (X), axial ratio (X/Y), area (S), and perimeter (P) on the one hand, and the corresponding MV sizes (Y(0), X(0), X(0)/Y(0), S(0), and P(0)) on the other. The 2D/3D functions make it possible to derive elliptical MV sizes from section profile size distributions, probability density functions (PDFs) for the latter being determined. We have applied the 2D/3D functions in studying axial ratios of thyroid hemocapillaries. A factual X/Y frequency histogram has been constructed and fitted by theoretical X/Y PDFs plotted for different sets of capillary sizes. The thyroid capillaries have been revealed to be clustered, 72.7% of them having X(0)/Y(0) approximately 1.6, 17.6%, X(0)/Y(0) approximately 1.0, and 9.7%, X(0)/Y(0) approximately 3.2. The proposed technique is instrumental in precise modeling of microcirculatory network geometry. PMID:12524478
Transition to turbulence in an elliptic vortex
NASA Technical Reports Server (NTRS)
Lundgren, Thomas S.; Mansour, N. N.
1993-01-01
We study the three dimensional instability and nonlinear growth of the two dimensional flow described by the stream function Psi = (A sin b1 x sin b2 y)/(b1(exp 2) + b2(exp 2)) where b1 = pi/L1, b2 = pi/L2. This is a swirling flow in a box which is bounded by 0 less than x less than L1, 0 less than y less than L2 and is infinite in the z direction. This flow is a solution of the Navier-Stokes equation with A = exp(-v(b1(exp 2) + b2(exp 2))t) which slowly decays. We seek a viscous solution which starts near this one and slips along but does not penetrate the bounding walls. The vorticity of the basic flow is w(sub z) = A sin b1 x sin b2 y which has maximum value A at the center of the box and drops to zero at the boundaries. We can think of the resulting flow as that of a captive vortex.
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
Modal analysis of wake fields and its application to elliptical pill-box cavity with finite aperture
NASA Astrophysics Data System (ADS)
Kim, S. H.; Chen, K. W.; Yang, J. S.
1990-11-01
The potential of the wake-field produced by a bunch of relativistic charged particles passing through a pill-box cavity is expressed by using Floquet's theorem, and an obvious requirement that the energy gain over all acceleration cavity of many pill boxes must be proportional to the number of pill boxes, based on the previous modal approach (BWW theory). It is found that the wake-field is consisted of two classes of modes: the longitudinal modes which are independent of the aperture and the pill-box gap, the hybrid (pill-box) modes which are dependent of the pill-box gap. The wake field is predominated by the fundamental longitudinal mode whose wavelength is on the order of the effective diameter of the cavity, and its magnitude is inversely proportional to the cross sectional area of the cavity for practical cavities with small apertures. Both longitudinal and transverse wake fields due to the longitudinal modes in an elliptical pill box cavity are expressed analytically in a closed series form by solving exactly the longitudinal eigenmode equation in the elliptical cylindrical coordinates in terms of Mathieu functions. It is found that both longitudinal and transverse wake fields whose amplitudes per driving charge are greater than 100 MV/m/μC can be generated in an elliptical cavity.
NASA Astrophysics Data System (ADS)
Wang, Rui-Rong; Jia, Guo; Fang, Zhi-Heng; Wang, Wei; Meng, Xiang-Fu; Xie, Zhi-Yong; Zhang, Fan
2014-11-01
The X-ray spectrometer used in high-energy-density plasma experiments generally requires both broad X-ray energy coverage and high temporal, spatial, and spectral resolutions for overcoming the difficulties imposed by the X-ray background, debris, and mechanical shocks. By using an elliptical crystal together with a streak camera, we resolve this issue at the SG-II laser facility. The carefully designed elliptical crystal has a broad spectral coverage with high resolution, strong rejection of the diffuse and/or fluorescent background radiation, and negligible source broadening for extended sources. The spectra that are Bragg reflected (23° < θ < 38°) from the crystal are focused onto a streak camera slit 18 mm long and about 80 μm wide, to obtain a time-resolved spectrum. With experimental measurements, we demonstrate that the quartz(1011) elliptical analyzer at the SG-II laser facility has a single-shot spectral range of (4.64-6.45) keV, a typical spectral resolution of E/ΔE = 560, and an enhanced focusing power in the spectral dimension. For titanium (Ti) data, the lines of interest show a distribution as a function of time and the temporal variations of the He-α and Li-like Ti satellite lines and their spatial profiles show intensity peak red shifts. The spectrometer sensitivity is illustrated with a temporal resolution of better than 25 ps, which satisfies the near-term requirements of high-energy-density physics experiments.
Modal analysis of wake fields and its application to elliptical pill-box cavity with finite aperture
Kim, S.H. ); Chen, K.W.; Yang, J.S. )
1990-11-15
The potential of the wake-field produced by a bunch of relativistic charged particles passing through a pill-box cavity is expressed by using Floquet's theorem, and an obvious requirement that the energy gain over all acceleration cavity of many pill boxes must be proportional to the number of pill boxes, based on the previous modal approach (BWW theory). It is found that the wake-field is consisted of two classes of modes: the longitudinal modes which are independent of the aperture and the pill-box gap, the hybrid (pill-box) modes which are dependent of the pill-box gap. The wake field is predominated by the fundamental longitudinal mode whose wavelength is on the order of the effective diameter of the cavity, and its magnitude is inversely proportional to the cross sectional area of the cavity for practical cavities with small apertures. Both longitudinal and transverse wake fields due to the longitudinal modes in an elliptical pill box cavity are expressed analytically in a closed series form by solving exactly the longitudinal eigenmode equation in the elliptical cylindrical coordinates in terms of Mathieu functions. It is found that both longitudinal and transverse wake fields whose amplitudes per driving charge are greater than 100 MV/m/{mu}C can be generated in an elliptical cavity.
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.
Wake potential in a semi-elliptic pill-box cavity
NASA Astrophysics Data System (ADS)
Yang, J. S.; Chen, K. W.
1989-10-01
In this article we compared the wake potential in a cavity of semi-elliptic cross section and elliptic cross section. The semi-elliptic cavity is considered to have an advantage that we can experimentally simulate an elliptic cavity with one beam line. It is found that we can produce considerably strong accelerating fields inside this cavity. We calculate the resonant modes of this cavity using previous analytical mode analysis1. Also the wake field inside this cavity is derived analytically and numerical results are presented to determine the usefulness of this cavity.
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.
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.
Elliptic flow of identified particles in Pb-Pb collisions at the LHC
NASA Astrophysics Data System (ADS)
Dobrin, A.
2014-11-01
The elliptic flow coefficient, v2, is presented for π±, K±, KS0,p +pbar, ϕ, Λ +Λbar, Ξ- +Ξbar+, Ω- +Ωbar+ in Pb-Pb collisions at √{sNN} = 2.76 TeV with the ALICE detector. Results obtained with the scalar product method are reported as a function of transverse momentum, pT, out to pT = 6 GeV / c at different collision centralities. For pT < 2 GeV / c, v2 exhibits a particle mass dependence. Particles tend to group into mesons and baryons for pT > 3 GeV / c. Deviations from the number of constituent quark scaling at the level of ± 20% are found for pT > 2- 3 GeV / c. The results are compared to hydrodynamic calculations coupled to a hadronic cascade model.
Singh, O.; Krinsky, S.
1997-07-01
In October 1996, the elliptically polarized wiggler, installed in the X13 straight section of the NSLS X-ray ring, was commissioned at an operating frequency of 100 hz. This wiggler generates circularly polarized photons in the energy range of 0.1 to 10 keV with AC modulation of polarization helicity. The vertical magnetic field is produced by a hybrid permanent magnet structure, and the horizontal magnetic field is generated by an electromagnet capable of switching at frequencies up to 100 hz. Here, the authors discuss the compensation of the residual vertical and horizontal orbit motion utilizing a time-domain algorithm employing a function generator to drive trim coils at the wiggler ends, and the wideband high precision orbit measurement system of the X-ray ring. The residual orbit motion has been reduced to a level below 1 micron, and the device has been run in regular operations with no negative effect on other users.
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.
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.
Series solutions of the Sitnikov restricted N+1-body problem: elliptic case
NASA Astrophysics Data System (ADS)
Shahbaz Ullah, M.; Majda, B.; Ullah, M. Zafar; Shahnawaz Ullah, M.
2015-06-01
Following Giacaglia (1967), in Sect. 2 we have developed equation of motion of the Sitnikov restricted N+1-body problem in elliptic case. We assumed that the primaries are at the vertices of a regular N-gon so the distances of the primaries from center of mass are time depending. In Sect. 3 we have linearized the equation of motion to obtain the Hill's type equation and then find the approximate solution. In Sects. 4 and 5 the series solutions of the Sitnikov restricted N+1-body problem have been developed by the method of Lindstedt-Poincaré and iteration of Green's function respectively. In Sect. 6 the two series solutions have been compared graphically by putting N=2, 3 and 4 for different eccentricity.
Transformation of two and three-dimensional regions by elliptic systems
NASA Technical Reports Server (NTRS)
Mastin, C. Wayne; Thompson, Joe F.
1986-01-01
Grid smoothing and orthogonalization procedures were developed and implemented in the construction of two and three dimensional grids. The procedures are based on the variational methods of grid generation. The two-dimensional examples were computed using the MSU IRIS Graphics Workstation. It was demonstrated that the elliptic grid generation equations, with arbitrary forcing functions, can be solved, in their variational formulation, using a gradient method. Since gradient methods have a global convergence property, the divergence problems often encountered when using SOR iterative methods can be avoided. It is not to be concluded, however, that SOR methods should be abandoned, since gradient methods tend to converge very slowly. In fact, slow convergence was the major problem encountered in the three-dimensional grids. Further progress was made on the continuing effort to develop conservative interpolation formulas for overlapping grids.
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.
Scattering of cylindrical electric field waves from an elliptical dielectric cylindrical shell
NASA Astrophysics Data System (ADS)
Urbanik, E. A.
1982-12-01
This thesis examines the scattering of cylindrical waves by large dielectric scatterers of elliptic cross section. The solution method was the method of moments using a Galerkin approach. Sinusoidal basis and testing functions were used resulting in a higher convergence rate. The higher rate of convergence made it possible for the program to run on the Aeronautical Systems Division's CYBER computers without any special storage methods. This report includes discussion on moment methods, solution of integral equations, and the relationship between the electric field and the source region or self cell singularity. Since the program produced unacceptable run times, no results are contained herein. The importance of this work is the evaluation of the practicality of moment methods using standard techniques. The long run times for a mid-sized scatterer demonstrate the impracticality of moment methods for dielectrics using standard techniques.
Comparison of two methods for simulation of hard X-ray nanofocusing by elliptical mirrors.
Kewish, C. M.; Macrander, A. T.; Assoufid, L.; Qian, J.; X-Ray Science Division
2007-11-11
Wave-optical calculations are essential for predicting the X-ray focusing performance of precisely figured elliptical mirrors. The complex wavefield in the vicinity of the focal plane of a mirror with RMS height error in the nanometer range compared to the best-fit ellipse has been calculated using two methods. A pupil function method that treats the surface topography of a mirror as an aberration to a perfect ellipse was used to obtain the reflected amplitude and phase around the focal point downstream. The results were compared with direct propagation of waves from a point source, and it was found that both methods were in good agreement. Each approach provides advantages that are useful in designing mirrors to achieve diffraction limited focusing.
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.
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.
Rayleigh wave ellipticity across the Iberian Peninsula and Morocco
NASA Astrophysics Data System (ADS)
Gómez García, Clara; Villaseñor, Antonio
2015-04-01
Spectral amplitude ratios between horizontal and vertical components (H/V ratios) from seismic records are useful to evaluate site effects, predict ground motion and invert for S velocity in the top several hundred meters. These spectral ratios can be obtained from both ambient noise and earthquakes. H/V ratios from ambient noise depend on the content and predominant wave types: body waves, Rayleigh waves, a mixture of different waves, etc. The H/V ratio computed in this way is assumed to measure Rayleigh wave ellipticity since ambient vibrations are dominated by Rayleigh waves. H/V ratios from earthquakes are able to determine the local crustal structure at the vicinity of the recording station. These ratios obtained from earthquakes are based on surface wave ellipticity measurements. Although long period (>20 seconds) Rayleigh H/V ratio is not currently used because of large scatter has been reported and uncertainly about whether these measurements are compatible with traditional phase and group velocity measurements, we will investigate whether it is possible to obtain stable estimates after collecting statistics for many earthquakes. We will use teleseismic events from shallow earthquakes (depth ≤ 40 km) between 2007 January 1 and 2012 December 31 with M ≥ 6 and we will compute H/V ratios for more than 400 stations from several seismic networks across the Iberian Peninsula and Morocco for periods between 20 and 100 seconds. Also H/V ratios from cross-correlations of ambient noise in different components for each station pair will be computed. Shorter period H/V ratio measurements based on ambient noise cross-correlations are strongly sensitive to near-surface structure, rather than longer period earthquake Rayleigh waves. The combination of ellipticity measurements based on earthquakes and ambient noise will allow us to perform a joint inversion with Rayleigh wave phase velocity. Upper crustal structure is better constrained by the joint inversion compared
Two-dimensional gap solitons in elliptic-lattice potentials
He Yingji; Malomed, Boris A.; Hu Bambi
2010-03-15
We study two-dimensional (2D) matter-wave gap solitons trapped in an elliptically deformed concentric lattice potential, within the framework of the Gross-Pitaevskii equation (GPE) with self-attraction or self-repulsion. For a fixed eccentricity of the lattice, soliton families are found in both the repulsive and attractive models. In the former case, the analysis reveals two kinds of gap solitons trapped in the first oval trough (the ring-shaped potential minimum closest to the center): elliptic annular solitons (EASs), and double solitons (DSs), which are formed by two tightly localized density peaks located at diametrically opposite points of the trough, with zero phase difference between them. With the decrease of the norm, the density distribution in the EAS along the azimuthal direction changes from nearly uniform to double-peaked and, eventually, to the DS. In the attractive model, there exist only DSs in the oval trough, while EASs are not found. All such solitons without the angular momentum (l=0) are fully stable. For l{ne}0, vortical solitons--both EASs with a sufficiently large norm (in the repulsive model) and DSs (in models with both signs of the nonlinearity)--are quasistable, exhibiting rocking motion in the elliptic trough (we consider the cases of l=1 and l=2). At smaller values of the norm, the vortical annular solitons (in the repulsive model) are unstable. Stable fundamental solitons trapped in the central potential well are investigated, too, in both the attractive and repulsive models, by means of the variational approximation and numerical methods.
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
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.
Optical proximity correction challenges with highly elliptical contacts
NASA Astrophysics Data System (ADS)
Cork, Chris; Barnes, Levi; Ping, Yang; Li, Xiaohai; Jang, Stephen
2010-09-01
The steady march of Moore's law demands ever smaller feature sizes to be printed and Optical Proximity Correction to correct to ever tighter dimensional tolerances. Recently pitch doubling techniques has relieved the pressure on CD reduction, which instead of being achieved lithographically are reduced by subsequent etching or chemical interaction with spin-on layers. CD tolerance reductions, however, still need to match the overall design rule shrinkage. The move to immersion lithography, where effective Numerical Apertures now reach 1.35, has been accompanied by a significantly reduction in depth of focus, especially on isolated contacts. To remedy this, RET techniques such as assist feature placement, have been implemented. Certain local placements of assist features and neighboring contacts are observed to result in highly elliptical contacts being printed. In some layouts small changes in the aspect ratio of the contact on the mask leads to strong changes in the aspect ratio of the printed contact, whereas in other layouts the response is very weak. This effect can be described as an aspect ratio MEEF. The latter type of contact can pose a significant challenge to the OPC recipe which is driven by the need to place the printed contour within a small range of distance from target points placed on the midpoint of edges of a nominally square contact. The OPC challenge naturally will be compounded when the target layout is rectangular in the opposite sense to the natural elliptical shape of the printed contact. Approaches to solving this can vary from intervening at the assist feature placement stage, at the possible loss of depth of focus, to accepting a certain degree of ellipticity in the final contour and making the OPC recipe concentrate on minimizing any residual errors. This paper investigates which contact layouts are most challenging, discusses the compromises associated with achieving the correction target and results are shown from a few different
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.
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.
On an Elliptic Equation Arising from Composite Materials
NASA Astrophysics Data System (ADS)
Dong, Hongjie; Zhang, Hong
2016-03-01
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.
Symmetry energy from elliptic flow in 197Au + 197Au
NASA Astrophysics Data System (ADS)
Russotto, P.; Wu, P. Z.; Zoric, M.; Chartier, M.; Leifels, Y.; Lemmon, R. C.; Li, Q.; Łukasik, J.; Pagano, A.; Pawłowski, P.; Trautmann, W.
2011-03-01
The elliptic-flow ratio of neutrons with respect to protons or light complex particles in reactions of neutron-rich systems at relativistic energies is proposed as an observable sensitive to the strength of the symmetry term in the equation of state at supra-normal densities. The results obtained from the existing FOPI/LAND data for 197Au + 197Au collisions at 400 MeV/nucleon in comparison with the UrQMD model favor a moderately soft symmetry term with a density dependence of the potential term proportional to (ρ /ρ0) γ with γ = 0.9 ± 0.4.
Dynamical models of elliptical galaxies - I. Simple methods
NASA Astrophysics Data System (ADS)
Agnello, A.; Evans, N. W.; Romanowsky, A. J.
2014-08-01
We study dynamical models for elliptical galaxies, deriving the projected kinematic profiles in a form that is valid for general surface brightness laws and (spherical) total mass profiles, without the need for any explicit deprojection. We provide accurate approximations of the line of sight and aperture-averaged velocity dispersion profiles for galaxies with total mass density profiles with slope near -2 and with modest velocity anisotropy using only single or double integrals, respectively. This is already sufficient to recover many of the kinematic properties of nearby ellipticals. As an application, we provide two different sets of mass estimators for elliptical galaxies, based on either the velocity dispersion at a location at or near the effective radius, or the aperture-averaged velocity dispersion. In the large aperture (virial) limit, mass estimators are naturally independent of anisotropy. The spherical mass enclosed within the effective radius Re can be estimated as 2.4 R_e < σ 2_p > / G, where < σ ^2_p > is the average of the squared velocity dispersion over a finite aperture. This formula does not depend on assumptions such as mass-follows-light, and is a compromise between the cases of small and large aperture sizes. Its general agreement with results from other methods in the literature makes it a reliable means to infer masses in the absence of detailed kinematic information. If on the other hand the velocity dispersion profile is available, tight mass estimates can be found that are independent of the mass-model and anisotropy profile. In particular, for a de Vaucouleurs surface brightness, the velocity dispersion measured at ≈1Re yields a tight mass estimate (with 10 per cent accuracy) at ≈3Re that is independent of the mass model and the anisotropy profile. This allows us to probe the importance of dark matter at radii where it dominates the mass budget of galaxies. Explicit formulae are given for small anisotropy, large radii and/or power
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
Conceptual design of a hybrid-type elliptically polarizing undulator
NASA Astrophysics Data System (ADS)
Sasaki, Shigemi
2002-03-01
A hybrid-type planar undulator was designed to generate circularly polarized radiation. It is an APPLE-type design consisting of four rows of hybrid structures that can be shifted with respect to each other. The magnetic field on axis can thus be adjusted so it can have linear or circular polarization including intermediate (elliptical polarization) positions. A short-period device of this kind can provide 100% circularly polarized radiation in a hard x-ray region when it is installed in a high-energy storage ring, such as the Advanced Photon Source.
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
The origin of magnetic fields in elliptical galaxies
NASA Astrophysics Data System (ADS)
Shukurov, Anvar
We argue that interstellar gas in elliptical galaxies can be turbulent, with turbulent scale and velocity of 400 pc and 20 km s-1 respectively. An upper limit on turbulent velocity, ~=50 km s-1, follows from the requirement that the turbulence dissipation rate does not exceed the X-ray gas luminosity. The turbulence can generate random magnetic fields of 0.3 μG strength at the above scale via fluctuation dynamo action. The resulting Faraday rotation is random, with a typical value of 5-30 rad m-2, consistent with observational evidence available.
Protein phase diagrams: The physics behind their elliptic shape
NASA Astrophysics Data System (ADS)
Lesch, Harald; Hecht, Christoph; Friedrich, Josef
2004-12-01
We relate the condition for the elliptic shape of the phase diagram of proteins to the degree of correlation in the fluctuations of the changes of enthalpy and volume at the denaturing-refolding transition. Since this degree cannot be larger than 1, hyperbolically shaped diagrams are not likely to exist. Experiments show that the correlation factor is actually quite low for proteins implying that one-order parameter is not enough to describe the folding-denaturing transition. These findings seem to be the thermodynamic manifestation of the glasslike properties of proteins despite the fact that the transition itself is of first order.
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.
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.
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.
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 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.
Exact sub-grid interface correction schemes for elliptic interface problems
Huh, J.S.; Sethian, J.A.
2008-12-09
We introduce a non-conforming finite element method for second order elliptic interface problems. Our approach applies to problems in which discontinuous coefficients and singular sources on the interface may give rise to jump discontinuities in either the solution or its normal derivative. Given a standard background mesh and an interface that passes between elements, the key idea is to construct a singular correction function which satisfies the prescribed jump conditions, providing accurate sub-grid resolution of the discontinuities. Utilizing the closest point extension and an implicit interface representation by the signed distance function, an algorithm is established to construct the correction function. The result is a function which is supported only on the interface elements, represented by the regular basis functions, and bounded independently of the interface location with respect to the background mesh. In the particular case of a constant second order coefficient, our regularization by singular function is straightforward, and the resulting left-hand-side is identical to that of a regular problem without introducing any instability. The influence of the regularization appears solely on the right-hand-side, which simplifies the implementation. In the more general case of discontinuous second order coefficients, a normalization is invoked which introduces a constraint equation on the interface. This results in a problem statement similar to that of a saddle-point problem. We employ two-level-iteration as the solution strategy, which exhibits aspects similar to those of iterative preconditioning strategies.
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%.
NASA Astrophysics Data System (ADS)
Birken, Ralf Andreas
A new real-time in-field interpretation and visualization scheme and software, using neural networks for the detection and localization of buried waste, and the boundaries of waste sites, has been developed. The capabilities and limitations of the high-frequency (1 kHz to 1 MHz and 31 kHz to 32 MHz) electromagnetic ellipticity systems are analyzed by numerically studying the sensitivity of the acquired 3D-ellipticity to model parameters describing the geometry of the systems and the electrical parameters of layered-earth models. Changes in ellipticity due to coil misalignment in standard operating mode are typically just 1% to 2%. Changes due to variations in layered-earth model parameters (resistivity, relative dielectric constant, and thickness) are typically at least one order of magnitude higher. Hence, it will be possible to resolve these parameters. For conductive models (resistivity <50 Omegam) it will be hard to determine the relative dielectric constant and for models with high relative dielectric constants it will be hard to determine the resistivity, especially if it is greater than 1000 Omegam. The results of the sensitivity analysis contribute considerably to the training of several neural networks to determine the electrical properties of the subsurface. The two classes of artificial neural network paradigms utilized in this study are the radial basis function and the modular neural network algorithms. One-dimensional layered-earth inversions are performed by neural networks using ellipticity data. The three-dimensional localization of metallic objects (e.g. drums) is done by visualizing the results of one particular halfspace neural network technique. Several small conductive objects have been detected by applying this technique to data collected in controlled physical modeling field experiments. Classification neural networks are trained on field data to categorize ellipticity soundings into either a target or a background class. Two environmental
Mergers in galaxy groups. I. Structure and properties of elliptical remnants
Taranu, Dan S.; Dubinski, John; Yee, H. K. C.
2013-11-20
We present collisionless simulations of dry mergers in groups of 3 to 25 galaxies to test the hypothesis that elliptical galaxies form at the centers of such groups. Mock observations of the central remnants confirm their similarity to ellipticals, despite having no dissipational component. We vary the profile of the original spiral's bulge and find that ellipticals formed from spirals with exponential bulges have too low Sersic indices. Mergers of spirals with de Vaucouleurs (classical) bulges produce remnants with larger Sersic indices correlated with luminosity, as with Sloan Digital Sky Survey ellipticals. Exponential bulge mergers are better fits to faint ellipticals, whereas classical bulge mergers better match luminous ellipticals. Similarly, luminous ellipticals are better reproduced by remnants undergoing many (>5) mergers, and fainter ellipticals by those with fewer mergers. The remnants follow tight size-luminosity and velocity dispersion-luminosity (Faber-Jackson) relations (<0.12 dex scatter), demonstrating that stochastic merging can produce tight scaling relations if the merging galaxies also follow tight scaling relations. The slopes of the size-luminosity and Faber-Jackson relations are close to observations but slightly shallower in the former case. Both relations' intercepts are offset—remnants are too large but have too low dispersions at fixed luminosity. Some remnants show substantial (v/σ > 0.1) rotational support, although most are slow rotators and few are very fast rotators (v/σ > 0.5). These findings contrast with previous studies concluding that dissipation is necessary to produce ellipticals from binary mergers of spirals. Multiple, mostly minor and dry mergers can produce bright ellipticals, whereas significant dissipation could be required to produce faint, rapidly rotating ellipticals.
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
Dual Stellar Halos in the Standard Elliptical Galaxy M105 and Formation of Massive Galaxies
NASA Astrophysics Data System (ADS)
Lee, Myung Gyoon
2015-08-01
M105 in the Leo I Group is a textbook example of a standard elliptical galaxy. Old red giant stars in the halo of M105 are easily resolved in the HST images so that it is an ideal target to study the structure and composition of stellar halos in elliptical galaxies. It is only one of the few elliptical galaxies for which we can study their stellar halos using the resolved stars. We present photometry of the resolved stars in its inner region at R~4 arcmin, obtained from F606W and F814W images in the Hubble Space Telescope archive. Then we combine this with photometry of the remote outer region at R~12 arcmin studied before. Deep color-magnitude diagrams of the resolved stars in the inner region show a prominent red giant branch (RGB) with a large color range, while those for the outer region show better a narrow blue RGB. We derive the metallicity of the RGB stars using the isochrones. The metallicity distribution function of the RGB stars shows the existence of two distinct subpopulations: a dominant metal-rich population and a much weaker metal-poor population. The peak metallicity of the metal-rich population changes little as galactocentric distance increases, while the fraction of the metal-poor population increases. The radial number density profile of the metal-poor RGB stars is flatter in the outer region than that of the metal-rich RGB stars. These provide strong evidence that there are two distinct stellar halos in this galaxy, blue (metal-poor) and red (metal-rich) halos, which is consistent with the results based on the study of the globular cluster systems in bright early-type galaxies (Park \\& Lee 2013,ApJ,773, 27). We discuss the implications of these results with regard to the formation of massive early-type galaxies in the dual halo mode formation scenario as well as in the two-phase formation scenario based on similuations.
Anisotropy in Dynamical Models of Elliptical Galaxy Dark Halos
NASA Astrophysics Data System (ADS)
Forestell, Amy; Gebhardt, K.
2013-07-01
Abstract (2,250 Maximum Characters): We discuss the orbital anisotropy results of axisymmetric orbit-superposition dynamical models of elliptical galaxies NGC 821 and NGC 4697. For NGC 821 stellar kinematics are used to determine the best-fitted dark halo (Forestell 2010), then we determine the orbital properties required for planetary nebulae to match the observed kinematic data (Romanowsky et al. 2003) in that assumed dark halo. For NGC 4697 we use both stellar and planetary nebula kinematics (Pinkney et al. 2003, Mendez et al. 2009) to model the galaxy dark halo. In both galaxies we find that the planetary nebulae, which are located at large radii, show radial anisotropy. This is consistent with the results of Dekel et al. (2005), who use disk galaxy merger simulations to show that large anisotropies can be created in the resulting elliptical galaxies and that this anisotropy in combination with the different density profile of a young population could explain how the low dispersions from planetary nebulae measurements are also consistent with typical dark matter halos.
Integrated photoelasticity through imaging fourier polarimetry of an elliptic retarder.
Berezhna, S; Berezhnyy, I; Takashi, M
2001-02-10
It is shown that three optical parameters that are necessary for stress computation in integrated photoelasticity can be measured with high accuracy by use of a Fourier polarimetry method. Inasmuch as a photoelastic sample, which is an object of investigation in integrated photoelasticity, is a kind of an elliptic retarder, the technique presented here measures relative retardation delta, azimuth angle theta, and ellipticity angle epsilon instead of the characteristic parameters that traditionally have been used in integrated photoelasticity. The ability of the new technique to provide better accuracy with a simpler setup has been proved experimentally. Furthermore, the technique is self-contained as for phase measurement; i.e., it automatically performs phase unwrapping at the points where phase data exceed the value of pi. The full value of a phase at a certain point is retrieved by processing of pi-modulo phase data that have been precisely measured at several wavelengths. The usefulness of the new method for integrated photoelasticity has been demonstrated through measurement of a diametrically compressed disk viewed at oblique light incidence. PMID:18357041
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.
A halo model for intrinsic alignments of galaxy ellipticities
NASA Astrophysics Data System (ADS)
Schneider, Michael D.; Bridle, Sarah
2010-03-01
Correlations between intrinsic ellipticities of galaxies are a potentially important systematic error when constraining dark energy properties from weak gravitational lensing (cosmic shear) surveys. In the absence of perfectly known galaxy redshifts, some modelling of the galaxy intrinsic alignments is likely to be required to extract the lensing signal to sufficient accuracy. We present a new model based on the placement of galaxies into dark matter haloes. The central galaxy ellipticity follows the large-scale potential and, in the simplest case, the satellite galaxies point at the halo centre. The two-halo term is then dominated by the linear-alignment model and the one-halo term provides a motivated extension of intrinsic alignment models to small scales. We provide fitting formulae for the spatial projected source power spectra for both intrinsic-intrinsic (II) and gravitational-intrinsic (GI) correlations. We illustrate the potential impact of ignoring intrinsic alignments on cosmological parameter constraints from non-tomographic surveys, finding that σ8 could be underestimated by up to the size of the current 1σ error bar from cosmic shear if very small scales are included in the analysis. Finally, we highlight areas of interest for numerical simulations of dark matter clustering and galaxy formation that can further constrain the intrinsic alignment signal.
Circular, elliptic and oval billiards in a gravitational field
NASA Astrophysics Data System (ADS)
da Costa, Diogo Ricardo; Dettmann, Carl P.; Leonel, Edson D.
2015-05-01
We consider classical dynamical properties of a particle in a constant gravitational force and making specular reflections with circular, elliptic or oval boundaries. The model and collision map are described and a detailed study of the energy regimes is made. The linear stability of fixed points is studied, yielding exact analytical expressions for parameter values at which a period-doubling bifurcation occurs. The dynamics is apparently ergodic at certain energies in all three models, in contrast to the regularity of the circular and elliptic billiard dynamics in the field-free case. This finding is confirmed using a sensitive test involving Lyapunov weighted dynamics. In the last part of the paper a time dependence is introduced in the billiard boundary, where it is shown that for the circular billiard the average velocity saturates for zero gravitational force but in the presence of gravitational it increases with a very slow growth rate, which may be explained using Arnold diffusion. For the oval billiard, where chaos is present in the static case, the particle has an unlimited velocity growth with an exponent of approximately 1/6.
Signed Decomposition Method for Scalar Multiplication in Elliptic Curve Cryptography
NASA Astrophysics Data System (ADS)
Said, M. R. M.; Mohamed, M. A.; Atan, K. A. Mohd; Zulkarnain, Z. Ahmad
2010-11-01
Addition chain is the solution to computability constraint of the problematic large number arithmetic. In elliptic curve cryptography, a point arithmetic on elliptic curve can be reduced to repetitive addition and doubling operations. Based on this idea, various methods were proposed, lately a decomposition method based on prime decomposition was put forward. This method uses a pre-generated set of rules to calculate an addition chain for n. Though the method shows it own advantage over others in some cases, but some improvements is still avail. We develop an enhancement version called signed decomposition method which takes rule from decomposition method as an input. We also generalize the idea of a prime rule to an integer rule. An improvement is done to the original add rule in decomposition method by allowing subtraction operation to terms. In so doing, we optimize the original form of add rule. The result shows not only an improvement over decomposition method but also become an all time superior compare to preceeding methods. Furthermore, having secret key in a form of rule will put up extra security to the message under communication.
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. PMID:25769218
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.
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.
NASA Astrophysics Data System (ADS)
Prokopeva, L. J.; Kildishev, A. V.
2016-04-01
We propose a new class of elliptic omnidirectional concentrators focusing light on a disk, a thin strip, or a rod. Our ray-tracing and full-wave simulations of new elliptic designs show flawless focusing and absorbing performance at complete acceptance angles.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Peng, Hao; Xu, Shijie
2015-11-01
The multi-revolution elliptic halo (ME-Halo) orbit is a kind of strictly periodic orbit existing in the elliptic restricted three-body problem (ERTBP) model. Its remarkable features include that it survives the eccentricity perturbation of the primaries, it has a long period commeasurable with the primary period and that its stability property varies greatly as the eccentricity. The authors utilized continuation methods together with the multi-segment optimization method to generate two groups of ME-Halo orbits, and then systematically investigated their stability evolution with respect to the eccentricity and the mass ratio of the primaries. These parameters show complicate impacts on the stability. Some ME-Halo orbits can possess more than one pairs of real eigenvalue, some have negative real eigenvalues or complex eigenvalues out of the unit circle. For certain parameters, continuation failures are observed to be accompanied by a series of eigenvalue collision and bifurcations. The results in this paper can help to understand the nonautonomous dynamic of the ERTBP and can further aid in understanding the dynamical environment for real-world applications and, thus, contribute to the trajectory development process.