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…
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…
Improvement to the averaging method using the Jacobian elliptic function
NASA Astrophysics Data System (ADS)
Okabe, T.; Kondou, T.
2009-02-01
The averaging method was improved by using the Jacobian elliptic sine (sn), cosine (cn) and delta (dn) functions as generating solutions in order to obtain a highly accurate periodic solution for a strongly nonlinear dynamical system. The proposed method can be applied to a relatively general nonlinear system based on the single degree-of-freedom Duffing equation. Two methods of stability analysis were applied and evaluated for the approximate solutions obtained by the proposed method. The approximate solutions obtained by the proposed method for practical examples were compared to the solutions obtained by the shooting method. The results confirmed that the proposed method provides a more accurate solution and more accurate stability analysis results than those obtained by the conventional averaging method that uses trigonometric functions as the generating solution.
NASA Astrophysics Data System (ADS)
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.
Gravity modeling: the Jacobian function and its approximation
NASA Astrophysics Data System (ADS)
Strykowski, G.; Lauritsen, N. L. B.
2012-04-01
In mathematics, the elements of a Jacobian matrix are the first-order partial derivatives of a scalar function or a vector function with respect to another vector. In inversion theory of geophysics the elements of a Jacobian matrix are a measure of the change of the output signal caused by a local perturbation of a parameter of a given (Earth) model. The elements of a Jacobian matrix can be determined from the general Jacobian function. In gravity modeling this function consists of the "geometrical part" (related to the relative location in 3D of a field point with respect to the source element) and the "source-strength part" (related to the change of mass density of the source element). The explicit (functional) expressions for the Jacobian function can be quite complicated and depend both on the coordinates used (Cartesian, spherical, ellipsoidal) and on the mathematical parametrization of the source (e.g. the homogenous rectangular prism). In practice, and irrespective of the exact expression for the Jacobian function, its value on a computer will always be rounded to a finite number of digits. In fact, in using the exact formulas such finite representation may cause numerical instabilities. If the Jacobian function is smooth enough, it is an advantage to approximate it by a simpler function, e.g. a piecewise-polynomial, which numerically is more robust than the exact formulas and which is more suitable for the subsequent integration. In our contribution we include a whole family of the Jacobian functions which are associated with all the partial derivatives of the gravitational potential of order 0 to 2, i.e. including all the elements of the gravity gradient tensor. The quality of the support points for the subsequent polynomial approximation of the Jacobian function is ensured by using the exact prism formulas in quadruple precision. We will show some first results. Also, we will discuss how such approximated Jacobian functions can be used for large scale
Fourier Series and Elliptic Functions
ERIC Educational Resources Information Center
Fay, Temple H.
2003-01-01
Non-linear second-order differential equations whose solutions are the elliptic functions "sn"("t, k"), "cn"("t, k") and "dn"("t, k") are investigated. Using "Mathematica", high precision numerical solutions are generated. From these data, Fourier coefficients are determined yielding approximate formulas for these non-elementary functions that are…
Fourier Series and Elliptic Functions
ERIC Educational Resources Information Center
Fay, Temple H.
2003-01-01
Non-linear second-order differential equations whose solutions are the elliptic functions "sn"("t, k"), "cn"("t, k") and "dn"("t, k") are investigated. Using "Mathematica", high precision numerical solutions are generated. From these data, Fourier coefficients are determined yielding approximate formulas for these non-elementary functions that are…
Force-free Jacobian equilibria for Vlasov-Maxwell plasmas
Abraham-Shrauner, B.
2013-10-15
New analytic force-free Vlasov-Maxwell equilibria for thin current sheets are presented. The magnetic flux densities are expressed in terms of Jacobian elliptic functions of one Cartesian spatial coordinate. The magnetic flux densities reduce to previously reported hyperbolic functions in one limit and sinusoidal functions in another limit of the modulus k. A much wider class of nonlinear force-free Vlasov-Maxwell equilibria open expanded possibilities for modeling of solar system, astrophysical and laboratory plasmas. Modified Maxwellian distribution functions are determined explicitly in terms of Jacobian elliptic functions. Conditions for double peaked distribution functions that could be unstable are developed.
Elliptic Functions with Disconnected Julia Sets
NASA Astrophysics Data System (ADS)
Koss, Lorelei
2016-06-01
In this paper, we investigate elliptic functions of the form fΛ = 1/(1 + (℘Λ)2), where ℘Λ is the Weierstrass elliptic function on a real rhombic lattice. We show that a typical function in this family has a superattracting fixed point at the origin and five other equivalence classes of critical points. We investigate conditions on the lattice which guarantee that fΛ has a double toral band, and we show that this family contains the first known examples of elliptic functions for which the Julia set is disconnected but not Cantor.
Elliptical billiards and hyperelliptic functions
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Bisetti, Fabrizio
2012-06-01
Recent trends in hydrocarbon fuel research indicate that the number of species and reactions in chemical kinetic mechanisms is rapidly increasing in an effort to provide predictive capabilities for fuels of practical interest. In order to cope with the computational cost associated with the time integration of stiff, large chemical systems, a novel approach is proposed. The approach combines an exponential integrator and Krylov subspace approximations to the exponential function of the Jacobian matrix. The components of the approach are described in detail and applied to the ignition of stoichiometric methane-air and iso-octane-air mixtures, here described by two widely adopted chemical kinetic mechanisms. The approach is found to be robust even at relatively large time steps and the global error displays a nominal third-order convergence. The performance of the approach is improved by utilising an adaptive algorithm for the selection of the Krylov subspace size, which guarantees an approximation to the matrix exponential within user-defined error tolerance. The Krylov projection of the Jacobian matrix onto a low-dimensional space is interpreted as a local model reduction with a well-defined error control strategy. Finally, the performance of the approach is discussed with regard to the optimal selection of the parameters governing the accuracy of its individual components.
Pendulum, elliptic functions, and relative cohomology classes
NASA Astrophysics Data System (ADS)
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.
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.
Jacobi elliptic functions: A review of nonlinear oscillatory application problems
NASA Astrophysics Data System (ADS)
Kovacic, Ivana; Cveticanin, Livija; Zukovic, Miodrag; Rakaric, Zvonko
2016-10-01
This review paper is concerned with the applications of Jacobi elliptic functions to nonlinear oscillators whose restoring force has a monomial or binomial form that involves cubic and/or quadratic nonlinearity. First, geometric interpretations of three basic Jacobi elliptic functions are given and their characteristics are discussed. It is shown then how their different forms can be utilized to express exact solutions for the response of certain free conservative oscillators. These forms are subsequently used as a starting point for a presentation of different quantitative techniques for obtaining an approximate response for free perturbed nonlinear oscillators. An illustrative example is provided. Further, two types of externally forced nonlinear oscillators are reviewed: (i) those that are excited by elliptic-type excitations with different exact and approximate solutions; (ii) those that are damped and excited by harmonic excitations, but their approximate response is expressed in terms of Jacobi elliptic functions. Characteristics of the steady-state response are discussed and certain qualitative differences with respect to the classical Duffing oscillator excited harmonically are pointed out. Parametric oscillations of the oscillators excited by an elliptic-type forcing are considered as well, and the differences with respect to the stability chart of the classical Mathieu equation are emphasized. The adjustment of the Melnikov method to derive the general condition for the onset of homoclinic bifurcations in a system parametrically excited by an elliptic-type forcing is provided and compared with those corresponding to harmonic excitations. Advantages and disadvantages of the use of Jacobi elliptic functions in nonlinear oscillatory application problems are discussed and some suggestions for future work are given.
The Jacobian factor in free energy simulations
NASA Astrophysics Data System (ADS)
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.
Applications of Elliptic Integral and Elliptic Function to Electric Power Cable Problems
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Cardona, Carlos; Gomez, Humberto
2016-06-01
Recently the CHY approach has been extended to one loop level using elliptic functions and modular forms over a Jacobian variety. Due to the difficulty in manipulating these kind of functions, we propose an alternative prescription that is totally algebraic. This new proposal is based on an elliptic algebraic curve embedded in a mathbb{C}{P}^2 space. We show that for the simplest integrand, namely the n - gon, our proposal indeed reproduces the expected result. By using the recently formulated Λ-algorithm, we found a novel recurrence relation expansion in terms of tree level off-shell amplitudes. Our results connect nicely with recent results on the one-loop formulation of the scattering equations. In addition, this new proposal can be easily stretched out to hyperelliptic curves in order to compute higher genus.
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.
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…
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…
The collective coordinates Jacobian
NASA Astrophysics Data System (ADS)
Schwartz, Moshe; Vinograd, Guy
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.
A Jacobian generalization of the pseudo-Nambu-Goldstone boson potential
NASA Astrophysics Data System (ADS)
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.
Wave functions of elliptical quantum dots in a magnetic field
NASA Astrophysics Data System (ADS)
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.
Some new addition formulae for Weierstrass elliptic functions
Eilbeck, J. Chris; England, Matthew; Ônishi, Yoshihiro
2014-01-01
We present new addition formulae for the Weierstrass functions associated with a general elliptic curve. We prove the structure of the formulae in n-variables and give the explicit addition formulae for the 2- and 3-variable cases. These new results were inspired by new addition formulae found in the case of an equianharmonic curve, which we can now observe as a specialization of the results here. The new formulae, and the techniques used to find them, also follow the recent work for the generalization of Weierstrass functions to curves of higher genus. PMID:25383018
Current State and Future Prospect of Applications of Elliptic Function to Electric Power Field
NASA Astrophysics Data System (ADS)
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.
Miniaturized LTCC elliptic-function lowpass filters with side stopbands
Hsieh, Lung -Hwa; Dai, Steve Xunhu
2015-05-28
A compact, high-selectivity, and wide stopband lowpass filter is highly demanded in wireless communication systems to suppress adjacent harmonics and unwanted signals. In this letter, a new miniaturized lowpass filter with elliptic-function frequency response is introduced. The filter is fabricated in multilayer low temperature cofired ceramics. The size of the miniaturized filter is 5.5 × 3.9 × 1.72 mm3. As a result, the measured insertion loss of the filter is better than 0.37 dB from DC to 1.28 GHz and the measured stopband of the filter is great than 22 dB from 2.3 to 7.5 GHz.
A giant elliptical galaxy with a lightweight initial mass function
NASA Astrophysics Data System (ADS)
Smith, Russell J.; Lucey, John R.
2013-09-01
We present new observations of the closest known strong-lensing galaxy, the σ ≈ 330 km s- 1 giant elliptical ESO325-G004, made with the ESO Very Large Telescope. The low redshift of the lens (zl = 0.035) results in arcs being formed at a small fraction of the effective radius (REin = 2.85 arcsec ≈ Reff/4). At such small radii, stars dominate the lensing mass, so that lensing provides a direct probe of the stellar mass-to-light ratio, with only small corrections needed for dark matter. However, the redshift of the galaxy lensed by ESO325-G004 was unknown until now, so the lensing mass was not securely determined. Using X-SHOOTER, we have detected multiple spectral lines, from two bright parts of the arc system, and measured a source redshift of zs = 2.141. Combined with lens modelling constraints, this yields a total mass inside the Einstein radius of 1.50 ± 0.06 × 1011 M⊙. We estimate the range of possible contribution of dark matter to the lensing mass, using halo profile statistics from cosmological N-body simulations. Subtracting this component yields a stellar mass-to-light ratio for the lens of M*/LF814W = 3.14^{+0.24}_{-0.42} (M/L)_{{odot }, F814W}. Using VIMOS, we have also obtained very high signal-to-noise spectroscopy for the lens galaxy. Fitting models to this spectrum confirms that ESO325-G004 has a very old stellar population. For a Milky-Way-like (Kroupa) initial mass function (IMF), the stellar population fit yields a predicted stellar mass-to-light ratio of ΥMW = 3.01 ± 0.25 (M/L)⊙, F814W. Hence, the mass attributable to stars with a Kroupa IMF is consistent with the lensing estimate. By contrast, a Salpeter (or heavier) IMF is disfavoured at the 99.8 per cent confidence level. A `heavyweight' IMF, with a mass twice as large as the Kroupa case, is firmly excluded for this galaxy. Such an IMF has been proposed for more distant elliptical lenses, and also to explain strong dwarf-star-sensitive spectral features, in particular the Na I
Permutation symmetry for theta functions
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.
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.
Boundary-value problems for elliptic functional-differential equations and their applications
NASA Astrophysics Data System (ADS)
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.
Joint inversion of body wave receiver function and Rayleigh wave ellipticity
NASA Astrophysics Data System (ADS)
Chong, J.; Ni, S.; Chu, R.
2015-12-01
In recent years, surface wave dispersion has been used to image lithospheric structure jointly with receiver function, or Rayleigh wave ellipticity (Julia et al., 2000; Lin et al., 2012). Because surface wave dispersion is the total propagation effect of the travel path, the joint inversion relies on dense seismic arrays or high seismicity to obtain local velocity structure. However, both receiver function and Rayleigh wave ellipticity are single station measurements with localized sensitivities and could be combined for joint inversion naturally. In this study we explored the feasibility of the joint inversion of Rayleigh wave ellipticity and receiver function. We performed sensitivity tests with forward modeling, and found that the receiver function is sensitive to sharp velocity interfaces but shows weak sensitivity to long wavelength structure, almost complementary to Rayleigh wave ellipticity. Therefore, joint inversion with two single-station measurements provides tighter constraints on the velocity structure beneath the seismic station. A joint inversion algorithm based on the Fast Simulated Annealing method is developed to invert Rayleigh wave ellipticity and receiver function for the lithospheric structure. Application of the algorithm to the Indian Craton and the Williston Basin in the United States demonstrates its effectiveness in reducing the non-uniqueness of the inversion. However, the joint inversion is not sensitive to average crustal velocity, suggesting the need to combine surface wave dispersion, receiver function and Rayleigh wave ellipticity to more accurately resolve the velocity structure. ReferenceJuliá, J., C. Ammon, R. Herrmann, and A. Correig, 2000. Joint inversion of receiver function and surface wave dispersion observations, Geophys. J. Int., 143(1), 99-112. Lin F.C., Schmandt B. and Tsai V.C., 2012. Joint inversion of Rayleigh wave phase velocity and ellipticity using USArray: constraining velocity and density structure in the upper
On uniform approximation of elliptic functions by Padé approximants
NASA Astrophysics Data System (ADS)
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.
Mao, Shi-Chun; Wu, Zhen-Sen
2008-12-01
An exact solution to the two-dimensional scattering properties of an anisotropic elliptic cylinder for transverse electric polarization is presented. The internal field in an anisotropic elliptic cylinder is expressed as integral representations of Mathieu functions and Fourier series. The coefficients of the series expansion are obtained by imposing boundary conditions on the anisotropic-free-space interface. A matrix is developed to solve the nonorthogonality properties of Mathieu functions at the interface between two different media. Numerical results are given for the bistatic radar cross section and the amplitude of the total magnetic field along the x and y axes. The result is in agreement with that available as expected when an elliptic cylinder degenerates to a circular one.
Dynamically consistent Jacobian inverse for mobile manipulators
NASA Astrophysics Data System (ADS)
Ratajczak, Joanna; Tchoń, Krzysztof
2016-06-01
By analogy to the definition of the dynamically consistent Jacobian inverse for robotic manipulators, we have designed a dynamically consistent Jacobian inverse for mobile manipulators built of a non-holonomic mobile platform and a holonomic on-board manipulator. The endogenous configuration space approach has been exploited as a source of conceptual guidelines. The new inverse guarantees a decoupling of the motion in the operational space from the forces exerted in the endogenous configuration space and annihilated by the dual Jacobian inverse. A performance study of the new Jacobian inverse as a tool for motion planning is presented.
Jacobi elliptic functions and the complete solution to the bead on the hoop problem
NASA Astrophysics Data System (ADS)
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.
Solving the differential biochemical Jacobian from metabolomics covariance data.
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.
Solving the Differential Biochemical Jacobian from Metabolomics Covariance Data
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
Globular Cluster Luminosity Functions and Specific Frequencies in Dwarf Elliptical Galaxies
NASA Astrophysics Data System (ADS)
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.
Estimates of azimuthal numbers associated with elementary elliptic cylinder wave functions
NASA Astrophysics Data System (ADS)
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.
Origin of a Bottom-heavy Stellar Initial Mass Function in Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Bekki, Kenji
2013-12-01
We investigate the origin of a bottom-heavy stellar initial mass function (IMF) recently observed in elliptical galaxies by using chemical evolution models with a non-universal IMF. We adopt the variable Kroupa IMF with the three slopes (α1, α2, and α3) dependent on metallicities ([Fe/H]) and densities (ρg) of star-forming gas clouds and thereby search for the best IMF model that can reproduce (1) the observed steep IMF slope (α2 ~ 3, i.e., bottom-heavy) for low stellar masses (m <= 1 M ⊙) and (2) the correlation of α2 with chemical properties of elliptical galaxies in a self-consistent manner. We find that if the IMF slope α2 depends on both [Fe/H] and ρg, then elliptical galaxies with higher [Mg/Fe] can have steeper α2 (~3) in our models. We also find that the observed positive correlation of stellar mass-to-light ratios (M/L) with [Mg/Fe] in elliptical galaxies can be quantitatively reproduced in our models with α2vpropβ[Fe/H] + γlog ρg, where β ~ 0.5 and γ ~ 2. We discuss whether the IMF slopes for low-mass (α2) and high-mass stars (α3) need to vary independently from each other to explain a number of IMF-related observational results self-consistently. We also briefly discuss why α2 depends differently on [Fe/H] in dwarf and giant elliptical galaxies.
On the modularity of certain functions from the Gromov–Witten theory of elliptic orbifolds
Bringmann, Kathrin; Rolen, Larry; Zwegers, Sander
2015-01-01
In this paper, we study modularity of several functions which naturally arose in a recent paper of Lau and Zhou on open Gromov–Witten potentials of elliptic orbifolds. They derived a number of examples of indefinite theta functions, and we provide modular completions for several such functions which involve more complicated objects than ordinary modular forms. In particular, we give new closed formulae for special indefinite theta functions of type (1,2) in terms of products of mock modular forms. This formula is also of independent interest. PMID:26715996
Matrix coefficient identification in an elliptic equation with the convex energy functional method
NASA Astrophysics Data System (ADS)
Hinze, Michael; Nhan Tam Quyen, Tran
2016-08-01
In this paper we study the inverse problem of identifying the diffusion matrix in an elliptic PDE from measurements. The convex energy functional method with Tikhonov regularization is applied to tackle this problem. For the discretization we use the variational discretization concept, where the PDE is discretized with piecewise linear, continuous finite elements. We show the convergence of approximations. Using a suitable source condition, we prove an error bound for discrete solutions. For the numerical solution we propose a gradient-projection algorithm and prove the strong convergence of its iterates to a solution of the identification problem. Finally, we present a numerical experiment which illustrates our theoretical results.
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.
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.
Formal convergence characteristics of elliptically constrained incremental Newton-Raphson algorithms
NASA Technical Reports Server (NTRS)
Padovan, J.; Arechaga, T.
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.
Formal convergence characteristics of elliptically constrained incremental Newton-Raphson algorithms
NASA Technical Reports Server (NTRS)
Padovan, J.; Arechaga, T.
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.
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.
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.
PERSPECTIVES ON INTRACLUSTER ENRICHMENT AND THE STELLAR INITIAL MASS FUNCTION IN ELLIPTICAL GALAXIES
Loewenstein, Michael
2013-08-10
Stars formed in galaxy cluster potential wells must be responsible for the high level of enrichment measured in the intracluster medium (ICM); however, there is increasing tension between this truism and the parsimonious assumption that the stars in the generally old population studied optically in cluster galaxies emerged from the same formation sites at the same epochs. We construct a phenomenological cluster enrichment model to demonstrate that ICM elemental abundances are underestimated by a factor >2 for standard assumptions about the stellar population-a discrepancy we call the ''cluster elemental abundance paradox''. Recent evidence of an elliptical galaxy initial mass function (IMF) skewed to low masses deepens the paradox. We quantify the adjustments to the star formation efficiency and IMF, and Type Ia supernovae (SNIa) production efficiency, required to resolve this while being consistent with the observed ICM abundance pattern. The necessary enhancement in metal enrichment may, in principle, originate in the observed stellar population if a larger fraction of stars in the supernova-progenitor mass range form from an IMF that is either bottom-light or top-heavy, with the latter in some conflict with observed ICM abundance ratios. Other alternatives that imply more modest revisions to the IMF, mass return and remnant fractions, and primordial fraction, posit an increase in the fraction of 3-8 M{sub Sun} stars that explode as SNIa or assume that there are more stars than conventionally thought-although the latter implies a high star formation efficiency. We discuss the feasibility of these various solutions and the implications for the diversity of star formation in the universe, the process of elliptical galaxy formation, and the origin of this ''hidden'' source of ICM metal enrichment.
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.
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
NASA Astrophysics Data System (ADS)
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.
A special class of Painlevé differential systems that generalize the elliptic functions a)
NASA Astrophysics Data System (ADS)
Gaffet, B.
2015-04-01
The elliptic functions of order 2 may be viewed as the ratios Z2/Z1 of the solutions of a differential system of the general form: Zi 3 / 8 /d 2 (Z j / Z i) d u 2 = Z j R i i - Z i R ij (i ≠ j , i , j = 1 , … , n), where n = 2, u is the independent variable, and the Rij are the homogeneous quadratic functions of the n variables Zi. The general solution of systems of this form automatically consists, for all n, of purely meromorphic functions. For arbitrary values of n, the system consists of n (n - 1) equations for (n - 1) inhomogeneous variables Zi/Z1, and the question arises as to whether there may exist systems of the above form, with n > 2, which are equivalent to a non-over-determined differential system of p equations, when n-p-1 appropriately chosen algebraic constraints are imposed on the dependent variables. In the present work, we show that such systems do exist, with n = 4 and n = 8, and are in fact special cases of the Dyson model (1968) of a spinning cloud of ellipsoidal shape, expanding adiabatically into a vacuum.
A function space approach to state and model error estimation for elliptic systems
NASA Technical Reports Server (NTRS)
Rodriguez, G.
1983-01-01
An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal esimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed. While this paper focuses on theoretical developments, applications arising in the area of large structure static shape determination are contained in a closely related paper (Rodriguez and Scheid, 1982).
A function space approach to state and model error estimation for elliptic systems
NASA Technical Reports Server (NTRS)
Rodriguez, G.
1983-01-01
An approach is advanced for the concurrent estimation of the state and of the model errors of a system described by elliptic equations. The estimates are obtained by a deterministic least-squares approach that seeks to minimize a quadratic functional of the model errors, or equivalently, to find the vector of smallest norm subject to linear constraints in a suitably defined function space. The minimum norm solution can be obtained by solving either a Fredholm integral equation of the second kind for the case with continuously distributed data or a related matrix equation for the problem with discretely located measurements. Solution of either one of these equations is obtained in a batch-processing mode in which all of the data is processed simultaneously or, in certain restricted geometries, in a spatially scanning mode in which the data is processed recursively. After the methods for computation of the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the corresponding estimation error is conducted. Based on this analysis, explicit expressions for the mean-square estimation error associated with both the state and model error estimates are then developed.
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.
Superposition of elliptic functions as solutions for a large number of nonlinear equations
NASA Astrophysics Data System (ADS)
Khare, Avinash; Saxena, Avadh
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.
Superposition of elliptic functions as solutions for a large number of nonlinear equations
Khare, Avinash; Saxena, Avadh
2014-03-15
For a large number of nonlinear equations, both discrete and continuum, we demonstrate a kind of linear superposition. We show that whenever a nonlinear equation admits solutions in terms of both Jacobi elliptic functions cn(x, m) and dn(x, m) with modulus m, then it also admits solutions in terms of their sum as well as difference. We have checked this in the case of several nonlinear equations such as the nonlinear Schrödinger equation, MKdV, a mixed KdV-MKdV system, a mixed quadratic-cubic nonlinear Schrödinger equation, the Ablowitz-Ladik equation, the saturable nonlinear Schrödinger equation, λϕ{sup 4}, the discrete MKdV as well as for several coupled field equations. Further, for a large number of nonlinear equations, we show that whenever a nonlinear equation admits a periodic solution in terms of dn{sup 2}(x, m), it also admits solutions in terms of dn {sup 2}(x,m)±√(m) cn (x,m) dn (x,m), even though cn(x, m)dn(x, m) is not a solution of these nonlinear equations. Finally, we also obtain superposed solutions of various forms for several coupled nonlinear equations.
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
NASA Astrophysics Data System (ADS)
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.
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
EMG-based facial gesture recognition through versatile elliptic basis function neural network
2013-01-01
Background Recently, the recognition of different facial gestures using facial neuromuscular activities has been proposed for human machine interfacing applications. Facial electromyograms (EMGs) analysis is a complicated field in biomedical signal processing where accuracy and low computational cost are significant concerns. In this paper, a very fast versatile elliptic basis function neural network (VEBFNN) was proposed to classify different facial gestures. The effectiveness of different facial EMG time-domain features was also explored to introduce the most discriminating. Methods In this study, EMGs of ten facial gestures were recorded from ten subjects using three pairs of surface electrodes in a bi-polar configuration. The signals were filtered and segmented into distinct portions prior to feature extraction. Ten different time-domain features, namely, Integrated EMG, Mean Absolute Value, Mean Absolute Value Slope, Maximum Peak Value, Root Mean Square, Simple Square Integral, Variance, Mean Value, Wave Length, and Sign Slope Changes were extracted from the EMGs. The statistical relationships between these features were investigated by Mutual Information measure. Then, the feature combinations including two to ten single features were formed based on the feature rankings appointed by Minimum-Redundancy-Maximum-Relevance (MRMR) and Recognition Accuracy (RA) criteria. In the last step, VEBFNN was employed to classify the facial gestures. The effectiveness of single features as well as the feature sets on the system performance was examined by considering the two major metrics, recognition accuracy and training time. Finally, the proposed classifier was assessed and compared with conventional methods support vector machines and multilayer perceptron neural network. Results The average classification results showed that the best performance for recognizing facial gestures among all single/multi-features was achieved by Maximum Peak Value with 87.1% accuracy
JFKengine: A Jacobian and Forward Kinematics Generator
Fischer, K.N.
2003-02-13
During robot path planning and control the equations that describe the robot motions are determined and solved. Historically these expressions were derived analytically off-line. For robots that must adapt to their environment or perform a wide range of tasks, a way is needed to rapidly re-derive these expressions to take into account the robot kinematic changes, such as when a tool is added to the end-effector. The JFKengine software was developed to automatically produce the expressions representing the manipulator arm motion, including the manipulator arm Jacobian and the forward kinematic expressions. Its programming interface can be used in conjunction with robot simulation software or with robot control software. Thus, it helps to automate the process of configuration changes for serial robot manipulators. If the manipulator undergoes a geometric change, such as tool acquisition, then JFKengine can be invoked again from the control or simulation software, passing it parameters for the new arm configuration. This report describes the automated processes that are implemented by JFKengine to derive the kinematic equations and the programming interface by which it is invoked. Then it discusses the tree data structure that was chosen to store the expressions, followed by several examples of portions of expressions as represented in the tree. The C++ classes and their methods that implement the expression differentiation and evaluation operations are described. The algorithms used to construct the Jacobian and forward kinematic equations using these basic building blocks are then illustrated. The activity described in this report is part of a larger project entitled ''Multi-Optimization Criteria-Based Robot Behavioral Adaptability and Motion Planning'' that focuses on the development of a methodology for the generalized resolution of robot motion equations with time-varying configurations, constraints, and task objective criteria. A specific goal of this project is
Jackson, Kurt; Merriman, Harold; Campbell, Jeremy
2010-09-01
Decreased functional walking capacity is a common consequence of stroke. Identifying practical and cost-effective methods to improve walking in individuals with stroke is an important goal of rehabilitation professionals. Participants were 3 men with chronic (>6 month) stroke, who could walk on level surfaces either without an assistive device or with a single-point cane. Participants trained 2 to 3 times per week for 8 weeks, using an elliptical machine. The training target was 20 minutes of uninterrupted training, while maintaining predetermined parameters of heart rate and perceived exertion. Outcome measures assessed before and after training included habitual and fast gait speed, 6-minute walk test (6MWT), Timed "Up & Go" test, and Berg Balance Scale. Following training there was no change in walking speed. There was no change in 6MWT performance for participants 1 and 2. While participant 3 showed a 25% improvement in 6MWT, this change did not meet the minimal detectable change for walking speed in individuals with stroke. All participants demonstrated improved Berg Balance Scale performance (9%-28%), with participant 1 exceeding the minimal detectable change in this measure. Timed Up & Go test performance improved by 5% to 15% in all participants. Elliptical training appears to be a safe and feasible training alternative for ambulatory individuals with chronic stroke. Training 2 to 3 days per week resulted in no improvements in walking speed; however, participants did demonstrate variable improvements in endurance, balance, and functional mobility. It is possible that a higher training frequency and/or training speed are required to influence walking performance in individuals who are ambulatory. Equipment design, principles of exercise prescription, and participant characteristics should be considered when selecting elliptical training as an intervention.
Off-diagonal Jacobian support for Nodal BCs
Peterson, John W.; Andrs, David; Gaston, Derek R.; Permann, Cody J.; Slaughter, Andrew E.
2015-01-01
In this brief note, we describe the implementation of o-diagonal Jacobian computations for nodal boundary conditions in the Multiphysics Object Oriented Simulation Environment (MOOSE) [1] framework. There are presently a number of applications [2{5] based on the MOOSE framework that solve complicated physical systems of partial dierential equations whose boundary conditions are often highly nonlinear. Accurately computing the on- and o-diagonal Jacobian and preconditioner entries associated to these constraints is crucial for enabling ecient numerical solvers in these applications. Two key ingredients are required for properly specifying the Jacobian contributions of nonlinear nodal boundary conditions in MOOSE and nite element codes in general: 1. The ability to zero out entire Jacobian matrix rows after \
Garcia-Botella, Angel; Fernandez-Balbuena, Antonio Alvarez; Bernabeu, Eusebio
2006-10-10
Nonimaging optics is a field devoted to the design of optical components for applications such as solar concentration or illumination. In this field, many different techniques have been used to produce optical devices, including the use of reflective and refractive components or inverse engineering techniques. However, many of these optical components are based on translational symmetries, rotational symmetries, or free-form surfaces. We study a new family of nonimaging concentrators called elliptical concentrators. This new family of concentrators provides new capabilities and can have different configurations, either homofocal or nonhomofocal. Translational and rotational concentrators can be considered as particular cases of elliptical concentrators.
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.
Near-infrared line-strengths in elliptical galaxies: evidence for initial mass function variations?
NASA Astrophysics Data System (ADS)
Cenarro, A. J.; Gorgas, J.; Vazdekis, A.; Cardiel, N.; Peletier, R. F.
2003-02-01
We present new relations between recently defined line-strength indices in the near-infrared (CaT*, CaT, PaT, MgI and sTiO) and central velocity dispersion (σ0) for a sample of 35 early-type galaxies, showing evidence for significant anti-correlations between CaII triplet indices (CaT* and CaT) and log σ0. These relations are interpreted in the light of our recent evolutionary synthesis model predictions, suggesting the existence of important Ca underabundances with respect to Fe and/or an increase of the dwarf to giant stars ratio along the mass sequence of elliptical galaxies.
Dynamics on strata of trigonal Jacobians and some integrable problems of rigid body motion
NASA Astrophysics Data System (ADS)
Braden, H. W.; Enolski, V. Z.; Fedorov, Yu N.
2013-07-01
We present an algebraic geometrical and analytical description of the Goryachev case of rigid body motion. It belongs to a family of systems sharing the same properties: although completely integrable, they are not algebraically integrable, their solution is not meromorphic in the complex time and involves dynamics on the strata of the Jacobian varieties of trigonal curves. Although the strata of hyperelliptic Jacobians have already appeared in the literature in the context of some dynamical systems, the Goryachev case is the first example of an integrable system whose solution involves a more general curve. Several new features (and formulae) are encountered in the solution given in terms of sigma-functions of such a curve.
pyJac: Analytical Jacobian generator for chemical kinetics
NASA Astrophysics Data System (ADS)
Niemeyer, Kyle E.; Curtis, Nicholas J.; Sung, Chih-Jen
2017-06-01
Accurate simulations of combustion phenomena require the use of detailed chemical kinetics in order to capture limit phenomena such as ignition and extinction as well as predict pollutant formation. However, the chemical kinetic models for hydrocarbon fuels of practical interest typically have large numbers of species and reactions and exhibit high levels of mathematical stiffness in the governing differential equations, particularly for larger fuel molecules. In order to integrate the stiff equations governing chemical kinetics, generally reactive-flow simulations rely on implicit algorithms that require frequent Jacobian matrix evaluations. Some in situ and a posteriori computational diagnostics methods also require accurate Jacobian matrices, including computational singular perturbation and chemical explosive mode analysis. Typically, finite differences numerically approximate these, but for larger chemical kinetic models this poses significant computational demands since the number of chemical source term evaluations scales with the square of species count. Furthermore, existing analytical Jacobian tools do not optimize evaluations or support emerging SIMD processors such as GPUs. Here we introduce pyJac, a Python-based open-source program that generates analytical Jacobian matrices for use in chemical kinetics modeling and analysis. In addition to producing the necessary customized source code for evaluating reaction rates (including all modern reaction rate formulations), the chemical source terms, and the Jacobian matrix, pyJac uses an optimized evaluation order to minimize computational and memory operations. As a demonstration, we first establish the correctness of the Jacobian matrices for kinetic models of hydrogen, methane, ethylene, and isopentanol oxidation (number of species ranging 13-360) by showing agreement within 0.001% of matrices obtained via automatic differentiation. We then demonstrate the performance achievable on CPUs and GPUs using py
Algorithmic vs. finite difference Jacobians for infrared atmospheric radiative transfer
NASA Astrophysics Data System (ADS)
Schreier, Franz; Gimeno García, Sebastián; Vasquez, Mayte; Xu, Jian
2015-10-01
Jacobians, i.e. partial derivatives of the radiance and transmission spectrum with respect to the atmospheric state parameters to be retrieved from remote sensing observations, are important for the iterative solution of the nonlinear inverse problem. Finite difference Jacobians are easy to implement, but computationally expensive and possibly of dubious quality; on the other hand, analytical Jacobians are accurate and efficient, but the implementation can be quite demanding. GARLIC, our "Generic Atmospheric Radiation Line-by-line Infrared Code", utilizes algorithmic differentiation (AD) techniques to implement derivatives w.r.t. atmospheric temperature and molecular concentrations. In this paper, we describe our approach for differentiation of the high resolution infrared and microwave spectra and provide an in-depth assessment of finite difference approximations using "exact" AD Jacobians as a reference. The results indicate that the "standard" two-point finite differences with 1 K and 1% perturbation for temperature and volume mixing ratio, respectively, can exhibit substantial errors, and central differences are significantly better. However, these deviations do not transfer into the truncated singular value decomposition solution of a least squares problem. Nevertheless, AD Jacobians are clearly recommended because of the superior speed and accuracy.
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Castro, Manuel J.; Gallardo, José M.; Marquina, Antonio
2017-10-01
We present recent advances in PVM (Polynomial Viscosity Matrix) methods based on internal approximations to the absolute value function, and compare them with Chebyshev-based PVM solvers. These solvers only require a bound on the maximum wave speed, so no spectral decomposition is needed. Another important feature of the proposed methods is that they are suitable to be written in Jacobian-free form, in which only evaluations of the physical flux are used. This is particularly interesting when considering systems for which the Jacobians involve complex expressions, e.g., the relativistic magnetohydrodynamics (RMHD) equations. On the other hand, the proposed Jacobian-free solvers have also been extended to the case of approximate DOT (Dumbser-Osher-Toro) methods, which can be regarded as simple and efficient approximations to the classical Osher-Solomon method, sharing most of it interesting features and being applicable to general hyperbolic systems. To test the properties of our schemes a number of numerical experiments involving the RMHD equations are presented, both in one and two dimensions. The obtained results are in good agreement with those found in the literature and show that our schemes are robust and accurate, running stable under a satisfactory time step restriction. It is worth emphasizing that, although this work focuses on RMHD, the proposed schemes are suitable to be applied to general hyperbolic systems.
Elliptic integrals: Symmetry and symbolic integration
Carlson, B.C. |
1997-12-31
Computation of elliptic integrals, whether numerical or symbolic, has been aided by the contributions of Italian mathematicians. Tricomi had a strong interest in iterative algorithms for computing elliptic integrals and other special functions, and his writings on elliptic functions and elliptic integrals have taught these subjects to many modern readers (including the author). The theory of elliptic integrals began with Fagnano`s duplication theorem, a generalization of which is now used iteratively for numerical computation in major software libraries. One of Lauricella`s multivariate hypergeometric functions has been found to contain all elliptic integrals as special cases and has led to the introduction of symmetric canonical forms. These forms provide major economies in new integral tables and offer a significant advantage also for symbolic integration of elliptic integrals. Although partly expository the present paper includes some new proofs and proposes a new procedure for symbolic integration.
Elliptic flow in small systems due to elliptic gluon distributions?
NASA Astrophysics Data System (ADS)
Hagiwara, Yoshikazu; Hatta, Yoshitaka; Xiao, Bo-Wen; Yuan, Feng
2017-08-01
We investigate the contributions from the so-called elliptic gluon Wigner distributions to the rapidity and azimuthal correlations of particles produced in high energy pp and pA collisions by applying the double parton scattering mechanism. We compute the 'elliptic flow' parameter v2 as a function of the transverse momentum and rapidity, and find qualitative agreement with experimental observations. This shall encourage further developments with more rigorous studies of the elliptic gluon distributions and their applications in hard scattering processes in pp and pA collisions.
Challenges of Inversely Estimating Jacobian from Metabolomics Data
Sun, Xiaoliang; Länger, Bettina; Weckwerth, Wolfram
2015-01-01
Inferring dynamics of metabolic networks directly from metabolomics data provides a promising way to elucidate the underlying mechanisms of biological systems, as reported in our previous studies (Weckwerth, 2011; Sun and Weckwerth, 2012; Nägele et al., 2014) by a differential Jacobian approach. The Jacobian is solved from an overdetermined system of equations as JC + CJT = −2D, called Lyapunov Equation in its generic form,1 where J is the Jacobian, C is the covariance matrix of metabolomics data, and D is the fluctuation matrix. Lyapunov Equation can be further simplified as the linear form Ax = b. Frequently, this linear equation system is ill-conditioned, i.e., a small variation in the right side b results in a big change in the solution x, thus making the solution unstable and error-prone. At the same time, inaccurate estimation of covariance matrix and uncertainties in the fluctuation matrix bring biases to the solution x. Here, we first reviewed common approaches to circumvent the ill-conditioned problems, including total least squares, Tikhonov regularization, and truncated singular value decomposition. Then, we benchmarked these methods on several in silico kinetic models with small to large perturbations on the covariance and fluctuation matrices. The results identified that the accuracy of the reverse Jacobian is mainly dependent on the condition number of A, the perturbation amplitude of C, and the stiffness of the kinetic models. Our research contributes a systematical comparison of methods to inversely solve Jacobian from metabolomics data. PMID:26636075
NASA Astrophysics Data System (ADS)
Yu. Moshin, Pavel; Reshetnyak, Alexander A.
2016-07-01
We continue our research1-4 and extend the class of finite BRST-anti-BRST transformations with odd-valued parameters λa, a = 1, 2, introduced in these works. In doing so, we evaluate the Jacobians induced by finite BRST-anti-BRST transformations linear in functionally-dependent parameters, as well as those induced by finite BRST-anti-BRST transformations with arbitrary functional parameters. The calculations cover the cases of gauge theories with a closed algebra, dynamical systems with first-class constraints, and general gauge theories. The resulting Jacobians in the case of linearized transformations are different from those in the case of polynomial dependence on the parameters. Finite BRST-anti-BRST transformations with arbitrary parameters induce an extra contribution to the quantum action, which cannot be absorbed into a change of the gauge. These transformations include an extended case of functionally-dependent parameters that implies a modified compensation equation, which admits nontrivial solutions leading to a Jacobian equal to unity. Finite BRST-anti-BRST transformations with functionally-dependent parameters are applied to the Standard Model, and an explicit form of functionally-dependent parameters λa is obtained, providing the equivalence of path integrals in any 3-parameter Rξ-like gauges. The Gribov-Zwanziger theory is extended to the case of the Standard Model, and a form of the Gribov horizon functional is suggested in the Landau gauge, as well as in Rξ-like gauges, in a gauge-independent way using field-dependent BRST-anti-BRST transformations, and in Rξ-like gauges using transverse-like non-Abelian gauge fields.
NASA Astrophysics Data System (ADS)
Gubbiotti, G.; Carlotti, G.; Okuno, T.; Grimsditch, M.; Giovannini, L.; Montoncello, F.; Nizzoli, F.
2005-11-01
Brillouin light scattering (BLS) spectra have been measured in arrays of cylindrical Permalloy dots with elliptical cross section, 200nm wide, 15nm thick, and eccentricities from 1 to 3. Several spin modes are observed and their frequencies tracked as a function of the direction of the applied 1.5kOe magnetic field H . The experimental data are interpreted within the framework of the recently introduced dynamical matrix method to calculate spin excitations in magnetic particles. We find that the mode frequencies strongly depend on the eccentricity of the dots and on the direction of the applied field. For fields along the principal axes the solutions can be classified into: (i) modes localized near the particle ends, (ii) modes with nodal lines perpendicular to H (backwardlike modes), (iii) modes with nodal lines parallel to H (Damon-Eshbach-like modes) and (iv) modes with both parallel and perpendicular nodal lines. In cases where the frequencies of two modes in different families are similar, some hybridization between the modes is observed. For H along nonsymmetry directions only the modes of type (i) remain reasonably well defined, other modes can at best be described as hybrids of modes in the above categories. Determining which of the modes is active in BLS experiments leads to excellent agreement with the experimental results.
Streamline integration as a method for two-dimensional elliptic grid generation
NASA Astrophysics Data System (ADS)
Wiesenberger, M.; Held, M.; Einkemmer, L.
2017-07-01
We propose a new numerical algorithm to construct a structured numerical elliptic grid of a doubly connected domain. Our method is applicable to domains with boundaries defined by two contour lines of a two-dimensional function. Furthermore, we can adapt any analytically given boundary aligned structured grid, which specifically includes polar and Cartesian grids. The resulting coordinate lines are orthogonal to the boundary. Grid points as well as the elements of the Jacobian matrix can be computed efficiently and up to machine precision. In the simplest case we construct conformal grids, yet with the help of weight functions and monitor metrics we can control the distribution of cells across the domain. Our algorithm is parallelizable and easy to implement with elementary numerical methods. We assess the quality of grids by considering both the distribution of cell sizes and the accuracy of the solution to elliptic problems. Among the tested grids these key properties are best fulfilled by the grid constructed with the monitor metric approach.
The Effects of Instrumental Elliptical Polarization on Stellar Point Spread Function Fine Structure
NASA Technical Reports Server (NTRS)
Carson, Joseph C.; Kern, Brian D.; Breckinridge, James B.; Trauger, John T.
2005-01-01
We present procedures and preliminary results from a study on the effects of instrumental polarization on the fine structure of the stellar point spread function (PSF). These effects are important to understand because the the aberration caused by instrumental polarization on an otherwise diffraction-limited will likely have have severe consequences for extreme high contrast imaging systems such as NASA's planned Terrestrial Planet Finder (TPF) mission and the proposed NASA Eclipse mission. The report here, describing our efforts to examine these effects, includes two parts: 1) a numerical analysis of the effect of metallic reflection, with some polarization-specific retardation, on a spherical wavefront; 2) an experimental approach for observing this effect, along with some preliminary laboratory results. While the experimental phase of this study requires more fine-tuning to produce meaningful results, the numerical analysis indicates that the inclusion of polarization-specific phase effects (retardation) results in a point spread function (PSF) aberration more severe than the amplitude (reflectivity) effects previously recorded in the literature.
NASA Astrophysics Data System (ADS)
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.
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.
Ellipticities of Elliptical Galaxies in Different Environments
NASA Astrophysics Data System (ADS)
Chen, Cheng-Yu; Hwang, Chorng-Yuan; Ko, Chung-Ming
2016-10-01
We studied the ellipticity distributions of elliptical galaxies in different environments. From the ninth data release of the Sloan Digital Sky Survey, we selected galaxies with absolute {r}\\prime -band magnitudes between -21 and -22. We used the volume number densities of galaxies as the criterion for selecting the environments of the galaxies. Our samples were divided into three groups with different volume number densities. The ellipticity distributions of the elliptical galaxies differed considerably in these three groups of different density regions. We deprojected the observed 2D ellipticity distributions into intrinsic 3D shape distributions, and the result showed that the shapes of the elliptical galaxies were relatively spherically symmetric in the high density region (HDR) and that relatively more flat galaxies were present in the low density region (LDR). This suggests that the ellipticals in the HDRs and LDRs have different origins or that different mechanisms might be involved. The elliptical galaxies in the LDR are likely to have evolved from mergers in relatively anisotropic structures, such as filaments and webs, and might contain information on the anisotropic spatial distribution of their parent mergers. By contrast, elliptical galaxies in the HDR might be formed in more isotropic structures, such as galaxy clusters, or they might encounter more torqueing effects compared with galaxies in LDRs, thereby becoming rounder.
Commutative Families of the Elliptic Macdonald Operator
NASA Astrophysics Data System (ADS)
Saito, Yosuke
2014-03-01
In the paper [J. Math. Phys. 50 (2009), 095215, 42 pages], Feigin, Hashizume, Hoshino, Shiraishi, and Yanagida constructed two families of commuting operators which contain the Macdonald operator (commutative families of the Macdonald operator). They used the Ding-Iohara-Miki algebra and the trigonometric Feigin-Odesskii algebra. In the previous paper [arXiv:1301.4912], the present author constructed the elliptic Ding-Iohara-Miki algebra and the free field realization of the elliptic Macdonald operator. In this paper, we show that by using the elliptic Ding-Iohara-Miki algebra and the elliptic Feigin-Odesskii algebra, we can construct commutative families of the elliptic Macdonald operator. In Appendix, we will show a relation between the elliptic Macdonald operator and its kernel function by the free field realization.
Endomorphism rings of certain Jacobians in finite characteristic
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}.
Multi-GPU Jacobian Accelerated Computing for Soft Field Tomography
Borsic, A.; Attardo, E. A.; Halter, R. J.
2012-01-01
Image reconstruction in soft-field tomography is based on an inverse problem formulation, where a forward model is fitted to the data. In medical applications, where the anatomy presents complex shapes, it is common to use Finite Element Models to represent the volume of interest and to solve a partial differential equation that models the physics of the system. Over the last decade, there has been a shifting interest from 2D modeling to 3D modeling, as the underlying physics of most problems are three-dimensional. Though the increased computational power of modern computers allows working with much larger FEM models, the computational time required to reconstruct 3D images on a fine 3D FEM model can be significant, on the order of hours. For example, in Electrical Impedance Tomography applications using a dense 3D FEM mesh with half a million elements, a single reconstruction iteration takes approximately 15 to 20 minutes with optimized routines running on a modern multi-core PC. It is desirable to accelerate image reconstruction to enable researchers to more easily and rapidly explore data and reconstruction parameters. Further, providing high-speed reconstructions are essential for some promising clinical application of EIT. For 3D problems 70% of the computing time is spent building the Jacobian matrix, and 25% of the time in forward solving. In the present work, we focus on accelerating the Jacobian computation by using single and multiple GPUs. First, we discuss an optimized implementation on a modern multi-core PC architecture and show how computing time is bounded by the CPU-to-memory bandwidth; this factor limits the rate at which data can be fetched by the CPU. Gains associated with use of multiple CPU cores are minimal, since data operands cannot be fetched fast enough to saturate the processing power of even a single CPU core. GPUs have a much faster memory bandwidths compared to CPUs and better parallelism. We are able to obtain acceleration factors of
Image Ellipticity from Atmospheric Aberrations
de Vries, W H; Olivier, S S; Asztalos, S J; Rosenberg, L J; Baker, K L
2007-03-06
We investigate the ellipticity of the point-spread function (PSF) produced by imaging an unresolved source with a telescope, subject to the effects of atmospheric turbulence. It is important to quantify these effects in order to understand the errors in shape measurements of astronomical objects, such as those used to study weak gravitational lensing of field galaxies. The PSF modeling involves either a Fourier transform of the phase information in the pupil plane or a ray-tracing approach, which has the advantage of requiring fewer computations than the Fourier transform. Using a standard method, involving the Gaussian weighted second moments of intensity, we then calculate the ellipticity of the PSF patterns. We find significant ellipticity for the instantaneous patterns (up to more than 10%). Longer exposures, which we approximate by combining multiple (N) images from uncorrelated atmospheric realizations, yield progressively lower ellipticity (as 1/{radical}N). We also verify that the measured ellipticity does not depend on the sampling interval in the pupil plane using the Fourier method. However, we find that the results using the ray-tracing technique do depend on the pupil sampling interval, representing a gradual breakdown of the geometric approximation at high spatial frequencies. Therefore, ray tracing is generally not an accurate method of modeling PSF ellipticity induced by atmospheric turbulence unless some additional procedure is implemented to correctly account for the effects of high spatial frequency aberrations. The Fourier method, however, can be used directly to accurately model PSF ellipticity, which can give insights into errors in the statistics of field galaxy shapes used in studies of weak gravitational lensing.
Isolated elliptical galaxies in the local Universe
NASA Astrophysics Data System (ADS)
Lacerna, I.; Hernández-Toledo, H. M.; Avila-Reese, V.; Abonza-Sane, J.; del Olmo, A.
2016-04-01
Context. We have studied a sample of 89 very isolated, elliptical galaxies at z < 0.08 and compared their properties with elliptical galaxies located in a high-density environment such as the Coma supercluster. Aims: Our aim is to probe the role of environment on the morphological transformation and quenching of elliptical galaxies as a function of mass. In addition, we elucidate the nature of a particular set of blue and star-forming isolated ellipticals identified here. Methods: We studied physical properties of ellipticals, such as color, specific star formation rate, galaxy size, and stellar age, as a function of stellar mass and environment based on SDSS data. We analyzed the blue and star-forming isolated ellipticals in more detail, through photometric characterization using GALFIT, and infer their star formation history using STARLIGHT. Results: Among the isolated ellipticals ≈20% are blue, ≲8% are star forming, and ≈10% are recently quenched, while among the Coma ellipticals ≈8% are blue and just ≲1% are star forming or recently quenched. There are four isolated galaxies (≈4.5%) that are blue and star forming at the same time. These galaxies, with masses between 7 × 109 and 2 × 1010 h-2 M⊙, are also the youngest galaxies with light-weighted stellar ages ≲1 Gyr and exhibit bluer colors toward the galaxy center. Around 30-60% of their present-day luminosity, but only <5% of their present-day mass, is due to star formation in the last 1 Gyr. Conclusions: The processes of morphological transformation and quenching seem to be in general independent of environment since most of elliptical galaxies are "red and dead", although the transition to the red sequence should be faster for isolated ellipticals. In some cases, the isolated environment seems to propitiate the rejuvenation of ellipticals by recent (<1 Gyr) cold gas accretion.
Differential spectral synthesis with a library of elliptical galaxies
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.
Belobo Belobo, D; Ben-Bolie, G H; Kofane, T C
2015-04-01
By using the F-expansion method associated with four auxiliary equations, i.e., the Bernoulli equation, the Riccati equation, the Lenard equation, and the hyperbolic equation, we present exact explicit solutions describing the dynamics of matter-wave condensates with time-varying two- and three-body nonlinearities. Condensates are trapped in a harmonic potential and they exchange atoms with the thermal cloud. These solutions include the generalized Jacobi elliptic function solutions, hyperbolic function solutions, and trigonometric function solutions. In addition, we have also found rational function solutions. Solutions constructed here have many free parameters that can be used to manipulate and control some important features of the condensate, such as the position, width, velocity, acceleration, and homogeneous phase. The stability of the solutions is confirmed by their long-time numerical behavior.
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.
Zhao, Bo; Wang, Lei; Tan, Jiu-Bin
2015-09-08
This paper presents the design and realization of a three degrees of freedom (DOFs) displacement measurement system composed of Hall sensors, which is built for the XYθz displacement measurement of the short stroke stage of the reticle stage of lithography. The measurement system consists of three pairs of permanent magnets mounted on the same plane on the short stroke stage along the Y, Y, X directions, and three single axis Hall sensors correspondingly mounted on the frame of the reticle stage. The emphasis is placed on the decoupling and magnetic field fitting of the three DOFs measurement system. The model of the measurement system is illustrated, and the XY positions and θZ rotation of the short stroke stage can be obtained by decoupling the sensor outputs. A magnetic field fitting by an elliptic function-based compensation method is proposed. The practical field intensity of a permanent magnet at a certain plane height can be substituted for the output voltage of a Hall sensors, which can be expressed by the elliptic function through experimental data as the crucial issue to calculate the three DOFs displacement. Experimental results of the Hall sensor displacement measurement system are presented to validate the proposed three DOFs measurement system.
Zhao, Bo; Wang, Lei; Tan, Jiu-Bin
2015-01-01
This paper presents the design and realization of a three degrees of freedom (DOFs) displacement measurement system composed of Hall sensors, which is built for the XYθz displacement measurement of the short stroke stage of the reticle stage of lithography. The measurement system consists of three pairs of permanent magnets mounted on the same plane on the short stroke stage along the Y, Y, X directions, and three single axis Hall sensors correspondingly mounted on the frame of the reticle stage. The emphasis is placed on the decoupling and magnetic field fitting of the three DOFs measurement system. The model of the measurement system is illustrated, and the XY positions and θZ rotation of the short stroke stage can be obtained by decoupling the sensor outputs. A magnetic field fitting by an elliptic function-based compensation method is proposed. The practical field intensity of a permanent magnet at a certain plane height can be substituted for the output voltage of a Hall sensors, which can be expressed by the elliptic function through experimental data as the crucial issue to calculate the three DOFs displacement. Experimental results of the Hall sensor displacement measurement system are presented to validate the proposed three DOFs measurement system. PMID:26370993
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.
NASA Astrophysics Data System (ADS)
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.
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.
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.
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.
Iterative learning control and the singularity robust Jacobian inverse for mobile manipulators
NASA Astrophysics Data System (ADS)
Tchoń, Krzysztof
2010-11-01
The method of iterative learning control, to a large extent, has been inspired by robotics research, focused on the control of stationary manipulators. In this article we deal with the inverse kinematics problem for mobile manipulators, and show that a very basic singularity robust Jacobian inverse can be derived in a natural way within the framework of iterative learning control. To achieve this objective we have exploited the endogenous configuration space approach. The introduced Jacobian inverse defines the singularity robust Jacobian inverse kinematics algorithm for mobile manipulators. A Kantorovich-type estimate of the region of guaranteed convergence of the algorithm is derived. For two example kinematics, this estimate has been computed efficiently.
Low-rank Quasi-Newton updates for Robust Jacobian lagging in Newton methods
Brown, J.; Brune, P.
2013-07-01
Newton-Krylov methods are standard tools for solving nonlinear problems. A common approach is to 'lag' the Jacobian when assembly or preconditioner setup is computationally expensive, in exchange for some degradation in the convergence rate and robustness. We show that this degradation may be partially mitigated by using the lagged Jacobian as an initial operator in a quasi-Newton method, which applies unassembled low-rank updates to the Jacobian until the next full reassembly. We demonstrate the effectiveness of this technique on problems in glaciology and elasticity. (authors)
Solving Nonlinear Solid Mechanics Problems with the Jacobian-Free Newton Krylov Method
J. D. Hales; S. R. Novascone; R. L. Williamson; D. R. Gaston; M. R. Tonks
2012-06-01
The solution of the equations governing solid mechanics is often obtained via Newton's method. This approach can be problematic if the determination, storage, or solution cost associated with the Jacobian is high. These challenges are magnified for multiphysics applications with many coupled variables. Jacobian-free Newton-Krylov (JFNK) methods avoid many of the difficulties associated with the Jacobian by using a finite difference approximation. BISON is a parallel, object-oriented, nonlinear solid mechanics and multiphysics application that leverages JFNK methods. We overview JFNK, outline the capabilities of BISON, and demonstrate the effectiveness of JFNK for solid mechanics and solid mechanics coupled to other PDEs using a series of demonstration problems.
NASA Astrophysics Data System (ADS)
Tala-Tebue, E.; Tsobgni-Fozap, D. C.; Kenfack-Jiotsa, A.; Kofane, T. C.
2014-06-01
Using the Jacobi elliptic functions and the alternative ( G'/ G-expansion method including the generalized Riccati equation, we derive exact soliton solutions for a discrete nonlinear electrical transmission line in (2+1) dimension. More precisely, these methods are general as they lead us to diverse solutions that have not been previously obtained for the nonlinear electrical transmission lines. This study seeks to show that it is not often necessary to transform the equation of the network into a well-known differential equation before finding its solutions. The solutions obtained by the current methods are generalized periodic solutions of nonlinear equations. The shape of solutions can be well controlled by adjusting the parameters of the network. These exact solutions may have significant applications in telecommunication systems where solitons are used to codify or for the transmission of data.
Elliptical Laguerre-Gaussian correlated Schell-model beam.
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.
A continuum limit of the chiral Jacobian in lattice gauge theory
NASA Astrophysics Data System (ADS)
Fujikawa, Kazuo
1999-04-01
We study the implications of the index theorem and chiral Jacobian in lattice gauge theory, which have been formulated by Hasenfratz, Laliena and Niedermayer and by Lüscher, on the continuum formulation of the chiral Jacobian and anomaly. We take a continuum limit of the lattice Jacobian factor without referring to the perturbative expansion and recover the result of continuum theory by using only the general properties of the lattice Dirac operator. This procedure is based on a set of well-defined rules and thus provides an alternative approach to the conventional analysis of the chiral Jacobian and related anomaly in continuum theory. By using an explicit form of the lattice Dirac operator introduced by Neuberger, which satisfies the Ginsparg-Wilson relation, we illustrate our calculation in some detail. We also briefly comment on the index theorem with a finite cut-off from the present viewpoint.
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.
NASA Astrophysics Data System (ADS)
Ni, Xiao-Ting; Wu, Xin
2014-10-01
The time-transformed leapfrog scheme of Mikkola & Aarseth was specifically designed for a second-order differential equation with two individually separable forms of positions and velocities. It can have good numerical accuracy for extremely close two-body encounters in gravitating few-body systems with large mass ratios, but the non-time-transformed one does not work well. Following this idea, we develop a new explicit symplectic integrator with an adaptive time step that can be applied to a time-dependent Hamiltonian. Our method relies on a time step function having two distinct but equivalent forms and on the inclusion of two pairs of new canonical conjugate variables in the extended phase space. In addition, the Hamiltonian must be modified to be a new time-transformed Hamiltonian with three integrable parts. When this method is applied to the elliptic restricted three-body problem, its numerical precision is explicitly higher by several orders of magnitude than the nonadaptive one's, and its numerical stability is also better. In particular, it can eliminate the overestimation of Lyapunov exponents and suppress the spurious rapid growth of fast Lyapunov indicators for high-eccentricity orbits of a massless third body. The present technique will be useful for conservative systems including N-body problems in the Jacobian coordinates in the the field of solar system dynamics, and nonconservative systems such as a time-dependent barred galaxy model in a rotating coordinate system.
The Structure of Galaxies. III. Two Structural Families of Ellipticals
NASA Astrophysics Data System (ADS)
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.
Nakamura, Kunio; Guizard, Nicolas; Fonov, Vladimir S; Narayanan, Sridar; Collins, D Louis; Arnold, Douglas L
2014-01-01
Gray matter atrophy provides important insights into neurodegeneration in multiple sclerosis (MS) and can be used as a marker of neuroprotection in clinical trials. Jacobian integration is a method for measuring volume change that uses integration of the local Jacobian determinants of the nonlinear deformation field registering two images, and is a promising tool for measuring gray matter atrophy. Our main objective was to compare the statistical power of the Jacobian integration method to commonly used methods in terms of the sample size required to detect a treatment effect on gray matter atrophy. We used multi-center longitudinal data from relapsing-remitting MS patients and evaluated combinations of cross-sectional and longitudinal pre-processing with SIENAX/FSL, SPM, and FreeSurfer, as well as the Jacobian integration method. The Jacobian integration method outperformed these other commonly used methods, reducing the required sample size by a factor of 4-5. The results demonstrate the advantage of using the Jacobian integration method to assess neuroprotection in MS clinical trials.
Jacobian transformed and detailed balance approximations for photon induced scattering
NASA Astrophysics Data System (ADS)
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
NASA Technical Reports Server (NTRS)
Janin, G.; Bond, V. R.
1980-01-01
An independent variable different from the time for elliptic orbit integration is used. Such a time transformation provides an analytical step-size regulation along the orbit. An intermediate anomaly (an anomaly intermediate between the eccentric and the true anomaly) is suggested for optimum performances. A particular case of an intermediate anomaly (the elliptic anomaly) is defined, and its relation with the other anomalies is developed.
Elliptic Gaussian optical vortices
NASA Astrophysics Data System (ADS)
Kotlyar, V. V.; Kovalev, A. A.; Porfirev, A. P.
2017-05-01
We analyze an elliptic optical vortex embedded into a Gaussian beam. Explicit closed expressions for the complex amplitude and normalized orbital angular momentum (OAM) of such a beam are derived. The resulting elliptic Gaussian vortex (EGV) is shown to have a fractional OAM whose maximal value equal to the topological charge n of a conventional Gauss vortex is attained for a zero-ellipticity vortex. As the beam propagates, the major axis of the intensity ellipse in the beam cross section rotates, making the angle of 90° between the initial plane and the focal plane of a spherical lens. On the major axis of the intensity ellipse, there are n intensity nulls of the EGV, with the distance between them varying with propagation distance and varying ellipticity. The distance between the intensity nulls is found to be maximal in the focal plane for a given ellipticity. For zero ellipticity, all intensity nulls get merged into a single n -times degenerate on-axis intensity null. The experimental results are in good agreement with theory.
Elliptic pfaffians and solvable lattice models
NASA Astrophysics Data System (ADS)
Rosengren, Hjalmar
2016-08-01
We introduce and study twelve multivariable theta functions defined by pfaffians with elliptic function entries. We show that, when the crossing parameter is a cubic root of unity, the domain wall partition function for the eight-vertex-solid-on-solid model can be written as a sum of two of these pfaffians. As a limit case, we express the domain wall partition function for the three-colour model as a sum of two Hankel determinants. We also show that certain solutions of the TQ-equation for the supersymmetric eight-vertex model can be expressed in terms of elliptic pfaffians.
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.
An elliptic Virasoro symmetry in 6d
NASA Astrophysics Data System (ADS)
Nieri, Fabrizio
2017-09-01
We define an elliptic deformation of the Virasoro algebra. We conjecture that the R^4× T^2 Nekrasov partition function reproduces the chiral blocks of this algebra. We support this proposal by showing that at special points in the moduli space the 6d Nekrasov partition function reduces to the partition function of a 4d vortex theory supported on R^2× T^2 , which is in turn captured by a free field correlator of vertex operators and screening charges of the elliptic Virasoro algebra.
Multilevel filtering elliptic preconditioners
NASA Technical Reports Server (NTRS)
Kuo, C. C. Jay; Chan, Tony F.; Tong, Charles
1989-01-01
A class of preconditioners is presented for elliptic problems built on ideas borrowed from the digital filtering theory and implemented on a multilevel grid structure. They are designed to be both rapidly convergent and highly parallelizable. The digital filtering viewpoint allows the use of filter design techniques for constructing elliptic preconditioners and also provides an alternative framework for understanding several other recently proposed multilevel preconditioners. Numerical results are presented to assess the convergence behavior of the new methods and to compare them with other preconditioners of multilevel type, including the usual multigrid method as preconditioner, the hierarchical basis method and a recent method proposed by Bramble-Pasciak-Xu.
NASA Astrophysics Data System (ADS)
Mrowczynski, Stanislaw; Shuryak, Edward V.
2003-08-01
We suggest to perform systematic measurements of the elliptic flow fluctuations which are sensitive to the early stage dynamics of heavy-ion collisions at high-energies. Significant flow fluctuations are shown to be generated due to the formation of topological clusters and development of the filamentation instability. The statistical noise and hydrodynamic fluctuations are also estimated.
Using ADIFOR and ADIC to provide Jacobians for the SNES component of PETSc
Wu, Po-Ting; Bischof, C.H.; Hovland, P.D.
1997-11-01
The solution of large-scale nonlinear problems is important to many areas of computational science. The SNES component of PETSc provides a robust and flexible suite of numerical routines for the solving such problems. These routines generally utilize the Jacobian matrix. We present a strategy for using ADIFOR or ADIC to assist in the development of a subroutine for computing this matrix. We illustrate this strategy using one of the PETSc example programs and four different approaches to computing the Jacobian via automatic differentiation.
2015-11-16
At the centre of this amazing image is the elliptical galaxy NGC 3610. Surrounding the galaxy are a wealth of other galaxies of all shapes. There are spiral galaxies, galaxies with a bar in their central regions, distorted galaxies and elliptical galaxies, all visible in the background. In fact, almost every bright dot in this image is a galaxy — the few foreground stars are clearly distinguishable due to the diffraction spikes that overlay their images. NGC 3610 is of course the most prominent object in this image — and a very interesting one at that! Discovered in 1793 by William Herschel, it was later found that this elliptical galaxy contains a disc. This is very unusual, as discs are one of the main distinguishing features of a spiral galaxy. And NGC 3610 even hosts a memarkable bright disc. The reason for the peculiar shape of NGC 3610 stems from its formation history. When galaxies form, they usually resemble our galaxy, the Milky Way, with flat discs and spiral arms where star formation rates are high and which are therefore very bright. An elliptical galaxy is a much more disordered object which results from the merging of two or more disc galaxies. During these violent mergers most of the internal structure of the original galaxies is destroyed. The fact that NGC 3610 still shows some structure in the form of a bright disc implies that it formed only a short time ago. The galaxy’s age has been put at around four billion years and it is an important object for studying the early stages of evolution in elliptical galaxies.
On the explicit solutions of the elliptic Calogero system
NASA Astrophysics Data System (ADS)
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 ∑j
NASA Astrophysics Data System (ADS)
Gao, C.; Lekic, V.
2016-12-01
When constraining the structure of the Earth's continental lithosphere, multiple seismic observables are often combined due to their complementary sensitivities.The transdimensional Bayesian (TB) approach in seismic inversion allows model parameter uncertainties and trade-offs to be quantified with few assumptions. TB sampling yields an adaptive parameterization that enables simultaneous inversion for different model parameters (Vp, Vs, density, radial anisotropy), without the need for strong prior information or regularization. We use a reversible jump Markov chain Monte Carlo (rjMcMC) algorithm to incorporate different seismic observables - surface wave dispersion (SWD), Rayleigh wave ellipticity (ZH ratio), and receiver functions - into the inversion for the profiles of shear velocity (Vs), compressional velocity (Vp), density (ρ), and radial anisotropy (ξ) beneath a seismic station. By analyzing all three data types individually and together, we show that TB sampling can eliminate the need for a fixed parameterization based on prior information, and reduce trade-offs in model estimates. We then explore the effect of different types of misfit functions for receiver function inversion, which is a highly non-unique problem. We compare the synthetic inversion results using the L2 norm, cross-correlation type and integral type misfit function by their convergence rates and retrieved seismic structures. In inversions in which only one type of model parameter (Vs for the case of SWD) is inverted, assumed scaling relationships are often applied to account for sensitivity to other model parameters (e.g. Vp, ρ, ξ). Here we show that under a TB framework, we can eliminate scaling assumptions, while simultaneously constraining multiple model parameters to varying degrees. Furthermore, we compare the performance of TB inversion when different types of model parameters either share the same or use independent parameterizations. We show that different parameterizations
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.
NASA Astrophysics Data System (ADS)
Auclair, J.-P.; Lemieux, J.-F.; Tremblay, L. B.; Ritchie, H.
2017-07-01
New numerical solvers are being considered in response to the rising computational cost of properly solving the sea ice momentum equation at high resolution. The Jacobian free version of Newton's method has allowed models to obtain the converged solution faster than other implicit solvers used previously. To further improve on this recent development, the analytical Jacobian of the 1D sea ice momentum equation is derived and used inside Newton's method. The results are promising in terms of computational efficiency. Although robustness remains an issue for some test cases, it is improved compared to the Jacobian free approach. In order to make use of the strong points of both the new and Jacobian free methods, a hybrid preconditioner using the Picard and Jacobian matrices to improve global and local convergence, respectively, is also introduced. This preconditioner combines the robustness and computational efficiency of the previously used preconditioning matrices when solving the sea ice momentum equation.
NASA Astrophysics Data System (ADS)
Goldstein, Paweł; Hajłasz, Piotr
2017-07-01
We construct an almost everywhere approximately differentiable, orientation and measure preserving homeomorphism of a unit n-dimensional cube onto itself, whose Jacobian is equal to -1 almost everywhere. Moreover, we prove that our homeomorphism can be uniformly approximated by orientation and measure preserving diffeomorphisms.
Simple Evaluation of the Chiral Jacobian with the Overlap Dirac Operator
NASA Astrophysics Data System (ADS)
Suzuki, H.
1999-07-01
The chiral Jacobian, which is defined with Neuberger's overlap Dirac operator of the lattice fermion, is explicitly evaluated in the continuum limit without expanding it in the gauge coupling constant. Our calculational scheme is simple and straightforward. We determine a coefficient of the chiral anomaly for general values of the mass parameter and the Wilson parameter of the overlap Dirac operator.
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.
Elliptic constructions of hyperkahler metrics
NASA Astrophysics Data System (ADS)
Ionas, Radu Aurelian
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.
NASA Astrophysics Data System (ADS)
Chak, Yew-Chung; Varatharajoo, Renuganth
2016-07-01
Many spacecraft attitude control systems today use reaction wheels to deliver precise torques to achieve three-axis attitude stabilization. However, irrecoverable mechanical failure of reaction wheels could potentially lead to mission interruption or total loss. The electrically-powered Solar Array Drive Assemblies (SADA) are usually installed in the pitch axis which rotate the solar arrays to track the Sun, can produce torques to compensate for the pitch-axis wheel failure. In addition, the attitude control of a flexible spacecraft poses a difficult problem. These difficulties include the strong nonlinear coupled dynamics between the rigid hub and flexible solar arrays, and the imprecisely known system parameters, such as inertia matrix, damping ratios, and flexible mode frequencies. In order to overcome these drawbacks, the adaptive Jacobian tracking fuzzy control is proposed for the combined attitude and sun-tracking control problem of a flexible spacecraft during attitude maneuvers in this work. For the adaptation of kinematic and dynamic uncertainties, the proposed scheme uses an adaptive sliding vector based on estimated attitude velocity via approximate Jacobian matrix. The unknown nonlinearities are approximated by deriving the fuzzy models with a set of linguistic If-Then rules using the idea of sector nonlinearity and local approximation in fuzzy partition spaces. The uncertain parameters of the estimated nonlinearities and the Jacobian matrix are being adjusted online by an adaptive law to realize feedback control. The attitude of the spacecraft can be directly controlled with the Jacobian feedback control when the attitude pointing trajectory is designed with respect to the spacecraft coordinate frame itself. A significant feature of this work is that the proposed adaptive Jacobian tracking scheme will result in not only the convergence of angular position and angular velocity tracking errors, but also the convergence of estimated angular velocity to
On the probability distributions of ellipticity
NASA Astrophysics Data System (ADS)
Viola, M.; Kitching, T. D.; Joachimi, B.
2014-04-01
In this paper we derive an exact full expression for the 2D probability distribution of the ellipticity of an object measured from data, only assuming Gaussian noise in pixel values. This is a generalization of the probability distribution for the ratio of single random variables, that is well known, to the multivariate case. This expression is derived within the context of the measurement of weak gravitational lensing from noisy galaxy images. We find that the third flattening, or ɛ-ellipticity, has a biased maximum likelihood but an unbiased mean; and that the third eccentricity, or normalized polarization χ, has both a biased maximum likelihood and a biased mean. The very fact that the bias in the ellipticity is itself a function of the ellipticity requires an accurate knowledge of the intrinsic ellipticity distribution of the galaxies in order to properly calibrate shear measurements. We use this expression to explore strategies for calibration of biases caused by measurement processes in weak gravitational lensing. We find that upcoming weak-lensing surveys like KiDS or DES require calibration fields of the order of several square degrees and 1.2 mag deeper than the wide survey in order to correct for the noise bias. Future surveys like Euclid will require calibration fields of order 40 square degree and several magnitude deeper than the wide survey. We also investigate the use of the Stokes parameters to estimate the shear as an alternative to the ellipticity. We find that they can provide unbiased shear estimates at the cost of a very large variance in the measurement. The PYTHON code used to compute the distributions presented in the paper and to perform the numerical calculations are available on request.
The properties of radio ellipticals
NASA Astrophysics Data System (ADS)
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.
Random Matrix Theory and Elliptic Curves
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
Parallel Computation of the Jacobian Matrix for Nonlinear Equation Solvers Using MATLAB
NASA Technical Reports Server (NTRS)
Rose, Geoffrey K.; Nguyen, Duc T.; Newman, Brett A.
2017-01-01
Demonstrating speedup for parallel code on a multicore shared memory PC can be challenging in MATLAB due to underlying parallel operations that are often opaque to the user. This can limit potential for improvement of serial code even for the so-called embarrassingly parallel applications. One such application is the computation of the Jacobian matrix inherent to most nonlinear equation solvers. Computation of this matrix represents the primary bottleneck in nonlinear solver speed such that commercial finite element (FE) and multi-body-dynamic (MBD) codes attempt to minimize computations. A timing study using MATLAB's Parallel Computing Toolbox was performed for numerical computation of the Jacobian. Several approaches for implementing parallel code were investigated while only the single program multiple data (spmd) method using composite objects provided positive results. Parallel code speedup is demonstrated but the goal of linear speedup through the addition of processors was not achieved due to PC architecture.
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.
NASA Astrophysics Data System (ADS)
Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil
2016-08-01
We develop a new approach for solving the nonlinear Richards' equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioning strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. We also show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.
Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil
2016-04-29
We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioningmore » strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.« less
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.
Reduction Formulae for Products of Theta Functions
Walker, P. L.
2012-01-01
In four cases it is already known that the product of two distinct Jacobian theta functions having the same variable z and the same nome q is a multiple of a single Jacobian theta function, with the multiple independent of z. The main purpose of the present note is to show that this property also applies in the remaining two cases. PMID:26900529
Enhanced Elliptic Grid Generation
NASA Technical Reports Server (NTRS)
Kaul, Upender K.
2007-01-01
An enhanced method of elliptic grid generation has been invented. Whereas prior methods require user input of certain grid parameters, this method provides for these parameters to be determined automatically. "Elliptic grid generation" signifies generation of generalized curvilinear coordinate grids through solution of elliptic partial differential equations (PDEs). Usually, such grids are fitted to bounding bodies and used in numerical solution of other PDEs like those of fluid flow, heat flow, and electromagnetics. Such a grid is smooth and has continuous first and second derivatives (and possibly also continuous higher-order derivatives), grid lines are appropriately stretched or clustered, and grid lines are orthogonal or nearly so over most of the grid domain. The source terms in the grid-generating PDEs (hereafter called "defining" PDEs) make it possible for the grid to satisfy requirements for clustering and orthogonality properties in the vicinity of specific surfaces in three dimensions or in the vicinity of specific lines in two dimensions. The grid parameters in question are decay parameters that appear in the source terms of the inhomogeneous defining PDEs. The decay parameters are characteristic lengths in exponential- decay factors that express how the influences of the boundaries decrease with distance from the boundaries. These terms govern the rates at which distance between adjacent grid lines change with distance from nearby boundaries. Heretofore, users have arbitrarily specified decay parameters. However, the characteristic lengths are coupled with the strengths of the source terms, such that arbitrary specification could lead to conflicts among parameter values. Moreover, the manual insertion of decay parameters is cumbersome for static grids and infeasible for dynamically changing grids. In the present method, manual insertion and user specification of decay parameters are neither required nor allowed. Instead, the decay parameters are
NASA 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).
2015-11-30
Like a lighthouse in the fog the luminous core of NGC 2768 slowly fades outwards to a dull white haze in this image taken by the NASA/ESA Hubble Space Telescope. NGC 2768 is an elliptical galaxy in the constellation of Ursa Major (The Great Bear). It is a huge bundle of stars, dominated by a bright central region, where a supermassive black hole feasts on a constant stream of gas and dust being fed to it by its galactic host. The galaxy is also marked by a prominent plume of dust reaching out from the centre and lying perpendicular to the galaxy’s plane. This dust conceals a symmetrical, s-shaped pair of jets that are being produced by the supermassive black hole as it feeds.
Beyond CFT: Deformed Virasoro and Elliptic Algebras
NASA Astrophysics Data System (ADS)
Odake, Satoru
Introduction Conformal Field Theory and Virasoro Algebra Conformal Field Theory Virasoro Algebra Free Field Realization Deformed Virasoro Algebra (A1(1) Type) Definition and Consistency Conformal Limit Representation Theory Free Field Realization Higher DVA Currents Solvable Lattice Models and Elliptic Algebras Solvable Lattice Models and Yang-Baxter Equation Corner Transfer Matrices and Vertex Operators Introduction to Quasi-Hopf Algebra Elliptic Quantum Groups Free Field Approach to ABF Model ABF Model Vertex Operators Local Height Probability Form Factor OPE and Trace Screening Operators and Vertex Operators DVA (A2(2) Type) and Dilute AL Models DVA (A2(2)) Free Field Realization Dilute AL Models Free Field Approach OPE and trace Conclusion References Some Formulas Some Functions Delta Function Some Summations Some Integrals Hausdorff Formula Trace Technique
C1,1 regularity for degenerate elliptic obstacle problems
NASA Astrophysics Data System (ADS)
Daskalopoulos, Panagiota; Feehan, Paul M. N.
2016-03-01
The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerate-elliptic partial differential operator, where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. In mathematical finance, solutions to the obstacle problem for the elliptic Heston operator correspond to value functions for perpetual American-style options on the underlying asset. With the aid of weighted Sobolev spaces and weighted Hölder spaces, we establish the optimal C 1 , 1 regularity (up to the boundary of the half-plane) for solutions to obstacle problems for the elliptic Heston operator when the obstacle functions are sufficiently smooth.
MIB Galerkin method for elliptic interface problems
Xia, Kelin; Zhan, Meng; Wei, Guo-Wei
2014-01-01
Summary Material interfaces are omnipresent in the real-world structures and devices. Mathematical modeling of material interfaces often leads to elliptic partial differential equations (PDEs) with discontinuous coefficients and singular sources, which are commonly called elliptic interface problems. The development of high-order numerical schemes for elliptic interface problems has become a well defined field in applied and computational mathematics and attracted much attention in the past decades. Despite of significant advances, challenges remain in the construction of high-order schemes for nonsmooth interfaces, i.e., interfaces with geometric singularities, such as tips, cusps and sharp edges. The challenge of geometric singularities is amplified when they are associated with low solution regularities, e.g., tip-geometry effects in many fields. The present work introduces a matched interface and boundary (MIB) Galerkin method for solving two-dimensional (2D) elliptic PDEs with complex interfaces, geometric singularities and low solution regularities. The Cartesian grid based triangular elements are employed to avoid the time consuming mesh generation procedure. Consequently, the interface cuts through elements. To ensure the continuity of classic basis functions across the interface, two sets of overlapping elements, called MIB elements, are defined near the interface. As a result, differentiation can be computed near the interface as if there is no interface. Interpolation functions are constructed on MIB element spaces to smoothly extend function values across the interface. A set of lowest order interface jump conditions is enforced on the interface, which in turn, determines the interpolation functions. The performance of the proposed MIB Galerkin finite element method is validated by numerical experiments with a wide range of interface geometries, geometric singularities, low regularity solutions and grid resolutions. Extensive numerical studies confirm
MIB Galerkin method for elliptic interface problems.
Xia, Kelin; Zhan, Meng; Wei, Guo-Wei
2014-12-15
Material interfaces are omnipresent in the real-world structures and devices. Mathematical modeling of material interfaces often leads to elliptic partial differential equations (PDEs) with discontinuous coefficients and singular sources, which are commonly called elliptic interface problems. The development of high-order numerical schemes for elliptic interface problems has become a well defined field in applied and computational mathematics and attracted much attention in the past decades. Despite of significant advances, challenges remain in the construction of high-order schemes for nonsmooth interfaces, i.e., interfaces with geometric singularities, such as tips, cusps and sharp edges. The challenge of geometric singularities is amplified when they are associated with low solution regularities, e.g., tip-geometry effects in many fields. The present work introduces a matched interface and boundary (MIB) Galerkin method for solving two-dimensional (2D) elliptic PDEs with complex interfaces, geometric singularities and low solution regularities. The Cartesian grid based triangular elements are employed to avoid the time consuming mesh generation procedure. Consequently, the interface cuts through elements. To ensure the continuity of classic basis functions across the interface, two sets of overlapping elements, called MIB elements, are defined near the interface. As a result, differentiation can be computed near the interface as if there is no interface. Interpolation functions are constructed on MIB element spaces to smoothly extend function values across the interface. A set of lowest order interface jump conditions is enforced on the interface, which in turn, determines the interpolation functions. The performance of the proposed MIB Galerkin finite element method is validated by numerical experiments with a wide range of interface geometries, geometric singularities, low regularity solutions and grid resolutions. Extensive numerical studies confirm the
NASA Astrophysics Data System (ADS)
Kaus, B.; Popov, A.
2015-12-01
The analytical expression for the Jacobian is a key component to achieve fast and robust convergence of the nonlinear Newton-Raphson iterative solver. Accomplishing this task in practice often requires a significant algebraic effort. Therefore it is quite common to use a cheap alternative instead, for example by approximating the Jacobian with a finite difference estimation. Despite its simplicity it is a relatively fragile and unreliable technique that is sensitive to the scaling of the residual and unknowns, as well as to the perturbation parameter selection. Unfortunately no universal rule can be applied to provide both a robust scaling and a perturbation. The approach we use here is to derive the analytical Jacobian for the coupled set of momentum, mass, and energy conservation equations together with the elasto-visco-plastic rheology and a marker in cell/staggered finite difference method. The software project LaMEM (Lithosphere and Mantle Evolution Model) is primarily developed for the thermo-mechanically coupled modeling of the 3D lithospheric deformation. The code is based on a staggered grid finite difference discretization in space, and uses customized scalable solvers form PETSc library to efficiently run on the massively parallel machines (such as IBM Blue Gene/Q). Currently LaMEM relies on the Jacobian-Free Newton-Krylov (JFNK) nonlinear solver, which approximates the Jacobian-vector product using a simple finite difference formula. This approach never requires an assembled Jacobian matrix and uses only the residual computation routine. We use an approximate Jacobian (Picard) matrix to precondition the Krylov solver with the Galerkin geometric multigrid. Because of the inherent problems of the finite difference Jacobian estimation, this approach doesn't always result in stable convergence. In this work we present and discuss a matrix-free technique in which the Jacobian-vector product is replaced by analytically-derived expressions and compare results
Elliptic Hermite-Gaussian soliton in anisotropic strong nonlocal media
NASA Astrophysics Data System (ADS)
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.
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.
Extended skew-symmetric form for summation-by-parts operators and varying Jacobians
NASA Astrophysics Data System (ADS)
Ranocha, Hendrik; Öffner, Philipp; Sonar, Thomas
2017-08-01
A generalised analytical notion of summation-by-parts (SBP) methods is proposed, extending the concept of SBP operators in the correction procedure via reconstruction (CPR), a framework of high-order methods for conservation laws. For the first time, SBP operators with dense norms and not including boundary points are used to get an entropy stable split-form of Burgers' equation. Moreover, overcoming limitations of the finite difference framework, stability for curvilinear grids and dense norms is obtained for SBP CPR methods by using a suitable way to compute the Jacobian.
Acceleration of k-Eigenvalue / Criticality Calculations using the Jacobian-Free Newton-Krylov Method
Dana Knoll; HyeongKae Park; Chris Newman
2011-02-01
We present a new approach for the $k$--eigenvalue problem using a combination of classical power iteration and the Jacobian--free Newton--Krylov method (JFNK). The method poses the $k$--eigenvalue problem as a fully coupled nonlinear system, which is solved by JFNK with an effective block preconditioning consisting of the power iteration and algebraic multigrid. We demonstrate effectiveness and algorithmic scalability of the method on a 1-D, one group problem and two 2-D two group problems and provide comparison to other efforts using silmilar algorithmic approaches.
Multi-GPU Jacobian accelerated computing for soft-field tomography.
Borsic, A; Attardo, E A; Halter, R J
2012-10-01
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 (FEMs) to represent the volume of interest and 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 3D. Although 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 (EIT) applications using a dense 3D FEM mesh with half a million elements, a single reconstruction iteration takes approximately 15-20 min 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. Furthermore, providing high-speed reconstructions is 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 this 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 the 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 much faster memory bandwidths compared to CPUs and better parallelism. We are able to obtain acceleration factors of 20
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.
ELLIPT2D: A Flexible Finite Element Code Written Python
Pletzer, A.; Mollis, J.C.
2001-03-22
The use of the Python scripting language for scientific applications and in particular to solve partial differential equations is explored. It is shown that Python's rich data structure and object-oriented features can be exploited to write programs that are not only significantly more concise than their counter parts written in Fortran, C or C++, but are also numerically efficient. To illustrate this, a two-dimensional finite element code (ELLIPT2D) has been written. ELLIPT2D provides a flexible and easy-to-use framework for solving a large class of second-order elliptic problems. The program allows for structured or unstructured meshes. All functions defining the elliptic operator are user supplied and so are the boundary conditions, which can be of Dirichlet, Neumann or Robbins type. ELLIPT2D makes extensive use of dictionaries (hash tables) as a way to represent sparse matrices.Other key features of the Python language that have been widely used include: operator over loading, error handling, array slicing, and the Tkinter module for building graphical use interfaces. As an example of the utility of ELLIPT2D, a nonlinear solution of the Grad-Shafranov equation is computed using a Newton iterative scheme. A second application focuses on a solution of the toroidal Laplace equation coupled to a magnetohydrodynamic stability code, a problem arising in the context of magnetic fusion research.
Focusing of an elliptical mirror based system with aberrations
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Arshad, M.; Seadawy, Aly R.; Lu, Dianchen
2017-08-01
The higher-order nonlinear Schrödinger equation (NLSE) with fourth-order dispersion, cubic-quintic terms, self-steepening and nonlinear dispersive terms describes the propagation of extremely short pulses in optical fibers. In this paper, the elliptic function, bright and dark solitons and solitary wave solutions of higher-order NLSE are constructed by employing a modified extended direct algebraic method, which has important applications in applied mathematics and physics. Furthermore, we also present the formation conditions of the bright and dark solitons for this equation. The modulation instability is utilized to discuss the stability of these solutions, which shows that all solutions are exact and stable. Many other higher-order nonlinear evolution equations arising in applied sciences can also be solved by this powerful, effective and reliable method.
Jacobian-Based Iterative Method for Magnetic Localization in Robotic Capsule Endoscopy.
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°.
Royuela-Del-Val, Javier; Cordero-Grande, Lucilio; Simmross-Wattenberg, Federico; Martín-Fernández, Marcos; Alberola-López, Carlos
2017-03-01
To eliminate the need of spatial intraframe regularization in a recently reported dynamic MRI compressed-sensing-based reconstruction method with motion compensation and to increase its performance. We propose a new regularization metric based on the introduction of a spatial weighting measure given by the Jacobian of the estimated deformations. It shows convenient discretization properties and, as a byproduct, it also provides a theoretical support to a result reported by others based on an intuitive design. The method has been applied to the reconstruction of both short and long axis views of the heart of four healthy volunteers. Quantitative image quality metrics as well as straightforward visual assessment are reported. Short and long axis reconstructions of cardiac cine MRI sequences have shown superior results than previously reported methods both in terms of quantitative metrics and of visual assessment. Fine details are better preserved due to the lack of additional intraframe regularization, with no significant image artifacts even for an acceleration factor of 12. The proposed Jacobian Weighted temporal Total Variation results in better reconstructions of highly undersampled cardiac cine MRI than previously proposed methods and sets a theoretical ground for forward and backward predictors used elsewhere. Magn Reson Med 77:1208-1215, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.
Jacobian-Based Iterative Method for Magnetic Localization in Robotic Capsule Endoscopy
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
NASA Astrophysics Data System (ADS)
Hammond, G. E.; Valocchi, A. J.; Lichtner, P. C.
2005-04-01
Modern multicomponent geochemical transport models require the use of parallel computation for carrying out three-dimensional, field-scale simulations due to extreme memory and processing demands. However, to fully exploit the advanced computational power provided by today's supercomputers, innovative parallel algorithms are needed. We demonstrate the use of Jacobian-free Newton-Krylov (JFNK) within the Newton-Raphson method to reduce memory and processing requirements on high-performance computers. We also demonstrate the use of physics-based preconditioners, which are often necessary when using JFNK since no explicit Jacobian matrix is ever formed. We apply JFNK to simulate enhanced in situ bioremediation of a NAPL source zone, which entails highly coupled geochemical and biodegradation reactions. The algorithm's performance is evaluated and compared with conventional solvers and preconditioners. We found that JFNK provided substantial saving in memory (i.e. 30-60%) on problems utilizing up to 512 processors on LANL's ASCI Q. However, the performance based on wallclock time was less advantageous, coming out on par with conventional techniques. In addition, we illustrate deficiencies in physics-based preconditioner performance for biogeochemical transport problems with components that undergo significant sorption or form a local quasi-stationary state.
Recovery Discontinuous Galerkin Jacobian-Free Newton-Krylov Method for All-Speed Flows
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.
Extending the Belavin-Knizhnik "wonderful formula" by the characterization of the Jacobian
NASA Astrophysics Data System (ADS)
Matone, Marco
2012-10-01
A long-standing question in string theory is to find the explicit expression of the bosonic measure, a crucial issue also in determining the superstring measure. Such a measure was known up to genus three. Belavin and Knizhnik conjectured an expression for genus four which has been proved in the framework of the recently introduced vector-valued Teichmüller modular forms. It turns out that for g ≥ 4 the bosonic measure is expressed in terms of such forms. In particular, the genus four Belavin-Knizhnik "wonderful formula" has a remarkable extension to arbitrary genus whose structure is deeply related to the characterization of the Jacobian locus. Furthermore, it turns out that the bosonic string measure has an elegant geometrical interpretation as generating the quadrics in ℙ g-1 characterizing the Riemann surface. All this leads to identify forms on the Siegel upper half-space that, if certain conditions related to the characterization of the Jacobian are satisfied, express the bosonic measure as a multiresidue in the Siegel upper half-space. We also suggest that it may exist a super analog on the super Siegel half-space.
STRUCTURE AND FORMATION OF ELLIPTICAL AND SPHEROIDAL GALAXIES
Kormendy, John; Fisher, David B.; Cornell, Mark E.; Bender, Ralf E-mail: dbfisher@astro.as.utexas.edu E-mail: bender@usm.uni-muenchen.de
2009-05-15
New surface photometry of all known elliptical galaxies in the Virgo cluster is combined with published data to derive composite profiles of brightness, ellipticity, position angle, isophote shape, and color over large radius ranges. These provide enough leverage to show that Sersic log I {proportional_to} r {sup 1/n} functions fit the brightness profiles I(r) of nearly all ellipticals remarkably well over large dynamic ranges. Therefore, we can confidently identify departures from these profiles that are diagnostic of galaxy formation. Two kinds of departures are seen at small radii. All 10 of our ellipticals with total absolute magnitudes M{sub VT} {<=} -21.66 have cuspy cores-'missing light'-at small radii. Cores are well known and naturally scoured by binary black holes (BHs) formed in dissipationless ('dry') mergers. All 17 ellipticals with -21.54 {<=} M{sub VT} {<=} -15.53 do not have cores. We find a new distinct component in these galaxies: all coreless ellipticals in our sample have extra light at the center above the inward extrapolation of the outer Sersic profile. In large ellipticals, the excess light is spatially resolved and resembles the central components predicted in numerical simulations of mergers of galaxies that contain gas. In the simulations, the gas dissipates, falls toward the center, undergoes a starburst, and builds a compact stellar component that, as in our observations, is distinct from the Sersic-function main body of the elliptical. But ellipticals with extra light also contain supermassive BHs. We suggest that the starburst has swamped core scouring by binary BHs. That is, we interpret extra light components as a signature of formation in dissipative ('wet') mergers. Besides extra light, we find three new aspects to the ('E-E') dichotomy into two types of elliptical galaxies. Core galaxies are known to be slowly rotating, to have relatively anisotropic velocity distributions, and to have boxy isophotes. We show that they have
Joseph, Ilon
2014-05-27
Jacobian-free Newton-Krylov (JFNK) algorithms are a potentially powerful class of methods for solving the problem of coupling codes that address dfferent physics models. As communication capability between individual submodules varies, different choices of coupling algorithms are required. The more communication that is available, the more possible it becomes to exploit the simple sparsity pattern of the Jacobian, albeit of a large system. The less communication that is available, the more dense the Jacobian matrices become and new types of preconditioners must be sought to efficiently take large time steps. In general, methods that use constrained or reduced subsystems can offer a compromise in complexity. The specific problem of coupling a fluid plasma code to a kinetic neutrals code is discussed as an example.
NASA Astrophysics Data System (ADS)
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.
Elliptic vortices in composite Mathieu lattices
Ye Fangwei; Mihalache, Dumitru; Hu Bambi
2009-05-15
We address the elliptically shaped vortex solitons in defocusing nonlinear media imprinted with a composite Mathieu lattice. Elliptic vortices feature anisotropic patterns both in intensity and phase, and can only exist when their energy flows exceed some certain threshold. Single-charged elliptic vortices are found to arise via bifurcation from dipole modes, which is an example in the context of optics studies of symmetry breaking bifurcations for the phase dislocations of different dimensionalities. Higher-order elliptic vortices with topological charge S could exhibit spatially separated S single-charged phase singularities, leading to their stabilization. The salient features of reported elliptic vortices qualitatively hold for other elliptic shaped confining potentials.
Energy and the Elliptical Orbit
NASA Astrophysics Data System (ADS)
Nettles, Bill
2009-03-01
In the January 2007 issue of The Physics Teacher, Prentis, Fulton, Hesse, and Mazzino describe a laboratory exercise in which students use a geometrical analysis inspired by Newton to show that an elliptical orbit and an inverse-square law force go hand in hand. The historical, geometrical, and teamwork aspects of the exercise are useful and important. This paper presents an exercise which uses an energy/angular momentum conservation model for elliptical orbits. This exercise can be done easily by an individual student and on regular notebook-sized paper.
Guided modes of elliptical metamaterial waveguides
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.
Formation, evolution and properties of isolated field elliptical galaxies
NASA Astrophysics Data System (ADS)
Niemi, Sami-Matias; Heinämäki, Pekka; Nurmi, Pasi; Saar, Enn
2010-06-01
We study the properties, evolution and formation mechanisms of isolated field elliptical (IfE) galaxies. We create a `mock' catalogue of IfE galaxies from the Millennium Simulation Galaxy Catalogue, and trace their merging histories. The formation, identity and assembly redshifts of simulated isolated and non-isolated elliptical galaxies are studied and compared. Observational and numerical data are used to compare age, mass and the colour-magnitude relation. Our results, based on simulation data, show that almost 7 per cent of all elliptical galaxies brighter than -19mag in B band can be classified as IfE galaxies. Results also show that isolated elliptical galaxies have a rather flat luminosity function; a number density of ~3 × 10-6h3Mpc-3mag-1, throughout their B-band magnitudes. IfE galaxies show bluer colours than non-isolated elliptical galaxies and they appear younger, in a statistical sense, according to their mass-weighted age. IfE galaxies also form and assemble at lower redshifts compared to non-isolated elliptical galaxies. About 46 per cent of IfE galaxies have undergone at least one major merging event in their formation history, while the same fraction is only ~33 per cent for non-isolated ellipticals. Almost all (~98 per cent) isolated elliptical galaxies show merging activity during their evolution, pointing towards the importance of mergers in the formation of IfE galaxies. The mean time of the last major merging is at z ~ 0.6 or 6Gyr ago for isolated ellipticals, while non-isolated ellipticals experience their last major merging significantly earlier at z ~ 1.1 or 8Gyr ago. After inspecting merger trees of simulated IfE galaxies, we conclude that three different, yet typical, formation mechanisms can be identified: solitude, coupling and cannibalism. Our results also predict a previously unobserved population of blue, dim and light galaxies that fulfil observational criteria to be classified as IfE galaxies. This separate population comprises
An Elliptic Garnier System from Interpolation
NASA Astrophysics Data System (ADS)
Yamada, Yasuhiko
2017-09-01
Considering a certain interpolation problem, we derive a series of elliptic difference isomonodromic systems together with their Lax forms. These systems give a multivariate extension of the elliptic Painlevé equation.
Nonclassical properties of odd and even elliptical states
NASA Astrophysics Data System (ADS)
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.
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.
NASA Astrophysics Data System (ADS)
Lin, J.; Lin, C. C.; Lo, H.-S.
2009-10-01
Interest in complex robotic systems is growing in new application areas. An example of such a robotic system is a dexterous manipulator mounted on an oscillatory base. In literature, such systems are known as macro/micro systems. This work proposes pseudo-inverse Jacobian feedback control laws and applies grey relational analysis for tuning outer-loop PID control parameters of Cartesian computed-torque control law for robotic manipulators mounted on oscillatory bases. The priority when modifying controller parameters should be the top ranking importance among parameters. Grey relational grade is utilized to investigate the sensitivity of tuning the auxiliary signal PID of the Cartesian computed-torque law to achieve desired performance. Results of this study can be feasible to numerous mechanical systems, such as mobile robots, gantry cranes, underwater robots, and other dynamic systems mounted on oscillatory bases, for moving the end-effector to a desired Cartesian position.
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. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.
The ESS elliptical cavity cryomodules
NASA Astrophysics Data System (ADS)
Darve, Christine; Bosland, Pierre; Devanz, Guillaume; Olivier, Gilles; Renard, Bertrand; Thermeau, Jean-Pierre
2014-01-01
The European Spallation Source (ESS) is a multi-disciplinary research centre under design and construction in Lund, Sweden. This new facility is funded by a collaboration of 17 European countries and is expected to be up to 30 times brighter than today's leading facilities and neutron sources. The ESS will enable new opportunities for researchers in the fields of life sciences, energy, environmental technology, cultural heritage and fundamental physics. A 5 MW long pulse proton accelerator is used to reach this goal. The pulsed length is 2.86 ms, the repetition frequency is 14 Hz (4 % duty cycle), and the beam current is 62.5 mA. The superconducting section of the Linac accelerates the beam from 80 MeV to 2.0 GeV. It is composed of one string of spoke cavity cryomodule and two strings of elliptical cavity cryomodules. These cryomodules contain four elliptical Niobium cavities operating at 2 K and at a frequency of 704.42 MHz. This paper introduces the thermo-mechanical design, the prototyping and the expected operation of the ESS elliptical cavity cryomodules. An Elliptical Cavity Cryomodule Technology Demonstrator (ECCTD) will be built and tested in order to validate the ESS series production.
Wavelength meter having elliptical wedge
Hackel, R.P.; Feldman, M.
1992-12-01
A wavelength meter is disclosed which can determine the wavelength of a laser beam from a laser source within an accuracy range of two parts in 10[sup 8]. The wavelength meter has wedge having an elliptically shaped face to the optical path of the laser source and includes interferometer plates which form a vacuum housing. 7 figs.
Wavelength meter having elliptical wedge
Hackel, Richard P.; Feldman, Mark
1992-01-01
A wavelength meter is disclosed which can determine the wavelength of a laser beam from a laser source within an accuracy range of two parts in 10.sup.8. The wavelength meter has wedge having an elliptically shaped face to the optical path of the laser source and includes interferometer plates which form a vacuum housing.
Energy and the Elliptical Orbit
ERIC Educational Resources Information Center
Nettles, Bill
2009-01-01
In the January 2007 issue of "The Physics Teacher," Prentis, Fulton, Hesse, and Mazzino describe a laboratory exercise in which students use a geometrical analysis inspired by Newton to show that an elliptical orbit and an inverse-square law force go hand in hand. The historical, geometrical, and teamwork aspects of the exercise are useful and…
The ESS elliptical cavity cryomodules
Darve, Christine; Bosland, Pierre; Devanz, Guillaume; Renard, Bertrand; Olivier, Gilles; Thermeau, Jean-Pierre
2014-01-29
The European Spallation Source (ESS) is a multi-disciplinary research centre under design and construction in Lund, Sweden. This new facility is funded by a collaboration of 17 European countries and is expected to be up to 30 times brighter than today’s leading facilities and neutron sources. The ESS will enable new opportunities for researchers in the fields of life sciences, energy, environmental technology, cultural heritage and fundamental physics. A 5 MW long pulse proton accelerator is used to reach this goal. The pulsed length is 2.86 ms, the repetition frequency is 14 Hz (4 % duty cycle), and the beam current is 62.5 mA. The superconducting section of the Linac accelerates the beam from 80 MeV to 2.0 GeV. It is composed of one string of spoke cavity cryomodule and two strings of elliptical cavity cryomodules. These cryomodules contain four elliptical Niobium cavities operating at 2 K and at a frequency of 704.42 MHz. This paper introduces the thermo-mechanical design, the prototyping and the expected operation of the ESS elliptical cavity cryomodules. An Elliptical Cavity Cryomodule Technology Demonstrator (ECCTD) will be built and tested in order to validate the ESS series production.
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…
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.
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.
NASA Astrophysics Data System (ADS)
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.
An improved nearly-orthogonal structured mesh generation system with smoothness control functions
USDA-ARS?s Scientific Manuscript database
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...
Elliptic surface grid generation on minimal and parametrized surfaces
NASA Technical Reports Server (NTRS)
Spekreijse, S. P.; Nijhuis, G. H.; Boerstoel, J. W.
1995-01-01
An elliptic grid generation method, which generates boundary conforming grids in a two dimensional physical space, is presented. The method is based on the composition of an algebraic and elliptic transformation. The composite mapping obeys the Poisson grid generation system with control functions specified by the algebraic transformation. It is shown that the grid generation on a minimal surface in a three dimensional space is equivalent to the grid generation in a two dimensional domain in physical space. A second elliptic grid generation method, which generates boundary conforming grids on smooth surfaces, is presented. Concerning surface modeling, it is shown that bicubic Hermit interpolation is an excellent method to generate a smooth surface crossing a discrete set of control points.
System Size, Energy, Pseudorapidity, and Centrality Dependence of Elliptic Flow
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.
Magneto-optic rotation and ellipticity of ultrathin ferromagnetic films
NASA Astrophysics Data System (ADS)
Moog, E. R.; Zak, J.; Huberman, M. L.; Bader, S. D.
1989-05-01
Magneto-optic rotation φ' and ellipticity φ'' values are reported as a function of thickness for 0-400 Å of bcc Fe(100) epitaxially deposited on Au(100) for both s- and p-polarized He-Ne laser light. The values are derived from a formula that connects φ' and φ'' with our recently reported longitudinal Kerr-effect measurements of φm=(φ'2+φ''2)1/2 and the parameters of two optical compensators that are used to convert ellipticity to rotation. The measurements were made in situ through an ultrahigh-vacuum window; our approach eliminates the effect of the window birefringence. The dominant contribution to φm reverses from being φ'' in the ultrathin limit to being φ' in the thick-film limit. Also, in the 0-30 Å range, the rotation remains near zero while the ellipticity increases linearly.
Calderón's method on an elliptical domain.
Muller, P A; Isaacson, D; Newell, J C; Saulnier, G J
2013-06-01
One possible application for electrical impedance tomography is in medical imaging where lung and heart function may be monitored. One drawback of current algorithms is that they are implemented for use in a circular domain, but a human thorax is more elliptical than circular. In this paper, a reconstruction algorithm based on the work of Calderón (1980 Seminar on Numerical Analysis and its Applications to Continuum Physics (Rio de Janeiro) pp 65-75) on the inverse conductivity problem is derived for an elliptical domain. It is explained how this reconstruction algorithm uses a transformed Dirichlet-to-Neumann map. Experimental results from an elliptical tank are given to show how correct domain modelling reduces the artefacts produced by this version of Calderón's reconstruction algorithm.
Cold dust in elliptical galaxies.
NASA Astrophysics Data System (ADS)
Wiklind, T.; Henkel, C.
1995-05-01
We have observed the λ1250 µm flux in 8 elliptical galaxies using the MPIfR 7-channel bolometer system attachet to the IRAM 30-m telescope. Five of the galaxies are detected at more than 3σ, two are tentatively detected and for one we obtained an upper limit. For two of the detected galaxies, the CO(2-1) line makes a significant contribution to the measured λ1250 µm flux. A comparison of the λ1250 µm fluxes, corrected for the CO(2-1) line contribution, with IRAS 60 and 100µm data shows that there is a colt dust component (Td~<20K) in two of the ellipticals. The other galaxies have λ1250 µm fluxes consistent with a one-temperature component, with Td typically between 20-30K.
Counterrotating cores in elliptical galaxies
NASA Astrophysics Data System (ADS)
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.
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.
A Jacobian-Free Newton Krylov Method for Mortar-Discretized Thermomechanical Contact Problems
Glen Hansen
2011-07-01
Multibody contact problems are common within the field of multiphysics simulation. Applications involving thermomechanical contact scenarios are also quite prevalent. Such problems can be challenging to solve due to the likelihood of thermal expansion affecting contact geometry which, in turn, can change the thermal behavior of the components being analyzed. This paper explores a simple model of a light water reactor nuclear reactor fuel rod, which consists of cylindrical pellets of uranium dioxide (UO2) fuel sealed within a Zircalloy cladding tube. The tube is initially filled with helium gas, which fills the gap between the pellets and cladding tube. The accurate modeling of heat transfer across the gap between fuel pellets and the protective cladding is essential to understanding fuel performance, including cladding stress and behavior under irradiated conditions, which are factors that affect the lifetime of the fuel. The thermomechanical contact approach developed here is based on the mortar finite element method, where Lagrange multipliers are used to enforce weak continuity constraints at participating interfaces. In this formulation, the heat equation couples to linear mechanics through a thermal expansion term. Lagrange multipliers are used to formulate the continuity constraints for both heat flux and interface traction at contact interfaces. The resulting system of nonlinear algebraic equations are cast in residual form for solution of the transient problem. A Jacobian-free Newton Krylov method is used to provide for fully-coupled solution of the coupled thermal contact and heat equations.
A Jacobian-free Newton Krylov method for mortar-discretized thermomechanical contact problems
Hansen, Glen
2011-07-20
Multibody contact problems are common within the field of multiphysics simulation. Applications involving thermomechanical contact scenarios are also quite prevalent. Such problems can be challenging to solve due to the likelihood of thermal expansion affecting contact geometry which, in turn, can change the thermal behavior of the components being analyzed. This paper explores a simple model of a light water reactor nuclear fuel rod, which consists of cylindrical pellets of uranium dioxide (UO{sub 2}) fuel sealed within a Zircalloy cladding tube. The tube is initially filled with helium gas, which fills the gap between the pellets and cladding tube. The accurate modeling of heat transfer across the gap between fuel pellets and the protective cladding is essential to understanding fuel performance, including cladding stress and behavior under irradiated conditions, which are factors that affect the lifetime of the fuel. The thermomechanical contact approach developed here is based on the mortar finite element method, where Lagrange multipliers are used to enforce weak continuity constraints at participating interfaces. In this formulation, the heat equation couples to linear mechanics through a thermal expansion term. Lagrange multipliers are used to formulate the continuity constraints for both heat flux and interface traction at contact interfaces. The resulting system of nonlinear algebraic equations are cast in residual form for solution of the transient problem. A Jacobian-free Newton Krylov method is used to provide for fully-coupled solution of the coupled thermal contact and heat equations.
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.
Optimization of computations for adjoint field and Jacobian needed in 3D CSEM inversion
NASA Astrophysics Data System (ADS)
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 (comp`utational 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.
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.
NASA Astrophysics Data System (ADS)
Bernardara, M.; Tabuada, G.
2016-06-01
Conjectures of Beilinson-Bloch type predict that the low-degree rational Chow groups of intersections of quadrics are one-dimensional. This conjecture was proved by Otwinowska in [20]. By making use of homological projective duality and the recent theory of (Jacobians of) non-commutative motives, we give an alternative proof of this conjecture in the case of a complete intersection of either two quadrics or three odd-dimensional quadrics. Moreover, we prove that in these cases the unique non-trivial algebraic Jacobian is the middle one. As an application, we make use of Vial's work [26], [27] to describe the rational Chow motives of these complete intersections and show that smooth fibrations into such complete intersections over bases S of small dimension satisfy Murre's conjecture (when \\dim (S)≤ 1), Grothendieck's standard conjecture of Lefschetz type (when \\dim (S)≤ 2), and Hodge's conjecture (when \\dim(S)≤ 3).
On the Dichotomy between Normal and Dwarf Ellipticals
NASA Astrophysics Data System (ADS)
Schombert, James M.
2017-05-01
> ) which overlaps the dwarf elliptical sample (62 galaxies) in luminosity and size. The faint ellipticals extend the linear structural correlations found for bright ellipticals into parameter space not occupied by dwarf ellipticals indicating a dichotomy exists between the two types. In particular, many faint ellipticals have significantly higher effective surface brightnesses compared to dwarf ellipticals which eliminates any connection at a set stellar mass. Template analysis of the three subsets of ellipticals demonstrates that the bright and faint ellipticals follow the same trends of profile shape (weak homology), but that dwarf ellipticals form a separate and distinct structural class with lower central surface brightnesses and extended isophotal radii.
An Implicit Energy-Conservative 2D Fokker-Planck Algorithm. II. Jacobian-Free Newton-Krylov Solver
NASA Astrophysics Data System (ADS)
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.
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.
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.
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.
Counterrotating Cores in Elliptical Galaxies.
NASA Astrophysics Data System (ADS)
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
Skewness of elliptic flow fluctuations
NASA Astrophysics Data System (ADS)
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.
Theoretical results for starved elliptical contacts
NASA Technical Reports Server (NTRS)
Hamrock, B. J.; Dowson, D.
1983-01-01
Eighteen cases were used in the theoretical study of the influence of lubricant starvation on film thickness and pressure in elliptical elastohydrodynamic conjunctions. From the results a simple and important critical dimensionless inlet boundary distance at which lubricant starvation becomes significant was specified. This inlet boundary distance defines whether a fully flooded or a starved condition exists in the contact. Furthermore, it was found that the film thickness for a starved condition is written in dimensionless terms as a function of the inlet distance parameter and the film thickness for a fully flooded condition. Contour plots of pressure and film thickness in and around the contact are shown for fully flooded and starved conditions.
Horizon complementarity in elliptic de Sitter space
NASA Astrophysics Data System (ADS)
Hackl, Lucas; Neiman, Yasha
2015-02-01
We study a quantum field in elliptic de Sitter space dS4/Z2—the spacetime obtained from identifying antipodal points in dS4. We find that the operator algebra and Hilbert space cannot be defined for the entire space, but only for observable causal patches. This makes the system into an explicit realization of the horizon complementarity principle. In the absence of a global quantum theory, we propose a recipe for translating operators and states between observers. This translation involves information loss, in accordance with the fact that two observers see different patches of the spacetime. As a check, we recover the thermal state at the de Sitter temperature as a state that appears the same to all observers. This thermal state arises from the same functional that, in ordinary dS4, describes the Bunch-Davies vacuum.
Elliptic Bessel processes and elliptic Dyson models realized as temporally inhomogeneous processes
NASA Astrophysics Data System (ADS)
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.
Advanced Light Source elliptical wiggler
NASA Astrophysics Data System (ADS)
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.
Matrix factorizations and elliptic fibrations
NASA Astrophysics Data System (ADS)
Omer, Harun
2016-09-01
I use matrix factorizations to describe branes at simple singularities of elliptic fibrations. Each node of the corresponding Dynkin diagrams of the ADE-type singularities is associated with one indecomposable matrix factorization which can be deformed into one or more factorizations of lower rank. Branes with internal fluxes arise naturally as bound states of the indecomposable factorizations. Describing branes in such a way avoids the need to resolve singularities. This paper looks at gauge group breaking from E8 fibers down to SU (5) fibers due to the relevance of such fibrations for local F-theory GUT models. A purpose of this paper is to understand how the deformations of the singularity are understood in terms of its matrix factorizations. By systematically factorizing the elliptic fiber equation, this paper discusses geometries which are relevant for building semi-realistic local models. In the process it becomes evident that breaking patterns which are identical at the level of the Kodaira type of the fibers can be inequivalent at the level of matrix factorizations. Therefore the matrix factorization picture supplements information which the conventional less detailed descriptions lack.
Elliptical galaxies kinematics within general relativity with renormalization group effects
Rodrigues, Davi C.
2012-09-01
The renormalization group framework can be applied to Quantum Field Theory on curved space-time, but there is no proof whether the beta-function of the gravitational coupling indeed goes to zero in the far infrared or not. In a recent paper [1] we have shown that the amount of dark matter inside spiral galaxies may be negligible if a small running of the General Relativity coupling G is present (δG/G{sub 0}∼<10{sup −7} across a galaxy). Here we extend the proposed model to elliptical galaxies and present a detailed analysis on the modeling of NGC 4494 (an ordinary elliptical) and NGC 4374 (a giant elliptical). In order to compare our results to a well known alternative model to the standard dark matter picture, we also evaluate NGC 4374 with MOND. In this galaxy MOND leads to a significative discrepancy with the observed velocity dispersion curve and has a significative tendency towards tangential anisotropy. On the other hand, the approach based on the renormalization group and general relativity (RGGR) could be applied with good results to these elliptical galaxies and is compatible with lower mass-to-light ratios (of about the Kroupa IMF type)
Elliptic solitons in optical fiber media
NASA Astrophysics Data System (ADS)
Fandio Jubgang, Défi, Jr.; Dikandé, Alain M.; Sunda-Meya, A.
2015-11-01
We examine the evolution of a time-varying perturbation signal pumped into a monomode fiber in the anomalous dispersion regime. We establish analytically that the perturbation evolves into a conservative pattern of periodic pulses whose structures and profiles share a close similarity with the so-called soliton-crystal states recently observed in fiber media [see, e.g., A. Haboucha et al., Phys. Rev. A 78, 043806 (2008), 10.1103/PhysRevA.78.043806; D. Y. Tang et al., Phys. Rev. Lett. 101, 153904 (2008), 10.1103/PhysRevLett.101.153904; F. Amrani et al., Opt. Express 19, 13134 (2011), 10.1364/OE.19.013134]. We derive mathematically and generate numerically a crystal of solitons using time-division multiplexing of identical pulses. We suggest that at very fast pumping rates, the pulse signals overlap and create an unstable signal that is modulated by the fiber nonlinearity to become a periodic lattice of pulse solitons that can be described by elliptic functions. We carry out a linear stability analysis of the soliton-crystal structure and establish that the correlation of centers of mass of interacting pulses broadens their internal-mode spectrum, some modes of which are mutually degenerate. While it has long been known that high-intensity periodic pulse trains in optical fibers are generated from the phenomenon of modulational instability of continuous waves, the present study provides evidence that they can also be generated via temporal multiplexing of an infinitely large number of equal-intensity single pulses to give rise to stable elliptic solitons.
AGN-controlled cooling in elliptical galaxies
NASA Astrophysics Data System (ADS)
Best, P. N.; Kaiser, C. R.; Heckman, T. M.; Kauffmann, G.
2006-05-01
A long-standing problem for models of galaxy formation has been the mismatch between the predicted shape of the mass function of dark matter halos and the observed shape of the luminosity function of galaxies. The number of massive haloes is predicted to decrease as a power law (N~M-2) out to very large masses, while the galaxy luminosity function cuts off exponentially at luminosities above L*. This implies that the efficiency with which gas cools onto massive systems is lower than expected. This letter investigates the role of radio-loud active galactic nuclei (AGN) in continually re-heating the cooling gas. By combining two observational results, the time-averaged energy output associated with recurrent radio source activity is determined, as a function of the black hole mass of the host galaxy: . It is shown that for massive elliptical galaxies this radio-source heating balances the radiative energy losses from the hot gas surrounding the galaxy. The recurrent radio-loud AGN activity may therefore provide a self-regulating feedback mechanism capable of controlling the rate of growth of galaxies.
Thermopile detector of light ellipticity
Lu, Feng; Lee, Jongwon; Jiang, Aiting; Jung, Seungyong; Belkin, Mikhail A.
2016-01-01
Polarimetric imaging is widely used in applications from material analysis to biomedical diagnostics, vision and astronomy. The degree of circular polarization, or light ellipticity, is associated with the S3 Stokes parameter which is defined as the difference in the intensities of the left- and right-circularly polarized components of light. Traditional way of determining this parameter relies on using several external optical elements, such as polarizers and wave plates, along with conventional photodetectors, and performing at least two measurements to distinguish left- and right-circularly polarized light components. Here we theoretically propose and experimentally demonstrate a thermopile photodetector element that provides bipolar voltage output directly proportional to the S3 Stokes parameter of the incident light. PMID:27703152
A Robust Elliptic Grid Generator
NASA Astrophysics Data System (ADS)
Knupp, Patrick M.
1992-06-01
A variational principle is proposed that results in a robust elliptic grid generator having many of the strengths of original Winslow or homogeneous Thompson-Thames-Mastin method (hTTM). The new grid generator places grid lines more uniformly over the domain than does hTTM, without loss of orthogonality. Numerically generated examples are given to demonstrate these effects. Grid quality measures are introduced to quantify differences between discrete grids. Both the hTTM and the new grid generator can generate folded grids on certain pathological regions, but overall they are very robust. Grid weighting for solution-adaptive calculations is briefly considered. Generalization of the new method to surface and volume grid generation is straightforward.
Structure and Formation of Elliptical and Spheroidal Galaxies
NASA Astrophysics Data System (ADS)
Kormendy, John; Fisher, David B.; Cornell, Mark E.; Bender, Ralf
2009-05-01
New surface photometry of all known elliptical galaxies in the Virgo cluster is combined with published data to derive composite profiles of brightness, ellipticity, position angle, isophote shape, and color over large radius ranges. These provide enough leverage to show that Sérsic log I vprop r 1/n functions fit the brightness profiles I(r) of nearly all ellipticals remarkably well over large dynamic ranges. Therefore, we can confidently identify departures from these profiles that are diagnostic of galaxy formation. Two kinds of departures are seen at small radii. All 10 of our ellipticals with total absolute magnitudes MVT <= -21.66 have cuspy cores—"missing light"—at small radii. Cores are well known and naturally scoured by binary black holes (BHs) formed in dissipationless ("dry") mergers. All 17 ellipticals with -21.54 <= MVT <= -15.53 do not have cores. We find a new distinct component in these galaxies: all coreless ellipticals in our sample have extra light at the center above the inward extrapolation of the outer Sérsic profile. In large ellipticals, the excess light is spatially resolved and resembles the central components predicted in numerical simulations of mergers of galaxies that contain gas. In the simulations, the gas dissipates, falls toward the center, undergoes a starburst, and builds a compact stellar component that, as in our observations, is distinct from the Sérsic-function main body of the elliptical. But ellipticals with extra light also contain supermassive BHs. We suggest that the starburst has swamped core scouring by binary BHs. That is, we interpret extra light components as a signature of formation in dissipative ("wet") mergers. Besides extra light, we find three new aspects to the ("E-E") dichotomy into two types of elliptical galaxies. Core galaxies are known to be slowly rotating, to have relatively anisotropic velocity distributions, and to have boxy isophotes. We show that they have Sérsic indices n > 4 uncorrelated
On the homogenization of semilinear elliptic operators in perforated domains
Matevossian, O A; Pikulin, S V
2002-04-30
A second-order semilinear elliptic equation whose lower term has power-like growth at infinity with respect to the unknown function is considered. It is proved that a sequence of its solutions in perforated domains converges to a solution in the non-perforated domain as the diameters of the holes converge to zero with a rate depending on the power exponent of the lower term.
The Information Metric for Univariate Linear Elliptic Models.
1987-06-01
Mahalanobis distance . This result enables us to construct new statistical tests and to recover earlier results as special cases. n.ncasife DISCLAIMXI NOTICE...half-space whose geodesic Rao distance is an increasing hyperbolic function of a modified Mahalanobis distance . This result enables us to construct...phrases: elliptic distributicn, Fisher information matrix, hyperbolic metric, information metric, Mahalanobis distance , Rao distance . This work is
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.
Sampling random directions within an elliptical cone
NASA Astrophysics Data System (ADS)
Hall, D. C.
2017-10-01
This work extends the spherical surface sampling algorithm in order to uniformly generate random directions within an elliptical cone. This has applications in Monte Carlo particle transport simulations, for example modeling asymmetric beam divergence or scattering interactions. Two methods are presented. The first obeys the strict boundary of the elliptical cone. The second relaxes this requirement, increasing the range of generated directions by up to 10% for elliptical cones of extreme eccentricity. However, the second method is able to generate directions beyond the equator.
On Fibonacci Numbers Which Are Elliptic Carmichael
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...CM elliptic curve with CM field different from Q( √ −1), then the set of n for which the nth Fibonacci number Fn is elliptic Carmichael for E is of...number. 1. REPORT DATE 27 DEC 2014 2. REPORT TYPE 3. DATES COVERED 00-00-2014 to 00-00-2014 4. TITLE AND SUBTITLE On Fibonacci Numbers Which Are
Sampling random directions within an elliptical cone.
Hall, D C
2017-10-01
This work extends the spherical surface sampling algorithm in order to uniformly generate random directions within an elliptical cone. This has applications in Monte Carlo particle transport simulations, for example modeling asymmetric beam divergence or scattering interactions. Two methods are presented. The first obeys the strict boundary of the elliptical cone. The second relaxes this requirement, increasing the range of generated directions by up to 10% for elliptical cones of extreme eccentricity. However, the second method is able to generate directions beyond the equator.
NASA Astrophysics Data System (ADS)
Borazjani, Iman; Asgharzadeh, Hafez
2015-11-01
Flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates with explicit and semi-implicit schemes. Implicit schemes can be used to overcome these restrictions. However, implementing implicit solver for nonlinear equations including Navier-Stokes is not straightforward. Newton-Krylov subspace methods (NKMs) are one of the most advanced iterative methods to solve non-linear equations such as implicit descritization of the Navier-Stokes equation. The efficiency of NKMs massively depends on the Jacobian formation method, e.g., automatic differentiation is very expensive, and matrix-free methods slow down as the mesh is refined. Analytical Jacobian is inexpensive method, but derivation of analytical Jacobian for Navier-Stokes equation on staggered grid is challenging. The NKM with a novel analytical Jacobian was developed and validated against Taylor-Green vortex and pulsatile flow in a 90 degree bend. The developed method successfully handled the complex geometries such as an intracranial aneurysm with multiple overset grids, and immersed boundaries. It is shown that the NKM with an analytical Jacobian is 3 to 25 times faster than the fixed-point implicit Runge-Kutta method, and more than 100 times faster than automatic differentiation depending on the grid (size) and the flow problem. The developed methods are fully parallelized with parallel efficiency of 80-90% on the problems tested.
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.
MegaLUT: Correcting ellipticity measurements of galaxies
NASA Astrophysics Data System (ADS)
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.
Surface brightness and intrinsic luminosity of ellipticals
NASA Astrophysics Data System (ADS)
Dhar, Barun Kumar; Williams, Liliya L. R.
2012-11-01
We show that the surface brightness profiles of elliptical galaxies can be parametrized using a linear superposition of two or three components, each of which is described by functions developed in Dhar & Williams as the 2D projections of a 3D Einasto density profile. For a sample of 23 ellipticals in and around the Virgo Cluster with total absolute V magnitude -24 < MVT < -15, our multicomponent models span a dynamic range up to 106 in surface brightness and up to 105 in radius down to the resolution limit of the Hubble Space Telescope, have a median rms of 0.032 mag arcsec-2 consistent with the rms of 0.03 from random errors of the data, and are statistically justified at >3σ. Our models indicate that (i) the central component is more concentrated than the outer component; and (ii) the central component of massive shallow-cusp ('core') galaxies is much more luminous, extended and concentrated than that of steep-cusp ('cuspy') galaxies, with their near exponential central profiles indicating disc-like systems, whose existence must be verified spectroscopically. Galaxy structure can thus be modelled extremely well with a central mass excess for all galaxies. This is not necessarily contrary to the notion of a mass deficit in 'core' galaxies, since mass ejection due to core scouring by a supermassive black hole (SMBH) binary could have affected the shape of the central components. However, we show that the existence, amount, radial extent and sign of such deficits disagree substantially in the literature, both for a given galaxy and on an average over a sample. We discuss possible implications and suggest that SMBH binaries are unlikely to be the sole mechanism for producing the large 'cores' of massive galaxies. Using results from the SAURON survey, we deduce that under certain conditions of symmetry, inclination angles and degree of triaxiality, the intrinsic (3D) density of light can be well described with a multicomponent Einasto model for both steep- and
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.
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.
Spiraling elliptic beam in nonlocal nonlinear media.
Liang, Guo; Guo, Qi; Cheng, Wenjing; Yin, Naiqiang; Wu, Ping; Cao, Hongmin
2015-09-21
Analytically discussed is the dynamical properties of the spiraling elliptic beams in nonlocal nonlinear media. This class of spiraling elliptic beams carry the orbital angular momentum (OAM), and can rotate on the cross section perpendicular to the propagation direction during the propagations. The optical intensity, the beam width, and specially the angular velocity are both analytically and numerically discussed in details. We shown that both the deviations from the critical power and the deviations from the critical OAM can make the spiraling elliptic beams breathe. The decrease (increase) of the OAM or the increase (decrease) of the power can both make the spiraling elliptic breathers contract (diffract), however, there still exist differences between them. The rotating speed can be changed by the input optical power or the input OAM, which may have potential applications in the controlling of the optical beams.
Theory of the quadrature elliptic birdcage coil.
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.
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.
Elastohydrodynamic lubrication of elliptical contacts
NASA Technical Reports Server (NTRS)
Hamrock, B. J.
1981-01-01
The determination of the minimum film thickness within contact is considered for both fully flooded and starved conditions. A fully flooded conjunction is one in which the film thickness is not significantly changed when the amount of lubricant is increased. The fully flooded results presented show the influence of contact geometry on minimum film thickness as expressed by the ellipticity parameter and the dimensionless speed, load, and materials parameters. These results are applied to materials of high elastic modulus (hard EHL), such as metal, and to materials of low elastic modulus(soft EHL), such as rubber. In addition to the film thickness equations that are developed, contour plots of pressure and film thickness are given which show the essential features of elastohydrodynamically lubricated conjunctions. The crescent shaped region of minimum film thickness, with its side lobes in which the separation between the solids is a minimum, clearly emerges in the numerical solutions. In addition to the 3 presented for the fully flooded results, 15 more cases are used for hard EHL contacts and 18 cases are used for soft EHL contacts in a theoretical study of the influence of lubricant starvation on film thickness and pressure. From the starved results for both hard and soft EHL contacts, a simple and important dimensionless inlet boundary distance is specified. This inlet boundary distance defines whether a fully flooded or a starved condition exists in the contact. Contour plots of pressure and film thickness in and around the contact are shown for conditions.
Elliptical Acoustic Particle Motion in Underwater Waveguides
2013-03-27
source/receiver geometry. In waveguides with nearly horizontal boundaries, the vertical component of the instantaneous intensity can be used to provide an...cause a phase modu- lation of the vertical component of the particle velocity with resulting elliptical particle motion in the vertical plane. This...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
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.
Multiple solutions for resonant semilinear elliptic problems in
NASA Astrophysics Data System (ADS)
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.
Existence of solution for a generalized quasilinear elliptic problem
NASA Astrophysics Data System (ADS)
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.
A transmission line model for propagation in elliptical core optical fibers
Georgantzos, E.; Boucouvalas, A. C.; Papageorgiou, C.
2015-12-31
The calculation of mode propagation constants of elliptical core fibers has been the purpose of extended research leading to many notable methods, with the classic step index solution based on Mathieu functions. This paper seeks to derive a new innovative method for the determination of mode propagation constants in single mode fibers with elliptic core by modeling the elliptical fiber as a series of connected coupled transmission line elements. We develop a matrix formulation of the transmission line and the resonance of the circuits is used to calculate the mode propagation constants. The technique, used with success in the case of cylindrical fibers, is now being extended for the case of fibers with elliptical cross section. The advantage of this approach is that it is very well suited to be able to calculate the mode dispersion of arbitrary refractive index profile elliptical waveguides. The analysis begins with the deployment Maxwell’s equations adjusted for elliptical coordinates. Further algebraic analysis leads to a set of equations where we are faced with the appearance of harmonics. Taking into consideration predefined fixed number of harmonics simplifies the problem and enables the use of the resonant circuits approach. According to each case, programs have been created in Matlab, providing with a series of results (mode propagation constants) that are further compared with corresponding results from the ready known Mathieu functions method.
Age and metallicity gradients in fossil ellipticals
NASA Astrophysics Data System (ADS)
Eigenthaler, P.; Zeilinger, W. W.
2013-05-01
Context. Fossil galaxy groups are speculated to be old and highly evolved systems of galaxies that formed early in the universe and had enough time to deplete their L∗ galaxies through successive mergers of member galaxies, building up one massive central elliptical, but retaining the group X-ray halo. Aims: Considering that fossils are the remnants of mergers in ordinary groups, the merger history of the progenitor group is expected to be imprinted in the fossil central galaxy (FCG). We present for the first time radial gradients of single-stellar population (SSP) ages and metallicites in a sample of FCGs to constrain their formation scenario. We also measure line-strength gradients for the strongest absorption features in these galaxies. Methods: We took deep spectra with the long-slit spectrograph ISIS at the William Herschel Telescope (WHT) for six FCGs. The obtained spectra are fit with Pegase HR SSP models within the full-spectrum fitting package ULySS yielding SSP ages and metallicities of the stellar populations. We measure radial gradients of SSP ages and metallicities along the major axes. Lick indices are measured for the strongest absorption features to determine line-strength gradients and compare with the full-spectrum fitting results. Results: Our sample comprises some of the most massive galaxies in the universe exhibiting an average central velocity dispersion of σ0 = 271 ± 28 km s-1. Metallicity gradients are throughout negative with comparatively flat slopes of ∇[Fe/H] = -0.19 ± 0.08 while age gradients are found to be insignificant (∇age = 0.00 ± 0.05). All FCGs lie on the fundamental plane, suggesting that they are virialised systems. We find that gradient strengths and central metallicities are similar to those found in cluster ellipticals of similar mass. Conclusions: The comparatively flat metallicity gradients with respect to those predicted by monolithic collapse (∇Z = -0.5) suggest that fossils are indeed the result of
Galerkin Methods for Nonlinear Elliptic Equations.
NASA Astrophysics Data System (ADS)
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
Kinematical and Dynamical Modeling of Elliptical Galaxies
NASA Astrophysics Data System (ADS)
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.
Fabrication of elliptical SRF cavities
NASA Astrophysics Data System (ADS)
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
Parametrizations of elliptic curves by Shimura curves and by classical modular curves
Ribet, Kenneth A.; Takahashi, Shuzo
1997-01-01
Fix an isogeny class 𝒜 of semistable elliptic curves over Q. The elements of 𝒜 have a common conductor N, which is a square-free positive integer. Let D be a divisor of N which is the product of an even number of primes—i.e., the discriminant of an indefinite quaternion algebra over Q. To D we associate a certain Shimura curve X0D(N/D), whose Jacobian is isogenous to an abelian subvariety of J0(N). There is a unique A ∈ 𝒜 for which one has a nonconstant map πD : X0D(N/D) → A whose pullback A → Pic0(X0D(N/D)) is injective. The degree of πD is an integer δD which depends only on D (and the fixed isogeny class 𝒜). We investigate the behavior of δD as D varies. PMID:11607751
Shape measurement biases from underfitting and ellipticity gradients
Bernstein, Gary M.
2010-08-21
With this study, precision weak gravitational lensing experiments require measurements of galaxy shapes accurate to <1 part in 1000. We investigate measurement biases, noted by Voigt and Bridle (2009) and Melchior et al. (2009), that are common to shape measurement methodologies that rely upon fitting elliptical-isophote galaxy models to observed data. The first bias arises when the true galaxy shapes do not match the models being fit. We show that this "underfitting bias" is due, at root, to these methods' attempts to use information at high spatial frequencies that has been destroyed by the convolution with the point-spread function (PSF) and/or by sampling. We propose a new shape-measurement technique that is explicitly confined to observable regions of k-space. A second bias arises for galaxies whose ellipticity varies with radius. For most shape-measurement methods, such galaxies are subject to "ellipticity gradient bias". We show how to reduce such biases by factors of 20–100 within the new shape-measurement method. The resulting shear estimator has multiplicative errors < 1 part in 10^{3} for high-S/N images, even for highly asymmetric galaxies. Without any training or recalibration, the new method obtains Q = 3000 in the GREAT08 Challenge of blind shear reconstruction on low-noise galaxies, several times better than any previous method.
Properties of Ellipticity Correlation with Atmospheric Structure from Gemini South
Asztalos, S J; Treadway, T; de Vries, W H; Rosenberg, L J; Burke, D; Claver, C; Saha, A; Puxley, P
2006-12-21
Cosmic shear holds great promise for a precision independent measurement of {Omega}{sub m}, the mass density of the universe relative to the critical density. The signal is expected to be weak, so a thorough understanding of systematic effects is crucial. An important systematic effect is the atmosphere: shear power introduced by the atmosphere is larger than the expected signal. Algorithms exist to extract the cosmic shear from the atmospheric component, though a measure of their success applied to a range of seeing conditions is lacking. To gain insight into atmospheric shear, Gemini South imaging in conjunction with ground condition and satellite wind data were obtained. We find that under good seeing conditions Point-Spread-Function (PSF) correlations persist well beyond the separation typical of high-latitude stars. Under these conditions, ellipticity residuals based on a simple PSF interpolation can be reduced to within a factor of a few of the shot-noise induced ellipticity floor. We also find that the ellipticity residuals are highly correlated with wind direction. Finally, we correct stellar shapes using a more sophisticated procedure and generate shear statistics from stars. Under all seeing conditions in our data set the residual correlations lie everywhere below the target signal level. For good seeing we find that the systematic error attributable to atmospheric turbulence is comparable in magnitude to the statistical error (shape noise) over angular scales relevant to present lensing surveys.
Properties of Ellipticity Correlation with Atmospheric Structure From Gemini South
Asztalos, Stephen J.; de Vries, W.H.; Rosenberg, L.J; Treadway, T.; Burke, D.; Claver, C.; Saha, A.; Puxley, P.; /Gemini Observ., La Serena
2007-01-17
Cosmic shear holds great promise for a precision independent measurement of {Omega}{sub m}, the mass density of the universe relative to the critical density. The signal is expected to be weak, so a thorough understanding of systematic effects is crucial. An important systematic effect is the atmosphere: shear power introduced by the atmosphere is larger than the expected signal. Algorithms exist to extract the cosmic shear from the atmospheric component, though a measure of their success applied to a range of seeing conditions is lacking. To gain insight into atmospheric shear, Gemini South imaging in conjunction with ground condition and satellite wind data were obtained. We find that under good seeing conditions Point-Spread-Function (PSF) correlations persist well beyond the separation typical of high-latitude stars. Under these conditions, ellipticity residuals based on a simple PSF interpolation can be reduced to within a factor of a few of the shot-noise induced ellipticity floor. We also find that the ellipticity residuals are highly correlated with wind direction. Finally, we correct stellar shapes using a more sophisticated procedure and generate shear statistics from stars. Under all seeing conditions in our data set the residual correlations lie everywhere below the target signal level. For good seeing we find that the systematic error attributable to atmospheric turbulence is comparable in magnitude to the statistical error (shape noise) over angular scales relevant to present lensing surveys.
Anisotropic elliptic optical fibers. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Kang, Soon Ahm
1991-01-01
The exact characteristic equation for an anisotropic elliptic optical fiber is obtained for odd and even hybrid modes in terms of infinite determinants utilizing Mathieu and modified Mathieu functions. A simplified characteristic equation is obtained by applying the weakly guiding approximation such that the difference in the refractive indices of the core and the cladding is small. The simplified characteristic equation is used to compute the normalized guide wavelength for an elliptical fiber. When the anisotropic parameter is equal to unity, the results are compared with the previous research and they are in close agreement. For a fixed value normalized cross-section area or major axis, the normalized guide wavelength lambda/lambda(sub 0) for an anisotropic elliptic fiber is small for the larger value of anisotropy. This condition indicates that more energy is carried inside of the fiber. However, the geometry and anisotropy of the fiber have a smaller effect when the normalized cross-section area is very small or very large.
Instability of a supersonic shock free elliptic jet
Baty, R.S. ); Seiner, J.M.; Ponton, M.K. . Langley Research Center)
1990-01-01
This paper presents a comparison of the measured and the computed spatial stability properties of an aspect ratio 2 supersonic shock free elliptic jet. The shock free nature of the elliptic jet provides an ideal test of validity of modeling the large scale coherent structures in the initial mixing region of noncircular supersonic jets with linear hydrodynamic stability theory. Both aerodynamic and acoustic data were measured. The data are used to compute the mean velocity profiles and to provide a description of the spatial composition of pressure waves in the elliptic jet. A hybrid numerical scheme is applied to solve the Rayleigh problem governing the inviscid linear spatial stability of the jet. The measured mean velocity profiles are used to provide a qualitative model for the cross sectional geometry and the smooth velocity profiles used in the stability analysis. Computational results are presented for several modes of instability at two jet cross sections. The acoustic measurements show that a varicose instability is the jet's perferred mode of motion. The stability analysis predicts that the Strouhal number varies linearly as a function of axial distance in the jet's initial mixing region, which is in good qualitative agreement with previous measurements. 18 refs., 18 figs., 1 tab.
Shape measurement biases from underfitting and ellipticity gradients
Bernstein, Gary M.
2010-08-21
With this study, precision weak gravitational lensing experiments require measurements of galaxy shapes accurate to <1 part in 1000. We investigate measurement biases, noted by Voigt and Bridle (2009) and Melchior et al. (2009), that are common to shape measurement methodologies that rely upon fitting elliptical-isophote galaxy models to observed data. The first bias arises when the true galaxy shapes do not match the models being fit. We show that this "underfitting bias" is due, at root, to these methods' attempts to use information at high spatial frequencies that has been destroyed by the convolution with the point-spread function (PSF)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
Ellipticity and triangularity effects in tokamak Alfven spectrum
NASA Astrophysics Data System (ADS)
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)
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.
Prediction of galaxy ellipticities and reduction of shape noise in cosmic shear measurements
NASA Astrophysics Data System (ADS)
Croft, Rupert A. C.; Freeman, Peter E.; Schuster, Thomas S.; Schafer, Chad M.
2017-08-01
The intrinsic scatter in the ellipticities of galaxies about the mean shape, known as `shape noise', is the most important source of noise in weak lensing shear measurements. Several approaches for reducing shape noise have recently been put forward, using information beyond photometry, such as radio polarization and optical spectroscopy. Here we investigate how well the intrinsic ellipticities of galaxies can be predicted using other exclusively photometric parameters. These (such as galaxy colours) are already available in the data and do not necessitate additional, often expensive observations. We apply a regression technique, generalized additive models to the publicly released galaxy property data from CFHTLenS. We find that the individual galaxy ellipticities can be predicted from other photometric parameters to better precision than the scatter about the mean ellipticity. The ellipticity contribution to the shear can apparently therefore be measured to higher precision, comparable to using a larger sample of galaxies. Using only parameters unaffected by lensing (e.g. surface brightness, colour), our best-fitting model leads to a gain (for the ellipticity contribution only) equivalent to having 12 per cent more galaxies in the sample. Allowing parameters correlated with lensing increases the apparent gains (we find 52.5 per cent), but these would likely be negated by correlations between the predictor and measured shear. We caution that the ultimate usefulness of this method will depend on careful treatment of the effect of the point spread function and input parameter measurement. This is to avoid information on the ellipticity contaminating the estimated ellipticity through observational effects rather than true physical correlations.
NASA Astrophysics Data System (ADS)
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 0.015
Asgharzadeh, Hafez; Borazjani, Iman
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
NASA Astrophysics Data System (ADS)
Asgharzadeh, Hafez; Borazjani, Iman
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
Ultraluminous Infrared Mergers: Elliptical Galaxies in Formation?
NASA Astrophysics Data System (ADS)
Genzel, R.; Tacconi, L. J.; Rigopoulou, D.; Lutz, D.; Tecza, M.
2001-12-01
We report high-quality near-IR spectroscopy of 12 ultraluminous infrared galaxy mergers (ULIRGs). Our new VLT and Keck data provide ~0.5" resolution, stellar and gas kinematics of these galaxies, most of which are compact systems in the last merger stages. We confirm that ULIRG mergers are ``ellipticals in formation.'' Random motions dominate their stellar dynamics, but significant rotation is common. Gasdynamics and stellar dynamics are decoupled in most systems. ULIRGs fall on or near the fundamental plane of hot stellar systems, and especially on its less evolution-sensitive, reff-σ projection. The ULIRG velocity dispersion distribution, their location in the fundamental plane, and their distribution of vrotsini/σ closely resemble those of intermediate-mass (~L*), elliptical galaxies with moderate rotation. As a group ULIRGs do not resemble giant ellipticals with large cores and little rotation. Our results are in good agreement with other recent studies indicating that disky ellipticals with compact cores or cusps can form through dissipative mergers of gas-rich disk galaxies while giant ellipticals with large cores have a different formation history. Based on observations at the European Southern Observatory, Chile (ESO 65.N-0266, 65.N-0289), and on observations at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, The University of California, and the National Aeronautics and Space Administration. The Keck Observatory was made possible by the general financial support by the W. M. Keck Foundation.
An elliptic parameterisation of the Zamolodchikov model
NASA Astrophysics Data System (ADS)
Bazhanov, Vladimir V.; Mangazeev, Vladimir V.; Okada, Yuichiro; Sergeev, Sergey M.
2013-06-01
The Zamolodchikov model describes an exact relativistic factorized scattering theory of straight strings in (2+1)-dimensional space-time. It also defines an integrable 3D lattice model of statistical mechanics and quantum field theory. The three-string S-matrix satisfies the tetrahedron equation which is a 3D analog of the Yang-Baxter equation. Each S-matrix depends on three dihedral angles formed by three intersecting planes, whereas the tetrahedron equation contains five independent spectral parameters, associated with angles of an Euclidean tetrahedron. The vertex weights are given by rather complicated expressions involving square roots of trigonometric function of the spectral parameters, which is quite unusual from the point of view of 2D solvable lattice models. In this paper we consider a particular four-parameter specialisation of the tetrahedron equation when one of its vertices goes to infinity and the tetrahedron itself degenerates into an infinite prism. We show that in this limit all the vertex weights in the tetrahedron equation can be represented as meromorphic functions on an elliptic curve. Moreover we show that a special reduction of the tetrahedron equation in this case leads precisely to an example of the tetrahedral Zamolodchikov algebra, previously constructed by Korepanov. This algebra plays important role for a "layered" construction of the Shastry's R-matrix and the 2D S-matrix appearing in the problem of the ADS/CFT correspondence for N=4 SUSY Yang-Mills theory in four dimensions. Possible applications of our results in this field are briefly discussed.
NASA Astrophysics Data System (ADS)
Büsing, Henrik
2013-04-01
Two-phase flow in porous media occurs in various settings, such as the sequestration of CO2 in the subsurface, radioactive waste management, the flow of oil or gas in hydrocarbon reservoirs, or groundwater remediation. To model the sequestration of CO2, we consider a fully coupled formulation of the system of nonlinear, partial differential equations. For the solution of this system, we employ the Box method after Huber & Helmig (2000) for the space discretization and the fully implicit Euler method for the time discretization. After linearization with Newton's method, it remains to solve a linear system in every Newton step. We compare different iterative methods (BiCGStab, GMRES, AGMG, c.f., [Notay (2012)]) combined with different preconditioners (ILU0, ASM, Jacobi, and AMG as preconditioner) for the solution of these systems. The required Jacobians can be obtained elegantly with automatic differentiation (AD) [Griewank & Walther (2008)], a source code transformation providing exact derivatives. We compare the performance of the different iterative methods with their respective preconditioners for these linear systems. Furthermore, we analyze linear systems obtained by approximating the Jacobian with finite differences in terms of Newton steps per time step, steps of the iterative solvers and the overall solution time. Finally, we study the influence of heterogeneities in permeability and porosity on the performance of the iterative solvers and their robustness in this respect. References [Griewank & Walther(2008)] Griewank, A. & Walther, A., 2008. Evaluating Derivatives: Principles and Techniques of Algorithmic Differentiation, SIAM, Philadelphia, PA, 2nd edn. [Huber & Helmig(2000)] Huber, R. & Helmig, R., 2000. Node-centered finite volume discretizations for the numerical simulation of multiphase flow in heterogeneous porous media, Computational Geosciences, 4, 141-164. [Notay(2012)] Notay, Y., 2012. Aggregation-based algebraic multigrid for convection
Morphological analysis of nearby elliptical galaxies
NASA Astrophysics Data System (ADS)
Preetha, A. U.; Jithesh, V.; Joseph, Dhanya; Nikesh, N.; Ravikumar, C. D.
We report correlations among bulge-disk parameters for a sample of twenty nearby (<30 Mpc) elliptical galaxies with K band observations from (Two Micron All Sky Survey (2MASS)). The global photometric parameters were extracted using the code ``GALFIT'' assuming Sersic bulge with an optional exponential disk. The sample contains all elliptical galaxies from Swartz et al. (2004) with identified non nuclear ultra luminous sources (ULXs) with intrinsic luminosities of LX > 10^{39} ergs/s in the 0.5-8.0 keV energy band. Out of 20 galaxies, seven (35%) shows no significant disk component in it. The rest of the galaxies in the sample show significant disk component with a mean B/T ratio 0.29±0.06. No obvious differences were obtained in various two and three parameter correlations with that of Coma cluster ellipticals, even though our sample is from the nearby Universe.
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.
Highly confined photonic nanojet from elliptical particles
NASA Astrophysics Data System (ADS)
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.
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.
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
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.
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.
Elliptical Particle Clustering in Cellular Flows
NASA Astrophysics Data System (ADS)
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.
Metallicity Gradients in the Halos of Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Greene, Jenny E.; Ma, Chung-Pei; Goulding, Andrew; McConnell, Nicholas J.; Blakeslee, John P.; Davis, Timothy; Thomas, Jens
2016-08-01
We discuss the stellar halos of massive elliptical galaxies, as revealed by our ambitious integral-field spectroscopic survey MASSIVE. We show that metallicity drops smoothly as a function of radius out to ~ 2.5 Re , while the [α/Fe] abundance ratios stay flat. The stars in the outskirts likely formed rapidly (to explain the high ratio of alpha to Fe) but in a relatively shallow potential (to explain the low metallicities). This is consistent with expectations for a two-phase growth of massive galaxies, in which the second phase involves accretion of small satellites. We also show some preliminary study of the gas content of these most MASSIVE galaxies.
Spiraling elliptic solitons in lossy nonlocal nonlinear media.
Liang, Guo; Cheng, Wenjing; Dai, Zhiping; Jia, Tingjian; Wang, Meng; Li, Huangxin
2017-05-15
We address the propagation dynamics of the spiraling elliptic beams in nonlocal nonlinear media with losses based on the variational approach. It is found that the spiraling elliptic beams exhibit complicated behaviors, which result from the combined effects of the losses and orbital angular momentum (OAM). The OAM brings in an effective anisotropic diffraction and rotation for the spiraling elliptic beams. However, due to the losses, the rotation of the spiraling beams slows down. Besides, the ellipticity of the spiraling elliptic beams is greatly affected by the lossesand the OAM. When the OAM is not equal to its critical value, a periodic oscillation of the ellipticity is found in the presence of losses. However, when the OAM is equal to the critical one, the ellipticity of the spiraling elliptic beam remains unchanged during propagation regardless of the loss factor. The comparisons between our approximate analytic solutions and numerical simulations confirm our results.
Buckling of elliptical rings under uniform external pressure
Tang, Y.
1991-04-03
A thin, elastic elliptical ring is subjected to uniform external pressure. The lowest critical pressure is computed and presented for various ratio of the major axis to the minor axis of the elliptical ring. It is found that the critical pressure for an elliptical ring is higher than that for the circular ring whose diameter is equal to the major axis of the elliptical ring. It can be shown that under the same external pressure, the axial force developed in the elliptical ring is less than that developed in the corresponding circular ring. Thus, a higher pressure is required to buckle the elliptical rings. Therefore, by changing the shape of the ring from circular to elliptical, the capability of the ring to sustain the external pressure can be increased substantially. The results of this study can be useful in the design of elliptical reinforcing rings and thin-walled tubes subjected to external pressure.
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.
Elliptic Hypergeometry of Supersymmetric Dualities II. Orthogonal Groups, Knots, and Vortices
NASA Astrophysics Data System (ADS)
Spiridonov, V. P.; Vartanov, G. S.
2014-01-01
We consider Seiberg electric-magnetic dualities for 4 d SYM theories with SO( N) gauge group. For all such known theories we construct superconformal indices (SCIs) in terms of elliptic hypergeometric integrals. Equalities of these indices for dual theories lead both to proven earlier special function identities and new conjectural relations for integrals. In particular, we describe a number of new elliptic beta integrals associated with the s-confining theories with the spinor matter fields. Reductions of some dualities from SP(2 N) to SO(2 N) or SO(2 N + 1) gauge groups are described. Interrelation of SCIs and the Witten anomaly is briefly discussed. Possible applications of the elliptic hypergeometric integrals to a two-parameter deformation of 2 d conformal field theory and related matrix models are indicated. Connections of the reduced SCIs with the state integrals of knot theory, generalized AGT duality for (3 + 3) d theories, and a 2 d vortex partition function are described.
NASA Astrophysics Data System (ADS)
Ahn, Woo Sang; Park, Sung Ho; Jung, Sang Hoon; Choi, Wonsik; Do Ahn, Seung; Shin, Seong Soo
2014-06-01
The purpose of this study is to determine the radial dose function of HDR 192Ir source based on Monte Carlo simulation using elliptic cylindrical phantom, similar to realistic shape of pelvis, in brachytherapy dosimetric study. The elliptic phantom size and shape was determined by analysis of dimensions of pelvis on CT images of 20 patients treated with brachytherapy for cervical cancer. The radial dose function obtained using the elliptic cylindrical water phantom was compared with radial dose functions for different spherical phantom sizes, including the Williamsion's data loaded into conventional planning system. The differences in the radial dose function for the different spherical water phantoms increase with radial distance, r, and the largest differences in the radial dose function appear for the smallest phantom size. The radial dose function of the elliptic cylindrical phantom significantly decreased with radial distance in the vertical direction due to different scatter condition in comparison with the Williamson's data. Considering doses to ICRU rectum and bladder points, doses to reference points can be underestimated up to 1-2% at the distance from 3 to 6 cm. The radial dose function in this study could be used as realistic data for calculating the brachytherapy dosimetry for cervical cancer.
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.
Body tides on an elliptical rotating earth
NASA Technical Reports Server (NTRS)
Wahr, J. M.
1978-01-01
The complete tidal response of an elliptical, rotating, elastic Earth is found to contain small displacements which do not fit into the conventional Love number framework. Corresponding observable tidal quantities (gravity, tilt, strain, Eulerian potential, etc.) are modified by the addition of small latitude dependent terms.
Inertial Wave Turbulence Driven by Elliptical Instability
NASA Astrophysics Data System (ADS)
Le Reun, Thomas; Favier, Benjamin; Barker, Adrian J.; Le Bars, Michael
2017-07-01
The combination of elliptical deformation of streamlines and vorticity can lead to the destabilization of any rotating flow via the elliptical instability. Such a mechanism has been invoked as a possible source of turbulence in planetary cores subject to tidal deformations. The saturation of the elliptical instability has been shown to generate turbulence composed of nonlinearly interacting waves and strong columnar vortices with varying respective amplitudes, depending on the control parameters and geometry. In this Letter, we present a suite of numerical simulations to investigate the saturation and the transition from vortex-dominated to wave-dominated regimes. This is achieved by simulating the growth and saturation of the elliptical instability in an idealized triply periodic domain, adding a frictional damping to the geostrophic component only, to mimic its interaction with boundaries. We reproduce several experimental observations within one idealized local model and complement them by reaching more extreme flow parameters. In particular, a wave-dominated regime that exhibits many signatures of inertial wave turbulence is characterized for the first time. This regime is expected in planetary interiors.
Nomenclature of polarized light - Elliptical polarization
NASA Technical Reports Server (NTRS)
Clarke, D.
1974-01-01
Alternative handedness and sign conventions for relating the orientation of elliptical polarization are discussed. The discussion proceeds under two headings: (1) snapshot picture, where the emphasis for the convention is contained in the concept of handedness; and (2) angular momentum consideration, where the emphasis for the convention is strongly associated with mathematical convention and the sign of the fourth Stokes parameter.
Elliptic genera from multi-centers
NASA Astrophysics Data System (ADS)
Gaddam, Nava
2016-05-01
I show how elliptic genera for various Calabi-Yau threefolds may be understood from supergravity localization using the quantization of the phase space of certain multi-center configurations. I present a simple procedure that allows for the enumeration of all multi-center configurations contributing to the polar sector of the elliptic genera — explicitly verifying this in the cases of the quintic in {P} 4, the sextic in {W}{P} (2,1,1,1,1), the octic in {W}{P} (4,1,1,1,1) and the dectic in {W}{P} (5,2,1,1,1). With an input of the corresponding `single-center' indices (Donaldson-Thomas invariants), the polar terms have been known to determine the elliptic genera completely. I argue that this multi-center approach to the low-lying spectrum of the elliptic genera is a stepping stone towards an understanding of the exact microscopic states that contribute to supersymmetric single center black hole entropy in {N} = 2 supergravity.
Suppression of collapse for spiraling elliptic solitons.
Desyatnikov, Anton S; Buccoliero, Daniel; Dennis, Mark R; Kivshar, Yuri S
2010-02-05
We reveal that orbital angular momentum can suppress catastrophic self-focusing in nonlinear Kerr media supporting stable spiraling solitons with an elliptic cross section. We discuss the necessary requirements for observation of this effect with coherent optical and matter waves.
Relative elliptic theory and the Sobolev problem
NASA Astrophysics Data System (ADS)
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.
Elliptical instability in stably stratified fluid interiors
NASA Astrophysics Data System (ADS)
Vidal, J.; Hollerbach, R.; Schaeffer, N.; Cebron, D.
2016-12-01
Self-sustained magnetic fields in celestial bodies (planets, moons, stars) are due to flows in internal electrically conducting fluids. These fluid motions are often attributed to convection, as it is the case for the Earth's liquid core and the Sun. However some past or present liquid cores may be stably stratified. Alternative mechanisms may thus be needed to understand the dynamo process in these celestial objects. Turbulent flows driven by mechanical forcings, such as tides or precession, seem very promising since they are dynamo capable. However the effect of density stratification is not clear, because it can stabilize or destabilize mechanically-driven flows.To mimic an elliptical distortion due to tidal forcing in spherical geometry (full sphere and shell), we consider a theoretical base flow with elliptical streamlines and an associated density profile. It allows to keep the numerical efficiency of spectral methods in this geometry. The flow satisfies the stress-free boundary condition. We perform the stability analysis of the base state using three-dimensional simulations to study both the linear and nonlinear regimes. Stable and unstable density profiles are considered. A complementary local stability analysis (WKB) is also performed. We show that elliptical instability can still grow upon a stable stratification. We also study the mixing of the stratification by the elliptical instability. Finally we look at the dynamo capability of these flows.
Circular and Elliptic Submerged Impinging Water Jets
NASA Astrophysics Data System (ADS)
Claudey, Eric; Benedicto, Olivier; Ravier, Emmanuel; Gutmark, Ephraim
1999-11-01
Experiments and CFD have been performed to study circular and elliptic jets in a submerged water jet facility. The tests included discharge coefficient measurement to evaluate pressure losses encountered in noncircular nozzles compared to circular ones. Three-dimensional pressure mappings on the impingement surface and PIV measurement of the jet mean and turbulent velocity have been performed at different compound impingement angles relative to the impingement surface and at different stand-off distances. The objective was to investigate the effect of the non-circular geometry on the flow field and on the impact region. The tests were performed in a close loop system in which the water was pumped through the nozzles into a clear Plexiglas tank. The Reynolds numbers were typically in the range of 250000. Discharge coefficients of the elliptic nozzle was somewhat lower than that of the circular jet but spreading rate and turbulence level were higher. Pressure mapping showed that the nozzle exit geometry had an effect on the pressure distribution in the impact region and that high-pressure zones were generated at specific impact points. PIV measurements showed that for a same total exit area, the elliptic jets affected a surface area that is 8the equivalent circular. The turbulence level in the elliptic jet tripled due to the nozzle design. Results of the CFD model were in good agreement with the experimental data.
Transverse Mercator Projection Via Elliptic Integrals
NASA Technical Reports Server (NTRS)
Wallis, David E.
1992-01-01
Improved method of construction of U.S. Army's universal transverse Mercator grid system based on Gauss-Kruger transverse Mercator projection and on use of elliptic integrals of second kind. Method can be used to map entire northern or southern hemisphere with respect to single principal meridian.
ELLIPTIC FLOW, INITIAL ECCENTRICITY AND ELLIPTIC FLOW FLUCTUATIONS IN HEAVY ION COLLISIONS AT RHIC.
NOUICER,R.; ALVER, B.; BACK, B.B.; BAKER, M.D.; BALLINTIJN, M.; BARTON, D.S.; ET AL.
2007-02-19
We present measurements of elliptic flow and event-by-event fluctuations established by the PHOBOS experiment. Elliptic flow scaled by participant eccentricity is found to be similar for both systems when collisions with the same number of participants or the same particle area density are compared. The agreement of elliptic flow between Au+Au and Cu+Cu collisions provides evidence that the matter is created in the initial stage of relativistic heavy ion collisions with transverse granularity similar to that of the participant nucleons. The event-by-event fluctuation results reveal that the initial collision geometry is translated into the final state azimuthal particle distribution, leading to an event-by-event proportionality between the observed elliptic flow and initial eccentricity.
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
Elliptical instability in terrestrial planets and moons
NASA Astrophysics Data System (ADS)
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
NASA Astrophysics Data System (ADS)
Djidel, S.; Bouamar, M.; Khedrouche, D.
2016-04-01
This paper presents a performances study of UWB monopole antenna using half-elliptic radiator conformed on elliptical surface. The proposed antenna, simulated using microwave studio computer CST and High frequency simulator structure HFSS, is designed to operate in frequency interval over 3.1 to 40 GHz. Good return loss and radiation pattern characteristics are obtained in the frequency band of interest. The proposed antenna structure is suitable for ultra-wideband applications, which is, required for many wearable electronics applications.
The Ellipticity Distribution of Ambiguously Blended Objects
NASA Astrophysics Data System (ADS)
Dawson, William A.; Schneider, Michael D.; Tyson, J. Anthony; Jee, M. James
2016-01-01
Using overlapping fields with space-based Hubble Space Telescope and ground-based Subaru Telescope imaging we identify a population of blended galaxies that are blended to such a large degree that they are detected as single objects in the ground-based monochromatic imaging, which we label “ambiguous blends.” For deep imaging data, such as the depth targeted with the Large Synoptic Survey Telescope (LSST), the ambiguous blend population is both large (∼14%) and has a distribution of ellipticities that is different from that of unblended objects in a way that will likely be important for weak lensing measurements. Most notably, for a limiting magnitude of i ∼ 27 we find that ambiguous blending results in a ∼14% increase in shear noise (or an ∼12% decrease in the effective projected number density of lensed galaxies; neff) due to (1) larger intrinsic ellipticity dispersion, and (2) a scaling with the galaxy number density Ngal that is shallower than 1/&sqrt;{{N}{gal}}. For the LSST Gold Sample (i < 25.3) there is a ∼7% increase in shear noise (or ∼7% decrease in neff). More importantly than these increases in the shear noise, we find that the ellipticity distribution of ambiguous blends has an rms that is 13% larger than that of non-blended galaxies. Given the need of future weak lensing surveys to constrain the ellipticity distribution of galaxies to better than a percent in order to mitigate cosmic shear multiplicative biases, if it is unaccounted for, the different ellipticity distribution of ambiguous blends could be a dominant systematic.
The Ages of Dwarf Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Rakos, Karl; Schombert, James
2004-03-01
We present narrowband photometry of 91 dwarf elliptical galaxies in the Coma and Fornax Clusters taken with the Strömgren (uvby) filter system. Dividing the sample by dwarf morphology into nucleated (dEN) and nonnucleated (dE) dwarfs reveals two distinct populations of early-type systems based on integrated colors. The class of dEN galaxies are redder in their continuum colors as compared to bright cluster ellipticals and dE type dwarfs, and their position in multicolor diagrams can only be explained by an older mean age for their underlying stellar populations. By comparison with the narrowband photometry of the M87 globular cluster system, we find that dEN's are a higher metallicity continuation of the old, metal-poor color sequence of galactic globular clusters and the blue population of M87 globular clusters. Bright ellipticals and dE dwarfs, on the other hand, follow the color sequence of the metal-rich, red population of M87 globular clusters. A comparison to SED models, convolved to a simple metallicity model, finds that dEN's and blue globular clusters are 3 to 4 Gyr older than cluster ellipticals and 5 Gyr older than dE type galaxies. The implication is that globular clusters and dEN galaxies are primordial and have metallicities set by external constraints such as the enrichment of their formation clouds. Bright ellipticals and dE galaxies have metallicities and ages that suggest an extended phase of initial star formation that produces a younger mean age, even if their formation epoch is similar to that of dEN's and blue globular clusters, and an internally driven chemical evolutionary history.
Caldera Ellipticity Through Regional Tectonic Deformation
NASA Astrophysics Data System (ADS)
Holohan, E. P.; Troll, V. R.; Walter, T. R.; van Wyk de Vries, B.; Byrne, P. K.
2005-12-01
Collapse calderas are delimited by reverse ring faults and surrounded by peripheral concentric normal faults. In the simplest scenario, circular magma chambers produce circular calderas. Many calderas are elliptical in shape, however, particularly those in highly active tectonic settings. Several factors may explain caldera ellipticity in such regimes: 1) Initial geometry of magma chamber(s) 2) Distribution and orientation of pre-existing regional faults, and 3) Influence of the regional stress field on caldera fault geometries. To better understand relationships between caldera morphology, reservoir geometry and regional tectonics, we conducted two analogue experimental series: One series investigated the influence of orthogonal tectonic stresses on caldera and chamber shapes. In all cases where tectonic stress was applied across circular chambers (balloons), elliptical calderas were produced. Pre-existing basement structures also influenced the shape of calderas, either increasing or reducing elongation. Intrusion of silicon gel into tectonically active sand piles showed that silicon gel chambers responded systematically to applied tectonic stress, and that associated calderas would be elliptical in shape. A second series examined the effect of strike slip faulting on magma chambers and associated calderas. We used sand to simulate brittle crust and cream honey to simulate granitic magma. With a sufficiently high transtensive component, pull-apart-like half grabens formed above the passive honey chamber. Chamber evacuation following strike-slip deformation produced arcuate reverse faults that were again occasionally affected by regional structures. From our results, we identify a number of controls for elliptical caldera formation in tectonically active settings, including initial chamber geometry, caldera fault distortion, and interaction with pre-existing structures. Our results indicate that the final caldera surface expression will be the result of interplay
Elliptic blending model: A new near-wall Reynolds-stress turbulence closure
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
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.
Jacobi-Bessel Analysis Of Antennas With Elliptical Apertures.
NASA Technical Reports Server (NTRS)
Rahmat-Samii, Y.
1989-01-01
Coordinate transformation improves convergence pattern analysis of elliptical-aperture antennas. Modified version of Jacobi-Bessel expansion for vector diffraction analysis of reflector antennas uses coordinate transformation to improve convergence with elliptical apertures. Expansion converges rapidly for antennas with circular apertures, but less rapidly for elliptical apertures. Difference in convergence behavior between circular and elliptical Jacobi-Bessel algorithms indicated by highest values of indices m, n, and p required to achieve same accuracy in computed radiation pattern of offset paraboloidal antenna with elliptical aperture.
Hydrostatic equilibrium profiles for gas in elliptical galaxies
NASA Astrophysics Data System (ADS)
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.
Vibration of in-vacuo elliptic cylindrical shells
NASA Astrophysics Data System (ADS)
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.
Exact semi-geostrophic flows in an elliptical ocean basin
NASA Astrophysics Data System (ADS)
McCann, Robert J.; Oberman, Adam M.
2004-09-01
A new family of exact solutions is analysed, which models two-dimensional circulations of an ideal fluid in a uniformly rotating elliptical tank, under the semi-geostrophic approximation from meteorology and oceanography. The fluid pressure and stream function remain quadratic functions of space at each instant in time, and their fluctuations are described by a single degree of freedom Hamiltonian system depending on two conserved parameters: domain eccentricity and the constant value of potential vorticity. These parameters determine the presence or absence of periodic orbits with arbitrarily long periods, fixed points of the dynamics, and aperiodic homoclinic orbits linking hyperbolic saddle points. The energy relative to these parameters selects the frequency and direction in which isobars nutate or precess, as well as the steady circulation direction of the fluctuating flow. The canonically conjugate variables are the moment of inertia and angle of inclination of an elliptical inverse-potential-vorticity patch evolving in dual coordinates. Appendix and figures prepared by Maxim Trokhimtchouk.
Analysis of the Dynamic Characteristics of Elliptical Gears
NASA Astrophysics Data System (ADS)
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.
Magnetic properties of elliptical and stadium-shaped nanoparticles: Effect of the shape anisotropy
NASA Astrophysics Data System (ADS)
Corona, R. M.; Altbir, D.; Escrig, J.
2012-11-01
Elliptical and stadium-shaped nanoparticles as a function of their geometry have been investigated using numerical simulations. The effect of the shape anisotropy of the particles on coercivity and remanence together with the angular dependence of the remanence and coercivity are addressed. Our results demonstrate that the stadium-shaped particles have many of the outstanding properties of elliptical particles, but also have unique properties, such that the coercivity and remanence remain stable for a wide range of geometry parameters, and exhibit a peculiar angular dependence in the coercivity. These properties suggest that they can be useful for applications in the area of magnetic recording systems.
A new method for the identification of non-Gaussian line profiles in elliptical galaxies
NASA Technical Reports Server (NTRS)
Van Der Marel, Roeland P.; Franx, Marijn
1993-01-01
A new parameterization for the line profiles of elliptical galaxies, the Gauss-Hermite series, is proposed. This approach expands the line profile as a sum of orthogonal functions which minimizes the correlations between the errors in the parameters of the fit. This method also make use of the fact that Gaussians provide good low-order fits to observed line profiles. The method yields measurements of the line strength, mean radial velocity, and the velocity dispersion as well as two extra parameters, h3 and h4, that measure asymmetric and symmetric deviations of the line profiles from a Gaussian, respectively. The new method was used to derive profiles for three elliptical galaxies which all have asymmetric line profiles on the major axis with symmetric deviations from a Gaussian. Results confirm that elliptical galaxies have complex structures due to their complex formation history.
NASA Astrophysics Data System (ADS)
Sondak, David; Smith, Leslie; Waleffe, Fabian; Boonkasame, Anakewit
2014-11-01
Computational studies of coherent Rayleigh-Bénard convection in a two-dimensional channel with no-slip top and bottom walls are performed in order to determine scaling laws for a range of Rayleigh (Ra) and Prandtl (Pr) numbers. Since these coherent states are unstable, a Jacobian-free Newton-GMRES algorithm is developed. This approach allows us to determine scaling of the Nusselt number (Nu) with Ra by tracking unstable solutions to the Boussinesq equations. Scaling laws are presented for the primary solution that bifurcates from the conducting state at Ra ~ 1708 , becomes unstable in a Hopf bifurcation at Ra ~ 5 . 4 ×104 but have been computed up to Ra ~ 5 ×106 . We also determine scaling laws for the optimal heat transport up to Ra ~108 . Mechanisms for the observed behavior are discussed including the relationship between the optimal solution and the primary solution as well as the effect of Pr . We explore properties of the algorithm and review its potential as a tool in determining scaling laws for thermal convection as well as some areas for improvement. Extensions of this work to three-dimensional Rayleigh-Bénard convection will be discussed. Partial support from NSF-DMS Grant 1147523 is gratefully acknowledged.
NASA Astrophysics Data System (ADS)
Listyaningrum, Risca; Muhlis, Faid; Soesilo, Joko; Palupi, Indriati Retno
2017-07-01
The subduction zone occurs in Java Island analyzed based on data of tectonic earthquake. Earthquake data used is P wave velocity accessed from the ISC website from 1900-2013 years located along the Java Island. ISC is an organization that provides a variety of data tectonic earthquakes around the world, but the data used is the data before relocation. Relocation needs to reposition the hypocenter, so it can result a new position based on geological model. The relocation is using Jacobian's matrix and AK135 velocity model of P wave in each depth. The tomography process using FMTOMO software from result of new hypocenter represent the subsurface condition at a depth of 0-700 km. The result of hypocenter relocation is shifted horizontally to the southeast while vertically relatively shallow. The results obtained from the tomographic analysis of north-south section show the response of the velocity wave where high value shown in blue color as subduction zone and low value shown red color under volcanic as the partial melting. Tomographic 3D visualization displayed by Voxler software shows the different subduction in Java Island. Result of 3D analysis indicate that the subduction in West Java until Central Java relatively sloping than subduction in East Java.
NASA Astrophysics Data System (ADS)
Fujii, Fumio; Yamakawa, Yuki; Noguchi, Hirohisa
2010-07-01
In the previous publications of the authors, an eigenanalysis-free computational procedure has been proposed to extract the bifurcation buckling mode(s) from the LDL T -decomposed symmetric stiffness matrix in the vicinity of a stability point. Any eigensolver, for instance, inverse iteration or subspace method, is not necessary. The procedure has been verified in numerical examples and well works in multiple and clustered bifurcation problems too. This present paper will extend the eigenanalysis-free procedure to the LDU-decomposed non-symmetric Jacobian matrix, from which both left and right critical eigenvectors relevant to the stability point may be extracted in a similar way. The idea is mathematical and totally independent of the physical problem to be solved, so that it is applicable to any non-symmetric square matrix in stability problems including plasticity with non-associated flow rules, contact and fluid-structure interaction. The linear-algebraic background of non-symmetric eigenvalue problems is firstly described. The present paper will then mention the role play of the left and right critical eigenvectors in stability analysis and the eigenanalysis-free LDU-procedure is proposed. Numerical examples of elastoplastic bifurcation are illustrated for verification and discussion. In APPENDICES, a bench model visualizes the mechanical meaning of the left and right critical singular vectors of a rectangular matrix.
Elliptic genera and 3d gravity
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
Elliptic genera and 3d gravity
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 K_{3}, 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.
Elliptic Genera and 3d Gravity
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.
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
Convergence results for elliptic quasivariational inequalities
NASA Astrophysics Data System (ADS)
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.
An elliptical wiggler beamline for the ALS
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.
Performance of an elliptically tapered neutron guide
NASA Astrophysics Data System (ADS)
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.
Performance of the ALS elliptical wiggler
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 structure`s 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 field`s 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.
The Stellar Halos of Massive Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Greene, Jenny E.; Murphy, Jeremy D.; Comerford, Julia M.; Gebhardt, Karl; Adams, Joshua J.
2012-05-01
We use the Mitchell Spectrograph (formerly VIRUS-P) on the McDonald Observatory 2.7 m Harlan J. Smith Telescope to search for the chemical signatures of massive elliptical galaxy assembly. The Mitchell Spectrograph is an integral-field spectrograph with a uniquely wide field of view (107'' × 107''), allowing us to achieve remarkably high signal-to-noise ratios of ~20-70 pixel-1 in radial bins of 2-2.5 times the effective radii of the eight galaxies in our sample. Focusing on a sample of massive elliptical galaxies with stellar velocity dispersions σ* > 150 km s-1, we study the radial dependence in the equivalent widths (EW) of key metal absorption lines. By twice the effective radius, the Mgb EWs have dropped by ~50%, and only a weak correlation between σ* and Mgb EW remains. The Mgb EWs at large radii are comparable to those seen in the centers of elliptical galaxies that are ~ an order of magnitude less massive. We find that the well-known metallicity gradients often observed within an effective radius continue smoothly to 2.5 Re , while the abundance ratio gradients remain flat. Much like the halo of the Milky Way, the stellar halos of our galaxies have low metallicities and high α-abundance ratios, as expected for very old stars formed in small stellar systems. Our observations support a picture in which the outer parts of massive elliptical galaxies are built by the accretion of much smaller systems whose star formation history was truncated at early times.
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.
Do elliptical galaxies suffer from warp?
NASA Astrophysics Data System (ADS)
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.
Molecular Gas in Elliptical Galaxies: Erratum
NASA Astrophysics Data System (ADS)
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:
Crack Path Prediction Near an Elliptical Inhomogeneity
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
Deformed Virasoro Algebras from Elliptic Quantum Algebras
NASA Astrophysics Data System (ADS)
Avan, J.; Frappat, L.; Ragoucy, E.
2017-09-01
We revisit the construction of deformed Virasoro algebras from elliptic quantum algebras of vertex type, generalizing the bilinear trace procedure proposed in the 1990s. It allows us to make contact with the vertex operator techniques that were introduced separately at the same period. As a by-product, the method pinpoints two critical values of the central charge for which the center of the algebra is extended, as well as (in the gl(2) case) a Liouville formula.
THE STELLAR HALOS OF MASSIVE ELLIPTICAL GALAXIES
Greene, Jenny E.; Murphy, Jeremy D.; Comerford, Julia M.; Gebhardt, Karl; Adams, Joshua J.
2012-05-01
We use the Mitchell Spectrograph (formerly VIRUS-P) on the McDonald Observatory 2.7 m Harlan J. Smith Telescope to search for the chemical signatures of massive elliptical galaxy assembly. The Mitchell Spectrograph is an integral-field spectrograph with a uniquely wide field of view (107'' Multiplication-Sign 107''), allowing us to achieve remarkably high signal-to-noise ratios of {approx}20-70 pixel{sup -1} in radial bins of 2-2.5 times the effective radii of the eight galaxies in our sample. Focusing on a sample of massive elliptical galaxies with stellar velocity dispersions {sigma}{sub *} > 150 km s{sup -1}, we study the radial dependence in the equivalent widths (EW) of key metal absorption lines. By twice the effective radius, the Mgb EWs have dropped by {approx}50%, and only a weak correlation between {sigma}{sub *} and Mgb EW remains. The Mgb EWs at large radii are comparable to those seen in the centers of elliptical galaxies that are {approx} an order of magnitude less massive. We find that the well-known metallicity gradients often observed within an effective radius continue smoothly to 2.5 R{sub e} , while the abundance ratio gradients remain flat. Much like the halo of the Milky Way, the stellar halos of our galaxies have low metallicities and high {alpha}-abundance ratios, as expected for very old stars formed in small stellar systems. Our observations support a picture in which the outer parts of massive elliptical galaxies are built by the accretion of much smaller systems whose star formation history was truncated at early times.
Integrable mappings via rational elliptic surfaces
NASA Astrophysics Data System (ADS)
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.
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.
NASA Astrophysics Data System (ADS)
Kordy, M.; Wannamaker, P.; Maris, V.; Cherkaev, E.; Hill, G.
2016-01-01
We have developed an algorithm, which we call HexMT, for 3-D simulation and inversion of magnetotelluric (MT) responses using deformable hexahedral finite elements that permit incorporation of topography. Direct solvers parallelized on symmetric multiprocessor (SMP), single-chassis workstations with large RAM are used throughout, including the forward solution, parameter Jacobians and model parameter update. In Part I, the forward simulator and Jacobian calculations are presented. We use first-order edge elements to represent the secondary electric field (E), yielding accuracy O(h) for E and its curl (magnetic field). For very low frequencies or small material admittivities, the E-field requires divergence correction. With the help of Hodge decomposition, the correction may be applied in one step after the forward solution is calculated. This allows accurate E-field solutions in dielectric air. The system matrix factorization and source vector solutions are computed using the MKL PARDISO library, which shows good scalability through 24 processor cores. The factorized matrix is used to calculate the forward response as well as the Jacobians of electromagnetic (EM) field and MT responses using the reciprocity theorem. Comparison with other codes demonstrates accuracy of our forward calculations. We consider a popular conductive/resistive double brick structure, several synthetic topographic models and the natural topography of Mount Erebus in Antarctica. In particular, the ability of finite elements to represent smooth topographic slopes permits accurate simulation of refraction of EM waves normal to the slopes at high frequencies. Run-time tests of the parallelized algorithm indicate that for meshes as large as 176 × 176 × 70 elements, MT forward responses and Jacobians can be calculated in ˜1.5 hr per frequency. Together with an efficient inversion parameter step described in Part II, MT inversion problems of 200-300 stations are computable with total run times
Electron dynamics in an elliptical bubble regime
NASA Astrophysics Data System (ADS)
Hemmati, Atefeh; Sedaghatizadeh, Mahmoud; Kordbacheh, Amir Hossein Ahmadkhan
2017-09-01
In this paper, the dynamics of the electron in an elliptical bubble regime is investigated. In this regime, a high intensity laser pulse in a plasma creates an electron cavity called the blow-out (bubble or cavitation) regime which is usually considered to be in a spherical shape at rest. Through balancing the ponderomotive potential of a non-plane laser pulse and bubble electrostatic potential, the shape of the bubble is analyzed to be elliptical in contrast to most available theories which indicate the spherical bubble. Thus, the present model introduces a different dynamics for the electron compared with the spherical one. The longitudinal electric field experienced by the electron and also the electron energy gain in the elliptical model is investigated to be more than that in the spherical model. Moreover, it is found that the shape of the bubble will influence the electron trapping range so that the electron is bounded more in the spherical bubble. As a result, it is crucially important to take the shape of the bubble influence on the electron acceleration process into account. The results indicate that the distribution of the electromagnetic fields inside the bubble in the ellipse model is more close to particle-in-cell simulation compared to the spherical one [Kostyukov et al., Phys. Plasmas 11(11), 5256 (2004)].
Dust and Ionized Gas in Elliptical Galaxies
NASA Astrophysics Data System (ADS)
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
Elliptic Solvers for Adaptive Mesh Refinement Grids
Quinlan, D.J.; Dendy, J.E., Jr.; Shapira, Y.
1999-06-03
We are developing multigrid methods that will efficiently solve elliptic problems with anisotropic and discontinuous coefficients on adaptive grids. The final product will be a library that provides for the simplified solution of such problems. This library will directly benefit the efforts of other Laboratory groups. The focus of this work is research on serial and parallel elliptic algorithms and the inclusion of our black-box multigrid techniques into this new setting. The approach applies the Los Alamos object-oriented class libraries that greatly simplify the development of serial and parallel adaptive mesh refinement applications. In the final year of this LDRD, we focused on putting the software together; in particular we completed the final AMR++ library, we wrote tutorials and manuals, and we built example applications. We implemented the Fast Adaptive Composite Grid method as the principal elliptic solver. We presented results at the Overset Grid Conference and other more AMR specific conferences. We worked on optimization of serial and parallel performance and published several papers on the details of this work. Performance remains an important issue and is the subject of continuing research work.
Vortex precession in thin elliptical ferromagnetic nanodisks
NASA Astrophysics Data System (ADS)
Zaspel, C. E.
2017-07-01
The magnetostatic energy is calculated for a magnetic vortex in a noncircular elliptical nanodisk. It is well-known that the energy of a vortex in the circular disk is minimized though an ansatz that eliminates the magnetostatic charge at the disk edge. Beginning with this ansatz for the circular disk, a conformal mapping of a circle interior onto the interior of an ellipse results in the magnetization of the elliptical disk. This magnetization in the interior of an ellipse also has no magnetostatic charge at the disk edge also minimizing the magnetostatic energy. As expected the energy has a quadratic dependence on the displacement of the vortex core from the ellipse center, but reflecting the lower symmetry of the ellipse. Through numerical integration of the magnetostatic integral a general expression for the energy is obtained for ellipticity values from 1.0 to about 0.3. Finally a general expression for the gyrotropic frequency as described by the Thiele equation is obtained.
Fast space-variant elliptical filtering using box splines.
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.
A heterogeneous stochastic FEM framework for elliptic PDEs
Hou, Thomas Y. Liu, Pengfei
2015-01-15
We introduce a new concept of sparsity for the stochastic elliptic operator −div(a(x,ω)∇(⋅)), which reflects the compactness of its inverse operator in the stochastic direction and allows for spatially heterogeneous stochastic structure. This new concept of sparsity motivates a heterogeneous stochastic finite element method (HSFEM) framework for linear elliptic equations, which discretizes the equations using the heterogeneous coupling of spatial basis with local stochastic basis to exploit the local stochastic structure of the solution space. We also provide a sampling method to construct the local stochastic basis for this framework using the randomized range finding techniques. The resulting HSFEM involves two stages and suits the multi-query setting: in the offline stage, the local stochastic structure of the solution space is identified; in the online stage, the equation can be efficiently solved for multiple forcing functions. An online error estimation and correction procedure through Monte Carlo sampling is given. Numerical results for several problems with high dimensional stochastic input are presented to demonstrate the efficiency of the HSFEM in the online stage.
Optimal Lorentz-augmented spacecraft formation flying in elliptic orbits
NASA Astrophysics Data System (ADS)
Huang, Xu; Yan, Ye; Zhou, Yang
2015-06-01
An electrostatically charged spacecraft accelerates as it moves through the Earth's magnetic field due to the induced Lorentz force, providing a new means of propellantless electromagnetic propulsion for orbital maneuvers. The feasibility of Lorentz-augmented spacecraft formation flying in elliptic orbits is investigated in this paper. Assuming the Earth's magnetic field as a tilted dipole corotating with Earth, a nonlinear dynamical model that characterizes the orbital motion of Lorentz spacecraft in the vicinity of arbitrary elliptic orbits is developed. To establish a predetermined formation configuration at given terminal time, pseudospectral method is used to solve the optimal open-loop trajectories of hybrid control inputs consisted of Lorentz acceleration and thruster-generated control acceleration. A nontilted dipole model is also introduced to analyze the effect of dipole tilt angle via comparisons with the tilted one. Meanwhile, to guarantee finite-time convergence and system robustness against external perturbations, a continuous fast nonsingular terminal sliding mode controller is designed and the closed-loop system stability is proved by Lyapunov theory. Numerical simulations substantiate the validity of proposed open-loop and closed-loop control schemes, and the results indicate that an almost propellantless formation establishment can be achieved by choosing appropriate objective function in the pseudospectral method. Furthermore, compared to the nonsingular terminal sliding mode controller, the closed-loop controller presents superior convergence rate with only a bit more control effort. And the proposed controller can be applied in other Lorentz-augmented relative orbital control problems.
Evaluation of Spatial Anisotropy by Curvature Analysis of Elliptical Targets
Aleci, Carlo; Piana, Giulio; Anselmino, Franco
2010-01-01
Spatial relationship perception (SRP), defined as the function able to detect the difference between the perceived extent of a shape along the x/y cardinal coordinates, has been investigated in 42 eyes of 21 emmetropic subjects by means of a psychophysical test conceived on purpose. Aiming to the highest sensibility and since curvature detection is reckoned as an hyperacuity, elliptical stimuli have been chosen to measure the spatial relationship anisotropy (SRA) in the visual system. Observers turned out to be able to detect curvature differences along the elliptical contour as low as 33.6 sec arc, which in terms of SRP means an aspect ratio (i.e. the ratio between the height and the width of the ellipse) as low as 1.0022-1.0035. By comparing these results with those obtained in previous investigations from other curvature discrimination tasks, it is argued that recognition threshold is conditioned by the amount of space anisotropy of the visual system. Indeed, in about half of the recruited subjects, vertical/horizontal anisotropy is found to a certain extent and such SRA correlates with the recognition threshold (r= 0.69, p<0.01). There is direct evidence of visual spatial distortion and in particular increased anisotropy in neuro-ophtalmological diseases such as hemianopia and around scotomatous regions in the visual field. Thence, apart from theoretical considerations in physiological field, results collected in this study may be regarded as normative data for future clinical investigations. PMID:20802805
Demonstrating H- beam focusing using an elliptical einzel lens
NASA Astrophysics Data System (ADS)
Lawrie, S. R.; Faircloth, D. C.; Letchford, A. P.; Whitehead, M. O.; Wood, T.
2017-08-01
H- ion source research is being performed at the ISIS spallation neutron and muon facility on a dedicated Vessel for Extraction and Source Plasma Analyses (VESPA). The ion extraction and optics system presently being used on ISIS is centered on a combined-function sector dipole magnet. This traps cesium vapor escaping the ion source; mass-separates co-extracted electrons and stripped neutrals, and weak-focusses the highly asymmetric slit-shaped ion beam. Unfortunately the added drift length through the magnet under strong space-charge forces means up to 50% of the beam is collimated on the magnet. The VESPA has shown that the ISIS ion source actually produces 80 mA of beam current at standard settings, but because of magnet collimation only 55 mA is injected into the solenoid Low Energy Beam Transport (LEBT). A new purely electrostatic post-extraction system incorporating an einzel lens with an elliptical aperture is currently under test. This allows much greater flexibility of perveance and phase space matching for injection into the LEBT and Radio Frequency Quadrupole (RFQ). This paper discusses high voltage breakdown mitigation strategies and presents the first results of the novel elliptical transport system. So far, 70 mA of beam has been transported through the new system with a normalized transverse RMS emittance of 0.2 π mm mrad.
The geometry of finite difference discretizations of semilinear elliptic operators
NASA Astrophysics Data System (ADS)
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.
The superconformal index and an elliptic algebra of surface defects
NASA Astrophysics Data System (ADS)
Bullimore, Mathew; Fluder, Martin; Hollands, Lotte; Richmond, Paul
2014-10-01
In this paper we continue the study of the superconformal index of four-dimensional =2 theories of class in the presence of surface defects. Our main result is the construction of an algebra of difference operators, whose elements are labeled by irreducible representations of A N -1. For the fully antisymmetric tensor representations these difference operators are the Hamiltonians of the elliptic Ruijsenaars-Schneider system. The structure constants of the algebra are elliptic generalizations of the Littlewood-Richardson coefficients. In the Macdonald limit, we identify the difference operators with local operators in the two-dimensional TQFT interpretation of the superconformal index. We also study the dimensional reduction to difference operators acting on the three-sphere partition function, where they characterize supersymmetric defects supported on a circle, and show that they are transformed to supersymmetric Wilson loops under mirror symmetry. Finally, we compare to the difference operators that create 't Hooft loops in the four-dimensional =2* theory on a four-sphere by embedding the three-dimensional theory as an S-duality domain wall.
NASA Astrophysics Data System (ADS)
Asgharzadeh, Hafez; Borazjani, Iman
2014-11-01
Time step-size restrictions and low convergence rates are major bottle necks for implicit solution of the Navier-Stokes in simulations involving complex geometries with moving boundaries. Newton-Krylov method (NKM) is a combination of a Newton-type method for super-linearly convergent solution of nonlinear equations and Krylov subspace methods for solving the Newton correction equations, which can theoretically address both bottle necks. The efficiency of this method vastly depends on the Jacobian forming scheme e.g. automatic differentiation is very expensive and Jacobian-free methods slow down as the mesh is refined. A novel, computationally efficient analytical Jacobian for NKM was developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered curvilinear grids with immersed boundaries. The NKM was validated and verified against Taylor-Green vortex and pulsatile flow in a 90 degree bend and efficiently handles complex geometries such as an intracranial aneurysm with multiple overset grids, pulsatile inlet flow and immersed boundaries. The NKM method is shown to be more efficient than the semi-implicit Runge-Kutta methods and Jabobian-free Newton-Krylov methods. We believe NKM can be applied to many CFD techniques to decrease the computational cost. This work was supported partly by the NIH Grant R03EB014860, and the computational resources were partly provided by Center for Computational Research (CCR) at University at Buffalo.
Luanjing Guo; Hai Huang; Derek Gaston; Cody Permann; David Andrs; George Redden; Chuan Lu; Don Fox; Yoshiko Fujita
2013-03-01
Modeling large multicomponent reactive transport systems in porous media is particularly challenging when the governing partial differential algebraic equations (PDAEs) are highly nonlinear and tightly coupled due to complex nonlinear reactions and strong solution-media interactions. Here we present a preconditioned Jacobian-Free Newton-Krylov (JFNK) solution approach to solve the governing PDAEs in a fully coupled and fully implicit manner. A well-known advantage of the JFNK method is that it does not require explicitly computing and storing the Jacobian matrix during Newton nonlinear iterations. Our approach further enhances the JFNK method by utilizing physics-based, block preconditioning and a multigrid algorithm for efficient inversion of the preconditioner. This preconditioning strategy accounts for self- and optionally, cross-coupling between primary variables using diagonal and off-diagonal blocks of an approximate Jacobian, respectively. Numerical results are presented demonstrating the efficiency and massive scalability of the solution strategy for reactive transport problems involving strong solution-mineral interactions and fast kinetics. We found that the physics-based, block preconditioner significantly decreases the number of linear iterations, directly reducing computational cost; and the strongly scalable algebraic multigrid algorithm for approximate inversion of the preconditioner leads to excellent parallel scaling performance.
The anisotropic Ising correlations as elliptic integrals: duality and differential equations
NASA Astrophysics Data System (ADS)
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.
Monopoles and Modifications of Bundles over Elliptic Curves
NASA Astrophysics Data System (ADS)
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.
Djidel, S.; Bouamar, M.; Khedrouche, D.
2016-04-21
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.
Time-resolved dynamical Franz-Keldysh effect produced by an elliptically polarized laser
NASA Astrophysics Data System (ADS)
Otobe, T.
2016-10-01
An analytical formula is reported describing the time-resolved dynamical Franz-Keldysh effect (Tr-DFKE) produced by an elliptically polarized laser at subfemtosecond timescale. The Houston function is assumed as the time-dependent wave function of the parabolic two-band system. For elliptical polarization, the resulting formula exhibits subcycle changes in the optical properties; the modulation of the dielectric function is smaller than that for linear polarization. In contrast, the subcycle modulation of the dielectric function, a significant feature of the Tr-DFKE, disappears for a circularly polarized laser. This analytical formula shows good qualitative agreement with the first-principle calculation employing the time-dependent density functional theory for diamond.
Curious Case of a Stripped Elliptical Galaxy
NASA Astrophysics Data System (ADS)
Kohler, Susanna
2017-05-01
MUSE fields of view (1 1 for each square) are superimposed on a pseudo-color image of the elliptical galaxy in Abell 2670. The blue blobs lie in the opposite direction to the galactic center. [Sheen et al. 2017]An elliptical galaxy in the cluster Abell 2670 has been discovered with some unexpected features. What conditions led to this galaxys unusual morphology?Unexpected JellyfishWe often see galaxies that have been disrupted or reshaped due to their motion within a cluster but these are usually late-type galaxies like our own. Such gas-rich galaxies are distorted by ram pressure as they fall into the cluster center, growing long tails of stripped gas and young stars that earn them the name jellyfish galaxies.But early-type, elliptical galaxies have long since used up or cleared out most of their gas, and they correspondingly form very few new stars. Its therefore unsurprising that theyve never before been spotted to have jellyfish-like features.Panels a and b show zoomed-in observations of some of the star-forming blobs with tadpole-like morphology. Panel c shows a schematic illustration of how ram-pressure stripping causes this shape. [Adapted from Sheen et al. 2017]New deep observations of an elliptical galaxy in the cluster Abell 2670, however, have revealed some unexpected structures for an early-type galaxy. Led by Yun-Kyeong Sheen (Korea Astronomy and Space Science Institute), a team of scientists now reports on the optical and spectroscopic observations of this galaxy, made with the MUSE instrument on the Very Large Telescope in Chile.Tadpole BlobsThese observations reveal a number of features, including starbursts at the galactic center, 80-parsec-long tails of ionized gas, disturbed halo features, and several blue star-forming blobs with tadpole-like morphology in the surrounding region. The blobs have stellar tails that point in the direction of motion of the galaxy (toward the cluster center) and streams of ionized gas that point in the opposite
NASA Astrophysics Data System (ADS)
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.
The Puzzlingly Small Ca II Triplet Absorption in Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Saglia, R. P.; Maraston, Claudia; Thomas, Daniel; Bender, Ralf; Colless, Matthew
2002-11-01
We measure the central values (within Re/8) of the Ca II triplet line indices CaT* and CaT and the Paschen index PaT at 8600 Å for a 93% complete sample of 75 nearby early-type galaxies with BT<12 mag and Vgal<2490 km s-1. We find that the values of CaT* are constant to within 5% over the range of central velocity dispersions 100 km s-1<=σ<=340 km s-1, while the PaT (and CaT) values are mildly anticorrelated with σ. Using simple and composite stellar population models, we show the following: (1) The measured CaT* and CaT are lower than expected from simple stellar population (SSP) models with Salpeter initial mass functions (IMFs) and with metallicities and ages derived from optical Lick (Fe, Mg, and Hβ) indices. Uncertainties in the calibration, the fitting functions, and the SSP modeling taken separately cannot explain the discrepancy. On average, the observed PaT values are within the range allowed by the models and the large uncertainties in the fitting functions. (2) The steepening of the IMF at low masses required to lower the CaT* and CaT indices to the observed values is incompatible with the measured FeH index at 9916 Å and the dynamical mass-to-light ratios of elliptical galaxies. (3) Composite stellar populations with a low-metallicity component reduce the disagreement, but rather artificial metallicity distributions are needed. Another explanation may be that calcium is indeed underabundant in elliptical galaxies.
NASA Technical Reports Server (NTRS)
Baskaran, S.
1974-01-01
The cut-off frequencies for high order circumferential modes were calculated for various eccentricities of an elliptic duct section. The problem was studied with a view to the reduction of jet engine compressor noise by elliptic ducts, instead of circular ducts. The cut-off frequencies for even functions decrease with increasing eccentricity. The third order eigen frequencies are oscillatory as the eccentricity increases for odd functions. The eigen frequencies decrease for higher order odd functions inasmuch as, for higher orders, they assume the same values as those for even functions. Deformation of a circular pipe into an elliptic one of sufficiently large eccentricity produces only a small reduction in the cut-off frequency, provided the area of the pipe section is kept invariable.
On Fibonacci Numbers Which Are Elliptic Korselt Numbers
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...is a CM elliptic curve with CM field Q( √ −d), then the set of n for which the nth Fibonacci number Fn satisfies an elliptic Korselt criterion for Q...SUBTITLE On Fibonacci Numbers Which Are Elliptic Korselt Numbers 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d
Mixing characteristics of a ducted, elliptical jet with dump
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.
Two-dimensional elliptical electromagnetic superscatterer and superabsorber.
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.
Elliptic multiple zeta values and one-loop superstring amplitudes
NASA Astrophysics Data System (ADS)
Broedel, Johannes; Mafra, Carlos R.; Matthes, Nils; Schlotterer, Oliver
2015-07-01
We investigate iterated integrals on an elliptic curve, which are a natural genus-one generalization of multiple polylogarithms. These iterated integrals coincide with the multiple elliptic polylogarithms introduced by Brown and Levin when constrained to the real line. At unit argument they reduce to an elliptic analogue of multiple zeta values, whose network of relations we start to explore. A simple and natural application of this framework are one-loop scattering amplitudes in open superstring theory. In particular, elliptic multiple zeta values are a suitable language to express their low energy limit. Similar to the techniques available at tree-level, our formalism allows to completely automatize the calculation.
Colors of Ellipticals from GALEX to Spitzer
NASA Astrophysics Data System (ADS)
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.
Elliptic polarisation of the polar motion excitation
NASA Astrophysics Data System (ADS)
Bizouard, Christian
2016-02-01
Because of its geophysical interpretation, Earth's polar motion excitation is generally decomposed into prograde (counter-clockwise) and retrograde (clockwise) circular terms at fixed frequency. Yet, these later are commonly considered as specific to the frequency and to the underlying geophysical process, and no study has raised the possibility that they could share features independent from frequency. Complex Fourier Transform permits to determine retrograde and prograde circular terms of the observed excitation and of its atmospheric, oceanic and hydrological counterparts. The total prograde and retrograde parts of these excitations are reconstructed in time domain. Then, complex linear correlation between retrograde and conjugate prograde parts is observed for both the geodetic excitation and the matter term of the hydro-atmospheric excitation. In frequency domain, the ratio of the retrograde circular terms with their corresponding conjugate prograde terms favours specific values: the amplitude ratio follows a probabilistic gamma distribution centred around 1.5 (maximum for 1), and the argument ratio obeys a distribution close to a normal law centred around 2 α = 160°. These frequency and time domain characteristics mean an elliptical polarisation towards α ={˜ } 80° East with an ellipticity of 0.8, mostly resulting from the matter term of the hydro-atmospheric excitation. Whatsoever the frequency band above 0.4 cpd, the hydro-atmospheric matter term tends to be maximal in the geographic areas surrounding the great meridian circle of longitude {˜ }80° or {˜ } 260° East. The favoured retrograde/prograde amplitude ratio around 1.5 or equivalently the ellipticity of 0.8 can result from the amplification of pressure waves propagating towards the west by the normal atmospheric mode Ψ _3^1 around 10 days.
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.
Elliptic Rydberg states as direction indicators
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.
Young circumnuclear disks in elliptical galaxies
NASA Astrophysics Data System (ADS)
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.
Attosecond Temporal Gating with Elliptically Polarized Light
Dudovich, N.; Smirnova, O.; Ivanov, M. Yu.; Villeneuve, D. M.; Corkum, P. B.; Levesque, J.; Zeidler, D.; Comtois, D.
2006-12-22
Temporal gating allows high accuracy time-resolved measurements of a broad range of ultrafast processes. By manipulating the interaction between an atom and an intense laser field, we extend gating into the nonlinear medium in which attosecond optical and electron pulses are generated. Our gate is an amplitude gate induced by ellipticity of the fundamental pulse. The gate modulates the spectrum of the high harmonic emission and we use the measured modulation to characterize the sub-laser-cycle dynamics of the recollision electron wave packet.
Elliptic waveforms for inspiralling compact binaries
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Cohl, H. S.; Volkmer, H.
2012-09-01
A fundamental solution of Laplace’s equation in three dimensions is expanded in harmonic functions that are separated in parabolic or elliptic cylinder coordinates. There are two expansions in each case which reduce to expansions of the Bessel functions J0(kr) or K0(kr), r2 = (x - x0)2 + (y - y0)2, in parabolic and elliptic cylinder harmonics. Advantage is taken of the fact that K0(kr) is a fundamental solution and J0(kr) is the Riemann function of partial differential equations on the Euclidean plane.
Inner and Outer Photometric Structure of Elliptical Galaxies
NASA Astrophysics Data System (ADS)
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.
Heterogeneous domain decomposition for singularly perturbed elliptic boundary value problems
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.
Vortex chirality in exchange-biased elliptical magnetic rings.
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.
Some Expansions of the Elliptic Motion to High Eccentricities
NASA Astrophysics Data System (ADS)
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...
Magnetic flux studies in horizontally cooled elliptical superconducting cavities
Martinello, M. Checchin, M.; Grassellino, A. Crawford, A. C.; Melnychuk, O.; Romanenko, A.; Sergatskov, D. A.
2015-07-28
Previous studies on magnetic flux expulsion as a function of cooldown procedures for elliptical superconducting radio frequency (SRF) niobium cavities showed that when the cavity beam axis is placed parallel to the helium cooling flow and sufficiently large thermal gradients are achieved, all magnetic flux could be expelled and very low residual resistance could be achieved. In this paper, we investigate flux trapping for the case of resonators positioned perpendicularly to the helium cooling flow, which is more representative of how SRF cavities are cooled in accelerators and for different directions of the applied magnetic field surrounding the resonator. We show that different field components have a different impact on the surface resistance, and several parameters have to be considered to fully understand the flux dynamics. A newly discovered phenomenon of concentration of flux lines at the cavity top leading to temperature rise at the cavity equator is presented.
Magnetic flux studies in horizontally cooled elliptical superconducting cavities
Martinello, M.; Checchin, M.; Grassellino, A.; ...
2015-07-29
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. Wemore » 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.« less
A new approach to flow through a region bounded by two ellipses of the same ellipticity
NASA Astrophysics Data System (ADS)
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.
Flow around a helically twisted elliptic cylinder
Kim, Woojin; Lee, Jungil; Choi, Haecheon
2016-05-15
In the present study, we conduct unsteady three-dimensional simulations of flows around a helically twisted elliptic (HTE) cylinder at the Reynolds numbers of 100 and 3900, based on the free-stream velocity and square root of the product of the lengths of its major and minor axes. A parametric study is conducted for Re = 100 by varying the aspect ratio (AR) of the elliptic cross section and the helical spanwise wavelength (λ). Depending on the values of AR and λ, the flow in the wake contains the characteristic wavelengths of λ, 2λ, 6λ, or even longer than 60λ, showing a wide diversity of flows in the wake due to the shape change. The drag on the optimal (i.e., having lowest drag) HTE cylinder (AR = 1.3 and λ = 3.5d) is lower by 18% than that of the circular cylinder, and its lift fluctuations are zero owing to complete suppression of vortex shedding in the wake. This optimal HTE configuration reduces the drag by 23% for Re = 3900 where the wake is turbulent, showing that the HTE cylinder reduces the mean drag and lift fluctuations for both laminar and turbulent flows.
Thermodynamics of Inozemtsev's elliptic spin chain
NASA Astrophysics Data System (ADS)
Klabbers, Rob
2016-06-01
We study the thermodynamic behaviour of Inozemtsev's long-range elliptic spin chain using the Bethe ansatz equations describing the spectrum of the model in the infinite-length limit. We classify all solutions of these equations in that limit and argue which of these solutions determine the spectrum in the thermodynamic limit. Interestingly, some of the solutions are not selfconjugate, which puts the model in sharp contrast to one of the model's limiting cases, the Heisenberg XXX spin chain. Invoking the string hypothesis we derive the thermodynamic Bethe ansatz equations (TBA-equations) from which we determine the Helmholtz free energy in thermodynamic equilibrium and derive the associated Y-system. We corroborate our results by comparing numerical solutions of the TBA-equations to a direct computation of the free energy for the finite-length hamiltonian. In addition we confirm numerically the interesting conjecture put forward by Finkel and González-López that the original and supersymmetric versions of Inozemtsev's elliptic spin chain are equivalent in the thermodynamic limit.
Integrated X-Ray Reflectivity Measurements for Elliptically Curved PET Crystals
Haugh, M J; Ross, P W; Regan, P W; Magoon, J; Shoup, M J; Barrios, M A; Emig, J A; Fournier, K B
2012-04-26
Spectroscopy provides valuable information about the temperature and density of a compressed pellet in a plasma. Elliptically curved pentaerythritol (PET) crystals are used as components for spectrometers. Their elliptical geometry gives several advantages related to spectral energy range, source focus, and spectral image compression.[1] The crystal curvature increases the spectrometer throughput but at the cost of a loss in resolution. Four different crystals are used in a spectrometer at the National Ignition Facility (NIF) target chamber at Lawrence Livermore National Laboratory (LLNL). Figure 1 shows the arrangement of the elliptical PET crystals in the snout of a NIF target diagnostic shown in Figure 2. The spectrum from the crystals is captured by four image plates located behind the crystals. A typical mandrel, the darkened section, upon which the PET crystal is glued, is shown in Figure 3, which also shows the complete ellipse. There are four elliptical segment types, each having the same major axis but a different minor axis. The crystals are 150 mm long in the diffraction direction and 25.4 mm high. Two crystals of each type were calibrated. The throughput for each spectrometer is determined by the integrated reflectivity of the PET crystal.[1] The goal of this effort was to measure the reflectivity curve of the PET curved crystal at several energies and determine the integrated reflectivity and the curve width as a function of the X-ray spectral energy and location on the ellipse where the beam strikes.
Ellipticity and the spurious solution problem of k•p envelope equations
NASA Astrophysics Data System (ADS)
Veprek, Ratko G.; Steiger, Sebastian; Witzigmann, Bernd
2007-10-01
We present an explanation to the spurious solution problem affecting the k•p envelope function method, indicating that the problem is mathematically caused by loss of ellipticity of the differential operator. Focusing on direct band gap zinc-blende heterostructures, we derive criteria that must be fulfilled by the input parameters in order to establish ellipticity. Using these criteria, we compare symmetrized operators with Burt-Foreman [B. A. Foreman, Phys. Rev. B 56, R12748 (1997)] operator ordering. We substantiate our arguments with numerical results obtained using linear finite elements. We find that the space of stable input parameters is very narrow and demonstrate that Burt-Foreman operator ordering together with experimental k•p input parameters leads to near-elliptic envelope equations in the 4×4 and 6×6 models, whereas symmetrization yields strong nonellipticity. In the k•p 8×8 model, the procedure of renormalizing parameters of the 4×4 model generally yields parameters producing spurious solutions, even for Burt-Foreman operator ordering. We find that this problem can be resolved by using a smaller optical matrix parameter Ep . This suggests that the parametrization of k•p models for heterostructures of any dimensionality must be reviewed, checking against the mathematical ellipticity of the equation system.
NASA Astrophysics Data System (ADS)
Yang, J. S.; Chen, K. W.
1989-10-01
It was known from a complete model analysis1,2 that the wake potential in the pill-box cavity is predominantly determined by a few longitudinal modes counting from the fundamental longitudinal mode. An approach to find the longitudinal modes of an elliptical cavity is developed by means of the coordinate transformation method. It is found that the field configuration and eigenfrequencies of the elliptical cavity can be expressed in a closed form in terms of Mathieu functions. Inserting the closed form solution of modes into the previous analytical formula for the wake field, the wake field is expressed too in a closed form solution, which is convenient for numerical calculation. Thus, a numerical method to calculate expediently the wake field is developed, and a model calculation is presented.
Properties of Dwarf Ellipticals in Low-Density Environments
NASA Astrophysics Data System (ADS)
Sur, Debnil; Guhathakurta, P.; Toloba, E.
2013-01-01
Dwarf elliptical galaxies have been studied only in dense cluster environments, where they are the most common type of object. While this suggests that their location affects their formation and evolution, the role of distance is not fully understood. Thus, to investigate the physical processes that shape these galaxies, we have conducted a study of dwarf elliptical galaxies (dEs) in low-density environments to compare their properties with those in clusters. Catalogs of such objects have not been created; thus, we have developed a novel objective method to find new dEs through comparing photometric properties with those of galaxies in the Virgo Cluster Catalog. This method utilizes optical colors, surface brightness and ellipticity, and it confirms smoothness through visual classification. In this last step, we found a very low contamination rate, which suggests the procedure’s utility in finding dEs. Through the NSA Sloan Atlas, we have analyzed the spectrophotometric properties of the dE candidates as a function of distance to the nearest massive galaxy, which we refer to as their host. We have found that these dEs are younger and more actively forming stars than dEs in denser regions. This is consistent with a transformation scenario in which low luminosity spiral galaxies are affected by the environment and transformed into quiescent galaxies. This low density regime contains objects in an intermediate state between the spiral galaxy and the classical dE in Virgo, where no star formation is ongoing. The correlation of the studied properties with the distance to the host galaxy provides new evidence that the dEs are created by a process called ram-pressure stripping: the interstellar medium of a host galaxy removes the gas of a smaller star-forming galaxy and provokes its quenching. We are currently analysing Keck/DEIMOS spectroscopy of some of the dE candidates from our catalog to explore in more detail their connection to cluster dEs. Possible similarities
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]…
Elliptical Orbit [arrow right] 1/r[superscript 2] Force
ERIC Educational Resources Information Center
Prentis, Jeffrey; Fulton, Bryan; Hesse, Carol; Mazzino, Laura
2007-01-01
Newton's proof of the connection between elliptical orbits and inverse-square forces ranks among the "top ten" calculations in the history of science. This time-honored calculation is a highlight in an upper-level mechanics course. It would be worthwhile if students in introductory physics could prove the relation "elliptical orbit" [arrow right]…
Prospects of Elliptic Flow Studies at NICA/MPD
NASA Astrophysics Data System (ADS)
Geraksiev, Nikolay
2016-01-01
As a key observable, anisotropic flow presents a unique insight into heavy ion collision physics. The presented poster reveals the prospects of studying elliptic flow at the NICA/MPD facility through the UrQMD model. Here, results for the elliptic flow of simulated and reconstructed hadrons at the planned NICA energy range are presented.
Modeling roughness effects in turbulent boundary layers using elliptic relaxation
NASA Astrophysics Data System (ADS)
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.
Dynamic susceptibility of onion in ferromagnetic elliptical nanoring
NASA Astrophysics Data System (ADS)
Mu, Congpu; Song, Jiefang; Xu, Jianghong; Wen, Fusheng
2016-06-01
Micromagnetic simulation was performed to investigate the equilibrium state and dynamic susceptibility spectra of magnetic elliptical nanoring. There are two equilibrium states (onion and vortex) obtained in elliptical nanoring. The onion state can be used to record information in MRAM. And it is important to investigate the dynamic susceptibility spectra of onion state, which is closely related to writing and reading speed of magnetic memory devices. Those results show that two or three resonance peaks are found under different thickness of elliptical nanoring with onion state, respectively. The low resonance frequency of two resonance peaks is increasing with the arm width of the elliptical ring, but is decreasing with the thickness. However, the high frequency of two resonance peaks is decreasing with the arm width of the elliptical ring.
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.
Elliptical ion traps and trap arrays for quantum computation
NASA Astrophysics Data System (ADS)
Devoe, Ralph G.
1998-08-01
The properties of a rf quadrupole trap, the elliptical ion trap, are derived. Elliptical traps can confine large numbers of ions in the Lamb-Dicke regime due to a hitherto unrecognized mechanism unique to one-dimensional Coulomb crystals, implicit in the theories of Dubin and Schiffer. This follows from a linear crystal stability condition, which uniquely relates the crystal size to ellipticity, and a micromotion relation, which reveals a 1/5-root dependence on the number of trapped ions. Elliptical traps offer several advantages over linear traps in the Cirac-Zoller model of quantum computing, both for initial tests and as a potential method of creating a full-scale quantum computer. Numerical solutions of a one-electrode structure show that microscopic elliptical traps, each containing ~100 ions, can be constructed at a density of 100 traps/cm2, making possible arrays containing >106 ions in the Lamb-Dicke regime for precision spectroscopy or quantum computation.
Massive bulges are not just ellipticals surrounded by disks
NASA Astrophysics Data System (ADS)
Gadotti, Dimitri A.
2013-07-01
Using results from parametric multi-component multi-band image fitting of 1000 local massive galaxies in the SDSS, I investigate scaling relations of elliptical galaxies and bulges of disk galaxies. I show that ellipticals and bulges occupy different loci in both the edge-on and face-on views of the fundamental plane. In addition, ellipticals and bulges have offset mass-size relations (see Fig. 1). These results imply that massive bulges are not just massive ellipticals with a surrounding disk, a misconception driven by early studies. This is evidence that massive ellipticals and bulges have different formation histories, with important consequences for studies on galaxy formation and evolution. Full details can be seen in Gadotti (2009).
Elliptical silicon arrays with anisotropic optical and wetting properties.
Wang, Tieqiang; Li, Xiao; Zhang, Junhu; Wang, Xianzhe; Zhang, Xuemin; Zhang, Xun; Zhu, Difu; Hao, Yudong; Ren, Zhiyu; Yang, Bai
2010-08-17
We demonstrate a facile etching method to fabricate silicon elliptical pillar arrays (Si-EPAs) with unique anisotropic optical and wetting characters using polystyrene elliptical hemisphere arrays (EHAs) as mask. The EHAs were fabricated via a modified micromolding method. By varying the experimental conditions in the fabrication process, the morphology of the resulting microstructures can be controlled exactly. Because of the anisotropic morphology of the elliptical pillar, the Si-EPA shows unique anisotropic properties, such as anisotropic surface reflection and anisotropic wetting property. Additionally, through oblique evaporation deposition of Au and selective chemical modification to turn the elliptical pillars into "Janus" elliptical pillars, the "Janus" Si-EPA shows more peculiar anisotropic properties owing to the further increased asymmetry. We believe that the Si-EPAs will have potential applications in anisotropic optical and electronic devices.
Multipacting studies in elliptic SRF cavities
NASA Astrophysics Data System (ADS)
Prakash, Ram; Jana, Arup Ratan; Kumar, Vinit
2017-09-01
Multipacting is a resonant process, where the number of unwanted electrons resulting from a parasitic discharge rapidly grows to a larger value at some specific locations in a radio-frequency cavity. This results in a degradation of the cavity performance indicators (e.g. the quality factor Q and the maximum achievable accelerating gradient Eacc), and in the case of a superconducting radiofrequency (SRF) cavity, it leads to a quenching of superconductivity. Numerical simulations are essential to pre-empt the possibility of multipacting in SRF cavities, such that its design can be suitably refined to avoid this performance limiting phenomenon. Readily available computer codes (e.g.FishPact, MultiPac,CST-PICetc.) are widely used to simulate the phenomenon of multipacting in such cases. Most of the contemporary two dimensional (2D) codes such as FishPact, MultiPacetc. are unable to detect the multipacting in elliptic cavities because they use a simplistic secondary emission model, where it is assumed that all the secondary electrons are emitted with same energy. Some three-dimensional (3D) codes such as CST-PIC, which use a more realistic secondary emission model (Furman model) by following a probability distribution for the emission energy of secondary electrons, are able to correctly predict the occurrence of multipacting. These 3D codes however require large data handling and are slower than the 2D codes. In this paper, we report a detailed analysis of the multipacting phenomenon in elliptic SRF cavities and development of a 2D code to numerically simulate this phenomenon by employing the Furman model to simulate the secondary emission process. Since our code is 2D, it is faster than the 3D codes. It is however as accurate as the contemporary 3D codes since it uses the Furman model for secondary emission. We have also explored the possibility to further simplify the Furman model, which enables us to quickly estimate the growth rate of multipacting without
NASA Astrophysics Data System (ADS)
Tan, Meng-Chwan
2013-12-01
We generalize our analysis in [arXiv:1301.1977], and show that a 5d and 6d AGT correspondence for SU( N) — which essentially relates the relevant 5d and 6d Nekrasov instanton partition functions to the integrable representations of a q-deformed and elliptic affine -algebra — can be derived, purely physically, from the principle that the spacetime BPS spectra of string-dual M-theory compactifications ought to be equivalent. Via an appropriate defect, we also derive a "fully-ramified" version of the 5d and 6d AGT correspondence where integrable representations of a quantum and elliptic affine SU( N)-algebra at the critical level appear on the 2d side, and argue that the relevant "fully-ramified" 5d and 6d Nekrasov instanton partition functions are simultaneous eigenfunctions of commuting operators which define relativistic and elliptized integrable systems. As an offshoot, we also obtain various mathematically novel and interesting relations involving the double loop algebra of SU( N), elliptic Macdonald operators, equivariant elliptic genus of instanton moduli space, and more.
Investigating the Density of Isolated Field Elliptical Galaxies
NASA Astrophysics Data System (ADS)
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.
How Does Abundance Affect the Strength of UV Emission in Elliptical Galaxies?
NASA Technical Reports Server (NTRS)
Sonneborn, George (Technical Monitor); Brown, Thomas
2005-01-01
This program used the Far Ultraviolet Spectroscopic Explorer (FUSE) to observe elliptical galaxies with the intention of measuring the chemical abundances in their hot stellar populations. It was designed to complement an earlier FUSE program that observed elliptical galaxies with strong UV emission. The current program originally planned observations of two ellipticals with weak UV emission (M32 and M49). Once FUSE encountered pointing control problems in certain regions of the sky (particularly Virgo, which is very unfortunate for the study of ellipticals in general), M49 was replaced with the bulge of M31, which has a similar UV-to-optical flux ratio as the center of M49. As the closest elliptical galaxy and the one with the weakest UV-to-optical flux ratio, M32 was an obvious choice of target, but M49 was the ideal complementary target, because it has a very low reddening (unlike M32). With the inability of FUSE to point at Virgo, nearly all of the best elliptical galaxies (bright galaxies with low foreground extinction) were also lost, and this severely hampered three FUSE programs of the PI, all focused on the hot stellar populations of ellipticals. M31 was the best replacement for M49, but like M32, it suffers from significant foreground reddening. Strong Galactic ISM lines heavily contaminate the FUSE spectra of M31 and M32. These ISM lines are coincident with the photospheric lines from the stellar populations (whereas M49, with little foreground ISM and significant redshift, would not have suffered from this problem). We have reduced the faint (and thus difficult) data for M31 and M32, producing final co-added spectra representing all of the exposures, but we have not yet finished our analysis, due to the complication of the contaminating ISM. The silver lining here is the set of CHI lines at 1175 Angstroms, which are not significantly contaminated by the ISM. A comparison of the M31 spectrum with other galaxies observed by FEE showed a surprising result
The Carnegie-Irvine Galaxy Survey. III. The Three-component Structure of Nearby Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Huang, Song; Ho, Luis C.; Peng, Chien Y.; Li, Zhao-Yu; Barth, Aaron J.
2013-03-01
Motivated by recent developments in our understanding of the formation and evolution of massive galaxies, we explore the detailed photometric structure of a representative sample of 94 bright, nearby elliptical galaxies, using high-quality optical images from the Carnegie-Irvine Galaxy Survey. The sample spans a range of environments and stellar masses, from M * = 1010.2 to 1012.0 M ⊙. We exploit the unique capabilities of two-dimensional image decomposition to explore the possibility that local elliptical galaxies may contain photometrically distinct substructure that can shed light on their evolutionary history. Compared with the traditional one-dimensional approach, these two-dimensional models are capable of consistently recovering the surface brightness distribution and the systematic radial variation of geometric information at the same time. Contrary to conventional perception, we find that the global light distribution of the majority (gsim75%) of elliptical galaxies is not well described by a single Sérsic function. Instead, we propose that local elliptical galaxies generically contain three subcomponents: a compact (Re <~ 1 kpc) inner component with luminosity fraction f ≈ 0.1-0.15; an intermediate-scale (Re ≈ 2.5 kpc) middle component with f ≈ 0.2-0.25; and a dominant (f = 0.6), extended (Re ≈ 10 kpc) outer envelope. All subcomponents have average Sérsic indices n ≈ 1-2, significantly lower than the values typically obtained from single-component fits. The individual subcomponents follow well-defined photometric scaling relations and the stellar mass-size relation. We discuss the physical nature of the substructures and their implications for the formation of massive elliptical galaxies.
THE CARNEGIE-IRVINE GALAXY SURVEY. III. THE THREE-COMPONENT STRUCTURE OF NEARBY ELLIPTICAL GALAXIES
Huang, Song; Ho, Luis C.; Peng, Chien Y.; Li, Zhao-Yu; Barth, Aaron J.
2013-03-20
Motivated by recent developments in our understanding of the formation and evolution of massive galaxies, we explore the detailed photometric structure of a representative sample of 94 bright, nearby elliptical galaxies, using high-quality optical images from the Carnegie-Irvine Galaxy Survey. The sample spans a range of environments and stellar masses, from M{sub *} = 10{sup 10.2} to 10{sup 12.0} M{sub Sun }. We exploit the unique capabilities of two-dimensional image decomposition to explore the possibility that local elliptical galaxies may contain photometrically distinct substructure that can shed light on their evolutionary history. Compared with the traditional one-dimensional approach, these two-dimensional models are capable of consistently recovering the surface brightness distribution and the systematic radial variation of geometric information at the same time. Contrary to conventional perception, we find that the global light distribution of the majority ({approx}>75%) of elliptical galaxies is not well described by a single Sersic function. Instead, we propose that local elliptical galaxies generically contain three subcomponents: a compact (R{sub e} {approx}< 1 kpc) inner component with luminosity fraction f Almost-Equal-To 0.1-0.15; an intermediate-scale (R{sub e} Almost-Equal-To 2.5 kpc) middle component with f Almost-Equal-To 0.2-0.25; and a dominant (f = 0.6), extended (R{sub e} Almost-Equal-To 10 kpc) outer envelope. All subcomponents have average Sersic indices n Almost-Equal-To 1-2, significantly lower than the values typically obtained from single-component fits. The individual subcomponents follow well-defined photometric scaling relations and the stellar mass-size relation. We discuss the physical nature of the substructures and their implications for the formation of massive elliptical galaxies.
Shu, Yu; Buster, Thad W.; Taylor, Adam P.; Nelson, Carl A.
2011-01-01
Background The popularity of elliptical training has grown in rehabilitation, fitness, and home settings as a means for improving fitness and walking, yet many people with physical disabilities and chronic conditions experience difficulties when trying to use elliptical trainers. Objective The purpose of this study was to compare, for people with disabilities and chronic conditions, perceptions of safety, comfort, workout, and usability of 4 elliptical trainers before and after the development of a set of low-cost adaptations. Design This study was a quasi-experimental repeated-measures investigation. Methods Twenty adults with diverse medical conditions and functional abilities evaluated 4 elliptical trainers for safety, comfort, workout, and usability. Barriers to the use of the elliptical trainers and solutions to improve the use of the trainers were identified. Prototype modifications were designed, and participants reassessed the same features after the modifications were made. Results An integrated system (steps, bench, side rails, center rail or handle, deeper foot wells, and 1-handed heart rate monitor) was developed. Although at least 25% of participants required physical assistance to get on or off the elliptical trainers before modification, only one required this after modification. Before modification, only 1 participant was able to mount each device independently; after modification, 6 to 8 participants were able to do so. Up to 25% of participants continued to require assistance to initiate or sustain pedal movement. Compared with participants' ratings of the elliptical trainers before modification, those after modification were higher for safety (55% increase in visual analog scale ratings), comfort (43% higher), ability to achieve a good workout (23% greater), and usability (24% increase). Limitations To date, only 4 elliptical trainers have been studied with a small sample of convenience. Conclusions Elliptical trainers posed access challenges to
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.
Subregions of Motion and Elliptic Halo Orbits in the Elliptic Restricted Three-Body Problem
NASA Technical Reports Server (NTRS)
Campagnola, Stefano; Lo, Martin; Newton, Paul
2008-01-01
In this paper we present regions of motion and periodic orbits in the spatial elliptic restricted three body problem (ER3BP). Periodic orbits and regions of motion are fundamental keys to understand any dynamical system; for this reason the Hill's surfaces or the families of halo orbits have been extensively studied in the frame of the circular restricted three body problem. It is our opinion that their natural extensions to the ER3BP have not been studied enough. We divide the position space into forbidden subregions, subregions of motion and low-velocity subregions.We use these notions to define necessary condition for a transfer trajectory in the ER3BP. Also we compute branches of elliptic halo orbits bifurcating from halo orbits in the circular restricted three body problem. The new periodic orbits have principal periods and stability properties different from those of the originating halo orbit.
Crack-face displacements for embedded elliptic and semi-elliptical surface cracks
NASA Technical Reports Server (NTRS)
Raju, I. S.
1989-01-01
Analytical expressions for the crack-face displacements of an embedded elliptic crack in infinite solid subjected to arbitrary tractions are obtained. The tractions on the crack faces are assumed to be expressed in a polynomial form. These displacements expressions complete the exact solution of Vijayakumar and Atluri, and Nishioki and Atluri. For the special case of an embedded crack in an infinite solid subjected to uniform pressure loading, the present displacements agree with those by Green and Sneddon. The displacement equations derived were used with the finite-element alternating method (FEAM) for the analysis of a semi-elliptic surface crack in a finite solid subjected to remote tensile loading. The maximum opening displacements obtained with FEAM are compared to those with the finite-element method with singularity elements. The maximum crack opening displacements by the two methods showed good agreement.
Elliptical-anisotropic eikonal phase velocity tomography
NASA Astrophysics Data System (ADS)
de Ridder, S. A. L.; Biondi, B. L.; Nichols, D.
2015-02-01
We formulated an anisotropic eikonal tomography approach for phase velocities based on a two-dimensional elliptical-anisotropic wave equation. We can fit the parameters of the ellipse directly from measured first-order traveltime surface gradients and constrain these parameters to vary smoothly over space. The method is applied to Scholte waves in virtual seismic sources from stations in the Life of Field Seismic Ocean Bottom Cable array installed over the Ekofisk field. The fast directions of the azimuthally anisotropic Scholte wave velocities form a large circular pattern over the Ekofisk field. This pattern dominates the Scholte wave phase velocities at Ekofisk between 0.7 and 1.1 Hz. It results from the overburden stress state and from seafloor subsidence induced by decades of hydrocarbon extraction.
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.
Ultrasonic guided waves in elliptical annular cylinders.
Rajagopal, Prabhu; Pattanayak, Roson Kumar
2015-09-01
This paper studies the influence of cross-section ovalness or ellipticity on lower order axisymmetric guided wave modes in thin pipes. The second longitudinal mode L(0,2) and the fundamental torsional mode T(0,1) are studied, as these are of interest to current pipe inspection. The semi-analytical finite element (FE) method is mainly used, with three-dimensional FE simulations for visualization and cross-validation of results. The studies reveal that even a small degree of ovalness can affect mode shapes and velocities. The effect is more pronounced on the L(0,2) mode than on T(0,1) and this may be important for practical inspection applications.
Universal geometrical scaling of the elliptic flow
NASA Astrophysics Data System (ADS)
Andrés, C.; Dias de Deus, J.; Moscoso, A.; Pajares, C.; Salgado, Carlos A.
2015-03-01
The presence of scaling variables in experimental observables provide very valuable indications of the dynamics underlying a given physical process. In the last years, the search for geometric scaling, that is the presence of a scaling variable which encodes all geometrical information of the collision as well as other external quantities as the total energy, has been very active. This is motivated, in part, for being one of the genuine predictions of the Color Glass Condensate formalism for saturation of partonic densities. Here we extend these previous findings to the case of experimental data on elliptic flow. We find an excellent scaling for all centralities and energies, from RHIC to LHC, with a simple generalization of the scaling previously found for other observables and systems. Interestingly, the case of the photons, difficult to reconcile in most formalisms, nicely fit the scaling curve. We discuss on the possible interpretations of this finding in terms of initial or final state effects.
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.
On the velocity fields of elliptical galaxies
NASA Technical Reports Server (NTRS)
Statler, Thomas S.
1991-01-01
A family of self-consistent maximum entropy dynamical models is presented for the triaxial 'perfect ellipsoids'. These models are projected in different viewing geometries to explore the possible morphologies of the 2D radial-velocity fields of elliptical galaxies. It is found that, typically, about half the time an 'ordinary' velocity field is seen with a mixture of major- and minor-axis rotation. For other lines of sight, the velocity fields are more complicated, showing multiple peaks, steep gradients, strongly twisted contours, or kinematically distinct or counter-rotating cores. The origin of each of these velocity field morphologies is explained in terms of competing contributions from the major families of tube orbits.
Elliptical Muon Helical Cooling Channel Coils
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$_{\\phi}$.
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.
Elliptical Undulators HU256 for Synchrotron SOLEIL
Batrakov, A.; Churkin, I.; Ilyin, I.; Kolokolnikov, Yu.; Rouvinski, E.; Semenov, E.; Steshov, A.; Vobly, P.; Briquez, F.; Chubar, O.; Dael, A.; Marcouile, O.; Marteau, F.; Roux, G.; Valleau, M.
2007-01-19
Three elliptical undulators HU256 of electromagnetic type were produced, tested and magnetically measured by the Budker Institute of Nuclear Physics (Russia) for Synchrotron Soleil (France). The undulators have a new design of a Bx and Bz closed structure for insertion vacuum chamber. In the elliptical undulator HU256 with period of the magnetic fields of 256 mm, the vertical magnetic field (Bzmax=0.44 T) formed by 27 Bz laminated dipole magnets is symmetric, and the horizontal magnetic field (Bxmax=0.33 T) formed by 28 Bx laminated dipole magnets is asymmetric. The undulator can work in standard mode as well as in a quasi-periodical mode. The vertical magnetic field may be modulated by switching on the modulation coils placed on the Bz dipoles. Two power supply systems allow us to modulate the horizontal magnetic field, and change the radiation spectrum. The magnetic calculations of the individual dipoles and dipoles in ''undulator'' environment were executed by means of Mermaid 3D Code. The magnetic measurements of the individual dipoles had confirmed the magnetic calculations. On basis of semiempirical dependences from the mechanical characteristics the estimates of the magnetic parameters for all dipoles were calculated. Sorting of dipoles in the undulators have been done, and it has improved the magnetic parameters of the assembled undulators in comparison with the statistical estimations. The magnetic measurements of the undulators HU256 were carried out at Budker INP by Hall probes and at Soleil by Hall probes and Stretched Wire. Now the 1st undulator HU256 is installed at Soleil Storage Ring.
Ellipticals: core-Sérsic vs Nuker
NASA Astrophysics Data System (ADS)
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.
Elliptic Fourier analysis of mandibular shape.
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.
The Hodge-Elliptic Genus, Spinning BPS States, and Black Holes
NASA Astrophysics Data System (ADS)
Kachru, Shamit; Tripathy, Arnav
2017-10-01
We perform a refined count of BPS states in the compactification of M-theory on {K3 × T^2}, keeping track of the information provided by both the {SU(2)_L} and {SU(2)_R} angular momenta in the SO(4) little group. Mathematically, this four variable counting function may be expressed via the motivic Donaldson-Thomas counts of {K3 × T^2}, simultaneously refining Katz, Klemm, and Pandharipande's motivic stable pairs counts on K3 and Oberdieck-Pandharipande's Gromov-Witten counts on {K3 × T^2}. This provides the first full answer for motivic curve counts of a compact Calabi-Yau threefold. Along the way, we develop a Hodge-elliptic genus for Calabi-Yau manifolds—a new counting function for BPS states that interpolates between the Hodge polynomial and the elliptic genus of a Calabi-Yau.
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.
NASA Astrophysics Data System (ADS)
Park, Hyeongkae; Nourgaliev, Robert; Knoll, Dana
2007-11-01
The Discontinuous Galerkin (DG) method for compressible fluid flows is incorporated into the Jacobian-Free Newton-Krylov (JFNK) framework. Advantages of combining the DG with the JFNK are two-fold: a) enabling robust and efficient high-order-accurate modeling of all-speed flows on unstructured grids, opening the possibility for high-fidelity simulation of nuclear-power-industry-relevant flows; and b) ability to tightly, robustly and high-order-accurately couple with other relevant physics (neutronics, thermal-structural response of solids, etc.). In the present study, we focus on the physics-based preconditioning (PBP) of the Krylov method (GMRES), used as the linear solver in our implicit higher-order-accurate Runge-Kutta (ESDIRK) time discretization scheme; exploiting the compactness of the spatial discretization of the DG family. In particular, we utilize the Implicit Continuous-fluid Eulerian (ICE) method and investigate its efficacy as the PBP within the JFNK-DG method. Using the eigenvalue analysis, it is found that the ICE collapses the complex components of the all eigenvalues of the Jacobian matrix (associated with pressure waves) onto the real axis, and thereby enabling at least an order of magnitude faster simulations in nearly-incompressible/weakly-compressible regimes with a significant storage saving.
NASA Astrophysics Data System (ADS)
Shi, Zhong; Huang, Xuexiang; Hu, Tianjian; Tan, Qian; Hou, Yuzhuo
2016-10-01
Space teleoperation is an important space technology, and human-robot motion similarity can improve the flexibility and intuition of space teleoperation. This paper aims to obtain an appropriate kinematics mapping method of coupled Cartesian-joint space for space teleoperation. First, the coupled Cartesian-joint similarity principles concerning kinematics differences are defined. Then, a novel weighted augmented Jacobian matrix with a variable coefficient (WAJM-VC) method for kinematics mapping is proposed. The Jacobian matrix is augmented to achieve a global similarity of human-robot motion. A clamping weighted least norm scheme is introduced to achieve local optimizations, and the operating ratio coefficient is variable to pursue similarity in the elbow joint. Similarity in Cartesian space and the property of joint constraint satisfaction is analysed to determine the damping factor and clamping velocity. Finally, a teleoperation system based on human motion capture is established, and the experimental results indicate that the proposed WAJM-VC method can improve the flexibility and intuition of space teleoperation to complete complex space tasks.
On the solution of elliptic partial differential equations on regions with corners
NASA Astrophysics Data System (ADS)
Serkh, Kirill; Rokhlin, Vladimir
2016-01-01
In this paper we investigate the solution of boundary value problems on polygonal domains for elliptic partial differential equations. We observe that when the problems are formulated as the boundary integral equations of classical potential theory, the solutions are representable by series of elementary functions. In addition to being analytically perspicuous, the resulting expressions lend themselves to the construction of accurate and efficient numerical algorithms. The results are illustrated by a number of numerical examples.
On the solution of elliptic partial differential equations on regions with corners
Serkh, Kirill Rokhlin, Vladimir
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.
Gorodnichev, E. E.
2016-12-15
For elliptically polarized light incident on a two-dimensional medium with large inhomogeneities, the Stokes parameters of scattered waves are calculated. Multiple scattering is assumed to be sharply anisotropic. The degree of polarization of scattered radiation is shown to be a nonmonotonic function of depth when the incident wave is circularly polarized or its polarization vector is not parallel to the symmetry axis of the inhomogeneities.
Flow in elliptical vessels calculated for a physiological waveform.
Robertson, M B; Köhler, U; Hoskins, P R; Marshall, I
2001-01-01
Understanding the nature of pulsatile flow is an important issue in haemodynamics, especially the initiation and progression of vascular disease. The geometry of a non-circular vessel was idealised to an elliptical cross-section, and the dynamic properties of the flow were calculated for a physiological waveform. The Fourier harmonics for a common carotid waveform were determined, and the velocity profile and wall shear stress were calculated from the superposition of the individual contributions from each harmonic. The effects of ellipticity on the flow pattern were found to be significant. The velocity profile along the major axis of the elliptical cross-section developed a flattened peak, which widened as the vessel became more elliptical. Wall shear stress demonstrated an angular dependence in elliptical vessels, where the point of minimum shear stress was located at the end of the major axis. Comparison with a cylindrical vessel demonstrated a 3% decrease in peak wall shear stress (tau = 2.96, N.m(-2)) at the end of the major axis, and 10% in the mean wall shear stress (tau = 0.44 N. m(-2)), for an elliptical vessel (epsilon = 0.8). The temporal average wall shear stress, which has been associated with atherogenic sites, also displayed a minimum at the end of the major axis that decreased with more elliptical cross-sections. Copyright 2001 S. Karger AG, Basel
Discontinuous dual-primal mixed finite elements for elliptic problems
NASA Technical Reports Server (NTRS)
Bottasso, Carlo L.; Micheletti, Stefano; Sacco, Riccardo
2000-01-01
We propose a novel discontinuous mixed finite element formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the element level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed finite element methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.
TRANSVERSE MERCATOR MAP PROJECTION OF THE SPHEROID USING TRANSFORMATION OF THE ELLIPTIC INTEGRAL
NASA Technical Reports Server (NTRS)
Wallis, D. E.
1994-01-01
This program produces the Gauss-Kruger (constant meridional scale) Transverse Mercator Projection which is used to construct the U.S. Army's Universal Transverse Mercator (UTM) Grid System. The method is capable of mapping the entire northern hemisphere of the earth (and, by symmetry of the projection, the entire earth) accurately with respect to a single principal meridian, and is therefore mathematically insensitive to proximity either to the pole or the equator, or to the departure of the meridian from the central meridian. This program could be useful to any map-making agency. The program overcomes the limitations of the "series" method (Thomas, 1952) presently used to compute the UTM Grid, specifically its complicated derivation, non-convergence near the pole, lack of rigorous error analysis, and difficulty of obtaining increased accuracy. The method is based on the principle that the parametric colatitude of a point is the amplitude of the Elliptic Integral of the 2nd Kind, and this (irreducible) integral is the desired projection. Thus, a specification of the colatitude leads, most directly (and with strongest motivation) to a formulation in terms of amplitude. The most difficult problem to be solved was setting up the method so that the Elliptic Integral of the 2nd Kind could be used elsewhere than on the principal meridian. The point to be mapped is specified in conventional geographic coordinates (geodetic latitude and longitudinal departure from the principal meridian). Using the colatitude (complement of latitude) and the longitude (departure), the initial step is to map the point to the North Polar Stereographic Projection. The closed-form, analytic function that coincides with the North Polar Stereographic Projection of the spheroid along the principal meridian is put into a Newton-Raphson iteration that solves for the tangent of one half the parametric colatitude, generalized to the complex plane. Because the parametric colatitude is the amplitude of
Dusty Feedback from Massive Black Holes in Two Elliptical Galaxies
NASA Technical Reports Server (NTRS)
Temi, P.; Brighenti, F.; Mathews, W. G.; Amblard, A.; Riguccini, L.
2013-01-01
Far-infrared dust emission from elliptical galaxies informs us about galaxy mergers, feedback energy outbursts from supermassive black holes and the age of galactic stars. We report on the role of AGN feedback observationally by looking for its signatures in elliptical galaxies at recent epochs in the nearby universe. We present Herschel observations of two elliptical galaxies with strong and spatially extended FIR emission from colder grains 5-10 kpc distant from the galaxy cores. Extended excess cold dust emission is interpreted as evidence of recent feedback-generated AGN energy outbursts in these galaxies, visible only in the FIR, from buoyant gaseous outflows from the galaxy cores.
Jacobi-Bessel analysis of reflector antennas with elliptical apertures
NASA Technical Reports Server (NTRS)
Rahmat-Samii, Yahya
1987-01-01
Although many reflector antennas possess circular projected apertures, there are recent satellite and ground antenna applications for which it is desirable to employ reflectors with elliptical apertures. Here a modification of the Jacobi-Bessel expansion is presented for the diffraction analysis of reflectors with elliptical apertures. A comparative study is also performed between this modified Jacobi-Bessel algorithm and the one which uses the Jacobi-Bessel expansion over a circumscribing circular region. Numerical results are presented for offset reflectors with elliptical and circular apertures and the improved convergence properties of the modified algorithm are highlighted.
Exact geometric optics in a Morris-Thorne wormhole spacetime
Mueller, Thomas
2008-02-15
The simplicity of the Morris-Thorne wormhole spacetime permits us to determine null and timelike geodesics by means of elliptic integral functions and Jacobian elliptic functions. This analytic solution makes it possible to find a geodesic which connects two distant events. An exact gravitational lensing, an illumination calculation, and even an interactive visualization become possible.
NASA Astrophysics Data System (ADS)
Aoki, K.; Makino, S.; Katagi, T.; Kagoshima, K.
1993-04-01
A newly developed method of design for a shaped reflector antenna is described. A conventional quadratic reflector configuration is assumed; the reflectors are then modified to yield the desired aperture shape and field distribution by introducing shaping functions. This method is useful for designing antennas with an arbitrary shaped beam, such as an elliptical-beam antenna, and has been verified through a 4.7 m x 2.3 m dual-band earth-station antenna for the Japanese domestic satellite system CS. The measured aperture efficiency is more than 76 percent, and the ratio of the major and minor axes of the elliptical beam is 2:1.
NASA Astrophysics Data System (ADS)
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.
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.
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)
NASA Astrophysics Data System (ADS)
Oñorbe, J.; Domínguez-Tenreiro, R.; Sáiz, A.; Serna, A.
2007-03-01
We have analysed the mass and velocity distributions of two samples of relaxed elliptical-like objects (ELOs) identified, at z = 0, in a set of self-consistent hydrodynamical simulations operating in the context of a concordance cosmological model. ELOs have been identified as those virtual galaxies having a prominent, dynamically relaxed stellar spheroidal component, with no extended discs and very low gas content. Our analysis shows that they are embedded in extended, massive dark matter haloes, and they also have an extended corona of hot diffuse gas. Dark matter haloes have experienced adiabatic contraction along their assembly process. The relative ELO dark- to bright-mass content and space distributions show broken homology, and they are consistent with observational results on the dark matter fraction at the central regions, as well as on the gradients of the mass-to-light ratio profiles for boxy ellipticals, as a function of their stellar masses. These results indicate that massive ellipticals miss stars (i.e. baryons) at their central regions, as compared to less massive ones. Our simulations indicate that these missing baryons could be found beyond the virial radii as a hot, diffuse plasma. This mass homology breaking could have important implications to explain the physical origin of the Fundamental Plane relation. The projected stellar mass profiles of our virtual ellipticals can be well fitted by the Sérsic formula, with shape parameters n that agree, once a stellar mass-to-light ratio independent of position is assumed, with those obtained from surface brightness profiles of ellipticals. The agreement includes the empirical correlations of n with size, luminosity and velocity dispersion. The total mass density profiles show a power-law behaviour over a large r/rvir interval, consistent with data on massive lens ellipticals at shorter radii. The velocity dispersion profiles show kinematical segregation, with no systematic mass dependence (i.e. no
Periodic Orbits in a Second-Order Discontinuous System with an Elliptic Boundary
NASA Astrophysics Data System (ADS)
Li, Liping; Luo, Albert C. J.
2016-12-01
This paper develops the analytical conditions for the onset and disappearance of motion passability and sliding along an elliptic boundary in a second-order discontinuous system. A periodically forced system, described by two different linear subsystems, is considered mainly to demonstrate the methodology. The passable, sliding and grazing conditions of a flow to the elliptic boundary in the discontinuous dynamical system are provided through the analysis of the corresponding vector fields and G-functions. Moreover, by constructing appropriate generic mappings, periodic orbits in such a discontinuous system are predicted analytically. Finally, three different cases are discussed to illustrate the existence of periodic orbits with passable and/or sliding flows. The results obtained in this paper can be applied to the sliding mode control in discontinuous dynamical systems.
The generalized Euler-Poinsot rigid body equations: explicit elliptic solutions
NASA Astrophysics Data System (ADS)
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.
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.
Design of high-order elliptic filter from a versatile mode generic OTA-C structure
NASA Astrophysics Data System (ADS)
Ghosh, K.; Ray, B. N.
2015-03-01
A new synthesis methodology for high-order versatile mode programmable Operational transconductance amplifier and capacitor (OTA-C) generic filter structure is proposed. The structure fulfills the three main criteria of high frequency operation i.e it uses (1) less number of components (2) only single ended input OTAs (3) only grounded capacitors. Any nth order transfer function can be realised from it. Elliptic filter is designed from the generic structure using optimisation technique to reduce the number of OTAs. SPICE simulation with BSIM level 53 model and 0.13 μm process confirms the theoretical analysis. Frequency response of third-order and fourth-order elliptic filter is shown as representative set of simulated result. Sensitivity and non-ideal effect of the designed filter are studied.
NASA Astrophysics Data System (ADS)
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.
Trace Formula for Linear Hamiltonian Systems with its Applications to Elliptic Lagrangian Solutions
NASA Astrophysics Data System (ADS)
Hu, Xijun; Ou, Yuwei; Wang, Penghui
2015-04-01
In the present paper, we build up trace formulas for both the linear Hamiltonian systems and Sturm-Liouville systems. The formula connects the monodromy matrix of a symmetric periodic orbit with the infinite sum of eigenvalues of the Hessian of the action functional. A natural application is to study the non-degeneracy of linear Hamiltonian systems. Precisely, by the trace formula, we can give an estimation for the upper bound such that the non-degeneracy preserves. Moreover, we could estimate the relative Morse index by the trace formula. Consequently, a series of new stability criteria for the symmetric periodic orbits is given. As a concrete application, the trace formula is used to study the linear stability of elliptic Lagrangian solutions of the classical planar three-body problem, which depends on the mass parameter and the eccentricity . Based on the trace formula, we estimate the stable region and hyperbolic region of the elliptic Lagrangian solutions.
Elliptical-Tukey chirp signal for high-resolution, air-coupled ultrasonic imaging.
Pallav, Prakash; Gan, Tat Hean; Hutchins, David A
2007-08-01
A new signal processing method, which uses a modified chirp signal for air-coupled ultrasonic imaging, is described. A combination of the elliptical and Tukey window functions has been shown to give a better performance than the Hanning windowing used in most pulse-compression algorithms for air-coupled applications. The elliptical-Tukey chirp signal provides an improvement in both the resolution of images and signal-to-noise ratios. In addition, this type of signal also reduces the level of signal voltages required to drive the source transducer while maintaining the performance of the system. This approach, thus, may have wide interest in all forms of wide bandwidth ultrasonic imaging.
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.
NASA Astrophysics Data System (ADS)
Biskup, M.; Salvi, M.; Wolff, T.
2014-06-01
Given a resistor network on with nearest-neighbor conductances, the effective conductance in a finite set with a given boundary condition is the minimum of the Dirichlet energy over functions with the prescribed boundary values. For shift-ergodic conductances, linear (Dirichlet) boundary conditions and square boxes, the effective conductance scaled by the volume of the box converges to a deterministic limit as the box-size tends to infinity. Here we prove that, for i.i.d. conductances with a small ellipticity contrast, also a (non-degenerate) central limit theorem holds. The proof is based on the corrector method and the Martingale Central Limit Theorem; a key integrability condition is furnished by the Meyers estimate. More general domains, boundary conditions and ellipticity contrasts will be addressed in a subsequent paper.
Stable equilibria of elliptic roly-poly toys
NASA Astrophysics Data System (ADS)
Hong, Seok-In
2016-11-01
As an instructive (gravitational potential) energy approach, we show that the elliptic roly-poly has a richer and more useful profile (including the tilted configuration) of stable equilibria than conventional spherical or cylindrical roly-polys.
Elliptic Solvers with Adaptive Mesh Refinement on Complex Geometries
Phillip, B.
2000-07-24
Adaptive Mesh Refinement (AMR) is a numerical technique for locally tailoring the resolution computational grids. Multilevel algorithms for solving elliptic problems on adaptive grids include the Fast Adaptive Composite grid method (FAC) and its parallel variants (AFAC and AFACx). Theory that confirms the independence of the convergence rates of FAC and AFAC on the number of refinement levels exists under certain ellipticity and approximation property conditions. Similar theory needs to be developed for AFACx. The effectiveness of multigrid-based elliptic solvers such as FAC, AFAC, and AFACx on adaptively refined overlapping grids is not clearly understood. Finally, a non-trivial eye model problem will be solved by combining the power of using overlapping grids for complex moving geometries, AMR, and multilevel elliptic solvers.
Iterative methods for elliptic finite element equations on general meshes
NASA Technical Reports Server (NTRS)
Nicolaides, R. A.; Choudhury, Shenaz
1986-01-01
Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included.
Rigorous theory on elliptical mirror focusing for point scanning microscopy.
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.
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.
The removal of shear-ellipticity correlations from the cosmic shear signal via nulling techniques
NASA Astrophysics Data System (ADS)
Joachimi, B.; Schneider, P.
2008-09-01
Aims: To render cosmic shear an astronomical tool of high precision, it is essential to eliminate systematic effects upon its signal, one of the most significant ones being the intrinsic alignment of galaxies. The alignment in tidal fields that are created by the surrounding matter structure induces correlations between the intrinsic ellipticities of source galaxies, as well as correlations between the gravitational shear and the intrinsic ellipticity. While the former effect is restricted to physically close galaxy pairs and thus relatively easy to control, shear-ellipticity correlations occur for pairs at large separations. Because of the crudeness of current models of intrinsic alignment, we have developed a model-independent, purely geometrical method for removing the contamination of the cosmic shear signal by shear-ellipticity correlations. Methods: We remove the contributions to a tomographic cosmic shear signal that may be subject to contamination by shear-ellipticity correlations, making use of the characteristic dependence of these correlations on redshift. By introducing an appropriately chosen weight function to the lensing efficiency that nulls signals stemming from certain distances, new second-order measures of cosmic shear can be constructed that are free from intrinsic alignment. We present three approaches to determining such weight functions, optimized with respect to the amount of information the weighting preserves. After generalizing the construction of weight functions, the loss of information induced by this nulling technique and the subsequent degradation of constraints on cosmological parameters is quantified in a likelihood analysis. Results: For constructing optimal weight functions, good agreement is achieved between all approaches considered. In particular, a simplified analytical ansatz is shown to approximate the numerical results closely, significantly lowering computational efforts. For a survey divided into 20 redshift bins, we
Universal geometrical scaling of the elliptic flow
NASA Astrophysics Data System (ADS)
Andrés, C.; de Deus, J. Dias; Moscoso, A.; Pajares, C.; Salgado, Carlos A.
2015-09-01
The presence of scaling variables in experimental observables provides very valuable indications of the dynamics underlying a given physical process. In the last years, the search for geometric scaling, that is the presence of a scaling variable which encodes all geometrical information of the collision as well as other external quantities as the total energy, has been very active. This is motivated, in part, for being one of the genuine predictions of the color glass condensate formalism for saturation of partonic densities. Here we extend these previous findings to the case of experimental data on elliptic flow. We find an excellent scaling for all centralities and energies, from the BNL Relativistic Heavy Ion Collider to the CERN Large Hadron Collider, with a simple generalization of the scaling previously found for other observables and systems. Interestingly the case of the photons, difficult to reconcile in most formalisms, nicely fits the scaling curve. We discuss the possible interpretations of this finding in terms of initial or final state effects.
Beam-beam deflection and signature curves for elliptic beams
Ziemann, V.
1990-10-22
In this note we will present closed expressions for the beam-beam deflection angle for arbitrary elliptic beams including tilt. From these expressions signature curves, i.e., systematic deviations from the round beam deflection curve due to ellipticity or tilt are derived. In the course of the presentation we will prove that it is generally impossible to infer individual beam sizes from beam-beam deflection scans. 3 refs., 2 figs.
Transition of recollision trajectories from linear to elliptical polarization
Li, Yingbin; Yu, Benhai; Tang, Qingbin; ...
2016-03-15
Using a classical ensemble method, we revisit the topic of recollision and nonsequential double ionization with elliptically polarized laser fields. We focus on how the recollision mechanism transitions from short trajectories with linear polarization to long trajectories with elliptical polarization. Furthermore, we propose how this transition can be observed by measuring the carrier-envelop-phase dependence of the correlated electron momentum spectra using currently available few-cycle laser pulses.
Development of an Elliptical Trainer Physical Fitness Test
2006-04-02
rear-drive model elliptical trainer for placement in Navy gyms and ships. Despite the availability of the CT 9500 HR elliptical trainer for Navy...service members, it has not been evaluated as an alternate method to assess cardiovascular fitness in the PRT. The CT 9500 HR rear-drive model ...calculations are not available due to an impending patent application. In two productions of the CT 9500 HR model , the software for the distance
Scatter of elastic waves by a thin flat elliptical inhomogeneity
NASA Technical Reports Server (NTRS)
Fu, L. S.
1983-01-01
Elastodynamic fields of a single, flat, elliptical inhomogeneity embedded in an infinite elastic medium subjected to plane time harmonic waves are studied. Scattered displacement amplitudes and stress intensities are obtained in series form for an incident wave in an arbitrary direction. The cases of a penny shaped crack and an elliptical crack are given as examples. The analysis is valid for alpha a up to about two, where alpha is longitudinal wave number and a is a typical geometric parameter.
Bifurcations in elliptical, asymmetric non-neutral plasmas
NASA Astrophysics Data System (ADS)
Fajans, Joel; Gilson, Erik
1999-11-01
When subjected to a stationary, l=2 potential perturbation on the wall, a pure electron plasma will deform into an elliptical shape. At first, the plasma's ellipticity is proportional to the strength of the potential perturbation. Once the perturbation is increased beyond a critical value, the plasma equilibrium bifurcates into two off-axis states. This bifurcation has been observed experimentally and will be described in this poster. (see http://socrates.berkeley.edu/ fajans/EquilStab/EllipseBifurcation.avi)
Remarks of Elliptic Curves Derived from Ant Colony Routing
NASA Astrophysics Data System (ADS)
Jung, Sangsu; Kim, Daeyeoul; Singh, Dhananjay
2011-09-01
We deal with an ant colony based routing model for wireless multi-hop networks. Our model adopts an elliptic curve equation, which is beneficial to design pheromone dynamics for load balancing and packet delivery robustness. Due to the attribute of an elliptic curve equation, our model prevents the over-utilization of a specific node, distinctively from conventional ant colony based schemes. Numerical simulations exhibit the characteristics of our model with respect to various parameters.
Depth-resolved measurements with elliptically polarized reflectance spectroscopy
Bailey, Maria J.; Sokolov, Konstantin
2016-01-01
The ability of elliptical polarized reflectance spectroscopy (EPRS) to detect spectroscopic alterations in tissue mimicking phantoms and in biological tissue in situ is demonstrated. It is shown that there is a linear relationship between light penetration depth and ellipticity. This dependence is used to demonstrate the feasibility of a depth-resolved spectroscopic imaging using EPRS. The advantages and drawbacks of EPRS in evaluation of biological tissue are analyzed and discussed. PMID:27446712
The presence and nature of ellipticity in Appalachian hardwood logs
R. Edward Thomas; John S. Stanovick; Deborah. Conner
2017-01-01
The ellipticity of hardwood logs is most often observed and measured from either end of a log. However, due to the nature of hardwood tree growth and bucking practices, the assessment of ellipticity in thir manner may not be accurate. Trees grown on hillsides often develop supporting wood that gives the first few feet of theÂ log butt a significant degree of...
A class of variational-hemivariational inequalities of elliptic type
NASA Astrophysics Data System (ADS)
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.
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.
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.
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. Copyright © 2015 Elsevier B.V. All rights reserved.
Probing the Central Regions of Nearby Compact Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Davidge, T. J.; Beck, Tracy L.; McGregor, Peter J.
2008-04-01
K-band spectroscopic observations recorded with NIFS+ALTAIR on Gemini North are used to probe the central arcsecond of the compact elliptical galaxies NGC 4486B, NGC 5846A, and M32. The angular resolution of these data is ~0.1'' FWHM; this corresponds to a spatial scale of 12 pc in NGC 5846A, which is the most distant galaxy in the sample. Indices that probe the strengths of various atomic and molecular features are measured. The central stellar contents of NGC 4486B and NGC 5846A are similar in the sense that they occupy the same regions of the (Ca I,12CO), (Na I,12CO), and (13CO,12CO) diagrams. The NGC 4486B and NGC 5846A observations depart from the sequence defined by solar neighborhood giants in the (Na I,12CO) diagram in a sense that is consistent with both galaxies having nonsolar chemical mixtures. For comparison, the M32 data are consistent with a chemical enrichment history like that in the Galactic disk; M32 could not have formed from the stripping of a larger elliptical galaxy. The behavior of the near-infrared line indices as a function of radius is also investigated. The stellar content in the central arcsecond of M32 appears to be well mixed. However, the radial behavior of the indices in NGC 4486B and NGC 5846A show complicated behavior, with the gradients that are present at large radii breaking down or reversing within a few tenths of an arcsec of the nucleus. Based on the age gradients predicted from visible wavelength spectra, coupled with the radial behavior of the langFe Irang and 12CO(2, 0) indices, it is suggested that the nuclear regions of NGC 4486B and NGC 5846A harbor intermediate-age populations. Based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the National Science Foundation (NSF) on behalf of the Gemini partnership: the National Science Foundation (United States), the Science and Technology Facilities
NASA Astrophysics Data System (ADS)
Viallet, M.; Goffrey, T.; Baraffe, I.; Folini, D.; Geroux, C.; Popov, M. V.; Pratt, J.; Walder, R.
2016-02-01
This work is a continuation of our efforts to develop an efficient implicit solver for multidimensional hydrodynamics for the purpose of studying important physical processes in stellar interiors, such as turbulent convection and overshooting. We present an implicit solver that results from the combination of a Jacobian-free Newton-Krylov method and a preconditioning technique tailored to the inviscid, compressible equations of stellar hydrodynamics. We assess the accuracy and performance of the solver for both 2D and 3D problems for Mach numbers down to 10-6. Although our applications concern flows in stellar interiors, the method can be applied to general advection and/or diffusion-dominated flows. The method presented in this paper opens up new avenues in 3D modeling of realistic stellar interiors allowing the study of important problems in stellar structure and evolution.
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.
Shearkhani, O; Khademi, A; Eilaghi, A; Hojjat, S-P; Symons, S P; Heyn, C; Machnowska, M; Chan, A; Sahgal, A; Maralani, P J
2017-09-07
Accurate follow-up of metastatic brain tumors has important implications for patient prognosis and management. The aim of this study was to develop and evaluate the accuracy of a semiautomated algorithm in detecting growing or shrinking metastatic brain tumors on longitudinal brain MRIs. We used 50 pairs of successive MR imaging datasets, 30 on 1.5T and 20 on 3T, containing contrast-enhanced 3D T1-weighted sequences. These yielded 150 growing or shrinking metastatic brain tumors. To detect them, we completed 2 major steps: 1) spatial normalization and calculation of the Jacobian operator field to quantify changes between scans, and 2) metastatic brain tumor candidate segmentation and detection of volume-changing metastatic brain tumors with the Jacobian operator field. Receiver operating characteristic analysis was used to assess the detection accuracy of the algorithm, and it was verified with jackknife resampling. The reference standard was based on detections by a neuroradiologist. The areas under the receiver operating characteristic curves were 0.925 for 1.5T and 0.965 for 3T. Furthermore, at its optimal performance, the algorithm achieved a sensitivity of 85.1% and 92.1% and specificity of 86.7% and 91.3% for 1.5T and 3T, respectively. Vessels were responsible for most false-positives. Newly developed or resolved metastatic brain tumors were a major source of false-negatives. The proposed algorithm could detect volume-changing metastatic brain tumors on longitudinal brain MRIs with statistically high accuracy, demonstrating its potential as a computer-aided change-detection tool for complementing the performance of radiologists, decreasing inter- and intraobserver variability, and improving efficacy. © 2017 American Society of Neuroradiology.
Retrieval of Rayleigh Wave Ellipticity from Ambient Vibration Recordings
NASA Astrophysics Data System (ADS)
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
Retrieval of Rayleigh wave ellipticity from ambient vibration recordings
NASA Astrophysics Data System (ADS)
Maranò, Stefano; Hobiger, Manuel; Fäh, Donat
2017-04-01
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 maximum likelihood (ML) method presented in Maranò et al. 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 versus 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
An efficient code to solve the Kepler equation. Elliptic case
NASA Astrophysics Data System (ADS)
Raposo-Pulido, V.; Peláez, J.
2017-05-01
A new approach for solving Kepler equation for elliptical orbits is developed in this paper. This new approach takes advantage of the very good behaviour of the modified Newton-Raphson method when the initial seed is close to the looked for solution. To determine a good initial seed the eccentric anomaly domain [0, π] is discretized in several intervals and for each one of these intervals a fifth degree interpolating polynomial is introduced. The six coefficients of the polynomial are obtained by requiring six conditions at both ends of the corresponding interval. Thus the real function and the polynomial have equal values at both ends of the interval. Similarly relations are imposed for the two first derivatives. In the singular corner of the Kepler equation, M ≪ 1 and 1 - e ≪ 0 an asymptotic expansion is developed. In most of the cases, the seed generated leads to reach machine error accuracy with the modified Newton-Raphson method with no iterations or just one iteration. This approach improves the computational time compared with other methods currently in use.
Stress Analysis of Composite Cylindrical Shells With an Elliptical Cutout
NASA Technical Reports Server (NTRS)
Nemeth, M. P.; Oterkus, E.; Madenci, E.
2005-01-01
A special-purpose, semi-analytical solution method for determining the stress and deformation fields in a thin laminated-composite cylindrical shell with an elliptical cutout is presented. The analysis includes the effects of cutout size, shape, and orientation; nonuniform wall thickness; oval-cross-section eccentricity; and loading conditions. The loading conditions include uniform tension, uniform torsion, and pure bending. The analysis approach is based on the principle of stationary potential energy and uses Lagrange multipliers to relax the kinematic admissibility requirements on the displacement representations through the use of idealized elastic edge restraints. Specifying appropriate stiffness values for the elastic extensional and rotational edge restraints (springs) allows the imposition of the kinematic boundary conditions in an indirect manner, which enables the use of a broader set of functions for representing the displacement fields. Selected results of parametric studies are presented for several geometric parameters that demonstrate that analysis approach is a powerful means for developing design criteria for laminated-composite shells.
Stress Analysis of Composite Cylindrical Shells with an Elliptical Cutout
NASA Technical Reports Server (NTRS)
Oterkus, E.; Madenci, E.; Nemeth, M. P.
2007-01-01
A special-purpose, semi-analytical solution method for determining the stress and deformation fields in a thin laminated-composite cylindrical shell with an elliptical cutout is presented. The analysis includes the effects of cutout size, shape, and orientation; non-uniform wall thickness; oval-cross-section eccentricity; and loading conditions. The loading conditions include uniform tension, uniform torsion, and pure bending. The analysis approach is based on the principle of stationary potential energy and uses Lagrange multipliers to relax the kinematic admissibility requirements on the displacement representations through the use of idealized elastic edge restraints. Specifying appropriate stiffness values for the elastic extensional and rotational edge restraints (springs) allows the imposition of the kinematic boundary conditions in an indirect manner, which enables the use of a broader set of functions for representing the displacement fields. Selected results of parametric studies are presented for several geometric parameters that demonstrate that analysis approach is a powerful means for developing design criteria for laminated-composite shells.
Hovering control scheme to elliptical orbit via frozen parameter
NASA Astrophysics Data System (ADS)
Zhang, Jingrui; Zhao, Shuge; Zhang, Yao; Zhai, Guang
2015-01-01
In this paper, we analyze the hovering control operation of a target in an elliptical orbit based on frozen parameter. The relative dynamics of spacecraft in eccentric orbits can be described as linear time-varying systems with periodic parameters. Those periodic parameters are the orbital radius, angular velocity and angular acceleration. The time-varying characteristics of these periodic parameters were analyzed via a performance index which is obtained analytically with small fixed time interval. Then, the frozen time interval was obtained with a fixed performance index using a numerical method. A series of constant coefficient linear systems are then obtained to represent the periodic linear system, namely the relative motion dynamics. In the frozen time interval, the hovering control scheme was designed based on a Linear Quadratic Regulator (LQR). Numerical simulations showed that the hovering control performance is good, except the vicinity near the apogee and perigee, both of which exhibit a relative large performance index. Decreasing the performance index from 0.01 to 0.001 reduces the position errors from 5 m to 0.5 m during steady state. It is shown that this approach can save propellant and eliminate chatter during the convergence compared to Control Lyapunov Functions (CLF) approach.
Semi-coarsening AMLI preconditioning of higher order elliptic problems
NASA Astrophysics Data System (ADS)
Kraus, J.; Lymbery, M.; Margenov, S.
2012-10-01
The present paper presents the construction of a robust multilevel preconditioner for anisotropic bicubic finite element (FE) elliptic problems. More precisely, the behavior of the constant in the strengthened CBS inequality, which is important for studying (approximate) block factorizations of FE stiffness matrices, is analyzed in the case when the underlying conforming FE space consists of piecewise bicubic functions, and is decomposed according to hierarchical splittings that are based on semi-coarsening of the FE mesh. The presented theoretical estimates are further confirmed by numerically computed CBS constants for a rich set of parameters (coarsening factor and anisotropy ratio). The problem of solving efficiently systems with the pivot block matrices arising in the hierarchical basis two-level matrices is also addressed in this paper. Finally, combining the proven uniform estimates with the theory of the Algebraic Multilevel Iteration (AMLI) methods an optimal order multilevel algorithm whose total computational cost is proportional to the size of the discrete problem with a proportionality constant independent of the anisotropy ratio is obtained.
Mild solutions of semilinear elliptic equations in Hilbert spaces
NASA Astrophysics Data System (ADS)
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.
Acoustic scattering by elastic cylinders of elliptical cross-section and splitting up of resonances
Ancey, S. Bazzali, E. Gabrielli, P. Mercier, M.
2014-05-21
The scattering of a plane acoustic wave by an infinite elastic cylinder of elliptical cross section is studied from a modal formalism by emphasizing the role of the symmetries. More precisely, as the symmetry is broken in the transition from the infinite circular cylinder to the elliptical one, the splitting up of resonances is observed both theoretically and experimentally. This phenomenon can be interpreted using group theory. The main difficulty stands in the application of this theory within the framework of the vectorial formalism in elastodynamics. This method significantly simplifies the numerical treatment of the problem, provides a full classification of the resonances, and gives a physical interpretation of the splitting up in terms of symmetry breaking. An experimental part based on ultrasonic spectroscopy complements the theoretical study. A series of tank experiments is carried out in the case of aluminium elliptical cylinders immersed in water, in the frequency range 0 ≤ kr ≤ 50, where kr is the reduced wave number in the fluid. The symmetry is broken by selecting various cylinders of increasing eccentricity. More precisely, the greater the eccentricity, the higher the splitting up of resonances is accentuated. The experimental results provide a very good agreement with the theoretical ones, the splitting up is observed on experimental form functions, and the split resonant modes are identified on angular diagrams.
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)
X-ray properties of elliptical galaxies as determined by feedback from their central black holes
NASA Astrophysics Data System (ADS)
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.
A PAndAS view of the resolved stellar populations in M31 dwarf elliptical satellites
NASA Astrophysics Data System (ADS)
Crnojević, D.; PAndAS Collaboration
We present the first truly global view of the closest elliptical galaxies, the dwarf elliptical (dE) companions of M31 NGC147 and NGC185. We exploit the deep PAndAS photometric dataset in order to investigate the resolved stellar content and structure of these dEs out to larger distances than ever previously probed. From the analysis of their old red giant branch stars, we derive density maps, full surface brightness profiles and metallicity distribution functions. We find that NGC147 shows pronounced tidal tails likely due to its interaction with M31, while NGC185 retains a regular elliptical shape over its entire extent. The two dEs follow a Sersic profile out to ˜5 kpc, and the effective radii derived in this study are a factor of two larger than previous literature values. While NGC185 shows a significant gradient in metallicity (˜-0.05 dex/kpc), this is almost absent in NGC147. The detailed understanding of nearby dEs is crucial for the studies of more distant objects, and we discuss how internal and environmental processes could have influenced the evolution of NGC147 and NGC185 in light of our results.
Spectral Energy Distribution Mapping of Two Elliptical Galaxies on Sub-kpc Scales
NASA Astrophysics Data System (ADS)
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.
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.
NASA Astrophysics Data System (ADS)
Holden, B. P.; Franx, M.; Illingworth, G. D.; Postman, M.; van der Wel, A.; Kelson, D. D.; Blakeslee, J. P.; Ford, H.; Demarco, R.; Mei, S.
2009-03-01
We have compiled a sample of early-type cluster galaxies from 0 < z < 1.3 and measured the evolution of their ellipticity distributions. Our sample contains 487 galaxies in 17 z>0.3 clusters with high-quality space-based imaging and a comparable sample of 210 galaxies in 10 clusters at z < 0.05. We select early-type galaxies (elliptical and S0 galaxies) that fall within the cluster R 200, and which lie on the red-sequence in the magnitude range -19.3>MB > - 21, after correcting for luminosity evolution as measured by the fundamental plane. Our ellipticity measurements are made in a consistent manner over our whole sample. We perform extensive simulations to quantify the systematic and statistical errors, and find that it is crucial to use point-spread function (PSF)-corrected model fits; determinations of the ellipticity from Hubble Space Telescope image data that do not account for the PSF "blurring" are systematically and significantly biased to rounder ellipticities at redshifts z>0.3. We find that neither the median ellipticity, nor the shape of the ellipticity distribution of cluster early-type galaxies evolves with redshift from z ~ 0 to z>1 (i.e., over the last ~8 Gyr). The median ellipticity at z>0.3 is statistically identical with that at z < 0.05, being higher by only 0.01 ± 0.02 or 3 ± 6%, while the distribution of ellipticities at z>0.3 agrees with the shape of the z < 0.05 distribution at the 1-2% level (i.e., the probability that they are drawn from the same distribution is 98-99%). These results are strongly suggestive of an unchanging overall bulge-to-disk ratio distribution for cluster early-type galaxies over the last ~8 Gyr from z ~ 1 to z ~ 0. This result contrasts with that from visual classifications which show that the fraction of morphologically-selected disk-dominated early-type galaxies, or S0s, is significantly lower at z>0.4 than at z ~ 0. We find that the median disk-dominated early-type, or S0, galaxy has a somewhat higher
Observations On The Stability Of Elliptical Liquid Bridges
NASA Astrophysics Data System (ADS)
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.
Evolution of Elliptical Galaxies in the FORS Deep Field
NASA Astrophysics Data System (ADS)
Fritz, A.; Böhm, A.; Ziegler, B. L.
Much work has been done to study the evolution of elliptical galaxies in clusters of galaxies using scaling relations and line diagnostic diagrams. Concordant results are that the bulk of the stars for the majority of the galaxies are old and have been formed at a high redshift (e.g. Jørgensen et al. 1999, MNRAS 308, 833). But there are only a few observational studies on the evolution of field ellipticals (e.g. van Dokkum et al. 2001, ApJL 553, 39 or Koo, astro-ph/9906243) claiming that there is little difference to the cluster ellipticals. This is in contrast to expectations from hierarchical merging CDM models where giant field galaxies can still be formed at redshifts z<1 (e.g. Kauffmann 1996, MNRAS 218, 487). Therefore, we have observed spectroscopically most of the ellipticals in the FORS Deep Field (Appenzeller et al. 2000, The Messenger 100, 44) down to R=22m using the VLT/FORS1 and 2 instruments. The 34 galaxies are distributed in redshifts from z=0.16 to 0.62 with =0.35. Both the spectral resolution (1200) and the exposure times (5 h) were adequate to accurately determine absorption line strengths and velocity dispersions (σ). Here, we present first results on the evolution of the Faber-Jackson (L vs. σ) and Mg-σ relations and the age/metallicity and [Mg/Fe] abundance distributions of these field ellipticals.
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.
Sessile Nanodroplets on Elliptical Patches of Enhanced Lyophilicity
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
Elliptic Boundary Value Problems On Non-Smooth Domains
NASA Astrophysics Data System (ADS)
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
NASA Astrophysics Data System (ADS)
Dúmet-Montoya, H. S.; Caminha, G. B.; Makler, M.
2012-08-01
Context. Owing to their computational simplicity, models with elliptical potentials (pseudo-elliptical) are often used in gravitational lensing applications, in particular for mass modeling using arcs and for arc statistics. However, these models generally lead to negative mass distributions in some regions and to dumbbell-shaped surface density contours for high ellipticities. Aims: We revisit the physical limitations of the pseudo-elliptical Navarro-Frenk-White (PNFW) model, focusing on the behavior of the mass distribution close to the tangential critical curve, where tangential arcs are expected to be formed. We investigate the shape of the mass distribution on this region and the presence of negative convergence. We obtain a mapping from the PNFW to the NFW model with elliptical mass distribution (ENFW). We compare the arc cross section for both models, aiming to determine a domain of validity for the PNFW model in terms of its mass distribution and for the cross section. Methods: We defined a figure of merit to i) measure the deviation of the iso-convergence contours of the PNFW model to an elliptical shape, ii) assigned an ellipticity ɛΣ to these contours, iii) defined a corresponding iso-convergence contour for the ENFW model. We computed the arc cross section using the "infinitesimal circular source approximation". Results: We extend previous work by investigating the shape of the mass distribution of the PNFW model for a broad range of the potential ellipticity parameter ɛ and characteristic convergence Ks. We show that the maximum value of ɛ to avoid dumbbell-shaped mass distributions is explicitly dependent on Ks, with higher ellipticities (ɛ ≃ 0.5, i.e., ɛΣ ≃ 0.65) allowed for small Ks. We determine a relation between the ellipticity of the mass distribution ɛΣ and ɛ valid for any ellipticity. We also derive the relation of characteristic convergences, obtaining a complete mapping from PNFW to ENFW models, and provide fitting formulae for
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.
Dynamical properties of the soft-wall elliptical billiard.
Kroetz, Tiago; Oliveira, Hércules A; Portela, Jefferson S E; Viana, Ricardo L
2016-08-01
Physical systems such as optical traps and microwave cavities are realistically modeled by billiards with soft walls. In order to investigate the influence of the wall softness on the billiard dynamics, we study numerically a smooth two-dimensional potential well that has the elliptical (hard-wall) billiard as a limiting case. Considering two parameters, the eccentricity of the elliptical equipotential curves and the wall hardness, which defines the steepness of the well, we show that (1) whereas the hard-wall limit is integrable and thus completely regular, the soft wall elliptical billiard exhibits chaos, (2) the chaotic fraction of the phase space depends nonmonotonically on the hardness of the wall, and (3) the effect of the hardness on the dynamics depends strongly on the eccentricity of the billiard. We further show that the limaçon billiard can exhibit enhanced chaos induced by wall softness, which suggests that our findings generalize to quasi-integrable systems.
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.
Polar rotation angle identifies elliptic islands in unsteady dynamical systems
NASA Astrophysics Data System (ADS)
Farazmand, Mohammad; Haller, George
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.
Evolution of a barotropic shear layer into elliptical vortices.
Guha, Anirban; Rahmani, Mona; Lawrence, Gregory A
2013-01-01
When a barotropic shear layer becomes unstable, it produces the well-known Kelvin-Helmholtz instability (KHI). The nonlinear manifestation of the KHI is usually in the form of spiral billows. However, a piecewise linear shear layer produces a different type of KHI characterized by elliptical vortices of constant vorticity connected via thin braids. Using direct numerical simulation and contour dynamics, we show that the interaction between two counterpropagating vorticity waves is solely responsible for this KHI formation. We investigate the oscillation of the vorticity wave amplitude, the rotation and nutation of the elliptical vortex, and straining of the braids. Our analysis also provides a possible explanation for the formation and evolution of elliptical vortices appearing in geophysical and astrophysical flows, e.g., meddies, stratospheric polar vortices, Jovian vortices, Neptune's Great Dark Spot, and coherent vortices in the wind belts of Uranus.
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.
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.
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.
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.
Cluster flight control for fractionated spacecraft on an elliptic orbit
NASA Astrophysics Data System (ADS)
Xu, Ming; Liang, Yuying; Tan, Tian; Wei, Lixin
2016-08-01
This paper deals with the stabilization of cluster flight on an elliptic reference orbit by the Hamiltonian structure-preserving control using the relative position measurement only. The linearized Melton's relative equation is utilized to derive the controller and then the full nonlinear relative dynamics are employed to numerically evaluate the controller's performance. In this paper, the hyperbolic and elliptic eigenvalues and their manifolds are treated without distinction notations. This new treatment not only contributes to solving the difficulty in feedback of the unfixed-dimensional manifolds, but also allows more opportunities to set the controlled frequencies of foundational motions or to optimize control gains. Any initial condition can be stabilized on a Kolmogorov-Arnold-Moser torus near a controlled elliptic equilibrium. The motions are stabilized around the natural relative trajectories rather than track a reference relative configuration. In addition, the bounded quasi-periodic trajectories generated by the controller have advantages in rapid reconfiguration and unpredictable evolution.
He Min; Rapp, Ralf; Fries, Rainer J.
2010-09-15
The scaling properties of elliptic flow of hadrons produced in ultrarelativistic heavy-ion collisions are investigated at low transverse momenta, p{sub T} < or approx. 2 GeV. Utilizing empirical parametrizations of a thermalized fireball with collective-flow fields, the resonance recombination model (RRM) is employed to describe hadronization via quark coalescence at the hadronization transition. We reconfirm that RRM converts equilibrium quark distribution functions into equilibrated hadron spectra including the effects of space-momentum correlations on elliptic flow. This provides the basis for a controlled extraction of quark distributions of the bulk matter at hadronization from spectra of multistrange hadrons which are beligeved to decouple close to the critical temperature. The resulting elliptic flow from empirical fits at the BNL Relativistic Heavy Ion Collider exhibits transverse kinetic-energy and valence-quark scaling. Utilizing the well-established concept of sequential freeze-out, the scaling at low momenta extends to bulk hadrons ({pi}, K, p) at thermal freeze-out, albeit with different source parameters compared to chemical freeze-out. Elliptic-flow scaling is thus compatible with both equilibrium hydrodynamics and quark recombination.
Scaling of Elliptic Flow, Recombination and Sequential Freeze-Out of Hadrons in Heavy-Ion Collisions
Fries, R.; He, M., and Rapp, R.
2010-09-21
The scaling properties of elliptic flow of hadrons produced in ultrarelativistic heavy-ion collisions are investigated at low transverse momenta, p{sub T} {le} 2 GeV. Utilizing empirical parametrizations of a thermalized fireball with collective-flow fields, the resonance recombination model (RRM) is employed to describe hadronization via quark coalescence at the hadronization transition. We reconfirm that RRM converts equilibrium quark distribution functions into equilibrated hadron spectra including the effects of space-momentum correlations on elliptic flow. This provides the basis for a controlled extraction of quark distributions of the bulk matter at hadronization from spectra of multistrange hadrons which are believed to decouple close to the critical temperature. The resulting elliptic flow from empirical fits at the BNL Relativistic Heavy Ion Collider exhibits transverse kinetic-energy and valence-quark scaling. Utilizing the well-established concept of sequential freeze-out, the scaling at low momenta extends to bulk hadrons ({pi}, K, p) at thermal freeze-out, albeit with different source parameters compared to chemical freeze-out. Elliptic-flow scaling is thus compatible with both equilibrium hydrodynamics and quark recombination.
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.
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.
Magnetic field induced by elliptical instability in a rotating spheroid
NASA Astrophysics Data System (ADS)
Lacaze, L.; Herreman, W.; Le Bars, M.; Le Dizès, S.; Le Gal, P.
2006-10-01
The tidal or the elliptical instability of the rotating fluid flows is generated by the resonant interaction of the inertial waves. In a slightly elliptically deformed rotating sphere, the most unstable linear mode is called the spin-over mode, and is a solid body rotation versus an axis aligned with the maximum strain direction. In the non-viscous case, this instability corresponds to the median moment of the inertial instability of the solid rotating bodies. This analogy is furthermore illustrated by an elliptical top experiment, which shows the expected inviscid heteroclinic behaviour. In geophysics, the elliptical instability may appear in the molten liquid cores of the rotating planets, which are slightly deformed by the tidal gravitational effects of the close bodies. It may then participate in the general outer core dynamics and possibly the geodynamo process. In this context, Kerswell and Malkus (Kerswell, R.R. and Malkus, W.V.R., Tidal instability as the source for Io's magnetic signature. Geophys. Res. Lett., 1998, 25, 603 606) showed that the puzzling magnetic field of the Jovian satellite Io may indeed be induced by the elliptically unstable motions of its liquid core that deflect the Jupiter's magnetic field. Our magnetohydrodynamics (MHD) experiment is a toy-experiment of this geophysical situation and demonstrates for the first time the possibility of an induction of a magnetic field by the flow motions due to the elliptical instability. A full analytical calculation of the magnetic dipole induced by the spin-over is presented. Finally, exponential growths of this induced magnetic field in a slightly deformed rotating sphere filled with galinstan liquid metal are measured for different rotating rates. Their growth rates compare well with the theoretical predictions in the limit of a vanishing Lorentz force.
Mean Effects of Turbulence on Elliptic Instability in Fluids
NASA Astrophysics Data System (ADS)
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.
Centaurus A galaxy, type EO peculiar elliptical, also radio source
NASA Technical Reports Server (NTRS)
2002-01-01
Centaurus A galaxy, type EO peculiar elliptical, also radio source. CTIO 4-meter telescope, 1975. NGC 5128, a Type EO peculiar elliptical galaxy in the constellation Centaurus. This galaxy is one of the most luminous and massive galaxies known and is a strong source of both radio and X-ray radiation. Current theories suggest that the nucleus is experiencing giant explosions involving millions of stars and that the dark band across the galactic disk is material being ejected outward. Cerro Toloto 4-meter telescope photo. Photo credit: National Optical Astronomy Observatories
Event-by-event elliptic flow fluctuations from PHOBOS.
Alver, B.; Back, B. B.; Baker, M. D.; Ballintijn, M.; Barton, D. S.; Physics; BNL; Inst. of Nuclear Physics; Massachusetts Inst. of Tech.; National Central Univ.; Univ. of Maryland; Univ. of Rochester
2009-04-01
Recently PHOBOS has focused on the study of fluctuations and correlations in particle production in heavy-ion collisions at the highest energies delivered by the Relativistic Heavy Ion Collider (RHIC). In this report, we present results on event-by-event elliptic flow fluctuations in Au + Au collisions at {radical}s{sub NN} = 200 GeV. A data-driven method was used to estimate the dominant contribution from non-flow correlations. Over the broad range of collision centralities, the observed large elliptic flow fluctuations are in agreement with the fluctuations in the initial source eccentricity.
Elliptic flow in Au+Au collisions at RHIC.
Back, B. B.; Baker, M. D.; Ballintijn, M.; Barton, D. S.; Betts, R. R.; George, N.; Wuosmaa, A.; Physics; Massachusetts Inst. of Tech.; BNL; Univ. of Illinois at Chicago
2005-01-01
Elliptic flow is an interesting probe of the dynamical evolution of the dense system formed in the ultrarelativistic heavy ion collisions at the relativistic heavy ion collider (RHIC). The elliptic flow dependences on transverse momentum, centrality and pseudorapidity were measured using data collected by the PHOBOS detector, which offers a unique opportunity to study the azimuthal anisotropies of charged particles over a wide range of pseudorapidity. These measurements are presented, together with an overview of the analysis methods and a discussion of the results.
Plastic Deformation in Profile-Coated Elliptical KB Mirrors
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.
Rapid Cooling of Dusty Gas in Elliptical Galaxies
NASA Astrophysics Data System (ADS)
Mathews, William G.; Brighenti, Fabrizio
2003-06-01
We propose a stellar origin for the central dust clouds observed in most giant elliptical galaxies. Dusty gas ejected from evolving red giant stars in elliptical or cD galaxies can cool rapidly even after entering the hot X-ray-emitting gas. Cooling by thermal collisions with dust grains can be faster than either the dynamical time in the galactic potential or the grain sputtering time. Some grains survive in the cooled gas. Dusty stellar outflows cool more efficiently in the central regions, where the stellar metallicity is higher. Mergers with gas and dust-rich dwarf galaxies may occasionally occur but are not required to explain the observed dust clouds.
Gravitational radiation from dual neutron star elliptical binaries
NASA Technical Reports Server (NTRS)
Hils, Dieter
1991-01-01
General expressions are derived for the gravitational radiation incident on earth due to elliptical binary systems in the Galaxy. These results are applied to dual neutron star elliptical binaries. Calculations show that eccentric dual neutron star binaries lead to a moderate increase in gravitational flux density compared with circular systems for frequencies above approximately 0.0001 Hz. Tables of various quantities such as average gravitational luminosity, number of sources per unit bandwidth, energy spectral flux density, and gravitational wave strain density are given.
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.
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.
Tunneling phenomena in the open elliptic quantum billiard
NASA Astrophysics Data System (ADS)
Garcia-Gracia, Hipolito; Gutiérrez-Vega, Julio C.
2012-07-01
The study of open quantum billiards has gained popularity in the last decades, including different common and uncommon geometries such as the circular and stadium billiards. We present an extensive analysis of the elliptic quantum billiard with hyperbolic channels. We concentrate on the tunneling through an elliptic resonator-like structure. We analyze three different variations of the system: the first configuration has horizontal channels, then we study the system with vertical leads, and finally we displace both channels by the same angle to gain a more general perspective. We observed a very unusual phase distribution in the resonator cavity when there is no tunneling through the system.
Twisted Elliptic Genus for K3 and Borcherds Product
NASA Astrophysics Data System (ADS)
Eguchi, Tohru; Hikami, Kazuhiro
2012-11-01
We discuss the relation between the elliptic genus of K3 surface and the Mathieu group M 24. We find that some of the twisted elliptic genera for K3 surface, defined for conjugacy classes of the Mathieu group M 24, can be represented in a very simple manner in terms of the η product of the corresponding conjugacy classes. It is shown that our formula is a consequence of the identity between the Borcherds product and additive lift of some Siegel modular forms.
Stellar kinematics of X-ray bright massive elliptical galaxies
NASA Astrophysics Data System (ADS)
Lyskova, N.; Churazov, E.; Moiseev, A.; Sil'chenko, O.; Zhuravleva, I.
2014-07-01
We discuss a simple and fast method for estimating masses of early-type galaxies from optical data and compare the results with X-ray derived masses. The optical method relies only on the most basic observables such as the surface brightness I(R) and the line-of-sight velocity dispersion σp(R) profiles and provides an anisotropy-independent estimate of the galaxy circular speed Vc. The mass-anisotropy degeneracy is effectively overcome by evaluating Vc at a characteristic radius Rsweet defined from local properties of observed profiles. The sweet radius Rsweet is expected to lie close to R2, where I(R) ∝ R-2, and not far from the effective radius Reff. We apply the method to a sample of five X-ray bright elliptical galaxies observed with the 6 m telescope BTA-6 in Russia. We then compare the optical Vc estimate with the X-ray derived value, and discuss possible constraints on the non-thermal pressure in the hot gas and configuration of stellar orbits. We find that the average ratio of the optical Vc estimate to the X-ray one is equal to ≈0.98 with 11 per cent scatter, i.e. there is no evidence for the large non-thermal pressure contribution in the gas at ˜Rsweet. From analysis of the Lick indices Hβ, Mgb, Fe5270 and Fe5335, we calculate the mass of the stellar component within the sweet radius. We conclude that a typical dark matter fraction inside Rsweet in the sample galaxies is ˜60 per cent for the Salpeter initial mass function (IMF) and ˜75 per cent for the Kroupa IMF.
Testing adiabatic contraction with Sloan Digital Sky Survey elliptical galaxies
NASA Astrophysics Data System (ADS)
Schulz, A. E.; Mandelbaum, Rachel; Padmanabhan, Nikhil
2010-11-01
We study the profiles of 75086 elliptical galaxies from the Sloan Digital Sky Survey (SDSS) at both large (70-700h-170kpc) and small (~ 4h-170 kpc) scales. Weak lensing observations in the outskirts of the halo are combined with measurements of the stellar velocity dispersion in the interior regions of the galaxy for stacked galaxy samples. The weak lensing measurements are well characterized by a Navarro, Frenk and White (NFW) profile. The dynamical mass measurements exceed the extrapolated NFW profile even after the estimated stellar masses are subtracted, providing evidence for the modification of the dark matter profile by the baryons. This excess mass is quantitatively consistent with the predictions of the adiabatic contraction (AC) hypothesis. Our finding suggests that the effects of AC during galaxy formation are stable to subsequent bombardment from major and minor mergers. We explore several theoretical and observational systematics and conclude that they cannot account for the inferred mass excess. The most significant source of systematic error is in the initial mass function (IMF), which would have to increase the stellar mass estimates by a factor of two relative to the Kroupa IMF to fully explain the mass excess without AC. Such an increase could be achieved by switching from a Kroupa to a Salpeter IMF (with cut-off at 0.1 Msolar), but doing so would cause significant tension with results from SAURON. We demonstrate a connection between the level of contraction of the dark matter halo profile and scatter in the size luminosity relation, which is a projection of the fundamental plane. Whether or not AC is the mechanism supplying the excess mass, models of galaxy formation and evolution must reconcile the observed halo masses from weak lensing with the comparatively large dynamical masses at the half-light radii of the galaxies.
Solitary and Jacobi elliptic wave solutions of the generalized Benjamin-Bona-Mahony equation
NASA Astrophysics Data System (ADS)
Belobo, Didier Belobo; Das, Tapas
2017-07-01
Exact bright, dark, antikink solitary waves and Jacobi elliptic function solutions of the generalized Benjamin-Bona-Mahony equation with arbitrary power-law nonlinearity will be constructed in this work. The method used to carry out the integration is the F-expansion method. Solutions obtained have fractional and integer negative or positive power-law nonlinearities. These solutions have many free parameters such that they may be used to simulate many experimental situations, and to precisely control the dynamics of the system.
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.
Analytic Regularity and Polynomial Approximation of Parametric and Stochastic Elliptic PDEs
2010-05-31
parametric, elliptic PDEs in a bounded domain D with coefficients depending on possibly countably many parameters. It shows that the dependence of the...equations on a bounded Lipschitz domain D ⊂ Rd of the form −∇ · (a∇u) = f in D, u|∂D = 0, (1.1) where the diffusion coefficients a(x, y) are functions... bounded independently of y which is arbitrary in U , this is equivalent to the decay estimate |αk|+ |βk| ≤ C|k|−s, k ≥ 1, and therefore ‖ψj‖L∞(D) ≤ Cj−s, j
Optics ellipticity performance of an unobscured off-axis space telescope.
Zeng, Fei; Zhang, Xin; Zhang, Jianping; Shi, Guangwei; Wu, Hongbo
2014-10-20
With the development of astronomy, more and more attention is paid to the survey of dark matter. Dark matter cannot be seen directly but can be detected by weak gravitational lensing measurement. Ellipticity is an important parameter used to define the shape of a galaxy. Galaxy ellipticity changes with weak gravitational lensing and nonideal optics. With our design of an unobscured off-axis telescope, we implement the simulation and calculation of optics ellipticity. With an accurate model of optics PSF, the characteristic of ellipticity is modeled and analyzed. It is shown that with good optical design, the full field ellipticity can be quite small. The spatial ellipticity change can be modeled by cubic interpolation with very high accuracy. We also modeled the ellipticity variance with time and analyzed the tolerance. It is shown that the unobscured off-axis telescope has good ellipticity performance and fulfills the requirement of dark matter survey.
NASA Astrophysics Data System (ADS)
Sten, J. C.-E.; Fragoyiannis, G.; Vafeas, P.; Koivisto, P. K.; Dassios, G.
2017-05-01
The analytic computation of electric and magnetic fields near corners and edges is important in many applications related to science and engineering. However, such complicated situations are hard to deal with, since they accumulate charges and consequently they mathematically represent singularities. In order to model this singular behavior, we introduce a novel method, which is related to the geometry and the analysis of the ellipsoidal coordinate system. Indeed, adopting the benefits of the corresponding coordinate surfaces, we use a general non-circular double cone, being the asymptote of a two-sided hyperboloid of two sheets with elliptic cross section, which matches almost perfectly the particular physics and captures the corresponding essential features in a fully three-dimensional fashion. To this end, our analytical technique employs the ellipsoidal geometry and adapts the ellipsoidal functions (solutions of the well-known Lamé equation) so as to construct a new set of the so-called elliptic cross-sectional hyperboloidal harmonics, supplemented by the appropriate orthogonality rules on every constant coordinate surface. By first recollecting the key results of the coordinate system and the related potential functions, including the indispensable orthogonality results, we demonstrate our method to the solution of two boundary value problems in electrostatics. Both refer to a non-penetrable two-hyperboloid of elliptic cross section and its double-cone limit, the first one being charged and the second one scattering off a plane wave. Closed form expressions are derived for the related fields, while the already known formulae from the literature are readily recovered, all cases being followed by the appropriate numerical implementation.
Three-dimensional elliptic grid generation with fully automatic boundary constraints
NASA Astrophysics Data System (ADS)
Kaul, Upender K.
2010-08-01
A new procedure for generating smooth uniformly clustered three-dimensional structured elliptic grids is presented here which formulates three-dimensional boundary constraints by extending the two-dimensional counterpart presented by the author earlier. This fully automatic procedure obviates the need for manual specification of decay parameters over the six bounding surfaces of a given volume grid. The procedure has been demonstrated here for the Mars Science Laboratory (MSL) geometries such as aeroshell and canopy, as well as the Inflatable Aerodynamic Decelerator (IAD) geometry and a 3D analytically defined geometry. The new procedure also enables generation of single-block grids for such geometries because the automatic boundary constraints permit the decay parameters to evolve as part of the solution to the elliptic grid system of equations. These decay parameters are no longer just constants, as specified in the conventional approach, but functions of generalized coordinate variables over a given bounding surface. Since these decay functions vary over a given boundary, orthogonal grids around any arbitrary simply-connected boundary can be clustered automatically without having to break up the boundaries and the corresponding interior or exterior domains into various blocks for grid generation. The new boundary constraints are not limited to the simply-connected regions only, but can also be formulated around multiply-connected and isolated regions in the interior. The proposed method is superior to other methods of grid generation such as algebraic and hyperbolic techniques in that the grids obtained here are C2 continuous, whereas simple elliptic smoothing of algebraic or hyperbolic grids to enforce C2 continuity destroys the grid clustering near the boundaries. US patent 7231329.
A Galerkin formulation of the MIB method for three dimensional elliptic interface problems
Xia, Kelin; Wei, Guo-Wei
2014-01-01
We develop a three dimensional (3D) Galerkin formulation of the matched interface and boundary (MIB) method for solving elliptic partial differential equations (PDEs) with discontinuous coefficients, i.e., the elliptic interface problem. The present approach builds up two sets of elements respectively on two extended subdomains which both include the interface. As a result, two sets of elements overlap each other near the interface. Fictitious solutions are defined on the overlapping part of the elements, so that the differentiation operations of the original PDEs can be discretized as if there was no interface. The extra coefficients of polynomial basis functions, which furnish the overlapping elements and solve the fictitious solutions, are determined by interface jump conditions. Consequently, the interface jump conditions are rigorously enforced on the interface. The present method utilizes Cartesian meshes to avoid the mesh generation in conventional finite element methods (FEMs). We implement the proposed MIB Galerkin method with three different elements, namely, rectangular prism element, five-tetrahedron element and six-tetrahedron element, which tile the Cartesian mesh without introducing any new node. The accuracy, stability and robustness of the proposed 3D MIB Galerkin are extensively validated over three types of elliptic interface problems. In the first type, interfaces are analytically defined by level set functions. These interfaces are relatively simple but admit geometric singularities. In the second type, interfaces are defined by protein surfaces, which are truly arbitrarily complex. The last type of interfaces originates from multiprotein complexes, such as molecular motors. Near second order accuracy has been confirmed for all of these problems. To our knowledge, it is the first time for an FEM to show a near second order convergence in solving the Poisson equation with realistic protein surfaces. Additionally, the present work offers the
A Galerkin formulation of the MIB method for three dimensional elliptic interface problems.
Xia, Kelin; Wei, Guo-Wei
2014-10-01
We develop a three dimensional (3D) Galerkin formulation of the matched interface and boundary (MIB) method for solving elliptic partial differential equations (PDEs) with discontinuous coefficients, i.e., the elliptic interface problem. The present approach builds up two sets of elements respectively on two extended subdomains which both include the interface. As a result, two sets of elements overlap each other near the interface. Fictitious solutions are defined on the overlapping part of the elements, so that the differentiation operations of the original PDEs can be discretized as if there was no interface. The extra coefficients of polynomial basis functions, which furnish the overlapping elements and solve the fictitious solutions, are determined by interface jump conditions. Consequently, the interface jump conditions are rigorously enforced on the interface. The present method utilizes Cartesian meshes to avoid the mesh generation in conventional finite element methods (FEMs). We implement the proposed MIB Galerkin method with three different elements, namely, rectangular prism element, five-tetrahedron element and six-tetrahedron element, which tile the Cartesian mesh without introducing any new node. The accuracy, stability and robustness of the proposed 3D MIB Galerkin are extensively validated over three types of elliptic interface problems. In the first type, interfaces are analytically defined by level set functions. These interfaces are relatively simple but admit geometric singularities. In the second type, interfaces are defined by protein surfaces, which are truly arbitrarily complex. The last type of interfaces originates from multiprotein complexes, such as molecular motors. Near second order accuracy has been confirmed for all of these problems. To our knowledge, it is the first time for an FEM to show a near second order convergence in solving the Poisson equation with realistic protein surfaces. Additionally, the present work offers the
Four ways to compute the inverse of the complete elliptic integral of the first kind
NASA Astrophysics Data System (ADS)
Boyd, John P.
2015-11-01
The complete elliptic integral of the first kind arises in many applications. This article furnishes four different ways to compute the inverse of the elliptic integral. One motive for this study is simply that the author needed to compute the inverse integral for an application. Another is to develop a case study comparing different options for solving transcendental equations like those in the author's book (Boyd, 2014). A third motive is to develop analytical approximations, more useful to theorists than mere numbers. A fourth motive is to provide robust "black box" software for computing this function. The first solution strategy is "polynomialization" which replaces the elliptic integral by an exponentially convergent series of Chebyshev polynomials. The transcendental equation becomes a polynomial equation which is easily solved by finding the eigenvalues of the Chebyshev companion matrix. (The numerically ill-conditioned step of converting from the Chebyshev to monomial basis is never necessary). The second approximation is a regular perturbation series, accurate where the modulus is small. The third is a power-and-exponential series that converges over the entire range parameter range, albeit only sub-exponentially in the limit of zero modulus. Lastly, Newton's iteration is promoted from a local iteration to a global method by a Never-Failing Newton's Iteration (NFNI) in the form of the exponential of the ratio of a linear function divided by another linear polynomial. A short Matlab implementation is provided, easily translatable into other languages. The Matlab/Newton code is recommended for numerical purposes. The other methods are presented because (i) all are broadly applicable strategies useful for other rootfinding and inversion problems (ii) series and substitutions are often much more useful to theorists than numerical software and (iii) the Never-Failing Newton's Iteration was discovered only after a great deal of messing about with power series
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.
The dynamical fingerprint of core scouring in massive elliptical galaxies
Thomas, J.; Saglia, R. P.; Bender, R.; Erwin, P.; Fabricius, M.
2014-02-10
The most massive elliptical galaxies have low-density centers or cores that differ dramatically from the high-density centers of less massive ellipticals and bulges of disk galaxies. These cores have been interpreted as the result of mergers of supermassive black hole binaries, which depopulate galaxy centers by gravitationally slingshotting central stars toward large radii. Such binaries naturally form in mergers of luminous galaxies. Here, we analyze the population of central stellar orbits in 11 massive elliptical galaxies that we observed with the integral field spectrograph SINFONI at the European Southern Observatory Very Large Telescope. Our dynamical analysis is orbit-based and includes the effects of a central black hole, the mass distribution of the stars, and a dark matter halo. We show that the use of integral field kinematics and the inclusion of dark matter is important to conclude on the distribution of stellar orbits in galaxy centers. Six of our galaxies are core galaxies. In these six galaxies, but not in the galaxies without cores, we detect a coherent lack of stars on radial orbits in the core region and a uniform excess of radial orbits outside of it: when scaled by the core radius r{sub b} , the radial profiles of the classical anisotropy parameter β(r) are nearly identical in core galaxies. Moreover, they quantitatively match the predictions of black hole binary simulations, providing the first convincing dynamical evidence for core scouring in the most massive elliptical galaxies.