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
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.
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.
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.
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.
Flux Jacobian matrices and generaled Roe average for an equilibrium real gas
NASA Technical Reports Server (NTRS)
Vinokur, Marcel
1988-01-01
Inviscid flux Jacobian matrices and their properties used in numerical solutions of conservation laws are extended to general, equilibrium gas laws. Exact and approximate generalizations of the Roe average are presented. Results are given for one-dimensional flow, and then extended to three-dimensional flow with time-varying grids.
NASA Astrophysics Data System (ADS)
Chak, Yew-Chung; Varatharajoo, Renuganth
2016-07-01
Many spacecraft attitude control systems today use reaction wheels to deliver precise torques to achieve three-axis attitude stabilization. However, irrecoverable mechanical failure of reaction wheels could potentially lead to mission interruption or total loss. The electrically-powered Solar Array Drive Assemblies (SADA) are usually installed in the pitch axis which rotate the solar arrays to track the Sun, can produce torques to compensate for the pitch-axis wheel failure. In addition, the attitude control of a flexible spacecraft poses a difficult problem. These difficulties include the strong nonlinear coupled dynamics between the rigid hub and flexible solar arrays, and the imprecisely known system parameters, such as inertia matrix, damping ratios, and flexible mode frequencies. In order to overcome these drawbacks, the adaptive Jacobian tracking fuzzy control is proposed for the combined attitude and sun-tracking control problem of a flexible spacecraft during attitude maneuvers in this work. For the adaptation of kinematic and dynamic uncertainties, the proposed scheme uses an adaptive sliding vector based on estimated attitude velocity via approximate Jacobian matrix. The unknown nonlinearities are approximated by deriving the fuzzy models with a set of linguistic If-Then rules using the idea of sector nonlinearity and local approximation in fuzzy partition spaces. The uncertain parameters of the estimated nonlinearities and the Jacobian matrix are being adjusted online by an adaptive law to realize feedback control. The attitude of the spacecraft can be directly controlled with the Jacobian feedback control when the attitude pointing trajectory is designed with respect to the spacecraft coordinate frame itself. A significant feature of this work is that the proposed adaptive Jacobian tracking scheme will result in not only the convergence of angular position and angular velocity tracking errors, but also the convergence of estimated angular velocity to
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.
NASA Astrophysics Data System (ADS)
Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil
2016-08-01
We develop a new approach for solving the nonlinear Richards' equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioning strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. We also show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.
Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil
2016-08-01
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
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.
NASA Technical Reports Server (NTRS)
Chen, Yu-Che; Walker, Ian D.; Cheatham, John B., Jr.
1992-01-01
We present a unified formulation for the inverse kinematics of redundant arms, based on a special formulation of the null space of the Jacobian. By extending (appropriately re-scaling) previously used null space parameterizations, we obtain, in a unified fashion, the manipulability measure, the null space projector, and particular solutions for the joint velocities. We obtain the minimum norm pseudo-inverse solution as a projection from any particular solution, and the method provides an intuitive visualization of the self-motion. The result is a computationally efficient, consistent approach to computing redundant robot inverse kinematics.
Assessing the quality of curvilinear coordinate meshes by decomposing the Jacobian matrix
NASA Technical Reports Server (NTRS)
Kerlick, G. D.; Klopfer, G. H.
1982-01-01
An algebraic decomposition of the Jacobian matrix which relates physical and computational variables is presented. This invertible decomposition parameterizes the mesh by the physically intuitive qualities of cell orientation, cell orthogonality, cell volume, and cell aspect ratio. The decomposition can be used to analyze numerically generated curvilinear coordinate meshes and to assess the contribution of the mesh to the truncation error for any specific differential operator and algorithm. This is worked out in detail for Laplace's equation in nonconservative and conservative forms. The analysis is applied to the solution of the full potential code TAIR, showing grid plots, carpet plots, and truncation error for a NACA 0012 airfoil.
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.
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.
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.
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].
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.
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.
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.
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.
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.
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.
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.
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.
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
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
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.
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)
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.
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
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.
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.
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.
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.
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
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
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.
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.
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.
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.
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.
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.
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.
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.
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 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 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.
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.
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.
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 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 Solvers for Adaptive Mesh Refinement Grids
Quinlan, D.J.; Dendy, J.E., Jr.; Shapira, Y.
1999-06-03
We are developing multigrid methods that will efficiently solve elliptic problems with anisotropic and discontinuous coefficients on adaptive grids. The final product will be a library that provides for the simplified solution of such problems. This library will directly benefit the efforts of other Laboratory groups. The focus of this work is research on serial and parallel elliptic algorithms and the inclusion of our black-box multigrid techniques into this new setting. The approach applies the Los Alamos object-oriented class libraries that greatly simplify the development of serial and parallel adaptive mesh refinement applications. In the final year of this LDRD, we focused on putting the software together; in particular we completed the final AMR++ library, we wrote tutorials and manuals, and we built example applications. We implemented the Fast Adaptive Composite Grid method as the principal elliptic solver. We presented results at the Overset Grid Conference and other more AMR specific conferences. We worked on optimization of serial and parallel performance and published several papers on the details of this work. Performance remains an important issue and is the subject of continuing research work.
Fluxon Dynamics in Elliptic Annular Josephson Junctions
NASA Astrophysics Data System (ADS)
Monaco, Roberto; Mygind, Jesper
2016-04-01
We analyze the dynamics of a magnetic flux quantum (current vortex) trapped in a current-biased long planar elliptic annular Josephson tunnel junction. The system is modeled by a perturbed sine-Gordon equation that determines the spatial and temporal behavior of the phase difference across the tunnel barrier separating the two superconducting electrodes. In the absence of an external magnetic field, the fluxon dynamics in an elliptic annulus does not differ from that of a circular annulus where the stationary fluxon speed merely is determined by the system losses. The interaction between the vortex magnetic moment and a spatially homogeneous in-plane magnetic field gives rise to a tunable periodic non-sinusoidal potential which is strongly dependent on the annulus aspect ratio. We study the escape of the vortex from a well in the tilted potential when the bias current exceeds the depinning current. The smallest depinning current as well as the lowest sensitivity of the annulus to the external field is achieved when the axes ratio is equal to √{2}. The presented extensive numerical results are in good agreement with the findings of the perturbative approach. We also probe the rectifying properties of an asymmetric potential implemented with an egg-shaped annulus formed by two semi-elliptic arcs.
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
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
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.
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.
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
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]…
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.
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.
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
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.
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.
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.