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Gauss
Kinds of Gauss Terms modified by Gauss Selected AbstractsDynamic Wavelet Neural Network for Nonlinear Identification of Highrise BuildingsCOMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 5 2005Xiaomo Jiang Compared with conventional neural networks, training of a dynamic neural network for system identification of large-scale structures is substantially more complicated and time consuming because both input and output of the network are not single valued but involve thousands of time steps. In this article, an adaptive Levenberg,Marquardt least-squares algorithm with a backtracking inexact linear search scheme is presented for training of the dynamic fuzzy WNN model. The approach avoids the second-order differentiation required in the Gauss,Newton algorithm and overcomes the numerical instabilities encountered in the steepest descent algorithm with improved learning convergence rate and high computational efficiency. The model is applied to two highrise moment-resisting building structures, taking into account their geometric nonlinearities. Validation results demonstrate that the new methodology provides an efficient and accurate tool for nonlinear system identification of high-rising buildings. [source] Full waveform seismic inversion using a distributed system of computersCONCURRENCY AND COMPUTATION: PRACTICE & EXPERIENCE, Issue 11 2005Indrajit G. Roy Abstract The aim of seismic waveform inversion is to estimate the elastic properties of the Earth's subsurface layers from recordings of seismic waveform data. This is usually accomplished by using constrained optimization often based on very simplistic assumptions. Full waveform inversion uses a more accurate wave propagation model but is extremely difficult to use for routine analysis and interpretation. This is because computational difficulties arise due to: (1) strong nonlinearity of the inverse problem; (2) extreme ill-posedness; and (3) large dimensions of data and model spaces. We show that some of these difficulties can be overcome by using: (1) an improved forward problem solver and efficient technique to generate sensitivity matrix; (2) an iteration adaptive regularized truncated Gauss,Newton technique; (3) an efficient technique for matrix,matrix and matrix,vector multiplication; and (4) a parallel programming implementation with a distributed system of processors. We use a message-passing interface in the parallel programming environment. We present inversion results for synthetic and field data, and a performance analysis of our parallel implementation. Copyright © 2005 John Wiley & Sons, Ltd. [source] A parallel multigrid solver for high-frequency electromagnetic field analyses with small-scale PC clusterELECTRONICS & COMMUNICATIONS IN JAPAN, Issue 9 2008Kuniaki Yosui Abstract Finite element analyses of electromagnetic fields are commonly used for designing various electronic devices. The scale of the analyses becomes larger and larger, therefore, a fast linear solver is needed to solve linear equations arising from the finite element method. Since a multigrid solver is the fastest linear solver for these problems, parallelization of a multigrid solver is quite a useful approach. From the viewpoint of industrial applications, an effective usage of a small-scale PC cluster is important due to initial cost for introducing parallel computers. In this paper, a distributed parallel multigrid solver for a small-scale PC cluster is developed. In high-frequency electromagnetic analyses, a special block Gauss, Seidel smoother is used for the multigrid solver instead of general smoothers such as a Gauss, Seidel or Jacobi smoother in order to improve the convergence rate. The block multicolor ordering technique is applied to parallelize the smoother. A numerical example shows that a 3.7-fold speed-up in computational time and a 3.0-fold increase in the scale of the analysis were attained when the number of CPUs was increased from one to five. © 2009 Wiley Periodicals, Inc. Electron Comm Jpn, 91(9): 28, 36, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecj.10160 [source] Comparative study between two numerical methods for oxygen diffusion problemINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2009Vildan GülkaçArticle first published online: 28 APR 200 Abstract Two approximate numerical solutions of the oxygen diffusion problem are defined using three time-level of Crank,Nicolson equation and Gauss,Seidel iteration for three time-level of implicit method. Oxygen diffusion in a sike cell with simultaneous absorption is an important problem and has a wide range of medical applications. The problem is mathematically formulated through two different stages. At the first stage, the stable case having no oxygen transition in the isolated cell is searched, whereas at the second stage the moving boundary problem of oxygen absorbed by the tissues in the cell is searched. The results obtained by three time-level of implicit method and Gauss,Seidel iteration for three time-level of implicit method and the results gave a good agreement with the previous methods (J. Inst. Appl. Math. 1972; 10:19,33; 1974; 13:385,398; 1978; 22:467,477). Copyright © 2008 John Wiley & Sons, Ltd. [source] Analysis of the block Gauss,Seidel solution procedure for a strongly coupled model problem with reference to fluid,structure interactionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2009M. M. Joosten Abstract The block Gauss,Seidel procedure is widely used for the resolution of the strong coupling in the computer simulation of fluid,structure interaction. Based on a simple model problem, this work presents a detailed analysis of the convergence behaviour of the method. In particular, the model problem is used to highlight some aspects that arise in the context of the application of the block Gauss,Seidel method to FSI problems. Thus, the effects of the time integration schemes chosen, of relaxation techniques, of physical constraints and non-linearities on the convergence of the iterations are investigated. Copyright © 2008 John Wiley & Sons, Ltd. [source] A robust design method using variable transformation and Gauss,Hermite integrationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 12 2006Beiqing Huang Abstract Robust design seeks an optimal solution where the design objective is insensitive to the variations of input variables while the design feasibility under the variations is maintained. Accurate robustness assessment for both design objective and feasibility usually requires an intensive computational effort. In this paper, an accurate robustness assessment method with a moderate computational effort is proposed. The numerical Gauss,Hermite integration technique is employed to calculate the mean and standard deviation of the objective and constraint functions. To effectively use the Gauss,Hermite integration technique, a transformation from a general random variable into a normal variable is performed. The Gauss,Hermite integration and the transformation result in concise formulas and produce an accurate approximation to the mean and standard deviation. This approach is then incorporated into the framework of robust design optimization. The design of a two-bar truss and an automobile torque arm is used to demonstrate the effectiveness of the proposed method. The results are compared with the commonly used Taylor expansion method and Monte Carlo simulation in terms of accuracy and efficiency. Copyright © 2005 John Wiley & Sons, Ltd. [source] A dual mesh multigrid preconditioner for the efficient solution of hydraulically driven fracture problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2005A. P. Peirce Abstract We present a novel multigrid (MG) procedure for the efficient solution of the large non-symmetric system of algebraic equations used to model the evolution of a hydraulically driven fracture in a multi-layered elastic medium. The governing equations involve a highly non-linear coupled system of integro-partial differential equations along with the fracture front free boundary problem. The conditioning of the algebraic equations typically degrades as O(N3). A number of characteristics of this problem present significant new challenges for designing an effective MG strategy. Large changes in the coefficients of the PDE are dealt with by taking the appropriate harmonic averages of the discrete coefficients. Coarse level Green's functions for multiple elastic layers are constructed using a single dual mesh and superposition. Coarse grids that are sub-sets of the finest grid are used to treat mixed variable problems associated with ,pinch points.' Localized approximations to the Jacobian at each MG level are used to devise efficient Gauss,Seidel smoothers and preferential line iterations are used to eliminate grid anisotropy caused by large aspect ratio elements. The performance of the MG preconditioner is demonstrated in a number of numerical experiments. Copyright © 2005 John Wiley & Sons, Ltd. [source] Reduced modified quadratures for quadratic membrane finite elementsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2004Craig S. Long Abstract Reduced integration is frequently used in evaluating the element stiffness matrix of quadratically interpolated finite elements. Typical examples are the serendipity (Q8) and Lagrangian (Q9) membrane finite elements, for which a reduced 2 × 2 Gauss,Legendre integration rule is frequently used, as opposed to full 3 × 3 Gauss,Legendre integration. This ,softens' these element, thereby increasing accuracy, albeit at the introduction of spurious zero energy modes on the element level. This is in general not considered problematic for the ,hourglass' mode common to Q8 and Q9 elements, since this spurious mode is non-communicable. The remaining two zero energy modes occurring in the Q9 element are indeed communicable. However, in topology optimization for instance, conditions may arise where the non-communicable spurious mode associated with the elements becomes activated. To effectively suppress these modes altogether in elements employing quadratic interpolation fields, two modified quadratures are employed herein. For the Q8 and Q9 membrane elements, the respective rules are a five and an eight point rule. As compared to fully integrated elements, the new rules enhance element accuracy due to the introduction of soft, higher-order deformation modes. A number of standard test problems reveal that element accuracy remains comparable to that of the under-integrated counterparts. Copyright © 2004 John Wiley & Sons, Ltd. [source] Anisotropic mesh adaption by metric-driven optimizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2004Carlo L. Bottasso Abstract We describe a Gauss,Seidel algorithm for optimizing a three-dimensional unstructured grid so as to conform to a given metric. The objective function for the optimization process is based on the maximum value of an elemental residual measuring the distance of any simplex in the grid to the local target metric. We analyse different possible choices for the objective function, and we highlight their relative merits and deficiencies. Alternative strategies for conducting the optimization are compared and contrasted in terms of resulting grid quality and computational costs. Numerical simulations are used for demonstrating the features of the proposed methodology, and for studying some of its characteristics. Copyright © 2004 John Wiley & Sons, Ltd. [source] A numerical integration scheme for special finite elements for the Helmholtz equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2003Peter Bettess Abstract The theory for integrating the element matrices for rectangular, triangular and quadrilateral finite elements for the solution of the Helmholtz equation for very short waves is presented. A numerical integration scheme is developed. Samples of Maple and Fortran code for the evaluation of integration abscissæ and weights are made available. The results are compared with those obtained using large numbers of Gauss,Legendre integration points for a range of testing wave problems. The results demonstrate that the method gives correct results, which gives confidence in the procedures, and show that large savings in computation time can be achieved. Copyright © 2002 John Wiley & Sons, Ltd. [source] A Galerkin boundary integral method for multiple circular elastic inclusionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 10 2001S. G. Mogilevskaya Abstract The problem of an infinite, isotropic elastic plane containing an arbitrary number of circular elastic inclusions is considered. The analysis procedure is based on the use of a complex singular integral equation. The unknown tractions at each circular boundary are approximated by a truncated complex Fourier series. A system of linear algebraic equations is obtained by using the classical Galerkin method and the Gauss,Seidel algorithm is used to solve the system. Several numerical examples are considered to demonstrate the effectiveness of the approach. Copyright © 2001 John Wiley & Sons, Ltd. [source] Coupled solution of the species conservation equations using unstructured finite-volume methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2010Ankan Kumar Abstract A coupled solver was developed to solve the species conservation equations on an unstructured mesh with implicit spatial as well as species-to-species coupling. First, the computational domain was decomposed into sub-domains comprised of geometrically contiguous cells,a process similar to additive Schwarz decomposition. This was done using the binary spatial partitioning algorithm. Following this step, for each sub-domain, the discretized equations were developed using the finite-volume method, and solved using an iterative solver based on Krylov sub-space iterations, that is, the pre-conditioned generalized minimum residual solver. Overall (outer) iterations were then performed to treat explicitness at sub-domain interfaces and nonlinearities in the governing equations. The solver is demonstrated for both two-dimensional and three-dimensional geometries for laminar methane,air flame calculations with 6 species and 2 reaction steps, and for catalytic methane,air combustion with 19 species and 24 reaction steps. It was found that the best performance is manifested for sub-domain size of 2000 cells or more, the exact number depending on the problem at hand. The overall gain in computational efficiency was found to be a factor of 2,5 over the block (coupled) Gauss,Seidel procedure. All calculations were performed on a single processor machine. The largest calculations were performed for about 355 000 cells (4.6 million unknowns) and required 900,MB of peak runtime memory and 19,h of CPU on a single processor. Copyright © 2009 John Wiley & Sons, Ltd. [source] Shape reconstruction of an inverse boundary value problem of two-dimensional Navier,Stokes equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2010Wenjing Yan Abstract This paper is concerned with the problem of the shape reconstruction of two-dimensional flows governed by the Navier,Stokes equations. Our objective is to derive a regularized Gauss,Newton method using the corresponding operator equation in which the unknown is the geometric domain. The theoretical foundation for the Gauss,Newton method is given by establishing the differentiability of the initial boundary value problem with respect to the boundary curve in the sense of a domain derivative. The numerical examples show that our theory is useful for practical purpose and the proposed algorithm is feasible. Copyright © 2009 John Wiley & Sons, Ltd. [source] Multiple semi-coarsened multigrid method with application to large eddy simulationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2006F. E. Ham Abstract The Multiple Semi-coarsened Grid (MSG) multigrid method of Mulder (J. Comput. Phys. 1989; 83:303,323) is developed as a solver for fully implicit discretizations of the time-dependent incompressible Navier,Stokes equations. The method is combined with the Symmetric Coupled Gauss,Seidel (SCGS) smoother of Vanka (Comput. Methods Appl. Mech. Eng. 1986; 55:321,338) and its robustness demonstrated by performing a number of large-eddy simulations, including bypass transition on a flat plate and the turbulent thermally-driven cavity flow. The method is consistently able to reduce the non-linear residual by 5 orders of magnitude in 40,80 work units for problems with significant and varying coefficient anisotropy. Some discussion of the parallel implementation of the method is also included. Copyright © 2005 John Wiley & Sons, Ltd. [source] Finite volume multigrid method of the planar contraction flow of a viscoelastic fluidINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 8 2001H. Al Moatssime Abstract This paper reports on a numerical algorithm for the steady flow of viscoelastic fluid. The conservative and constitutive equations are solved using the finite volume method (FVM) with a hybrid scheme for the velocities and first-order upwind approximation for the viscoelastic stress. A non-uniform staggered grid system is used. The iterative SIMPLE algorithm is employed to relax the coupled momentum and continuity equations. The non-linear algebraic equations over the flow domain are solved iteratively by the symmetrical coupled Gauss,Seidel (SCGS) method. In both, the full approximation storage (FAS) multigrid algorithm is used. An Oldroyd-B fluid model was selected for the calculation. Results are reported for planar 4:1 abrupt contraction at various Weissenberg numbers. The solutions are found to be stable and smooth. The solutions show that at high Weissenberg number the domain must be long enough. The convergence of the method has been verified with grid refinement. All the calculations have been performed on a PC equipped with a Pentium III processor at 550 MHz. Copyright © 2001 John Wiley & Sons, Ltd. [source] The Gauss-Seidel fast affine projection algorithm for multichannel active noise control and sound reproduction systemsINTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSING, Issue 2-3 2005Martin Bouchard Abstract In the field of adaptive filtering, the fast implementations of affine projection algorithms are known to provide a good tradeoff between convergence speed and computational complexity. Such algorithms have recently been published for multichannel active noise control systems. Previous work reported that these algorithms can outperform more complex recursive least-squares algorithms when noisy plant models are used in active noise control systems. This paper proposes a new fast affine projection algorithm for multichannel active noise control or sound reproduction systems, based on the Gauss,Seidel solving scheme. The proposed algorithm has a lower complexity than the previously published algorithms, with the same convergence speed and the same good performance with noisy plant models, and a potential for better numerical stability. It provides the best performance/cost ratio. Details of the algorithm and its complexity are presented in the paper, with simulation results to validate its performance. Copyright © 2004 John Wiley & Sons, Ltd. [source] Reactive scattering within a time-dependent discrete variable representationINTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 5 2001G. D. Billing Abstract We have formulated a theory in which the quantum corrections to classical mechanics are easy to introduce. The method is based upon a time-dependent discrete variable representation (DVR) of the wavefunction with grid points defined by the Hermite part of a basis set, the so-called Gauss,Hermite basis set. The formulation introduces a set of grid points which follow the classical trajectory in space. With enough trajectories (DVR points), the method approaches the exact quantum formulation. With just a single grid point in a given degree of freedom, we have a classical mechanical description. © 2001 John Wiley & Sons, Inc. Int J Quant Chem, 2001 [source] Fixed-order H, control design via a partially augmented Lagrangian methodINTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 12 2003Pierre Apkarian Abstract In this paper we develop an augmented Lagrangian method to determine local optimal solutions of the reduced- and fixed-order H, synthesis problems. We cast these synthesis problems as optimization programs with a linear cost subject to linear matrix inequality (LMI) constraints along with nonlinear equality constraints representing a matrix inversion condition. The special feature of our algorithm is that only equality constraints are included in the augmented Lagrangian, while LMI constraints are kept explicitly in order to exploit currently available semi definite programming (SDP) codes. The step computation in the tangent problem is based on a Gauss,Newton model, and a specific line search and a first-order Lagrange multiplier update rule are used to enhance efficiency. A number of computational results are reported and underline the strong practical performance of the algorithm. Copyright © 2003 John Wiley & Sons, Ltd. [source] Near-optimum short-term fade prediction on satellite links at Ka and V-bandsINTERNATIONAL JOURNAL OF SATELLITE COMMUNICATIONS AND NETWORKING, Issue 1 2008Andrew P. Chambers Abstract Several short-term predictors of rain attenuation are implemented and tested using data recorded from a satellite link in Southern England, and a comparison is made in terms of the root-mean-square error and the cumulative distribution of under-predictions. A hybrid of an autoregressive moving average and adaptive linear element predictor is created that makes use of Gauss,Newton and gradient direction coefficient updates and exhibits the best prediction error performance of all prediction methods in the majority of cases. Copyright © 2007 John Wiley & Sons, Ltd. [source] Efficiency in the calculation of absorption corrections for cylindersJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 5-1 2010Takashi Ida Efficiency in the numerical calculation of absorption corrections for cylinders has been examined. Two mathematical expressions for the correction factors have been evaluated by two methods for numerical integration. It has been found that the Gauss,Legendre quadrature applied to the formula proposed by Thorkildsen & Larsen [Acta Cryst. (1998), A54, 172,185] gives results with relative errors ,10,6, using 12,×,12 terms in the numerical integration. The conventional approach, using Simpson's method in conjunction with the formula given by Dwiggins [Acta Cryst. (1975), A31, 146,148] for the absorption correction, is far less efficient. [source] Hard-modelled trilinear decomposition (HTD) for an enhanced kinetic multicomponent analysisJOURNAL OF CHEMOMETRICS, Issue 5 2002Yorck-Michael Neuhold Abstract We present a novel approach for kinetic, spectral and chromatographic resolution of trilinear data sets acquired from slow chemical reaction processes via repeated chromatographic analysis with diode array detection. The method is based on fitting rate constants of distinct chemical model reactions (hard-modelled, integrated rate laws) by a Newton,Gauss,Levenberg/Marquardt (NGL/M) optimization in combination with principal component analysis (PCA) and/or evolving factor analysis (EFA), both known as powerful methods from bilinear data analysis. We call our method hard-modelled trilinear decomposition (HTD). Compared with classical bilinear hard-modelled kinetic data analysis, the additional chromatographic resolution leads to two major advantages: (1) the differentiation of indistinguishable rate laws, as they can occur in consecutive first-order reactions; and (2) the circumvention of many problems due to rank deficiencies in the kinetic concentration profiles. In this paper we present the theoretical background of the algorithm and discuss selected chemical rate laws. Copyright © 2002 John Wiley & Sons, Ltd. [source] The Quenched Instationary Polymerization Systems (QUIPS)MACROMOLECULAR THEORY AND SIMULATIONS, Issue 2-3 2003Irene Schnöll-Bitai Abstract The common element of quenched instationary polymerization systems is that at a given time all radicals present are deactivated by an efficient and fast quench reaction. Quenched instationary polymerizations can be carried out in a variety of ways distinguished by the way periods differing in their initiation characteristics are combined. The total chain length distribution of the resulting polymer is always the sum of the quenched radical and polymer chain length distribution. This distribution is either completely or at least partially dominated by the contribution of the quenched radical spectrum. Depending on the experimental conditions monomodal or multimodal distributions are obtained which can be characterized by their extrema (maximum, points of inflection) and peak widths (absolute, relative). The location of the extrema are related to the experimental parameters and can be used in an unambiguous way for the direct determination of the rate constant of propagation. Absolute peak widths (defined as the difference between two succeeding points of inflection) are invariant quantities with respect to the number, molar mass and hyper distribution which is only true for Poisson (and narrow Gauss) distributions. Relative peak widths are a valuable tool for the direct determination of axial dispersion which occurs in size exclusion chromatography. Comparison of experimental and ideal relative peak widths can be used for the direct determination of the axial dispersion. The influence of the type of termination and [R0] (termination by combination) on the total (number) chain length distribution for single , -pulse initiation. [source] hp -Mortar boundary element method for two-body contact problems with frictionMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 17 2008Alexey Chernov Abstract We construct a novel hp -mortar boundary element method for two-body frictional contact problems for nonmatched discretizations. The contact constraints are imposed in the weak sense on the discrete set of Gauss,Lobatto points using the hp -mortar projection operator. The problem is reformulated as a variational inequality with the Steklov,Poincaré operator over a convex cone of admissible solutions. We prove an a priori error estimate for the corresponding Galerkin solution in the energy norm. Due to the nonconformity of our approach, the Galerkin error is decomposed into the approximation error and the consistency error. Finally, we show that the Galerkin solution converges to the exact solution as ,,((h/p)1/4) in the energy norm for quasiuniform discretizations under mild regularity assumptions. We solve the Galerkin problem with a Dirichlet-to-Neumann algorithm. The original two-body formulation is rewritten as a one-body contact subproblem with friction and a one-body Neumann subproblem. Then the original two-body frictional contact problem is solved with a fixed point iteration. Copyright © 2008 John Wiley & Sons, Ltd. [source] Dynamical modelling of luminous and dark matter in 17 Coma early-type galaxiesMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2007J. Thomas ABSTRACT Dynamical models for 17 early-type galaxies in the Coma cluster are presented. The galaxy sample consists of flattened, rotating as well as non-rotating early-types including cD and S0 galaxies with luminosities between MB=,18.79 and ,22.56. Kinematical long-slit observations cover at least the major-axis and minor-axis and extend to 1,4reff. Axisymmetric Schwarzschild models are used to derive stellar mass-to-light ratios and dark halo parameters. In every galaxy, the best fit with dark matter matches the data better than the best fit without. The statistical significance is over 95 per cent for eight galaxies, around 90 per cent for five galaxies and for four galaxies it is not significant. For the highly significant cases, systematic deviations between models without dark matter and the observed kinematics are clearly seen; for the remaining galaxies, differences are more statistical in nature. Best-fitting models contain 10,50 per cent dark matter inside the half-light radius. The central dark matter density is at least one order of magnitude lower than the luminous mass density, independent of the assumed dark matter density profile. The central phase-space density of dark matter is often orders of magnitude lower than that in the luminous component, especially when the halo core radius is large. The orbital system of the stars along the major-axis is slightly dominated by radial motions. Some galaxies show tangential anisotropy along the minor-axis, which is correlated with the minor-axis Gauss,Hermite coefficient H4. Changing the balance between data-fit and regularization constraints does not change the reconstructed mass structure significantly: model anisotropies tend to strengthen if the weight on regularization is reduced, but the general property of a galaxy to be radially or tangentially anisotropic does not change. This paper is aimed to set the basis for a subsequent detailed analysis of luminous and dark matter scaling relations, orbital dynamics and stellar populations. [source] Axisymmetric orbit models of N -body merger remnants: a dependency of reconstructed mass on viewing angleMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2007J. Thomas ABSTRACT We model mock observations of collisionless N -body disc,disc mergers with the same axisymmetric orbit superposition program that has been used to model elliptical galaxies in Coma. The remnants sample representatively the shape distribution of disc,disc mergers, including the most extreme cases, like highly prolate, maximally triaxial and dominantly oblate objects. The aim of our study is to better understand how the assumption of axial symmetry affects reconstructed masses and stellar motions of systems which are intrinsically not axisymmetric, whether the axisymmetry assumption then leads to a bias and how such a potential bias can be recognized in models of real galaxies. The mass recovery at the half-light radius depends on viewing angle and intrinsic shape: edge-on views allow to reconstruct total masses with an accuracy between 20 per cent (triaxial/prolate remnants) and 3 per cent (oblate remnant). Masses of highly flattened, face-on systems are underestimated by up to 50 per cent. Deviations in local mass densities can be larger where remnants are strongly triaxial or prolate. Luminous mass-to-light ratios are sensitive to box orbits in the remnants. Box orbits cause the central value of the Gauss,Hermite parameter H4 to vary with viewing angle. Reconstructed luminous mass-to-light ratios, as well as reconstructed central masses, follow this variation. Luminous mass-to-light ratios are always underestimated (up to a factor of 2.5). Respective dark haloes in the models can be overestimated by about the same amount, depending again on viewing angle. Reconstructed velocity anisotropies , depend on viewing angle as well as on the orbital composition of the remnant and are mostly accurate to about ,,= 0.2. Larger deviations can occur towards the centre or the outer regions, respectively. We construct N -body realizations of the Schwarzschild models to discuss chaotic orbits and the virial equilibrium in our models. In this study we explore the extreme limits of axisymmetric models. Apparently flattened, rotating ellipticals of intermediate mass are likely close to both, axial symmetry and edge-on orientation. Our results imply that Schwarzschild models allow a reconstruction of their masses and stellar anisotropies with high accuracy. [source] Modelling artificial night-sky brightness with a polarized multiple scattering radiative transfer computer codeMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2006Dana Xavier Kerola ABSTRACT As part of an ongoing investigation of radiative effects produced by hazy atmospheres, computational procedures have been developed for use in determining the brightening of the night sky as a result of urban illumination. The downwardly and upwardly directed radiances of multiply scattered light from an offending metropolitan source are computed by a straightforward Gauss,Seidel (G,S) iterative technique applied directly to the integrated form of Chandrasekhar's vectorized radiative transfer equation. Initial benchmark night-sky brightness tests of the present G,S model using fully consistent optical emission and extinction input parameters yield very encouraging results when compared with the double scattering treatment of Garstang, the only full-fledged previously available model. [source] Gas and stellar dynamics in NGC 1068: probing the galactic gravitational potentialMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2006Eric Emsellem ABSTRACT We present SAURON integral field spectrography of the central 1.5 kpc of the nearby Seyfert 2 galaxy NGC 1068, encompassing the well-known near-infrared (NIR) inner bar observed in the K band. We have successively disentangled the respective contributions of the ionized gas and stars, thus deriving their two-dimensional distribution and kinematics. The [O iii] and H, emission lines exhibit a very different spatial distribution and kinematics, the latter following inner spiral arms with clumps associated with star formation. Strong inward streaming motions are observed in both the H, and [O iii] kinematics. The stellar kinematics also exhibit clear signatures of a non-axisymmetric tumbling potential, with a twist in both the velocity and Gauss,Hermite h3 fields. We re-examined the long-slit data of Shapiro, Gerssen & van der Marel using a pPXF: a strong decoupling of the Gauss,Hermite term h3 is revealed, and the central decrease of Gauss,Hermite term h4 hinted in the SAURON data is confirmed. These data also suggest that NGC 1068 is a good candidate for a so-called , drop. We confirm the possible presence of two separate pattern speeds applying the Tremaine,Weinberg method to the Fabry,Perot H, map. We also examine the stellar kinematics of bars formed in N -body + smoothed particle hydrodynamics (SPH) simulations built from axisymmetric initial conditions approximating the luminosity distribution of NGC 1068. The resulting velocity, dispersion and higher order Gauss,Hermite moments successfully reproduce a number of properties observed in the two-dimensional kinematics of NGC 1068 and the long-slit data, showing that the kinematic signature of the NIR bar is imprinted in the stellar kinematics. The remaining differences between the models and the observed properties are likely mostly due to the exclusion of star formation and the lack of the primary large-scale oval/bar in the simulations. These models nevertheless suggest that the inner bar could drive a significant amount of gas down to a scale of , 300 pc. This would be consistent with the interpretation of the , drop in NGC 1068 being the result of central gas accretion followed by an episode of star formation. [source] The influence of binary stars on the kinematics of low-mass galaxiesMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2002S. De Rijcke In this paper, the influence of binary stars on the measured kinematics of dwarf galaxies is investigated. Using realistic distributions of the orbital parameters (semi-major axis, eccentricity, etc.), analytical expressions are derived for the changes induced by the presence of binary stars in the measured velocity moments of low-mass galaxies (such as the projected velocity dispersion and the fourth-order Gauss,Hermite coefficient h4). It is shown that there is a noticeable change in the observed velocity dispersion if the intrinsic velocity dispersion of a galaxy is of the same order as the binary velocity dispersion. The kurtosis of the line-of-sight velocity distribution (LOSVD) is affected even at higher values of the intrinsic velocity dispersion. Moreover, the LOSVD of the binary stars (i.e. the probability of finding a star in a binary system with a particular projected velocity) is given in closed form, approximating the constituent stars of all binaries to revolve on circular orbits around each other. With this binary LOSVD, we calculate the observed LOSVD, the latter quantifying the movement of stars along the line of sight caused both by the orbits of the stars through the galaxy and by the motion of the stars in binary systems. As suggested by the changes induced in the moments, the observed LOSVD becomes more peaked around zero velocity and develops broader high-velocity wings. These results are important in interpreting kinematics derived from integrated-light spectra of low-mass galaxies and many of the intermediate results are useful for comparison with Monte Carlo simulations. [source] Discovery of magnetic fields in the , Cephei star ,1 CMa and in several slowly pulsating B stars,MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY: LETTERS (ELECTRONIC), Issue 1 2006S. Hubrig ABSTRACT We present the results of a magnetic survey of a sample of eight , Cephei stars and 26 slowly pulsating B (SPBs) stars with the FOcal Reducer low dispersion Spectrograph at the Very Large Telescope. A weak mean longitudinal magnetic field of the order of a few hundred Gauss is detected in the , Cephei star ,1 CMa and in 13 SPB stars. The star ,1 CMa becomes the third magnetic star among the , Cephei stars. Before our study, the star , Cas was the only known magnetic SPB star. All magnetic SPB stars for which we gathered several magnetic field measurements show a field that varies in time. We do not find a relation between the evolution of the magnetic field with stellar age in our small sample. Our observations imply that , Cephei and SPB stars can no longer be considered as classes of non-magnetic pulsators, but the effect of the fields on the oscillation properties remains to be studied. [source] A robust multilevel approach for minimizing H(div)-dominated functionals in an H1 -conforming finite element spaceNUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, Issue 2-3 2004Travis M. Austin Abstract The standard multigrid algorithm is widely known to yield optimal convergence whenever all high-frequency error components correspond to large relative eigenvalues. This property guarantees that smoothers like Gauss,Seidel and Jacobi will significantly dampen all the high-frequency error components, and thus, produce a smooth error. This has been established for matrices generated from standard discretizations of most elliptic equations. In this paper, we address a system of equations that is generated from a perturbation of the non-elliptic operator I-grad div by a negative , ,. For ,near to one, this operator is elliptic, but as ,approaches zero, the operator becomes non-elliptic as it is dominated by its non-elliptic part. Previous research on the non-elliptic part has revealed that discretizing I-grad div with the proper finite element space allows one to define a robust geometric multigrid algorithm. The robustness of the multigrid algorithm depends on a relaxation operator that yields a smooth error. We use this research to assist in developing a robust discretization and solution method for the perturbed problem. To this end, we introduce a new finite element space for tensor product meshes that is used in the discretization, and a relaxation operator that succeeds in dampening all high-frequency error components. The success of the corresponding multigrid algorithm is first demonstrated by numerical results that quantitatively imply convergence for any ,is bounded by the convergence for ,equal to zero. Then we prove that convergence of this multigrid algorithm for the case of , equal to zero is independent of mesh size. Copyright © 2004 John Wiley & Sons, Ltd. [source] | ||||||||||||||||||||||||||||||||||