#### Sample records for jacobian elliptic function

1. 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…

2. Exact Jacobian elliptic function solutions and hyperbolic function solutions for Sawada Kotere equation with variable coefficient

Liu, Qing; Zhu, Jia-Min

2006-03-01

Variable-coefficient Sawada Kotere equation is researched. By the means of modified mapping method, we establish a mapping relation between the known solutions of elliptic functional equation and the unknown solutions of variable-coefficient Sawada Kotere equation. Based on the relation, we easily deduce abundant exact solutions of Jacobi elliptic function and of hyperbolic function to variable-coefficient Sawada Kotere equation. The merit of our method is that, without much extra effort, we circumvent integration and directly get the above all solutions in an uniform way.

3. Gravity modeling: the Jacobian function and its approximation

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

4. 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…

5. Force-free Jacobian equilibria for Vlasov-Maxwell plasmas

SciTech Connect

Abraham-Shrauner, B.

2013-10-15

New analytic force-free Vlasov-Maxwell equilibria for thin current sheets are presented. The magnetic flux densities are expressed in terms of Jacobian elliptic functions of one Cartesian spatial coordinate. The magnetic flux densities reduce to previously reported hyperbolic functions in one limit and sinusoidal functions in another limit of the modulus k. A much wider class of nonlinear force-free Vlasov-Maxwell equilibria open expanded possibilities for modeling of solar system, astrophysical and laboratory plasmas. Modified Maxwellian distribution functions are determined explicitly in terms of Jacobian elliptic functions. Conditions for double peaked distribution functions that could be unstable are developed.

6. Elliptic Functions with Disconnected Julia Sets

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.

7. Elliptical billiards and hyperelliptic functions

Crespi, Bruno; Chang, Shau-Jin; Shi, Kang-Jie

1993-06-01

The geometrical properties of the elliptical billiard system are related to Poncelet's theorem. This theorem states that if a polygon is inscribed in a conic and circumscribed about a second conic, every point of the former conic is a vertex of a polygon with the same number of sides and the same perimeter. Chang and Friedberg have extended this theorem to three and higher dimensions. They have shown that the geometrical properties of the hyperelliptic billiard system are related to the algebraic character of a Poincaré map in the phase space. The geometrical and algebraic properties of the system can be understood in terms of the analytical structure of the equations of motion. These equations form a complete system of Abelian integrals. The integrability of the physical system is reflected by the topology of the Riemann surfaces associated to these integrals. The algebraic properties are connected with the existence of addition formulas for hyperelliptic functions. The main purpose of this study is to establish such a connection, and to provide an algebraic proof of Poncelet's theorem in three and higher dimensions.

8. Integration of large chemical kinetic mechanisms via exponential methods with Krylov approximations to Jacobian matrix functions

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.

9. Pendulum, elliptic functions, and relative cohomology classes

Françoise, J.-P.; Garrido, P. L.; Gallavotti, G.

2010-03-01

Revisiting canonical integration of the classical pendulum around its unstable equilibrium, normal hyperbolic canonical coordinates are constructed and an identity between elliptic functions is found whose proof can be based on symplectic geometry and global relative cohomology. Alternatively it can be reduced to a well known identity between elliptic functions. Normal canonical action-angle variables are also constructed around the stable equilibrium and a corresponding identity is exhibited.

10. 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.

11. Jacobi elliptic functions: A review of nonlinear oscillatory application problems

Kovacic, Ivana; Cveticanin, Livija; Zukovic, Miodrag; Rakaric, Zvonko

2016-10-01

This review paper is concerned with the applications of Jacobi elliptic functions to nonlinear oscillators whose restoring force has a monomial or binomial form that involves cubic and/or quadratic nonlinearity. First, geometric interpretations of three basic Jacobi elliptic functions are given and their characteristics are discussed. It is shown then how their different forms can be utilized to express exact solutions for the response of certain free conservative oscillators. These forms are subsequently used as a starting point for a presentation of different quantitative techniques for obtaining an approximate response for free perturbed nonlinear oscillators. An illustrative example is provided. Further, two types of externally forced nonlinear oscillators are reviewed: (i) those that are excited by elliptic-type excitations with different exact and approximate solutions; (ii) those that are damped and excited by harmonic excitations, but their approximate response is expressed in terms of Jacobi elliptic functions. Characteristics of the steady-state response are discussed and certain qualitative differences with respect to the classical Duffing oscillator excited harmonically are pointed out. Parametric oscillations of the oscillators excited by an elliptic-type forcing are considered as well, and the differences with respect to the stability chart of the classical Mathieu equation are emphasized. The adjustment of the Melnikov method to derive the general condition for the onset of homoclinic bifurcations in a system parametrically excited by an elliptic-type forcing is provided and compared with those corresponding to harmonic excitations. Advantages and disadvantages of the use of Jacobi elliptic functions in nonlinear oscillatory application problems are discussed and some suggestions for future work are given.

12. Applications of Elliptic Integral and Elliptic Function to Electric Power Cable Problems

Watanabe, Kazuo

The paper proposes an application of elliptic function to a new measuring method of electric resistivity of outer-semiconductive layer of XLPE cable. The new measuring method may substitute the conventional method. The resistivity can be obtained easily by measuring resistance between two electrodes which are attached to a circumferential edge on one side of the outer-semiconductive layer of a cable core sample. The solution process is applicable to heat conduction as well as hydromechanics.

13. The Jacobian factor in free energy simulations

Boresch, Stefan; Karplus, Martin

1996-09-01

The role of Jacobian factors in free energy simulations is described. They provide a simple interpretation of moment of inertia correction'' and dynamic stretch free energy'' terms in such simulations. Since the relevant Jacobian factors can often be evaluated analytically by use of the configurational partition function of a polyatomic molecule, it is possible to subtract them from the simulation results when they make unphysical contributions. An important case arises in alchemical simulations that use a single topology method and introduce dummy particles to have the same number of atoms in the initial and final state. The more general utility of the Jacobian factors for simulations of complex systems is briefly discussed.

14. The correlation function of galaxy ellipticities produced by gravitational lensing

NASA Technical Reports Server (NTRS)

Miralda-Escude, Jordi

1991-01-01

The correlation of galaxy ellipticities produced by gravitational lensing is calculated as a function of the power spectrum of density fluctuations in the universe by generalizing an analytical method developed by Gunn (1967). The method is applied to a model where identical objects with spherically symmetric density profiles are randomly laid down in space, and to the cold dark matter model. The possibility of detecting this correlation is discussed. Although an ellipticity correlation can also be caused by an intrinsic alignment of the axes of galaxies belonging to a cluster or a supercluster, a method is suggested by which one type of correlation can be distinguished from another. The advantage of this ellipticity correlation is that it is one of the few astronomical observations that can directly probe large-scale mass fluctuations in the universe.

15. 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…

16. The collective coordinates Jacobian

2002-05-01

We develop an expansion for the Jacobian of the transformation from particle coordinates to collective coordinates. As a demonstration, we use the lowest order of the expansion in conjunction with a variational principle to obtain the Percus Yevick equation for a monodisperse hard sphere system and the Lebowitz equations for a polydisperse hard sphere system.

17. A Jacobian generalization of the pseudo-Nambu-Goldstone boson potential

Hipólito-Ricaldi, W. S.; Villanueva, J. R.

We enlarge the classes of inflaton and quintessence fields by generalizing the pseudo-Nambu-Goldstone boson potential by means of elliptic Jacobian functions, which are characterized by a parameter k. We use such a generalization to implement an inflationary era and a late acceleration of the universe. As an inflationary model, the Jacobian generalization leads us to a number of e-foldings and a primordial spectrum of perturbations compatible with the Planck Collaboration 2015. As a quintessence model, a study of the evolution of its equation-of-state (EoS) and its w‧-w plane helps us to classify it as a thawing model. This allows us to consider analytical approximations for the EoS recently discovered for thawing quintessence. By using JLA supernovae Ia and Hubble parameter H(z) data sets, we perform an observational analysis of the viability of the model as quintessence.

18. Wave functions of elliptical quantum dots in a magnetic field

Zhou, Daming; Lorke, Axel

2015-03-01

We use the variational principle to obtain the wave functions of elliptical quantum dots under the influence of an external magnetic field. For the first excited states, whose wave functions have recently been mapped experimentally, we find a simple expression, based on a linear combination of the wave functions in the absence of a magnetic field. The results illustrate how a magnetic field breaks the x-y symmetry and mixes the corresponding eigenstates. The obtained eigenenergies agree well with those obtained by more involved analytical and numerical methods.

19. Some new addition formulae for Weierstrass elliptic functions

PubMed Central

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

20. Current State and Future Prospect of Applications of Elliptic Function to Electric Power Field

Kinoshita, Haruka; Watanabe, Kazuo

The paper deals with the current state and future prospect of applications of elliptic function to the electric power and energy field. In particular, practical use of conformal mapping technology by elliptic function are introduced for electric power cables. Returning to Riemann's basic principle “thinking instead of calculation”, against the main current of numerical calculation, we have a new understanding of elliptic function analysis for the usefulness and the beautiful with simplicity and elegance.

1. Miniaturized LTCC elliptic-function lowpass filters with side stopbands

DOE PAGES

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.

2. Permutation symmetry for theta functions

SciTech Connect

Carlson, B.C.

2011-01-21

This paper does for combinations of theta functions most of what Carlson (2004) [1] did for Jacobian elliptic functions. In each case the starting point is the symmetric elliptic integral R{sub F} of the first kind. Its three arguments (formerly squared Jacobian elliptic functions but now squared combinations of theta functions) differ by constants. Symbols designating the constants can often be used to replace 12 equations by three with permutation symmetry (formerly in the letters c, d, n for the Jacobian case but now in the subscripts 2, 3, 4 for theta functions). Such equations include derivatives and differential equations, bisection and duplication relations, addition formulas (apparently new for theta functions), and an example of pseudoaddition formulas.

3. Elliptic Preconditioner for Accelerating the Self-Consistent Field Iteration in Kohn--Sham Density Functional Theory

SciTech Connect

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.

4. Boundary-value problems for elliptic functional-differential equations and their applications

Skubachevskii, A. L.

2016-10-01

Boundary-value problems are considered for strongly elliptic functional-differential equations in bounded domains. In contrast to the case of elliptic differential equations, smoothness of generalized solutions of such problems can be violated in the interior of the domain and may be preserved only on some subdomains, and the symbol of a self-adjoint semibounded functional-differential operator can change sign. Both necessary and sufficient conditions are obtained for the validity of a Gårding-type inequality in algebraic form. Spectral properties of strongly elliptic functional-differential operators are studied, and theorems are proved on smoothness of generalized solutions in certain subdomains and on preservation of smoothness on the boundaries of neighbouring subdomains. Applications of these results are found to the theory of non-local elliptic problems, to the Kato square-root problem for an operator, to elasticity theory, and to problems in non-linear optics. Bibliography: 137 titles.

5. On uniform approximation of elliptic functions by Padé approximants

Khristoforov, Denis V.

2009-06-01

Diagonal Padé approximants of elliptic functions are studied. It is known that the absence of uniform convergence of such approximants is related to them having spurious poles that do not correspond to any singularities of the function being approximated. A sequence of piecewise rational functions is proposed, which is constructed from two neighbouring Padé approximants and approximates an elliptic function locally uniformly in the Stahl domain. The proof of the convergence of this sequence is based on deriving strong asymptotic formulae for the remainder function and Padé polynomials and on the analysis of the behaviour of a spurious pole. Bibliography: 23 titles.

6. Joint inversion of body wave receiver function and Rayleigh wave ellipticity

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

7. Scattering by an infinite homogenous anisotropic elliptic cylinder in terms of Mathieu functions and Fourier series.

PubMed

Mao, Shi-Chun; Wu, Zhen-Sen

2008-12-01

An exact solution to the two-dimensional scattering properties of an anisotropic elliptic cylinder for transverse electric polarization is presented. The internal field in an anisotropic elliptic cylinder is expressed as integral representations of Mathieu functions and Fourier series. The coefficients of the series expansion are obtained by imposing boundary conditions on the anisotropic-free-space interface. A matrix is developed to solve the nonorthogonality properties of Mathieu functions at the interface between two different media. Numerical results are given for the bistatic radar cross section and the amplitude of the total magnetic field along the x and y axes. The result is in agreement with that available as expected when an elliptic cylinder degenerates to a circular one.

8. Dynamically consistent Jacobian inverse for mobile manipulators

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.

9. Jacobi elliptic functions and the complete solution to the bead on the hoop problem

Baker, Thomas E.; Bill, Andreas

2012-06-01

Jacobi elliptic functions are flexible functions that appear in a variety of problems in physics and engineering. We introduce and describe important features of these functions and present a physical example from classical mechanics where they appear: a bead on a spinning hoop. We determine the complete analytical solution for the motion of a bead on the driven hoop for arbitrary initial conditions and parameter values.

10. Globular Cluster Luminosity Functions and Specific Frequencies in Dwarf Elliptical Galaxies

Miller, B. W.; Lotz, J. M.

2005-12-01

We present the final results on the globular cluster luminosity functions (GCLFs) and specific frequencies (SN) from 69 dwarf elliptical galaxies in the HST Dwarf Elliptical Galaxy Snapshot Survey (Lotz et al. 2004). The GCLFs for the Virgo and Fornax clusters are well fit by a t5 function with a peak at MV0=-7.25 ± 0.2 and an equivalent Gaussian sigma of 1.2 magnitudes. These values are very similar to those of globular clusters systems in giant elliptical galaxies. We also confirm our previous results (Miller et al. 1998) that SN in nucleated dwarfs is about a factor of two higher than in non-nucleated dwarfs. We also discuss the fraction of the stellar mass in dwarf elliptical galaxies that is currently found in globular clusters. Supported by the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., on behalf of the international Gemini partnership of Argentina, Australia, Brazil, Canada, Chile, the United Kingdom, and the United States of America.

11. Solving the differential biochemical Jacobian from metabolomics covariance data.

PubMed

Nägele, Thomas; Mair, Andrea; Sun, Xiaoliang; Fragner, Lena; Teige, Markus; Weckwerth, Wolfram

2014-01-01

High-throughput molecular analysis has become an integral part in organismal systems biology. In contrast, due to a missing systematic linkage of the data with functional and predictive theoretical models of the underlying metabolic network the understanding of the resulting complex data sets is lacking far behind. Here, we present a biomathematical method addressing this problem by using metabolomics data for the inverse calculation of a biochemical Jacobian matrix, thereby linking computer-based genome-scale metabolic reconstruction and in vivo metabolic dynamics. The incongruity of metabolome coverage by typical metabolite profiling approaches and genome-scale metabolic reconstruction was solved by the design of superpathways to define a metabolic interaction matrix. A differential biochemical Jacobian was calculated using an approach which links this metabolic interaction matrix and the covariance of metabolomics data satisfying a Lyapunov equation. The predictions of the differential Jacobian from real metabolomic data were found to be correct by testing the corresponding enzymatic activities. Moreover it is demonstrated that the predictions of the biochemical Jacobian matrix allow for the design of parameter optimization strategies for ODE-based kinetic models of the system. The presented concept combines dynamic modelling strategies with large-scale steady state profiling approaches without the explicit knowledge of individual kinetic parameters. In summary, the presented strategy allows for the identification of regulatory key processes in the biochemical network directly from metabolomics data and is a fundamental achievement for the functional interpretation of metabolomics data.

12. Solving the Differential Biochemical Jacobian from Metabolomics Covariance Data

PubMed Central

Nägele, Thomas; Mair, Andrea; Sun, Xiaoliang; Fragner, Lena; Teige, Markus; Weckwerth, Wolfram

2014-01-01

High-throughput molecular analysis has become an integral part in organismal systems biology. In contrast, due to a missing systematic linkage of the data with functional and predictive theoretical models of the underlying metabolic network the understanding of the resulting complex data sets is lacking far behind. Here, we present a biomathematical method addressing this problem by using metabolomics data for the inverse calculation of a biochemical Jacobian matrix, thereby linking computer-based genome-scale metabolic reconstruction and in vivo metabolic dynamics. The incongruity of metabolome coverage by typical metabolite profiling approaches and genome-scale metabolic reconstruction was solved by the design of superpathways to define a metabolic interaction matrix. A differential biochemical Jacobian was calculated using an approach which links this metabolic interaction matrix and the covariance of metabolomics data satisfying a Lyapunov equation. The predictions of the differential Jacobian from real metabolomic data were found to be correct by testing the corresponding enzymatic activities. Moreover it is demonstrated that the predictions of the biochemical Jacobian matrix allow for the design of parameter optimization strategies for ODE-based kinetic models of the system. The presented concept combines dynamic modelling strategies with large-scale steady state profiling approaches without the explicit knowledge of individual kinetic parameters. In summary, the presented strategy allows for the identification of regulatory key processes in the biochemical network directly from metabolomics data and is a fundamental achievement for the functional interpretation of metabolomics data. PMID:24695071

13. Estimates of azimuthal numbers associated with elementary elliptic cylinder wave functions

Kovalev, V. A.; Radaev, Yu. N.

2014-05-01

The paper deals with issues related to the construction of solutions, 2 π-periodic in the angular variable, of the Mathieu differential equation for the circular elliptic cylinder harmonics, the associated characteristic values, and the azimuthal numbers needed to form the elementary elliptic cylinder wave functions. A superposition of the latter is one possible form for representing the analytic solution of the thermoelastic wave propagation problem in long waveguides with elliptic cross-section contour. The classical Sturm-Liouville problem for the Mathieu equation is reduced to a spectral problem for a linear self-adjoint operator in the Hilbert space of infinite square summable two-sided sequences. An approach is proposed that permits one to derive rather simple algorithms for computing the characteristic values of the angular Mathieu equation with real parameters and the corresponding eigenfunctions. Priority is given to the application of the most symmetric forms and equations that have not yet been used in the theory of the Mathieu equation. These algorithms amount to constructing a matrix diagonalizing an infinite symmetric pentadiagonal matrix. The problem of generalizing the notion of azimuthal number of a wave propagating in a cylindrical waveguide to the case of elliptic geometry is considered. Two-sided mutually refining estimates are constructed for the spectral values of the Mathieu differential operator with periodic and half-periodic (antiperiodic) boundary conditions.

14. On the modularity of certain functions from the Gromov–Witten theory of elliptic orbifolds

PubMed Central

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

15. 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.

16. Numerical pole assignment by eigenvalue Jacobian inversion

NASA Technical Reports Server (NTRS)

Sevaston, George E.

1986-01-01

A numerical procedure for solving the linear pole placement problem is developed which operates by the inversion of an analytically determined eigenvalue Jacobian matrix. Attention is given to convergence characteristics and pathological situations. It is not concluded that the algorithm developed is suitable for computer-aided control system design with particular reference to the scan platform pointing control system for the Galileo spacecraft.

17. Formal convergence characteristics of elliptically constrained incremental Newton-Raphson algorithms

NASA Technical Reports Server (NTRS)

1982-01-01

Various aspects of the convergence, uniqueness, and existence properties associated with solutions generated via the elliptically constrained incremental Newton-Raphson (ECINR) algorithm are analyzed. Several theorems are developed, and the formal behavior of the elliptically constrained scheme developed by Padovan (1981) is discussed in detail. Consideration is given to global and local rates of convergence, to the determination of the occurrence of safety zones wherein the algorithm yields inherently convergent results, to formal limitations on the class of functions which the scheme can be applied to solve, and to single and multidimensional formalisms on existence uniqueness and convergence. Special attention is given to functions whose Jacobian matrix exhibit positive, negative, semi and indefinite properties. Several significant advantages of ECINR over the classical INR are mentioned.

18. PERSPECTIVES ON INTRACLUSTER ENRICHMENT AND THE STELLAR INITIAL MASS FUNCTION IN ELLIPTICAL GALAXIES

SciTech Connect

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.

19. Flux Jacobian Matrices For Equilibrium Real Gases

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1990-01-01

Improved formulation includes generalized Roe average and extension to three dimensions. Flux Jacobian matrices derived for use in numerical solutions of conservation-law differential equations of inviscid flows of ideal gases extended to real gases. Real-gas formulation of these matrices retains simplifying assumptions of thermodynamic and chemical equilibrium, but adds effects of vibrational excitation, dissociation, and ionization of gas molecules via general equation of state.

20. Effects of off-axis elliptical training on reducing pain and improving knee function in individuals with patellofemoral pain

PubMed Central

Tsai, Liang-Ching; Lee, Song Joo; Yang, Aaron J.; Ren, Yupeng; Press, Joel M.; Zhang, Li-Qun

2014-01-01

Objective To examine whether an off-axis elliptical training program reduces pain and improves knee function in individuals with patellofemoral pain (PFP). Design Controlled laboratory study, pre-test-post-test. Setting University rehabilitation center. Participants Twelve adult subjects with PFP. Interventions Subjects with PFP completed an exercise program consisting of 18 sessions of lower extremity off-axis training using a custom-made elliptical trainer that allows frontal-plane sliding and transverse-plane pivoting of the footplates. Main Outcome Measures Changes in knee pain and function post-training and 6 weeks following training were evaluated using the Knee Injury and Osteoarthritis Outcome Score (KOOS) and International Knee Documentation Committee (IKDC) scores. Lower extremity off-axis control was assessed by pivoting and sliding instability, calculated as the root mean square (RMS) of the footplate pivoting angle and sliding distance during elliptical exercise. Subjects’ single-leg hop distance and proprioception in detecting lower extremity pivoting motion were also evaluated. Results Subjects reported significantly greater KOOS and IKDC scores (increased by 12–18 points) and hop distance (increased by 0.2 m) following training. A significant decrease in the pivoting and sliding RMS was also observed following training. Additionally, subjects with PFP demonstrated improved pivoting proprioception when tested under a minimum-weight-bearing position. Conclusions An off-axis elliptical training program was effective in enhancing lower extremity neuromuscular control on the frontal and transverse planes, reducing pain and improving knee function in persons with PFP. PMID:25591131

1. Elliptically Weighted HOLICs for Weak-lensing Shear Measurement. I. Definitions and Isotropic Point-spread Function Correction

Okura, Yuki; Futamase, Toshifumi

2011-03-01

We develop a new method of estimating gravitational shear by adopting an elliptical weight function to measure background galaxy images. In doing so, we introduce the new concept of "zero plane," which is an imaginary source plane where shapes of all sources are perfect circles, and regard the intrinsic shear as the result of an imaginary lensing distortion. This makes the relation between the observed shear, intrinsic shear, and lensing distortion much simpler, and thus higher-order calculations are easier. The elliptical weight function allows us to measure the multipole moments of the shapes of background galaxies more precisely by weighting brighter parts of the image highly, and to reduce systematic error due to insufficient expansion of the weight function in the original approach of Kaiser et al. (KSB). Point-spread function (PSF) correction in the elliptically weighted higher-order lensing image characteristics (E-HOLICs) method becomes more complicated than in the KSB method. In this paper, we study isotropic PSF correction in detail. By adopting the lensing distortion as the ellipticity of the weight function, we are able to show that the shear estimation in the E-HOLICs method reduces to solve a polynomial in the absolute magnitude of the distortion. We compare the systematic errors between our approach and that of KSB using the Shear Testing Programme 2 simulation. It is confirmed that the KSB method overestimates the input shear for images with large ellipticities, and E-HOLICs correctly estimates the input shear even for such images. Anisotropic PSF correction and analysis of real data will be presented in a forthcoming paper.

2. Determination of the modular elliptic function in problems of free-flow filtration

Anakhaev, K. N.

2016-09-01

The calculated dependences in elementary functions for determining the modular elliptic function λ(τ) =λ1 + iλ2 obtained on the basis of consecutive (six) conformal mappings of a curvilinear triangle to a complex half-plane are presented. Comparison of the values of λ(τ) from the proposed dependences with the results of the Hamel-Gunter exact analytical solution for the boundary contour of the curvilinear triangle, i.e., the real axis of the complex half-plane, gives a very close coincidence (with the largest error of ≤1%). The use of the complex values of the function λ(τ) for the entire internal region of the curvilinear triangle makes it possible to solve one of the most difficult problems of the theory of filtration (filtration through a rectangular dam) in the direct formulation and, for the first time, to construct the pattern of an equal filtration-rate field (the family of isotaches) over the entire internal region of the dam. In this case, the boundary values of filtration rates for special cases (along the sides and along the base of the dam) completely coincide with the results of the Masket exact analytical calculations.

3. Statistical properties of Jacobian maps and the realization of unbiased large-deformation nonlinear image registration.

PubMed

Leow, Alex D; Yanovsky, Igor; Chiang, Ming-Chang; Lee, Agatha D; Klunder, Andrea D; Lu, Allen; Becker, James T; Davis, Simon W; Toga, Arthur W; Thompson, Paul M

2007-06-01

Maps of local tissue compression or expansion are often computed by comparing magnetic resonance imaging (MRI) scans using nonlinear image registration. The resulting changes are commonly analyzed using tensor-based morphometry to make inferences about anatomical differences, often based on the Jacobian map, which estimates local tissue gain or loss. Here, we provide rigorous mathematical analyses of the Jacobian maps, and use themto motivate a new numerical method to construct unbiased nonlinear image registration. First, we argue that logarithmic transformation is crucial for analyzing Jacobian values representing morphometric differences. We then examine the statistical distributions of log-Jacobian maps by defining the Kullback-Leibler (KL) distance on material density functions arising in continuum-mechanical models. With this framework, unbiased image registration can be constructed by quantifying the symmetric KL-distance between the identity map and the resulting deformation. Implementation details, addressing the proposed unbiased registration as well as the minimization of symmetric image matching functionals, are then discussed and shown to be applicable to other registration methods, such as inverse consistent registration. In the results section, we test the proposed framework, as well as present an illustrative application mapping detailed 3-D brain changes in sequential magnetic resonance imaging scans of a patient diagnosed with semantic dementia. Using permutation tests, we show that the symmetrization of image registration statistically reduces skewness in the log-Jacobian map.

4. Superposition of elliptic functions as solutions for a large number of nonlinear equations

2014-03-01

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, λϕ4, 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 dn2(x, m), it also admits solutions in terms of dn^2(x,m) ± sqrt{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.

5. Planar elliptic growth

SciTech Connect

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.

6. L_p-estimates for the nontangential maximal function of the solution to a second-order elliptic equation

Gushchin, A. K.

2016-10-01

The paper is concerned with the properties of the solution to a Dirichlet problem for a homogeneous second-order elliptic equation with L_p-boundary function, p>1. The same conditions are imposed on the coefficients of the equation and the boundary of the bounded domain as were used to establish the solvability of this problem. The L_p-norm of the nontangential maximal function is estimated in terms of the L_p-norm of the boundary value. This result depends on a new estimate, proved below, for the nontangential maximal function in terms of an analogue of the Lusin area integral. Bibliography: 31 titles.

7. TU-G-BRA-03: Predicting Radiation Therapy Induced Ventilation Changes Using 4DCT Jacobian Calculations

SciTech Connect

Patton, T; Du, K; Bayouth, J; Christensen, G; Reinhardt, J

2015-06-15

Purpose: Longitudinal changes in lung ventilation following radiation therapy can be mapped using four-dimensional computed tomography(4DCT) and image registration. This study aimed to predict ventilation changes caused by radiation therapy(RT) as a function of pre-RT ventilation and delivered dose. Methods: 4DCT images were acquired before and 3 months after radiation therapy for 13 subjects. Jacobian ventilation maps were calculated from the 4DCT images, warped to a common coordinate system, and a Jacobian ratio map was computed voxel-by-voxel as the ratio of post-RT to pre-RT Jacobian calculations. A leave-one-out method was used to build a response model for each subject: post-RT to pre-RT Jacobian ratio data and dose distributions of 12 subjects were applied to the subject’s pre-RT Jacobian map to predict the post-RT Jacobian. The predicted Jacobian map was compared to the actual post-RT Jacobian map to evaluate efficacy. Within this cohort, 8 subjects had repeat pre-RT scans that were compared as a reference for no ventilation change. Maps were compared using gamma pass rate criteria of 2mm distance-to-agreement and 6% ventilation difference. Gamma pass rates were compared using paired t-tests to determine significant differences. Further analysis masked non-radiation induced changes by excluding voxels below specified dose thresholds. Results: Visual inspection demonstrates the predicted post-RT ventilation map is similar to the actual map in magnitude and distribution. Quantitatively, the percentage of voxels in agreement when excluding voxels receiving below specified doses are: 74%/20Gy, 73%/10Gy, 73%/5Gy, and 71%/0Gy. By comparison, repeat scans produced 73% of voxels within the 6%/2mm criteria. The agreement of the actual post-RT maps with the predicted maps was significantly better than agreement with pre-RT maps (p<0.02). Conclusion: This work validates that significant changes to ventilation post-RT can be predicted. The differences between the

8. New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

PubMed Central

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

9. ELLIPTICAL-WEIGHTED HOLICs FOR WEAK LENSING SHEAR MEASUREMENT. II. POINT-SPREAD FUNCTION CORRECTION AND APPLICATION TO A370

SciTech Connect

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.

10. Off-diagonal Jacobian support for Nodal BCs

SciTech Connect

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 \

11. Dynamics on strata of trigonal Jacobians and some integrable problems of rigid body motion

Braden, H. W.; Enolski, V. Z.; Fedorov, Yu N.

2013-07-01

We present an algebraic geometrical and analytical description of the Goryachev case of rigid body motion. It belongs to a family of systems sharing the same properties: although completely integrable, they are not algebraically integrable, their solution is not meromorphic in the complex time and involves dynamics on the strata of the Jacobian varieties of trigonal curves. Although the strata of hyperelliptic Jacobians have already appeared in the literature in the context of some dynamical systems, the Goryachev case is the first example of an integrable system whose solution involves a more general curve. Several new features (and formulae) are encountered in the solution given in terms of sigma-functions of such a curve.

12. Algorithmic vs. finite difference Jacobians for infrared atmospheric radiative transfer

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.

13. The two-loop sunrise integral around four space-time dimensions and generalisations of the Clausen and Glaisher functions towards the elliptic case

Adams, Luise; Bogner, Christian; Weinzierl, Stefan

2015-07-01

We present the result for the finite part of the two-loop sunrise integral with unequal masses in four space-time dimensions in terms of the O ( ɛ0) -part and the O ( ɛ1) -part of the sunrise integral around two space-time dimensions. The latter two integrals are given in terms of elliptic generalisations of Clausen and Glaisher functions. Interesting aspects of the result for the O ( ɛ1 ) -part of the sunrise integral around two space-time dimensions are the occurrence of depth two elliptic objects and the weights of the individual terms.

14. Finite field-dependent BRST-anti-BRST transformations: Jacobians and application to the Standard Model

Yu. Moshin, Pavel; Reshetnyak, Alexander A.

2016-07-01

We continue our research1-4 and extend the class of finite BRST-anti-BRST transformations with odd-valued parameters λa, a = 1, 2, introduced in these works. In doing so, we evaluate the Jacobians induced by finite BRST-anti-BRST transformations linear in functionally-dependent parameters, as well as those induced by finite BRST-anti-BRST transformations with arbitrary functional parameters. The calculations cover the cases of gauge theories with a closed algebra, dynamical systems with first-class constraints, and general gauge theories. The resulting Jacobians in the case of linearized transformations are different from those in the case of polynomial dependence on the parameters. Finite BRST-anti-BRST transformations with arbitrary parameters induce an extra contribution to the quantum action, which cannot be absorbed into a change of the gauge. These transformations include an extended case of functionally-dependent parameters that implies a modified compensation equation, which admits nontrivial solutions leading to a Jacobian equal to unity. Finite BRST-anti-BRST transformations with functionally-dependent parameters are applied to the Standard Model, and an explicit form of functionally-dependent parameters λa is obtained, providing the equivalence of path integrals in any 3-parameter Rξ-like gauges. The Gribov-Zwanziger theory is extended to the case of the Standard Model, and a form of the Gribov horizon functional is suggested in the Landau gauge, as well as in Rξ-like gauges, in a gauge-independent way using field-dependent BRST-anti-BRST transformations, and in Rξ-like gauges using transverse-like non-Abelian gauge fields.

15. Challenges of Inversely Estimating Jacobian from Metabolomics Data

PubMed Central

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

16. Spin dynamics in thin nanometric elliptical Permalloy dots: A Brillouin light scattering investigation as a function of dot eccentricity

Gubbiotti, G.; Carlotti, G.; Okuno, T.; Grimsditch, M.; Giovannini, L.; Montoncello, F.; Nizzoli, F.

2005-11-01

Brillouin light scattering (BLS) spectra have been measured in arrays of cylindrical Permalloy dots with elliptical cross section, 200nm wide, 15nm thick, and eccentricities from 1 to 3. Several spin modes are observed and their frequencies tracked as a function of the direction of the applied 1.5kOe magnetic field H . The experimental data are interpreted within the framework of the recently introduced dynamical matrix method to calculate spin excitations in magnetic particles. We find that the mode frequencies strongly depend on the eccentricity of the dots and on the direction of the applied field. For fields along the principal axes the solutions can be classified into: (i) modes localized near the particle ends, (ii) modes with nodal lines perpendicular to H (backwardlike modes), (iii) modes with nodal lines parallel to H (Damon-Eshbach-like modes) and (iv) modes with both parallel and perpendicular nodal lines. In cases where the frequencies of two modes in different families are similar, some hybridization between the modes is observed. For H along nonsymmetry directions only the modes of type (i) remain reasonably well defined, other modes can at best be described as hybrids of modes in the above categories. Determining which of the modes is active in BLS experiments leads to excellent agreement with the experimental results.

17. 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.

18. On the Finite Brst Transformations: the Jacobians and the Standard Model with the Gauge-Invariant Gribov Horizon

Reshetnyak, A. A.; Moshin, P. Yu.

2017-03-01

A review of the finite field-dependent Becchi-Rouet-Stora-Tyutin (BRST) and BRST-antiBRST transformations is presented. Exact rules for calculating the Jacobian of the corresponding change of variables in the partition function are given. Infrared peculiarities under Rξ-gauges in the Yang-Mills theory and the Standard Model are examined in a gauge-invariant way with an appropriate horizon functional and unaffected N = 1, 2 BRST symmetries.

19. A new method for point-spread function correction using the ellipticity of re-smeared artificial images in weak gravitational lensing shear analysis

SciTech Connect

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.

20. Ellipticities of Elliptical Galaxies in Different Environments

Chen, Cheng-Yu; Hwang, Chorng-Yuan; Ko, Chung-Ming

2016-10-01

We studied the ellipticity distributions of elliptical galaxies in different environments. From the ninth data release of the Sloan Digital Sky Survey, we selected galaxies with absolute {r}\\prime -band magnitudes between -21 and -22. We used the volume number densities of galaxies as the criterion for selecting the environments of the galaxies. Our samples were divided into three groups with different volume number densities. The ellipticity distributions of the elliptical galaxies differed considerably in these three groups of different density regions. We deprojected the observed 2D ellipticity distributions into intrinsic 3D shape distributions, and the result showed that the shapes of the elliptical galaxies were relatively spherically symmetric in the high density region (HDR) and that relatively more flat galaxies were present in the low density region (LDR). This suggests that the ellipticals in the HDRs and LDRs have different origins or that different mechanisms might be involved. The elliptical galaxies in the LDR are likely to have evolved from mergers in relatively anisotropic structures, such as filaments and webs, and might contain information on the anisotropic spatial distribution of their parent mergers. By contrast, elliptical galaxies in the HDR might be formed in more isotropic structures, such as galaxy clusters, or they might encounter more torqueing effects compared with galaxies in LDRs, thereby becoming rounder.

1. Commutative Families of the Elliptic Macdonald Operator

Saito, Yosuke

2014-03-01

In the paper [J. Math. Phys. 50 (2009), 095215, 42 pages], Feigin, Hashizume, Hoshino, Shiraishi, and Yanagida constructed two families of commuting operators which contain the Macdonald operator (commutative families of the Macdonald operator). They used the Ding-Iohara-Miki algebra and the trigonometric Feigin-Odesskii algebra. In the previous paper [arXiv:1301.4912], the present author constructed the elliptic Ding-Iohara-Miki algebra and the free field realization of the elliptic Macdonald operator. In this paper, we show that by using the elliptic Ding-Iohara-Miki algebra and the elliptic Feigin-Odesskii algebra, we can construct commutative families of the elliptic Macdonald operator. In Appendix, we will show a relation between the elliptic Macdonald operator and its kernel function by the free field realization.

2. Endomorphism rings of certain Jacobians in finite characteristic

SciTech Connect

Zarkhin, Yu G

2002-08-31

We prove that, under certain additional assumptions, the endomorphism ring of the Jacobian of a curve y{sup l}=f(x) contains a maximal commutative subring isomorphic to the ring of algebraic integers of the lth cyclotomic field. Here l is an odd prime dividing the degree n of the polynomial f and different from the characteristic of the algebraically closed ground field; moreover, n{>=}9. The additional assumptions stipulate that all coefficients of f lie in some subfield K over which its (the polynomial's) Galois group coincides with either the full symmetric group S{sub n} or with the alternating group A{sub n}.

3. Multi-GPU Jacobian Accelerated Computing for Soft Field Tomography

PubMed Central

Borsic, A.; Attardo, E. A.; Halter, R. J.

2012-01-01

Image reconstruction in soft-field tomography is based on an inverse problem formulation, where a forward model is fitted to the data. In medical applications, where the anatomy presents complex shapes, it is common to use Finite Element Models to represent the volume of interest and to solve a partial differential equation that models the physics of the system. Over the last decade, there has been a shifting interest from 2D modeling to 3D modeling, as the underlying physics of most problems are three-dimensional. Though the increased computational power of modern computers allows working with much larger FEM models, the computational time required to reconstruct 3D images on a fine 3D FEM model can be significant, on the order of hours. For example, in Electrical Impedance Tomography applications using a dense 3D FEM mesh with half a million elements, a single reconstruction iteration takes approximately 15 to 20 minutes with optimized routines running on a modern multi-core PC. It is desirable to accelerate image reconstruction to enable researchers to more easily and rapidly explore data and reconstruction parameters. Further, providing high-speed reconstructions are essential for some promising clinical application of EIT. For 3D problems 70% of the computing time is spent building the Jacobian matrix, and 25% of the time in forward solving. In the present work, we focus on accelerating the Jacobian computation by using single and multiple GPUs. First, we discuss an optimized implementation on a modern multi-core PC architecture and show how computing time is bounded by the CPU-to-memory bandwidth; this factor limits the rate at which data can be fetched by the CPU. Gains associated with use of multiple CPU cores are minimal, since data operands cannot be fetched fast enough to saturate the processing power of even a single CPU core. GPUs have a much faster memory bandwidths compared to CPUs and better parallelism. We are able to obtain acceleration factors of

4. Image Ellipticity from Atmospheric Aberrations

SciTech Connect

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.

5. Design and Realization of a Three Degrees of Freedom Displacement Measurement System Composed of Hall Sensors Based on Magnetic Field Fitting by an Elliptic Function.

PubMed

Zhao, Bo; Wang, Lei; Tan, Jiu-Bin

2015-09-08

This paper presents the design and realization of a three degrees of freedom (DOFs) displacement measurement system composed of Hall sensors, which is built for the XYθz displacement measurement of the short stroke stage of the reticle stage of lithography. The measurement system consists of three pairs of permanent magnets mounted on the same plane on the short stroke stage along the Y, Y, X directions, and three single axis Hall sensors correspondingly mounted on the frame of the reticle stage. The emphasis is placed on the decoupling and magnetic field fitting of the three DOFs measurement system. The model of the measurement system is illustrated, and the XY positions and θZ rotation of the short stroke stage can be obtained by decoupling the sensor outputs. A magnetic field fitting by an elliptic function-based compensation method is proposed. The practical field intensity of a permanent magnet at a certain plane height can be substituted for the output voltage of a Hall sensors, which can be expressed by the elliptic function through experimental data as the crucial issue to calculate the three DOFs displacement. Experimental results of the Hall sensor displacement measurement system are presented to validate the proposed three DOFs measurement system.

6. Design and Realization of a Three Degrees of Freedom Displacement Measurement System Composed of Hall Sensors Based on Magnetic Field Fitting by an Elliptic Function

PubMed Central

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

7. Differential spectral synthesis with a library of elliptical galaxies

SciTech Connect

Gregg, M.

1995-12-07

Spectrophotometry of elliptical galaxies spanning a large rang in luminosity is analyzed for cosmic variations in color and line strength. The results are used to construct a base sequence spectral energy distribution as a function line strength, color, and velocity dispersion, representing old, red, uniform elliptical galaxy stellar populations. The sequence can be used as the starting point for investigating and modeling the stellar populations of other systems such as dwarf ellipticals, merger remnants, and, eventually, high redshift ellipticals.

8. Evaluation of Jacobian determinants by Monte Carlo methods - Application to the quasiclassical approximation in molecular scattering.

NASA Technical Reports Server (NTRS)

La Budde, R. A.

1972-01-01

Sampling techniques have been used previously to evaluate Jacobian determinants that occur in classical mechanical descriptions of molecular scattering. These determinants also occur in the quasiclassical approximation. A new technique is described which can be used to evaluate Jacobian determinants which occur in either description. This method is expected to be valuable in the study of reactive scattering using the quasiclassical approximation.

9. THE OPTICAL COLORS OF GIANT ELLIPTICAL GALAXIES AND THEIR METAL-RICH GLOBULAR CLUSTERS INDICATE A BOTTOM-HEAVY INITIAL MASS FUNCTION

SciTech Connect

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.

10. Uniform and C^1-approximability of functions on compact subsets of \\mathbb R^2 by solutions of second-order elliptic equations

Paramonov, P. V.; Fedorovskii, K. Yu

1999-02-01

Several necessary and sufficient conditions for the existence of uniform or C^1-approximation of functions on compact subsets of \\mathbb R^2 by solutions of elliptic systems of the form c_{11}u_{x_1x_1}+2c_{12}u_{x_1x_2}+c_{22}u_{x_2x_2}=0 with constant complex coefficients c_{11}, c_{12} and c_{22} are obtained. The proofs are based on a refinement of Vitushkin's localization method, in which one constructs localized approximating functions by "gluing together" some special many-valued solutions of the above equations. The resulting conditions of approximation are of a topological and metric nature.

11. Color-magnitude relations within globular cluster systems of giant elliptical galaxies: The effects of globular cluster mass loss and the stellar initial mass function

SciTech Connect

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.

12. Supersonic Elliptical Ramp Inlet

NASA Technical Reports Server (NTRS)

Adamson, Eric E. (Inventor); Fink, Lawrence E. (Inventor); Fugal, Spencer R. (Inventor)

2016-01-01

A supersonic inlet includes a supersonic section including a cowl which is at least partially elliptical, a ramp disposed within the cowl, and a flow inlet disposed between the cowl and the ramp. The ramp may also be at least partially elliptical.

13. Stresses and deformations in elliptical contacts

NASA Technical Reports Server (NTRS)

Hamrock, B. J.

1980-01-01

Topics presented deal with defining conformal and nonconformal surfaces, curvature sum and difference, and surface and subsurface stresses in elliptical contacts. Load-deflection relationships for nonconformal contacts are developed. The deformation within the contact is, among other things, a function of the ellipticity parameter and elliptic integrals of the first and second kinds. Simplified expressions that allow quick calculations of the deformation to be made simply from a knowledge of the applied load, the material properties, and the geometry of the contacting elements are presented.

14. Low-rank Quasi-Newton updates for Robust Jacobian lagging in Newton methods

SciTech Connect

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)

15. Solving Nonlinear Solid Mechanics Problems with the Jacobian-Free Newton Krylov Method

SciTech Connect

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.

16. Elliptical Laguerre-Gaussian correlated Schell-model beam.

PubMed

Chen, Yahong; Liu, Lin; Wang, Fei; Zhao, Chengliang; Cai, Yangjian

2014-06-02

A new kind of partially coherent beam with non-conventional correlation function named elliptical Laguerre-Gaussian correlated Schell-model (LGCSM) beam is introduced. Analytical propagation formula for an elliptical LGCSM beam passing through a stigmatic ABCD optical system is derived. The elliptical LGCSM beam exhibits unique features on propagation, e.g., its intensity in the far field (or in the focal plane) displays an elliptical ring-shaped beam profile, being qualitatively different from the circular ring-shaped beam profile of the circular LGCSM beam. Furthermore, we carry out experimental generation of an elliptical LGCSM beam with controllable ellipticity, and measure its focusing properties. Our experimental results are consistent with the theoretical predictions. The elliptical LGCSM beam will be useful in atomic optics.

17. Disks in elliptical galaxies

SciTech Connect

Rix, H.; White, S.D.M. )

1990-10-01

The abundance and strength of disk components in elliptical galaxies are investigated by studying the photometric properties of models containing a spheroidal r exp 1/4-law bulge and a weak exponential disk. Pointed isophotes are observed in a substantial fraction of elliptical galaxies. If these isophote distortions are interpreted in the framework of the present models, then the statistics of observed samples suggest that almost all radio-weak ellipticals could have disks containing roughly 20 percent of the light. It is shown that the E5 galaxy NGC 4660 has the photometric signatures of a disk containing a third of the light. 30 refs.

18. The Structure of Galaxies. III. Two Structural Families of Ellipticals

Schombert, James M.

2015-11-01

Using isophotal radius correlations for a sample of Two Micron All Sky Survey ellipticals, we have constructed a series of template surface brightness profiles to describe the profile shapes of ellipticals as a function of luminosity. The templates are a smooth function of luminosity, yet are not adequately matched to any fitting function supporting the view that ellipticals are weakly nonhomologous with respect to structure. Through comparison to the templates, it is discovered that ellipticals are divided into two families: those well matched to the templates, and a second class of ellipticals with distinctly shallower profile slopes. We refer to this second type of ellipticals as D class, an old morphological designation acknowledging diffuse appearance on photographic material. D ellipticals cover the same range of luminosity, size, and kinematics as normal ellipticals, but maintain a signature of recent equal-mass dry mergers. We propose that normal ellipticals grow after an initial dissipation formation era by accretion of low-mass companions as outlined in hierarchical formation scenarios, while D ellipticals are the result of later equal-mass mergers producing shallow luminosity profiles.

19. Jacobian transformed and detailed balance approximations for photon induced scattering

Wienke, B. R.; Budge, K. G.; Chang, J. H.; Dahl, J. A.; Hungerford, A. L.

2012-01-01

Photon emission and scattering are enhanced by the number of photons in the final state, and the photon transport equation reflects this in scattering-emission kernels and source terms. This is often a complication in both theoretical and numerical analyzes, requiring approximations and assumptions about background and material temperatures, incident and exiting photon energies, local thermodynamic equilibrium, plus other related aspects of photon scattering and emission. We review earlier schemes parameterizing photon scattering-emission processes, and suggest two alternative schemes. One links the product of photon and electron distributions in the final state to the product in the initial state by Jacobian transformation of kinematical variables (energy and angle), and the other links integrands of scattering kernels in a detailed balance requirement for overall (integrated) induced effects. Compton and inverse Compton differential scattering cross sections are detailed in appropriate limits, numerical integrations are performed over the induced scattering kernel, and for tabulation induced scattering terms are incorporated into effective cross sections for comparisons and numerical estimates. Relativistic electron distributions are assumed for calculations. Both Wien and Planckian distributions are contrasted for impact on induced scattering as LTE limit points. We find that both transformed and balanced approximations suggest larger induced scattering effects at high photon energies and low electron temperatures, and smaller effects in the opposite limits, compared to previous analyzes, with 10-20% increases in effective cross sections. We also note that both approximations can be simply implemented within existing transport modules or opacity processors as an additional term in the effective scattering cross section. Applications and comparisons include effective cross sections, kernel approximations, and impacts on radiative transport solutions in 1D

20. The elliptic anomaly

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.

1. Elliptic pfaffians and solvable lattice models

Rosengren, Hjalmar

2016-08-01

We introduce and study twelve multivariable theta functions defined by pfaffians with elliptic function entries. We show that, when the crossing parameter is a cubic root of unity, the domain wall partition function for the eight-vertex-solid-on-solid model can be written as a sum of two of these pfaffians. As a limit case, we express the domain wall partition function for the three-colour model as a sum of two Hankel determinants. We also show that certain solutions of the TQ-equation for the supersymmetric eight-vertex model can be expressed in terms of elliptic pfaffians.

2. Dwarf elliptical galaxies

NASA Technical Reports Server (NTRS)

Ferguson, Henry C.; Binggeli, Bruno

1994-01-01

Dwarf elliptical (dE) galaxies, with blue absolute magnitudes typically fainter than M(sub B) = -16, are the most numerous type of galaxy in the nearby universe. Tremendous advances have been made over the past several years in delineating the properties of both Local Group satellite dE's and the large dE populations of nearby clusters. We review some of these advances, with particular attention to how well currently availiable data can constrain (a) models for the formation of dE's, (b) the physical and evolutionary connections between different types of galaxies that overlap in the same portion of the mass-spectrum of galaxies, (c) the contribution of dE's to the galaxy luminosity functions in clusters and the field, (d) the star-forming histories of dE's and their possible contribution to faint galaxy counts, and (e) the clustering properties of dE's. In addressing these issues, we highlight the extent to which selection effects temper these constraints, and outline areas where new data would be particularly valuable.

3. 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.

4. On the explicit solutions of the elliptic Calogero system

Gavrilov, L.; Perelomov, A. M.

1999-12-01

Let q1,q2,…,qN be the coordinates of N particles on the circle, interacting with the integrable potential ∑jelliptic function. We show that every symmetric elliptic function in q1,q2,…,qN is a meromorphic function in time. We give explicit formulas for these functions in terms of genus N-1 theta functions.

5. 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.

6. 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.

7. Elliptic constructions of hyperkahler metrics

In this dissertation we develop a twistor-theoretic method of constructing hyperkahler metrics from holomorphic functions and elliptic curves. We obtain, among other things, new results concerning the Atiyah-Hitchin manifold, asymptotically locally Euclidean spaces of type Dn and certain Swann bundles. For example, in the Atiyah-Hitchin case we derive in an explicit holomorphic coordinate basis closed-form formulas for the metric, the holomorphic symplectic form and all three Kahler potentials. The equation describing an asymptotically locally Euclidean space of type Dn is found to admit an algebraic formulation in terms of the group law on a Weierstrass cubic. This curve has the structure of a Cayley cubic for a pencil generated by two transversal plane conics, that is, it takes the form Y2 = det( A+XB ), where A and B are the defining 3 x 3 matrices of the conics. In this light, the equation can be interpreted as the closure condition for an elliptic billiard trajectory tangent to the conic B and bouncing into various conics of the pencil determined by the positions of the monopoles.

8. Adaptive Jacobian Fuzzy Attitude Control for Flexible Spacecraft Combined Attitude and Sun Tracking System

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

9. The properties of radio ellipticals

Sparks, W. B.; Disney, M. J.; Wall, J. V.; Rodgers, A. W.

1984-03-01

The authors present optical and additional radio data for the bright galaxies of the Disney & Wall survey. These data form the basis of a statistical comparison of the properties of radio elliptical galaxies to radio-quiet ellipticals. The correlations may be explained by the depth of the gravitational potential well in which the galaxy resides governing the circumstances under which an elliptical galaxy rids itself of internally produced gas.

10. Random Matrix Theory and Elliptic Curves

DTIC Science & Technology

2014-11-24

related to the intervals of prime numbers. 15. SUBJECT TERMS EOARD, Random Matrix theory, Riemann Hypothesis, Elliptic Curves 16. SECURITY...range of quantities of fundamental importance in number theory. In the cases of the Riemann zeta function and Dirichlet L-functions, this information...investigation using analytic techniques. As an indication of their significance, two of the Clay Millennium Prize Problems, the Riemann Hypothesis and the

11. New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation

DOE PAGES

Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil

2016-04-29

We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioningmore » strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.« less

12. New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards' equation

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.

13. New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation

SciTech Connect

Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil

2016-04-29

We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new 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. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.

14. 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

15. Modulated Elliptical Slot

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).

16. C1,1 regularity for degenerate elliptic obstacle problems

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.

17. MIB Galerkin method for elliptic interface problems

PubMed Central

Xia, Kelin; Zhan, Meng; Wei, Guo-Wei

2014-01-01

Summary Material interfaces are omnipresent in the real-world structures and devices. Mathematical modeling of material interfaces often leads to elliptic partial differential equations (PDEs) with discontinuous coefficients and singular sources, which are commonly called elliptic interface problems. The development of high-order numerical schemes for elliptic interface problems has become a well defined field in applied and computational mathematics and attracted much attention in the past decades. Despite of significant advances, challenges remain in the construction of high-order schemes for nonsmooth interfaces, i.e., interfaces with geometric singularities, such as tips, cusps and sharp edges. The challenge of geometric singularities is amplified when they are associated with low solution regularities, e.g., tip-geometry effects in many fields. The present work introduces a matched interface and boundary (MIB) Galerkin method for solving two-dimensional (2D) elliptic PDEs with complex interfaces, geometric singularities and low solution regularities. The Cartesian grid based triangular elements are employed to avoid the time consuming mesh generation procedure. Consequently, the interface cuts through elements. To ensure the continuity of classic basis functions across the interface, two sets of overlapping elements, called MIB elements, are defined near the interface. As a result, differentiation can be computed near the interface as if there is no interface. Interpolation functions are constructed on MIB element spaces to smoothly extend function values across the interface. A set of lowest order interface jump conditions is enforced on the interface, which in turn, determines the interpolation functions. The performance of the proposed MIB Galerkin finite element method is validated by numerical experiments with a wide range of interface geometries, geometric singularities, low regularity solutions and grid resolutions. Extensive numerical studies confirm

18. MIB Galerkin method for elliptic interface problems.

PubMed

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

19. Implementing a Matrix-free Analytical Jacobian to Handle Nonlinearities in Models of 3D Lithospheric Deformation

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

20. Elliptic Hermite-Gaussian soliton in anisotropic strong nonlocal media

Wang, Qing; Li, JingZhen

2016-01-01

The propagation of elliptic Hermite-Gaussian (HG) beam in strong nonlocal media with elliptic Gaussian-shaped response function was studied by variational approach as well as numerical simulate. The evolution equations of the beam widths in x- and y-directions are obtained and the elliptic HG soliton is found. For forming such a soliton, the ratio of the square of the beam width must be proportional to the ratio of the characteristic length of the material, and the initial power should be equal to the two critical powers in x- and y-directions. For the anisotropic nonlinearity of the media, the instability of the high-order elliptic HG beam is increase as the increase of the order.

1. Acceleration of k-Eigenvalue / Criticality Calculations using the Jacobian-Free Newton-Krylov Method

SciTech Connect

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.

2. Visualization of redundancy resolution for kinematically redundant robots through the Jacobian null space

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.

3. 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.

4. New insights into input relegation control for inverse kinematics of a redundant manipulator. Part 1, On the orthogonality of matrices B and J and comparison to the extended Jacobian method

SciTech Connect

Unseren, M.A.; Reister, D.B.

1995-07-01

A method for kinematically modeling a constrained rigid body mechanical system and a method for controlling such a system termed input relegation control (IRC) were applied to resolve the kinematic redundancy of a serial link manipulator moving in an open chain configuration in. A set of equations was introduced to define a new vector variable parameterizing the redundant degrees of freedom (DOF) as a linear function of the joint velocities. The new set was combined with the classical kinematic velocity model of manipulator and solved to yield a well specified solution for the joint velocities as a function of the Cartesian velocities of the end effector and of the redundant DOF variable. In the previous work a technique was proposed for selecting the matrix relating the redundant DOF variable to the joint velocities which resulted in it rows being orthogonal to the rows of the Jacobian matrix. The implications for such a selection were not discussed in. In Part 1 of this report a basis for the joint space is suggested which provides considerable insight into why picking the aforementioned matrix to be orthogonal to the Jacobian is advantageous. A second objective of Part 1 is to compare the IRC method to the Extended Jacobian method of Baillieul and Martin and other related methods.

5. Focusing of an elliptical mirror based system with aberrations

Liu, Jian; Ai, Min; Zhang, He; Wang, Chao; Tan, Jiubin

2013-10-01

The effect of primary aberrations on the focusing of an elliptical mirror based system is studied by using the Debye integral. Specifically, the apodization function for elliptical mirror is derived and expressed by the eccentricity of the elliptical mirror. For the elliptical mirror with low aperture, intensity distributions in the presence of aberrations near focus are presented based on the derived scalar theory, while for the high-aperture condition, vectorial theory is used to describe the electric field in the focal region. In particular, the effect of aberrations is studied under radially polarized illumination. Moreover, tolerance conditions are given based on the knowledge of focusing with aberrations. It is found that the elliptical mirror based system shares a similar level of tolerance conditions with that of the single lens, while both of them are more sensitive to the presence of astigmatism than other aberrations. It is believed that the results will theoretically support the application of the high-aperture elliptical mirror in scanning microscopy.

6. ELLIPT2D: A Flexible Finite Element Code Written Python

SciTech Connect

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.

7. STRUCTURE AND FORMATION OF ELLIPTICAL AND SPHEROIDAL GALAXIES

SciTech Connect

Kormendy, John; Fisher, David B.; Cornell, Mark E.; Bender, Ralf E-mail: dbfisher@astro.as.utexas.edu E-mail: bender@usm.uni-muenchen.de

2009-05-15

New surface photometry of all known elliptical galaxies in the Virgo cluster is combined with published data to derive composite profiles of brightness, ellipticity, position angle, isophote shape, and color over large radius ranges. These provide enough leverage to show that Sersic log I {proportional_to} r {sup 1/n} functions fit the brightness profiles I(r) of nearly all ellipticals remarkably well over large dynamic ranges. Therefore, we can confidently identify departures from these profiles that are diagnostic of galaxy formation. Two kinds of departures are seen at small radii. All 10 of our ellipticals with total absolute magnitudes M{sub VT} {<=} -21.66 have cuspy cores-'missing light'-at small radii. Cores are well known and naturally scoured by binary black holes (BHs) formed in dissipationless ('dry') mergers. All 17 ellipticals with -21.54 {<=} M{sub VT} {<=} -15.53 do not have cores. We find a new distinct component in these galaxies: all coreless ellipticals in our sample have extra light at the center above the inward extrapolation of the outer Sersic profile. In large ellipticals, the excess light is spatially resolved and resembles the central components predicted in numerical simulations of mergers of galaxies that contain gas. In the simulations, the gas dissipates, falls toward the center, undergoes a starburst, and builds a compact stellar component that, as in our observations, is distinct from the Sersic-function main body of the elliptical. But ellipticals with extra light also contain supermassive BHs. We suggest that the starburst has swamped core scouring by binary BHs. That is, we interpret extra light components as a signature of formation in dissipative ('wet') mergers. Besides extra light, we find three new aspects to the ('E-E') dichotomy into two types of elliptical galaxies. Core galaxies are known to be slowly rotating, to have relatively anisotropic velocity distributions, and to have boxy isophotes. We show that they have

8. Jacobian-Based Iterative Method for Magnetic Localization in Robotic Capsule Endoscopy.

PubMed

Di Natali, Christian; Beccani, Marco; Simaan, Nabil; Valdastri, Pietro

2016-04-01

The purpose of this study is to validate a Jacobian-based iterative method for real-time localization of magnetically controlled endoscopic capsules. The proposed approach applies finite-element solutions to the magnetic field problem and least-squares interpolations to obtain closed-form and fast estimates of the magnetic field. By defining a closed-form expression for the Jacobian of the magnetic field relative to changes in the capsule pose, we are able to obtain an iterative localization at a faster computational time when compared with prior works, without suffering from the inaccuracies stemming from dipole assumptions. This new algorithm can be used in conjunction with an absolute localization technique that provides initialization values at a slower refresh rate. The proposed approach was assessed via simulation and experimental trials, adopting a wireless capsule equipped with a permanent magnet, six magnetic field sensors, and an inertial measurement unit. The overall refresh rate, including sensor data acquisition and wireless communication was 7 ms, thus enabling closed-loop control strategies for magnetic manipulation running faster than 100 Hz. The average localization error, expressed in cylindrical coordinates was below 7 mm in both the radial and axial components and 5° in the azimuthal component. The average error for the capsule orientation angles, obtained by fusing gyroscope and inclinometer measurements, was below 5°.

9. Recovery Discontinuous Galerkin Jacobian-Free Newton-Krylov Method for All-Speed Flows

SciTech Connect

HyeongKae Park; Robert Nourgaliev; Vincent Mousseau; Dana Knoll

2008-07-01

A novel numerical algorithm (rDG-JFNK) for all-speed fluid flows with heat conduction and viscosity is introduced. The rDG-JFNK combines the Discontinuous Galerkin spatial discretization with the implicit Runge-Kutta time integration under the Jacobian-free Newton-Krylov framework. We solve fully-compressible Navier-Stokes equations without operator-splitting of hyperbolic, diffusion and reaction terms, which enables fully-coupled high-order temporal discretization. The stability constraint is removed due to the L-stable Explicit, Singly Diagonal Implicit Runge-Kutta (ESDIRK) scheme. The governing equations are solved in the conservative form, which allows one to accurately compute shock dynamics, as well as low-speed flows. For spatial discretization, we develop a “recovery” family of DG, exhibiting nearly-spectral accuracy. To precondition the Krylov-based linear solver (GMRES), we developed an “Operator-Split”-(OS) Physics Based Preconditioner (PBP), in which we transform/simplify the fully-coupled system to a sequence of segregated scalar problems, each can be solved efficiently with Multigrid method. Each scalar problem is designed to target/cluster eigenvalues of the Jacobian matrix associated with a specific physics.

10. Jacobian-Based Iterative Method for Magnetic Localization in Robotic Capsule Endoscopy

PubMed Central

Di Natali, Christian; Beccani, Marco; Simaan, Nabil; Valdastri, Pietro

2016-01-01

The purpose of this study is to validate a Jacobian-based iterative method for real-time localization of magnetically controlled endoscopic capsules. The proposed approach applies finite-element solutions to the magnetic field problem and least-squares interpolations to obtain closed-form and fast estimates of the magnetic field. By defining a closed-form expression for the Jacobian of the magnetic field relative to changes in the capsule pose, we are able to obtain an iterative localization at a faster computational time when compared with prior works, without suffering from the inaccuracies stemming from dipole assumptions. This new algorithm can be used in conjunction with an absolute localization technique that provides initialization values at a slower refresh rate. The proposed approach was assessed via simulation and experimental trials, adopting a wireless capsule equipped with a permanent magnet, six magnetic field sensors, and an inertial measurement unit. The overall refresh rate, including sensor data acquisition and wireless communication was 7 ms, thus enabling closed-loop control strategies for magnetic manipulation running faster than 100 Hz. The average localization error, expressed in cylindrical coordinates was below 7 mm in both the radial and axial components and 5° in the azimuthal component. The average error for the capsule orientation angles, obtained by fusing gyroscope and inclinometer measurements, was below 5°. PMID:27087799

11. Code Coupling via Jacobian-Free Newton-Krylov Algorithms with Application to Magnetized Fluid Plasma and Kinetic Neutral Models

SciTech Connect

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.

12. General formulation of rovibrational kinetic energy operators and matrix elements in internal bond-angle coordinates using factorized Jacobians

Kopp, Wassja A.; Leonhard, Kai

2016-12-01

We show how inverse metric tensors and rovibrational kinetic energy operators in terms of internal bond-angle coordinates can be obtained analytically following a factorization of the Jacobian worked out by Frederick and Woywod. The structure of these Jacobians is exploited in two ways: On one hand, the elements of the metric tensor as well as its determinant all have the form ∑rmsin (αn) cos (βo) . This form can be preserved by working with the adjugate metric tensor that can be obtained without divisions. On the other hand, the adjugate can be obtained with less effort by exploiting the lower triangular structure of the Jacobians. Together with a suitable choice of the wavefunction, we avoid singularities and show how to obtain analytical expressions for the rovibrational kinetic energy matrix elements.

13. Energy and the Elliptical Orbit

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.

14. Guided modes of elliptical metamaterial waveguides

SciTech Connect

Halterman, Klaus; Feng, Simin; Overfelt, P. L.

2007-07-15

The propagation of guided electromagnetic waves in open elliptical metamaterial waveguide structures is investigated. The waveguide contains a negative-index media core, where the permittivity {epsilon} and permeability {mu} are negative over a given bandwidth. The allowed mode spectrum for these structures is numerically calculated by solving a dispersion relation that is expressed in terms of Mathieu functions. By probing certain regions of parameter space, we find the possibility exists to have extremely localized waves that transmit along the surface of the waveguide.

15. Nonclassical properties of odd and even elliptical states

Wang, Yueyuan; Liao, Qinghong; Liu, Zhengjun; Wang, Jicheng; Liu, Shutian

2011-01-01

As a generalization of the optical circular states, elliptical states which are quantum superposition of coherent states on an ellipse in the α plane are constructed. The statistical properties of the states are investigated by using sub-Poissonian photon statistics, quadrature squeezing, Wigner function and phase distribution. It is shown that the elliptical states exhibit stronger quadrature squeezing. The interference fringes between the coherent states form the elliptic annuli of Fock states in the Wigner function picture. The phase distribution is no longer uniform as the circular states. An experimental scheme is proposed for generating equidistant coherent-state superpositions on an ellipse for the motion of the center of mass of a trapped ion.

16. PD plus error-dependent integral nonlinear controllers for robot manipulators with an uncertain Jacobian matrix.

PubMed

Huang, C Q; Xie, L F; Liu, Y L

2012-11-01

In framework of traditional PID controllers, there are only three parameters available to tune, as a result, performance of the resulting system is always limited. As for Cartesian regulation of robot manipulators with uncertain Jacobian matrix, a scheme of PID controllers with error-dependent integral action is proposed. Compare with traditional PID controllers, the error-dependent integration is employed in the proposed PID controller, in which more parameters are available to be tuned. It provides additional flexibility for controller characteristics and tuning as well, and hence makes better transient performance. In addition, asymptotic stability of the resulting closed-loop system is guaranteed. All signals in the system are bounded when exogenous disturbances and measurement noises are bounded. Numerical example demonstrates the superior transient performance of the proposed controller over the traditional one via Cartesian space set-point manipulation of two-link robotic manipulator.

17. Pseudo-inverse Jacobian control with grey relational analysis for robot manipulators mounted on oscillatory bases

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.

18. A fast nonrigid image registration with constraints on the Jacobian using large scale constrained optimization.

PubMed

Sdika, Michaël

2008-02-01

This paper presents a new nonrigid monomodality image registration algorithm based on B-splines. The deformation is described by a cubic B-spline field and found by minimizing the energy between a reference image and a deformed version of a floating image. To penalize noninvertible transformation, we propose two different constraints on the Jacobian of the transformation and its derivatives. The problem is modeled by an inequality constrained optimization problem which is efficiently solved by a combination of the multipliers method and the L-BFGS algorithm to handle the large number of variables and constraints of the registration of 3-D images. Numerical experiments are presented on magnetic resonance images using synthetic deformations and atlas based segmentation.

19. The ESS elliptical cavity cryomodules

SciTech Connect

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.

20. 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…

1. Wavelength meter having elliptical wedge

DOEpatents

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.

2. Wavelength meter having elliptical wedge

DOEpatents

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.

3. 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.; Hollingshead, M.; Goodman, H. Michael (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: 7 HIRS (High-resolution Infrared Sounder) and 4 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.

4. 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.

5. An improved nearly-orthogonal structured mesh generation system with smoothness control functions

Technology Transfer Automated Retrieval System (TEKTRAN)

This paper presents an improved nearly-orthogonal structured mesh generation system with a set of smoothness control functions, which were derived based on the ratio between the Jacobian of the transformation matrix and the Jacobian of the metric tensor. The proposed smoothness control functions are...

6. Estimation of relative permeability curves using an improved Levenberg-Marquardt method with simultaneous perturbation Jacobian approximation

Zhou, Kang; Hou, Jian; Fu, Hongfei; Wei, Bei; Liu, Yongge

2017-01-01

Relative permeability controls the flow of multiphase fluids in porous media. The estimation of relative permeability is generally solved by Levenberg-Marquardt method with finite difference Jacobian approximation (LM-FD). However, the method can hardly be used in large-scale reservoirs because of unbearably huge computational cost. To eliminate this problem, the paper introduces the idea of simultaneous perturbation to simplify the generation of the Jacobian matrix needed in the Levenberg-Marquardt procedure and denotes the improved method as LM-SP. It is verified by numerical experiments and then applied to laboratory experiments and a real commercial oilfield. Numerical experiment indicates that LM-SP uses only 16.1% computational cost to obtain similar estimation of relative permeability and prediction of production performance compared with LM-FD. Laboratory experiment also shows the LM-SP has a 60.4% decrease in simulation cost while a 68.5% increase in estimation accuracy compared with the earlier published results. This is mainly because LM-FD needs 2n (n is the number of controlling knots) simulations to approximate Jacobian in each iteration, while only 2 simulations are enough in basic LM-SP. The convergence rate and estimation accuracy of LM-SP can be improved by averaging several simultaneous perturbation Jacobian approximations but the computational cost of each iteration may be increased. Considering the estimation accuracy and computational cost, averaging two Jacobian approximations is recommended in this paper. As the number of unknown controlling knots increases from 7 to 15, the saved simulation runs by LM-SP than LM-FD increases from 114 to 1164. This indicates LM-SP is more suitable than LM-FD for multivariate problems. Field application further proves the applicability of LM-SP on large real field as well as small laboratory problems.

7. System Size, Energy, Pseudorapidity, and Centrality Dependence of Elliptic Flow

SciTech Connect

Alver, B.; Ballintijn, M.; Busza, W.; Decowski, M. P.; Gulbrandsen, K.; Henderson, C.; Kane, J. L.; Kulinich, P.; Li, W.; Loizides, C.; Reed, C.; Roland, C.; Roland, G.; Stephans, G. S. F.; Vale, C.; Nieuwenhuizen, G. J. van; Vaurynovich, S. S.; Verdier, R.; Veres, G. I.; Wenger, E.

2007-06-15

This Letter presents measurements of the elliptic flow of charged particles as a function of pseudorapidity and centrality from Cu-Cu collisions at 62.4 and 200 GeV using the PHOBOS detector at the Relativistic Heavy Ion Collider. The elliptic flow in Cu-Cu collisions is found to be significant even for the most central events. For comparison with the Au-Au results, it is found that the detailed way in which the collision geometry (eccentricity) is estimated is of critical importance when scaling out system-size effects. A new form of eccentricity, called the participant eccentricity, is introduced which yields a scaled elliptic flow in the Cu-Cu system that has the same relative magnitude and qualitative features as that in the Au-Au system.

8. 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.

9. Cold dust in elliptical galaxies.

Wiklind, T.; Henkel, C.

1995-05-01

We have observed the λ1250 µm flux in 8 elliptical galaxies using the MPIfR 7-channel bolometer system attachet to the IRAM 30-m telescope. Five of the galaxies are detected at more than 3σ, two are tentatively detected and for one we obtained an upper limit. For two of the detected galaxies, the CO(2-1) line makes a significant contribution to the measured λ1250 µm flux. A comparison of the λ1250 µm fluxes, corrected for the CO(2-1) line contribution, with IRAS 60 and 100µm data shows that there is a colt dust component (Td~<20K) in two of the ellipticals. The other galaxies have λ1250 µm fluxes consistent with a one-temperature component, with Td typically between 20-30K.

10. Counterrotating cores in elliptical galaxies

Balcella, Marc Comas

The dynamics of the merger between a high- and a low-elliptical galaxy was studied to understand how kinematically peculiar cores in elliptical galaxies might form. Numerical simulations of mergers provide rotation curves, surface density profiles, surface density contour plots and velocity maps of the merger remnants, as well as diagnostics on the dynamics such as phase-space diagrams. This type of merger can create counterrotating cores. The core of the smaller galaxy, of higher density, is not disrupted by the primary tidal field and sinks to the center of the primary as an independent dynamical subsystem. Core counterrotation occurs only when the initial merger orbit is retrograde with respect to the pin of the primary. The remnant has higher effective radius and lower mean central surface density than the primary galaxy, but a smaller core radius. The adsorption of orbital energy and angular momentum by the primary particles greatly modifies the kinematic structure of the larger galaxy. Twisted rotation axes and isophote twists appear over the whole body of the remnant. These diagnostics may be used to determine whether observed peculiar cores might have formed via an elliptical-elliptical merger. Galaxies with counterrotating cores should show a complex velocity field, isophotal irregularities, and, in general, a slow rotation in the main body of the galaxy. The present experiments are the first galaxy-satellite merger experiments involving an active, rotating secondary. They show that part of the orbital angular momentum is absorbed by the secondary, thus the secondary contributes to its own sinking: the sinking rate depends on the orientation of the secondary spin. Long-slit spectroscopic observations of NGC 3656 are reported.

11. Exploration of material removal rate of srf elliptical cavities as a function of media type and cavity shape on niobium and copper using centrifugal barrel polishing (cbp)

SciTech Connect

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.

12. The richness of the globular cluster system of NGC 3923: Clues to elliptical galaxy formation

NASA Technical Reports Server (NTRS)

Zepf, Stephen E.; Geisler, Doug; Ashman, Keith M.

1994-01-01

We present new data on the globular cluster system of the elliptical galaxy NGC 3923 which show that it has the most globular clusters per unit luminosity of any noncluster elliptical yet observed, with S(sub N) = 6.4 +/- 1.4. NGC 3923 is also among the brightest ellipticals outside of a galaxy cluster for which the number of globular clusters has been determined. Our observation of a large number of clusters per unit luminosity (high S(sub N)-value) for a bright elliptical in a sparse environment is consistent with the suggestion of Djorgovski and Santiago that the number of globular clusters is a power-law function of the luminosity with an exponent greater than 1. We relate this higher specific frequency of globular clusters in more luminous galaxies to other observations which indicate that the physical conditions within elliptical galaxies at the time of their formation were dependent on galaxy mass.

13. Joint contribution to fingertip movement during a number entry task: an application of Jacobian matrix.

PubMed

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.

14. Optimization of computations for adjoint field and Jacobian needed in 3D CSEM inversion

Dehiya, Rahul; Singh, Arun; Gupta, Pravin K.; Israil, M.

2017-01-01

We present the features and results of a newly developed code, based on Gauss-Newton optimization technique, for solving three-dimensional Controlled-Source Electromagnetic inverse problem. In this code a special emphasis has been put on representing the operations by block matrices for conjugate gradient iteration. We show how in the computation of Jacobian, the matrix formed by differentiation of system matrix can be made independent of frequency to optimize the operations at conjugate gradient step. The coarse level parallel computing, using OpenMP framework, is used primarily due to its simplicity in implementation and accessibility of shared memory multi-core computing machine to almost anyone. We demonstrate how the coarseness of modeling grid in comparison to source (computational receivers) spacing can be exploited for efficient computing, without compromising the quality of the inverted model, by reducing the number of adjoint calls. It is also demonstrated that the adjoint field can even be computed on a grid coarser than the modeling grid without affecting the inversion outcome. These observations were reconfirmed using an experiment design where the deviation of source from straight tow line is considered. Finally, a real field data inversion experiment is presented to demonstrate robustness of the code.

15. Chow groups of intersections of quadrics via homological projective duality and (Jacobians of) non-commutative motives

2016-06-01

Conjectures of Beilinson-Bloch type predict that the low-degree rational Chow groups of intersections of quadrics are one-dimensional. This conjecture was proved by Otwinowska in [20]. By making use of homological projective duality and the recent theory of (Jacobians of) non-commutative motives, we give an alternative proof of this conjecture in the case of a complete intersection of either two quadrics or three odd-dimensional quadrics. Moreover, we prove that in these cases the unique non-trivial algebraic Jacobian is the middle one. As an application, we make use of Vial's work [26], [27] to describe the rational Chow motives of these complete intersections and show that smooth fibrations into such complete intersections over bases S of small dimension satisfy Murre's conjecture (when \\dim (S)≤ 1), Grothendieck's standard conjecture of Lefschetz type (when \\dim (S)≤ 2), and Hodge's conjecture (when \\dim(S)≤ 3).

16. Time growth rate and field profiles of hybrid modes excited by a relativistic elliptical electron beam in an elliptical metallic waveguide with dielectric rod

SciTech Connect

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.

17. An Implicit Energy-Conservative 2D Fokker-Planck Algorithm. II. Jacobian-Free Newton-Krylov Solver

Chacón, L.; Barnes, D. C.; Knoll, D. A.; Miley, G. H.

2000-01-01

Energy-conservative implicit integration schemes for the Fokker-Planck transport equation in multidimensional geometries require inverting a dense, non-symmetric matrix (Jacobian), which is very expensive to store and solve using standard solvers. However, these limitations can be overcome with Newton-Krylov iterative techniques, since they can be implemented Jacobian-free (the Jacobian matrix from Newton's algorithm is never formed nor stored to proceed with the iteration), and their convergence can be accelerated by preconditioning the original problem. In this document, the efficient numerical implementation of an implicit energy-conservative scheme for multidimensional Fokker-Planck problems using multigrid-preconditioned Krylov methods is discussed. Results show that multigrid preconditioning is very effective in speeding convergence and decreasing CPU requirements, particularly in fine meshes. The solver is demonstrated on grids up to 128×128 points in a 2D cylindrical velocity space (vr, vp) with implicit time steps of the order of the collisional time scale of the problem, τ. The method preserves particles exactly, and energy conservation is improved over alternative approaches, particularly in coarse meshes. Typical errors in the total energy over a time period of 10τ remain below a percent.

18. 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.

19. Counterrotating Cores in Elliptical Galaxies.

Balcells, Marc Comas

The dynamics of the merger between a high- and a low-luminosity elliptical galaxy has been studied to understand how kinematically peculiar cores in elliptical galaxies might form. Numerical simulations of mergers provide rotation curves, surface density profiles, surface density contour plots and velocity maps of the merger remnants, as well as diagnostics on the dynamics such as phase-space diagrams. This type of merger can create counterrotating cores. The core of the smaller galaxy, of higher density, is not disrupted by the primary tidal field and sinks to the center of the primary as an independent dynamical subsystem. Core counterrotation occurs only when the initial merger orbit is retrograde with respect to the spin of the primary. The remnant has higher effective radius and lower mean central surface density than the primary galaxy, but a smaller core radius. The adsorption of orbital energy and angular momentum by the primary particles greatly modifies the kinematic structure of the larger galaxy. Twisted rotation axes and isophote twists appear over the whole body of the remnant. These diagnostics may be used to determine whether observed peculiar cores might have formed via an elliptical-elliptical merger. Galaxies with counterrotating cores should show a complex velocity field, isophotal irregularities, and, in general, a slow rotation in the main body of the galaxy. The present experiments are the first galaxy-satellite merger experiments involving an active, rotating secondary. They show that part of the orbital angular momentum is absorbed by the secondary, thus the secondary contributes to its own sinking: the sinking rate depends on the orientation of the secondary spin. Long-slit spectroscopic observations of NGC 3656 are reported. Rotation curves indicate that NGC 3656 contains a core spinning in a direction perpendicular to the rotation in the main body of the galaxy. Velocity reversals at intermediate radii are also observed. These features

20. Skewness of elliptic flow fluctuations

Giacalone, Giuliano; Yan, Li; Noronha-Hostler, Jacquelyn; Ollitrault, Jean-Yves

2017-01-01

Using event-by-event hydrodynamic calculations, we find that the fluctuations of the elliptic flow (v2) in the reaction plane have a negative skew. We compare the skewness of v2 fluctuations to that of initial eccentricity fluctuations. We show that skewness is the main effect lifting the degeneracy between higher-order cumulants, with negative skew corresponding to the hierarchy v2{4 } >v2{6 } observed in Pb+Pb collisions at the CERN Large Hadron Collider. We describe how the skewness can be measured experimentally and show that hydrodynamics naturally reproduces its magnitude and centrality dependence.

1. Elliptic Bessel processes and elliptic Dyson models realized as temporally inhomogeneous processes

Katori, Makoto

2016-10-01

The Bessel process with parameter D > 1 and the Dyson model of interacting Brownian motions with coupling constant β > 0 are extended to the processes in which the drift term and the interaction terms are given by the logarithmic derivatives of Jacobi's theta functions. They are called the elliptic Bessel process, eBES(D), and the elliptic Dyson model, eDYS(β), respectively. Both are realized on the circumference of a circle [0, 2πr) with radius r > 0 as temporally inhomogeneous processes defined in a finite time interval [0, t∗), t∗ < ∞. Transformations of them to Schrödinger-type equations with time-dependent potentials lead us to proving that eBES(D) and eDYS(β) can be constructed as the time-dependent Girsanov transformations of Brownian motions. In the special cases where D = 3 and β = 2, observables of the processes are defined and the processes are represented for them using the Brownian paths winding round a circle and pinned at time t∗. We show that eDYS(2) has the determinantal martingale representation for any observable. Then it is proved that eDYS(2) is determinantal for all observables for any finite initial configuration without multiple points. Determinantal processes are stochastic integrable systems in the sense that all spatio-temporal correlation functions are given by determinants controlled by a single continuous function called the spatio-temporal correlation kernel.

2. Horizon complementarity in elliptic de Sitter space

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.

3. 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.

4. Elliptical galaxies kinematics within general relativity with renormalization group effects

SciTech Connect

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)

5. Advanced Light Source elliptical wiggler

Hoyer, E.; Akre, J.; Humphries, D.; Marks, S.; Minamihara, Y.; Pipersky, P.; Plate, D.; Schlueter, R.

1995-02-01

A 3.5-m-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 at Lawrence Berkeley Laboratory. Calculations of spectral performance show that the flux of circularly polarized photons exceeds 1013 photons/s over the 50 eV to 10 keV operating range for current of 0.4 A and 1.5 GeV electron energy. This device features vertical and horizontal magnetic structures of 14 and 141/2 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.

6. Matrix factorizations and elliptic fibrations

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.

7. Thermopile detector of light ellipticity

PubMed Central

Lu, Feng; Lee, Jongwon; Jiang, Aiting; Jung, Seungyong; Belkin, Mikhail A.

2016-01-01

Polarimetric imaging is widely used in applications from material analysis to biomedical diagnostics, vision and astronomy. The degree of circular polarization, or light ellipticity, is associated with the S3 Stokes parameter which is defined as the difference in the intensities of the left- and right-circularly polarized components of light. Traditional way of determining this parameter relies on using several external optical elements, such as polarizers and wave plates, along with conventional photodetectors, and performing at least two measurements to distinguish left- and right-circularly polarized light components. Here we theoretically propose and experimentally demonstrate a thermopile photodetector element that provides bipolar voltage output directly proportional to the S3 Stokes parameter of the incident light. PMID:27703152

8. Jacobian-free Newton Krylov discontinuous Galerkin method and physics-based preconditioning for nuclear reactor simulations

SciTech Connect

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.

9. Implicit solution of Navier-Stokes equations on staggered curvilinear grids using a Newton-Krylov method with a novel analytical Jacobian.

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.

10. 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.

11. MegaLUT: Correcting ellipticity measurements of galaxies

Tewes, Malte; Cantale, Nicolas; Courbin, Frédéric; Kitching, Thomas; Meylan, Georges

2012-03-01

MegaLUT is a simple and fast method to correct ellipticity measurements of galaxies from the distortion by the instrumental and atmospheric point spread function (PSF), in view of weak lensing shear measurements. The method performs a classification of galaxies and associated PSFs according to measured shape parameters, and builds a lookup table of ellipticity corrections by supervised learning. This new method has been applied to the GREAT10 image analysis challenge, and demonstrates a refined solution that obtains the highly competitive quality factor of Q = 142, without any power spectrum denoising or training. Of particular interest is the efficiency of the method, with a processing time below 3 ms per galaxy on an ordinary CPU.

12. 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.

13. Existence of solution for a generalized quasilinear elliptic problem

Furtado, Marcelo F.; Silva, Edcarlos D.; Silva, Maxwell L.

2017-03-01

It establishes existence and multiplicity of solutions to the elliptic quasilinear Schrödinger equation -div(g2(u ) ∇u ) +g (u ) g'(u ) |∇u| 2 +V (x ) u =h (x ,u ) ,x ∈ℝN ,where g, h, V are suitable smooth functions. The function g is asymptotically linear at infinity and, for each fixed x ∈ℝN , the function h(x, s) behaves like s at the origin and s3 at infinity. In the proofs, we apply variational methods.

14. The noise from supersonic elliptic jets

NASA Technical Reports Server (NTRS)

Morris, Philip J.; Bhat, Thonse R. S.

1992-01-01

This paper presents calculations of the noise radiated by a supersonic elliptic jet. The large scale structures in the jet, that are the predominant source of noise in the downstream direction, are modeled as instability waves. The evolution of the instability waves is determined by a local, linear, inviscid analysis. An expression is derived for the acoustic field outside the jet and the far field directivity associated with each instability wave. Calculations are performed for a Mach 1.5 elliptic jet with aspect ratio 2:1 and a Mach 2.0 elliptic jet with aspect ratio 2:1 and a Mach 2.0 elliptic jet with aspect ratio 3:1. The mean flow development is taken from experimental results. Comparisons are made with far field acoustic measurements.

15. Theory of the quadrature elliptic birdcage coil.

PubMed

Leifer, M C

1997-11-01

This paper presents the theory of the quadrature birdcage coil wound on an elliptic cylindrical former. A conformal transformation of the ellipse to a circular geometry is used to derive the optimal sampling of the continuous surface current distribution to produce uniform magnetic fields within an elliptic cylinder. The analysis is rigorous for ellipses of any aspect ratio and shows how to produce quadrature operation of the elliptic birdcage with a conventional hybrid combiner. Insight gained from the transformation is also used to analyze field homogeneity, find the optimal RF shield shape, and specify component values to produce the correct current distribution in practice. Measurements and images from a 16-leg elliptic birdcage coil at both low and high frequencies show good quadrature performance, homogeneity, and sensitivity.

16. Multiple solutions for resonant semilinear elliptic problems in

López Garza, Gabriel; Rumbos, Adolfo J.

2005-05-01

We prove the existence of multiple nontrivial solutions for the semilinear elliptic problem -[Delta]u=h([lambda]u+g(u)) in , , where h[set membership, variant]L1[intersection]L[alpha] for [alpha]>N/2, N[greater-or-equal, slanted]3, g is a function that has at most linear growth at infinity, g(0)=0, and [lambda] is an eigenvalue of the corresponding linear problem -[Delta]u=[lambda]hu in , . Existence of multiple solutions, for certain values of g'(0), is obtained by imposing a generalized Landesman-Lazer type condition. We use the saddle point theorem of Ambrosetti and Rabinowitz and the mountain pass theorem, as well as a Morse-index result of Ambrosetti [A. Ambrosetti, Differential Equations with Multiple Solutions and Nonlinear Functional Analysis, Equadiff 82, Lecture Notes in Math., vol. 1017, Springer-Verlag, Berlin, 1983] and a Leray-Schauder index theorem for mountain pass type critical points due to Hofer [H. Hofer, A note on the Topological Degree at a critical Point of Mountain Pass Type, Proc. Amer. Math. Soc. 90 (1984) 309-315]. The results of this paper are based upon multiplicity results for resonant problems on bounded domains in [E. Landesman, S. Robinson, A. Rumbos, Multiple solutions of semilinear elliptic problems at resonance, Nonlinear Anal. 24 (1995) 1049-1059] and [S. Robinson, Multiple solutions for semilinear elliptic boundary value problems at resonance, Electron. J. Differential Equations 1995 (1995) 1-14], and complement a previous existence result by the authors in [G. López Garza, A. Rumbos, Resonance and strong resonance for semilinear elliptic equations in , Electron. J. Differential Equations 2003 (2003) 1-22] for resonant problems in in which g was assumed to be bounded.

17. Elastohydrodynamic lubrication of elliptical contacts

NASA Technical Reports Server (NTRS)

Hamrock, B. J.

1981-01-01

The determination of the minimum film thickness within contact is considered for both fully flooded and starved conditions. A fully flooded conjunction is one in which the film thickness is not significantly changed when the amount of lubricant is increased. The fully flooded results presented show the influence of contact geometry on minimum film thickness as expressed by the ellipticity parameter and the dimensionless speed, load, and materials parameters. These results are applied to materials of high elastic modulus (hard EHL), such as metal, and to materials of low elastic modulus(soft EHL), such as rubber. In addition to the film thickness equations that are developed, contour plots of pressure and film thickness are given which show the essential features of elastohydrodynamically lubricated conjunctions. The crescent shaped region of minimum film thickness, with its side lobes in which the separation between the solids is a minimum, clearly emerges in the numerical solutions. In addition to the 3 presented for the fully flooded results, 15 more cases are used for hard EHL contacts and 18 cases are used for soft EHL contacts in a theoretical study of the influence of lubricant starvation on film thickness and pressure. From the starved results for both hard and soft EHL contacts, a simple and important dimensionless inlet boundary distance is specified. This inlet boundary distance defines whether a fully flooded or a starved condition exists in the contact. Contour plots of pressure and film thickness in and around the contact are shown for conditions.

18. A transmission line model for propagation in elliptical core optical fibers

SciTech Connect

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.

19. REACTIVE TRANSPORT MODELING USING A PARALLEL FULLY-COUPLED SIMULATOR BASED ON PRECONDITIONED JACOBIAN-FREE NEWTON-KRYLOV

SciTech Connect

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.

20. Galerkin Methods for Nonlinear Elliptic Equations.

Murdoch, Thomas

Available from UMI in association with The British Library. Requires signed TDF. This thesis exploits in the nonlinear situation the optimal approximation property of the finite element method for linear, elliptic problems. Of particular interest are the steady state semiconductor equations in one and two dimensions. Instead of discretising the differential equations by the finite element method and solving the nonlinear algebraic equations by Newton's method, a Newton linearisation of the continuous problem is preferred and a sequence of linear problems solved until some convergence criterion is achieved. For nonlinear Poisson equations, this approach reduces to solving a sequence of linear, elliptic, self -adjoint problems, their approximation by the finite element being optimal in a suitably defined energy norm. Consequently, there is the potential to recover a smoother representation of the underlying solution at each step of the Newton iteration. When this approach is applied to the continuity equations for semiconductor devices, a sequence of linear problems of the form -_{nabla }(anabla u - bu) = f must be solved. The Galerkin method in its crude form does not adequately represent the true solution: however, generalising the framework to permit Petrov-Galerkin approximations remedies the situation. For one dimensional problems, the work of Barrett and Morton allows an optimal test space to be chosen at each step of the Newton iteration so that the resulting approximation is near optimal in a norm closely related to the standard L^2 norm. More detailed information about the underlying solution can then be obtained by recovering a solution of an appropriate form. For two-dimensional problems, since the optimal test functions are difficult to find in practice, an upwinding method due to Heinrich et.al. is used at each step of the Newton iteration. Also, a framework is presented in which various upwind methods may be compared. The thesis also addresses the

1. Kinematical and Dynamical Modeling of Elliptical Galaxies

Mamon, G. A.; Łokas, E.; Dekel, A.; Stoehr, F.; Cox, T. J.

Elements of kinematical and dynamical modeling of elliptical galaxies are presented. In projection, NFW models resemble Sérsic models, but with a very narrow range of shapes (m=3±1). The total density profile of ellipticals cannot be NFW-like because the predicted local M/L and aperture velocity dispersion within an effective radius (R_e) are much lower than observed. Stars must then dominate ellipticals out to a few R_e. Fitting an NFW model to the total density profile of Sérsic+NFW (stars+dark matter [DM]) ellipticals results in very high concentration parameters, as found by X-ray observers. Kinematical modeling of ellipticals assuming an isotropic NFW DM model underestimates M/L at the virial radius by a factor of 1.6 to 2.4, because dissipationless ΛCDM halos have slightly different density profiles and slightly radial velocity anisotropy. In N-body+gas simulations of ellipticals as merger remnants of spirals embedded in DM halos, the slope of the DM density profile is steeper when the initial spiral galaxies are gas-rich. The Hansen & Moore (2006) relation between anisotropy and the slope of the density profile breaks down for gas and DM, but the stars follow an analogous relation with slightly less radial anisotropies for a given density slope. Using kurtosis (h_4) to infer anisotropy in ellipticals is dangerous, as h4 is also sensitive to small levels of rotation. The stationary Jeans equation provides accurate masses out to 8 R_e. The discrepancy between the modeling of Romanowsky et al. (2003), indicating a dearth of DM in ellipticals, and the simulations analyzed by Dekel et al. (2005), which match the spectroscopic observations of ellipticals, is partly due to radial anisotropy and to observing oblate ellipticals face-on. However, one of the 15 solutions to the orbit modeling of Romanowsky et al. is found to have an amount and concentration of DM consistent with ΛCDM predictions.

2. Instability of a supersonic shock free elliptic jet

SciTech Connect

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.

3. Properties of Ellipticity Correlation with Atmospheric Structure from Gemini South

SciTech Connect

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.

4. Properties of Ellipticity Correlation with Atmospheric Structure From Gemini South

SciTech Connect

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.

5. Shape measurement biases from underfitting and ellipticity gradients

DOE PAGES

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

6. 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.

7. 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.

8. Shape measurement biases from underfitting and ellipticity gradients

SciTech Connect

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 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.

9. Ellipticity and triangularity effects in tokamak Alfven spectrum

Puerta, Julio; Martin, Pablo; Castro, Enrique; Valdeblanquez, Eder

2006-10-01

Plasma configurations with ellipticity and triangularity are usual in tokamak experiments. These plasmas can be studied using a new system of coordinates of recent publications. Here this method has been applied to study Alfven spectrum in axisymmetric tokamaks with different values of ellipticity and triangularity [1-3]. Previous authors have developed numerical methods to obtain the Alfven spectrum using the Shafranov-Solove'v equilibrium flux function where the parameter ellipticity is also included [3]. Here more general configurations are treated and compared with the results of these authors, as well as those derived for the geometric optics or WKBJ approximation. The Alfven wave dispersion relation is obtained by the linearization of the MHD equations around a stationary equilibrium and the results are obtained by numerical calculations. [1] P. Martin, M. G. Haines and E. Castro, Phys. Plasma 12, 082506 (2005) [2] L. L. Lao, S. P. Hishman and R. M. Wieland, Phys. Fluids 24, 1431 (1981); H. Weitzner's Appendix. [3] G. O. Ludwig, Plasma Phys. Controlled Fusion 37, 633 (1995) [4] S. Novo, M. N'uñez and J. Rojo, Phys. Fluids B 3, 2967 (1991)

10. Fabrication of elliptical SRF cavities

Singer, W.

2017-03-01

The technological and metallurgical requirements of material for high-gradient superconducting cavities are described. High-purity niobium, as the preferred metal for the fabrication of superconducting accelerating cavities, should meet exact specifications. The content of interstitial impurities such as oxygen, nitrogen, and carbon must be below 10 μg g-1. The hydrogen content should be kept below 2 μg g-1 to prevent degradation of the quality factor (Q-value) under certain cool-down conditions. The material should be free of flaws (foreign material inclusions or cracks and laminations) that can initiate a thermal breakdown. Traditional and alternative cavity mechanical fabrication methods are reviewed. Conventionally, niobium cavities are fabricated from sheet niobium by the formation of half-cells by deep drawing, followed by trim machining and electron beam welding. The welding of half-cells is a delicate procedure, requiring intermediate cleaning steps and a careful choice of weld parameters to achieve full penetration of the joints. A challenge for a welded construction is the tight mechanical and electrical tolerances. These can be maintained by a combination of mechanical and radio-frequency measurements on half-cells and by careful tracking of weld shrinkage. The main aspects of quality assurance and quality management are mentioned. The experiences of 800 cavities produced for the European XFEL are presented. Another cavity fabrication approach is slicing discs from the ingot and producing cavities by deep drawing and electron beam welding. Accelerating gradients at the level of 35-45 MV m-1 can be achieved by applying electrochemical polishing treatment. The single-crystal option (grain boundary free) is discussed. It seems that in this case, high performance can be achieved by a simplified treatment procedure. Fabrication of the elliptical resonators from a seamless pipe as an alternative is briefly described. This technology has yielded good

11. Shrinking of Cluster Ellipticals: A Tidal Stripping Explanation and Implications for the Intracluster Light

Cypriano, Eduardo S.; Sodré, Laerte, Jr.; Campusano, Luis E.; Dale, Daniel A.; Hardy, Eduardo

2006-05-01

We look for evidence of tidal stripping in elliptical galaxies through the analysis of homogeneous CCD data corresponding to a sample of 228 elliptical galaxies belonging to 24 clusters of galaxies at 0.015function of environmental (clustercentric distance, local galaxy density) and structural (cluster velocity dispersion, Bautz-Morgan type) properties. We find that, for any particular galaxy luminosity, the elliptical galaxies in the inner and denser regions of the clusters are about 5% smaller than those in the outer regions, which is in good agreement with the finding of Strom and Strom based on photographic photometry. The null hypothesis (i.e., galaxy sizes are independent of the clustercentric distance or density) is rejected at a significance level of better than 99.7%. The numerical models of Aguilar and White predict that tidal stripping can lead to changes in the whole structure of elliptical galaxies, producing shrinkage and brightening of the galaxy qualitatively consistent with our measurements and also with the findings of Trujillo and coworkers that more centrally concentrated elliptical galaxies populate denser regions. Our observational results can be interpreted as evidence for the stripping of stars from elliptical galaxies in the central/denser regions of clusters, contributing to the intracluster light observed in these structures.

12. A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries.

PubMed

2017-02-15

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the

13. A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries

2017-02-01

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for non-linear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form a preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the

14. Ultraluminous Infrared Mergers: Elliptical Galaxies in Formation?

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.

15. An elliptic parameterisation of the Zamolodchikov model

2013-06-01

The Zamolodchikov model describes an exact relativistic factorized scattering theory of straight strings in (2+1)-dimensional space-time. It also defines an integrable 3D lattice model of statistical mechanics and quantum field theory. The three-string S-matrix satisfies the tetrahedron equation which is a 3D analog of the Yang-Baxter equation. Each S-matrix depends on three dihedral angles formed by three intersecting planes, whereas the tetrahedron equation contains five independent spectral parameters, associated with angles of an Euclidean tetrahedron. The vertex weights are given by rather complicated expressions involving square roots of trigonometric function of the spectral parameters, which is quite unusual from the point of view of 2D solvable lattice models. In this paper we consider a particular four-parameter specialisation of the tetrahedron equation when one of its vertices goes to infinity and the tetrahedron itself degenerates into an infinite prism. We show that in this limit all the vertex weights in the tetrahedron equation can be represented as meromorphic functions on an elliptic curve. Moreover we show that a special reduction of the tetrahedron equation in this case leads precisely to an example of the tetrahedral Zamolodchikov algebra, previously constructed by Korepanov. This algebra plays important role for a "layered" construction of the Shastry's R-matrix and the 2D S-matrix appearing in the problem of the ADS/CFT correspondence for N=4 SUSY Yang-Mills theory in four dimensions. Possible applications of our results in this field are briefly discussed.

16. Comparison of iterative methods and preconditioners for two-phase flow in porous media using exact and approximate Jacobians

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

17. Multigrid solutions to quasi-elliptic schemes

NASA Technical Reports Server (NTRS)

Brandt, A.; Taasan, S.

1985-01-01

Quasi-elliptic schemes arise from central differencing or finite element discretization of elliptic systems with odd order derivatives on non-staggered grids. They are somewhat unstable and less accurate then corresponding staggered-grid schemes. When usual multigrid solvers are applied to them, the asymptotic algebraic convergence is necessarily slow. Nevertheless, it is shown by mode analyses and numerical experiments that the usual FMG algorithm is very efficient in solving quasi-elliptic equations to the level of truncation errors. Also, a new type of multigrid algorithm is presented, mode analyzed and tested, for which even the asymptotic algebraic convergence is fast. The essence of that algorithm is applicable to other kinds of problems, including highly indefinite ones.

18. Highly confined photonic nanojet from elliptical particles

Jalali, T.; Erni, D.

2014-07-01

Elliptically shaped particles with different size and refractive indices have been studied under plane wave illumination using simulation tools such as 2D-FDTD, 2D-MMP, and 3D-MMP. Owing to careful manipulation, the power distribution in the vicinity of the particles opposite boundary resulted in a tightly focused photonic nanojet. Their waists are significantly smaller than the diffraction limit while propagating over several optical wavelengths without significant divergence. In this paper, we report on the manipulation of the particles elliptical shapes and the underlying refractive indices with respect to a maximally confined power distribution in the resulting nanojet which has been parameterized according to both, the beam waist and the beam divergence. The result that elliptical particles (i.e. oblate spheroids) turned out to be superior to spherical ones was underpinned within a highly accurate and fast 3D-MMP simulation using ring multipoles.

19. Numerical implementation, verification and validation of two-phase flow four-equation drift flux model with Jacobian-free Newton–Krylov method

SciTech Connect

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. The 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.

20. Numerical implementation, verification and validation of two-phase flow four-equation drift flux model with Jacobian-free Newton–Krylov method

DOE PAGES

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

1. 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.

2. Elliptical Particle Clustering in Cellular Flows

Atis, Severine; Sapsis, Themistoklis; Peacock, Thomas

2015-11-01

The transport of finite-sized objects by fluid flows is relevant to a wide variety of phenomena, such as debris transport on the ocean surface or bacteria advection in fluid environment. The shape of the advected objects can strongly alter their coupling with the surrounding flow field, and hence, greatly affecting their dispersion by the flow. We present the results of investigations of the behavior of neutrally buoyant, elliptical particles in two-dimensional cellular flows. We find that their trajectories, and overall organization, are markedly different than for spherical particles, with clear clustering for the elliptical particles associated with vortices.

3. SIMULATIONS OF TURBULENCE INDUCED ELLIPTICITY OVER LARGE FIELDS-OF-VIEW: THE FIRST STEP TOWARDS ENABLING LSST WEAK LENSING SCIENCE

SciTech Connect

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.

4. Buckling of elliptical rings under uniform external pressure

SciTech Connect

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.

5. The Application of Elliptic Cylindrical Phantom in Brachytherapy Dosimetric Study of HDR 192Ir Source

Ahn, Woo Sang; Park, Sung Ho; Jung, Sang Hoon; Choi, Wonsik; Do Ahn, Seung; Shin, Seong Soo

2014-06-01

6. Adaptively deformed mesh based interface method for elliptic equations with discontinuous coefficients

PubMed Central

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

7. On Fibonacci Numbers Which Are Elliptic Carmichael

DTIC Science & Technology

2014-12-27

On Fibonacci numbers which are elliptic Carmichael Florian Luca School of Mathematics University of the Witwatersrand P. O. Box Wits 2050, South...was written during a visit of P. S. to the School of Mathematics of the University of the Witwatersrand in 2014. This author thanks the institution for

8. Elliptic genera from multi-centers

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.

9. Nomenclature of polarized light - Elliptical polarization

NASA Technical Reports Server (NTRS)

Clarke, D.

1974-01-01

Alternative handedness and sign conventions for relating the orientation of elliptical polarization are discussed. The discussion proceeds under two headings: (1) snapshot picture, where the emphasis for the convention is contained in the concept of handedness; and (2) angular momentum consideration, where the emphasis for the convention is strongly associated with mathematical convention and the sign of the fourth Stokes parameter.

10. Relative elliptic theory and the Sobolev problem

Sternin, B. Yu; Shatalov, V. E.

1996-12-01

An operator algebra associated with a smooth embedding i \\colon X\\hookrightarrow M is constructed. For elliptic elements of this algebra a finiteness theorem (the Fredholm property) is established, and the index is computed. A connection with Sobolev problems is shown.

11. Circular and Elliptic Submerged Impinging Water Jets

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.

12. 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.

13. ELLIPTIC FLOW, INITIAL ECCENTRICITY AND ELLIPTIC FLOW FLUCTUATIONS IN HEAVY ION COLLISIONS AT RHIC.

SciTech Connect

NOUICER,R.; ALVER, B.; BACK, B.B.; BAKER, M.D.; BALLINTIJN, M.; BARTON, D.S.; ET AL.

2007-02-19

We present measurements of elliptic flow and event-by-event fluctuations established by the PHOBOS experiment. Elliptic flow scaled by participant eccentricity is found to be similar for both systems when collisions with the same number of participants or the same particle area density are compared. The agreement of elliptic flow between Au+Au and Cu+Cu collisions provides evidence that the matter is created in the initial stage of relativistic heavy ion collisions with transverse granularity similar to that of the participant nucleons. The event-by-event fluctuation results reveal that the initial collision geometry is translated into the final state azimuthal particle distribution, leading to an event-by-event proportionality between the observed elliptic flow and initial eccentricity.

14. Elliptical instability in terrestrial planets and moons

Cebron, D.; Le Bars, M.; Moutou, C.; Le Gal, P.

2012-03-01

Context. The presence of celestial companions means that any planet may be subject to three kinds of harmonic mechanical forcing: tides, precession/nutation, and libration. These forcings can generate flows in internal fluid layers, such as fluid cores and subsurface oceans, whose dynamics then significantly differ from solid body rotation. In particular, tides in non-synchronized bodies and libration in synchronized ones are known to be capable of exciting the so-called elliptical instability, i.e. a generic instability corresponding to the destabilization of two-dimensional flows with elliptical streamlines, leading to three-dimensional turbulence. Aims: We aim here at confirming the relevance of such an elliptical instability in terrestrial bodies by determining its growth rate, as well as its consequences on energy dissipation, on magnetic field induction, and on heat flux fluctuations on planetary scales. Methods: Previous studies and theoretical results for the elliptical instability are re-evaluated and extended to cope with an astrophysical context. In particular, generic analytical expressions of the elliptical instability growth rate are obtained using a local WKB approach, simultaneously considering for the first time (i) a local temperature gradient due to an imposed temperature contrast across the considered layer or to the presence of a volumic heat source and (ii) an imposed magnetic field along the rotation axis, coming from an external source. Results: The theoretical results are applied to the telluric planets and moons of the solar system as well as to three Super-Earths: 55 CnC e, CoRoT-7b, and GJ 1214b. For the tide-driven elliptical instability in non-synchronized bodies, only the early Earth core is shown to be clearly unstable. For the libration-driven elliptical instability in synchronized bodies, the core of Io is shown to be stable, contrary to previously thoughts, whereas Europa, 55 CnC e, CoRoT-7b, and GJ 1214b cores can be unstable

15. Performances study of UWB monopole antennas using half-elliptic radiator conformed on elliptical surface

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.

16. The Ellipticity Distribution of Ambiguously Blended Objects

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.

17. Intrinsic galaxy shapes and alignments - I. Measuring and modelling COSMOS intrinsic galaxy ellipticities

Joachimi, B.; Semboloni, E.; Bett, P. E.; Hartlap, J.; Hilbert, S.; Hoekstra, H.; Schneider, P.; Schrabback, T.

2013-05-01

The statistical properties of the ellipticities of galaxy images depend on how galaxies form and evolve, and therefore constrain models of galaxy morphology, which are key to the removal of the intrinsic alignment contamination of cosmological weak lensing surveys, as well as to the calibration of weak lensing shape measurements. We construct such models based on the halo properties of the Millennium Simulation and confront them with a sample of 90 000 galaxies from the COSMOS Survey, covering three decades in luminosity and redshifts out to z = 2. The ellipticity measurements are corrected for effects of point spread function smearing, spurious image distortions and measurement noise. Dividing galaxies into early, late and irregular types, we find that early-type galaxies have up to a factor of 2 lower intrinsic ellipticity dispersion than late-type galaxies. None of the samples shows evidence for redshift evolution, while the ellipticity dispersion for late-type galaxies scales strongly with absolute magnitude at the bright end. The simulation-based models reproduce the main characteristics of the intrinsic ellipticity distributions although which model fares best depends on the selection criteria of the galaxy sample. We observe fewer close-to-circular late-type galaxy images in COSMOS than expected for a sample of randomly oriented circular thick discs and discuss possible explanations for this deficit.

18. Elliptic blending model: A new near-wall Reynolds-stress turbulence closure

Manceau, Rémi; Hanjalić, Kemal

2002-02-01

A new approach to modeling the effects of a solid wall in one-point second-moment (Reynolds-stress) turbulence closures is presented. The model is based on the relaxation of an inhomogeneous (near-wall) formulation of the pressure-strain tensor towards the chosen conventional homogeneous (far-from-a-wall) form using the blending function α, for which an elliptic equation is solved. The approach preserves the main features of Durbin's Reynolds-stress model, but instead of six elliptic equations (for each stress component), it involves only one, scalar elliptic equation. The model, called "the elliptic blending model," offers significant simplification, while still complying with the basic physical rationale for the elliptic relaxation concept. In addition to model validation against direct numerical simulation in a plane channel for Reτ=590, the model was applied in the computation of the channel flow at a "real-life" Reynolds number of 106, showing a good prediction of the logarithmic profile of the mean velocity.

19. Vibration of in-vacuo elliptic cylindrical shells

Boisvert, Jeffrey E.; Hayek, Sabih I.

2003-10-01

The equations of motion for the vibration of elliptic cylindrical shells of constant thickness were derived using a Galerkin approach. The elastic strain energy density used in this derivation has seven independent kinematic variables: three displacements, two thickness-shear, and two thickness-stretch. The resulting seven coupled algebraic equations are symmetric and positive definite. The shell has a constant thickness, h, finite length, L, and is simply supported at its ends, (z=0,L), where z is the axial coordinate. The elliptic cross-section is defined by the shape parameter, a, and the half-length of the major axis, l. The modal solutions are expanded in a doubly infinite series of comparison functions in terms of circular functions in the angular and axial coordinates. The natural frequencies and the mode shapes were obtained by the Galerkin method. Numerical results were obtained for several h/l and L/l ratios, and various shape parameters, including the limiting case of a simply supported cylindrical shell (a=100). [Work supported by ONR and the Navy/ASEE Summer Faculty Program.

20. Hydrostatic equilibrium profiles for gas in elliptical galaxies

Capelo, Pedro R.; Natarajan, Priyamvada; Coppi, Paolo S.

2010-09-01

We present an analytic formulation for the equilibrium gas density profile of early-type galaxies that explicitly includes the contribution of stars in the gravitational potential. We build a realistic model for an isolated elliptical galaxy and explore the equilibrium gas configurations as a function of multiple parameters. For an assumed central gas temperature kBT0 = 0.6 keV, we find that neglecting the gravitational effects of stars, which can contribute substantially in the innermost regions, leads to an underestimate of the enclosed baryonic gas mass by up to ~65 per cent at the effective radius and by up to ~15 per cent at the Navarro-Frenk-White (NFW) scale radius, depending on the stellar baryon fraction. This formula is therefore important for estimating the baryon fraction in an unbiased fashion. These new hydrostatic equilibrium solutions, derived for the isothermal and polytropic cases, can also be used to generate more realistic initial conditions for simulations of elliptical galaxies. Moreover, the new formulation is relevant when interpreting X-ray data. We compare our composite isothermal model to the standard β-model used to fit X-ray observations of early-type galaxies, to determine the value of the NFW scale radius rs. Assuming a 10 per cent stellar baryon fraction, we find that the exclusion of stars from the gravitational potential leads to (i) an underestimate of rs by ~80 per cent and (ii) an overestimate of the enclosed dark matter at rs by a factor of ~2, compared to the equivalent β-model fit results when stars are not taken into account. For higher stellar mass fractions, a β-model is unable to accurately reproduce our solution, indicating that when the observed surface brightness profile of an isolated elliptical galaxy is found to be well fitted by a β-model, the stellar mass fraction cannot be much greater than ~10 per cent.

1. Analysis of the Dynamic Characteristics of Elliptical Gears

Liu, Xing; Nagamura, Kazuteru; Ikejo, Kiyotaka

To date, elliptical gear has been commonly used in automobile, automatic machinery, pumps, flow meters and printing presses for its particular non-uniform rotation. However, the dynamic characteristics of elliptical gears have not been clarified yet. In this study, The calculation as well as the experiment of two elliptical gears, which are a single elliptical gear and a double elliptical gear, is carried out to analyze the dynamic characteristics of elliptical gears. General factors including the torque, the rotation speed and the tooth root stress of the test gears are investigated. According to the analysis conducted in this study, the dynamic input torque variation of elliptical gear becomes larger along with the increase of operating gear rotation speed and the experimental one increases much faster than the calculated one over the Critical Rotation Speed of Tooth Separation (CRSTS) of elliptical gear. The experimental input rotation speed varies according to the variation of input torque, leading to the difference between the experimental output rotation speed and the desired one. The calculation results of the CRSTS of elliptical gears are almost equal to the experimental ones. The dynamic load variation ratios of elliptical gear at different angular position as well as their changing trends with operating gear rotation speed are quite different from each other. And the experimental dynamic load variation ratios of elliptical gear show difference from the calculated ones because of tooth separation and tooth impact. The agreement of the calculation and experimental results proves the validity of this study.

2. Extracting the left and right critical eigenvectors from the LDU-decomposed non-symmetric Jacobian matrix in stability problems

Fujii, Fumio; Yamakawa, Yuki; Noguchi, Hirohisa

2010-07-01

In the previous publications of the authors, an eigenanalysis-free computational procedure has been proposed to extract the bifurcation buckling mode(s) from the LDL T -decomposed symmetric stiffness matrix in the vicinity of a stability point. Any eigensolver, for instance, inverse iteration or subspace method, is not necessary. The procedure has been verified in numerical examples and well works in multiple and clustered bifurcation problems too. This present paper will extend the eigenanalysis-free procedure to the LDU-decomposed non-symmetric Jacobian matrix, from which both left and right critical eigenvectors relevant to the stability point may be extracted in a similar way. The idea is mathematical and totally independent of the physical problem to be solved, so that it is applicable to any non-symmetric square matrix in stability problems including plasticity with non-associated flow rules, contact and fluid-structure interaction. The linear-algebraic background of non-symmetric eigenvalue problems is firstly described. The present paper will then mention the role play of the left and right critical eigenvectors in stability analysis and the eigenanalysis-free LDU-procedure is proposed. Numerical examples of elastoplastic bifurcation are illustrated for verification and discussion. In APPENDICES, a bench model visualizes the mechanical meaning of the left and right critical singular vectors of a rectangular matrix.

3. Convergence results for elliptic quasivariational inequalities

Sofonea, Mircea; Benraouda, Ahlem

2017-02-01

In this paper, we state and prove various convergence results for a general class of elliptic quasivariational inequalities with constraints. Thus, we prove the convergence of the solution of a class of penalized problems to the solution of the original inequality, as the penalty parameter converges to zero. We also prove a continuous dependence result of the solution with respect the convex set of constraints. Then, we consider a mathematical model which describes the equilibrium of an elastic rod attached to a nonlinear spring. We derive the variational formulation of the model which is in a form of an elliptic quasivariational inequality for the displacement field. We prove the unique weak solvability of the model, and then we state and prove two convergence results and provide their corresponding mechanical interpretation.

4. Performance Characteristics of a Preformed Elliptical Parachute

NASA Technical Reports Server (NTRS)

1963-01-01

Performance Characteristics of a Preformed Elliptical Parachute at Altitudes between 200,000 and 100,000 Thousand Feet Obtained by In-Flight Photography. The performance characteristics of a pre-formed elliptical parachute at altitudes between 200,000 and 100,000 feet were obtained by means of in-flight photography. The tests demonstrate that this type of parachute will open at altitudes of about 200,000 feet if conditions such as twisting of the suspension lines or draping of the suspension lines over the canopy do not occur. Drag-coefficient values between 0.6 and 0.8 were found to be reasonable for this type of parachute system in the altitude range between 200,000 and 100,000 feet. [Entire movie available on DVD from CASI as Doc ID 20070030980. Contact help@sti.nasa.gov

5. Performance of the ALS elliptical wiggler

SciTech Connect

Wang, C.X.; Schlueter, R.; Hoyer, E.; Heimann, P.

1993-08-01

The elliptical wiggler is a circularly polarized light source capable of providing very broad spectral coverage and high degree of circular polarization. The main features of an elliptical wiggler can be understood through analogy to bending magnet radiation. However, some aspects, such as the end structures influence on the degree of circular polarization, require more elaborate methods to characterize. We present an algorithm based on the stationary phase method, which allows calculation of radiation properties from an arbitrary electron trajectory; so a non-sinusoidal magnetic fields influence on the radiation performance can be taken into account. We show general radiation properties of an ellilptical wiggler and discuss factors affecting radiation performance. Practice issues encountered during the conceptual design of an ellilptical wiggler at the Advanced Light Source are addressed.

6. Performance of an elliptically tapered neutron guide

Mühlbauer, Sebastian; Stadlbauer, Martin; Böni, Peter; Schanzer, Christan; Stahn, Jochen; Filges, Uwe

2006-11-01

Supermirror coated neutron guides are used at all modern neutron sources for transporting neutrons over large distances. In order to reduce the transmission losses due to multiple internal reflection of neutrons, ballistic neutron guides with linear tapering have been proposed and realized. However, these systems suffer from an inhomogeneous illumination of the sample. Moreover, the flux decreases significantly with increasing distance from the exit of the neutron guide. We propose using elliptically tapered guides that provide a more homogeneous phase space at the sample position as well as a focusing at the sample. Moreover, the design of the guide system is simplified because ellipses are simply defined by their long and short axes. In order to prove the concept we have manufactured a doubly focusing guide and investigated its properties with neutrons. The experiments show that the predicted gains using the program package McStas are realized. We discuss several applications of elliptic guides in various fields of neutron physics.

7. An elliptical wiggler beamline for the ALS

SciTech Connect

Martynov, V.V. |; McKinney, W.R.; Padmore, H.A.

1995-10-01

A beamline for circularly polarized radiation produced by an elliptical wiggler has been designed at the ALS covering the broad energy range from 50 eV to 2000 eV. The rigorous theory of grating diffraction efficiency has been used to maximize transmitted flux. The nature of the elliptical wiggler insertion device creates a challenging optical problem due to the large source size in the vertical and horizontal directions. The requirement of high resolving power, combined with the broad tuning range and high heat loads complicate the design. These problems have been solved by using a variable included angle monochromator of the constant length type with high demagnification onto its entrance slit, and cooled optics.

8. Elliptic Genera and 3d Gravity

SciTech Connect

Benjamin, Nathan; Cheng, Miranda C. N.; Kachru, Shamit; Moore, Gregory W.; Paquette, Natalie M.

2016-03-30

We describe general constraints on the elliptic genus of a 2d supersymmetric conformal field theory which has a gravity dual with large radius in Planck units. We give examples of theories which do and do not satisfy the bounds we derive, by describing the elliptic genera of symmetric product orbifolds of K3, product manifolds, certain simple families of Calabi–Yau hypersurfaces, and symmetric products of the “Monster CFT”. We discuss the distinction between theories with supergravity duals and those whose duals have strings at the scale set by the AdS curvature. Under natural assumptions, we attempt to quantify the fraction of (2,2) supersymmetric conformal theories which admit a weakly curved gravity description, at large central charge.

9. Elliptic genera and 3d gravity

SciTech Connect

Benjamin, Nathan; Cheng, Miranda C. N.; Kachru, Shamit; Moore, Gregory W.; Paquette, Natalie M.

2016-03-30

Here, we describe general constraints on the elliptic genus of a 2d supersymmetric conformal field theory which has a gravity dual with large radius in Planck units. We give examples of theories which do and do not satisfy the bounds we derive, by describing the elliptic genera of symmetric product orbifolds of K3, product manifolds, certain simple families of Calabi–Yau hypersurfaces, and symmetric products of the “Monster CFT”. We discuss the distinction between theories with supergravity duals and those whose duals have strings at the scale set by the AdS curvature. Under natural assumptions, we attempt to quantify the fraction of (2,2) supersymmetric conformal theories which admit a weakly curved gravity description, at large central charge.

10. Elliptic genera and 3d gravity

DOE PAGES

Benjamin, Nathan; Cheng, Miranda C. N.; Kachru, Shamit; ...

2016-03-30

Here, we describe general constraints on the elliptic genus of a 2d supersymmetric conformal field theory which has a gravity dual with large radius in Planck units. We give examples of theories which do and do not satisfy the bounds we derive, by describing the elliptic genera of symmetric product orbifolds of K3, product manifolds, certain simple families of Calabi–Yau hypersurfaces, and symmetric products of the “Monster CFT”. We discuss the distinction between theories with supergravity duals and those whose duals have strings at the scale set by the AdS curvature. Under natural assumptions, we attempt to quantify the fractionmore » of (2,2) supersymmetric conformal theories which admit a weakly curved gravity description, at large central charge.« less

11. Crack Path Prediction Near an Elliptical Inhomogeneity

DTIC Science & Technology

1991-09-01

Prediction Near an Elliptical Inhomogeneity 1L162618AH80 6. AUTHOR(S) Edward M. Patton 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8 . PERFORMING...oriented crack. Erdogan and Gupta [ 8 ] later solved the problem in which the crack crosses the interface. These solutions are based on the Green’s...the crack propagation direction 8 is greatest. This criterion implies that the stress parallel to that direction would be a minimum, or that the

12. Photoacoustic cell using elliptical acoustic focusing

NASA Technical Reports Server (NTRS)

Heritier, J.-M.; Fouquet, J. E.; Siegman, A. E.

1982-01-01

A photoacoustic cell has been developed in the form of an elliptical cylinder in which essentially all the acoustic energy generated by a laser beam passing down one axis is focused onto a cylindrical acoustic tranducer located along the other axis. Preliminary measurements on a liquid-filled cell of this design show high sensitivity and a notably clean impulse response. A similar design may be useful for photoacoustic measurements in vapors as well.

13. Spectral methods for exterior elliptic problems

NASA Technical Reports Server (NTRS)

Canuto, C.; Hariharan, S. I.; Lustman, L.

1984-01-01

Spectral approximations for exterior elliptic problems in two dimensions are discussed. As in the conventional finite difference or finite element methods, the accuracy of the numerical solutions is limited by the order of the numerical farfield conditions. A spectral boundary treatment is introduced at infinity which is compatible with the infinite order interior spectral scheme. Computational results are presented to demonstrate the spectral accuracy attainable. Although a simple Laplace problem is examined, the analysis covers more complex and general cases.

14. Integrable mappings via rational elliptic surfaces

Tsuda, Teruhisa

2004-02-01

We present a geometric description of the QRT map (which is an integrable mapping introduced by Quispel, Roberts and Thompson) in terms of the addition formula of a rational elliptic surface. By this formulation, we classify all the cases when the QRT map is periodic; and show that its period is 2, 3, 4, 5 or 6. A generalization of the QRT map which acts birationally on a pencil of K3 surfaces, or Calabi-Yau manifolds, is also presented.

15. THE STELLAR HALOS OF MASSIVE ELLIPTICAL GALAXIES

SciTech Connect

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.

16. Elliptical Acoustic Particle Motion in Underwater Waveguides

DTIC Science & Technology

2013-03-27

approximation to the degree of circularity. This approximation, applied to acoustic pressure measurements from two closely spaced hydrophones made in...elliptical motion in the vertical plane can be approximated by vertical line array of closely spaced pressure sensors. We demonstrate in this paper how the...an approximate measure of circular- ity. Most importantly, Θ̃ can be formed from two closely spaced (< λ/4) hydrophones, extending this analysis of

17. Do elliptical galaxies suffer from warp?

Gamaleldin, A. I.

1990-06-01

Detailed surface isophotometry of NGC 1700 was performed. Luminosity profiles, ellipticity curve, reduced luminosity profiles, and the galaxy parameters are illustrated; the study also includes the variation of position angle with the distance from the center of the galaxy. An interesting feature of this object is the twisted shape of the outer isophote which does not appear as an ellipse but as an integral-sign shape, which is attributed to some kind of warp in the galaxy under investigation.

18. Molecular Gas in Elliptical Galaxies: Erratum

Lees, Joanna F.; Knapp, G. R.; Rupen, Michael P.; Phillips, T. G.

1992-09-01

In the paper "Molecular Gas in Elliptical Galaxies" by Joanna F. Lees, G. R. Knapp, Michael P. Rupen, and T. G. Phillips (ApJ, 379,177 [1991]), an error appeared on page 208. Two numbers which were quoted from Young and Knezek (1989) were inadvertently not converted from their CO-H_2_ conversion factor to ours (a difference of 40%). Page 208, column (1), lines 6-7 should read:

19. 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'' × 107''), allowing us to achieve remarkably high signal-to-noise ratios of ~20-70 pixel-1 in radial bins of 2-2.5 times the effective radii of the eight galaxies in our sample. Focusing on a sample of massive elliptical galaxies with stellar velocity dispersions σ* > 150 km s-1, we study the radial dependence in the equivalent widths (EW) of key metal absorption lines. By twice the effective radius, the Mgb EWs have dropped by ~50%, and only a weak correlation between σ* and Mgb EW remains. The Mgb EWs at large radii are comparable to those seen in the centers of elliptical galaxies that are ~ an order of magnitude less massive. We find that the well-known metallicity gradients often observed within an effective radius continue smoothly to 2.5 Re , while the abundance ratio gradients remain flat. Much like the halo of the Milky Way, the stellar halos of our galaxies have low metallicities and high α-abundance ratios, as expected for very old stars formed in small stellar systems. Our observations support a picture in which the outer parts of massive elliptical galaxies are built by the accretion of much smaller systems whose star formation history was truncated at early times.

20. 3-D magnetotelluric inversion including topography using deformed hexahedral edge finite elements and direct solvers parallelized on SMP computers - Part I: forward problem and parameter Jacobians

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

1. The anisotropic Ising correlations as elliptic integrals: duality and differential equations

McCoy, B. M.; Maillard, J.-M.

2016-10-01

We present the reduction of the correlation functions of the Ising model on the anisotropic square lattice to complete elliptic integrals of the first, second and third kind, the extension of Kramers-Wannier duality to anisotropic correlation functions, and the linear differential equations for these anisotropic correlations. More precisely, we show that the anisotropic correlation functions are homogeneous polynomials of the complete elliptic integrals of the first, second and third kind. We give the exact dual transformation matching the correlation functions and the dual correlation functions. We show that the linear differential operators annihilating the general two-point correlation functions are factorized in a very simple way, in operators of decreasing orders. Dedicated to A J Guttmann, for his 70th birthday.

2. Elliptic Solvers for Adaptive Mesh Refinement Grids

SciTech Connect

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.

3. Dust and Ionized Gas in Elliptical Galaxies

Goudfrooij, Paul

1995-05-01

The thesis presents results of a study of the optical and far-infrared properties of dust and ionized gas in a complete, blue magnitude-limited (B_T^0 < 12) sample of 56 luminous elliptical (E) galaxies. The main aim is to investigate the origin and fate of this interstellar material and possible implications for scenarios of galaxy formation and evolution. To ensure consistency in the assignment of morphological types, the galaxy sample was drawn exclusively from the Revised Shapley-Ames Catalog of Bright Galaxies. A deep, systematic optical survey has been performed, including CCD imaging through both broad-band filters and narrow-band filters. For each galaxy we have constructed colour index (B-V, B-I) images and images of the H-alpha+ [N II]-emitting gas to derive the distributions of dust features and ionized gas. Long-slit spectra have also been obtained in two resolutions. Low-resolution spectra (covering the whole optical region) are used to study the properties of the underlying stellar populations (e.g., metallicity gradients), and to study the excitation mechanism of the ionized gas. Additional medium-resolution (~2A) spectra in the wavelength region around H-alpha have been obtained for all sample elliptical galaxies containing ionized gas to study the kinematics of the gas, and derive pure H-alpha luminosities. In this thesis, analysis of the extensive imaging data and of the medium-resolution spectra is reported. In Chapter 1 we report an early result of our survey: The galaxy IC 1459 is found to exhibit a large (15 Kpc diameter) H-alpha+[N II] emission-line region, showing spiral structure. Patchy dust absorption is also found in the inner part of the emission-line region. This galaxy was already shown to contain a massive stellar core which counter-rotates rapidly with respect to the stellar body of the galaxy. Interestingly, the sense of rotation of the spiral "arms" of the ionized gas distribution is the same as that of the rapidly rotating

4. The geometry of finite difference discretizations of semilinear elliptic operators

Teles, Eduardo; Tomei, Carlos

2012-04-01

Discretizations by finite differences of some semilinear elliptic equations lead to maps F(u) = Au - f(u), u \\in {{R}}^n , given by nonlinear convex diagonal perturbations of symmetric matrices A. For natural nonlinearity classes, we consider the equation F(u) = y - tp, where t is a large positive number and p is a vector with negative coordinates. As the range of the derivative f'i of the coordinates of f encloses more eigenvalues of A, the number of solutions increases geometrically, eventually reaching 2n. This phenomenon, somewhat in contrast with behaviour associated with the Lazer-McKenna conjecture, has a very simple geometric explanation: a perturbation of a multiple fold gives rise to a function which sends connected components of its critical set to hypersurfaces with large rotation numbers with respect to vectors with very negative coordinates. Strictly speaking, the results have nothing to do with elliptic equations: they are properties of the interaction of a (self-adjoint) linear map with increasingly stronger nonlinear convex diagonal interactions.

5. Optimal Lorentz-augmented spacecraft formation flying in elliptic orbits

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.

6. A heterogeneous stochastic FEM framework for elliptic PDEs

SciTech Connect

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.

7. Fast space-variant elliptical filtering using box splines.

PubMed

Chaudhury, Kunal Narayan; Munoz-Barrutia, Arrate; Unser, Michael

2010-09-01

The efficient realization of linear space-variant (non-convolution) filters is a challenging computational problem in image processing. In this paper, we demonstrate that it is possible to filter an image with a Gaussian-like elliptic window of varying size, elongation and orientation using a fixed number of computations per pixel. The associated algorithm, which is based upon a family of smooth compactly supported piecewise polynomials, the radially-uniform box splines, is realized using preintegration and local finite-differences. The radially-uniform box splines are constructed through the repeated convolution of a fixed number of box distributions, which have been suitably scaled and distributed radially in an uniform fashion. The attractive features of these box splines are their asymptotic behavior, their simple covariance structure, and their quasi-separability. They converge to Gaussians with the increase of their order, and are used to approximate anisotropic Gaussians of varying covariance simply by controlling the scales of the constituent box distributions. Based upon the second feature, we develop a technique for continuously controlling the size, elongation and orientation of these Gaussian-like functions. Finally, the quasi-separable structure, along with a certain scaling property of box distributions, is used to efficiently realize the associated space-variant elliptical filtering, which requires O(1) computations per pixel irrespective of the shape and size of the filter.

8. The superconformal index and an elliptic algebra of surface defects

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.

9. A Parallel, Fully Coupled, Fully Implicit Solution to Reactive Transport in Porous Media Using the Preconditioned Jacobian-Free Newton-Krylov Method

SciTech Connect

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.

10. A Newton-Krylov method with approximate Jacobian for implicit solution of Navier-Stokes on staggered overset-curvilinear grids with immersed boundaries

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.

11. Monopoles and Modifications of Bundles over Elliptic Curves

Levin, Andrey M.; Olshanetsky, Mikhail A.; Zotov, Andrei V.

2009-06-01

Modifications of bundles over complex curves is an operation that allows one to construct a new bundle from a given one. Modifications can change a topological type of bundle. We describe the topological type in terms of the characteristic classes of the bundle. Being applied to the Higgs bundles modifications establish an equivalence between different classical integrable systems. Following Kapustin and Witten we define the modifications in terms of monopole solutions of the Bogomolny equation. We find the Dirac monopole solution in the case R × (elliptic curve). This solution is a three-dimensional generalization of the Kronecker series. We give two representations for this solution and derive a functional equation for it generalizing the Kronecker results. We use it to define Abelian modifications for bundles of arbitrary rank. We also describe non-Abelian modifications in terms of theta-functions with characteristic.

12. Composite stellar populations and element by element abundances in the Milky Way bulge and elliptical galaxies

Tang, Baitian; Worthey, Guy; Davis, A. Bianca

2014-12-01

This paper explores the integrated-light characteristics of the Milky Way (MW) bulge and to what extent they match those of elliptical galaxies in the local Universe. We model composite stellar populations with realistic abundance distribution functions (ADFs), tracking the trends of individual elements as a function of overall heavy element abundance as actually observed in MW bulge stars. The resultant predictions for absorption feature strengths from the MW bulge mimic elliptical galaxies better than solar neighbourhood stars do, but the MW bulge does not match elliptical galaxies, either. Comparing bulge versus elliptical galaxies, Fe, Ti, and Mg trend about the same for both but C, Na, and Ca seem irreconcilably different. Exploring the behaviour of abundance compositeness leads to the concepts of red lean' where a narrower ADF appears more metal rich than a wide one, and red spread' where the spectral difference between wide and narrow ADFs increases as the ADF peak is moved to more metal-rich values. Tests on the systematics of recovering abundance, abundance pattern, and age from composite stellar populations using single stellar population models were performed. The chemical abundance pattern was recovered adequately, though a few minor systematic effects were uncovered. The prospects of measuring the width of the ADF of an old stellar population were investigated and seem bright using UV to IR photometry.

13. Elliptic Length Scales in Laminar, Two-Dimensional Supersonic Flows

DTIC Science & Technology

2015-06-01

AFRL-RQ-WP-TP-2015-0109 ELLIPTIC LENGTH SCALES IN LAMINAR, TWO- DIMENSIONAL SUPERSONIC FLOWS James H. Miller Vehicle Technology Branch...SUBTITLE ELLIPTIC LENGTH SCALES IN LAMINAR, TWO-DIMENSIONAL SUPERSONIC FLOWS 5a. CONTRACT NUMBER In-house 5b. GRANT NUMBER 5c. PROGRAM ELEMENT...ANSI Std. Z39-18 1 Approved for public release; distribution unlimited. Elliptic Length Scales in Laminar, Two-Dimensional Supersonic Flows

14. Elliptic multiple zeta values and one-loop superstring amplitudes

Broedel, Johannes; Mafra, Carlos R.; Matthes, Nils; Schlotterer, Oliver

2015-07-01

We investigate iterated integrals on an elliptic curve, which are a natural genus-one generalization of multiple polylogarithms. These iterated integrals coincide with the multiple elliptic polylogarithms introduced by Brown and Levin when constrained to the real line. At unit argument they reduce to an elliptic analogue of multiple zeta values, whose network of relations we start to explore. A simple and natural application of this framework are one-loop scattering amplitudes in open superstring theory. In particular, elliptic multiple zeta values are a suitable language to express their low energy limit. Similar to the techniques available at tree-level, our formalism allows to completely automatize the calculation.

15. Two-dimensional elliptical electromagnetic superscatterer and superabsorber.

PubMed

Zang, Xiaofei; Jiang, Chun

2010-03-29

Using coordinate transformation stated earlier by Pendry et al. [Science 312, 1780 (2006)], we investigate the two-dimensional elliptical electromagnetic superscatterer and superabsorber, based on the concept of complementary media. Such an elliptical electromagnetic superscatterer (or superabsorber) is realized by coating an elliptical negative refractive material shell. The effectiveness of the elliptical electromagnetic superscatterer and superabsorber designs is verified by finite element simulations. The proposed design provides a more practical superscatterer (or superabsorber) geometry when compared to previous designs with axial and radial symmetries. Our results can be extended to an arbitrarily shaped electromagnetic superscatterer and superabsorber.

16. Mixing characteristics of a ducted, elliptical jet with dump

SciTech Connect

Schadow, K.C.; Wilson, K.J.; Parr, D.M.; Gutmark, E.

1986-01-01

Mixing between elliptical ducted air-jets with dump and nitrogen radially injected through the duct walls was experimentally studied using hot-wire anemometry and gas-sampling techniques. Mixing was considerably increased when the air-jet was issued from elliptical relative to circular jet-exit cross-sections. Elliptical jets issued from orifices provided better mixing than issued from pipes. Additional mixing enhancement was achieved when the elliptical jets were acoustically forced by excited resonant pressure waves of the duct. The mean and turbulence velocity measurements provided insight into the mechanism of the observed mixing enhancement.

17. Colors of Ellipticals from GALEX to Spitzer

Schombert, James M.

2016-12-01

Multi-color photometry is presented for a large sample of local ellipticals selected by morphology and isolation. The sample uses data from the Galaxy Evolution Explorer (GALEX), Sloan Digital Sky Survey (SDSS), Two Micron All-Sky Survey (2MASS), and Spitzer to cover the filters NUV, ugri, JHK and 3.6 μm. Various two-color diagrams, using the half-light aperture defined in the 2MASS J filter, are very coherent from color to color, meaning that galaxies defined to be red in one color are always red in other colors. Comparison to globular cluster colors demonstrates that ellipticals are not composed of a single age, single metallicity (e.g., [Fe/H]) stellar population, but require a multi-metallicity model using a chemical enrichment scenario. Such a model is sufficient to explain two-color diagrams and the color-magnitude relations for all colors using only metallicity as a variable on a solely 12 Gyr stellar population with no evidence of stars younger than 10 Gyr. The [Fe/H] values that match galaxy colors range from -0.5 to +0.4, much higher (and older) than population characteristics deduced from Lick/IDS line-strength system studies, indicating an inconsistency between galaxy colors and line indices values for reasons unknown. The NUV colors have unusual behavior, signaling the rise and fall of the UV upturn with elliptical luminosity. Models with blue horizontal branch tracks can reproduce this behavior, indicating the UV upturn is strictly a metallicity effect.

18. Young circumnuclear disks in elliptical galaxies

Sil'Chenko, Olga K.

2009-04-01

By means of integral-field spectroscopy with the Multi-Pupil Field/Fiber Spectrograph of the Russian 6-m telescope we have studied the central parts of NGC 759 and NGC 83— regular (non-interacting, without strong nuclear activity) round red luminous ( M B =-20.8--21.6) elliptical galaxies which are however known to possess molecular gas. In both galaxies we have found central stellar disks with the extension of 1-2 kpc along the radius which are evidently being formed just now.

19. Elliptic Rydberg states as direction indicators

SciTech Connect

Lindner, Netanel H.; Peres, Asher; Terno, Daniel R.

2003-10-01

The orientation in space of a Cartesian coordinate system can be indicated by the two vectorial constants of motion of a classical Keplerian orbit: the angular momentum and the Laplace-Runge-Lenz vector. In quantum mechanics, the states of a hydrogen atom that mimic classical elliptic orbits are the coherent states of the SO(4) rotation group. It is known how to produce these states experimentally. They have minimal dispersions of the two conserved vectors and can be used as direction indicators. We compare the fidelity of this transmission method with that of the idealized optimal method.

20. 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.

1. Elliptic waveforms for inspiralling compact binaries

Mikóczi, Balázs

2010-03-01

The inspiral of supermassive black hole binary systems with high orbital eccentricity are the most promising sources for the gravitational wave observatories. The importance of elliptic gravitational waveforms in various physical scenarios has been emphasized by several authors (Wahlquist 1987, Moreno-Garrido, Buitrago and Mediavilla 1994, Martel and Poisson 1999). Taking into account the eccentricity of the orbit in the total waveform improves the parameter estimation for these sources, as it is shown by the construction and analyzation of the Fisher information matrix. In our work we use the Fourier-Bessel analysis of the Kepler motion and the stationary phase approximation of time-depend waveforms.

2. Magnetic flux studies in horizontally cooled elliptical superconducting cavities

SciTech Connect

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.

3. Some Expansions of the Elliptic Motion to High Eccentricities

da Silva Fernandes, Sandro

1995-12-01

Some classic expansions of the elliptic motion — cosmE and sinmE — in powers of the eccentricity are extended to highly eccentric orbits, 0.6627...functions with respect to the eccentricity. The expansions have the same radius of convergence ρ(e*) of the extended solution of Kepler's equation, previously derived by the author. Some other simple expansions — (a/r), (r/a), (r/a) sinv, ..., — derived straightforward from the expansions ofE, cosE and sinE are also presented.

4. Heterogeneous domain decomposition for singularly perturbed elliptic boundary value problems

SciTech Connect

Garbey, M.; Kaper, H.G.

1995-04-14

A heterogeneous domain-decomposition method is presented for the numerical solution of singularly perturbed elliptic boundary value problem. The method, which is parallelizable at various levels, uses several ideas of asymptotic analysis. The sub-domains match the domains of validity of the local ({open_quotes}inner{close_quotes} and {open_quotes}outer{close_quotes}) asymptotic expansions, and cut-off functions are used to match solutions in neighboring subdomains. The positions of the interfaces, as well as the mesh widths, depend on the small parameter, {epsilon}. On the subdomains, iterative solution techniques are used, which may vary from one subdomain to another. The global convergence rate depends on {epsilon}; it generally increases like some power of (log({epsilon}{sup -1})){sup -1} as {epsilon} {down_arrow} 0. The method is illustrated on several two-dimensional singular perturbation problems.

5. Vortex chirality in exchange-biased elliptical magnetic rings.

PubMed

Jung, W; Castaño, F J; Ross, C A

2006-12-15

The flux-closed or "vortex" state in thin-film magnetic rings has been proposed as a data storage token, but it has proven difficult to control the vortex chirality in a simple manner. Here, a model is described that predicts the vortex chirality of an elliptical magnetic ring as a function of the direction of the applied field and of the exchange bias, based on the change in energy of the system as the domain walls move. Experimental measurements of chirality in Co and Co/IrMn magnetic rings with 3.2 microm major axis are in excellent agreement with the model. The vortex circulation direction can therefore be tailored with an appropriate combination of applied field direction and exchange bias direction with respect to the major axis.

6. Inner and Outer Photometric Structure of Elliptical Galaxies

Graham, Alister W.; Erwin, P.; Trujillo, I.; Asensio Ramos, A.

The Nuker model, when applied to the inner regions of core'' galaxies, is shown to produce systematic biases in the determination of the core break-radii''. These radii can easily be (and often have been, see Trujillo et al. 2003) over-estimated by more than 100%. Moreover, due to curvature in the outer profiles of early-type galaxies (i.e., beyond the break-radius), none of the Nuker model parameters are found to be robust quantities. A new empirical model that simultaneously describes both the inner and outer light-profiles of elliptical galaxies (and bulges in general) is presented. It consists of a Sérsic function with an inner power-law and a variable transition region.

7. A new approach to flow through a region bounded by two ellipses of the same ellipticity

Lal, K.; Chorlton, F.

1981-05-01

A new approach is presented to calculate steady flow of a laminar viscous incompressible fluid through a channel whose cross section is bounded by two ellipses with the same ellipticity. The Milne-Thomas approach avoids the stream function and is similar to the Rayleigh-Ritz approximation process of the calculus of variations in its first satisfying boundary conditions and then adjusting constants or multiplying functions to fit the differential equation.

8. Integrated X-Ray Reflectivity Measurements for Elliptically Curved PET Crystals

SciTech Connect

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.

9. Thermodynamics of Inozemtsev's elliptic spin chain

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.

10. 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]…

11. Prospects of Elliptic Flow Studies at NICA/MPD

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.

12. Dynamic susceptibility of onion in ferromagnetic elliptical nanoring

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.

13. Far-infrared mapping of dusty elliptical galaxies

NASA Technical Reports Server (NTRS)

Lees, Joanna F.; Harper, D. A.; Rupen, Michael P.; Knapp, G. R.

1994-01-01

Preliminary results from a program to map the thermal far-infrared emission from cool dust in elliptical galaxies using the Yerkes 60-Channel Camera on the Kuiper Airborne Observatory (KAO) are presented. The 160 micron emission from the elliptical NGC 6542 is apparently extended over the optical galaxy whereas the 100 micron emission is unresolved. This implies a dust temperature gradient consistent with that expected for dust with Galactic properties exposed to the general interstellar radiation field of the elliptical galaxy. Observations of the elliptical NGC 5666 and the NGC 7463/4/5 compact group (consisting of the elliptical NGC 7464, the S0 NGC 7465, and the spiral NGC 7463) are also discussed.

14. Modeling roughness effects in turbulent boundary layers using elliptic relaxation

George, Jacob; de Simone, Alejandro; Iaccarino, Gianluca; Jimenez, Javier

2010-11-01

We present results from the efforts towards modeling roughness in turbulent boundary layers using elliptic relaxation. This scheme, included in the v^2-f model and first formulated by Durbin (1993, JFM, vol. 249, p.465) for smooth-walls, uses an elliptic partial differential equation to incorporate near-wall turbulence anisotropy and non-local pressure-strain effects. The use of the elliptic PDE is extended to model roughness effects in various transitionally-rough and fully-rough boundary layers consisting of a uniform and sparse distribution of cylinders for which experimental data is available. The roughness effects are incorporated through the elliptic PDE by including the length and time scales that the roughness imposes upon the flow, which the experiment has shown to be constant within the rough-walls. Further modeling of roughness effects is considered by altering the source terms in the elliptic PDE.

15. Cotton-type and joint invariants for linear elliptic systems.

PubMed

Aslam, A; Mahomed, F M

2013-01-01

Cotton-type invariants for a subclass of a system of two linear elliptic equations, obtainable from a complex base linear elliptic equation, are derived both by spliting of the corresponding complex Cotton invariants of the base complex equation and from the Laplace-type invariants of the system of linear hyperbolic equations equivalent to the system of linear elliptic equations via linear complex transformations of the independent variables. It is shown that Cotton-type invariants derived from these two approaches are identical. Furthermore, Cotton-type and joint invariants for a general system of two linear elliptic equations are also obtained from the Laplace-type and joint invariants for a system of two linear hyperbolic equations equivalent to the system of linear elliptic equations by complex changes of the independent variables. Examples are presented to illustrate the results.

16. Investigating the Density of Isolated Field Elliptical Galaxies

Ulgen, E. Kaan

2016-02-01

In this thesis, 215.590 elliptical galaxies with M(r) ≤ -21 in the CFHTLS-W1 field which is covering 72 sq. deg on the sky are examined . Criterion given by Smith et al. (2004) has been used to determine isolated elliptical galaxies. 118 isolated elliptical galaxies have been determined in total. By using g, r and i photometric bands, the true-colour images of candidates are produced and visually inspected. In order to have a clean list of IfEs some candidates are excluded from the final sample after visual inspection. The final sample consists of 60 IfEs which corresponds to the 0.027 per cent of the whole sample. In other words, IfE density in the W1 is 0.8 IfE / sq.deg. Since the formation of the ellipticals in the isolated regions is not known clearly, it is crucial to determine IfEs and compare their photometric and morphological properties to the normal or cluster ellipticals. When the (g-i) distributions of three different elliptical galaxy class are compared, it is found that they have almost the same colours. When the redshift distributions of the galaxies are considered, it can be seen that IfEs formed later than the cluster and normal ellipticals. The average redshift of IfEs is determined as zphot=0.284, while for normal and cluster ellipticals, it is, respectively, 0.410 and 0.732. In addition, when the effective radii of the three elliptical systems are considered, it is found that the IfEs are bigger than the other two elliptical classes.

17. Subregions of Motion and Elliptic Halo Orbits in the Elliptic Restricted Three-Body Problem

NASA Technical Reports Server (NTRS)

Campagnola, Stefano; Lo, Martin; Newton, Paul

2008-01-01

In this paper we present regions of motion and periodic orbits in the spatial elliptic restricted three body problem (ER3BP). Periodic orbits and regions of motion are fundamental keys to understand any dynamical system; for this reason the Hill's surfaces or the families of halo orbits have been extensively studied in the frame of the circular restricted three body problem. It is our opinion that their natural extensions to the ER3BP have not been studied enough. We divide the position space into forbidden subregions, subregions of motion and low-velocity subregions.We use these notions to define necessary condition for a transfer trajectory in the ER3BP. Also we compute branches of elliptic halo orbits bifurcating from halo orbits in the circular restricted three body problem. The new periodic orbits have principal periods and stability properties different from those of the originating halo orbit.

18. Crack-face displacements for embedded elliptic and semi-elliptical surface cracks

NASA Technical Reports Server (NTRS)

Raju, I. S.

1989-01-01

Analytical expressions for the crack-face displacements of an embedded elliptic crack in infinite solid subjected to arbitrary tractions are obtained. The tractions on the crack faces are assumed to be expressed in a polynomial form. These displacements expressions complete the exact solution of Vijayakumar and Atluri, and Nishioki and Atluri. For the special case of an embedded crack in an infinite solid subjected to uniform pressure loading, the present displacements agree with those by Green and Sneddon. The displacement equations derived were used with the finite-element alternating method (FEAM) for the analysis of a semi-elliptic surface crack in a finite solid subjected to remote tensile loading. The maximum opening displacements obtained with FEAM are compared to those with the finite-element method with singularity elements. The maximum crack opening displacements by the two methods showed good agreement.

19. Elliptical Muon Helical Cooling Channel Coils

SciTech Connect

Kahn, S. A.; Flanagan, G.; Lopes, M. L.; Yonehara, K.

2013-09-01

A helical cooling channel (HCC) consisting of a pressurized gas absorber imbedded in a magnetic channel that provides solenoid, helical dipole and helical quadrupole fields has shown considerable promise in providing six-dimensional phase space reduction for muon beams. The most effective approach to implementing the desired magnetic field is a helical solenoid (HS) channel composed of short solenoid coils arranged in a helical pattern. The HS channel along with an external solenoid allows the B$_z$ and B$_{\\phi}$ components along the reference orbit to be set to any desired values. To set dB$_{\\phi}$/dr to the desired value for optimum focusing requires an additional variable to tune. We shall show that using elliptical shaped coils in the HS channel allows the flexibility to achieve the desired dB$_{\\phi}$/dr on the reference orbit without significant change to B$_z$ and B$_{\\phi}$.

20. Splitting of Forced Elliptic Jets and Flames

NASA Technical Reports Server (NTRS)

Hertzberg, J.; Carlton, J.; Schwieterman, M.; Davis, E.; Bradley, E.; Linne, M.

1997-01-01

The objective of this work is to understand the fluid dynamics in the interaction of large scale, three-dimensional vortex structures and transitional diffusion flames in a microgravity environment. The vortex structures are used to provide a known perturbation of the type used in passive and active shear layer control techniques. 'Passive techniques' refers to manipulation of the system geometry to influence the three dimensional dynamics of vortex structures, and 'active' refers to any technique which adds energy (acoustic or kinetic) to the flow to influence the shear layer vortex dynamics. In this work the passive forcing is provided by an elliptic jet cross-section, and the active forcing is incorporated by perturbing the jet velocity using a loudspeaker in the plenum section.

1. Magnetic elliptical polarization of Schumann resonances

NASA Technical Reports Server (NTRS)

Sentman, D. D.

1987-01-01

Measurements of orthogonal, horizontal components of the magnetic field in the ELF range obtained during September 1985 show that the Schumann resonance eigenfrequencies determined separately for the north-south and east-west magnetic components differ by as much as 0.5 Hz, suggesting that the underlying magnetic signal is not linearly polarized at such times. The high degree of magnetic ellipticity found suggests that the side multiplets of the Schumann resonances corresponding to azimuthally inhomogeneous normal modes are strongly excited in the highly asymmetric earth-ionosphere cavity. The dominant sense of polarization over the measurement passband is found to be right-handed during local daylight hours, and to be left-handed during local nighttime hours.

2. First-Order System Least-Squares for Second-Order Elliptic Problems with Discontinuous Coefficients

NASA Technical Reports Server (NTRS)

Manteuffel, Thomas A.; McCormick, Stephen F.; Starke, Gerhard

1996-01-01

The first-order system least-squares methodology represents an alternative to standard mixed finite element methods. Among its advantages is the fact that the finite element spaces approximating the pressure and flux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropriate error measure. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. Ellipticity of an appropriately scaled least-squares bilinear form of the size of the jumps in the coefficients leading to adequate finite element approximation results. The occurrence of singularities at interface corners and cross-points is discussed. and a weighted least-squares functional is introduced to handle such cases. Numerical experiments are presented for two test problems to illustrate the performance of this approach.

3. Quantum-orbit analysis for yield and ellipticity of high order harmonic generation with elliptically polarized laser field.

PubMed

Li, Yang; Zhu, Xiaosong; Zhang, Qingbin; Qin, Meiyan; Lu, Peixiang

2013-02-25

We perform a quantum-orbit analysis for the dependence of high-order-harmonic yield on the driving field ellipticity and the polarization properties of the generated high harmonics. The electron trajectories responsible for the emission of particular harmonics are identified. It is found that, in elliptically polarized driving field, the electrons have ellipticity-dependent initial velocities, which lead to the decrease of the ionization rate. Thus the harmonic yield steeply decreases with laser ellipticity. Besides, we show that the polarization properties of the harmonics are related to the complex momenta of the electron. The physical origin of the harmonic ellipticity is interpreted as the consequence of quantum-mechanical uncertainty of the electron momentum. Our results are verified with the experimental results as well as the numerical solutions of the time dependent Schrödinger equation from the literature.

4. Elliptic Fourier analysis of mandibular shape.

PubMed

Ferrario, V F; Sforza, C; Guazzi, M; Serrao, G

1996-01-01

Craniofacial growth and development involve both size and shape variations. Shape variations can be assessed independently from size using mathematical methods such as the elliptic Fourier analysis, which allows a global evaluation of the shape of organs identified by their outlines independently from size, spatial orientation, and relation to reference planes. The mandibular outlines were digitized from the tracings of the Bolton standards (lateral view) from 1 to 18 years of age, and the age differences in shape independently from size were quantified using the elliptic Fourier series. A "morphologic distance" MD (i.e., a measurement of differences in shape) between each younger mandible and the oldest one was computed using the relevant Fourier coefficients like the cartesian coordinates in standard metric measurements. MD equals 0 when the profiles are identical. MD (Y) between the Bolton standard at 18 years of age and all the other Bolton tracings were significantly correlated (correlation coefficient r = 0.987, P < or = 0.001) with age (X) (semi-logarithmic interpolation Y = -3.87.log(e) X + 13.593). Differences between the size-independent shape of the Bolton standard at 18 years and the relevant plot at 1 year were located at the chin, gonion, coronoid process, anterior border of the ramus. Size differences were measured from the areas enclosed by the mandibular outlines. Mandibular area (Y) increased about 2.58 times from 1 to 18 years of age (X) (Y = -0.071.X2 + 4.917.X + 35.904, r = 0.997, P < or = 0.001). The shape effect was largely overwhelmed by the very evident size increments, and it could be measured only using the proper mathematical methods. The method developed could also be applied to the comparison between healthy and diseased individuals.

5. Elliptical Undulators HU256 for Synchrotron SOLEIL

SciTech Connect

Batrakov, A.; Churkin, I.; Ilyin, I.; Kolokolnikov, Yu.; Rouvinski, E.; Semenov, E.; Steshov, A.; Vobly, P.; Briquez, F.; Chubar, O.; Dael, A.; Marcouile, O.; Marteau, F.; Roux, G.; Valleau, M.

2007-01-19

Three elliptical undulators HU256 of electromagnetic type were produced, tested and magnetically measured by the Budker Institute of Nuclear Physics (Russia) for Synchrotron Soleil (France). The undulators have a new design of a Bx and Bz closed structure for insertion vacuum chamber. In the elliptical undulator HU256 with period of the magnetic fields of 256 mm, the vertical magnetic field (Bzmax=0.44 T) formed by 27 Bz laminated dipole magnets is symmetric, and the horizontal magnetic field (Bxmax=0.33 T) formed by 28 Bx laminated dipole magnets is asymmetric. The undulator can work in standard mode as well as in a quasi-periodical mode. The vertical magnetic field may be modulated by switching on the modulation coils placed on the Bz dipoles. Two power supply systems allow us to modulate the horizontal magnetic field, and change the radiation spectrum. The magnetic calculations of the individual dipoles and dipoles in ''undulator'' environment were executed by means of Mermaid 3D Code. The magnetic measurements of the individual dipoles had confirmed the magnetic calculations. On basis of semiempirical dependences from the mechanical characteristics the estimates of the magnetic parameters for all dipoles were calculated. Sorting of dipoles in the undulators have been done, and it has improved the magnetic parameters of the assembled undulators in comparison with the statistical estimations. The magnetic measurements of the undulators HU256 were carried out at Budker INP by Hall probes and at Soleil by Hall probes and Stretched Wire. Now the 1st undulator HU256 is installed at Soleil Storage Ring.

6. Ellipticals: core-Sérsic vs Nuker

Bartlett, D. F.

2004-12-01

HST has given the first look at elliptical galaxies on scales <1". Lauer et al (1995) used the Wide Field Planetary Camera (WFPC -1) to map the intensity of light I(r) in the inner 10" of 45 type E and S0 galaxies. They discovered that about 40% of the 39 ellipticals could not be described by a single power law. These galaxies have a core region where the power law I ∝ r-γ is less steep than the outer region I ∝ r-β . The resulting Nuker law allows for a smooth transition between these regions at a break radius rb. The physical rb varies widely: 30 pc < rb < 1200 pc. Rest et al (2001) used WFPC -2 to confirm the original WFPC -1 results with additional galaxies. Using the full WFPC -2 mosaic, Trujillo, Erwin, Ramos, and Graham (2004) have extended the angular range of Rest et al by a factor between 3 and 8. They find that the extended outer region is incompatible with a Nuker law. Rather the power law for the outer region must be replaced by the Sérsic law, I(r) ∝ e-bn r1/n. They also find that the break radius is generally much reduced. Their published study of 9 core-Sérsic galaxies has 20 pc< rb <150 pc. The new range of rb fits well within 1 wavelength λ of the non-Newtonian sinusoidal gravity. Here the potential of a point mass is GM cos(2 π r/λ )/r and λ =425 pc. (Bartlett 2001, 2004). With this gravity, the potential towards the center of any spherical mass distribution varies as ± sin(2 π r/λ )/r. I identify the + sign with the core-Sérsic galaxies and the - sign with the pure Sérsic galaxies. I will relate Sérsic's n to cosmological time t.

7. On the solution of elliptic partial differential equations on regions with corners

SciTech Connect

2016-01-15

In this paper we investigate the solution of boundary value problems on polygonal domains for elliptic partial differential equations. We observe that when the problems are formulated as the boundary integral equations of classical potential theory, the solutions are representable by series of elementary functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.

8. On the solution of elliptic partial differential equations on regions with corners

2016-01-01

In this paper we investigate the solution of boundary value problems on polygonal domains for elliptic partial differential equations. We observe that when the problems are formulated as the boundary integral equations of classical potential theory, the solutions are representable by series of elementary functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.

9. Weighted augmented Jacobian matrix with a variable coefficient method for kinematics mapping of space teleoperation based on human-robot motion similarity

Shi, Zhong; Huang, Xuexiang; Hu, Tianjian; Tan, Qian; Hou, Yuzhuo

2016-10-01

Space teleoperation is an important space technology, and human-robot motion similarity can improve the flexibility and intuition of space teleoperation. This paper aims to obtain an appropriate kinematics mapping method of coupled Cartesian-joint space for space teleoperation. First, the coupled Cartesian-joint similarity principles concerning kinematics differences are defined. Then, a novel weighted augmented Jacobian matrix with a variable coefficient (WAJM-VC) method for kinematics mapping is proposed. The Jacobian matrix is augmented to achieve a global similarity of human-robot motion. A clamping weighted least norm scheme is introduced to achieve local optimizations, and the operating ratio coefficient is variable to pursue similarity in the elbow joint. Similarity in Cartesian space and the property of joint constraint satisfaction is analysed to determine the damping factor and clamping velocity. Finally, a teleoperation system based on human motion capture is established, and the experimental results indicate that the proposed WAJM-VC method can improve the flexibility and intuition of space teleoperation to complete complex space tasks.

10. Discontinuous dual-primal mixed finite elements for elliptic problems

NASA Technical Reports Server (NTRS)

Bottasso, Carlo L.; Micheletti, Stefano; Sacco, Riccardo

2000-01-01

We propose a novel discontinuous mixed finite element formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the element level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed finite element methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.

11. TRANSVERSE MERCATOR MAP PROJECTION OF THE SPHEROID USING TRANSFORMATION OF THE ELLIPTIC INTEGRAL

NASA Technical Reports Server (NTRS)

Wallis, D. E.

1994-01-01

This program produces the Gauss-Kruger (constant meridional scale) Transverse Mercator Projection which is used to construct the U.S. Army's Universal Transverse Mercator (UTM) Grid System. The method is capable of mapping the entire northern hemisphere of the earth (and, by symmetry of the projection, the entire earth) accurately with respect to a single principal meridian, and is therefore mathematically insensitive to proximity either to the pole or the equator, or to the departure of the meridian from the central meridian. This program could be useful to any map-making agency. The program overcomes the limitations of the "series" method (Thomas, 1952) presently used to compute the UTM Grid, specifically its complicated derivation, non-convergence near the pole, lack of rigorous error analysis, and difficulty of obtaining increased accuracy. The method is based on the principle that the parametric colatitude of a point is the amplitude of the Elliptic Integral of the 2nd Kind, and this (irreducible) integral is the desired projection. Thus, a specification of the colatitude leads, most directly (and with strongest motivation) to a formulation in terms of amplitude. The most difficult problem to be solved was setting up the method so that the Elliptic Integral of the 2nd Kind could be used elsewhere than on the principal meridian. The point to be mapped is specified in conventional geographic coordinates (geodetic latitude and longitudinal departure from the principal meridian). Using the colatitude (complement of latitude) and the longitude (departure), the initial step is to map the point to the North Polar Stereographic Projection. The closed-form, analytic function that coincides with the North Polar Stereographic Projection of the spheroid along the principal meridian is put into a Newton-Raphson iteration that solves for the tangent of one half the parametric colatitude, generalized to the complex plane. Because the parametric colatitude is the amplitude of

12. Dusty Feedback from Massive Black Holes in Two Elliptical Galaxies

NASA Technical Reports Server (NTRS)

Temi, P.; Brighenti, F.; Mathews, W. G.; Amblard, A.; Riguccini, L.

2013-01-01

Far-infrared dust emission from elliptical galaxies informs us about galaxy mergers, feedback energy outbursts from supermassive black holes and the age of galactic stars. We report on the role of AGN feedback observationally by looking for its signatures in elliptical galaxies at recent epochs in the nearby universe. We present Herschel observations of two elliptical galaxies with strong and spatially extended FIR emission from colder grains 5-10 kpc distant from the galaxy cores. Extended excess cold dust emission is interpreted as evidence of recent feedback-generated AGN energy outbursts in these galaxies, visible only in the FIR, from buoyant gaseous outflows from the galaxy cores.

13. On the convergence of the conditional gradient method as applied to the optimization of an elliptic equation

Chernov, A. V.

2015-02-01

The optimal control of a second-order semilinear elliptic diffusion-reaction equation is considered. Sufficient conditions for the convergence of the conditional gradient method are obtained without using assumptions (traditional for optimization theory) that ensure the Lipschitz continuity of the objective functional derivative. The total (over the entire set of admissible controls) preservation of solvability, a pointwise estimate of solutions, and the uniqueness of a solution to the homogeneous Dirichlet problem for a controlled elliptic equation are proved as preliminary results, which are of interest on their own.

14. Forward and inverse uncertainty quantification using multilevel Monte Carlo algorithms for an elliptic non-local equation

SciTech Connect

Jasra, Ajay; Law, Kody J. H.; Zhou, Yan

2016-01-01

Our paper considers uncertainty quantification for an elliptic nonlocal equation. In particular, it is assumed that the parameters which define the kernel in the nonlocal operator are uncertain and a priori distributed according to a probability measure. It is shown that the induced probability measure on some quantities of interest arising from functionals of the solution to the equation with random inputs is well-defined,s as is the posterior distribution on parameters given observations. As the elliptic nonlocal equation cannot be solved approximate posteriors are constructed. The multilevel Monte Carlo (MLMC) and multilevel sequential Monte Carlo (MLSMC) sampling algorithms are used for a priori and a posteriori estimation, respectively, of quantities of interest. Furthermore, these algorithms reduce the amount of work to estimate posterior expectations, for a given level of error, relative to Monte Carlo and i.i.d. sampling from the posterior at a given level of approximation of the solution of the elliptic nonlocal equation.

15. Interaction of elliptically polarised cross-degenerate cnoidal waves in an isotropic gyrotropic medium with spatial dispersion of cubic nonlinearity

SciTech Connect

Makarov, V A; Petnikova, V M; Shuvalov, V V

2015-09-30

Three unusual classes of particular analytical solutions to a system of four nonlinear equations are found for slowly varying complex amplitudes of circularly polarised components of the electric field. The system describes the self-action and interaction of two elliptically polarised plane waves collinearly propagating in an isotropic medium with second-order frequency dispersion and spatial dispersion of cubic nonlinearity. The solutions correspond to self-consistent combinations of two elliptically polarised cnoidal waves whose mutually orthogonal polarisation components vary in accordance with pairwise identical laws during propagation. At the same time, the amplitudes of the component with the same circular polarisation are proportional to two different elliptic Jacobi functions with the same periods. (nonlinear optical phenomena)

16. Formation Design Strategy for SCOPE High-Elliptic Formation Flying Mission

NASA Technical Reports Server (NTRS)

Tsuda, Yuichi

2007-01-01

The new formation design strategy using simulated annealing (SA) optimization is presented. The SA algorithm is useful to survey a whole solution space of optimum formation, taking into account realistic constraints composed of continuous and discrete functions. It is revealed that this method is not only applicable for circular orbit, but also for high-elliptic orbit formation flying. The developed algorithm is first tested with a simple cart-wheel motion example, and then applied to the formation design for SCOPE. SCOPE is the next generation geomagnetotail observation mission planned in JAXA, utilizing a formation flying techonology in a high elliptic orbit. A distinctive and useful heuristics is found by investigating SA results, showing the effectiveness of the proposed design process.

17. Evolutionary synthesis of the stellar population in elliptical galaxies. III. Detailed optical spectra

SciTech Connect

Gunn, J.E.; Stryker, L.L.; Tinsley, B.M.

1981-10-01

The evolutionary synthesis technique is used to construct population models for giant elliptical galaxies, using detailed spectrophotometric data for the galaxies and for stars obtained with the Oke multichannel spectrometer on the Hale telescope. We find that ellipticals are well represented by an old metal-rich population with a turnoff at B-Vapprox.0.80 and a turnoff mass function slope x< or approx. =1, plus a quite significant contribution from stars above the turnoff. The nature of these objects is discussed, and it is concluded that the present data and astrophysical constraints cannot distinguish between a small young population and a blue straggler population augmented by a few O stars.

18. Design of high-order elliptic filter from a versatile mode generic OTA-C structure

Ghosh, K.; Ray, B. N.

2015-03-01

A new synthesis methodology for high-order versatile mode programmable Operational transconductance amplifier and capacitor (OTA-C) generic filter structure is proposed. The structure fulfills the three main criteria of high frequency operation i.e it uses (1) less number of components (2) only single ended input OTAs (3) only grounded capacitors. Any nth order transfer function can be realised from it. Elliptic filter is designed from the generic structure using optimisation technique to reduce the number of OTAs. SPICE simulation with BSIM level 53 model and 0.13 μm process confirms the theoretical analysis. Frequency response of third-order and fourth-order elliptic filter is shown as representative set of simulated result. Sensitivity and non-ideal effect of the designed filter are studied.

19. The generalized Euler-Poinsot rigid body equations: explicit elliptic solutions

Fedorov, Yuri N.; Maciejewski, Andrzej J.; Przybylska, Maria

2013-10-01

The classical Euler-Poinsot case of the rigid body dynamics admits a class of simple but non-trivial integrable generalizations, which modify the Poisson equations describing the motion of the body in space. These generalizations possess first integrals which are polynomial in the angular momenta. We consider the modified Poisson equations as a system of linear equations with elliptic coefficients and show that all the solutions of it are single-valued. By using the vector generalization of the Picard theorem, we derive the solutions explicitly in terms of sigma-functions of the corresponding elliptic curve. The solutions are accompanied by a numerical example. We also compare the generalized Poisson equations with the classical third order Halphen equation.

20. Craik-Criminale solutions and elliptic instability in nonlinear-reactive closure models for turbulence

Fabijonas, Bruce R.; Holm, Darryl D.

2004-04-01

The Craik-Criminale class of exact solutions is examined for a nonlinear-reactive fluids theory that includes a family of turbulence closure models. These may be formally regarded as either large eddy simulation or Reynolds-averaged Navier-Stokes models of turbulence. All of the turbulence closure models in the class under investigation preserve the existence of elliptic instability, although they shift its angle of critical stability as a function of the rotation rate Ω of the coordinate system, the wave number β of the Kelvin wave, and the model parameter α, the turbulence correlation length. Elliptic instability allows a comparison among the properties of these models. It is emphasized that the physical mechanism for this instability is not wave-wave interaction, but rather wave, mean-flow interaction as governed by the choice of a model's nonlinearity.

1. A Central Limit Theorem for the Effective Conductance: Linear Boundary Data and Small Ellipticity Contrasts

Biskup, M.; Salvi, M.; Wolff, T.

2014-06-01

Given a resistor network on with nearest-neighbor conductances, the effective conductance in a finite set with a given boundary condition is the minimum of the Dirichlet energy over functions with the prescribed boundary values. For shift-ergodic conductances, linear (Dirichlet) boundary conditions and square boxes, the effective conductance scaled by the volume of the box converges to a deterministic limit as the box-size tends to infinity. Here we prove that, for i.i.d. conductances with a small ellipticity contrast, also a (non-degenerate) central limit theorem holds. The proof is based on the corrector method and the Martingale Central Limit Theorem; a key integrability condition is furnished by the Meyers estimate. More general domains, boundary conditions and ellipticity contrasts will be addressed in a subsequent paper.

2. Boxy isophotes, discs and dust lanes in elliptical galaxies

NASA Technical Reports Server (NTRS)

Lauer, T. R.

1985-01-01

CCD images of 42 elliptical and S0 galaxies are examined for low-contrast structures or subtle distortions of the isophotes from perfect ellipses. 75 percent of the galaxies have isophotes completely describable as concentric ellipses to within the photometry errors. 'Boxy' isophotes, stellar discs, and dust lanes are detected in the remaining 25 percent of the sample. The boxy elliptical galaxies appear dynamically indistinguishable from normal ellipticals and are therefore different from boxy bulges, which rotate rapidly. Most of the galaxies with faint discs, however, appear dynamically similar to S0 galaxies. Nearly edge-on dust lanes are found in four galaxies, which suggests that dust lanes may commonly occur in elliptical galaxies.

3. Rigorous theory on elliptical mirror focusing for point scanning microscopy.

PubMed

Liu, Jian; Tan, Jiubin; Wilson, Tony; Zhong, Cien

2012-03-12

A rigorous elliptical mirror focusing formula based on spherical wave transformation is derived as a kind of imaging technique with high NA for potential applications in molecule imaging, spectroscopy and industrial artifact microscopy. An apodization factor is given and used to compare the energy conversation rules in lens transmission and parabolic and elliptical mirror reflections. Simulation results indicate that the axial HFWHM of elliptical and parabolic mirrors is about 80% of the corresponding HFWHM of lens in case of NA = 1 and φs = 0, and the side lobe noise is also slightly lower than that of lens, but the transverse HFWHM of mirrors is comparatively wider despite the width of main lobe is still smaller. In comparison with parabolic mirror based system, an elliptical mirror based system is potentially promising in aberration control of incident beam when the aperture of mirror is enlarged to adapt a large stage or specimen container at a small beam shading ratio.

4. Elliptic Solvers with Adaptive Mesh Refinement on Complex Geometries

SciTech Connect

Phillip, B.

2000-07-24

Adaptive Mesh Refinement (AMR) is a numerical technique for locally tailoring the resolution computational grids. Multilevel algorithms for solving elliptic problems on adaptive grids include the Fast Adaptive Composite grid method (FAC) and its parallel variants (AFAC and AFACx). Theory that confirms the independence of the convergence rates of FAC and AFAC on the number of refinement levels exists under certain ellipticity and approximation property conditions. Similar theory needs to be developed for AFACx. The effectiveness of multigrid-based elliptic solvers such as FAC, AFAC, and AFACx on adaptively refined overlapping grids is not clearly understood. Finally, a non-trivial eye model problem will be solved by combining the power of using overlapping grids for complex moving geometries, AMR, and multilevel elliptic solvers.

5. Acoustic backscattering and radiation force on a rigid elliptical cylinder in plane progressive waves.

PubMed

Mitri, F G

2016-03-01

This work proposes a formal analytical theory using the partial-wave series expansion (PWSE) method in cylindrical coordinates, to calculate the acoustic backscattering form function as well as the radiation force-per-length on an infinitely long elliptical (non-circular) cylinder in plane progressive waves. The major (or minor) semi-axis of the ellipse coincides with the direction of the incident waves. The scattering coefficients for the rigid elliptical cylinder are determined by imposing the Neumann boundary condition for an immovable surface and solving a resulting system of linear equations by matrix inversion. The present method, which utilizes standard cylindrical (Bessel and Hankel) wave functions, presents an advantage over the solution for the scattering that is ordinarily expressed in a basis of elliptical Mathieu functions (which are generally non-orthogonal). Furthermore, an integral equation showing the direct connection of the radiation force function with the square of the scattering form function in the far-field from the scatterer (applicable for plane waves only), is noted and discussed. An important application of this integral equation is the adequate evaluation of the radiation force function from a bistatic measurement (i.e., in the polar plane) of the far-field scattering from any 2D object of arbitrary shape. Numerical predictions are evaluated for the acoustic backscattering form function and the radiation force function, which is the radiation force per unit length, per characteristic energy density, and per unit cross-sectional surface of the ellipse, with particular emphasis on the aspect ratio a/b, where a and b are the semi-axes, as well as the dimensionless size parameter kb, without the restriction to a particular range of frequencies. The results are particularly relevant in acoustic levitation, acousto-fluidics and particle dynamics applications.

6. Bifurcations in elliptical, asymmetric non-neutral plasmas

Fajans, Joel; Gilson, Erik

1999-11-01

When subjected to a stationary, l=2 potential perturbation on the wall, a pure electron plasma will deform into an elliptical shape. At first, the plasma's ellipticity is proportional to the strength of the potential perturbation. Once the perturbation is increased beyond a critical value, the plasma equilibrium bifurcates into two off-axis states. This bifurcation has been observed experimentally and will be described in this poster. (see http://socrates.berkeley.edu/ fajans/EquilStab/EllipseBifurcation.avi)

7. A class of variational-hemivariational inequalities of elliptic type

Liu, Zhenhai; Motreanu, Dumitru

2010-07-01

This paper is devoted to the existence of solutions for variational-hemivariational inequalities of elliptic type, with a higher order quasilinear principal part, at resonance as well as at nonresonance. The approach relies on the use of pseudomonotone operators. By means of the notion of Clarke's generalized gradient and the properties of the first eigenfunction of the quasilinear principal part, we also build a Landesman-Lazer theory in the nonsmooth framework of variational-hemivariational inequalities of elliptic type.

8. Remarks of Elliptic Curves Derived from Ant Colony Routing

Jung, Sangsu; Kim, Daeyeoul; Singh, Dhananjay

2011-09-01

We deal with an ant colony based routing model for wireless multi-hop networks. Our model adopts an elliptic curve equation, which is beneficial to design pheromone dynamics for load balancing and packet delivery robustness. Due to the attribute of an elliptic curve equation, our model prevents the over-utilization of a specific node, distinctively from conventional ant colony based schemes. Numerical simulations exhibit the characteristics of our model with respect to various parameters.

9. Depth-resolved measurements with elliptically polarized reflectance spectroscopy

PubMed Central

Bailey, Maria J.; Sokolov, Konstantin

2016-01-01

The ability of elliptical polarized reflectance spectroscopy (EPRS) to detect spectroscopic alterations in tissue mimicking phantoms and in biological tissue in situ is demonstrated. It is shown that there is a linear relationship between light penetration depth and ellipticity. This dependence is used to demonstrate the feasibility of a depth-resolved spectroscopic imaging using EPRS. The advantages and drawbacks of EPRS in evaluation of biological tissue are analyzed and discussed. PMID:27446712

10. Do massive black holes reside in elliptical galaxies?

NASA Technical Reports Server (NTRS)

Fabian, A. C.; Canizares, C. R.

1988-01-01

The accretion by a central black hole of the hot interstellar medium in an elliptical galaxy is investigated, and the minimum expected luminosity and manner of its emission is estimated. It is not obviously detected at any wavelength. The problem of 'starving the monster', if indeed there is a monster, is raised. The simplest conclusion from the evidence is that most bright elliptical galaxies do not contain massive black holes.

11. Beam-beam deflection and signature curves for elliptic beams

SciTech Connect

Ziemann, V.

1990-10-22

In this note we will present closed expressions for the beam-beam deflection angle for arbitrary elliptic beams including tilt. From these expressions signature curves, i.e., systematic deviations from the round beam deflection curve due to ellipticity or tilt are derived. In the course of the presentation we will prove that it is generally impossible to infer individual beam sizes from beam-beam deflection scans. 3 refs., 2 figs.

12. A Jacobian-free Newton-Krylov method for time-implicit multidimensional hydrodynamics. Physics-based preconditioning for sound waves and thermal diffusion

Viallet, M.; Goffrey, T.; Baraffe, I.; Folini, D.; Geroux, C.; Popov, M. V.; Pratt, J.; Walder, R.

2016-02-01

This work is a continuation of our efforts to develop an efficient implicit solver for multidimensional hydrodynamics for the purpose of studying important physical processes in stellar interiors, such as turbulent convection and overshooting. We present an implicit solver that results from the combination of a Jacobian-free Newton-Krylov method and a preconditioning technique tailored to the inviscid, compressible equations of stellar hydrodynamics. We assess the accuracy and performance of the solver for both 2D and 3D problems for Mach numbers down to 10-6. Although our applications concern flows in stellar interiors, the method can be applied to general advection and/or diffusion-dominated flows. The method presented in this paper opens up new avenues in 3D modeling of realistic stellar interiors allowing the study of important problems in stellar structure and evolution.

13. The application of Jacobian-free Newton-Krylov methods to reduce the spin-up time of ocean general circulation models

SciTech Connect

Bernsen, Erik; Dijkstra, Henk A.; Thies, Jonas; Wubs, Fred W.

2010-10-20

In present-day forward time stepping ocean-climate models, capturing both the wind-driven and thermohaline components, a substantial amount of CPU time is needed in a so-called spin-up simulation to determine an equilibrium solution. In this paper, we present methodology based on Jacobian-Free Newton-Krylov methods to reduce the computational time for such a spin-up problem. We apply the method to an idealized configuration of a state-of-the-art ocean model, the Modular Ocean Model version 4 (MOM4). It is shown that a typical speed-up of a factor 10-25 with respect to the original MOM4 code can be achieved and that this speed-up increases with increasing horizontal resolution.

14. Mild solutions of semilinear elliptic equations in Hilbert spaces

Federico, Salvatore; Gozzi, Fausto

2017-03-01

This paper extends the theory of regular solutions (C1 in a suitable sense) for a class of semilinear elliptic equations in Hilbert spaces. The notion of regularity is based on the concept of G-derivative, which is introduced and discussed. A result of existence and uniqueness of solutions is stated and proved under the assumption that the transition semigroup associated to the linear part of the equation has a smoothing property, that is, it maps continuous functions into G-differentiable ones. The validity of this smoothing assumption is fully discussed for the case of the Ornstein-Uhlenbeck transition semigroup and for the case of invertible diffusion coefficient covering cases not previously addressed by the literature. It is shown that the results apply to Hamilton-Jacobi-Bellman (HJB) equations associated to infinite horizon optimal stochastic control problems in infinite dimension and that, in particular, they cover examples of optimal boundary control of the heat equation that were not treatable with the approaches developed in the literature up to now.

15. Stress Analysis of Composite Cylindrical Shells with an Elliptical Cutout

NASA Technical Reports Server (NTRS)

Oterkus, E.; Madenci, E.; Nemeth, M. P.

2007-01-01

A special-purpose, semi-analytical solution method for determining the stress and deformation fields in a thin laminated-composite cylindrical shell with an elliptical cutout is presented. The analysis includes the effects of cutout size, shape, and orientation; non-uniform wall thickness; oval-cross-section eccentricity; and loading conditions. The loading conditions include uniform tension, uniform torsion, and pure bending. The analysis approach is based on the principle of stationary potential energy and uses Lagrange multipliers to relax the kinematic admissibility requirements on the displacement representations through the use of idealized elastic edge restraints. Specifying appropriate stiffness values for the elastic extensional and rotational edge restraints (springs) allows the imposition of the kinematic boundary conditions in an indirect manner, which enables the use of a broader set of functions for representing the displacement fields. Selected results of parametric studies are presented for several geometric parameters that demonstrate that analysis approach is a powerful means for developing design criteria for laminated-composite shells.

16. Stress Analysis of Composite Cylindrical Shells With an Elliptical Cutout

NASA Technical Reports Server (NTRS)

Nemeth, M. P.; Oterkus, E.; Madenci, E.

2005-01-01

A special-purpose, semi-analytical solution method for determining the stress and deformation fields in a thin laminated-composite cylindrical shell with an elliptical cutout is presented. The analysis includes the effects of cutout size, shape, and orientation; nonuniform wall thickness; oval-cross-section eccentricity; and loading conditions. The loading conditions include uniform tension, uniform torsion, and pure bending. The analysis approach is based on the principle of stationary potential energy and uses Lagrange multipliers to relax the kinematic admissibility requirements on the displacement representations through the use of idealized elastic edge restraints. Specifying appropriate stiffness values for the elastic extensional and rotational edge restraints (springs) allows the imposition of the kinematic boundary conditions in an indirect manner, which enables the use of a broader set of functions for representing the displacement fields. Selected results of parametric studies are presented for several geometric parameters that demonstrate that analysis approach is a powerful means for developing design criteria for laminated-composite shells.

17. Retrieval of Rayleigh Wave Ellipticity from Ambient Vibration Recordings

Maranò, Stefano; Hobiger, Manuel; Fäh, Donat

2017-01-01

The analysis of ambient vibrations is a useful tool in microzonation and geotechnical investigations. Ambient vibrations are composed to a large part of surface waves, both Love and Rayleigh waves. One reason to analyse surface waves is that they carry information about the subsurface. The dispersion curve of Rayleigh waves and Love waves can be retrieved using array processing techniques. The Rayleigh wave ellipticity, including the sense of rotation of the particle motion, can also be retrieved using array techniques. These quantities are used in an inversion procedure aimed at obtaining a structural model of the subsurface. The focus of this work is the retrieval of Rayleigh wave ellipticity. We show applications of the (ML) method presented in Maranó et al. (2012) to a number of sites in Switzerland. The sites examined are chosen to reflect a wide range of soil conditions that are of interest in microzonation studies. Using a synthetic wavefield with known structural model, we compare our results with theoretical ellipticity curves and we show the accuracy of the considered algorithm. The sense of rotation of the particle motion (prograde vs. retrograde) is also estimated. In addition, we show that by modelling the presence of both Love and Rayleigh waves it is possible to mitigate the disruptive influence of Love waves on the estimation of Rayleigh wave ellipticity. Using recordings from several real sites, we show that it is possible to retrieve the ellipticity curve over a broad range of frequencies. Fundamental modes and higher modes are retrieved. Singularities of the ellipticity, corresponding to a change of the sense of rotation from prograde to retrograde (or vice versa), are detected with great accuracy. Knowledge of Rayleigh wave ellipticity, including the sense of rotation, is useful in several ways. The ellipticity angle allows us to pinpoint accurately the frequency of singularities (i.e., peaks and zeros of the H/V representation of the

18. X-ray properties of elliptical galaxies as determined by feedback from their central black holes

Pellegrini, Silvia; Ciotti, Luca; Ostriker, Jeremiah

The centers of elliptical galaxies host supermassive black holes that - through feedback resulting from the accretion process - are believed to significantly affect their hot interstellar medium. The evolution of this hot gas together with that of the nuclear emission during the whole galaxies lifetime has been studied with the aid of high-resolution hydrodynamical simulations, with cooling and heating functions including photoionization plus Compton process, and specific for an average AGN spectral energy distribution (Ciotti and Ostriker 2007). It has been found that nuclear outbursts take place, with duty cycles at the present epoch small enough to account for the small fraction of massive ellipticals observed to be in the "on" (AGN) phase. More recently, the models have been extended to include low radiative efficiency states (ADAFs) and also mechanical coupling between the ISM and the nuclear outflows. Here we present the observational properties resulting for the simulated hot gas and for the nuclear emission. These properties are compared with those of real galaxies, particularly taking into account the recent Chandra results for ellipticals of the local (and possibly low redshift) Universe.

19. Spectral Energy Distribution Mapping of Two Elliptical Galaxies on Sub-kpc Scales

Amblard, A.; Temi, P.; Gaspari, M.; Brighenti, F.

2017-01-01

We use high-resolution Herschel-PACS data of two nearby elliptical galaxies, IC 1459 and NGC 2768, to characterize their dust and stellar content. IC 1459 and NGC 2768 have an unusually large amount of dust for elliptical galaxies ((1–3) × 105 {M}ȯ ); this dust is also not distributed along the stellar content. Using data from GALEX (ultra-violet) to PACS (far-infrared, FIR), we analyze the spectral energy distribution (SED) of these galaxies with CIGALEMC as a function of the projected position, binning images in 7.″2 pixels. From this analysis, we derive maps of SED parameters, such as the metallicity, the stellar mass, the fraction of young stars, and the dust mass. The larger amount of dust in FIR maps seems related in our model to a larger fraction of young stars which can reach up to 4% in the dustier area. The young stellar population is fitted as a recent (∼0.5 Gyr) short burst of star formation for both galaxies. The metallicities, which are fairly large at the center of both galaxies, decrease with the radial distance with a fairly steep gradient for elliptical galaxies.

20. Acoustic scattering by elastic cylinders of elliptical cross-section and splitting up of resonances

SciTech Connect

Ancey, S. Bazzali, E. Gabrielli, P. Mercier, M.

2014-05-21

The scattering of a plane acoustic wave by an infinite elastic cylinder of elliptical cross section is studied from a modal formalism by emphasizing the role of the symmetries. More precisely, as the symmetry is broken in the transition from the infinite circular cylinder to the elliptical one, the splitting up of resonances is observed both theoretically and experimentally. This phenomenon can be interpreted using group theory. The main difficulty stands in the application of this theory within the framework of the vectorial formalism in elastodynamics. This method significantly simplifies the numerical treatment of the problem, provides a full classification of the resonances, and gives a physical interpretation of the splitting up in terms of symmetry breaking. An experimental part based on ultrasonic spectroscopy complements the theoretical study. A series of tank experiments is carried out in the case of aluminium elliptical cylinders immersed in water, in the frequency range 0 ≤ kr ≤ 50, where kr is the reduced wave number in the fluid. The symmetry is broken by selecting various cylinders of increasing eccentricity. More precisely, the greater the eccentricity, the higher the splitting up of resonances is accentuated. The experimental results provide a very good agreement with the theoretical ones, the splitting up is observed on experimental form functions, and the split resonant modes are identified on angular diagrams.

1. Effects of confining walls on heat transfer from a vertical array of isothermal horizontal elliptic cylinders

SciTech Connect

Yousefi, T.; Paknezhad, M.; Ashjaee, M.; Yazdani, S.

2009-09-15

Steady state two-dimensional natural convection heat transfer from the vertical array of five horizontal isothermal elliptic cylinders with vertical major axis which confined between two adiabatic walls has been studied experimentally. Experiments were carried out using a Mach-Zehnder interferometer. The Rayleigh number based on cylinder major axis was in the range 10{sup 3}{<=}Ra{<=}2.5 x 10{sup 3}, and dimensionless wall spacing 1.5{<=} t/b{<=}9 and infinity. The effect of wall spacing and Rayleigh number on the heat transfer from the individual cylinder and the array were investigated. Experiments are performed for ratio wall spacing to major diameter t/b = 1.5, 2, 2.5, 3, 3.5, 4, 5, 6, 7, 8, 9 and infinity. A correlation based on the experimental data for the average Nusselt number of the array as a function of Ra and t/b is presented in the aforementioned ranges. A relation has been derived for optimum wall spacing at which the Nusselt number of the array attains its maximum value. At optimum wall spacing, approximately 10% increase in the heat transfer from the confined array of elliptic cylinders has been observed as compared to the unconfined case. Also, a heat transfer correlation has been proposed for a single elliptic cylinder with vertical major axis and has been compared with earlier works. (author)

2. A criterion for uniform approximability on arbitrary compact sets for solutions of elliptic equations

SciTech Connect

Mazalov, M Ya

2008-02-28

Let X be an arbitrary compact subset of the plane. It is proved that if L is a homogeneous elliptic operator with constant coefficients and locally bounded fundamental solution, then each function f that is continuous on X and satisfies the equation Lf = 0 at all interior points of X can be uniformly approximated on X by solutions of the same equation having singularities outside X. A theorem on uniform piecemeal approximation of a function is also established under weaker constraints than in the standard Vitushkin scheme. Bibliography: 24 titles.

3. The Ellipticities of Cluster Early-type Galaxies from z ~ 1 to z ~ 0: No Evolution in the Overall Distribution of Bulge-to-Disk Ratios

Holden, B. P.; Franx, M.; Illingworth, G. D.; Postman, M.; van der Wel, A.; Kelson, D. D.; Blakeslee, J. P.; Ford, H.; Demarco, R.; Mei, S.

2009-03-01

We have compiled a sample of early-type cluster galaxies from 0 < z < 1.3 and measured the evolution of their ellipticity distributions. Our sample contains 487 galaxies in 17 z>0.3 clusters with high-quality space-based imaging and a comparable sample of 210 galaxies in 10 clusters at z < 0.05. We select early-type galaxies (elliptical and S0 galaxies) that fall within the cluster R 200, and which lie on the red-sequence in the magnitude range -19.3>MB > - 21, after correcting for luminosity evolution as measured by the fundamental plane. Our ellipticity measurements are made in a consistent manner over our whole sample. We perform extensive simulations to quantify the systematic and statistical errors, and find that it is crucial to use point-spread function (PSF)-corrected model fits; determinations of the ellipticity from Hubble Space Telescope image data that do not account for the PSF "blurring" are systematically and significantly biased to rounder ellipticities at redshifts z>0.3. We find that neither the median ellipticity, nor the shape of the ellipticity distribution of cluster early-type galaxies evolves with redshift from z ~ 0 to z>1 (i.e., over the last ~8 Gyr). The median ellipticity at z>0.3 is statistically identical with that at z < 0.05, being higher by only 0.01 ± 0.02 or 3 ± 6%, while the distribution of ellipticities at z>0.3 agrees with the shape of the z < 0.05 distribution at the 1-2% level (i.e., the probability that they are drawn from the same distribution is 98-99%). These results are strongly suggestive of an unchanging overall bulge-to-disk ratio distribution for cluster early-type galaxies over the last ~8 Gyr from z ~ 1 to z ~ 0. This result contrasts with that from visual classifications which show that the fraction of morphologically-selected disk-dominated early-type galaxies, or S0s, is significantly lower at z>0.4 than at z ~ 0. We find that the median disk-dominated early-type, or S0, galaxy has a somewhat higher

4. Sessile Nanodroplets on Elliptical Patches of Enhanced Lyophilicity

PubMed Central

2017-01-01

We theoretically investigate the shape of a nanodroplet on a lyophilic elliptical patch in lyophobic surroundings on a flat substrate. To compute the droplet equilibrium shape, we minimize its interfacial free energy using both Surface Evolver and Monte Carlo calculations, finding good agreement between the two methods. We observe different droplet shapes, which are controlled by the droplet volume and the aspect ratio of the ellipse. In particular, we study the behavior of the nanodroplet contact angle along the three-phase contact line, explaining the different droplet shapes. Although the nanodroplet contact angle is constant and fixed by Young’s law inside and outside the elliptical patch, its value varies along the rim of the elliptical patch. We find that because of the pinning of the nanodroplet contact line at the rim of the elliptical patch, which has a nonconstant curvature, there is a regime of aspect ratios of the elliptical patch in which the nanodroplet starts expanding to the lyophobic part of the substrate, although there is still a finite area of the lyophilic patch free to be wetted. PMID:28248114

5. Elliptic Cones Alone and with Wings at Supersonic Speed

NASA Technical Reports Server (NTRS)

Jorgensen, Leland H

1958-01-01

To help fill the gap in the knowledge of aerodynamics of shapes intermediate between bodies of revolution and flat triangular wings, force and moment characteristics for elliptic cones have been experimentally determined for Mach numbers of 1.97 and 2.94. Elliptic cones having cross-sectional axis ratios from 1 through 6 and with lengths and base areas equal to circular cones of fineness ratios 3.67 and 5 have been studied for angles of bank of 0 degree and 90 degrees. Elliptic and circular cones in combination with triangular wings of aspect ratios 1 and 1.5 also have been considered. The angle-of-attack range was from 0 degree to about 16 degrees, and the Reynolds number was 8 x 10(6), based on model length. In addition to the forces and moments at angle of attack, pressure distributions for elliptic cones at zero angle of attack have been determined. The results of this investigation indicate that there are distinct aerodynamic advantages to the use of elliptic cones.

6. Observations On The Stability Of Elliptical Liquid Bridges

Uguz, A.

A liquid bridge is a region of liquid suspended between two solids. These bridges occur within natural and technological contexts. For long enough cylinders in zero gravity, the bridge collapses at what is known as the Plateau limit, i.e. the bridge becomes unstable when its length exceeds its circumference. This limit is reached when there is a balance between the stabilization effect of longitudinal curvature and the destabilization effect caused by transverse curvature. In this presentation, the effect of distortion of the circular end plates to the nearby elliptical ones is studied. The circular disks can be distorted to an ellipse by many ways: usually by either keeping the area of the circle constant, or by keeping the perimeter constant, which determines the shape of the elliptical liquid bridge. Our aim is to find out the critical length of a static elliptical liquid bridge where the bridge collapses and compare it with the critical length of a cylindrical bridge by requiring that the volume of the elliptical bridge suspended between the plates 'L' apart be equal to the volume of the nearby right circular. An analytical expression is given that will let us conclude that an elliptical liquid bridge is more stable than a circular one. In addition different results will be obtained for different operating conditions and these will be discussed.

7. Elliptic Boundary Value Problems On Non-Smooth Domains

Geng, Jun

2011-07-01

In this dissertation we study the Lp Neumann boundary problem for Laplace's equation in convex domains and the W1,p estimates for the second order elliptic equations with Neumann boundary data in Lipschitz domains. We also study the uniform W1, p estimates for homogenization of elliptic systems. In the case of convex domains we are able to show that the Lp Neumann problem for Laplace's equation is uniquely solvable for 1 < p < infinity. In the case of second order elliptic equations in Lipschitz domains, for any fixed p > 2, we prove that a weak reverse Holder inequality implies the W1, p estimates for solutions with Neumann boundary conditions. As a result, we are able to show that if the coefficient matrix for elliptic equation is symmetric and in VMO( Rn ), the W1,p estimates hold for 32 -- epsilon < p < 3 + epsilon if n ≥ 3, and for 43 -- epsilon < p < 4 + epsilon if n = 2. Finally, we show that the uniform W 1,p estimates for homogenization of elliptic systems hold when | 1p -- 1/2| < 12n + delta. KEYWORDS: Lipschitz domains; convex domains; Neumann problem; Dirichlet problem; Homogenization problem

8. Precession and circularization of elliptical space-tether motion

NASA Technical Reports Server (NTRS)

Chapel, Jim D.; Grosserode, Patrick

1993-01-01

In this paper, we present a simplified analytic model for predicting motion of long space tethers. The perturbation model developed here addresses skip rope motion, where each end of the tether is held in place and the middle of the tether swings with a motion similar to that of a child's skip rope. If the motion of the tether midpoint is elliptical rather than circular, precession of the ellipse complicates the procedures required to damp this motion. The simplified analytic model developed in this paper parametrically predicts the precession of elliptical skip rope motion. Furthermore, the model shows that elliptic skip rope motion will circularize when damping is present in the longitudinal direction. Compared with high-fidelity simulation results, this simplified model provides excellent predictions of these phenomena.

9. Mass distributions in elliptical galaxies at large radii

NASA Technical Reports Server (NTRS)

Sarazin, Craig L.

1987-01-01

Recently, X-ray observations have shown that elliptical galaxies generally contain large quantities of hot gas. Central dominant cluster ellipticals have even more gas, which they have accreted from the surrounding clusters. The mass distributions in these galaxies can be derived from the condition of hydrostatic equilibrium. M87, the best studied central dominant galaxy, has a massive, dark halo with a total mass of about 4 x 10 to the 12th solar masses within a radius of 300 kpc. The total mass-to-light ratio within this radius is at least 150 solar mass/solar luminosity. The X-ray observations of normal ellipticals also strongly suggest that they have heavy halos, although the distribution of the mass is much less certain than in M87.

10. Evolution of a barotropic shear layer into elliptical vortices.

PubMed

Guha, Anirban; Rahmani, Mona; Lawrence, Gregory A

2013-01-01

When a barotropic shear layer becomes unstable, it produces the well-known Kelvin-Helmholtz instability (KHI). The nonlinear manifestation of the KHI is usually in the form of spiral billows. However, a piecewise linear shear layer produces a different type of KHI characterized by elliptical vortices of constant vorticity connected via thin braids. Using direct numerical simulation and contour dynamics, we show that the interaction between two counterpropagating vorticity waves is solely responsible for this KHI formation. We investigate the oscillation of the vorticity wave amplitude, the rotation and nutation of the elliptical vortex, and straining of the braids. Our analysis also provides a possible explanation for the formation and evolution of elliptical vortices appearing in geophysical and astrophysical flows, e.g., meddies, stratospheric polar vortices, Jovian vortices, Neptune's Great Dark Spot, and coherent vortices in the wind belts of Uranus.

11. Ball bearing lubrication: The elastohydrodynamics of elliptical contacts

NASA Technical Reports Server (NTRS)

Hamrock, B. J.; Dowson, D.

1981-01-01

The history of ball bearings is examined, taking into account rollers and the wheel in the early civilizations, the development of early forms of rolling-element bearings in the classical civilizations, the Middle Ages, the Industrial Revolution, the emergence of the precision ball bearing, scientific studies of contact mechanics and rolling friction, and the past fifty years. An introduction to ball bearings is presented, and aspects of ball bearing mechanics are explored. Basic characteristics of lubrication are considered along with lubrication equations, the lubrication of rigid ellipsoidal solids, and elastohydrodynamic lubrication theory. Attention is given to the theoretical results for fully flooded elliptical hydrodynamic contacts, the theoretical results for starved elliptical contacts, experimental investigations, the elastohydrodynamics of elliptical contacts for materials of low elastic modulus, the film thickness for different regimes of fluid-film lubrication, and applications.

12. Elliptic jets, part 2. Dynamics of coherent structures: Pairing

NASA Technical Reports Server (NTRS)

Husain, Hyder S.; Hussain, Fazle

1992-01-01

The dynamics of the jet column mode of vortex pairing in the near field of an elliptic jet was investigated. Hot-wire measurements and flow visualization were used to examine the details of the pairing mechanism of nonplanar vortical elliptic structures and its effect on such turbulence measures as coherent velocities, incoherent turbulence intensities, incoherent and coherent Reynolds, stresses, turbulence production, and mass entrainment. It was found that pairing of elliptic vortices in the jet column does not occur uniformly around the entire perimeter, unlike in a circular jet. Merger occurs only in the initial major-axis plane. In the initial minor-axis plane, the trailing vortex rushes through the leading vortex without pairing and then breaks down violently, producing considerably greater entrainment and mixing than in circular or plane jets.

13. Polar rotation angle identifies elliptic islands in unsteady dynamical systems

2016-02-01

We propose rotation inferred from the polar decomposition of the flow gradient as a diagnostic for elliptic (or vortex-type) invariant regions in non-autonomous dynamical systems. We consider here two- and three-dimensional systems, in which polar rotation can be characterized by a single angle. For this polar rotation angle (PRA), we derive explicit formulas using the singular values and vectors of the flow gradient. We find that closed level sets of the PRA reveal elliptic islands in great detail, and singular level sets of the PRA uncover centers of such islands. Both features turn out to be objective (frame-invariant) for two-dimensional systems. We illustrate the diagnostic power of PRA for elliptic structures on several examples.

14. Systematic differences between the field and cluster elliptical galaxies

NASA Technical Reports Server (NTRS)

De Carvalho, R. R.; Djorgovski, S.

1992-01-01

Multivariate statistical techniques and fundamental plane fits are used here to study possible systematic differences between field ellipticals (FEs) and cluster ellipticals (CEs). The FEs show more intrinsic scatter in their properties, especially when stellar population variables are included. Pairwise correlations for the two samples are different; the correlations are systematically better for the cluster sample, meaning that ellipticals in the two samples populate their fundamental planes in different ways. Bivariate correlations are different for the two samples, implying that they have different fundamental planes. This is especially true for the correlations which include the population variables Mg2 and (B-V), which are sensitive both to the enrichment history and the storm formation history.

15. Dynamical properties of the soft-wall elliptical billiard.

PubMed

Kroetz, Tiago; Oliveira, Hércules A; Portela, Jefferson S E; Viana, Ricardo L

2016-08-01

Physical systems such as optical traps and microwave cavities are realistically modeled by billiards with soft walls. In order to investigate the influence of the wall softness on the billiard dynamics, we study numerically a smooth two-dimensional potential well that has the elliptical (hard-wall) billiard as a limiting case. Considering two parameters, the eccentricity of the elliptical equipotential curves and the wall hardness, which defines the steepness of the well, we show that (1) whereas the hard-wall limit is integrable and thus completely regular, the soft wall elliptical billiard exhibits chaos, (2) the chaotic fraction of the phase space depends nonmonotonically on the hardness of the wall, and (3) the effect of the hardness on the dynamics depends strongly on the eccentricity of the billiard. We further show that the limaçon billiard can exhibit enhanced chaos induced by wall softness, which suggests that our findings generalize to quasi-integrable systems.

16. Cluster flight control for fractionated spacecraft on an elliptic orbit

Xu, Ming; Liang, Yuying; Tan, Tian; Wei, Lixin

2016-08-01

This paper deals with the stabilization of cluster flight on an elliptic reference orbit by the Hamiltonian structure-preserving control using the relative position measurement only. The linearized Melton's relative equation is utilized to derive the controller and then the full nonlinear relative dynamics are employed to numerically evaluate the controller's performance. In this paper, the hyperbolic and elliptic eigenvalues and their manifolds are treated without distinction notations. This new treatment not only contributes to solving the difficulty in feedback of the unfixed-dimensional manifolds, but also allows more opportunities to set the controlled frequencies of foundational motions or to optimize control gains. Any initial condition can be stabilized on a Kolmogorov-Arnold-Moser torus near a controlled elliptic equilibrium. The motions are stabilized around the natural relative trajectories rather than track a reference relative configuration. In addition, the bounded quasi-periodic trajectories generated by the controller have advantages in rapid reconfiguration and unpredictable evolution.

17. Self-regulated cooling flows in elliptical galaxies and in cluster cores - Is exclusively low mass star formation really necessary?

NASA Technical Reports Server (NTRS)

Silk, J.; Djorgovski, S.; Wyse, R. F. G.; Bruzual A., G.

1986-01-01

A self-consistent treatment of the heating by supernovae associated with star formation in a spherically symmetric cooling flow in a cluster core or elliptical galaxy is presented. An initial stellar mass function similar to that in the solar neighborhood is adopted. Inferred star-formation rates, within the cooling region - typically the inner 100 kpc around dominant galaxies at the centers of cooling flows in XD clusters - are reduced by about a factor of 2, relative to rates inferred when the heat input from star formation is ignored. Truncated initial mass functions (IMFs) are also considered, in which massive star formation is suppressed in accordance with previous treatments, and colors are predicted for star formation in cooling flows associated with central dominant elliptical galaxies and with isolated elliptical galaxies surrounded by gaseous coronae. The low inferred cooling-flow rates around isolated elliptical galaxies are found to be insensitive to the upper mass cutoff in the IMF, provided that the upper mass cutoff exceeds 2 M solar mass. Comparison with observed colors favors a cutoff in the IMF above 1 M solar mass in at least two well-studied cluster cooling flows, but a normal IMF cannot be excluded definitively. Models for NGC 1275 support a young (less than about 3 Gyr) cooling flow. As for the isolated elliptical galaxies, the spread in colors is consistent with a normal IMF. A definitive test of the IMF arising via star formation in cooling flows requires either UV spectral data or supernova searches in the cooling-flow-centered galaxies.

18. High-order elliptically polarized harmonic generation in extended molecules with ultrashort intense bichromatic circularly polarized laser pulses

SciTech Connect

Yuan, Kai-Jun; Bandrauk, Andre D.

2010-06-15

Numerical solutions of the time-dependent Schroedinger equation (TDSE) for a two-dimensional H{sub 2}{sup +} molecule excited by a bichromatic ultrashort intense circularly polarized laser pulse with frequencies {omega}{sub 0} and 2{omega}{sub 0} and relative carrier envelope phase {phi} are used to explore the generation of high-order elliptically polarized harmonics as a function of internuclear distance R. Optimal values of {phi} and R for efficient and maximum molecular high-order harmonic generation (MHOHG) are determined from a classical model of collision with neighboring ions and confirmed from the TDSE nonperturbative simulations. Maximum elliptically polarized harmonic energies of I{sub p}+13.5U{sub p} are found, where I{sub p} is the ionization potential and U{sub p}=I{sub 0}/4m{sub e{omega}0}{sup 2} is the ponderomotive energy at intensity I{sub 0} and frequency {omega}{sub 0}. The polarization properties of MHOHG, phase difference {delta}, ellipticity {epsilon}, and orientation angle {phi} are presented as well. The high efficiency of the proposed MHOHG scheme should be useful for production of elliptically polarized attosecond extreme ultraviolet pulses.

19. Magnetic field induced by elliptical instability in a rotating spheroid

Lacaze, L.; Herreman, W.; Le Bars, M.; Le Dizès, S.; Le Gal, P.

2006-10-01

The tidal or the elliptical instability of the rotating fluid flows is generated by the resonant interaction of the inertial waves. In a slightly elliptically deformed rotating sphere, the most unstable linear mode is called the spin-over mode, and is a solid body rotation versus an axis aligned with the maximum strain direction. In the non-viscous case, this instability corresponds to the median moment of the inertial instability of the solid rotating bodies. This analogy is furthermore illustrated by an elliptical top experiment, which shows the expected inviscid heteroclinic behaviour. In geophysics, the elliptical instability may appear in the molten liquid cores of the rotating planets, which are slightly deformed by the tidal gravitational effects of the close bodies. It may then participate in the general outer core dynamics and possibly the geodynamo process. In this context, Kerswell and Malkus (Kerswell, R.R. and Malkus, W.V.R., Tidal instability as the source for Io's magnetic signature. Geophys. Res. Lett., 1998, 25, 603 606) showed that the puzzling magnetic field of the Jovian satellite Io may indeed be induced by the elliptically unstable motions of its liquid core that deflect the Jupiter's magnetic field. Our magnetohydrodynamics (MHD) experiment is a toy-experiment of this geophysical situation and demonstrates for the first time the possibility of an induction of a magnetic field by the flow motions due to the elliptical instability. A full analytical calculation of the magnetic dipole induced by the spin-over is presented. Finally, exponential growths of this induced magnetic field in a slightly deformed rotating sphere filled with galinstan liquid metal are measured for different rotating rates. Their growth rates compare well with the theoretical predictions in the limit of a vanishing Lorentz force.

20. Event-by-event elliptic flow fluctuations from PHOBOS.

SciTech Connect

Alver, B.; Back, B. B.; Baker, M. D.; Ballintijn, M.; Barton, D. S.; Physics; BNL; Inst. of Nuclear Physics; Massachusetts Inst. of Tech.; National Central Univ.; Univ. of Maryland; Univ. of Rochester

2009-04-01

Recently PHOBOS has focused on the study of fluctuations and correlations in particle production in heavy-ion collisions at the highest energies delivered by the Relativistic Heavy Ion Collider (RHIC). In this report, we present results on event-by-event elliptic flow fluctuations in Au + Au collisions at {radical}s{sub NN} = 200 GeV. A data-driven method was used to estimate the dominant contribution from non-flow correlations. Over the broad range of collision centralities, the observed large elliptic flow fluctuations are in agreement with the fluctuations in the initial source eccentricity.

1. Elliptic flow in Au+Au collisions at RHIC.

SciTech Connect

Back, B. B.; Baker, M. D.; Ballintijn, M.; Barton, D. S.; Betts, R. R.; George, N.; Wuosmaa, A.; Physics; Massachusetts Inst. of Tech.; BNL; Univ. of Illinois at Chicago

2005-01-01

Elliptic flow is an interesting probe of the dynamical evolution of the dense system formed in the ultrarelativistic heavy ion collisions at the relativistic heavy ion collider (RHIC). The elliptic flow dependences on transverse momentum, centrality and pseudorapidity were measured using data collected by the PHOBOS detector, which offers a unique opportunity to study the azimuthal anisotropies of charged particles over a wide range of pseudorapidity. These measurements are presented, together with an overview of the analysis methods and a discussion of the results.

2. Plastic Deformation in Profile-Coated Elliptical KB Mirrors

DOE PAGES

Liu, Chian; Conley, R.; Qian, J.; ...

2012-01-01

Profile coating has been successfully applied to produce elliptical Kirkpatrick-Baez (KB) mirrors using both cylindrical and flat Si substrates. Previously, focusing widths of 70 nm with 15-keV monochromatic and 80 nm with white beam were achieved using a flat Si substrate. Now, precision elliptical KB mirrors with sub-nm figure errors are produced with both Au and Pt coatings on flat substrates. Recent studies of bare Si-, Au-, and Pt-coated KB mirrors under prolonged synchrotron X-ray radiation and low-temperature vacuum annealing will be discussed in terms of film stress relaxation and Si plastic deformation.

3. Mean Effects of Turbulence on Elliptic Instability in Fluids

Fabijonas, Bruce R.; Holm, Darryl D.

2003-03-01

Elliptic instability in fluids is discussed in the context of the Lagrangian-averaged Navier-Stokes-alpha (LANS-α) turbulence model. This model preserves the Craik-Criminale (CC) family of solutions consisting of a columnar eddy and a Kelvin wave. The LANS-α model is shown to preserve elliptic instability. However, the model shifts the critical stability angle. This shift increases (decreases) the maximum growth rate for long (short) waves. It also introduces a band of stable CC solutions for short waves.

4. Elliptical flux vortices in YBa2Cu3O7

NASA Technical Reports Server (NTRS)

Hickman, H.; Dekker, A. J.; Chen, T. M.

1991-01-01

The most energetically favorable vortex in YBa2Cu3O7 forms perpendicular to an anisotropic plane. This vortex is elliptical in shape and is distinguished by an effective interchange of London penetration depths from one axis of the ellipse to another. By generalizing qualitatively from the isotropic to the anisotropic case, we suggest that the flux flow resistivity for the vortex that forms perpendicular to an anistropic plane should have a preferred direction. Similar reasoning indicates that the Kosterlitz-Thouless transition temperature for a vortex mediated transition should be lower if the vortex is elliptical in shape.

5. Two-dimensional subsonic compressible flow past elliptic cylinders

NASA Technical Reports Server (NTRS)

Kaplan, Carl

1938-01-01

The method of Poggi is used to calculate, for perfect fluids, the effect of compressibility upon the flow on the surface of an elliptic cylinder at zero angle of attack and with no circulation. The result is expressed in a closed form and represents a rigorous determination of the velocity of the fluid at the surface of the obstacle insofar as the second approximation is concerned. Comparison is made with Hooker's treatment of the same problem according to the method of Janzen and Rayleight and it is found that, for thick elliptic cylinders, the two methods agree very well. The labor of computation is considerably reduced by the present solution.

6. The divine clockwork: Bohr's correspondence principle and Nelson's stochastic mechanics for the atomic elliptic state

SciTech Connect

Durran, Richard; Neate, Andrew; Truman, Aubrey

2008-03-15

We consider the Bohr correspondence limit of the Schroedinger wave function for an atomic elliptic state. We analyze this limit in the context of Nelson's stochastic mechanics, exposing an underlying deterministic dynamical system in which trajectories converge to Keplerian motion on an ellipse. This solves the long standing problem of obtaining Kepler's laws of planetary motion in a quantum mechanical setting. In this quantum mechanical setting, local mild instabilities occur in the Keplerian orbit for eccentricities greater than (1/{radical}(2)) which do not occur classically.

7. Stellar kinematics of X-ray bright massive elliptical galaxies

Lyskova, N.; Churazov, E.; Moiseev, A.; Sil'chenko, O.; Zhuravleva, I.

2014-07-01

We discuss a simple and fast method for estimating masses of early-type galaxies from optical data and compare the results with X-ray derived masses. The optical method relies only on the most basic observables such as the surface brightness I(R) and the line-of-sight velocity dispersion σp(R) profiles and provides an anisotropy-independent estimate of the galaxy circular speed Vc. The mass-anisotropy degeneracy is effectively overcome by evaluating Vc at a characteristic radius Rsweet defined from local properties of observed profiles. The sweet radius Rsweet is expected to lie close to R2, where I(R) ∝ R-2, and not far from the effective radius Reff. We apply the method to a sample of five X-ray bright elliptical galaxies observed with the 6 m telescope BTA-6 in Russia. We then compare the optical Vc estimate with the X-ray derived value, and discuss possible constraints on the non-thermal pressure in the hot gas and configuration of stellar orbits. We find that the average ratio of the optical Vc estimate to the X-ray one is equal to ≈0.98 with 11 per cent scatter, i.e. there is no evidence for the large non-thermal pressure contribution in the gas at ˜Rsweet. From analysis of the Lick indices Hβ, Mgb, Fe5270 and Fe5335, we calculate the mass of the stellar component within the sweet radius. We conclude that a typical dark matter fraction inside Rsweet in the sample galaxies is ˜60 per cent for the Salpeter initial mass function (IMF) and ˜75 per cent for the Kroupa IMF.

8. Optics ellipticity performance of an unobscured off-axis space telescope.

PubMed

Zeng, Fei; Zhang, Xin; Zhang, Jianping; Shi, Guangwei; Wu, Hongbo

2014-10-20

With the development of astronomy, more and more attention is paid to the survey of dark matter. Dark matter cannot be seen directly but can be detected by weak gravitational lensing measurement. Ellipticity is an important parameter used to define the shape of a galaxy. Galaxy ellipticity changes with weak gravitational lensing and nonideal optics. With our design of an unobscured off-axis telescope, we implement the simulation and calculation of optics ellipticity. With an accurate model of optics PSF, the characteristic of ellipticity is modeled and analyzed. It is shown that with good optical design, the full field ellipticity can be quite small. The spatial ellipticity change can be modeled by cubic interpolation with very high accuracy. We also modeled the ellipticity variance with time and analyzed the tolerance. It is shown that the unobscured off-axis telescope has good ellipticity performance and fulfills the requirement of dark matter survey.

9. Three-dimensional elliptic grid generation with fully automatic boundary constraints

Kaul, Upender K.

2010-08-01

A new procedure for generating smooth uniformly clustered three-dimensional structured elliptic grids is presented here which formulates three-dimensional boundary constraints by extending the two-dimensional counterpart presented by the author earlier. This fully automatic procedure obviates the need for manual specification of decay parameters over the six bounding surfaces of a given volume grid. The procedure has been demonstrated here for the Mars Science Laboratory (MSL) geometries such as aeroshell and canopy, as well as the Inflatable Aerodynamic Decelerator (IAD) geometry and a 3D analytically defined geometry. The new procedure also enables generation of single-block grids for such geometries because the automatic boundary constraints permit the decay parameters to evolve as part of the solution to the elliptic grid system of equations. These decay parameters are no longer just constants, as specified in the conventional approach, but functions of generalized coordinate variables over a given bounding surface. Since these decay functions vary over a given boundary, orthogonal grids around any arbitrary simply-connected boundary can be clustered automatically without having to break up the boundaries and the corresponding interior or exterior domains into various blocks for grid generation. The new boundary constraints are not limited to the simply-connected regions only, but can also be formulated around multiply-connected and isolated regions in the interior. The proposed method is superior to other methods of grid generation such as algebraic and hyperbolic techniques in that the grids obtained here are C2 continuous, whereas simple elliptic smoothing of algebraic or hyperbolic grids to enforce C2 continuity destroys the grid clustering near the boundaries. US patent 7231329.

10. Four ways to compute the inverse of the complete elliptic integral of the first kind

Boyd, John P.

2015-11-01

The complete elliptic integral of the first kind arises in many applications. This article furnishes four different ways to compute the inverse of the elliptic integral. One motive for this study is simply that the author needed to compute the inverse integral for an application. Another is to develop a case study comparing different options for solving transcendental equations like those in the author's book (Boyd, 2014). A third motive is to develop analytical approximations, more useful to theorists than mere numbers. A fourth motive is to provide robust "black box" software for computing this function. The first solution strategy is "polynomialization" which replaces the elliptic integral by an exponentially convergent series of Chebyshev polynomials. The transcendental equation becomes a polynomial equation which is easily solved by finding the eigenvalues of the Chebyshev companion matrix. (The numerically ill-conditioned step of converting from the Chebyshev to monomial basis is never necessary). The second approximation is a regular perturbation series, accurate where the modulus is small. The third is a power-and-exponential series that converges over the entire range parameter range, albeit only sub-exponentially in the limit of zero modulus. Lastly, Newton's iteration is promoted from a local iteration to a global method by a Never-Failing Newton's Iteration (NFNI) in the form of the exponential of the ratio of a linear function divided by another linear polynomial. A short Matlab implementation is provided, easily translatable into other languages. The Matlab/Newton code is recommended for numerical purposes. The other methods are presented because (i) all are broadly applicable strategies useful for other rootfinding and inversion problems (ii) series and substitutions are often much more useful to theorists than numerical software and (iii) the Never-Failing Newton's Iteration was discovered only after a great deal of messing about with power series

11. A Galerkin formulation of the MIB method for three dimensional elliptic interface problems

PubMed Central

Xia, Kelin; Wei, Guo-Wei

2014-01-01

We develop a three dimensional (3D) Galerkin formulation of the matched interface and boundary (MIB) method for solving elliptic partial differential equations (PDEs) with discontinuous coefficients, i.e., the elliptic interface problem. The present approach builds up two sets of elements respectively on two extended subdomains which both include the interface. As a result, two sets of elements overlap each other near the interface. Fictitious solutions are defined on the overlapping part of the elements, so that the differentiation operations of the original PDEs can be discretized as if there was no interface. The extra coefficients of polynomial basis functions, which furnish the overlapping elements and solve the fictitious solutions, are determined by interface jump conditions. Consequently, the interface jump conditions are rigorously enforced on the interface. The present method utilizes Cartesian meshes to avoid the mesh generation in conventional finite element methods (FEMs). We implement the proposed MIB Galerkin method with three different elements, namely, rectangular prism element, five-tetrahedron element and six-tetrahedron element, which tile the Cartesian mesh without introducing any new node. The accuracy, stability and robustness of the proposed 3D MIB Galerkin are extensively validated over three types of elliptic interface problems. In the first type, interfaces are analytically defined by level set functions. These interfaces are relatively simple but admit geometric singularities. In the second type, interfaces are defined by protein surfaces, which are truly arbitrarily complex. The last type of interfaces originates from multiprotein complexes, such as molecular motors. Near second order accuracy has been confirmed for all of these problems. To our knowledge, it is the first time for an FEM to show a near second order convergence in solving the Poisson equation with realistic protein surfaces. Additionally, the present work offers the

12. A Galerkin formulation of the MIB method for three dimensional elliptic interface problems.

PubMed

Xia, Kelin; Wei, Guo-Wei

2014-10-01

We develop a three dimensional (3D) Galerkin formulation of the matched interface and boundary (MIB) method for solving elliptic partial differential equations (PDEs) with discontinuous coefficients, i.e., the elliptic interface problem. The present approach builds up two sets of elements respectively on two extended subdomains which both include the interface. As a result, two sets of elements overlap each other near the interface. Fictitious solutions are defined on the overlapping part of the elements, so that the differentiation operations of the original PDEs can be discretized as if there was no interface. The extra coefficients of polynomial basis functions, which furnish the overlapping elements and solve the fictitious solutions, are determined by interface jump conditions. Consequently, the interface jump conditions are rigorously enforced on the interface. The present method utilizes Cartesian meshes to avoid the mesh generation in conventional finite element methods (FEMs). We implement the proposed MIB Galerkin method with three different elements, namely, rectangular prism element, five-tetrahedron element and six-tetrahedron element, which tile the Cartesian mesh without introducing any new node. The accuracy, stability and robustness of the proposed 3D MIB Galerkin are extensively validated over three types of elliptic interface problems. In the first type, interfaces are analytically defined by level set functions. These interfaces are relatively simple but admit geometric singularities. In the second type, interfaces are defined by protein surfaces, which are truly arbitrarily complex. The last type of interfaces originates from multiprotein complexes, such as molecular motors. Near second order accuracy has been confirmed for all of these problems. To our knowledge, it is the first time for an FEM to show a near second order convergence in solving the Poisson equation with realistic protein surfaces. Additionally, the present work offers the

13. On an algorithm for solving parabolic and elliptic equations

D'Ascenzo, N.; Saveliev, V. I.; Chetverushkin, B. N.

2015-08-01

The present-day rapid growth of computer power, in particular, parallel computing systems of ultrahigh performance requires a new approach to the creation of models and solution algorithms for major problems. An algorithm for solving parabolic and elliptic equations is proposed. The capabilities of the method are demonstrated by solving astrophysical problems on high-performance computer systems with massive parallelism.

14. Spectroscopic ellipsometer based on direct measurement of polarization ellipticity

SciTech Connect

Watkins, Lionel R.

2011-06-20

A polarizer-sample-Wollaston prism analyzer ellipsometer is described in which the ellipsometric angles {psi} and {Delta} are determined by direct measurement of the elliptically polarized light reflected from the sample. With the Wollaston prism initially set to transmit p- and s-polarized light, the azimuthal angle P of the polarizer is adjusted until the two beams have equal intensity. This condition yields {psi}={+-}P and ensures that the reflected elliptically polarized light has an azimuthal angle of {+-}45 deg. and maximum ellipticity. Rotating the Wollaston prism through 45 deg. and adjusting the analyzer azimuth until the two beams again have equal intensity yields the ellipticity that allows {Delta} to be determined via a simple linear relationship. The errors produced by nonideal components are analyzed. We show that the polarizer dominates these errors but that for most practical purposes, the error in {psi} is negligible and the error in {Delta} may be corrected exactly. A native oxide layer on a silicon substrate was measured at a single wavelength and multiple angles of incidence and spectroscopically at a single angle of incidence. The best fit film thicknesses obtained were in excellent agreement with those determined using a traditional null ellipsometer.

15. The infrared emission from the elliptical galaxy NGC 1052

NASA Technical Reports Server (NTRS)

Becklin, E. E.; Tokunaga, A. T.; Wynn-Williams, C. G.

1982-01-01

Multi-aperture IR photometry of the elliptical galaxy NGC 1052 shows that its IR excess is confined to a region smaller than 2 arc sec (300 pc) in diameter coincident with the visible nucleus. It is suggested that the emission in the 5-20 micron range arises from dust heated by the nonthermal source seen at other wavelengths.

16. Supersonic flow calculations for a cone with an elliptic flare

NASA Technical Reports Server (NTRS)

Lehrhaupt, H.

1970-01-01

A three-dimensional supersonic flow program is presented for calculating the flow field about a cone at zero angle of attack with an elliptical flare. The program is irrotational, and results remain valid in the region ahead of the first relected characteristic from the points of shock where the shock is no longer axisymmetric.

17. An elliptic singularly perturbed problem with two parameters I

Teofanov, Lj.; Roos, H. G.

2007-09-01

In this paper we consider a singularly perturbed elliptic problem with two small parameters posed on the unit square. Its solution may have exponential, parabolic and corner layers. We give a decomposition of the solution into regular and layer components and derive pointwise bounds on the components and their derivatives. The estimates are obtained by the analysis of appropriate problems on unbounded domains.

18. On Fibonacci Numbers Which Are Elliptic Korselt Numbers

DTIC Science & Technology

2014-11-17

On Fibonacci numbers which are elliptic Korselt numbers Florian Luca School of Mathematics University of the Witwatersrand P. O. Box Wits 2050, South... Witwatersrand . This author thanks this institution for hospitality. 6 References [1] W. R. Alford, A. Granville and C. Pomerance, “There are infinitely

19. Micromagnetic simulation of hysteresis loop of elliptic permalloy nanorings

Mishra, Amaresh Chandra

2016-09-01

Magnetic hysteresis behavior of isotropic permalloy elliptic nanorings of outer semi-major axis length (aout) 100 nm and thickness (t) 20 nm were studied with respect to the variation of two parameters: outer semiminor axis length (bout) and the difference between outer and inner dimensions (r). The outer semiminor axis length (bout) varied from 90 nm to 20 nm which covers from nearly circular nanoring to elliptic nanoring of high aspect ratio. The value of r varied in steps of 10 nm. Micromagnetic simulation of in-plane hysteresis curve of these nanorings revealed that the remanent state of all of these elliptic rings are onion states if the magnetic field is applied along the longer side of the elliptic rings. If the magnetic field is applied along the shorter side, then the remanent states turn out to be vortex state. The hysteresis loss indicated by area of the hysteresis loop was found to be decreasing gradually with the increment of either r or bout. On the other hand, the remanent magnetization increased with increment of r but decreased with the increment of bout. The changes were attributed to three parameters mainly: inner curvature, exchange energy and demagnetization energy. The changes in loop area were discussed in light of variation of these three parameters.

20. Elastohydrodynamics of elliptical contacts for materials of low elastic modulus

NASA Technical Reports Server (NTRS)

Hamrock, B. J.; Dowson, D.

1983-01-01

The influence of the ellipticity parameter k and the dimensionless speed U, load W, and materials G parameters on minimum film thickness for materials of low elastic modulus was investigated. The ellipticity parameter was varied from 1 (a ball-on-plane configuration) to 12 (a configuration approaching a line contact); U and W were each varied by one order of magnitude. Seventeen cases were used to generate the minimum- and central-film-thickness relations. The influence of lubricant starvation on minimum film thickness in starved elliptical, elastohydrodynamic configurations was also investigated for materials of low elastic modulus. Lubricant starvation was studied simply by moving the inlet boundary closer to the center of the conjunction in the numerical solutions. Contour plots of pressure and film thickness in and around the contact were presented for both fully flooded and starved lubrication conditions. It is evident from these figures that the inlet pressure contours become less circular and closer to the edge of the Hertzian contact zone and that the film thickness decreases substantially as the serverity of starvation increases. The results presented reveal the essential features of both fully flooded and starved, elliptical, elastohydrodynamic conjunctions for materials of low elastic modulus.

1. Effect of curvature on domain wall motion in elliptical nanorings

Kaya, Fikriye Idil; Bickel, Jessica; Aidala, Katherine

2014-03-01

Understanding domain wall (DW) motion in ferromagnetic nanostructures is important to realize proposed magnetic data storage and logic devices. We investigate the effect of curvature on DW pinning and motion by studying elliptical rings using micromagnetic simulations. Elliptical rings with constant width have varying curvature, with the lowest curvature at the minor axis, and the greatest curvature at the major axis. DWs can be created at any angular position within the ellipse by the application of an appropriate uniform magnetic field. However, only some of these positions are stable when the field is removed. We study the stability and depinning of the DWs by applying a slowly increasing elliptical magnetic field to determine the magnitude of the field at which the DWs begin to move. By varying the major to minor axis ratio, we examine the effect of curvature on DW pinning. A larger field is required to move DWs in regions of higher curvature (near the major axis) than lower curvature (near the minor axis). Overall, we see that increasing the major to minor axis ratio of elliptical nanorings requires increasing field strength to depin the DWs along the major axis. Work supported in part by NSF DMR-1207924 and NSF CMMI-1025020. Simulations performed at the CNS computational facilities at Harvard University, a member of the NNIN supported by NSF Award No. ECS-0335765.

2. Buckling characteristic of multi-laminated composite elliptical cylindrical shells

Kassegne, Samuel Kinde; Chun, Kyoung-Sik

2015-03-01

Fiber-reinforced composite materials continue to experience increased adoption in aerospace, marine, automobile, and civil structures due to their high specific strength, high stiffness, and light weight. This increased use has been accompanied by applications involving non-traditional configurations such as compression members with elliptical cross-sections. To model such shapes, we develop and report an improved generalized shell element called 4EAS-FS through a combination of enhanced assumed strain and the substitute shear strain fields. A flat shell element has been developed by combining a membrane element with drilling degree-of-freedom and a plate bending element. We use the element developed to determine specifically buckling loads and mode shapes of composite laminates with elliptical cross-section including transverse shear deformations. The combined influence of shell geometry and elliptical cross-sectional parameters, fiber angle, and lay-up on the buckling loads of an elliptical cylinder is examined. It is hoped that the critical buckling loads and mode shapes presented here will serve as a benchmark for future investigations.

3. Deep convection in elliptical and polygonal eyewalls of tropical cyclones

Kuo, Hung-Chi; Cheng, Wei-Yi; Yang, Yi-Ting; Hendricks, Eric A.; Peng, Melinda S.

2016-12-01

In observations, tropical cyclones with cyclonically rotating elliptical eyewalls are often characterized by wave number 2 (WN2) deep convection located at the edge of the major axis. A simple modeling framework is used to understand this phenomenon, where a nondivergent barotropic model (NBM) is employed to represent the elliptical vortex in the free atmosphere, and an asymmetric slab boundary layer (SBL) model is used to simulate the frictional boundary layer (BL) underneath the free atmosphere. The interaction is one way in that the overlying cyclonic flow drives the BL, but the BL pumping does not feed back to the overlying flow. The nonlinear-balanced pressure field from the NBM drives the winds in the SBL model, which then causes BL convergence and pumping near the eyewall. The strong updrafts at the edge of the major axis for the elliptic vortex in the BL are induced by the larger convergent radial wind from the asymmetric distribution of the pressure fields of the free atmosphere with noncircular vortex. The large radial inflow maintains the supergradient wind at the edge of the elliptical vortex. The results emphasize the cyclonic rotation of the WN2 feature of strong updrafts at the top of the BL from the local shock-like BL radial wind structure. Similar radial profiles and strong BL top updrafts occur at the edges of higher-order polygonal eyewalls with the magnitude of the peak updraft decreasing as the wave number structure of the vortex increases.

4. The dynamical fingerprint of core scouring in massive elliptical galaxies

SciTech Connect

Thomas, J.; Saglia, R. P.; Bender, R.; Erwin, P.; Fabricius, M.

2014-02-10

The most massive elliptical galaxies have low-density centers or cores that differ dramatically from the high-density centers of less massive ellipticals and bulges of disk galaxies. These cores have been interpreted as the result of mergers of supermassive black hole binaries, which depopulate galaxy centers by gravitationally slingshotting central stars toward large radii. Such binaries naturally form in mergers of luminous galaxies. Here, we analyze the population of central stellar orbits in 11 massive elliptical galaxies that we observed with the integral field spectrograph SINFONI at the European Southern Observatory Very Large Telescope. Our dynamical analysis is orbit-based and includes the effects of a central black hole, the mass distribution of the stars, and a dark matter halo. We show that the use of integral field kinematics and the inclusion of dark matter is important to conclude on the distribution of stellar orbits in galaxy centers. Six of our galaxies are core galaxies. In these six galaxies, but not in the galaxies without cores, we detect a coherent lack of stars on radial orbits in the core region and a uniform excess of radial orbits outside of it: when scaled by the core radius r{sub b} , the radial profiles of the classical anisotropy parameter β(r) are nearly identical in core galaxies. Moreover, they quantitatively match the predictions of black hole binary simulations, providing the first convincing dynamical evidence for core scouring in the most massive elliptical galaxies.

Li, G. D.; Aspey, R. A.; Kong, M. G.; Gibson, J. R.; Jones, G. R.

1999-01-01

Optical polarization processes in a parallel-sided glass element used in a Faraday rotation current sensor have been considered. In such sensors the path length necessary to produce sufficient rotation of the plane of polarization is produced by a multiplicity of reflections within the glass element. It is shown that such reflections induce ellipticity of polarization and that this affects the current-sensing performance of the sensor. Two reflection cases, corresponding to total internal reflections at a glass-air interface and reflections by aluminium-coated surfaces, are considered. The latter are shown to produce higher optical attenuation but a lower degree of elliptical polarization. The implications of the induced elliptical polarization in relation to chromatically modulated polychromatic light are considered. It is shown that the resolution of the Faraday sensing is improved by minimizing the ellipticity of the polarization with the aluminium-coated reflections. However a greater dynamic range and signal strength may be achievable with the total internal reflection element.

6. Shielding of elliptic guides with direct sight to the moderator

Böni, P.; Grünauer, F.; Schanzer, C.

2010-12-01

With the invention of elliptic guides, the neutron flux at instruments can be increased significantly even without sacrificing resolution. In addition, the phase space homogeneity of the delivered neutrons is improved. Using superpolished metal substrates that are coated with supermirror, it is now possible to install neutron guides close to the moderator thus decreasing the illumination losses of the guide and reducing the background because the entrance window of the elliptic guide can be decreased significantly. We have performed Monte Carlo simulations using the program package MCNP5 to calculate the shielding requirements for an elliptic guide geometry assuming that the initial guide section elements are composed of Al substrates. We show that shielding made from heavy concrete shields the neutron and γ-radiation effectively to levels below 1 μSv/h. It is shown that the elliptic geometry allows to match the phase space of the transported neutrons easily to the needs of the instruments to be installed. In particular it is possible to maintain a compact phase space during the transport of the neutrons because the reflection losses are strongly reduced.

7. Towards a cladistics of double Yangians and elliptic algebras*

Arnaudon, D.; Avan, J.; Frappat, L.; Ragoucy, E.; Rossi, M.

2000-09-01

A self-contained description of algebraic structures, obtained by combinations of various limit procedures applied to vertex and face sl(2) elliptic quantum affine algebras, is given. New double Yangian structures of dynamical type are defined. Connections between these structures are established. A number of them take the form of twist-like actions. These are conjectured to be evaluations of universal twists.

8. Observation of Charge Asymmetry Dependence of Pion Elliptic Flow and the Possible Chiral Magnetic Wave in Heavy-Ion Collisions

Adamczyk, L.; Adkins, J. K.; Agakishiev, G.; Aggarwal, M. M.; Ahammed, Z.; Alekseev, I.; Alford, J.; Aparin, A.; Arkhipkin, D.; Aschenauer, E. C.; Averichev, G. S.; Banerjee, A.; Bellwied, R.; Bhasin, A.; Bhati, A. K.; Bhattarai, P.; Bielcik, J.; Bielcikova, J.; Bland, L. C.; Bordyuzhin, I. G.; Bouchet, J.; Brandin, A. V.; Bunzarov, I.; Burton, T. P.; Butterworth, J.; Caines, H.; Calderón de la Barca Sánchez, M.; Campbell, J. M.; Cebra, D.; Cervantes, M. C.; Chakaberia, I.; Chaloupka, P.; Chang, Z.; Chattopadhyay, S.; Chen, J. H.; Chen, X.; Cheng, J.; Cherney, M.; Christie, W.; Contin, G.; Crawford, H. J.; Das, S.; De Silva, L. C.; Debbe, R. R.; Dedovich, T. G.; Deng, J.; Derevschikov, A. A.; di Ruzza, B.; Didenko, L.; Dilks, C.; Dong, X.; Drachenberg, J. L.; Draper, J. E.; Du, C. M.; Dunkelberger, L. E.; Dunlop, J. C.; Efimov, L. G.; Engelage, J.; Eppley, G.; Esha, R.; Evdokimov, O.; Eyser, O.; Fatemi, R.; Fazio, S.; Federic, P.; Fedorisin, J.; Feng, Z.; Filip, P.; Fisyak, Y.; Flores, C. E.; Fulek, L.; Gagliardi, C. A.; Garand, D.; Geurts, F.; Gibson, A.; Girard, M.; Greiner, L.; Grosnick, D.; Gunarathne, D. S.; Guo, Y.; Gupta, S.; Gupta, A.; Guryn, W.; Hamad, A.; Hamed, A.; Haque, R.; Harris, J. W.; He, L.; Heppelmann, S.; Heppelmann, S.; Hirsch, A.; Hoffmann, G. W.; Hofman, D. J.; Horvat, S.; Huang, H. Z.; Huang, B.; Huang, X.; Huck, P.; Humanic, T. J.; Igo, G.; Jacobs, W. W.; Jang, H.; Jiang, K.; Judd, E. G.; Kabana, S.; Kalinkin, D.; Kang, K.; Kauder, K.; Ke, H. W.; Keane, D.; Kechechyan, A.; Khan, Z. H.; Kikola, D. P.; Kisel, I.; Kisiel, A.; Koetke, D. D.; Kollegger, T.; Kosarzewski, L. K.; Kotchenda, L.; Kraishan, A. F.; Kravtsov, P.; Krueger, K.; Kulakov, I.; Kumar, L.; Kycia, R. A.; Lamont, M. A. C.; Landgraf, J. M.; Landry, K. D.; Lauret, J.; Lebedev, A.; Lednicky, R.; Lee, J. H.; Li, W.; Li, Y.; Li, C.; Li, N.; Li, Z. M.; Li, X.; Li, X.; Lisa, M. A.; Liu, F.; Ljubicic, T.; Llope, W. J.; Lomnitz, M.; Longacre, R. S.; Luo, X.; Ma, L.; Ma, R.; Ma, Y. G.; Ma, G. L.; Magdy, N.; Majka, R.; Manion, A.; Margetis, S.; Markert, C.; Masui, H.; Matis, H. S.; McDonald, D.; Meehan, K.; Minaev, N. G.; Mioduszewski, S.; Mohanty, B.; Mondal, M. M.; Morozov, D. A.; Mustafa, M. K.; Nandi, B. K.; Nasim, Md.; Nayak, T. K.; Nigmatkulov, G.; Nogach, L. V.; Noh, S. Y.; Novak, J.; Nurushev, S. B.; Odyniec, G.; Ogawa, A.; Oh, K.; Okorokov, V.; Olvitt, D. L.; Page, B. S.; Pak, R.; Pan, Y. X.; Pandit, Y.; Panebratsev, Y.; Pawlik, B.; Pei, H.; Perkins, C.; Peterson, A.; Pile, P.; Planinic, M.; Pluta, J.; Poljak, N.; Poniatowska, K.; Porter, J.; Posik, M.; Poskanzer, A. M.; Pruthi, N. K.; Putschke, J.; Qiu, H.; Quintero, A.; Ramachandran, S.; Raniwala, S.; Raniwala, R.; Ray, R. L.; Ritter, H. G.; Roberts, J. B.; Rogachevskiy, O. V.; Romero, J. L.; Roy, A.; Ruan, L.; Rusnak, J.; Rusnakova, O.; Sahoo, N. R.; Sahu, P. K.; Sakrejda, I.; Salur, S.; Sandweiss, J.; Sarkar, A.; Schambach, J.; Scharenberg, R. P.; Schmah, A. M.; Schmidke, W. B.; Schmitz, N.; Seger, J.; Seyboth, P.; Shah, N.; Shahaliev, E.; Shanmuganathan, P. V.; Shao, M.; Sharma, B.; Sharma, M. K.; Shen, W. Q.; Shi, S. S.; Shou, Q. Y.; Sichtermann, E. P.; Sikora, R.; Simko, M.; Skoby, M. J.; Smirnov, D.; Smirnov, N.; Song, L.; Sorensen, P.; Spinka, H. M.; Srivastava, B.; Stanislaus, T. D. S.; Stepanov, M.; Stock, R.; Strikhanov, M.; Stringfellow, B.; Sumbera, M.; Summa, B. J.; Sun, X.; Sun, X. M.; Sun, Z.; Sun, Y.; Surrow, B.; Svirida, D. N.; Szelezniak, M. A.; Tang, Z.; Tang, A. H.; Tarnowsky, T.; Tawfik, A. N.; Thomas, J. H.; Timmins, A. R.; Tlusty, D.; Tokarev, M.; Trentalange, S.; Tribble, R. E.; Tribedy, P.; Tripathy, S. K.; Trzeciak, B. A.; Tsai, O. D.; Ullrich, T.; Underwood, D. G.; Upsal, I.; Van Buren, G.; van Nieuwenhuizen, G.; Vandenbroucke, M.; Varma, R.; Vasiliev, A. N.; Vertesi, R.; Videbaek, F.; Viyogi, Y. P.; Vokal, S.; Voloshin, S. A.; Vossen, A.; Wang, F.; Wang, Y.; Wang, H.; Wang, J. S.; Wang, Y.; Wang, G.; Webb, G.; Webb, J. C.; Wen, L.; Westfall, G. D.; Wieman, H.; Wissink, S. W.; Witt, R.; Wu, Y. F.; Xiao, Z.; Xie, W.; Xin, K.; Xu, Y. F.; Xu, N.; Xu, Z.; Xu, Q. H.; Xu, H.; Yang, Y.; Yang, Y.; Yang, C.; Yang, S.; Yang, Q.; Ye, Z.; Yepes, P.; Yi, L.; Yip, K.; Yoo, I.-K.; Yu, N.; Zbroszczyk, H.; Zha, W.; Zhang, X. P.; Zhang, J. B.; Zhang, J.; Zhang, Z.; Zhang, S.; Zhang, Y.; Zhang, J. L.; Zhao, F.; Zhao, J.; Zhong, C.; Zhou, L.; Zhu, X.; Zoulkarneeva, Y.; Zyzak, M.; STAR Collaboration

2015-06-01

We present measurements of π- and π+ elliptic flow, v2, at midrapidity in Au +Au collisions at √{sNN }=200 , 62.4, 39, 27, 19.6, 11.5, and 7.7 GeV, as a function of event-by-event charge asymmetry, Ach, based on data from the STAR experiment at RHIC. We find that π- (π+) elliptic flow linearly increases (decreases) with charge asymmetry for most centrality bins at √{sNN }=27 GeV and higher. At √{sNN }=200 GeV , the slope of the difference of v2 between π- and π+ as a function of Ach exhibits a centrality dependence, which is qualitatively similar to calculations that incorporate a chiral magnetic wave effect. Similar centrality dependence is also observed at lower energies.

9. Fully Automated Single-Zone Elliptic Grid Generation for Mars Science Laboratory (MSL) Aeroshell and Canopy Geometries

NASA Technical Reports Server (NTRS)

kaul, Upender K.

2008-01-01

A procedure for generating smooth uniformly clustered single-zone grids using enhanced elliptic grid generation has been demonstrated here for the Mars Science Laboratory (MSL) geometries such as aeroshell and canopy. The procedure obviates the need for generating multizone grids for such geometries, as reported in the literature. This has been possible because the enhanced elliptic grid generator automatically generates clustered grids without manual prescription of decay parameters needed with the conventional approach. In fact, these decay parameters are calculated as decay functions as part of the solution, and they are not constant over a given boundary. Since these decay functions vary over a given boundary, orthogonal grids near any arbitrary boundary can be clustered automatically without having to break up the boundaries and the corresponding interior domains into various zones for grid generation.

10. Observation of Charge Asymmetry Dependence of Pion Elliptic Flow and the Possible Chiral Magnetic Wave in Heavy-Ion Collisions.

PubMed

Adamczyk, L; Adkins, J K; Agakishiev, G; Aggarwal, M M; Ahammed, Z; Alekseev, I; Alford, J; Aparin, A; Arkhipkin, D; Aschenauer, E C; Averichev, G S; Banerjee, A; Bellwied, R; Bhasin, A; Bhati, A K; Bhattarai, P; Bielcik, J; Bielcikova, J; Bland, L C; Bordyuzhin, I G; Bouchet, J; Brandin, A V; Bunzarov, I; Burton, T P; Butterworth, J; Caines, H; Calderón de la Barca Sánchez, M; Campbell, J M; Cebra, D; Cervantes, M C; Chakaberia, I; Chaloupka, P; Chang, Z; Chattopadhyay, S; Chen, J H; Chen, X; Cheng, J; Cherney, M; Christie, W; Contin, G; Crawford, H J; Das, S; De Silva, L C; Debbe, R R; Dedovich, T G; Deng, J; Derevschikov, A A; di Ruzza, B; Didenko, L; Dilks, C; Dong, X; Drachenberg, J L; Draper, J E; Du, C M; Dunkelberger, L E; Dunlop, J C; Efimov, L G; Engelage, J; Eppley, G; Esha, R; Evdokimov, O; Eyser, O; Fatemi, R; Fazio, S; Federic, P; Fedorisin, J; Feng, Z; Filip, P; Fisyak, Y; Flores, C E; Fulek, L; Gagliardi, C A; Garand, D; Geurts, F; Gibson, A; Girard, M; Greiner, L; Grosnick, D; Gunarathne, D S; Guo, Y; Gupta, S; Gupta, A; Guryn, W; Hamad, A; Hamed, A; Haque, R; Harris, J W; He, L; Heppelmann, S; Heppelmann, S; Hirsch, A; Hoffmann, G W; Hofman, D J; Horvat, S; Huang, H Z; Huang, B; Huang, X; Huck, P; Humanic, T J; Igo, G; Jacobs, W W; Jang, H; Jiang, K; Judd, E G; Kabana, S; Kalinkin, D; Kang, K; Kauder, K; Ke, H W; Keane, D; Kechechyan, A; Khan, Z H; Kikola, D P; Kisel, I; Kisiel, A; Koetke, D D; Kollegger, T; Kosarzewski, L K; Kotchenda, L; Kraishan, A F; Kravtsov, P; Krueger, K; Kulakov, I; Kumar, L; Kycia, R A; Lamont, M A C; Landgraf, J M; Landry, K D; Lauret, J; Lebedev, A; Lednicky, R; Lee, J H; Li, W; Li, Y; Li, C; Li, N; Li, Z M; Li, X; Li, X; Lisa, M A; Liu, F; Ljubicic, T; Llope, W J; Lomnitz, M; Longacre, R S; Luo, X; Ma, L; Ma, R; Ma, Y G; Ma, G L; Magdy, N; Majka, R; Manion, A; Margetis, S; Markert, C; Masui, H; Matis, H S; McDonald, D; Meehan, K; Minaev, N G; Mioduszewski, S; Mohanty, B; Mondal, M M; Morozov, D A; Mustafa, M K; Nandi, B K; Nasim, Md; Nayak, T K; Nigmatkulov, G; Nogach, L V; Noh, S Y; Novak, J; Nurushev, S B; Odyniec, G; Ogawa, A; Oh, K; Okorokov, V; Olvitt, D L; Page, B S; Pak, R; Pan, Y X; Pandit, Y; Panebratsev, Y; Pawlik, B; Pei, H; Perkins, C; Peterson, A; Pile, P; Planinic, M; Pluta, J; Poljak, N; Poniatowska, K; Porter, J; Posik, M; Poskanzer, A M; Pruthi, N K; Putschke, J; Qiu, H; Quintero, A; Ramachandran, S; Raniwala, S; Raniwala, R; Ray, R L; Ritter, H G; Roberts, J B; Rogachevskiy, O V; Romero, J L; Roy, A; Ruan, L; Rusnak, J; Rusnakova, O; Sahoo, N R; Sahu, P K; Sakrejda, I; Salur, S; Sandweiss, J; Sarkar, A; Schambach, J; Scharenberg, R P; Schmah, A M; Schmidke, W B; Schmitz, N; Seger, J; Seyboth, P; Shah, N; Shahaliev, E; Shanmuganathan, P V; Shao, M; Sharma, B; Sharma, M K; Shen, W Q; Shi, S S; Shou, Q Y; Sichtermann, E P; Sikora, R; Simko, M; Skoby, M J; Smirnov, D; Smirnov, N; Song, L; Sorensen, P; Spinka, H M; Srivastava, B; Stanislaus, T D S; Stepanov, M; Stock, R; Strikhanov, M; Stringfellow, B; Sumbera, M; Summa, B J; Sun, X; Sun, X M; Sun, Z; Sun, Y; Surrow, B; Svirida, D N; Szelezniak, M A; Tang, Z; Tang, A H; Tarnowsky, T; Tawfik, A N; Thomas, J H; Timmins, A R; Tlusty, D; Tokarev, M; Trentalange, S; Tribble, R E; Tribedy, P; Tripathy, S K; Trzeciak, B A; Tsai, O D; Ullrich, T; Underwood, D G; Upsal, I; Van Buren, G; van Nieuwenhuizen, G; Vandenbroucke, M; Varma, R; Vasiliev, A N; Vertesi, R; Videbaek, F; Viyogi, Y P; Vokal, S; Voloshin, S A; Vossen, A; Wang, F; Wang, Y; Wang, H; Wang, J S; Wang, Y; Wang, G; Webb, G; Webb, J C; Wen, L; Westfall, G D; Wieman, H; Wissink, S W; Witt, R; Wu, Y F; Xiao, Z; Xie, W; Xin, K; Xu, Y F; Xu, N; Xu, Z; Xu, Q H; Xu, H; Yang, Y; Yang, Y; Yang, C; Yang, S; Yang, Q; Ye, Z; Yepes, P; Yi, L; Yip, K; Yoo, I-K; Yu, N; Zbroszczyk, H; Zha, W; Zhang, X P; Zhang, J B; Zhang, J; Zhang, Z; Zhang, S; Zhang, Y; Zhang, J L; Zhao, F; Zhao, J; Zhong, C; Zhou, L; Zhu, X; Zoulkarneeva, Y; Zyzak, M

2015-06-26

We present measurements of π(-) and π(+) elliptic flow, v(2), at midrapidity in Au+Au collisions at √[s(NN)]=200, 62.4, 39, 27, 19.6, 11.5, and 7.7 GeV, as a function of event-by-event charge asymmetry, A(ch), based on data from the STAR experiment at RHIC. We find that π(-) (π(+)) elliptic flow linearly increases (decreases) with charge asymmetry for most centrality bins at √[s(NN)]=27  GeV and higher. At √[s(NN)]=200  GeV, the slope of the difference of v(2) between π(-) and π(+) as a function of A(ch) exhibits a centrality dependence, which is qualitatively similar to calculations that incorporate a chiral magnetic wave effect. Similar centrality dependence is also observed at lower energies.

11. Elliptic Capture Orbits for Missions to the Near Planets

NASA Technical Reports Server (NTRS)

Casal, Federico G.; Swenson, Byron L.; Mascy, Alfred C.

1968-01-01

Elliptic capture orbits around Mars and Venus have often been considered as means for reducing arrival and departure energy requirements for two-way missions. It had also generally been feared that the energy savings obtained by capturing a spacecraft into a highly elliptical orbit (rather than a near circular orbit of the same periapsis) would largely be offset by the penalties incurred in aligning the semi-major axis of the ellipse in such a way as to obtain the proper orientation of the departure hyperbola. This paper, presents the results of an analysis which takes into consideration the penalties arising from the requirement to match the orientation of the elliptical orbit with the asymptote of the departure hyperbola. The scientific aspects of elliptical orbits around the target planet are discussed, and it is shown that such orbits exhibit characteristics which may be considered advantageous or disadvantageous depending on the purpose of the mission. Alignment of ' the semi-major axis of the capture, ellipse relative to the, asymptote of the escape hyperbola was found not to be a critical requirement since the kinetic energy remains high over a substantial portion of the elliptical capture orbit. This 'means that the escape stage can operate efficiently even when ignited at some angle from the true periapsis point. Considerable freedom in choosing this angle is available at little propulsive cost. The resulting latitude in the choice of angles between arrival and escape asymptotes makes it possible to consider a wide variety of interplanetary transfers and planetary staytimes without the need for separate propulsive maneuvers to realign the capture ellipse before departure., Special consideration has also been g1ven to plane change maneuvers around the planet. These may be required for reasons of orbit dynamics or scientific experimentation and are not uniquely tied to elliptical captures. The sensitivity of the mass of the excursion module to the

12. Applications of high-resolution spatial discretization scheme and Jacobian-free Newton–Krylov method in two-phase flow problems

SciTech Connect

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2015-09-01

The majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many nuclear thermal–hydraulics applications, it is desirable to use higher-order numerical schemes to reduce numerical errors. High-resolution spatial discretization schemes provide high order spatial accuracy in smooth regions and capture sharp spatial discontinuity without nonphysical spatial oscillations. In this work, we adapted an existing high-resolution spatial discretization scheme on staggered grids in two-phase flow applications. Fully implicit time integration schemes were also implemented to reduce numerical errors from operator-splitting types of time integration schemes. The resulting nonlinear system has been successfully solved using the Jacobian-free Newton–Krylov (JFNK) method. The high-resolution spatial discretization and high-order fully implicit time integration numerical schemes were tested and numerically verified for several two-phase test problems, including a two-phase advection problem, a two-phase advection with phase appearance/disappearance problem, and the water faucet problem. Numerical results clearly demonstrated the advantages of using such high-resolution spatial and high-order temporal numerical schemes to significantly reduce numerical diffusion and therefore improve accuracy. Our study also demonstrated that the JFNK method is stable and robust in solving two-phase flow problems, even when phase appearance/disappearance exists.

13. Application of Jacobian-free Newton–Krylov method in implicitly solving two-fluid six-equation two-phase flow problems: Implementation, validation and benchmark

SciTech Connect

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-03-09

This work represents a first-of-its-kind successful application to employ advanced numerical methods in solving realistic two-phase flow problems with two-fluid six-equation two-phase flow model. These advanced numerical methods include high-resolution spatial discretization scheme with staggered grids (high-order) fully implicit time integration schemes, and Jacobian-free Newton–Krylov (JFNK) method as the nonlinear solver. The computer code developed in this work has been extensively validated with existing experimental flow boiling data in vertical pipes and rod bundles, which cover wide ranges of experimental conditions, such as pressure, inlet mass flux, wall heat flux and exit void fraction. Additional code-to-code benchmark with the RELAP5-3D code further verifies the correct code implementation. The combined methods employed in this work exhibit strong robustness in solving two-phase flow problems even when phase appearance (boiling) and realistic discrete flow regimes are considered. Transitional flow regimes used in existing system analysis codes, normally introduced to overcome numerical difficulty, were completely removed in this work. As a result, this in turn provides the possibility to utilize more sophisticated flow regime maps in the future to further improve simulation accuracy.

14. Application of Jacobian-free Newton–Krylov method in implicitly solving two-fluid six-equation two-phase flow problems: Implementation, validation and benchmark

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-03-09

This work represents a first-of-its-kind successful application to employ advanced numerical methods in solving realistic two-phase flow problems with two-fluid six-equation two-phase flow model. These advanced numerical methods include high-resolution spatial discretization scheme with staggered grids (high-order) fully implicit time integration schemes, and Jacobian-free Newton–Krylov (JFNK) method as the nonlinear solver. The computer code developed in this work has been extensively validated with existing experimental flow boiling data in vertical pipes and rod bundles, which cover wide ranges of experimental conditions, such as pressure, inlet mass flux, wall heat flux and exit void fraction. Additional code-to-code benchmark with the RELAP5-3Dmore » code further verifies the correct code implementation. The combined methods employed in this work exhibit strong robustness in solving two-phase flow problems even when phase appearance (boiling) and realistic discrete flow regimes are considered. Transitional flow regimes used in existing system analysis codes, normally introduced to overcome numerical difficulty, were completely removed in this work. As a result, this in turn provides the possibility to utilize more sophisticated flow regime maps in the future to further improve simulation accuracy.« less

15. Implementation of the Jacobian-free Newton-Krylov method for solving the for solving the first-order ice sheet momentum balance

SciTech Connect

Salinger, Andy; Evans, Katherine J; Lemieux, Jean-Francois; Holland, David; Payne, Tony; Price, Stephen; Knoll, Dana

2011-01-01

We have implemented the Jacobian-free Newton-Krylov (JFNK) method for solving the rst-order ice sheet momentum equation in order to improve the numerical performance of the Community Ice Sheet Model (CISM), the land ice component of the Community Earth System Model (CESM). Our JFNK implementation is based on signicant re-use of existing code. For example, our physics-based preconditioner uses the original Picard linear solver in CISM. For several test cases spanning a range of geometries and boundary conditions, our JFNK implementation is 1.84-3.62 times more efficient than the standard Picard solver in CISM. Importantly, this computational gain of JFNK over the Picard solver increases when rening the grid. Global convergence of the JFNK solver has been signicantly improved by rescaling the equation for the basal boundary condition and through the use of an inexact Newton method. While a diverse set of test cases show that our JFNK implementation is usually robust, for some problems it may fail to converge with increasing resolution (as does the Picard solver). Globalization through parameter continuation did not remedy this problem and future work to improve robustness will explore a combination of Picard and JFNK and the use of homotopy methods.

16. Experimental study on elliptical vibration cutting for optical microstructures

Li, Guo; Che, Lin; Wang, Bo; Ding, Fei; Zhang, Chen Feng

2014-08-01

In the processing technology of optical microstructure, mechanical processing with high efficiency and quality is still dominating. However, with microstructure surface quality higher and higher, the precision and ultra precision cutting technology has been difficult to meet the needs of reality, and it still remains a big issue in production efficiency and cost. In this case, the elliptical vibration cutting method is created. At present, research on the effect of elliptical vibration cutting on surface quality of microstructures with special optical properties such as V-groove, micro pyramid and sinusoidal grid surface is rarely seen. This paper focuses on the elliptical vibration cutting process of arc groove and V-groove, aiming at finding the discipline of various parameters (frequency, amplitude, feed rate) and analyzing the surface quality through experiments. Firstly, the principle of elliptical vibration cutting is introduced, the cutting mechanism and the theoretical error are analyzed, and a vibration cutting system is designed for precision machining. Because the surface quality and burr play have a huge impact on optical microstructure, effects of the vibration frequency (0-2kHz), amplitude (0.5-2.5μm) as well as feed rate (6-30mm/min) on surface quality and burr suppression are analyzed. The experimental results show that compared to normal cutting, elliptical vibration cutting has obvious advantages. With the increases of the frequency and amplitude, the surface quality improves significantly, the surface roughness is changed from 61.5nm to 25.3nm, and burr has been suppressed to some extent.

17. MIB method for elliptic equations with multi-material interfaces.

PubMed

Xia, Kelin; Zhan, Meng; Wei, Guo-Wei

2011-06-01

Elliptic partial differential equations (PDEs) are widely used to model real-world problems. Due to the heterogeneous characteristics of many naturally occurring materials and man-made structures, devices, and equipments, one frequently needs to solve elliptic PDEs with discontinuous coefficients and singular sources. The development of high-order elliptic interface schemes has been an active research field for decades. However, challenges remain in the construction of high-order schemes and particularly, for nonsmooth interfaces, i.e., interfaces with geometric singularities. The challenge of geometric singularities is amplified when they are originated from two or more material interfaces joining together or crossing each other. High-order methods for elliptic equations with multi-material interfaces have not been reported in the literature to our knowledge. The present work develops matched interface and boundary (MIB) method based schemes for solving two-dimensional (2D) elliptic PDEs with geometric singularities of multi-material interfaces. A number of new MIB schemes are constructed to account for all possible topological variations due to two-material interfaces. The geometric singularities of three-material interfaces are significantly more difficult to handle. Three new MIB schemes are designed to handle a variety of geometric situations and topological variations, although not all of them. The performance of the proposed new MIB schemes is validated by numerical experiments with a wide range of coefficient contrasts, geometric singularities, and solution types. Extensive numerical studies confirm the designed second order accuracy of the MIB method for multi-material interfaces, including a case where the derivative of the solution diverges.

18. From Flat Substrate to Elliptical KB Mirror by Profile Coating

SciTech Connect

Liu Chian; Conley, R.; Assoufid, L.; Cai, Z.; Qian, J.; Macrander, A.T.

2004-05-12

For microfocusing x-ray mirrors, an elliptical shape is essential for aberration-free optics. However, it is difficult to polish elliptical mirrors to x-ray-quality smoothness. Profile coatings have been applied on both cylindrical and flat Si substrates to make the desired elliptical shape. In a profile-coating process, the sputter source power is kept constant, while the substrate is passed over a contoured mask at a constant speed to obtain a desired profile along the direction perpendicular to the substrate-moving direction. The shape of the contour was derived from a desired profile and the thickness distribution of the coating material at the substrate level. The thickness distribution was measured on films coated on Si wafers using a spectroscopic ellipsometer with computer-controlled X-Y translation stages. The mirror coating profile is determined from the difference between the ideal surface figure of a focusing ellipse and the surface figure obtained from a long trace profiler measurement on the substrate. The number of passes and the moving speed of the substrate are determined according to the required thickness and the growth-rate calibration of a test run. A KB mirror pair was made using Au as a coating material and cylindrically polished mirrors as substrates. Synchrotron x-ray results using this KB mirror pair showed a focused spot size of 0.4 x 0.4 {mu}m2. This technique has also been applied for making elliptical KB mirrors from flat Si substrates. The challenges and solutions associated with elliptical profile coating on flat substrates will be discussed.

19. From Flat Substrate to Elliptical KB Mirror by Profile Coating

Liu, Chian; Conley, R.; Assoufid, L.; Cai, Z.; Qian, J.; Macrander, A. T.

2004-05-01

For microfocusing x-ray mirrors, an elliptical shape is essential for aberration-free optics. However, it is difficult to polish elliptical mirrors to x-ray-quality smoothness. Profile coatings have been applied on both cylindrical and flat Si substrates to make the desired elliptical shape. In a profile-coating process, the sputter source power is kept constant, while the substrate is passed over a contoured mask at a constant speed to obtain a desired profile along the direction perpendicular to the substrate-moving direction. The shape of the contour was derived from a desired profile and the thickness distribution of the coating material at the substrate level. The thickness distribution was measured on films coated on Si wafers using a spectroscopic ellipsometer with computer-controlled X-Y translation stages. The mirror coating profile is determined from the difference between the ideal surface figure of a focusing ellipse and the surface figure obtained from a long trace profiler measurement on the substrate. The number of passes and the moving speed of the substrate are determined according to the required thickness and the growth-rate calibration of a test run. A KB mirror pair was made using Au as a coating material and cylindrically polished mirrors as substrates. Synchrotron x-ray results using this KB mirror pair showed a focused spot size of 0.4 × 0.4 μm2. This technique has also been applied for making elliptical KB mirrors from flat Si substrates. The challenges and solutions associated with elliptical profile coating on flat substrates will be discussed.

20. MIB method for elliptic equations with multi-material interfaces

PubMed Central

Xia, Kelin; Zhan, Meng; Wei, Guo-Wei

2011-01-01

Elliptic partial differential equations (PDEs) are widely used to model real-world problems. Due to the heterogeneous characteristics of many naturally occurring materials and man-made structures, devices, and equipments, one frequently needs to solve elliptic PDEs with discontinuous coefficients and singular sources. The development of high-order elliptic interface schemes has been an active research field for decades. However, challenges remain in the construction of high-order schemes and particularly, for nonsmooth interfaces, i.e., interfaces with geometric singularities. The challenge of geometric singularities is amplified when they are originated from two or more material interfaces joining together or crossing each other. High-order methods for elliptic equations with multi-material interfaces have not been reported in the literature to our knowledge. The present work develops matched interface and boundary (MIB) method based schemes for solving two-dimensional (2D) elliptic PDEs with geometric singularities of multi-material interfaces. A number of new MIB schemes are constructed to account for all possible topological variations due to two-material interfaces. The geometric singularities of three-material interfaces are significantly more difficult to handle. Three new MIB schemes are designed to handle a variety of geometric situations and topological variations, although not all of them. The performance of the proposed new MIB schemes is validated by numerical experiments with a wide range of coefficient contrasts, geometric singularities, and solution types. Extensive numerical studies confirm the designed second order accuracy of the MIB method for multi-material interfaces, including a case where the derivative of the solution diverges. PMID:21691433

1. Maximal Sobolev regularity for solutions of elliptic equations in infinite dimensional Banach spaces endowed with a weighted Gaussian measure

Cappa, G.; Ferrari, S.

2016-12-01

Let X be a separable Banach space endowed with a non-degenerate centered Gaussian measure μ. The associated Cameron-Martin space is denoted by H. Let ν =e-U μ, where U : X → R is a sufficiently regular convex and continuous function. In this paper we are interested in the W 2 , 2 regularity of the weak solutions of elliptic equations of the type

2. The Numerical Calculation of Flow Past Conical Bodies Supporting Elliptic Conical Shock Waves at Finite Angles of Incidence

NASA Technical Reports Server (NTRS)

Briggs, Benjamin R.

1960-01-01

The inverse method, with the shock wave prescribed to be an elliptic cone at a finite angle of incidence, is applied to calculate numerically the supersonic perfect-gas flow past conical bodies not having axial symmetry. Two formulations of the problem are employed, one using a pair of stream functions and the other involving entropy and components of velocity. A number of solutions are presented, illustrating the numerical methods employed, and showing the effects of moderate variation of the initial parameters.

3. Optimization of an inclined elliptic impinging jet with cross flow for enhancing heat transfer

Heo, Man-Woong; Lee, Ki-Don; Kim, Kwang-Yong

2011-06-01

This work presents a parametric study and optimization of a single impinging jet with cross flow to enhance heat transfer with two design variables. The fluid flow and heat transfer have been analyzed using three-dimensional compressible Reynolds-averaged Navier-Stokes equations with a uniform heat flux condition being applied to the impingement plate. The aspect ratio of the elliptic jet hole and the angle of inclination of the jet nozzle are chosen as the two design variables, and the area-averaged Nusselt number on a limited target plate is set as the objective function. The effects of the design variables on the heat transfer performance have been evaluated, and the objective function has been found to be more sensitive to the angle of inclination of the jet nozzle than to the aspect ratio of the elliptic jet hole. The optimization has been performed by using the radial basis neural network model. Through the optimization, the area-averaged Nusselt number increased by 7.89% compared to that under the reference geometry.

4. A new perspective on the integrability of Inozemtsev’s elliptic spin chain

SciTech Connect

Finkel, Federico; González-López, Artemio

2014-12-15

The aim of this paper is studying from an alternative point of view the integrability of the spin chain with long-range elliptic interactions introduced by Inozemtsev. Our analysis relies on some well-established conjectures characterizing the chaotic vs. integrable behavior of a quantum system, formulated in terms of statistical properties of its spectrum. More precisely, we study the distribution of consecutive levels of the (unfolded) spectrum, the power spectrum of the spectral fluctuations, the average degeneracy, and the equivalence to a classical vertex model. Our results are consistent with the general consensus that this model is integrable, and that it is closer in this respect to the Heisenberg chain than to its trigonometric limit (the Haldane–Shastry chain). On the other hand, we present some numerical and analytical evidence showing that the level density of Inozemtsev’s chain is asymptotically Gaussian as the number of spins tends to infinity, as is the case with the Haldane–Shastry chain. We are also able to compute analytically the mean and the standard deviation of the spectrum, showing that their asymptotic behavior coincides with that of the Haldane–Shastry chain. - Highlights: • Construction of Inozemtsev’s elliptic spin chain using Polychronakos’s freezing trick. • Numerical evidence of the Gaussian character of the level density. • Exact computation and asymptotics of the mean and standard deviation of the spectrum. • Evidence of the chain’s integrability from key statistical properties of its spectrum. • Exact evaluation of finite sums of powers of Weierstrass’s elliptic function.

5. Imprints of the molecular-orbital geometry on the high-harmonic ellipticity.

PubMed

Qin, Meiyan; Zhu, Xiaosong; Liu, Kunlong; Zhang, Qingbin; Lu, Peixiang

2012-08-27

The influence of the orbital symmetry on the ellipticity of the high-order harmonics is investigated. It is found that the ellipticity maps have distinct shapes for the molecular orbitals with different symmetry. Our analysis shows that the feature of the harmonic ellipticity map is essentially determined by the nodal structure of the nonsymmetric orbital. The results indicate that the molecular-orbital geometry is imprinted on the ellipticity of the high-order harmonics, which invites the use of ellipticity measurements as a probe of the orbital structure for polar molecules.

6. Numerical solutions of nonlinear STIFF initial value problems by perturbed functional iterations

NASA Technical Reports Server (NTRS)

Dey, S. K.

1982-01-01

Numerical solution of nonlinear stiff initial value problems by a perturbed functional iterative scheme is discussed. The algorithm does not fully linearize the system and requires only the diagonal terms of the Jacobian. Some examples related to chemical kinetics are presented.

7. Parabolic versus elliptic focusing - Optimization of the focusing design of a cold triple-axis neutron spectrometer by Monte-Carlo simulations

Komarek, A. C.; Böni, P.; Braden, M.

2011-08-01

We present Monte-Carlo simulations for the focusing design of a novel cold-neutron triple-axis spectrometer to be installed at the end position of the cold guide NL-1 of the research reactor FRM-II in Munich, Germany. Our simulations are of general relevance for the design of triple-axis spectrometers at end positions of neutron guides. Using the McStas program code we performed ray trajectories to compare parabolic and elliptic focusing concepts. In addition the design of the monochromator was optimized concerning crystal size and mosaic spread. The parabolic focusing concept is superior to the elliptic alternative in view of the neutron intensity distribution as a function of energy and divergence. In particular, the elliptical configuration leads to an inhomogeneous divergence distribution.

8. Ultrawideband doublet pulse generation based on nonlinear polarization rotation of an elliptically polarized beam and its distribution over a fiber/wireless link.

PubMed

Chang, You Min; Lee, Junsu; Lee, Ju Han

2010-09-13

Proposed herein is an alternative photonic scheme for the generation of a doublet UWB pulse, which is based on the nonlinear polarization rotation of an elliptically polarized probe beam. The proposed scheme is a modified optical-fiber Kerr shutter that uses an elliptically polarized probe beam together with a linearly polarized control beam. Through theoretical analysis, it was shown that the optical-fiber-based Kerr shutter is capable of producing an ideal transfer function for the successful conversion of input Gaussian pulses into doublet pulses under special elliptical polarization states of the probe beam. An experimental verification was subsequently carried out to verify the working principle. Finally, the system performance of the generated UWB doublet pulses was assessed by propagating them over a 25-km-long standard single-mode fiber link, followed by wireless transmission. Error-free transmission was successfully achieved.

9. Vibration and Noise Characteristics of Elliptical Gears due to Non-Uniform Rotation

Liu, Xing; Nagamura, Kazuteru; Ikejo, Kiyotaka

Elliptical gear is a typical non-circular gear, which transmits a variable-ratio rotation and power simultaneously. Due to the non-uniform rotation, the vibration and noise of elliptical gears demonstrate particular characteristics which should be paid attention to in practical application. In this paper, two elliptical gears, which are a single elliptical gear and a double elliptical gear, have been investigated to analyze the vibration and noise characteristics of elliptical gears. The corresponding circular gears for comparison are also investigated. General factors including the torque, the rotation speed, the gear vibration acceleration and the gear noise of the four test gears are measured by running test. The root mean square of the Circumferential Vibration Acceleration (CVA) and the sound pressure level of the noise of elliptical gears are obtained from the measured results and compared with those of circular gears to clarify the vibration and noise characteristics of elliptical gears. Furthermore, the frequency analysis of the CVA of elliptical gears is conducted by Fast Fourier Transform Algorithm (FFT) and compared with that of circular gears. The main vibration component of elliptical gear is uncovered according to the obtained frequency spectra. In addition, the Critical Rotation Speeds of Tooth Separation (CRSTS) of elliptical gear is obtained and its relation with load torque is unveiled.

10. Random source generating far field with elliptical flat-topped beam profile

Zhang, Yongtao; Cai, Yangjian

2014-07-01

Circular and rectangular multi-Gaussian Schell-model (MGSM) sources which generate far fields with circular and rectangular flat-topped beam profiles were introduced just recently (Sahin and Korotkova 2012 Opt. Lett. 37 2970; Korotkova 2014 Opt. Lett. 39 64). In this paper, a random source named an elliptical MGSM source is introduced. An analytical expression for the propagation factor of an elliptical MGSM beam is derived. Furthermore, an analytical propagation formula for an elliptical MGSM beam passing through a stigmatic ABCD optical system is derived, and its propagation properties in free space are studied. It is interesting to find that an elliptical MGSM source generates a far field with an elliptical flat-topped beam profile, being qualitatively different from that of circular and rectangular MGSM sources. The ellipticity and the flatness of the elliptical flat-topped beam profile in the far field are determined by the initial coherence widths and the beam index, respectively.

11. Controlling the magnetic susceptibility in an artificial elliptical quantum ring by magnetic flux and external Rashba effect

SciTech Connect

2015-03-21

Magnetic susceptibility is investigated in a man-made elliptical quantum ring in the presence of Rashba spin-orbit interactions and the magnetic flux. It is shown that magnetic susceptibility as a function of magnetic flux changes between negative and positive signs periodically. The periodicity of the Aharonov-Bohm oscillations depends on the geometry of the region where magnetic field is applied, the eccentricity, and number of sites in each chain ring (the elliptical ring is composed of chain rings). The magnetic susceptibility sign can be reversed by tuning the Rashba spin-orbit strength as well. Both the magnetic susceptibility strength and sign can be controlled via external spin-orbit interactions, which can be exploited in spintronics and nanoelectronics.

12. The Observability of Abundance Ratio Effects in Elliptical Galaxies

Serven, J. L.; Worthey, G.; Briley, M. M.

2004-12-01

Using synthetic spectra we construct a simple model of an elliptical galaxy, with a velocity dispersion σ = 200 km s-1. Absorption feature indices are defined for C, N, O, Na, Mg, Al, Si, S, K, Ca, Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Sr, Ba, and Eu as a first step in determining the abundances of these elements in stellar populations, such as elliptical galaxies, for which integrated light spectra are available. Then using these indices and assuming a photon error such that S/N = 100 around 5000 Å , the feasibility of measuring individual elements in real galaxies is assessed. Of the elements studied only S, K, Cu, Zn, and Eu appear to be difficult to determine; the rest appear to be at least feasible.

13. Decoupling antennas in printed technology using elliptical metasurface cloaks

SciTech Connect

Bernety, Hossein M. E-mail: yakovlev@olemiss.edu; Yakovlev, Alexander B. E-mail: yakovlev@olemiss.edu

2016-01-07

In this paper, we extend the idea of reducing the electromagnetic interactions between transmitting radiators to the case of widely used planar antennas in printed technology based on the concept of mantle cloaking. Here, we show that how lightweight elliptical metasurface cloaks can be engineered to restore the intrinsic properties of printed antennas with strip inclusions. In order to present the novel approach, we consider two microstrip-fed monopole antennas resonating at slightly different frequencies cloaked by confocal elliptical metasurfaces formed by arrays of sub-wavelength periodic elements, partially embedded in the substrate. The presence of the metasurfaces leads to the drastic suppression of mutual near-field and far-field couplings between the antennas, and thus, their radiation patterns are restored as if they were isolated. Moreover, it is worth noting that this approach is not limited to printed radiators and can be applied to other planar structures as well.

14. Propagation of light in a circular array of elliptical fibres

Alexeyev, C. N.; Milione, G.; Pogrebnaya, A. O.; Yavorsky, M. A.

2016-02-01

We have studied transformation of discrete light beams in circular arrays of elliptical fibres, in which the orientation of ellipses' axes linearly depends on the angular position of the fibre in the array and makes an half-integer number p of full rotations while tracing along its contour. We have derived analytical expressions for the spectra and supermodes that allow for evanescent coupling between the fibres in the next-neighbour approximation. We have studied the transformative properties of such an array and shown that it can generate cylindrical vector beams (CVBs) of TE and TM types. We have shown that the type of generated beam depends on the orientation of linear polarization of the incident beam. In this way, the circular array of strongly elliptical fibres enables polarization control over the type of the generated CVB. We have also shown that such arrays can change the topological charge of an incoming discrete optical vortex by the doubled array's index p.

15. Tailoring the magnetization reversal of elliptical dots using exchange bias.

SciTech Connect

Sort, J.; Buchanan, K. S.; Pearson, J. E.; Hoffmann, A.; Menendez, E.; Salazar-Alvarez, G.; Baro, M. D.; Miron, M.; Rodamcq, B.; Dieny, B.; ICREA; Univ. Autonoma of Barcelona; Insti. Catala de Nanotecnologia; SPINTEC

2008-01-01

Exchange bias effects have been studied in elliptical dots composed of ferromagnetic Ni{sub 80}Fe{sub 20}-antiferromagnetic Ir{sub 20}Mn{sub 80} bilayers. The magnetization reversal mechanisms and magnetic configurations have been investigated by magneto-optic Kerr effect and magnetic force microscopy. Although the obtained bias fields in these dots are relatively small, the magnetization reversal is found to be influenced by the ferromagnetic-antiferromagnetic coupling. Namely, for some off-axis angles of measurement, the magnetization reversal mechanism of the Ni{sub 80}Fe{sub 20}-Ir{sub 20}Mn{sub 80} ellipses depends on whether exchange bias is induced along the minor or major axis of the ellipses. Hence, exchange bias is shown to be an effective means for tailoring the magnetization reversal of elliptical dots after sample fabrication.

16. Is the Capsular Bag Perimeter Round or Elliptical?

PubMed Central

Amigó, Alfredo; Bonaque-González, Sergio

2016-01-01

Purpose: To report findings that could suggest an elliptical shape of the capsular bag. Methods: Five eyes of three patients with axial length greater than 24 mm underwent phacoemulsification cataract surgery with plate-haptic multifocal toric intraocular lens (IOL) implantation oriented in the vertical meridian. Results: In all cases, correct orientation of the IOLs was verified 30 minutes after surgery. After 24 hours, all eyes demonstrated unwanted rotation of the IOLs ranging from 15 to 45 degrees. The IOLs remained stable in the new position in all cases until adhesion of the capsular bag took place. Conclusion: These observations could suggest that the perimeter of the capsular bag has an elliptical shape. Therefore, the IOL tends to become fixated in a meridian of the capsular bag that best fits the diagonal diameter of the IOL. PMID:27413495

17. Design of elliptic cylindrical thermal cloak with layered structure

Yuan, Xuebo; Lin, Guochang; Wang, Youshan

2017-01-01

Thermal cloak has potential applications in thermal protection and sensing. Based on the theories of spatial transformation and effective medium, layered structure of elliptic cylindrical thermal cloak was designed. According to theoretical analysis and numerical simulation, the layered structure has typical characteristics of perfect thermal cloak. The external temperature field remains unchanged, while the internal temperature gradient decreases obviously. Meanwhile, the cloaking effect is stable in any direction. The cloaking effect can be improved by increasing the number of discretization layers or reducing the cloak thickness. The elliptic cylindrical cloak can be considered as cylindrical cloak when the focal distance is close to zero. This study has provided an effective way for realizing thermal cloak with more complex shapes.

18. A New Elliptical Model for Device-Free Localization

PubMed Central

Lei, Qian; Zhang, Haijian; Sun, Hong; Tang, Linling

2016-01-01

Device-free localization (DFL) based on wireless sensor networks (WSNs) is expected to detect and locate a person without the need for any wireless devices. Radio tomographic imaging (RTI) has attracted wide attention from researchers as an emerging important technology in WSNs. However, there is much room for improvement in localization estimation accuracy. In this paper, we propose a geometry-based elliptical model and adopt the orthogonal matching pursuit (OMP) algorithm. The new elliptical model uses not only line-of-sight information, but also non-line-of-sight information, which divides one ellipse into several areas with different weights. Meanwhile the OMP, which can eliminate extra bright spots in image reconstruction, is used to derive an image estimator. The experimental results demonstrate that the proposed algorithm could improve the accuracy of positioning by up to 23.8% for one person and 33.3% for two persons over some state-of-the-art RTI methods. PMID:27110788

19. Power loss in electrical steel under elliptically rotating flux conditions

SciTech Connect

Salz, W.; Hempel, K.A.

1996-03-01

The power loss of electrical steel sheet given in the data sheets of the steel manufacturers is related to linearly alternating flux conditions, measured with an Epstein frame or a single sheet tester, respectively. In the application of the material in electrical machines, the authors find large areas with rotational flux conditions, i.e., in the T-joint region of three-phase power transformers or above the stator teeth of three-phase motors and generators. The most general description of the magnetization process in this case is an elliptically rotating flux. The paper outlines the magnetic behavior of steel sheet under these flux conditions, and finally defines a simple method to predict the total power loss under elliptically rotating flux from data measured under linearly alternating and circularly rotating flux conditions only.

20. Analysis of multigrid algorithms for nonsymmetric and indefinite elliptic problems

SciTech Connect

Bramble, J.H.; Pasciak, J.E.; Xu, J.

1988-10-01

We prove some new estimates for the convergence of multigrid algorithms applied to nonsymmetric and indefinite elliptic boundary value problems. We provide results for the so-called 'symmetric' multigrid schemes. We show that for the variable V-script-cycle and the W-script-cycle schemes, multigrid algorithms with any amount of smoothing on the finest grid converge at a rate that is independent of the number of levels or unknowns, provided that the initial grid is sufficiently fine. We show that the V-script-cycle algorithm also converges (under appropriate assumptions on the coarsest grid) but at a rate which may deteriorate as the number of levels increases. This deterioration for the V-script-cycle may occur even in the case of full elliptic regularity. Finally, the results of numerical experiments are given which illustrate the convergence behavior suggested by the theory.

1. Void ellipticity distribution as a probe of cosmology.

PubMed

Park, Daeseong; Lee, Jounghun

2007-02-23

Cosmic voids refer to the large empty regions in the Universe with a very low number density of galaxies. Voids are likely to be severely disturbed by the tidal effect from the surrounding dark matter. We derive a completely analytic model for the void ellipticity distribution from physical principles. We use the spatial distribution of galaxies in a void as a measure of its shape, tracking the trajectory of the void galaxies under the influence of the tidal field using Lagrangian perturbation theory. Our model implies that the void ellipticity distribution depends sensitively on the cosmological parameters. Testing our model against the high-resolution Millennium Run simulation, we find excellent quantitative agreements of the analytic predictions with the numerical results.

2. Sole Inversion Precomputation for Elliptic Curve Scalar Multiplications

Dahmen, Erik; Okeya, Katsuyuki

This paper presents a new approach to precompute points [3]P, [5]P, ..., [2k-1]P, for some k ≥ 2 on an elliptic curve over \\mathbb{F}_p. Those points are required for the efficient evaluation of a scalar multiplication, the most important operation in elliptic curve cryptography. The proposed method precomputes the points in affine coordinates and needs only one single field inversion for the computation. The new method is superior to all known methods that also use one field inversion, if the required memory is taken into consideration. Compared to methods that require several field inversions for the precomputation, the proposed method is faster for a broad range of ratios of field inversions and field multiplications. The proposed method benefits especially from ratios as they occur on smart cards.

3. Contribution of minor mergers to the growth of elliptical galaxies

Peralta de Arriba, L.; Balcells, M.; Trujillo, I.; Falcón-Barroso, J.

2013-05-01

Size evolution studies have shown that the structural properties of the elliptical galaxies dramatically changed with cosmic time (e. g. Trujillo et al. 2007). This result challenges the ideas developed from the detailed analyses of the stellar populations of these galaxies in the nearby universe. The study of the local elliptical galaxies has revealed their stars are old, and formed over short-timescales (see the review by Renzini 2006). In order to resolve this discrepancy, it has been hypothesized that new material continuously accretes in minor merger events (Naab et al. 2007). Index-index diagrams are a promising way to probe the minor merger scenario. However, a large sample of galaxies is required for this goal. In this poster we present our preliminary index measurements of a subsample of galaxies studied by Trujillo et al. (2007) using the spectra published by the DEEP2 DR4 survey (Newman et al. 2012).

4. Remarks on strongly elliptic systems in Lipschitz domains

Agranovich, M. S.

2012-10-01

We present some remarks to the general theory of strongly elliptic second-order systems in bounded Lipschitz domains. The most important remarks are related to the use of the "Weyl decomposition" of the solution space. In particular, we suggest a simplified approach to the unique choice of the right-hand side of the system and the conormal derivative in the Neumann problem and obtain two-sided a priori estimates for the solutions. We consider the transmission problem for two systems in domains with a common Lipschitz boundary without the assumption that the coefficients do not have jumps on that boundary. We construct examples of strongly elliptic second-order systems for which the Neumann problem is not Fredholm.

5. Mott scattering in an elliptically polarized laser field

SciTech Connect

Attaourti, Y.; Manaut, B.; Taj, S.

2004-08-01

We study Mott scattering in the presence of a strong elliptically polarized field. Using the first Born approximation and the Dirac-Volkov states for the electron, we obtain an analytic formula for the unpolarized differential cross section. This generalizes the results found for the linearly polarized field by Li et al. [ 67, 063409 (2003)] and for the circularly polarized field by Attaourti and Manaut [ 68, 067401 (2003)].

6. Towards a theory of automated elliptic mesh generation

NASA Technical Reports Server (NTRS)

Cordova, J. Q.

1992-01-01

The theory of elliptic mesh generation is reviewed and the fundamental problem of constructing computational space is discussed. It is argued that the construction of computational space is an NP-Complete problem and therefore requires a nonstandard approach for its solution. This leads to the development of graph-theoretic, combinatorial optimization and integer programming algorithms. Methods for the construction of two dimensional computational space are presented.

7. Elliptic Curve Cryptography on Smart Cards Without Coprocessors

DTIC Science & Technology

2000-09-20

ELLIPTIC CURVE CRYPTOGRAPHY ON SMART CARDS WITHOUT COPROCESSORS Adam D. Woodbury Electrical and Computer Engineering Department adw@ece.wpi.edu...christof@ece.wpi.edu Worcester Polytechnic Institute Worcester, MA 01609 USA The Fourth Smart Card Research and Advanced Applications (CARDIS 2000...cost microprocessors with reasonable performance. We focus in this paper on the Intel 8051 family of microcontrollers popular in smart cards and other

8. Elliptic nozzle aspect ratio effect on controlled jet propagation

Aravindh Kumar, S. M.; Rathakrishnan, Ethirajan

2017-04-01

The present study deals with the control of a Mach 2 elliptic jet from a convergent–divergent elliptic nozzle of aspect ratio 4 using tabs at the nozzle exit. The experiments were carried out for rectangular and triangular tabs of the same blockage, placed along the major and minor axes of the nozzle exit, at different levels of nozzle expansion. The triangular tabs along the minor axis promoted superior mixing compared to the other controlled jets and caused substantial core length reduction at all the nozzle pressure ratios studied. The rectangular tabs along the minor axis caused core length reduction at all pressure ratios, but the values were minimal compared to that of triangular tabs along the minor axis. For all the test conditions, the mixing promotion caused by tabs along the major axis was inferior to that of tabs along the minor axis. The waves present in the core of controlled jets were visualized using a shadowgraph. Comparison of the present results with the results of a controlled Mach 2 elliptic jet of aspect ratio 2 (Aravindh Kumar and Sathakrishnan 2016 J. Propulsion Power 32 121–33, Aravindh Kumar and Rathakrishnan 2016 J. Aerospace Eng. at press (doi:10.1177/0954410016652921)) show that for all levels of expansion, the mixing effectiveness of triangular tabs along the minor axis of an aspect ratio 4 nozzle is better than rectangular or triangular tabs along the minor axis of an aspect ratio 2 nozzle.

9. Elliptical Fourier analysis: fundamentals, applications, and value for forensic anthropology.

PubMed

Caple, Jodi; Byrd, John; Stephan, Carl N

2017-02-17

The numerical description of skeletal morphology enables forensic anthropologists to conduct objective, reproducible, and structured tests, with the added capability of verifying morphoscopic-based analyses. One technique that permits comprehensive quantification of outline shape is elliptical Fourier analysis. This curve fitting technique allows a form's outline to be approximated via the sum of multiple sine and cosine waves, permitting the profile perimeter of an object to be described in a dense (continuous) manner at a user-defined level of precision. A large amount of shape information (the entire perimeter) can thereby be collected in contrast to other methods relying on sparsely located landmarks where information falling in between the landmarks fails to be acquired. First published in 1982, elliptical Fourier analysis employment in forensic anthropology from 2000 onwards reflects a slow uptake despite large computing power that makes its calculations easy to conduct. Without hurdles arising from calculation speed or quantity, the slow uptake may partly reside with the underlying mathematics that on first glance is extensive and potentially intimidating. In this paper, we aim to bridge this gap by pictorially illustrating how elliptical Fourier harmonics work in a simple step-by-step visual fashion to facilitate universal understanding and as geared towards increased use in forensic anthropology. We additionally provide a short review of the method's utility for osteology, a summary of past uses in forensic anthropology, and software options for calculations that largely save the user the trouble of coding customized routines.

10. Casimir force between a microfabricated elliptic cylinder and a plate

SciTech Connect

Decca, R. S.; Fischbach, E.; Klimchitskaya, G. L.; Krause, D. E.; Lopez, D.; Mostepanenko, V. M.

2011-10-15

We investigate the Casimir force between a microfabricated elliptic cylinder (cylindrical lens) and a plate made of real materials. After a brief discussion of the fabrication procedure, which typically results in elliptic rather than circular cylinders, the Lifshitz-type formulas for the Casimir force and for its gradient are derived. In the specific case of equal semiaxes, the resulting formulas coincide with those derived previously for circular cylinders. The nanofabrication procedure may also result in asymmetric cylindrical lenses obtained from parts of two different cylinders, or rotated through some angle about the axis of the cylinder. In these cases, the Lifshitz-type formulas for the Casimir force between a lens and a plate and for its gradient are also derived, and the influence of lens asymmetry is determined. Additionally, we obtain an expression for the shift of the natural frequency of a micromachined oscillator with an attached elliptic cylindrical lens interacting with a plate via the Casimir force in a nonlinear regime.

11. Theoretical results for fully flooded, elliptical hydrodynamic contacts

NASA Technical Reports Server (NTRS)

Hamrock, B. J.; Dowson, D.

1982-01-01

The influence of the ellipticity parameter and the dimensionless speed, load, and materials parameters on minimum film thickness was investigated. The ellipticity parameter was varied from 1 (a ball-on-plate configuration) to 8 (a configuration approaching a line contact). The dimensionless speed parameter was varied over a range of nearly two orders of magnitude. Conditions corresponding to the use of solid materials of bronze, steel, and silicon nitride and lubricants of praffinic and naphthemic mineral oils were considered in obtaining the exponent in the dimensionless materials parameter. Thirty-four different cases were used in obtaining the minimum film thickness formula H min = 3.63U to the 0.68 power G to the 0.49 power W to the -0.073 power 1-e to the 0.68K power). A simplified expression for the ellipticity parameter was found where k = 1.03 (r(y)/r(x)) to the 0.64 power. Contour plots were also shown which indicate in detail the pressure spike and two side lobes in which the minimum film thickness occurs. These theoretical solutions of film thickness have all the essential features of the previously reported experimental observations based upon optical interferometry.

12. Lost and found dark matter in elliptical galaxies.

PubMed

Dekel, A; Stoehr, F; Mamon, G A; Cox, T J; Novak, G S; Primack, J R

2005-09-29

There is strong evidence that the mass of the Universe is dominated by dark matter, which exerts gravitational attraction but whose exact nature is unknown. In particular, all galaxies are believed to be embedded in massive haloes of dark matter. This view has recently been challenged by the observation of surprisingly low random stellar velocities in the outskirts of ordinary elliptical galaxies, which has been interpreted as indicating a lack of dark matter. Here we show that the low velocities are in fact compatible with galaxy formation in dark-matter haloes. Using numerical simulations of disk-galaxy mergers, we find that the stellar orbits in the outer regions of the resulting ellipticals are very elongated. These stars were torn by tidal forces from their original galaxies during the first close passage and put on outgoing trajectories. The elongated orbits, combined with the steeply falling density profile of the observed tracers, explain the observed low velocities even in the presence of large amounts of dark matter. Projection effects when viewing a triaxial elliptical can lead to even lower observed velocities along certain lines of sight.

13. Red blood cell micromanipulation with elliptical laser beam profile optical tweezers in different osmolarity conditions

Spyratou, E.; Makropoulou, M.; Serafetinides, A. A.

2011-07-01

In this work optical tweezers with elliptical beam profiles have been developed in order to examine the effect of optical force on fresh red blood cells (RBC) in isotonic, hypertonic and hypotonic buffer solutions. Considering that the optical force depends essentially on the cell surface and the cytoplasmic refractive index, it is obvious that biochemical modifications associated with different states of the cell will influence its behaviour in the optical trap. Line optical tweezers were used to manipulate simultaneously more than one red blood cell. After we have been manipulated a RBC with an elliptical laser beam profile in an isotonic or hypertonic buffer, we noticed that it rotates by itself when gets trapped by optical tweezers and undergoes folding. Further shape deformations can be observed attributed to the competition between alignment and rotational torque which are transferred by laser light to the cell. In hypotonic buffer RBCs become spherical and do not rotate or fold since the resultant force due to rays emerging from diametrically opposite points of the cell leads to zero torque. Manipulation of fresh red blood cells in isotonic solution by line optical tweezers leads to folding and elongation of trapped RBCs. Membrane elasticity properties such as bending modulus can be estimated by measuring RBC's folding time in function with laser power.

14. A new weak Galerkin finite element method for elliptic interface problems

Mu, Lin; Wang, Junping; Ye, Xiu; Zhao, Shan

2016-11-01

A new weak Galerkin (WG) finite element method is introduced and analyzed in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. Extensive numerical experiments have been conducted to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.

15. A new weak Galerkin finite element method for elliptic interface problems

SciTech Connect

Mu, Lin; Wang, Junping; Ye, Xiu; Zhao, Shan

2016-08-26

We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments in order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.

16. Heat transfer enhancement of PCM melting in 2D horizontal elliptical tube using metallic porous matrix

2016-12-01

In this study, the melting process of ice as a phase-change material (PCM) saturated with a nickel-steel porous matrix inside a horizontal elliptical tube is investigated. Due to the low thermal conductivity of the PCM, it is motivated to augment the heat transfer performance of the system simultaneously by finding an optimum value of the aspect ratio and impregnating a metallic porous matrix into the base PCM. The lattice Boltzmann method with a double distribution function formulated based on the enthalpy method, is applied at the representative elementary volume scale under the local thermal equilibrium assumption between the PCM and porous matrix in the composite. While reducing or increasing the aspect ratio of the circular tubes leads to the expedited melting, the 90° inclination of each elliptical tube in the case of the pure PCM melting does not affect the melting rate. With the reduction in the porosity, the effective thermal conductivity and melting rate in all tubes promoted. Although the natural convection is fully suppressed due to the significant flow blockage in the porous structure, the melting rates are generally increased in all cases.

17. Wave-optical simulation of hard X-ray nanofocusing by precisely figured elliptical mirrors

Macrander, Albert; Kewish, Cameron; Assoufid, Lahsen; Qian, Jun

2007-03-01

Computer simulations of nanofocusing by elliptical mirrors are presented wherein the diffraction and propagation of coherent hard X-rays are predicted using wave-optical calculations. Surface height data acquired via microstitching interferometry were used to calculate the complex pupil function of a mirror, taking into account the Fresnel reflectivity and treating the surface topography as an aberration to a perfect elliptical mirror. The reflected wavefield amplitude and phase downstream of the mirror were obtained by numerically evaluating the Fresnel-Kirchhoff diffraction integral. Simulated intensity profiles, and contours (isophotes) around the focal plane are presented for coherent illumination by a 15 keV point source, which indicate nearly diffraction-limited focusing at the 40 nm level. The effect of high spatial frequency microroughness on nanofocusing was investigated by low-pass filtering the Fourier spectrum of the residual height profile. Simulations using the filtered metrology data revealed that roughness length scales shorter than 0.1 mm have a minor effect on the focal spot size and intensity.

18. Wave-optical simulation of hard-x-ray nanofocusing by precisely figured elliptical mirrors

Kewish, Cameron M.; Assoufid, Lahsen; Macrander, Albert T.; Qian, Jun

2007-04-01

Computer simulations of nanofocusing by elliptical mirrors are presented wherein the diffraction and propagation of coherent hard x rays are predicted using wave-optical calculations. Surface height data acquired via microstitching interferometry were used to calculate the complex pupil function of a mirror, taking into account the Fresnel reflectivity and treating the surface topography as an aberration to a perfect elliptical mirror. The reflected wave-field amplitude and phase downstream of the mirror were obtained by numerically evaluating the Fresnel-Kirchhoff diffraction integral. Simulated intensity profiles and contours (isophotes) around the focal plane are presented for coherent illumination by a 15 keV point source, which indicate nearly diffraction-limited focusing at the 40 nm level. The effect of high spatial frequency microroughness on nanofocusing was investigated by low-pass filtering the Fourier spectrum of the residual height profile. Simulations using the filtered metrology data confirmed that roughness length scales shorter than 0.1 mm have a minor effect on the focal spot size and intensity.

19. Wave-optical simulation of hard-x-ray nanofocusing by precisely figured elliptical mirrors.

PubMed

Kewish, Cameron M; Assoufid, Lahsen; Macrander, Albert T; Qian, Jun

2007-04-10

Computer simulations of nanofocusing by elliptical mirrors are presented wherein the diffraction and propagation of coherent hard x rays are predicted using wave-optical calculations. Surface height data acquired via microstitching interferometry were used to calculate the complex pupil function of a mirror, taking into account the Fresnel reflectivity and treating the surface topography as an aberration to a perfect elliptical mirror. The reflected wave-field amplitude and phase downstream of the mirror were obtained by numerically evaluating the Fresnel-Kirchhoff diffraction integral. Simulated intensity profiles and contours (isophotes) around the focal plane are presented for coherent illumination by a 15 keV point source, which indicate nearly diffraction-limited focusing at the 40 nm level. The effect of high spatial frequency microroughness on nanofocusing was investigated by low-pass filtering the Fourier spectrum of the residual height profile. Simulations using the filtered metrology data confirmed that roughness length scales shorter than 0.1 mm have a minor effect on the focal spot size and intensity.

20. Wave-optical simulation of hard-x-ray nanofocusing by precisely figured elliptical mirrors

SciTech Connect

Kewish, Cameron M.; Assoufid, Lahsen; Macrander, Albert T.; Qian Jun

2007-04-10

Computer simulations of nanofocusing by elliptical mirrors are presented wherein the diffraction and propagation of coherent hard x rays are predicted using wave-optical calculations. Surface height data acquired via microstitching interferometry were used to calculate the complex pupil function of a mirror, taking into account the Fresnel reflectivity and treating the surface topography as an aberration to a perfect elliptical mirror. The reflected wave-field amplitude and phase downstream of the mirror were obtained by numerically evaluating the Fresnel-Kirchhoff diffraction integral. Simulated intensity profiles and contours (isophotes) around the focal plane are presented for coherent illumination by a15 keV point source, which indicate nearly diffraction-limited focusing at the40 nm level. The effect of high spatial frequency microroughness on nanofocusing was investigated by low-pass filtering the Fourier spectrum of the residual height profile. Simulations using the filtered metrology data confirmed that roughness length scales shorter than0.1 mm have a minor effect on the focal spot size and intensity.

1. A substantial population of low-mass stars in luminous elliptical galaxies.

PubMed

van Dokkum, Pieter G; Conroy, Charlie

2010-12-16

The stellar initial mass function (IMF) describes the mass distribution of stars at the time of their formation and is of fundamental importance for many areas of astrophysics. The IMF is reasonably well constrained in the disk of the Milky Way but we have very little direct information on the form of the IMF in other galaxies and at earlier cosmic epochs. Here we report observations of the Na (I) doublet and the Wing-Ford molecular FeH band in the spectra of elliptical galaxies. These lines are strong in stars with masses less than 0.3M(⊙) (where M(⊙) is the mass of the Sun) and are weak or absent in all other types of stars. We unambiguously detect both signatures, consistent with previous studies that were based on data of lower signal-to-noise ratio. The direct detection of the light of low-mass stars implies that they are very abundant in elliptical galaxies, making up over 80% of the total number of stars and contributing more than 60% of the total stellar mass. We infer that the IMF in massive star-forming galaxies in the early Universe produced many more low-mass stars than the IMF in the Milky Way disk, and was probably slightly steeper than the Salpeter form in the mass range 0.1M(⊙) to 1M(⊙).

2. Heterogeneous mixtures of elliptical particles: Directly resolving local and global properties and responses

Liu, Qianlong; Reifsnider, Kenneth L.

2013-02-01

In our earlier papers, Prosperetti’s seminal Physalis method for fluid flows was extended to directly resolve electric fields in finite-sized particles and to investigate accurately the mutual fluid-particle, particle-particle, and particle-boundary interactions for circular/spherical particles. For the first time, the method makes the accurate prediction of the local charge distribution, force and torque on finite-sized particles possible. In the present work, the method is extended to heterogeneous mixtures of elliptical particles to further investigate the effects of the orientation and anisotropy. The direct resolution of the effect of fields in heterogeneous mixtures of elliptical particles to determine local and global properties and responses has many applications in engineering, mechanics, physics, chemistry, and biology. The method can be applied to heterogeneous materials, heterogeneous functional materials, microfluidics, and devices such as electric double layer capacitors. In the present paper, the accuracy of the method is extensively investigated even for very challenging problems, for example, for elongated rod-like particles with very high aspect ratios. The accuracy and efficiency of the method suggests that it can be used for many important applications of broad interest.

3. Ellipticity-dependent ionization/dissociation of carbon dioxide in strong laser fields

Zhang, Jun-Feng; Ma, Ri; Zuo, Wan-Long; Lv, Hang; Huang, Hong-Wei; Xu, Hai-Feng; Jin, Ming-Xing; Ding, Da-Jun

2015-03-01

Ionization and dissociation of linear triatomic molecules, carbon dioxide, are studied in 50-fs 800-nm strong laser fields using time-of-flight mass spectrometer. The yields of double charged ions and various fragment ions (CO+, On+, and Cn+ (n = 1, 2)) are measured as a function of ellipticity of laser polarization in the intensity range from 5.0 × 1013 W/cm2 to 6.0 × 1014 W/cm2. The results demonstrate that non-sequential double ionization, which is induced by laser-driven electron recollision, dominates double ionization of CO2 in the strong IR laser field with intensity lower than 2.0 × 1014 W/cm2. The electron recollision could also have contribution in strong-field multiple ionization and formation of fragments of CO2 molecules. The present study indicates that the intensity and ellipticity dependence of ions yields can be used to probe the complex dynamics of strong-field ionization/dissociation of polyatomic molecules. Project supported by the National Basic Research Program of China (Grant No. 2013CB922200) and the National Natural Science Foundation of China (Grant Nos. 11034003 and 11274140).

4. Elliptic differential operators on Lipschitz domains and abstract boundary value problems.

PubMed

Behrndt, Jussi; Micheler, Till

2014-11-15

This paper consists of two parts. In the first part, which is of more abstract nature, the notion of quasi-boundary triples and associated Weyl functions is developed further in such a way that it can be applied to elliptic boundary value problems on non-smooth domains. A key feature is the extension of the boundary maps by continuity to the duals of certain range spaces, which directly leads to a description of all self-adjoint extensions of the underlying symmetric operator with the help of abstract boundary values. In the second part of the paper a complete description is obtained of all self-adjoint realizations of the Laplacian on bounded Lipschitz domains, as well as Kreĭn type resolvent formulas and a spectral characterization in terms of energy dependent Dirichlet-to-Neumann maps. These results can be viewed as the natural generalization of recent results by Gesztesy and Mitrea for quasi-convex domains. In this connection we also characterize the maximal range spaces of the Dirichlet and Neumann trace operators on a bounded Lipschitz domain in terms of the Dirichlet-to-Neumann map. The general results from the first part of the paper are also applied to higher order elliptic operators on smooth domains, and particular attention is paid to the second order case which is illustrated with various examples.

5. A new weak Galerkin finite element method for elliptic interface problems

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu; ...

2016-08-26

We introduce and analyze a new weak Galerkin (WG) finite element method in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. We conducted extensive numerical experiments inmore » order to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.« less

6. Elliptic integral evaluations of Bessel moments

SciTech Connect

Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Glasser, M.L.

2008-01-06

We record what is known about the closed forms for variousBessel function moments arising in quantum field theory, condensed mattertheory and other parts of mathematical physics. More generally, wedevelop formulae for integrals of products of six or fewer Besselfunctions. In consequence, we are able to discover and prove closed formsfor c(n,k) := Int_0 inf tk K_0 n(t) dt, with integers n = 1, 2, 3, 4 andk greater than or equal to 0, obtaining new results for the even momentsc3,2k and c4,2k . We also derive new closed forms for the odd momentss(n,2k+1) := Int_0 inf t(2k+1) I_0(t) K_0n(t) dt,with n = 3, 4 and fort(n,2k+1) := Int_0 inf t(2k+1) I_02(t) K_0(n-2) dt, with n = 5, relatingthe latter to Green functions on hexagonal, diamond and cubic lattices.We conjecture the values of s(5,2k+1), make substantial progress on theevaluation of c(5,2k+1), s(6,2k+1) and t(6,2k+1) and report more limitedprogress regarding c(5,2k), c(6,2k+1) and c(6,2k). In the process, weobtain 8 conjectural evaluations, each of which has been checked to 1200decimal places. One of these lies deep in 4-dimensional quantum fieldtheory and two are probably provable by delicate combinatorics. Thereremains a hard core of five conjectures whose proofs would be mostinstructive, to mathematicians and physicists alike.

7. Degenerate elliptic inequalities with critical growth

Fang, Ming

This article is motivated by the fact that very little is known about variational inequalities of general principal differential operators with critical growth. The concentration compactness principle of P.L. Lions [P.L. Lions, The concentration compactness principle in the calculus of variation. The limit case I, Rev. Mat. Iberoamericana 1 (1) (1985) 145-201; P.L. Lions, The concentration compactness principle in the calculus of variation. The limit case II, Rev. Mat. Iberoamericana 1 (2) (1985) 45-121] is a widely applied technique in the analysis of Palais-Smale sequences. For critical growth problems involving principal differential operators Laplacian or p-Laplacian, much has been accomplished in recent years, whereas very little has been done for problems involving more general main differential operators since a nonlinearity is observed between the corresponding functional I(u) and measure μ introduced in the concentration compactness method. In this paper, we investigate a Leray-Lions type operator and behaviors of its ( sequence.

8. Forward and inverse uncertainty quantification using multilevel Monte Carlo algorithms for an elliptic non-local equation

DOE PAGES

Jasra, Ajay; Law, Kody J. H.; Zhou, Yan

2016-01-01

Our paper considers uncertainty quantification for an elliptic nonlocal equation. In particular, it is assumed that the parameters which define the kernel in the nonlocal operator are uncertain and a priori distributed according to a probability measure. It is shown that the induced probability measure on some quantities of interest arising from functionals of the solution to the equation with random inputs is well-defined,s as is the posterior distribution on parameters given observations. As the elliptic nonlocal equation cannot be solved approximate posteriors are constructed. The multilevel Monte Carlo (MLMC) and multilevel sequential Monte Carlo (MLSMC) sampling algorithms are usedmore » for a priori and a posteriori estimation, respectively, of quantities of interest. Furthermore, these algorithms reduce the amount of work to estimate posterior expectations, for a given level of error, relative to Monte Carlo and i.i.d. sampling from the posterior at a given level of approximation of the solution of the elliptic nonlocal equation.« less

9. The development of a three-dimensional partially elliptic flow computer program for combustor research

NASA Technical Reports Server (NTRS)

Pan, Y. S.

1978-01-01

A three dimensional, partially elliptic, computer program was developed. Without requiring three dimensional computer storage locations for all flow variables, the partially elliptic program is capable of predicting three dimensional combustor flow fields with large downstream effects. The program requires only slight increase of computer storage over the parabolic flow program from which it was developed. A finite difference formulation for a three dimensional, fully elliptic, turbulent, reacting, flow field was derived. Because of the negligible diffusion effects in the main flow direction in a supersonic combustor, the set of finite-difference equations can be reduced to a partially elliptic form. Only the pressure field was governed by an elliptic equation and requires three dimensional storage; all other dependent variables are governed by parabolic equations. A numerical procedure which combines a marching integration scheme with an iterative scheme for solving the elliptic pressure was adopted.

10. A numerical technique for linear elliptic partial differential equations in polygonal domains

PubMed Central

Hashemzadeh, P.; Fokas, A. S.; Smitheman, S. A.

2015-01-01

Integral representations for the solution of linear elliptic partial differential equations (PDEs) can be obtained using Green's theorem. However, these representations involve both the Dirichlet and the Neumann values on the boundary, and for a well-posed boundary-value problem (BVPs) one of these functions is unknown. A new transform method for solving BVPs for linear and integrable nonlinear PDEs usually referred to as the unified transform (or the Fokas transform) was introduced by the second author in the late Nineties. For linear elliptic PDEs, this method can be considered as the analogue of Green's function approach but now it is formulated in the complex Fourier plane instead of the physical plane. It employs two global relations also formulated in the Fourier plane which couple the Dirichlet and the Neumann boundary values. These relations can be used to characterize the unknown boundary values in terms of the given boundary data, yielding an elegant approach for determining the Dirichlet to Neumann map. The numerical implementation of the unified transform can be considered as the counterpart in the Fourier plane of the well-known boundary integral method which is formulated in the physical plane. For this implementation, one must choose (i) a suitable basis for expanding the unknown functions and (ii) an appropriate set of complex values, which we refer to as collocation points, at which to evaluate the global relations. Here, by employing a variety of examples we present simple guidelines of how the above choices can be made. Furthermore, we provide concrete rules for choosing the collocation points so that the condition number of the matrix of the associated linear system remains low. PMID:25792955

11. A numerical technique for linear elliptic partial differential equations in polygonal domains.

PubMed

Hashemzadeh, P; Fokas, A S; Smitheman, S A

2015-03-08

Integral representations for the solution of linear elliptic partial differential equations (PDEs) can be obtained using Green's theorem. However, these representations involve both the Dirichlet and the Neumann values on the boundary, and for a well-posed boundary-value problem (BVPs) one of these functions is unknown. A new transform method for solving BVPs for linear and integrable nonlinear PDEs usually referred to as the unified transform (or the Fokas transform) was introduced by the second author in the late Nineties. For linear elliptic PDEs, this method can be considered as the analogue of Green's function approach but now it is formulated in the complex Fourier plane instead of the physical plane. It employs two global relations also formulated in the Fourier plane which couple the Dirichlet and the Neumann boundary values. These relations can be used to characterize the unknown boundary values in terms of the given boundary data, yielding an elegant approach for determining the Dirichlet to Neumann map. The numerical implementation of the unified transform can be considered as the counterpart in the Fourier plane of the well-known boundary integral method which is formulated in the physical plane. For this implementation, one must choose (i) a suitable basis for expanding the unknown functions and (ii) an appropriate set of complex values, which we refer to as collocation points, at which to evaluate the global relations. Here, by employing a variety of examples we present simple guidelines of how the above choices can be made. Furthermore, we provide concrete rules for choosing the collocation points so that the condition number of the matrix of the associated linear system remains low.

12. The demagnetizing energies of a uniformly magnetized cylinder with an elliptic cross-section

Goode, D. A.; Rowlands, G.

2003-12-01

Analytic expressions for the demagnetizing energies are obtained in the form of partial series, for long elliptic cylinders and for squat ones where the ellipticity of the cross-section is unrestrained. This leaves just a small range where the demagnetizing energies are not well defined. It is found that by replacing the elliptic cylinders with rectangular blocks, a good approximation to the demagnetizing energy may be made in this small range.

13. Elliptical metasurfaces for cloaking and antenna applications at microwave and terahertz frequencies

Mehrpourbernety, Hossein

microwave frequencies. In this work, we propose a novel approach to reduce the mutual coupling between two closely spaced strip dipole antennas with the elliptical metasurfaces formed by conformal printed arrays of sub-wavelength periodic elements. We show that by covering each strip with the metasurface cloak, the antennas become invisible to each other and their radiation patterns are restored as if they were isolated. The electromagnetic scattering analysis pertained to the case of antennas with the frequencies far from each other is shown to be as a good approximation of a 2-D metallic strip scattering cancellation problem solved by expressing the incident and scattered fields in terms of radial and angular Mathieu functions, with the use of sheet impedance boundary conditions at the metasurface. In addition, we extend the novel approach based on the concept of mantle cloaking in order to reduce the mutual near-field and far-field coupling between planar antennas in printed technology. To present the idea, we consider two microstrip-fed monopole antennas resonating at slightly different frequencies and show that by cloaking the radiating part of each antenna, the antennas become invisible to each other, and thus, the mutual coupling between the antennas is suppressed drastically. The cloak structure is realized by a conformal elliptical metasurface formed by confocal printed arrays of sub-wavelength periodic elements, partially embedded in the substrate. The presence of the metasurfaces leads to the restoration of the radiation patterns of the antennas as if they were isolated.

14. Elliptic Flow in Au+Au Collisions at √sNN = 130 GeV

Ackermann, K. H.; Adams, N.; Adler, C.; Ahammed, Z.; Ahmad, S.; Allgower, C.; Amsbaugh, J.; Anderson, M.; Anderssen, E.; Arnesen, H.; Arnold, L.; Averichev, G. S.; Baldwin, A.; Balewski, J.; Barannikova, O.; Barnby, L. S.; Baudot, J.; Beddo, M.; Bekele, S.; Belaga, V. V.; Bellwied, R.; Bennett, S.; Bercovitz, J.; Berger, J.; Betts, W.; Bichsel, H.; Bieser, F.; Bland, L. C.; Bloomer, M.; Blyth, C. O.; Boehm, J.; Bonner, B. E.; Bonnet, D.; Bossingham, R.; Botlo, M.; Boucham, A.; Bouillo, N.; Bouvier, S.; Bradley, K.; Brady, F. P.; Braithwaite, E. S.; Braithwaite, W.; Brandin, A.; Brown, R. L.; Brugalette, G.; Byrd, C.; Caines, H.; Calderón de La Barca Sánchez, M.; Cardenas, A.; Carr, L.; Carroll, J.; Castillo, J.; Caylor, B.; Cebra, D.; Chatopadhyay, S.; Chen, M. L.; Chen, W.; Chen, Y.; Chernenko, S. P.; Cherney, M.; Chikanian, A.; Choi, B.; Chrin, J.; Christie, W.; Coffin, J. P.; Conin, L.; Consiglio, C.; Cormier, T. M.; Cramer, J. G.; Crawford, H. J.; Danilov, V. I.; Dayton, D.; Demello, M.; Deng, W. S.; Derevschikov, A. A.; Dialinas, M.; Diaz, H.; Deyoung, P. A.; Didenko, L.; Dimassimo, D.; Dioguardi, J.; Dominik, W.; Drancourt, C.; Draper, J. E.; Dunin, V. B.; Dunlop, J. C.; Eckardt, V.; Edwards, W. R.; Efimov, L. G.; Eggert, T.; Emelianov, V.; Engelage, J.; Eppley, G.; Erazmus, B.; Etkin, A.; Fachini, P.; Feliciano, C.; Ferenc, D.; Ferguson, M. I.; Fessler, H.; Finch, E.; Fine, V.; Fisyak, Y.; Flierl, D.; Flores, I.; Foley, K. J.; Fritz, D.; Gagunashvili, N.; Gans, J.; Gazdzicki, M.; Germain, M.; Geurts, F.; Ghazikhanian, V.; Gojak, C.; Grabski, J.; Grachov, O.; Grau, M.; Greiner, D.; Greiner, L.; Grigoriev, V.; Grosnick, D.; Gross, J.; Guilloux, G.; Gushin, E.; Hall, J.; Hallman, T. J.; Hardtke, D.; Harper, G.; Harris, J. W.; He, P.; Heffner, M.; Heppelmann, S.; Herston, T.; Hill, D.; Hippolyte, B.; Hirsch, A.; Hjort, E.; Hoffmann, G. W.; Horsley, M.; Howe, M.; Huang, H. Z.; Humanic, T. J.; Hümmler, H.; Hunt, W.; Hunter, J.; Igo, G. J.; Ishihara, A.; Ivanshin, Yu. I.; Jacobs, P.; Jacobs, W. W.; Jacobson, S.; Jared, R.; Jensen, P.; Johnson, I.; Jones, P. G.; Judd, E.; Kaneta, M.; Kaplan, M.; Keane, D.; Kenney, V. P.; Khodinov, A.; Klay, J.; Klein, S. R.; Klyachko, A.; Koehler, G.; Konstantinov, A. S.; Kormilitsyne, V.; Kotchenda, L.; Kotov, I.; Kovalenko, A. D.; Kramer, M.; Kravtsov, P.; Krueger, K.; Krupien, T.; Kuczewski, P.; Kuhn, C.; Kunde, G. J.; Kunz, C. L.; Kutuev, R. Kh.; Kuznetsov, A. A.; Lakehal-Ayat, L.; Lamas-Valverde, J.; Lamont, M. A.; Landgraf, J. M.; Lange, S.; Lansdell, C. P.; Lasiuk, B.; Laue, F.; Lebedev, A.; Lecompte, T.; Leonhardt, W. J.; Leontiev, V. M.; Leszczynski, P.; Levine, M. J.; Li, Q.; Li, Q.; Li, Z.; Liaw, C.-J.; Lin, J.; Lindenbaum, S. J.; Lindenstruth, V.; Lindstrom, P. J.; Lisa, M. A.; Liu, H.; Ljubicic, T.; Llope, W. J.; Locurto, G.; Long, H.; Longacre, R. S.; Lopez-Noriega, M.; Lopiano, D.; Love, W. A.; Lutz, J. R.; Lynn, D.; Madansky, L.; Maier, R.; Majka, R.; Maliszewski, A.; Margetis, S.; Marks, K.; Marstaller, R.; Martin, L.; Marx, J.; Matis, H. S.; Matulenko, Yu. A.; Matyushevski, E. A.; McParland, C.; McShane, T. S.; Meier, J.; Melnick, Yu.; Meschanin, A.; Middlekamp, P.; Mikhalin, N.; Miller, B.; Milosevich, Z.; Minaev, N. G.; Minor, B.; Mitchell, J.; Mogavero, E.; Moiseenko, V. A.; Moltz, D.; Moore, C. F.; Morozov, V.; Morse, R.; de Moura, M. M.; Munhoz, M. G.; Mutchler, G. S.; Nelson, J. M.; Nevski, P.; Ngo, T.; Nguyen, M.; Nguyen, T.; Nikitin, V. A.; Nogach, L. V.; Noggle, T.; Norman, B.; Nurushev, S. B.; Nussbaum, T.; Nystrand, J.; Odyniec, G.; Ogawa, A.; Ogilvie, C. A.; Olchanski, K.; Oldenburg, M.; Olson, D.; Ososkov, G. A.; Ott, G.; Padrazo, D.; Paic, G.; Pandey, S. U.; Panebratsev, Y.; Panitkin, S. Y.; Pavlinov, A. I.; Pawlak, T.; Pentia, M.; Perevotchikov, V.; Peryt, W.; Petrov, V. A.; Pinganaud, W.; Pirogov, S.; Platner, E.; Pluta, J.; Polk, I.; Porile, N.; Porter, J.; Poskanzer, A. M.; Potrebenikova, E.; Prindle, D.; Pruneau, C.; Puskar-Pasewicz, J.; Rai, G.; Rasson, J.; Ravel, O.; Ray, R. L.; Razin, S. V.; Reichhold, D.; Reid, J.; Renfordt, R. E.; Retiere, F.; Ridiger, A.; Riso, J.; Ritter, H. G.; Roberts, J. B.; Roehrich, D.; Rogachevski, O. V.; Romero, J. L.; Roy, C.; Russ, D.; Rykov, V.; Sakrejda, I.; Sanchez, R.; Sandler, Z.; Sandweiss, J.; Sappenfield, P.; Saulys, A. C.; Savin, I.; Schambach, J.; Scharenberg, R. P.; Scheblien, J.; Scheetz, R.; Schlueter, R.; Schmitz, N.; Schroeder, L. S.; Schulz, M.; Schüttauf, A.; Sedlmeir, J.; Seger, J.; Seliverstov, D.; Seyboth, J.; Seyboth, P.; Seymour, R.; Shakaliev, E. I.; Shestermanov, K. E.; Shi, Y.; Shimanskii, S. S.; Shuman, D.; Shvetcov, V. S.; Skoro, G.; Smirnov, N.; Smykov, L. P.; Snellings, R.; Solberg, K.; Sowinski, J.; Spinka, H. M.; Srivastava, B.; Stephenson, E. J.; Stock, R.; Stolpovsky, A.; Stone, N.; Stone, R.; Strikhanov, M.; Stringfellow, B.; Stroebele, H.; Struck, C.; Suaide, A. A.; Sugarbaker, E.; Suire, C.; Symons, T. J.; Takahashi, J.; Tang, A. H.; Tarchini, A.; Tarzian, J.; Thomas, J. H.; Tikhomirov, V.; Szanto de Toledo, A.; Tonse, S.; Trainor, T.; Trentalange, S.; Tokarev, M.; Tonjes, M. B.; Trofimov, V.; Tsai, O.; Turner, K.; Ullrich, T.; Underwood, D. G.; Vakula, I.; van Buren, G.; Vandermolen, A. M.; Vanyashin, A.; Vasilevski, I. M.; Vasiliev, A. N.; Vigdor, S. E.; Visser, G.; Voloshin, S. A.; Vu, C.; Wang, F.; Ward, H.; Weerasundara, D.; Weidenbach, R.; Wells, R.; Wells, R.; Wenaus, T.; Westfall, G. D.; Whitfield, J. P.; Whitten, C.; Wieman, H.; Willson, R.; Wilson, K.; Wirth, J.; Wisdom, J.; Wissink, S. W.; Witt, R.; Wolf, J.; Wood, L.; Xu, N.; Xu, Z.; Yakutin, A. E.; Yamamoto, E.; Yang, J.; Yepes, P.; Yokosawa, A.; Yurevich, V. I.; Zanevski, Y. V.; Zhang, J.; Zhang, W. M.; Zhu, J.; Zimmerman, D.; Zoulkarneev, R.; Zubarev, A. N.

2001-01-01

Elliptic flow from nuclear collisions is a hadronic observable sensitive to the early stages of system evolution. We report first results on elliptic flow of charged particles at midrapidity in Au+Au collisions at sNN = 130 GeV using the STAR Time Projection Chamber at the Relativistic Heavy Ion Collider. The elliptic flow signal, v2, averaged over transverse momentum, reaches values of about 6% for relatively peripheral collisions and decreases for the more central collisions. This can be interpreted as the observation of a higher degree of thermalization than at lower collision energies. Pseudorapidity and transverse momentum dependence of elliptic flow are also presented.

15. Excess ellipticity of hot and cold spots in the WMAP data?

SciTech Connect

Berntsen, Eirik; Hansen, Frode K. E-mail: frodekh@astro.uio.no

2013-12-10

We investigate claims of excess ellipticity of hot and cold spots in the Wilkinson Microwave Anisotropy Probe (WMAP) data. Using the cosmic microwave background (CMB) data from 7 yr of observations by the WMAP satellite, we find, contrary to previous claims of a 10σ detection of excess ellipticity in the 3 yr data, that the ellipticity of hot and cold spots is perfectly consistent with simulated CMB maps based on the concordance cosmology. We further test for excess obliquity and excess skewness/kurtosis of ellipticity and obliquity and find the WMAP7 data consistent with Gaussian simulated maps.

16. Interpreting the Elliptical Crater Populations on Mars, Venus, and the Moon

Bottke, William F.; Love, Stanley G.; Tytell, David; Glotch, Timothy

2000-05-01

Asteroids or comets striking a planetary surface at very shallow angles produce elliptical-shaped craters. According to laboratory impact experiments (D. E. Gault and J. A. Wedekind 1978, Proc. Lunar Planet. Sci. Conf. 9th, 3843-3875), elliptical craters result from impact angles within ˜5° of horizontal and less than 1% of projectiles with isotropic impact trajectories create elliptical craters. This result disagrees with survey results which suggest that approximately 5% of all kilometer-sized craters formed on Mars, Venus, and the Moon have elliptical shapes. To explain this discrepancy, we examined the threshold incidence angle necessary to produce elliptical craters in laboratory impact experiments. Recent experiments show that aluminum targets produce elongated craters at much steeper impact angles than sand targets. This suggests that target properties are as important as the projectile's impact angle in determining the eventual ellipticity of the crater. Creating a model which interpolates between impact data produced using sand and aluminum targets, we derive a new elliptical crater threshold angle of 12° from horizontal for Mars, Venus, and the Moon. This leads to a predicted proportion of elliptical craters that matches observations within uncertainty given a random projectile population. We conclude that the observed proportion of elliptical craters on these bodies is a natural by-product of projectiles striking at random angles, and that no additional formation mechanisms are needed.

17. DIRECT DETECTIONS OF YOUNG STARS IN NEARBY ELLIPTICAL GALAXIES

SciTech Connect

Ford, H. Alyson; Bregman, Joel N.

2013-06-20

Small amounts of star formation in elliptical galaxies are suggested by several results: surprisingly young ages from optical line indices, cooling X-ray gas, and mid-infrared dust emission. Such star formation has previously been difficult to directly detect, but using ultraviolet Hubble Space Telescope Wide Field Camera 3 imaging, we have identified individual young stars and star clusters in four nearby ellipticals. Ongoing star formation is detected in all galaxies, including three ellipticals that have previously exhibited potential signposts of star-forming conditions (NGC 4636, NGC 4697, and NGC 4374), as well as the typical ''red and dead'' NGC 3379. The current star formation in our closest targets, where we are most complete, is between 2.0 and 9.8 Multiplication-Sign 10{sup -5} M{sub Sun} yr{sup -1}. The star formation history was roughly constant from 0.5 to 1.5 Gyr (at (3-5) Multiplication-Sign 10{sup -4} M{sub Sun} yr{sup -1}), but decreased by a factor of several in the past 0.3 Gyr. Most star clusters have a mass between 10{sup 2} and 10{sup 4} M{sub Sun }. The specific star formation rates of {approx}10{sup -16} yr{sup -1} (at the present day) or {approx}10{sup -14} yr{sup -1} (when averaging over the past Gyr) imply that a fraction 10{sup -8} of the stellar mass is younger than 100 Myr and 10{sup -5} is younger than 1 Gyr, quantifying the level of frosting of recent star formation over the otherwise passive stellar population. There is no obvious correlation between either the presence or spatial distribution of postulated star formation indicators and the star formation we detect.

18. AGB Connection and Ultraviolet Luminosity Excess in Elliptical Galaxies

Buzzoni, Alberto; González-Lópezlira, Rosa A.

2008-10-01

Relying on infrared surface brightness fluctuactions to trace AGB properties in a sample of elliptical galaxies in the Virgo and Fornax Clusters, we assess the puzzling origin of the UV upturn'' phenomenon, recently traced to the presence of a hot horizontal branch (HB) stellar component. The UV upturn actually signals a profound change in the galaxy stellar populations, involving both the hot stellar component and red giant evolution. In particular, the strengthening of the UV rising branch is always seen to correspond to a shortening in AGB deployment; this trend can be readily interpreted as an age effect, perhaps mildly modulated by metal abundance. Brightest stars in ellipticals are all found to be genuine AGB members, all the way, and with the AGB tip exceeding the RGB tip by some 0.5-1.5 mag. The inferred core mass of these stars is found to be lesssim0.57 M⊙ among giant ellipticals. This value accounts for the recognized deficiency of planetary nebulae in these galaxies, as a result of a lengthy transition time for the post-AGB stellar core to become a hard UV emitter and eventually fire up'' the nebula. The combined study of galaxy (1550 - V)0 color and integrated Hβ index points to a a bimodal temperature distribution for the HB with both a red clump and an extremely blue component, in a relative proportion [N(RHB) : N(BHB)] ~ [80 : 20]. For the BHB stellar population, [Fe/H] values of either simeq-0.7 or gtrsim+0.5 dex may provide the optimum ranges to feed the needed low-mass stars (M*ll 0.58 M⊙) that at some stage begin to join the standard red clump stars.

19. On the elliptic genera of manifolds of Spin(7) holonomy

SciTech Connect

Benjamin, Nathan; Harrison, Sarah M.; Kachru, Shamit; Paquette, Natalie M.; Whalen, Daniel

2015-12-16

Superstring compactification on a manifold of Spin(7) holonomy gives rise to a 2d worldsheet conformal field theory with an extended supersymmetry algebra. The N=1 superconformal algebra is extended by additional generators of spins 2 and 5/2, and instead of just superconformal symmetry one has a c = 12 realization of the symmetry group SW(3/2,2). In this paper, we compute the characters of this supergroup and decompose the elliptic genus of a general Spin(7) compactification in terms of these characters. Here, we find suggestive relations to various sporadic groups, which are made more precise in a companion paper.

20. On the Elliptic Genera of Manifolds of Spin(7) Holonomy

SciTech Connect

Benjamin, Nathan; Harrison, Sarah M.; Kachru, Shamit; Paquette, Natalie M.; Whalen, Daniel

2015-12-16

Superstring compactification on a manifold of Spin(7) holonomy gives rise to a 2d worldsheet conformal field theory with an extended supersymmetry algebra. The N=1N=1 superconformal algebra is extended by additional generators of spins 2 and 5/2, and instead of just superconformal symmetry one has a c = 12 realization of the symmetry group SW(3/2,2)SW(3/2,2) . In this paper, we compute the characters of this supergroup and decompose the elliptic genus of a general Spin(7) compactification in terms of these characters. We find suggestive relations to various sporadic groups, which are made more precise in a companion paper.

1. Optimization design of a 20-in. elliptical MCP-PMT

Chen, Ping; Tian, Jinshou; Wei, Yonglin; Liu, Hulin; Sai, Xiaofeng; He, Jianping; Chen, Lin; Wang, Xing; Lu, Yu

2017-01-01

This paper describes the simulation work for optimizing the newly developed 20-in. elliptical MCP-PMT by enlarging the outside diameters of the two focusing electrodes and the open area of the glass bulb. Effects of biasing voltages applied to the two focusing electrodes and the MCP input facet are studied. With the new design of the 20 in. MCP-PMT, the transit time spread of the prototype can be less than 3 ns and the collection efficiency is as much as the present prototype.

2. Chopper z-scan technique for elliptic Gaussian beams.

PubMed

Dávila-Pintle, J A; Reynoso-Lara, E; Bravo-García, Y E

2016-09-05

This paper reports an improvement to the chopper z-scan technique for elliptic Gaussian beams. This improvement results in a higher sensitivity by measuring the ratio of eclipsing time to rotating period (duty cycle) of a chopper that eclipses the beam along the main axis. It is shown that the z-scan curve of the major axis is compressed along the z-axis. This compression factor is equal to the ratio between the minor and major axes. It was found that the normalized peak-valley difference with respect to the linear value does not depend on the axis along which eclipsing occurs.

3. Incomplete block factorization preconditioning for indefinite elliptic problems

SciTech Connect

Guo, Chun-Hua

1996-12-31

The application of the finite difference method to approximate the solution of an indefinite elliptic problem produces a linear system whose coefficient matrix is block tridiagonal and symmetric indefinite. Such a linear system can be solved efficiently by a conjugate residual method, particularly when combined with a good preconditioner. We show that specific incomplete block factorization exists for the indefinite matrix if the mesh size is reasonably small. And this factorization can serve as an efficient preconditioner. Some efforts are made to estimate the eigenvalues of the preconditioned matrix. Numerical results are also given.

4. Exact revision of the elliptically bent mirror theory

SciTech Connect

Mao Chengwen; Yu Xiaohan; Xiao Tiqiao; Li Aiguo; Yang Ke; Wang Hua; Yan Fen; Deng Biao

2011-06-01

One of the main hurdles for nanometer focusing by a bending mirror lies in the theoretical surface errors by its approximations used for the traditional theory. The impacts of approximations and analytical corrections have been discussed, and the elliptically bent mirror theory has been described during exact mathematical analysis without any approximations. These approximations are harmful for the focusing system with bigger grazing angle, bigger mirror length, and bigger numerical aperture. The properties of equal-moment and single-moment bent mirrors have been described and discussed. Because of its obvious advantages, a single-moment bending mirror has high potential ability for nanometer focusing.

5. Generators for the elliptic curve y2 = x3-nx

Fujita, Yasutsugu; Terai, Nobuhiro

2010-07-01

Let E:y2 = x3-nx be an elliptic curve over the rationals with a positive integer n. Mordell's theorem asserts that the group of rational points on E is finitely generated. Our interest is in the generators for its free part. Duquesne (2007) showed that if n = (2k2-2k+1)(18k2+30k+17) is square-free, then certain two points of infinite order can always be in a system of generators. We generalize this result and show that the same is true for "infinitely many" infinite families n = n(k,l) with two variables.

6. Some fast elliptic solvers on parallel architectures and their complexities

NASA Technical Reports Server (NTRS)

1989-01-01

The discretization of separable elliptic partial differential equations leads to linear systems with special block triangular matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconsistant coefficients. A method was recently proposed to parallelize and vectorize BCR. Here, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches, including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational complexity lower than that of parallel BCR.

7. Some fast elliptic solvers on parallel architectures and their complexities

NASA Technical Reports Server (NTRS)

1989-01-01

The discretization of separable elliptic partial differential equations leads to linear systems with special block tridiagonal matrices. Several methods are known to solve these systems, the most general of which is the Block Cyclic Reduction (BCR) algorithm which handles equations with nonconstant coefficients. A method was recently proposed to parallelize and vectorize BCR. In this paper, the mapping of BCR on distributed memory architectures is discussed, and its complexity is compared with that of other approaches including the Alternating-Direction method. A fast parallel solver is also described, based on an explicit formula for the solution, which has parallel computational compelxity lower than that of parallel BCR.

8. Irreducible vector bundles on some elliptic non-Kahler threefolds

Brînzănescu, Vasile; Vuletescu, Victor

2015-05-01

We study rank-2 vector bundles on non-Kähler threefolds π : X → B, which are elliptic principal bundles with at least one non-zero Chern class over a complex surface B with no curves. In this case, we prove that every rank-2 irreducible vector bundle on X is a pull-back from B up to a twist by a line bundle. These 2-vector bundles are, via the Kobayashi-Hitchin correspondence, solutions of the Yang-Mills equations on the threefold X.

9. Construction of preconditioners for elliptic problems by substructuring. II

SciTech Connect

Bramble, J.H.; Pasciak, J.E.; Schatz, A.H.

1987-07-01

We give a method for constructing preconditioners for the discrete systems arising in the approximation of solutions of elliptic boundary value problems. These preconditioners are based on domain decomposition techniques and lead to algorithms which are well suited for parallel computing environments. The method presented in this paper leads to a preconditioned system with condition number proportional to d/h where d is the subdomain size and h is the mesh size. These techniques are applied to singularly perturbed problems and problems in the three dimensions. The results of numerical experiments illustrating the performance of the method on problems in two and three dimensions are given.

10. The construction of preconditioners for elliptic problems by substructuring, IV

SciTech Connect

Bramble, J.H.; Pasciak, J.E.; Schatz, A.H.

1989-07-01

We consider the problem of solving the algebraic system of equations which result from the discretization of elliptic boundary value problems defined on three-dimensional Euclidean space. We develop preconditioners for such systems based on substructuring (also known as domain decomposition). The resulting algorithms are well suited to emerging parallel computing architectures. We describe two techniques for developing these preconditioners. A theory for the analysis of the condition number for the resulting preconditioned system is given and the results of supporting numerical experiments are presented.

11. Iterative schemes for nonsymmetric and indefinite elliptic boundary value problems

SciTech Connect

Bramble, J.H.; Leyk, Z.; Pasciak, J.E.

1993-01-01

The purpose of this paper is twofold. The first is to describe some simple and robust iterative schemes for nonsymmetric and indefinite elliptic boundary value problems. The schemes are based in the Sobolev space H ([Omega]) and require minimal hypotheses. The second is to develop algorithms utilizing a coarse-grid approximation. This leads to iteration matrices whose eigenvalues lie in the right half of the complex plane. In fact, for symmetric indefinite problems, the iteration is reduced to a well-conditioned symmetric positive definite system which can be solved by conjugate gradient interation. Applications of the general theory as well as numerical examples are given. 20 refs., 8 tabs.

12. The construction of preconditioners for elliptic problems by substructuring, IV

SciTech Connect

Bramble, J.H.; Pasciak, J.E.; Schatz, A.H.

1987-06-01

We consider the problem of solving the algebraic system of equations which result from the discretization of elliptic boundary value problems defined on three dimensional Euclidean space. We develop preconditioners for such systems based on substructuring (also known as domain decomposition). The resulting algorithms are well suited to emerging parallel computing architectures. We describe two techniques for developing these precondictioners. A theory for the analysis of the condition number for the resulting preconditioned system is given and the results of supporting numerical experiments are presented. 16 refs., 2 tabs.

13. Iterative method for elliptic problems on regions partitioned into substructures

SciTech Connect

Bramble, J.H.; Pasciak, J.E.; Schatz, A.H.

1986-04-01

Some new preconditioners for discretizations of elliptic boundary problems are studied. With these preconditioners, the domain under consideration is broken into subdomains and preconditioners are defined which only require the solution of matrix problems on the subdomains. Analytic estimates are given which guarantee that under appropriate hypotheses, the preconditioned iterative procedure converges to the solution of the discrete equations with a rate per iteration that is independent of the number of unknowns. Numerical examples are presented which illustrate the theoretically predicted iterative convergence rates.

14. Optimal Control of the Obstacle for an Elliptic Variational Inequality

SciTech Connect

Adams, D. R.; Lenhart, S. M.; Yong, J.

1998-09-15

An optimal control problem for an elliptic obstacle variational inequality is considered. The obstacle is taken to be the control and the solution to the obstacle problem is taken to be the state. The goal is to find the optimal obstacle from H{sup 1}{sub 0} ({omega}) so that the state is close to the desired profile while the H{sup 1}({omega}) norm of the obstacle is not too large. Existence, uniqueness, and regularity as well as some characterizations of the optimal pairs are established.

15. Orientation and resonance locks for satellites in the elliptic orbit.

NASA Technical Reports Server (NTRS)

Liu, H.-S.

1972-01-01

In order to achieve the maximum strength of higher resonance locks for satellites in the elliptic orbit, the condition of satellite orientation during the process of deployment is established. It is shown that for maximum strength locks the axis of the minimum moment of inertia of satellites should point toward the attracting body at plus or minus (5/8) pi and 0 values of the true anomaly f. This condition of deployment is applicable to all cases of resonance rotation regardless of the value of lock number k and orbit eccentricity e.

16. Lipschitz Regularity for Elliptic Equations with Random Coefficients

Armstrong, Scott N.; Mourrat, Jean-Christophe

2016-01-01

We develop a higher regularity theory for general quasilinear elliptic equations and systems in divergence form with random coefficients. The main result is a large-scale L ∞-type estimate for the gradient of a solution. The estimate is proved with optimal stochastic integrability under a one-parameter family of mixing assumptions, allowing for very weak mixing with non-integrable correlations to very strong mixing (for example finite range of dependence). We also prove a quenched L 2 estimate for the error in homogenization of Dirichlet problems. The approach is based on subadditive arguments which rely on a variational formulation of general quasilinear divergence-form equations.

17. Characterization of the shape stability for nonlinear elliptic problems

Bucur, Dorin

We characterize all geometric perturbations of an open set, for which the solution of a nonlinear elliptic PDE of p-Laplacian type with Dirichlet boundary condition is stable in the L-norm. The necessary and sufficient conditions are jointly expressed by a geometric property associated to the γ-convergence. If the dimension N of the space satisfies N-1

18. Singular Solutions of Fully Nonlinear Elliptic Equations and Applications

Armstrong, Scott N.; Sirakov, Boyan; Smart, Charles K.

2012-08-01

We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of {R^n} , and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragmén-Lindelöf result as well as a principle of positive singularities in certain Lipschitz domains.

19. Conforming and nonconforming virtual element methods for elliptic problems

SciTech Connect

Cangiani, Andrea; Manzini, Gianmarco; Sutton, Oliver J.

2016-08-03

Here we present, in a unified framework, new conforming and nonconforming virtual element methods for general second-order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and nonsymmetric parts and conditions for stability and accuracy on their discrete counterparts are established. These conditions are shown to lead to optimal H1- and L2-error estimates, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the two methods is shown to be comparable.

20. Conforming and nonconforming virtual element methods for elliptic problems

DOE PAGES

Cangiani, Andrea; Manzini, Gianmarco; Sutton, Oliver J.

2016-08-03

Here we present, in a unified framework, new conforming and nonconforming virtual element methods for general second-order elliptic problems in two and three dimensions. The differential operator is split into its symmetric and nonsymmetric parts and conditions for stability and accuracy on their discrete counterparts are established. These conditions are shown to lead to optimal H1- and L2-error estimates, confirmed by numerical experiments on a set of polygonal meshes. The accuracy of the numerical approximation provided by the two methods is shown to be comparable.

1. Depletion forces on circular and elliptical obstacles induced by active matter

Leite, L. R.; Lucena, D.; Potiguar, F. Q.; Ferreira, W. P.

2016-12-01

Depletion forces exerted by self-propelled particles on circular and elliptical passive objects are studied using numerical simulations. We show that a bath of active particles can induce repulsive and attractive forces which are sensitive to the shape and orientation of the passive objects (either horizontal or vertical ellipses). The resultant force on the passive objects due to the active particles is studied as a function of the shape and orientation of the passive objects, magnitude of the angular noise, and distance between the passive objects. By increasing the distance between obstacles the magnitude of the repulsive depletion force increases, as long as such a distance is less than one active particle diameter. For longer distances, the magnitude of the force always decreases with increasing distance. We also found that attractive forces may arise for vertical ellipses at high enough area fraction.

2. Comparison of two methods for simulation of hard X-ray nanofocusing by elliptical mirrors.

SciTech Connect

Kewish, C. M.; Macrander, A. T.; Assoufid, L.; Qian, J.; X-Ray Science Division

2007-11-11

Wave-optical calculations are essential for predicting the X-ray focusing performance of precisely figured elliptical mirrors. The complex wavefield in the vicinity of the focal plane of a mirror with RMS height error in the nanometer range compared to the best-fit ellipse has been calculated using two methods. A pupil function method that treats the surface topography of a mirror as an aberration to a perfect ellipse was used to obtain the reflected amplitude and phase around the focal point downstream. The results were compared with direct propagation of waves from a point source, and it was found that both methods were in good agreement. Each approach provides advantages that are useful in designing mirrors to achieve diffraction limited focusing.

3. Comparison of two methods for simulation of hard X-ray nanofocusing by elliptical mirrors

Kewish, Cameron M.; Macrander, Albert T.; Assoufid, Lahsen; Qian, Jun

2007-11-01

Wave-optical calculations are essential for predicting the X-ray focusing performance of precisely figured elliptical mirrors. The complex wavefield in the vicinity of the focal plane of a mirror with RMS height error in the nanometer range compared to the best-fit ellipse has been calculated using two methods. A pupil function method that treats the surface topography of a mirror as an aberration to a perfect ellipse was used to obtain the reflected amplitude and phase around the focal point downstream. The results were compared with direct propagation of waves from a point source, and it was found that both methods were in good agreement. Each approach provides advantages that are useful in designing mirrors to achieve diffraction limited focusing.

4. Pattern drilling exploration: Optimum pattern types and hole spacings when searching for elliptical shaped targets

USGS Publications Warehouse

Drew, L.J.

1979-01-01

In this study the selection of the optimum type of drilling pattern to be used when exploring for elliptical shaped targets is examined. The rhombic pattern is optimal when the targets are known to have a preferred orientation. Situations can also be found where a rectangular pattern is as efficient as the rhombic pattern. A triangular or square drilling pattern should be used when the orientations of the targets are unknown. The way in which the optimum hole spacing varies as a function of (1) the cost of drilling, (2) the value of the targets, (3) the shape of the targets, (4) the target occurrence probabilities was determined for several examples. Bayes' rule was used to show how target occurrence probabilities can be revised within a multistage pattern drilling scheme. ?? 1979 Plenum Publishing Corporation.

5. Transient sloshing in half-full horizontal elliptical tanks under lateral excitation

2011-07-01

A semi-analytical mathematical model is developed to study the transient liquid sloshing characteristics in half-full horizontal cylindrical containers of elliptical cross section subjected to arbitrary lateral external acceleration. The problem solution is achieved by employing the linear potential theory in conjunction with conformal mapping, resulting in linear systems of ordinary differential equations which are truncated and then solved numerically by implementing Laplace transform technique followed by Durbin's numerical inversion scheme. A ramp-step function is used to simulate the lateral acceleration excitation during an idealized turning maneuver. The effects of tank aspect ratio, excitation input time, and baffle configuration on the resultant sloshing characteristics are examined. Limiting cases are considered and good agreements with available analytic and numerical solutions as well as experimental data are obtained.

6. Orbit compensation for the time-varying elliptically polarized wiggler with switching frequency at 100 hz

SciTech Connect

Singh, O.; Krinsky, S.

1997-07-01

In October 1996, the elliptically polarized wiggler, installed in the X13 straight section of the NSLS X-ray ring, was commissioned at an operating frequency of 100 hz. This wiggler generates circularly polarized photons in the energy range of 0.1 to 10 keV with AC modulation of polarization helicity. The vertical magnetic field is produced by a hybrid permanent magnet structure, and the horizontal magnetic field is generated by an electromagnet capable of switching at frequencies up to 100 hz. Here, the authors discuss the compensation of the residual vertical and horizontal orbit motion utilizing a time-domain algorithm employing a function generator to drive trim coils at the wiggler ends, and the wideband high precision orbit measurement system of the X-ray ring. The residual orbit motion has been reduced to a level below 1 micron, and the device has been run in regular operations with no negative effect on other users.

7. Multigrid method applied to the solution of an elliptic, generalized eigenvalue problem

SciTech Connect

Alchalabi, R.M.; Turinsky, P.J.

1996-12-31

The work presented in this paper is concerned with the development of an efficient MG algorithm for the solution of an elliptic, generalized eigenvalue problem. The application is specifically applied to the multigroup neutron diffusion equation which is discretized by utilizing the Nodal Expansion Method (NEM). The underlying relaxation method is the Power Method, also known as the (Outer-Inner Method). The inner iterations are completed using Multi-color Line SOR, and the outer iterations are accelerated using Chebyshev Semi-iterative Method. Furthermore, the MG algorithm utilizes the consistent homogenization concept to construct the restriction operator, and a form function as a prolongation operator. The MG algorithm was integrated into the reactor neutronic analysis code NESTLE, and numerical results were obtained from solving production type benchmark problems.

8. Behavior of three modes of decay channels and their self-energies of elliptic dielectric microcavity

Park, Kyu-Won; Kim, Jaewan; Jeong, Kabgyun

2016-09-01

The Lamb shift (self-energy) of an elliptic dielectric microcavity is studied. We show that the size of the Lamb shift, which is a small energy shift due to the system-environment coupling in the quantum regime, is dependent on the geometry of the boundary conditions. It shows a global transition depending on the eccentricity of the ellipsis. These transitions can be classified into three types of decay channels known as whispering-gallery modes, stable-bouncing-ball modes, and unstable-bouncing-ball modes. These modes are manifested through the Poincaré surface of section with the Husimi distribution function in classical phase space. It is found that the similarity (measured in Bhattacharyya distance) between the Husimi distributions below critical lines of two different modes increases as the difference of their self-energies decreases when the quality factors of the modes are on the same order of magnitude.

9. Separation of variables in anisotropic models and non-skew-symmetric elliptic r-matrix

Skrypnyk, Taras

2016-11-01

We solve a problem of separation of variables for the classical integrable hamiltonian systems possessing Lax matrices satisfying linear Poisson brackets with the non-skew-symmetric, non-dynamical elliptic so(3)⊗ so(3) -valued classical r-matrix. Using the corresponding Lax matrices, we present a general form of the "separating functions" B(u) and A(u) that generate the coordinates and the momenta of separation for the associated models. We consider several examples and perform the separation of variables for the classical anisotropic Euler's top, Steklov-Lyapunov model of the motion of anisotropic rigid body in the liquid, two-spin generalized Gaudin model and "spin" generalization of Steklov-Lyapunov model.

10. Effective Numerical Methods for Solving Elliptical Problems in Strengthened Sobolev Spaces

NASA Technical Reports Server (NTRS)

D'yakonov, Eugene G.

1996-01-01

Fourth-order elliptic boundary value problems in the plane can be reduced to operator equations in Hilbert spaces G that are certain subspaces of the Sobolev space W(sub 2)(exp 2)(Omega) is identical with G(sup (2)). Appearance of asymptotically optimal algorithms for Stokes type problems made it natural to focus on an approach that considers rot w is identical with (D(sub 2)w - D(sub 1)w) is identical with vector of u as a new unknown vector-function, which automatically satisfies the condition div vector of u = 0. In this work, we show that this approach can also be developed for an important class of problems from the theory of plates and shells with stiffeners. The main mathematical problem was to show that the well-known inf-sup condition (normal solvability of the divergence operator) holds for special Hilbert spaces. This result is also essential for certain hydrodynamics problems.

11. A Kernel-free Boundary Integral Method for Elliptic Boundary Value Problems ⋆

PubMed Central

Ying, Wenjun; Henriquez, Craig S.

2013-01-01

This paper presents a class of kernel-free boundary integral (KFBI) methods for general elliptic boundary value problems (BVPs). The boundary integral equations reformulated from the BVPs are solved iteratively with the GMRES method. During the iteration, the boundary and volume integrals involving Green's functions are approximated by structured grid-based numerical solutions, which avoids the need to know the analytical expressions of Green's functions. The KFBI method assumes that the larger regular domain, which embeds the original complex domain, can be easily partitioned into a hierarchy of structured grids so that fast elliptic solvers such as the fast Fourier transform (FFT) based Poisson/Helmholtz solvers or those based on geometric multigrid iterations are applicable. The structured grid-based solutions are obtained with standard finite difference method (FDM) or finite element method (FEM), where the right hand side of the resulting linear system is appropriately modified at irregular grid nodes to recover the formal accuracy of the underlying numerical scheme. Numerical results demonstrating the efficiency and accuracy of the KFBI methods are presented. It is observed that the number of GM-RES iterations used by the method for solving isotropic and moderately anisotropic BVPs is independent of the sizes of the grids that are employed to approximate the boundary and volume integrals. With the standard second-order FEMs and FDMs, the KFBI method shows a second-order convergence rate in accuracy for all of the tested Dirichlet/Neumann BVPs when the anisotropy of the diffusion tensor is not too strong. PMID:23519600

12. Feasibility of using a compact elliptical device to increase energy expenditure during sedentary activities

PubMed Central

Rovniak, Liza S.; Denlinger, LeAnn; Duveneck, Ellen; Sciamanna, Christopher N.; Kong, Lan; Freivalds, Andris; Ray, Chester A.

2013-01-01

Objectives This study aimed to evaluate the feasibility of using a compact elliptical device to increase energy expenditure during sedentary activities. A secondary aim was to evaluate if two accelerometers attached to the elliptical device could provide reliable and valid assessments of participants’ frequency and duration of elliptical device use. Design Physically inactive adults (n = 32, age range = 25–65) were recruited through local advertisements and selected using stratified random sampling based on sex, body mass index (BMI), and age. Methods Indirect calorimetry was used to assess participants’ energy expenditure while seated and while using the elliptical device at a self-selected intensity level. Participants also self-reported their interest in using the elliptical device during sedentary activities. Two Actigraph GT3X accelerometers were attached to the elliptical device to record time-use patterns. Results Participants expended a median of 179.1 kilocalories per hour while using the elliptical device (range = 108.2–269.0), or a median of 87.9 more kilocalories (range = 19.7–178.6) than they would expend per hour of sedentary sitting. Participants reported high interest in using the elliptical device during TV watching and computer work, but relatively low interest in using the device during office meetings. Women reported greater interest in using the elliptical device than men. The two accelerometers recorded identical time-use patterns on the elliptical device and demonstrated concurrent validity with time-stamped computer records. Conclusions Compact elliptical devices could increase energy expenditure during sedentary activities, and may provide proximal environmental cues for increasing energy expenditure across multiple life domains. PMID:24035273

13. Development of an innovative device for ultrasonic elliptical vibration cutting.

PubMed

Zhou, Ming; Hu, Linhua

2015-07-01

An innovative ultrasonic elliptical vibration cutting (UEVC) device with 1st resonant mode of longitudinal vibration and 3rd resonant mode of bending vibration was proposed in this paper, which can deliver higher output power compared to previous UEVC devices. Using finite element method (FEM), resonance frequencies of the longitudinal and bending vibrations were tuned to be as close as possible in order to excite these two vibrations using two-phase driving voltages at a single frequency, while wave nodes of the longitudinal and bending vibrations were also adjusted to be as coincident as possible for mounting the device at a single fixed point. Based on the simulation analysis results a prototype device was fabricated, then its vibration characteristics were evaluated by an impedance analyzer and a laser displacement sensor. With two-phase sinusoidal driving voltages both of 480 V(p-p) at an ultrasonic frequency of 20.1 kHz, the developed prototype device achieved an elliptical vibration with a longitudinal amplitude of 8.9 μm and a bending amplitude of 11.3 μm. The performance of the developed UEVC device is assessed by the cutting tests of hardened steel using single crystal diamond tools. Experimental results indicate that compared to ordinary cutting process, the tool wear is reduced significantly by using the proposed device.

14. Two high-velocity encounters of elliptical galaxies

NASA Technical Reports Server (NTRS)

Balcells, Marc; Borne, Kirk D.; Hoessel, John G.

1989-01-01

This paper describes results obtained on a simulation of two high-velocity encounters of NGC 4782/4783 and NGC 2672/2673 binary elliptical galaxies which differ substantially in mass ratio (about 1 for the first pair, and about 10 for the second). CCD images and velocities obtained from digital spectra were used to constrain simulations of the galaxy collisions. The binary orbital elements, the orientation of the orbit in the sky, the time since pericenter, and the dynamical mass of the pair were derived. Results suggested that the dumb-bell galaxy NGC 4782/4783 is not a supermassive galaxy, as was claimed earlier on the basis of the high relative velocity and high central dispersion, but has a moderate mass to luminosity ratio M/L(B) of about 10. It was concluded that its trajectory changed from hyperbolic to elliptical as a result of energy lost during the collision. It was found that the NGC 2672/2673 also has a moderate M/L(B) of about 7.

15. Analysis and Numerical Treatment of Elliptic Equations with Stochastic Data

Cheng, Shi

Many science and engineering applications are impacted by a significant amount of uncertainty in the model. Examples include groundwater flow, microscopic biological system, material science and chemical engineering systems. Common mathematical problems in these applications are elliptic equations with stochastic data. In this dissertation, we examine two types of stochastic elliptic partial differential equations(SPDEs), namely nonlinear stochastic diffusion reaction equations and general linearized elastostatic problems in random media. We begin with the construction of an analysis framework for this class of SPDEs, extending prior work of Babuska in 2010. We then use the framework both for establishing well-posedness of the continuous problems and for posing Galerkintype numerical methods. In order to solve these two types of problems, single integral weak formulations and stochastic collocation methods are applied. Moreover, a priori error estimates for stochastic collocation methods are derived, which imply that the rate of convergence is exponential, along with the order of polynomial increasing in the space of random variables. As expected, numerical experiments show the exponential rate of convergence, verified by a posterior error analysis. Finally, an adaptive strategy driven by a posterior error indicators is designed.

16. The distribution of Infrared point sources in nearby elliptical galaxies

Gogoi, Rupjyoti; Misra, Ranjeev; Puthiyaveettil, Shalima

Infra-red point sources in nearby early-type galaxies are often counterparts of sources in other wavebands such as optical and X-rays. In particular, the IR counterpart of X-ray sources may be due to a globular cluster hosting the X-ray source or could be associated directly with the binary, providing crucial information regarding their environment. In general, the IR sources would be from globular clusters and their IR colors would provide insight into their stellar composition. However, many of the IR sources maybe background objects and it is important to identify them or at least quantify the level of background contamination. Archival Spitzer IRAC images provide a unique opportunity to study these sources in nearby Ellipticals and in particular to estimate the distributions of their IR luminosity, color and distance from the center. We will present the results of such an analysis for three nearby galaxies. We have also estimated the background contamination using several blank fields. Our preliminary results suggest that IR colors can be effectively used to differentiate between the background and sources in the galaxy, and that the distribution of sources are markedly different for different Elliptical galaxies.

17. Experimental study of elliptical jet from sub to supercritical conditions

SciTech Connect

Muthukumaran, C. K.; Vaidyanathan, Aravind

2014-04-15

The jet mixing at supercritical conditions involves fluid dynamics as well as thermodynamic phenomena. All the jet mixing studies at critical conditions to the present date have focused only on axisymmetric jets. When the liquid jet is injected into supercritical environment, the thermodynamic transition could be well understood by considering one of the important fluid properties such as surface tension since it decides the existence of distinct boundary between the liquid and gaseous phase. It is well known that an elliptical liquid jet undergoes axis-switching phenomena under atmospheric conditions due to the presence of surface tension. The experimental investigations were carried out with low speed elliptical jet under supercritical condition. Investigation of the binary component system with fluoroketone jet and N{sub 2} gas as environment shows that the surface tension force dominates for a large downstream distance, indicating delayed thermodynamic transition. The increase in pressure to critical state at supercritical temperature is found to expedite the thermodynamic transition. The ligament like structures has been observed rather than droplets for supercritical pressures. However, for the single component system with fluoroketone jet and fluoroketone environment shows that the jet disintegrates into droplets as it is subjected to the chamber conditions even for the subcritical pressures and no axis switching phenomenon is observed. For a single component system, as the pressure is increased to critical state, the liquid jet exhibits gas-gas like mixing behavior and that too without exhibiting axis-switching behavior.

18. Elliptic flow in heavy-ion collisions at NICA energies

B. Ivanov, Yu.; Soldatov, A. A.

2016-08-01

The transverse-momentum-integrated elliptic flow of charged particles at midrapidity, v2 (charged), and that of identified hadrons from Au+Au collisions are analyzed in the range of incident energies relevant to the Nuclotron-based Ion Collider Facility (NICA). Simulations are performed within a three-fluid model employing three different equations of state (EoSs): a purely hadronic EoS and two versions of the EoS involving the deconfinement transition-a first-order phase transition and a smooth crossover one. The present simulations demonstrate low sensitivity of v2 (charged) to the EoS. All considered scenarios equally well reproduce recent STAR data on v2 (charged) for mid-central Au+Au collisions and properly describe its change of sign at the incident energy decrease below √{s_{NN}} ≈ 3.5 GeV. The predicted integrated elliptic flow of various species exhibits a stronger dependence on the EoS. A noticeable sensitivity to the EoS is found for anti-protons and, to a lesser extent, for K- mesons. Presently there are no experimental data that could verify these predictions. Future experiments at NICA could corroborate these findings.

19. New Traveling Wave Solutions for a Class of Nonlinear Evolution Equations

Bai, Cheng-Jie; Zhao, Hong; Xu, Heng-Ying; Zhang, Xia

The deformation mapping method is extended to solve a class of nonlinear evolution equations (NLEEs). Many types of explicit and exact traveling wave solutions, which contain solitary wave solutions, trigonometric function solutions, and Jacobian elliptic function solutions, are obtained by a simple algebraic transformation relation between the solutions of the NLEEs and those of the cubic nonlinear Klein-Gordon (NKG) equation.

20. Lateral Migration and Rotational Motion of Elliptic Particles in Planar Poiseuille Flow

NASA Technical Reports Server (NTRS)

Qi, Dewei; Luo, Li-Shi; Aravamuthan, Raja; Strieder, William; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

Simulations of elliptic particulate suspensions in the planar Poiseuille flow are performed by using the lattice Boltzmann equation. Effects of the multi-particle on the lateral migration and rotational motion of both neutrally and non-neutrally buoyant elliptic particles are investigated. Low and intermediate total particle volume fraction f(sub a) = 13%, 15%, and 40% are considered in this work.

1. Some Improvements on Signed Window Algorithms for Scalar Multiplications in Elliptic Curve Cryptosystems

NASA Technical Reports Server (NTRS)

Vo, San C.; Biegel, Bryan (Technical Monitor)

2001-01-01

Scalar multiplication is an essential operation in elliptic curve cryptosystems because its implementation determines the speed and the memory storage requirements. This paper discusses some improvements on two popular signed window algorithms for implementing scalar multiplications of an elliptic curve point - Morain-Olivos's algorithm and Koyarna-Tsuruoka's algorithm.

2. The Sylvester equation and the elliptic Korteweg-de Vries system

Sun, Ying-ying; Zhang, Da-jun; Nijhoff, Frank W.

2017-03-01

The elliptic potential Korteweg-de Vries lattice system is a multi-component extension of the lattice potential Korteweg-de Vries equation, whose soliton solutions are associated with an elliptic Cauchy kernel (i.e., a Cauchy kernel on the torus). In this paper we generalize the class of solutions by allowing the spectral parameter to be a full matrix obeying a matrix version of the equation of the elliptic curve, and for the Cauchy matrix to be a solution of a Sylvester type matrix equation subject to this matrix elliptic curve equation. The construction involves solving the matrix elliptic curve equation by using Toeplitz matrix techniques, and analysing the solution of the Sylvester equation in terms of Jordan normal forms. Furthermore, we consider the continuum limit system associated with the elliptic potential Korteweg-de Vries system, and analyse the dynamics of the soliton solutions, which reveals some new features of the elliptic system in comparison to the non-elliptic case.

3. A Novel Numerical Algorithm of Numerov Type for 2D Quasi-linear Elliptic Boundary Value Problems

Mohanty, R. K.; Kumar, Ravindra

2014-11-01

In this article, using three function evaluations, we discuss a nine-point compact scheme of O(Δ y2 + Δ x4) based on Numerov-type discretization for the solution of 2D quasi-linear elliptic equations with given Dirichlet boundary conditions, where Δy > 0 and Δx > 0 are grid sizes in y- and x-directions, respectively. Iterative methods for diffusion-convection equation are discussed in detail. We use block iterative methods to solve the system of algebraic linear and nonlinear difference equations. Comparative results of some physical problems are given to illustrate the usefulness of the proposed method.

4. A reconstruction algorithm based on topological gradient for an inverse problem related to a semilinear elliptic boundary value problem

Beretta, Elena; Manzoni, Andrea; Ratti, Luca

2017-03-01

In this paper we develop a reconstruction algorithm for the solution of an inverse boundary value problem dealing with a semilinear elliptic partial differential equation of interest in cardiac electrophysiology. The goal is the detection of small inhomogeneities located inside a domain Ω , where the coefficients of the equation are altered, starting from observations of the solution of the equation on the boundary \\partial Ω . Exploiting theoretical results recently achieved in [13], we implement a reconstruction procedure based on the computation of the topological gradient of a suitable cost functional. Numerical results obtained for several test cases finally assess the feasibility and the accuracy of the proposed technique.

5. Stability of two groups of multi-revolution elliptic halo orbits in the elliptic restricted three-body problem

Peng, Hao; Xu, Shijie

2015-11-01

The multi-revolution elliptic halo (ME-Halo) orbit is a kind of strictly periodic orbit existing in the elliptic restricted three-body problem (ERTBP) model. Its remarkable features include that it survives the eccentricity perturbation of the primaries, it has a long period commeasurable with the primary period and that its stability property varies greatly as the eccentricity. The authors utilized continuation methods together with the multi-segment optimization method to generate two groups of ME-Halo orbits, and then systematically investigated their stability evolution with respect to the eccentricity and the mass ratio of the primaries. These parameters show complicate impacts on the stability. Some ME-Halo orbits can possess more than one pairs of real eigenvalue, some have negative real eigenvalues or complex eigenvalues out of the unit circle. For certain parameters, continuation failures are observed to be accompanied by a series of eigenvalue collision and bifurcations. The results in this paper can help to understand the nonautonomous dynamic of the ERTBP and can further aid in understanding the dynamical environment for real-world applications and, thus, contribute to the trajectory development process.

6. New schemes in the adjustment of bendable, elliptical mirrors using a long trace profiler

SciTech Connect

Rah, S.

1997-08-01

The Long Trace Profiler (LTP), an instrument for measuring the slope profile of long X-ray mirrors, has been used for adjusting bendable mirrors. Often an elliptical profile is desired for the mirror surface, since many synchrotron applications involve imaging a point source to a point image. Several techniques have been used in the past for adjusting the profile measured in height or slope of a bendable mirror. Underwood et al. have used collimated X-rays for achieving desired surface shape for bent glass optics. Non linear curve fitting using the simplex algorithm was later used to determine the best fit ellipse to the surface under test. A more recent method uses a combination of least squares polynomial fitting to the measured slope function in order to enable rapid adjustment to the desired shape. The mirror has mechanical adjustments corresponding to the first and second order terms of the desired slope polynomial, which correspond to defocus and coma, respectively. The higher order terms are realized by shaping the width of the mirror to produce the optimal elliptical surface when bent. The difference between desired and measured surface slope profiles allows us to make methodical adjustments to the bendable mirror based on changes in the signs and magnitudes of the polynomial coefficients. This technique gives rapid convergence to the desired shape of the measured surface, even when we have no information about the bender, other than the desired shape of the optical surface. Nonlinear curve fitting can be used at the end of the process for fine adjustments, and to determine the over all best fit parameters of the surface. This technique could be generalized to other shapes such as toroids.

7. Acoustic radiation force on a rigid elliptical cylinder in plane (quasi)standing waves

SciTech Connect

Mitri, F. G.

2015-12-07

The acoustic radiation force on a 2D elliptical (non-circular) cylinder centered on the axis of wave propagation of plane quasi-standing and standing waves is derived, based on the partial-wave series expansion (PWSE) method in cylindrical coordinates. A non-dimensional acoustic radiation force function, which is the radiation force per unit length, per characteristic energy density and per unit cross-sectional surface of the ellipse, is defined in terms of the scattering coefficients that are determined by applying the Neumann boundary condition for an immovable surface. A system of linear equations involving a single numerical integration procedure is solved by matrix inversion. Numerical simulations showing the transition from the quasi-standing to the (equi-amplitude) standing wave behaviour are performed with particular emphasis on the aspect ratio a/b, where a and b are the ellipse semi-axes, as well as the dimensionless size parameter kb (where k is the wavenumber), without the restriction to a particular range of frequencies. It is found that at high kb values > 1, the radiation force per length with broadside incidence is larger, whereas the opposite situation occurs in the long-wavelength limit (i.e., kb < 1). The results are particularly relevant in acoustic levitation of elliptical cylinders, the acoustic stabilization of liquid columns in a host medium, acousto-fluidics devices, and other particle dynamics applications to name a few. Moreover, the formalism presented here may be effectively applied to compute the acoustic radiation force on other 2D surfaces of arbitrary shape such as super-ellipses, Chebyshev cylindrical particles, or other non-circular geometries.

8. Fully differential study on dissociative ionization dynamics of deuteron molecules in strong elliptical laser fields

Shao, Yun; He, Peilun; Liu, Ming-Ming; Sun, Xufei; Li, Min; Deng, Yongkai; Wu, Chengyin; He, Feng; Gong, Qihuang; Liu, Yunquan

2017-03-01

Deuteron momentum distributions from the dissociative ionization of D2 in intense elliptically polarized laser fields have been explored in a joint experimental and numerical study. The asymmetrical charge localization in the dissociative D2 + offers a large torque, and thus an elliptically polarized laser field efficiently rotates the molecular ion during its dissociation, resulting in the emission of deuterons finally deviating from the bond direction at the instant of tunneling ionization of D2. The rotating torque of the molecular ions increases with the field ellipticity, leading to an ellipticity-dependent tilt angle for the deuteron momentum distribution. Due to the notable rotation of D2 + during its dissociation, the photoelectron angular distributions in the laboratory frame and the molecular frame are distinct, which illustrates that the axial recoil approximation is broken for discussing the photoelectron angular distributions of molecules in elliptically polarized laser fields.

9. Dark matter deprivation in the field elliptical galaxy NGC 7507

Lane, Richard R.; Salinas, Ricardo; Richtler, Tom

2015-02-01

Context. Previous studies have shown that the kinematics of the field elliptical galaxy NGC 7507 do not necessarily require dark matter. This is troubling because, in the context of ΛCDM cosmologies, all galaxies should have a large dark matter component. Aims: Our aims are to determine the rotation and velocity dispersion profile out to larger radii than do previous studies, and, therefore, more accurately estimate of the dark matter content of the galaxy. Methods: We use penalised pixel-fitting software to extract velocities and velocity dispersions from GMOS slit mask spectra. Using Jeans and MONDian modelling, we then produce models with the goal of fitting the velocity dispersion data. Results: NGC 7507 has a two-component stellar halo, with the outer halo counter rotating with respect to the inner halo, with a kinematic boundary at a radius of ~110'' (~12.4 kpc). The velocity dispersion profile exhibits an increase at ~70'' (~7.9 kpc), reminiscent of several other elliptical galaxies. Our best fit models are those under mild anisotropy, which include ~100 times less dark matter than predicted by ΛCDM, although mildly anisotropic models that are completely dark matter free fit the measured dynamics almost equally well. Our MONDian models, both isotropic and anisotropic, systematically fail to reproduce the measured velocity dispersions at almost all radii. Conclusions: The counter-rotating outer halo implies a merger remnant, as does the increase in velocity dispersion at ~70''. From simulations it seems plausible that the merger that caused the increase in velocity dispersion was a spiral-spiral merger. Our Jeans models are completely consistent with a no dark matter scenario, however, some dark matter can be accommodated, although at much lower concentrations than predicted by ΛCDM simulations. This indicates that NGC 7507 may be a dark matter free elliptical galaxy. Regardless of whether NGC 7507 is completely dark matter free or very dark matter poor

10. Violent Relaxation, Dynamical Instabilities and the Formation of Elliptical Galaxies

Aguilar, L. A.

1990-11-01

11. Quasi-exact-solvability of the {{A}_{2}}/{{G}_{2}} elliptic model: algebraic forms, sl(3)/{{g}^{(2)}} hidden algebra, and polynomial eigenfunctions

Sokolov, Vladimir V.; Turbiner, Alexander V.

2015-04-01

The potential of the A2 quantum elliptic model (three-body Calogero-Moser elliptic model) is defined by the pairwise three-body interaction through the Weierstrass ℘-function and has a single coupling constant. A change of variables has been found, which are A2 elliptic invariants, such that the potential becomes a rational function, while the flat space metric, as well as its associated vector, are polynomials in two variables. It is shown that the model possesses the hidden sl(3) algebra—the Hamiltonian is an element of the universal enveloping algebra {{U}sl(3)} for the arbitrary coupling constant—thus, it is equivalent to the sl(3)-quantum Euler-Arnold top. The integral, in a form of the third order differential operator with polynomial coefficients, is constructed explicitly, being also an element of {{U}sl(3)}. It is shown that there exists a discrete sequence of the coupling constants for which a finite number of polynomial eigenfunctions, up to a (non-singular) gauge factor, occurs. For these values of the coupling constants there exists a particular integral: it commutes with the Hamiltonian in action on the space of polynomial eigenfunctions, and the Hamiltonian is invariant with respect to two-dimensional projective transformations. It is shown that the A2 model has another hidden algebra {{g}(2)} introduced in Rosenbaum et al (1998 Int. J. Mod. Phys. A 13 3885). The potential of the G2 quantum elliptic model (three-body Wolfes elliptic model) is defined by the pairwise and three-body interactions through the Weierstrass ℘-function and has two coupling constants. A change of variables has been found, which are G2 elliptic invariants, such that the potential becomes a rational function, while the flat space metric, as well as its associated vector, are polynomials in two variables. It is shown the model possesses the hidden {{g}(2)} algebra. It is shown that there exists a discrete family of the coupling constants for which a finite number of

12. Analysis of a parallelized nonlinear elliptic boundary value problem solver with application to reacting flows

NASA Technical Reports Server (NTRS)

Keyes, David E.; Smooke, Mitchell D.

1987-01-01

A parallelized finite difference code based on the Newton method for systems of nonlinear elliptic boundary value problems in two dimensions is analyzed in terms of computational complexity and parallel efficiency. An approximate cost function depending on 15 dimensionless parameters is derived for algorithms based on stripwise and boxwise decompositions of the domain and a one-to-one assignment of the strip or box subdomains to processors. The sensitivity of the cost functions to the parameters is explored in regions of parameter space corresponding to model small-order systems with inexpensive function evaluations and also a coupled system of nineteen equations with very expensive function evaluations. The algorithm was implemented on the Intel Hypercube, and some experimental results for the model problems with stripwise decompositions are presented and compared with the theory. In the context of computational combustion problems, multiprocessors of either message-passing or shared-memory type may be employed with stripwise decompositions to realize speedup of O(n), where n is mesh resolution in one direction, for reasonable n.

13. Blow-up rate and uniqueness of singular radial solutions for a class of quasi-linear elliptic equations

Xie, Zhifu; Zhao, Chunshan

We establish the uniqueness and the blow-up rate of the large positive solution of the quasi-linear elliptic problem -Δu=λu-b(x)h(u) in B(x) with boundary condition u=+∞ on ∂B(x), where B(x) is a ball centered at x∈R with radius R, N⩾3, 2⩽p<∞, λ>0 are constants and the weight function b is a positive radially symmetrical function. We only require h(u) to be a locally Lipschitz function with h(u)/u increasing on (0,∞) and h(u)˜u for large u with q>p-1. Our results extend the previous work [Z. Xie, Uniqueness and blow-up rate of large solutions for elliptic equation -Δu=λu-b(x)h(u), J. Differential Equations 247 (2009) 344-363] from case p=2 to case 2⩽p<∞.

14. Dust and ionized gas in active radio elliptical galaxies

NASA Technical Reports Server (NTRS)

Forbes, D. A.; Sparks, W. B.; Macchetto, F. D.

1990-01-01

The authors present broad and narrow bandwidth imaging of three southern elliptical galaxies which have flat-spectrum active radio cores (NGC 1052, IC 1459 and NGC 6958). All three contain dust and extended low excitation optical line emission, particularly extensive in the case of NGC 1052 which has a large H alpha + (NII) luminosity. Both NGC 1052 and IC 1459 have a spiral morphology in emission-line images. All three display independent strong evidence that a merger or infall event has recently occurred, i.e., extensive and infalling HI gas in NGC 1052, a counter-rotating core in IC 1459 and Malin-Carter shells in NGC 6958. This infall event is the most likely origin for the emission-line gas and dust, and the authors are currently investigating possible excitation mechanisms (Sparks et al. 1990).

15. Multisatellite constellation configuration selection for multiregional highly elliptical orbit constellations

NASA Technical Reports Server (NTRS)

Matossian, Mark G.

1994-01-01

The Archimedes Project is a joint effort of the European Space Agency (ESA) and the National Space Development Agency of Japan (NASDA). The primary goal of the Archimedes project is to perform a technical feasibility analysis and preliminary design of a highly inclined multisatellite constellation for direct broadcast and mobile communications services for Europe, Japan and much of North America. This report addresses one aspect of this project, specifically an analysis of continuous satellite coverage using multiregional highly elliptical orbits (M-HEO's). The analysis methodology and ensuing software tool, named SPIFF, were developed specifically for this project by the author during the summer of 1992 under the STA/NSF Summer Institute in Japan Program at Tsukuba Space Center.

16. Asymptotics of solutions of some nonlinear elliptic systems

SciTech Connect

Bidaut-Veron, M.F.; Raoux, T.

1996-12-31

This paper deals with the local and global behaviour of the positive solutions of the semilinear elliptic system in R{sup N} (N{ge}3) {Delta}u+{vert_bar}x{vert_bar}{sup {sigma}}u{sup q}v{sup p+1} =0, {Delta}v+{vert_bar}x{vert_bar}{sup {sigma}}u{sup q+1}v{sup p}=0, where {sigma},p,q{epsilon}R, and p,q>0. Our main results in the fact that the solutions satisfy Harnack inequality when Q = p+q+1<(N+2)/(N-2), which gives local estimates. Without this assumption on Q, we give the precise behaviour of the solutions, provided that these estimates are true. When Q < (N+2)/(N-2), the solutions can also present an anisotropic behaviour. 34 refs.

17. Atmospheric braking to circularize an elliptical Venus orbit

NASA Technical Reports Server (NTRS)

Mcronald, A. D.; Nock, K. T.

1977-01-01

The use of atmospheric drag to circularize an elliptical spacecraft orbit at Venus is analyzed parametrically for the Venus Orbital Imaging Radar Mission (VOIR) in 1983. Navigation, maneuver, and guidance requirements are discussed for the decay of a 24-hr orbit to a close circular orbit in about 30-60 days. A prototype 'Aerobrake' is described which is approximately 5 m in diameter and 25 kg in mass and which replaces a chemical retroengine of about 1300 kg in mass (delta V = 2.5 km/s) by a 700 kg in-orbit mass. The aerobrake, a light deployable Inconel sheet, shields the spacecraft from the flow and radiates the aerodynamic heating.

18. Explicit guidance of drag modulated aeroassisted transfer between elliptical orbits

NASA Technical Reports Server (NTRS)

Vinh, N. X.; Mease, K. D.; Hanson, J. M.; Johannesen, J. R.

1984-01-01

This paper presents the complete analysis of the problem of minimum-fuel aeroassisted transfer between coplanar elliptical orbits in the case where the orientation of the final orbit is free for selection in the optimization process. The comparison between the optimal pure propulsive transfer and the idealized aeroassisted transfer, by several passages through the atmosphere, is made. In the case where aeroassisted transfer provides fuel saving, a practical scheme for its realization by one passage is proposed. The maneuver consists of three phases: a deorbit phase for nonzero entry angle, followed by an atmospheric fly-through with variable drag control and completed by a postatmospheric phase. An explicit guidance formula for drag control is derived and it is shown that the required exit speed for ascent to the final orbit can be obtained with a very high degree of accuracy.

19. Stellar Population Synthesis of the Elliptical Galaxy NGC 4649

Chun, Mun-Suk; Gim, Moon-Whan; Sohn, Young-Jong

2001-12-01

We investigated population of the elliptical galaxy NGC 4649 using the spectral synthesis technique based on the linear program in the spectral regions between 3160Å to 10800Å. We used the spectral data of stars obtained by Gunn & Stryker (1983), and the integrated spectrum of NGC 4649 observed by Bertola et al. (1982). Among four models with different main sequence turn-off points, G8-K0V main sequence turn-off model is best fitted to the integrated spectrum of NGC 4649. We also found that super metal rich K giants are needed to describe the absorption lines in the long wavelength regions of integrated spectrum of NGC 4649. The mass to absolute light ratio obtained from the spectral synthesis is ~20 similar to those calculated dynamically.

20. On the elliptical polarization of Jupiter's decametric radio emission

NASA Technical Reports Server (NTRS)

Melrose, D. B.; Dulk, G. A.

1991-01-01

The origin of the 100 percent elliptical polarization of Jupiter's decametric radio emission is investigated. The transfer of polarized radiation when coupling of the Stokes parameters is important is studied, and it is found, in agreement with earlier authors, that the density in and near the source region must be so low that the polarization remains fixed along the ray path. The polarization of the cyclotron maser radiation in these circumstances is determined, and it is found that the dispersion relation of the rarefied plasma composed of energetic, anisotropic electrons is like that in the vacuum. It is also found that the growth rate is sufficient to saturate the maser and account for the observed brightness temperature. Possible sources of plasma in and near the source region in Jupiter's inner, polar magnetosphere are considered.

1. A domain decomposition algorithm for solving large elliptic problems

SciTech Connect

Nolan, M.P.

1991-01-01

AN algorithm which efficiently solves large systems of equations arising from the discretization of a single second-order elliptic partial differential equation is discussed. The global domain is partitioned into not necessarily disjoint subdomains which are traversed using the Schwarz Alternating Procedure. On each subdomain the multigrid method is used to advance the solution. The algorithm has the potential to decrease solution time when data is stored across multiple levels of a memory hierarchy. Results are presented for a virtual memory, vector multiprocessor architecture. A study of choice of inner iteration procedure and subdomain overlap is presented for a model problem, solved with two and four subdomains, sequentially and in parallel. Microtasking multiprocessing results are reported for multigrid on the Alliant FX-8 vector-multiprocessor. A convergence proof for a class of matrix splittings for the two-dimensional Helmholtz equation is given. 70 refs., 3 figs., 20 tabs.

2. Dynamical modeling of elliptical galaxies. II. numerical prolate models

SciTech Connect

Lake, G.

1981-01-01

The analytical solutions of Paper I are generalized using the self-consistent field method. These prolate models are constructed using only two integrals of motion, the energy (E) and the angular momentum about the axis of symmetry, (L/sub z/). They are the first models with flattening greater than E4 which possess elliptical isophotes and realistic density profiles. The singularity in the surface brightness which characterized the models of Paper I has been removed by smoothing the extreme suppression of L/sub z/. The new models (like those of Paper I) still show a sharp rise in the velocity dispersion at the center. This feature is due to the strongly anisotropic velocity dispersions, rather than the existence of a supermassive object.

3. Grid Setting in Seismic Tomography for Elliptical Anisotropic Media

Cardarelli, E.; Cerreto, A.

2017-03-01

In this study, we discuss the adjustment of grid definition in relation to seismic tomography in the case of elliptical anisotropic media. To optimize cell numbers and dimensions, the results of a staggered grid method are used to define an adjusted grid as a starting model for inversion. This procedure can be iterated, although improvements are not assured. First, two synthetic models with growing level of complexity are performed. Next, data from a previously conducted field survey are analyzed by introducing staggered grids. Finally, the results are compared with the previous results. The adjusted grid represents a technique that can be used to obtain an effective way of discretizing the model domain for further inversion, which often improves results for the velocity model. These conclusions can also be applied to isotropic media, as described in this study.

4. Truncated stacked elliptical patch antenna for broadband performance

Sharma, Vijay; Sharma, Brajraj; Sharma, K. B.; Bhatnagar, D.

2013-01-01

A new design of a single-feed truncated elliptical patch antenna with and without slots for broadband performance with stacked arrangement is proposed in this paper and its performance is tested in free space. This multilayered rectangular microstrip antenna is designed and analyzed by using the ie3d simulation software. In between conducting and ground plane, designed antenna has two glass epoxy fr-4 substrates separated by an air substrate to attain broadband performance. The impedance bandwidth of designed antenna is better than 2.11GHz or 60% with respect to the central frequency. The simulated e plane co and cross radiation patterns are identical in shape for most of the part of bandwidth however at higher frequency side due to the presence of higher modes and cross polarization the radiation pattern are no more directive normal to patch geometry.

5. Algorithms and data structures for adaptive multigrid elliptic solvers

NASA Technical Reports Server (NTRS)

Vanrosendale, J.

1983-01-01

Adaptive refinement and the complicated data structures required to support it are discussed. These data structures must be carefully tuned, especially in three dimensions where the time and storage requirements of algorithms are crucial. Another major issue is grid generation. The options available seem to be curvilinear fitted grids, constructed on iterative graphics systems, and unfitted Cartesian grids, which can be constructed automatically. On several grounds, including storage requirements, the second option seems preferrable for the well behaved scalar elliptic problems considered here. A variety of techniques for treatment of boundary conditions on such grids are reviewed. A new approach, which may overcome some of the difficulties encountered with previous approaches, is also presented.

6. Construction of preconditioners for elliptic problems by substructuring, III

SciTech Connect

Bramble, J.H.; Pasciak, J.E.; Schatz, A.H.

1988-10-01

In earlier parts of this series of papers, we constructed preconditioners for the discrete systems of equations arising from the numerical approximation of elliptic boundary value problems. The resulting algorithms are well suited for implementation on computers with parallel architecture. In this paper, we will develop a technique which utilizes these earlier methods to derive even more efficient preconditioners. The iterative algorithms using these new preconditioners converge to the solution of the discrete equations with a rate that is independent of the number of unknowns. These preconditioners involve an incomplete Chebyshev iteration for boundary interface conditions which results in a negligible increase in the amount of computational work. Theoretical estimates and the results of numerical experiments are given which demonstrate the effectiveness of the methods.

7. Construction of preconditioners for elliptic problems by substructuring. I

SciTech Connect

Bramble, J.H.; Pasciak, J.E.; Schatz, A.H.

1986-07-01

We consider the problem of solving the algebraic system of equations which arise from the discretization of symmetric elliptic boundary value problems via finite element methods. A new class of preconditioners for the discrete system is developed based on substructuring (also known as domain decomposition). The resulting preconditioned algorithms are well suited to emerging parallel computing architectures. The proposed methods are applicable to problems on general domains involving differential operators with rather general coefficients. A basic theory for the analysis of the condition number of the preconditioned system (which determines the iterative convergence rate of the algorithm) is given. Techniques for applying the theory and algorithms to problems with irregular geometry are discussed and the results of extensive numerical experiments are reported.

8. Optimal least-squares finite element method for elliptic problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Povinelli, Louis A.

1991-01-01

An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.

9. WEAK GALERKIN METHODS FOR SECOND ORDER ELLIPTIC INTERFACE PROBLEMS

PubMed Central

MU, LIN; WANG, JUNPING; WEI, GUOWEI; YE, XIU; ZHAO, SHAN

2013-01-01

Weak Galerkin methods refer to general finite element methods for partial differential equations (PDEs) in which differential operators are approximated by their weak forms as distributions. Such weak forms give rise to desirable flexibilities in enforcing boundary and interface conditions. A weak Galerkin finite element method (WG-FEM) is developed in this paper for solving elliptic PDEs with discontinuous coefficients and interfaces. Theoretically, it is proved that high order numerical schemes can be designed by using the WG-FEM with polynomials of high order on each element. Extensive numerical experiments have been carried to validate the WG-FEM for solving second order elliptic interface problems. High order of convergence is numerically confirmed in both L2 and L∞ norms for the piecewise linear WG-FEM. Special attention is paid to solve many interface problems, in which the solution possesses a certain singularity due to the nonsmoothness of the interface. A challenge in research is to design nearly second order numerical methods that work well for problems with low regularity in the solution. The best known numerical scheme in the literature is of order O(h) to O(h1.5) for the solution itself in L∞ norm. It is demonstrated that the WG-FEM of the lowest order, i.e., the piecewise constant WG-FEM, is capable of delivering numerical approximations that are of order O(h1.75) to O(h2) in the L∞ norm for C1 or Lipschitz continuous interfaces associated with a C1 or H2 continuous solution. PMID:24072935

10. Underexpanded Screeching Jets From Circular, Rectangular, and Elliptic Nozzles

NASA Technical Reports Server (NTRS)

Panda, J.; Raman, G.; Zaman, K. B. M. Q.

2004-01-01

The screech frequency and amplitude, the shock spacing, the hydrodynamic-acoustic standing wave spacing, and the convective velocity of large organized structures are measured in the nominal Mach number range of 1.1 less than or = Mj less that or = l0.9 for supersonic, underexpanded jets exhausting from a circular, a rectangular and an elliptic nozzle. This provides a carefully measured data set useful in comparing the importance of various physical parameters in the screech generation process. The hydrodynamic-acoustic standing wave is formed between the potential pressure field of large turbulent structures and the acoustic pressure field of the screech sound. It has been demonstrated earlier that in the currently available screech frequency prediction models replacement of the shock spacing by the standing wave spacing provides an exact expression. In view of this newly found evidence, a comparison is made between the average standing wavelength and the average shock spacing. It is found that there exists a small, yet important, difference, which is dependent on the azimuthal screech mode. For example, in the flapping modes of circular, rectangular, and elliptic jets, the standing wavelength is slightly longer than the shock spacing, while for the helical screech mode in a circular jet the opposite is true. This difference accounts for the departure of the existing models from predicting the exact screech frequency. Another important parameter, necessary in screech prediction, is the convective velocity of the large organized structures. It is demonstrated that the presence of the hydrodynamic-acoustic standing wave, even inside the jet shear layer, becomes a significant source of error in the convective velocity data obtained using the conventional methods. However, a new relationship, using the standing wavelength and screech frequency is shown to provide more accurate results.

11. Early-Type Galaxies in Extremely Isolated Environments: Typical Ellipticals?

Marcum, Pamela M.; Aars, Christian E.; Fanelli, Michael N.

2004-06-01

We have conducted a BVR imaging survey of nine early-type galaxies previously verified to exist in extremely isolated environments. Our goals are to establish a baseline of morphological and photometric properties for spheroidal systems evolving in extremely low-density environments and to compare these properties with signatures predicted for merged galaxy groups. We find that these isolated systems are underluminous by at least a magnitude compared with objects identified as merged group remnants in other studies. Image processing techniques sensitive to shell features produced no detections, a result in strong contrast to the high frequency of such structures found in other isolated elliptical galaxies. Two objects, KIG 164 and KIG 870, appear to be merger remnants, as indicated by their disturbed morphology, apparent tidal features, and blue colors. KIG 164 exhibits an asymmetric nuclear morphology and a low surface brightness bridge'' between it and a possible dwarf satellite. KIG 870 shows both fan-shaped emission at large radii and a possible double nucleus. Two other galaxies, KIG 412 and KIG 792, are also blue, but without any morphological peculiarities, suggesting that these systems are advanced mergers, older than KIG 164 and KIG 870. Two systems appear to be isolated lenticular galaxies with no evidence of a merger history. Based on their red colors, good fit to a R1/4-law light distribution, and the lack of morphological peculiarities, two other galaxies, KIG 557 and KIG 824, are found to be excellent candidates for passively evolving primordial elliptical galaxies formed early in cosmic time. Optical data were obtained with the 2.1 m Otto Struve telescope at McDonald Observatory, which is operated by the University of Texas at Austin.

12. The similar stellar populations of quiescent spiral and elliptical galaxies

Robaina, Aday R.; Hoyle, Ben; Gallazzi, Anna; Jiménez, Raul; van der Wel, Arjen; Verde, Licia

2012-12-01

We compare the stellar population properties in the central regions of visually classified non-star-forming spiral and elliptical galaxies from Galaxy Zoo and Sloan Digital Sky Survey (SDSS) Data Release 7. The galaxies lie in the redshift range 0.04 < z < 0.1 and have stellar masses larger than log M* = 10.4. We select only face-on spiral galaxies in order to avoid contamination by light from the disc in the SDSS fibre and enabling the robust visual identification of spiral structure. Overall, we find that galaxies with larger central stellar velocity dispersions, regardless of morphological type, have older ages, higher metallicities and an increased overabundance of α-elements. Age and α-enhancement, at fixed velocity dispersion, do not depend on morphological type. The only parameter that, at a given velocity dispersion, correlates with morphological type is metallicity, where the metallicity of the bulges of spiral galaxies is 0.07 dex higher than that of the ellipticals. However, for galaxies with a given total stellar mass, this dependence on morphology disappears. Under the assumption that, for our sample, the velocity dispersion traces the mass of the bulge alone, as opposed to the total mass (bulge+disc) of the galaxy, our results imply that the formation epoch of galaxy and the duration of its star-forming period are linked to the mass of the bulge. The extent to which metals are retained within the galaxy, and not removed as a result of outflows, is determined by the total mass of the galaxy.

13. WEAK GALERKIN METHODS FOR SECOND ORDER ELLIPTIC INTERFACE PROBLEMS.

PubMed

Mu, Lin; Wang, Junping; Wei, Guowei; Ye, Xiu; Zhao, Shan

2013-10-01

Weak Galerkin methods refer to general finite element methods for partial differential equations (PDEs) in which differential operators are approximated by their weak forms as distributions. Such weak forms give rise to desirable flexibilities in enforcing boundary and interface conditions. A weak Galerkin finite element method (WG-FEM) is developed in this paper for solving elliptic PDEs with discontinuous coefficients and interfaces. Theoretically, it is proved that high order numerical schemes can be designed by using the WG-FEM with polynomials of high order on each element. Extensive numerical experiments have been carried to validate the WG-FEM for solving second order elliptic interface problems. High order of convergence is numerically confirmed in both L2 and L∞ norms for the piecewise linear WG-FEM. Special attention is paid to solve many interface problems, in which the solution possesses a certain singularity due to the nonsmoothness of the interface. A challenge in research is to design nearly second order numerical methods that work well for problems with low regularity in the solution. The best known numerical scheme in the literature is of order [Formula: see text] to [Formula: see text] for the solution itself in L∞ norm. It is demonstrated that the WG-FEM of the lowest order, i.e., the piecewise constant WG-FEM, is capable of delivering numerical approximations that are of order [Formula: see text] to [Formula: see text] in the L∞ norm for C(1) or Lipschitz continuous interfaces associated with a C(1) or H(2) continuous solution.

14. Elliptically framed tip-tilt mirror optimized for stellar tracking

Clark, James H.; Penado, F. E.; Petak, Jeremy

2015-09-01

We compare a design innovation of an elliptically framed tip-tilt optical tracker with an existing circularly framed tracker for the Navy Precision Optical Interferometer. The tracker stabilizes a 12.5 cm stellar beam on a target hundreds of meters away and requires an increase in operational frequency. We reduced mass and size by integrating an elliptical mirror as one of the rotating components, which eliminated a rotating frame. We used the same materials as the existing tracker; however, light-weighted both the aluminum frame and Zerodur® mirror. We generated a computer-aided design model, converted it into a finite element model and performed modal analysis on two load cases. In load case 1, we tied down three points on the bottom surface of the tracker corresponding to the tie-down points of the comparison tracker. This reveals a first mode (lowest) frequency of 140 Hz, a factor of two over the baseline tracker's first mode frequency of 67 Hz. In load case 2, we constrained four additional points inboard of the corners of the tracker base, for a total of seven tie-downs, simulating a firmly bolted and secured mount. The first mode of vibration for this case is 211 Hz, an increase over load case 1 by a factor of 1.5 and more than three times the fundamental frequency of the existing tracker. We conclude that these geometrical changes with the additional tie-down bolts are a viable solution path forward to improve steering speed and recommend a continuation with this effort.

15. Aspect ratio effect on shock-accelerated elliptic gas cylinders

Zou, Liyong; Liao, Shenfei; Liu, Cangli; Wang, Yanping; Zhai, Zhigang

2016-03-01

The evolution of an elliptic heavy-gas (SF6) cylinder accelerated by a planar weak shock wave is investigated experimentally using particle image velocimetry (PIV) diagnostics, and the emphasis is on the aspect ratio effect on shock-elliptic cylinder interaction. Experiments are conducted at five different aspect ratios (the ratio of length in streamwise and spanwise directions) varied from 0.25 to 4.0. PIV raw images and quantitative flow field data are obtained at t = 0.6 ms after the shock impact. As the aspect ratio increases, the interface morphology develops faster owing to more vorticity produced along the interface and smaller vortex spacing between the two vortex cores. For each case in this study, the maximal fluctuating velocity locates at the middle point of the two counter-vortices. The histograms of fluctuating velocity reveal that a distinct double-peak structure appears in the largest aspect ratio case in comparison with a single-peak structure in the smallest aspect ratio case. The vortex velocities predicted by the theoretical model [G. Rudinger and L. M. Somers, "Behaviour of small regions of different gases carried in accelerated gas flows," J. Fluid Mech. 7, 161-176 (1960)] agree well with the experimental ones. With the increase of aspect ratio, the maximal value of vorticity increases as well as the circulation, and more low-magnitude quantities are generated, which indicates the formation of multi-scale flow structure in the late mixing process. It is found that the experimental circulation of the vortex motion is reasonably estimated by the ideal point vortex-pair model.

16. A new refinement indicator for adaptive parameterization: Application to the estimation of the diffusion coefficient in an elliptic problem

Hayek, Mohamed; Ackerer, Philippe; Sonnendrücker, Éric

2009-02-01

We propose a new refinement indicator (NRI) for adaptive parameterization to determine the diffusion coefficient in an elliptic equation in two-dimensional space. The diffusion coefficient is assumed to be a piecewise constant space function. The unknowns are both the parameter values and the zonation. Refinement indicators are used to localize parameter discontinuities in order to construct iteratively the zonation (parameterization). The refinement indicator is obtained usually by using the first-order effect on the objective function of removing degrees of freedom for a current set of parameters. In this work, in order to reduce the computation costs, we propose a new refinement indicator based on the second-order effect on the objective function. This new refinement indicator depends on the objective function, and its first and second derivatives with respect to the parameter constraints. Numerical experiments show the high efficiency of the new refinement indicator compared to the standard one.

17. Approximations of optimal control problems for semilinear elliptic equations with discontinuous coefficients and states and with controls in the coefficients multiplying the highest derivatives

Lubyshev, F. V.; Fairuzov, M. E.

2016-07-01

Mathematical formulations of nonlinear optimal control problems for semilinear elliptic equations with discontinuous coefficients and solutions and with controls in the coefficients multiplying the highest derivatives are studied. Finite difference approximations of optimization problems are constructed, and the approximation error is estimated with respect to the state and the cost functional. Weak convergence of the approximations with respect to the control is proved. The approximations are regularized in the sense of Tikhonov.

18. High-beta analytic equilibria in circular, elliptical, and D-shaped large aspect ratio axisymmetric configurations with poloidal and toroidal flows

López, O. E.; Guazzotto, L.

2017-03-01

The Grad-Shafranov-Bernoulli system of equations is a single fluid magnetohydrodynamical description of axisymmetric equilibria with mass flows. Using a variational perturbative approach [E. Hameiri, Phys. Plasmas 20, 024504 (2013)], analytic approximations for high-beta equilibria in circular, elliptical, and D-shaped cross sections in the high aspect ratio approximation are found, which include finite toroidal and poloidal flows. Assuming a polynomial dependence of the free functions on the poloidal flux, the equilibrium problem is reduced to an inhomogeneous Helmholtz partial differential equation (PDE) subject to homogeneous Dirichlet conditions. An application of the Green's function method leads to a closed form for the circular solution and to a series solution in terms of Mathieu functions for the elliptical case, which is valid for arbitrary elongations. To extend the elliptical solution to a D-shaped domain, a boundary perturbation in terms of the triangularity is used. A comparison with the code FLOW [L. Guazzotto et al., Phys. Plasmas 11(2), 604-614 (2004)] is presented for relevant scenarios.

19. Observation of charge asymmetry dependence of pion elliptic flow and the possible chiral magnetic wave in heavy-ion collisions

SciTech Connect

2015-06-26

We present measurements of π⁻ and π⁺ elliptic flow, v₂, at midrapidity in Au+Au collisions at √sNN = 200, 62.4, 39, 27, 19.6, 11.5, and 7.7 GeV, as a function of event-by-event charge asymmetry, Ach, based on data from the STAR experiment at RHIC. We find that π⁻ (π⁺) elliptic flow linearly increases (decreases) with charge asymmetry for most centrality bins at √sNN = 27 GeV and higher. At √sNN = 200 GeV, the slope of the difference of v₂ between π⁻ and π⁺ as a function of Ach exhibits a centrality dependence, which is qualitatively similar to calculations that incorporate a chiral magnetic wave effect. In addition, similar centrality dependence is also observed at lower energies.

20. Observation of charge asymmetry dependence of pion elliptic flow and the possible chiral magnetic wave in heavy-ion collisions

DOE PAGES