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Sample records for smoothing newton method

  1. A Non-smooth Newton Method for Multibody Dynamics

    SciTech Connect

    Erleben, K.; Ortiz, R.

    2008-09-01

    In this paper we deal with the simulation of rigid bodies. Rigid body dynamics have become very important for simulating rigid body motion in interactive applications, such as computer games or virtual reality. We present a novel way of computing contact forces using a Newton method. The contact problem is reformulated as a system of non-linear and non-smooth equations, and we solve this system using a non-smooth version of Newton's method. One of the main contribution of this paper is the reformulation of the complementarity problems, used to model impacts, as a system of equations that can be solved using traditional methods.

  2. Inexact Newton dogleg methods.

    SciTech Connect

    Shadid, John Nicolas; Simonis, Joseph P.; Pawlowski, Roger Patrick; Walker, Homer Franklin

    2005-05-01

    The dogleg method is a classical trust-region technique for globalizing Newton's method. While it is widely used in optimization, including large-scale optimization via truncated-Newton approaches, its implementation in general inexact Newton methods for systems of nonlinear equations can be problematic. In this paper, we first outline a very general dogleg method suitable for the general inexact Newton context and provide a global convergence analysis for it. We then discuss certain issues that may arise with the standard dogleg implementational strategy and propose modified strategies that address them. Newton-Krylov methods have provided important motivation for this work, and we conclude with a report on numerical experiments involving a Newton-GMRES dogleg method applied to benchmark CFD problems.

  3. Sometimes "Newton's Method" Always "Cycles"

    ERIC Educational Resources Information Center

    Latulippe, Joe; Switkes, Jennifer

    2012-01-01

    Are there functions for which Newton's method cycles for all non-trivial initial guesses? We construct and solve a differential equation whose solution is a real-valued function that two-cycles under Newton iteration. Higher-order cycles of Newton's method iterates are explored in the complex plane using complex powers of "x." We find a class of…

  4. Structural optimization using Newton Modified Barrier Method

    NASA Astrophysics Data System (ADS)

    Khot, N. S.; Polyak, R.; Schneur, R.

    1992-09-01

    The Newton Modified Barrier Method (NMBM) was applied to a structural optimization problem with large numbers of design variables and constraints. This mathematical optimization algorithm was based on Modified Barrier Function (MBF) theory and the global converging step version of the Newton Method for smooth unconstrained optimization. For illustrating the convergence characteristics of this method to structural optimization, a truss structure with 721 design variables with constraints on displacements and minimum size requirements was solved. The convergence to the optimum was found to be monotonic. The rate of convergence was compared with solving the same problem with ASTROS and optimality criteria approach.

  5. Fractal aspects and convergence of Newton`s method

    SciTech Connect

    Drexler, M.

    1996-12-31

    Newton`s Method is a widely established iterative algorithm for solving non-linear systems. Its appeal lies in its great simplicity, easy generalization to multiple dimensions and a quadratic local convergence rate. Despite these features, little is known about its global behavior. In this paper, we will explain a seemingly random global convergence pattern using fractal concepts and show that the behavior of the residual is entirely explicable. We will also establish quantitative results for the convergence rates. Knowing the mechanism of fractal generation, we present a stabilization to the orthodox Newton method that remedies the fractal behavior and improves convergence.

  6. [Isaac Newton's Anguli Contactus method].

    PubMed

    Wawrzycki, Jarosław

    2014-01-01

    In this paper we discuss the geometrical method for calculating the curvature of a class of curves from the third Book of Isaac Newton's Principia. The method involves any curve which is generated from an elementary curve (actually from any curve whose curvature we known of) by means of transformation increasing the polar angular coordinate in a constant ratio, but unchanging the polar radial angular coordinate.

  7. The Lyapunov spectrum as the Newton method

    NASA Astrophysics Data System (ADS)

    Iommi, Godofredo

    2012-05-01

    For a class of dynamical systems, the cookie-cutter maps, we prove that the Lyapunov spectrum coincides with the map given by the Newton-Raphson method applied to the derivative of the pressure function.

  8. Subsampled Hessian Newton Methods for Supervised Learning.

    PubMed

    Wang, Chien-Chih; Huang, Chun-Heng; Lin, Chih-Jen

    2015-08-01

    Newton methods can be applied in many supervised learning approaches. However, for large-scale data, the use of the whole Hessian matrix can be time-consuming. Recently, subsampled Newton methods have been proposed to reduce the computational time by using only a subset of data for calculating an approximation of the Hessian matrix. Unfortunately, we find that in some situations, the running speed is worse than the standard Newton method because cheaper but less accurate search directions are used. In this work, we propose some novel techniques to improve the existing subsampled Hessian Newton method. The main idea is to solve a two-dimensional subproblem per iteration to adjust the search direction to better minimize the second-order approximation of the function value. We prove the theoretical convergence of the proposed method. Experiments on logistic regression, linear SVM, maximum entropy, and deep networks indicate that our techniques significantly reduce the running time of the subsampled Hessian Newton method. The resulting algorithm becomes a compelling alternative to the standard Newton method for large-scale data classification.

  9. Generalized Newton Method for Energy Formulation in Image Processing

    DTIC Science & Technology

    2008-04-01

    Blurred (b) - Newton with LH (c) - Standard Newton (d) - Newton with Ls Fig. 5.2. Deblurring of the clown image with different Newton-like methods...proposed method, the inner product can be adapted to the problem at hand. In the second example, Figure 5.2, the 330 × 291 clown image was additionally

  10. A combined modification of Newton`s method for systems of nonlinear equations

    SciTech Connect

    Monteiro, M.T.; Fernandes, E.M.G.P.

    1996-12-31

    To improve the performance of Newton`s method for the solution of systems of nonlinear equations a modification to the Newton iteration is implemented. The modified step is taken as a linear combination of Newton step and steepest descent directions. In the paper we describe how the coefficients of the combination can be generated to make effective use of the two component steps. Numerical results that show the usefulness of the combined modification are presented.

  11. Solving a Class of Nonlinear Eigenvalue Problems by Newton's Method

    SciTech Connect

    Gao, Weiguo; Yang, Chao; Meza, Juan C.

    2009-07-02

    We examine the possibility of using the standard Newton's method for solving a class of nonlinear eigenvalue problems arising from electronic structure calculation. We show that the Jacobian matrix associated with this nonlinear system has a special structure that can be exploited to reduce the computational complexity of the Newton's method. Preliminary numerical experiments indicate that the Newton's method can be more efficient for small problems in which a few smallest eigenpairs are needed.

  12. Newton-Krylov methods applied to nonequilibrium radiation diffusion

    SciTech Connect

    Knoll, D.A.; Rider, W.J.; Olsen, G.L.

    1998-03-10

    The authors present results of applying a matrix-free Newton-Krylov method to a nonequilibrium radiation diffusion problem. Here, there is no use of operator splitting, and Newton`s method is used to convert the nonlinearities within a time step. Since the nonlinear residual is formed, it is used to monitor convergence. It is demonstrated that a simple Picard-based linearization produces a sufficient preconditioning matrix for the Krylov method, thus elevating the need to form or store a Jacobian matrix for Newton`s method. They discuss the possibility that the Newton-Krylov approach may allow larger time steps, without loss of accuracy, as compared to an operator split approach where nonlinearities are not converged within a time step.

  13. Newton

    NASA Astrophysics Data System (ADS)

    Wilson, C.; Murdin, P.

    2000-11-01

    Isaac Newton (1642-1727) is known pre-eminently for discoveries in mathematics (binomial theorem and fundamental theorem of the calculus), optics (the heterogeneity of white light) and mechanics (laws of motion and universal gravitation). Not undisputed are some questions of priority and how in detail to characterize these achievements. Beyond question, however, is the foundational characte...

  14. Newton-Krylov-Schwarz methods in unstructured grid Euler flow

    SciTech Connect

    Keyes, D.E.

    1996-12-31

    Newton-Krylov methods and Krylov-Schwarz (domain decomposition) methods have begun to become established in computational fluid dynamics (CFD) over the past decade. The former employ a Krylov method inside of Newton`s method in a Jacobian-free manner, through directional differencing. The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that relies primarily on local information, for data-parallel concurrency. They may be composed as Newton-Krylov-Schwarz (NKS) methods, which seem particularly well suited for solving nonlinear elliptic systems in high-latency, distributed-memory environments. We give a brief description of this family of algorithms, with an emphasis on domain decomposition iterative aspects. We then describe numerical simulations with Newton-Krylov-Schwarz methods on an aerodynamic application emphasizing comparisons with a standard defect-correction approach and subdomain preconditioner consistency.

  15. Structural Optimization Using the Newton Modified Barrier Method

    NASA Technical Reports Server (NTRS)

    Khot, N. S.; Polyak, R. A.; Schneur, R.; Berke, L.

    1995-01-01

    The Newton Modified Barrier Method (NMBM) is applied to structural optimization problems with large a number of design variables and constraints. This nonlinear mathematical programming algorithm was based on the Modified Barrier Function (MBF) theory and the Newton method for unconstrained optimization. The distinctive feature of the NMBM method is the rate of convergence that is due to the fact that the design remains in the Newton area after each Lagrange multiplier update. This convergence characteristic is illustrated by application to structural problems with a varying number of design variables and constraints. The results are compared with those obtained by optimality criteria (OC) methods and by the ASTROS program.

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

    SciTech Connect

    Brown, J.; Brune, P.

    2013-07-01

    Newton-Krylov methods are standard tools for solving nonlinear problems. A common approach is to 'lag' the Jacobian when assembly or preconditioner setup is computationally expensive, in exchange for some degradation in the convergence rate and robustness. We show that this degradation may be partially mitigated by using the lagged Jacobian as an initial operator in a quasi-Newton method, which applies unassembled low-rank updates to the Jacobian until the next full reassembly. We demonstrate the effectiveness of this technique on problems in glaciology and elasticity. (authors)

  17. Choosing the forcing terms in an inexact Newton method

    SciTech Connect

    Eisenstat, S.C.; Walker, H.F.

    1994-12-31

    An inexact Newton method is a generalization of Newton`s method for solving F(x) = 0, F: {Re}{sup n} {r_arrow} {Re}{sup n}, in which each step reduces the norm of the local linear model of F. At the kth iteration, the norm reduction is usefully expressed by the inexact Newton condition where x{sub k} is the current approximate solution and s{sub k} is the step. In many applications, an {eta}{sub k} is first specified, and then an S{sub k} is found for which the inexact Newton condition holds. Thus {eta}{sub k} is often called a {open_quotes}forcing term{close_quotes}. In practice, the choice of the forcing terms is usually critical to the efficiency of the method and can affect robustness as well. Here, the authors outline several promising choices, discuss theoretical support for them, and compare their performance in a Newton iterative (truncated Newton) method applied to several large-scale problems.

  18. Optimization: NURBS and the quasi-Newton method

    NASA Astrophysics Data System (ADS)

    Coburn, Todd Dale

    Optimization is important in both engineering and mathematics. The Quasi-Newton Method is widely used for optimization due to its speed and efficiency. NonUniform Rational B-Splines (NURBS) are piecewise parametric approximations to curves and surfaces. NURBS have great curve-fitting properties that can be applied to improve optimization performance. This dissertation investigated the use of NURBS in optimization, focusing primarily on the coupling of NURBS with the Quasi-Newton Method. A hybrid optimization procedure dubbed the NURBS-Quasi-Newton (NQN) Method was developed and utilized that can virtually assure that the global minimum will be found. A Method was also developed to implement Pure NURBS Optimization (PNO), which can be used to optimize non-continuous and singular functions as well as functions of point cloud data. It was concluded that NURBS offer significant benefits for optimization, both individually and coupled with Quasi-Newton Methods.

  19. Smoothed Profile Method to Simulate Colloidal Particles in Complex Fluids

    NASA Astrophysics Data System (ADS)

    Yamamoto, Ryoichi; Nakayama, Yasuya; Kim, Kang

    A new direct numerical simulation scheme, called "Smoothed Profile (SP) method," is presented. The SP method, as a direct numerical simulation of particulate flow, provides a way to couple continuum fluid dynamics with rigid-body dynamics through smoothed profile of colloidal particle. Our formulation includes extensions to colloids in multicomponent solvents such as charged colloids in electrolyte solutions. This method enables us to compute the time evolutions of colloidal particles, ions, and host fluids simultaneously by solving Newton, advection-diffusion, and Navier-Stokes equations so that the electro-hydrodynamic couplings can be fully taken into account. The electrophoretic mobilities of charged spherical particles are calculated in several situations. The comparisons with approximation theories show quantitative agreements for dilute dispersions without any empirical parameters.

  20. Newton's method for large bound-constrained optimization problems.

    SciTech Connect

    Lin, C.-J.; More, J. J.; Mathematics and Computer Science

    1999-01-01

    We analyze a trust region version of Newton's method for bound-constrained problems. Our approach relies on the geometry of the feasible set, not on the particular representation in terms of constraints. The convergence theory holds for linearly constrained problems and yields global and superlinear convergence without assuming either strict complementarity or linear independence of the active constraints. We also show that the convergence theory leads to an efficient implementation for large bound-constrained problems.

  1. Approximate Newton-type methods via theory of control

    NASA Astrophysics Data System (ADS)

    Yap, Chui Ying; Leong, Wah June

    2014-12-01

    In this paper, we investigate the possible use of control theory, particularly theory on optimal control to derive some numerical methods for unconstrained optimization problems. Based upon this control theory, we derive a Levenberg-Marquardt-like method that guarantees greatest descent in a particular search region. The implementation of this method in its original form requires inversion of a non-sparse matrix or equivalently solving a linear system in every iteration. Thus, an approximation of the proposed method via quasi-Newton update is constructed. Numerical results indicate that the new method is more effective and practical.

  2. Newton like: Minimal residual methods applied to transonic flow calculations

    NASA Technical Reports Server (NTRS)

    Wong, Y. S.

    1984-01-01

    A computational technique for the solution of the full potential equation is presented. The method consists of outer and inner iterations. The outer iterate is based on a Newton like algorithm, and a preconditioned Minimal Residual method is used to seek an approximate solution of the system of linear equations arising at each inner iterate. The present iterative scheme is formulated so that the uncertainties and difficulties associated with many iterative techniques, namely the requirements of acceleration parameters and the treatment of additional boundary conditions for the intermediate variables, are eliminated. Numerical experiments based on the new method for transonic potential flows around the NACA 0012 airfoil at different Mach numbers and different angles of attack are presented, and these results are compared with those obtained by the Approximate Factorization technique. Extention to three dimensional flow calculations and application in finite element methods for fluid dynamics problems by the present method are also discussed. The Inexact Newton like method produces a smoother reduction in the residual norm, and the number of supersonic points and circulations are rapidly established as the number of iterations is increased.

  3. A 3D Contact Smoothing Method

    SciTech Connect

    Puso, M A; Laursen, T A

    2002-05-02

    Smoothing of contact surfaces can be used to eliminate the chatter typically seen with node on facet contact and give a better representation of the actual contact surface. The latter affect is well demonstrated for problems with interference fits. In this work we present two methods for the smoothing of contact surfaces for 3D finite element contact. In the first method, we employ Gregory patches to smooth the faceted surface in a node on facet implementation. In the second method, we employ a Bezier interpolation of the faceted surface in a mortar method implementation of contact. As is well known, node on facet approaches can exhibit locking due to the failure of the Babuska-Brezzi condition and in some instances fail the patch test. The mortar method implementation is stable and provides optimal convergence in the energy of error. In the this work we demonstrate the superiority of the smoothed versus the non-smoothed node on facet implementations. We also show where the node on facet method fails and some results from the smoothed mortar method implementation.

  4. Preconditioning Newton-Krylor Methods for Variably Saturated Flow

    SciTech Connect

    Woodward, C.; Jones, J

    2000-01-07

    In this paper, we compare the effectiveness of three preconditioning strategies in simulations of variably saturated flow. Using Richards' equation as our model, we solve the nonlinear system using a Newton-Krylov method. Since Krylov solvers can stagnate, resulting in slow convergence, we investigate different strategies of preconditioning the Jacobian system. Our work uses a multigrid method to solve the preconditioning systems, with three different approximations to the Jacobian matrix. One approximation lags the nonlinearities, the second results from discarding selected off-diagonal contributions, and the third matrix considered is the full Jacobian. Results indicate that although the Jacobian is more accurate, its usage as a preconditioning matrix should be limited, as it requires much more storage than the simpler approximations. Also, simply lagging the nonlinearities gives a preconditioning matrix that is almost as effective as the full Jacobian but much easier to compute.

  5. Multiple predictor smoothing methods for sensitivity analysis.

    SciTech Connect

    Helton, Jon Craig; Storlie, Curtis B.

    2006-08-01

    The use of multiple predictor smoothing methods in sampling-based sensitivity analyses of complex models is investigated. Specifically, sensitivity analysis procedures based on smoothing methods employing the stepwise application of the following nonparametric regression techniques are described: (1) locally weighted regression (LOESS), (2) additive models, (3) projection pursuit regression, and (4) recursive partitioning regression. The indicated procedures are illustrated with both simple test problems and results from a performance assessment for a radioactive waste disposal facility (i.e., the Waste Isolation Pilot Plant). As shown by the example illustrations, the use of smoothing procedures based on nonparametric regression techniques can yield more informative sensitivity analysis results than can be obtained with more traditional sensitivity analysis procedures based on linear regression, rank regression or quadratic regression when nonlinear relationships between model inputs and model predictions are present.

  6. Method for producing smooth inner surfaces

    DOEpatents

    Cooper, Charles A.

    2016-05-17

    The invention provides a method for preparing superconducting cavities, the method comprising causing polishing media to tumble by centrifugal barrel polishing within the cavities for a time sufficient to attain a surface smoothness of less than 15 nm root mean square roughness over approximately a 1 mm.sup.2 scan area. The method also provides for a method for preparing superconducting cavities, the method comprising causing polishing media bound to a carrier to tumble within the cavities. The method also provides for a method for preparing superconducting cavities, the method comprising causing polishing media in a slurry to tumble within the cavities.

  7. Parallel full-waveform inversion in the frequency domain by the Gauss-Newton method

    NASA Astrophysics Data System (ADS)

    Zhang, Wensheng; Zhuang, Yuan

    2016-06-01

    In this paper, we investigate the full-waveform inversion in the frequency domain. We first test the inversion ability of three numerical optimization methods, i.e., the steepest-descent method, the Newton-CG method and the Gauss- Newton method, for a simple model. The results show that the Gauss-Newton method performs well and efficiently. Then numerical computations for a benchmark model named Marmousi model by the Gauss-Newton method are implemented. Parallel algorithm based on message passing interface (MPI) is applied as the inversion is a typical large-scale computational problem. Numerical computations show that the Gauss-Newton method has good ability to reconstruct the complex model.

  8. Rotorcraft Smoothing Via Linear Time Periodic Methods

    DTIC Science & Technology

    2007-07-01

    Optimal Control Methodology for Rotor Vibration Smoothing . . 30 vii Page IV. Mathematic Foundations of Linear Time Periodic Systems . . . . 33 4.1 The...62 6.3 The Maximum Likelihood Estimator . . . . . . . . . . . 63 6.4 The Cramer-Rao Inequality . . . . . . . . . . . . . . . . 66 6.4.1 Statistical ...adjustments for vibration reduction. 2.2.2.4 1980’s to late 1990’s. Rotor vibrational reduction methods during the 1980’s began to adopt a mathematical

  9. Solving Cocoa Pod Sigmoid Growth Model with Newton Raphson Method

    NASA Astrophysics Data System (ADS)

    Chang, Albert Ling Sheng; Maisin, Navies

    Cocoa pod growth modelling are useful in crop management, pest and disease management and yield forecasting. Recently, the Beta Growth Function has been used to determine the pod growth model due to its unique for the plant organ growth which is zero growth rate at both the start and end of a precisely defined growth period. Specific pod size (7cm to 10cm in length) is useful in cocoa pod borer (CPB) management for pod sleeving or pesticide spraying. The Beta Growth Function is well-fitted to the pods growth data of four different cocoa clones under non-linear function with time (t) as its independent variable which measured pod length and diameter weekly started at 8 weeks after fertilization occur until pods ripen. However, the same pod length among the clones did not indicate the same pod age since the morphological characteristics for cocoa pods vary among the clones. Depending on pod size for all the clones as guideline in CPB management did not give information on pod age, therefore it is important to study the pod age at specific pod sizes on different clones. Hence, Newton Raphson method is used to solve the non-linear equation of the Beta Growth Function of four different group of cocoa pod at specific pod size.

  10. Newton's method: A link between continuous and discrete solutions of nonlinear problems

    NASA Technical Reports Server (NTRS)

    Thurston, G. A.

    1980-01-01

    Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.

  11. Comparing Three Methods for Teaching Newton's Second Law

    NASA Astrophysics Data System (ADS)

    Wittmann, Michael C.; Anderson, Mindi Kvaal; Smith, Trevor I.

    2009-11-01

    As a follow-up to a study comparing learning of Newton's Third Law when using three different forms of tutorial instruction, we have compared student learning of Newton's Second Law (NSL) when students use the Tutorials in Introductory Physics, Activity-Based Tutorials, or Open Source Tutorials. We split an algebra-based, life sciences physics course in 3 groups and measured students' pre- and post-instruction scores on the Force and Motion Conceptual Evaluation (FMCE). We look at only the NSL-related clusters of questions on the FMCE to compare students' performance and normalized gains. Students entering the course are not significantly different, and students using the Tutorials in Introductory Physics show the largest normalized gains in answering question on the FMCE correctly. These gains are significant in only one cluster of questions, the Force Sled cluster.

  12. The combined use of the Newton-Raphson method and the conjugate gradient method for solving elastoplastic problems

    NASA Astrophysics Data System (ADS)

    Movchan, A. A.; Brodskij, S. I.

    The paper is concerned with the elastic-plastic analysis of an axisymmetric bimetal joint under loading. A system of nonlinear equations describing this elastic-plastic problem are solved by using a modified version of the Newton-Raphson method. To increase the computational efficiency, a procedure is proposed whereby the Newton-Raphson method is combined with a version of the conjugate gradient method.

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

    SciTech Connect

    J. D. Hales; S. R. Novascone; R. L. Williamson; D. R. Gaston; M. R. Tonks

    2012-06-01

    The solution of the equations governing solid mechanics is often obtained via Newton's method. This approach can be problematic if the determination, storage, or solution cost associated with the Jacobian is high. These challenges are magnified for multiphysics applications with many coupled variables. Jacobian-free Newton-Krylov (JFNK) methods avoid many of the difficulties associated with the Jacobian by using a finite difference approximation. BISON is a parallel, object-oriented, nonlinear solid mechanics and multiphysics application that leverages JFNK methods. We overview JFNK, outline the capabilities of BISON, and demonstrate the effectiveness of JFNK for solid mechanics and solid mechanics coupled to other PDEs using a series of demonstration problems.

  14. Application of Newton's method to the postbuckling of rings under pressure loadings

    NASA Technical Reports Server (NTRS)

    Thurston, Gaylen A.

    1989-01-01

    The postbuckling response of circular rings (or long cylinders) is examined. The rings are subjected to four types of external pressure loadings; each type of pressure is defined by its magnitude and direction at points on the buckled ring. Newton's method is applied to the nonlinear differential equations of the exact inextensional theory for the ring problem. A zeroth approximation for the solution of the nonlinear equations, based on the mode shape corresponding to the first buckling pressure, is derived in closed form for each of the four types of pressure. The zeroth approximation is used to start the iteration cycle in Newton's method to compute numerical solutions of the nonlinear equations. The zeroth approximations for the postbuckling pressure-deflection curves are compared with the converged solutions from Newton's method and with similar results reported in the literature.

  15. On a class of Newton-like methods for solving nonlinear equations

    NASA Astrophysics Data System (ADS)

    Argyros, Ioannis K.

    2009-06-01

    We provide a semilocal convergence analysis for a certain class of Newton-like methods considered also in [I.K. Argyros, A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space, J. Math. Anal. Appl. 298 (2004) 374-397; I.K. Argyros, Computational theory of iterative methods, in: C.K. Chui, L. Wuytack (Eds.), Series: Studies in Computational Mathematics, vol. 15, Elsevier Publ. Co, New York, USA, 2007; J.E. Dennis, Toward a unified convergence theory for Newton-like methods, in: L.B. Rall (Ed.), Nonlinear Functional Analysis and Applications, Academic Press, New York, 1971], in order to approximate a locally unique solution of an equation in a Banach space. Using a combination of Lipschitz and center-Lipschitz conditions, instead of only Lipschitz conditions [F.A. Potra, Sharp error bounds for a class of Newton-like methods, Libertas Math. 5 (1985) 71-84], we provide an analysis with the following advantages over the work in [F.A. Potra, Sharp error bounds for a class of Newton-like methods, Libertas Math. 5 (1985) 71-84] which improved the works in [W.E. Bosarge, P.L. Falb, A multipoint method of third order, J. Optimiz. Theory Appl. 4 (1969) 156-166; W.E. Bosarge, P.L. Falb, Infinite dimensional multipoint methods and the solution of two point boundary value problems, Numer. Math. 14 (1970) 264-286; J.E. Dennis, On the Kantorovich hypothesis for Newton's method, SIAM J. Numer. Anal. 6 (3) (1969) 493-507; J.E. Dennis, Toward a unified convergence theory for Newton-like methods, in: L.B. Rall (Ed.), Nonlinear Functional Analysis and Applications, Academic Press, New York, 1971; H.J. Kornstaedt, Ein allgemeiner Konvergenzstaz fü r verschä rfte Newton-Verfahrem, in: ISNM, vol. 28, Birkhaü ser Verlag, Basel and Stuttgart, 1975, pp. 53-69; P. Laasonen, Ein überquadratisch konvergenter iterativer algorithmus, Ann. Acad. Sci. Fenn. Ser I 450 (1969) 1-10; F.A. Potra, On a modified secant method, L'analyse num

  16. A multigrid Newton-Krylov method for flux-limited radiation diffusion

    SciTech Connect

    Rider, W.J.; Knoll, D.A.; Olson, G.L.

    1998-09-01

    The authors focus on the integration of radiation diffusion including flux-limited diffusion coefficients. The nonlinear integration is accomplished with a Newton-Krylov method preconditioned with a multigrid Picard linearization of the governing equations. They investigate the efficiency of the linear and nonlinear iterative techniques.

  17. Newton's method for nonlinear stochastic wave equations driven by one-dimensional Brownian motion.

    PubMed

    Leszczynski, Henryk; Wrzosek, Monika

    2017-02-01

    We consider nonlinear stochastic wave equations driven by one-dimensional white noise with respect to time. The existence of solutions is proved by means of Picard iterations. Next we apply Newton's method. Moreover, a second-order convergence in a probabilistic sense is demonstrated.

  18. A high-order fast method for computing convolution integral with smooth kernel

    NASA Astrophysics Data System (ADS)

    Qiang, Ji

    2010-02-01

    In this paper we report on a high-order fast method to numerically calculate convolution integral with smooth non-periodic kernel. This method is based on the Newton-Cotes quadrature rule for the integral approximation and an FFT method for discrete summation. The method can have an arbitrarily high-order accuracy in principle depending on the number of points used in the integral approximation and a computational cost of O(Nlog(N)), where N is the number of grid points. For a three-point Simpson rule approximation, the method has an accuracy of O(h), where h is the size of the computational grid. Applications of the Simpson rule based algorithm to the calculation of a one-dimensional continuous Gauss transform and to the calculation of a two-dimensional electric field from a charged beam are also presented.

  19. A high-order fast method for computing convolution integral with smooth kernel

    SciTech Connect

    Qiang, Ji

    2009-09-28

    In this paper we report on a high-order fast method to numerically calculate convolution integral with smooth non-periodic kernel. This method is based on the Newton-Cotes quadrature rule for the integral approximation and an FFT method for discrete summation. The method can have an arbitrarily high-order accuracy in principle depending on the number of points used in the integral approximation and a computational cost of O(Nlog(N)), where N is the number of grid points. For a three-point Simpson rule approximation, the method has an accuracy of O(h{sup 4}), where h is the size of the computational grid. Applications of the Simpson rule based algorithm to the calculation of a one-dimensional continuous Gauss transform and to the calculation of a two-dimensional electric field from a charged beam are also presented.

  20. 3D CSEM data inversion using Newton and Halley class methods

    NASA Astrophysics Data System (ADS)

    Amaya, M.; Hansen, K. R.; Morten, J. P.

    2016-05-01

    For the first time in 3D controlled source electromagnetic data inversion, we explore the use of the Newton and the Halley optimization methods, which may show their potential when the cost function has a complex topology. The inversion is formulated as a constrained nonlinear least-squares problem which is solved by iterative optimization. These methods require the derivatives up to second order of the residuals with respect to model parameters. We show how Green's functions determine the high-order derivatives, and develop a diagrammatical representation of the residual derivatives. The Green's functions are efficiently calculated on-the-fly, making use of a finite-difference frequency-domain forward modelling code based on a multi-frontal sparse direct solver. This allow us to build the second-order derivatives of the residuals keeping the memory cost in the same order as in a Gauss-Newton (GN) scheme. Model updates are computed with a trust-region based conjugate-gradient solver which does not require the computation of a stabilizer. We present inversion results for a synthetic survey and compare the GN, Newton, and super-Halley optimization schemes, and consider two different approaches to set the initial trust-region radius. Our analysis shows that the Newton and super-Halley schemes, using the same regularization configuration, add significant information to the inversion so that the convergence is reached by different paths. In our simple resistivity model examples, the convergence speed of the Newton and the super-Halley schemes are either similar or slightly superior with respect to the convergence speed of the GN scheme, close to the minimum of the cost function. Due to the current noise levels and other measurement inaccuracies in geophysical investigations, this advantageous behaviour is at present of low consequence, but may, with the further improvement of geophysical data acquisition, be an argument for more accurate higher-order methods like those

  1. A Newton Cooperative Genetic Algorithm Method for In Silico Optimization of Metabolic Pathway Production

    PubMed Central

    Mohamad, Mohd Saberi; Abdullah, Afnizanfaizal

    2015-01-01

    This paper presents an in silico optimization method of metabolic pathway production. The metabolic pathway can be represented by a mathematical model known as the generalized mass action model, which leads to a complex nonlinear equations system. The optimization process becomes difficult when steady state and the constraints of the components in the metabolic pathway are involved. To deal with this situation, this paper presents an in silico optimization method, namely the Newton Cooperative Genetic Algorithm (NCGA). The NCGA used Newton method in dealing with the metabolic pathway, and then integrated genetic algorithm and cooperative co-evolutionary algorithm. The proposed method was experimentally applied on the benchmark metabolic pathways, and the results showed that the NCGA achieved better results compared to the existing methods. PMID:25961295

  2. Nonlinear parameter identification: Ballistic range experience applicable to flight testing. [using Gauss-Newton method

    NASA Technical Reports Server (NTRS)

    Chapman, G.; Kirk, D.

    1974-01-01

    The parameter identification scheme being used is a differential correction least squares procedure (Gauss-Newton method). The position, orientation, and derivatives of these quantities with respect to the parameters of interest (i.e., sensitivity coefficients) are determined by digital integration of the equations of motion and the parametric differential equations. The application of this technique to three vastly different sets of data is used to illustrate the versatility of the method and to indicate some of the problems that still remain.

  3. Improved FRFT-based method for estimating the physical parameters from Newton's rings

    NASA Astrophysics Data System (ADS)

    Wu, Jin-Min; Lu, Ming-Feng; Tao, Ran; Zhang, Feng; Li, Yang

    2017-04-01

    Newton's rings are often encountered in interferometry, and in analyzing them, we can estimate the physical parameters, such as curvature radius and the rings' center. The fractional Fourier transform (FRFT) is capable of estimating these physical parameters from the rings despite noise and obstacles, but there is still a small deviation between the estimated coordinates of the rings' center and the actual values. The least-squares fitting method is popularly used for its accuracy but it is easily affected by the initial values. Nevertheless, with the estimated results from the FRFT, it is easy to meet the requirements of initial values. In this paper, the proposed method combines the advantages of the fractional Fourier transform (FRFT) with the least-squares fitting method in analyzing Newton's rings fringe patterns. Its performance is assessed by analyzing simulated and actual Newton's rings images. The experimental results show that the proposed method is capable of estimating the parameters in the presence of noise and obstacles. Under the same conditions, the estimation results are better than those obtained with the original FRFT-based method, especially for the rings' center. Some applications are shown to illustrate that the improved FRFT-based method is an important technique for interferometric measurements.

  4. Mesh independent convergence of the modified inexact Newton method for a second order nonlinear problem

    SciTech Connect

    Kim, T; Pasciak, J E; Vassilevski, P S

    2004-09-20

    In this paper, we consider an inexact Newton method applied to a second order nonlinear problem with higher order nonlinearities. We provide conditions under which the method has a mesh-independent rate of convergence. To do this, we are required to first, set up the problem on a scale of Hilbert spaces and second, to devise a special iterative technique which converges in a higher than first order Sobolev norm. We show that the linear (Jacobian) system solved in Newton's method can be replaced with one iterative step provided that the initial nonlinear iterate is accurate enough. The closeness criteria can be taken independent of the mesh size. Finally, the results of numerical experiments are given to support the theory.

  5. Short Communication: A Parallel Newton-Krylov Method for Navier-Stokes Rotorcraft Codes

    NASA Astrophysics Data System (ADS)

    Ekici, Kivanc; Lyrintzis, Anastasios S.

    2003-05-01

    The application of Krylov subspace iterative methods to unsteady three-dimensional Navier-Stokes codes on massively parallel and distributed computing environments is investigated. Previously, the Euler mode of the Navier-Stokes flow solver Transonic Unsteady Rotor Navier-Stokes (TURNS) has been coupled with a Newton-Krylov scheme which uses two Conjugate-Gradient-like (CG) iterative methods. For the efficient implementation of Newton-Krylov methods to the Navier-Stokes mode of TURNS, efficient preconditioners must be used. Parallel implicit operators are used and compared as preconditioners. Results are presented for two-dimensional and three-dimensional viscous cases. The Message Passing Interface (MPI) protocol is used, because of its portability to various parallel architectures.

  6. Comparing Three Methods for Teaching Newton's Third Law

    ERIC Educational Resources Information Center

    Smith, Trevor I.; Wittman, Michael C.

    2007-01-01

    Although guided-inquiry methods for teaching introductory physics have been individually shown to be more effective at improving conceptual understanding than traditional lecture-style instruction, researchers in physics education have not studied differences among reform-based curricula in much detail. Several researchers have developed…

  7. Modeling of hydrogen-assisted cracking in iron crystal using a quasi-Newton method.

    PubMed

    Telitchev, Igor Ye; Vinogradov, Oleg

    2008-07-01

    A Quasi-Newton method was applied in the context of a molecular statics approach to simulate the phenomenon of hydrogen embrittlement of an iron lattice. The atomic system is treated as a truss-type structure. The interatomic forces between the hydrogen-iron and the iron-iron atoms are defined by Morse and modified Morse potential functions, respectively. Two-dimensional hexagonal and 3D bcc crystal structures were subjected to tensile numerical tests. It was shown that the Inverse Broyden's Algorithm-a quasi-Newton method-provides a computationally efficient technique for modeling of the hydrogen-assisted cracking in iron crystal. Simulation results demonstrate that atoms of hydrogen placed near the crack tip produce a strong deformation and crack propagation effect in iron lattice, leading to a decrease in the residual strength of numerically tested samples.

  8. Helicopter trim analysis by shooting and finite element methods with optimally damped Newton iterations

    NASA Technical Reports Server (NTRS)

    Achar, N. S.; Gaonkar, G. H.

    1993-01-01

    Helicopter trim settings of periodic initial state and control inputs are investigated for convergence of Newton iteration in computing the settings sequentially and in parallel. The trim analysis uses a shooting method and a weak version of two temporal finite element methods with displacement formulation and with mixed formulation of displacements and momenta. These three methods broadly represent two main approaches of trim analysis: adaptation of initial-value and finite element boundary-value codes to periodic boundary conditions, particularly for unstable and marginally stable systems. In each method, both the sequential and in-parallel schemes are used, and the resulting nonlinear algebraic equations are solved by damped Newton iteration with an optimally selected damping parameter. The impact of damped Newton iteration, including earlier-observed divergence problems in trim analysis, is demonstrated by the maximum condition number of the Jacobian matrices of the iterative scheme and by virtual elimination of divergence. The advantages of the in-parallel scheme over the conventional sequential scheme are also demonstrated.

  9. Subspace accelerated inexact Newton method for large scale wave functions calculations in Density Functional Theory

    SciTech Connect

    Fattebert, J

    2008-07-29

    We describe an iterative algorithm to solve electronic structure problems in Density Functional Theory. The approach is presented as a Subspace Accelerated Inexact Newton (SAIN) solver for the non-linear Kohn-Sham equations. It is related to a class of iterative algorithms known as RMM-DIIS in the electronic structure community. The method is illustrated with examples of real applications using a finite difference discretization and multigrid preconditioning.

  10. Modified Newton-Raphson GRAPE methods for optimal control of spin systems

    NASA Astrophysics Data System (ADS)

    Goodwin, D. L.; Kuprov, Ilya

    2016-05-01

    Quadratic convergence throughout the active space is achieved for the gradient ascent pulse engineering (GRAPE) family of quantum optimal control algorithms. We demonstrate in this communication that the Hessian of the GRAPE fidelity functional is unusually cheap, having the same asymptotic complexity scaling as the functional itself. This leads to the possibility of using very efficient numerical optimization techniques. In particular, the Newton-Raphson method with a rational function optimization (RFO) regularized Hessian is shown in this work to require fewer system trajectory evaluations than any other algorithm in the GRAPE family. This communication describes algebraic and numerical implementation aspects (matrix exponential recycling, Hessian regularization, etc.) for the RFO Newton-Raphson version of GRAPE and reports benchmarks for common spin state control problems in magnetic resonance spectroscopy.

  11. Comparison of three newton-like nonlinear least-squares methods for estimating parameters of ground-water flow models

    USGS Publications Warehouse

    Cooley, R.L.; Hill, M.C.

    1992-01-01

    Three methods of solving nonlinear least-squares problems were compared for robustness and efficiency using a series of hypothetical and field problems. A modified Gauss-Newton/full Newton hybrid method (MGN/FN) and an analogous method for which part of the Hessian matrix was replaced by a quasi-Newton approximation (MGN/QN) solved some of the problems with appreciably fewer iterations than required using only a modified Gauss-Newton (MGN) method. In these problems, model nonlinearity and a large variance for the observed data apparently caused MGN to converge more slowly than MGN/FN or MGN/QN after the sum of squared errors had almost stabilized. Other problems were solved as efficiently with MGN as with MGN/FN or MGN/QN. Because MGN/FN can require significantly more computer time per iteration and more computer storage for transient problems, it is less attractive for a general purpose algorithm than MGN/QN.

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

    SciTech Connect

    Dana Knoll; HyeongKae Park; Chris Newman

    2011-02-01

    We present a new approach for the $k$--eigenvalue problem using a combination of classical power iteration and the Jacobian--free Newton--Krylov method (JFNK). The method poses the $k$--eigenvalue problem as a fully coupled nonlinear system, which is solved by JFNK with an effective block preconditioning consisting of the power iteration and algebraic multigrid. We demonstrate effectiveness and algorithmic scalability of the method on a 1-D, one group problem and two 2-D two group problems and provide comparison to other efforts using silmilar algorithmic approaches.

  13. Postprocessing Fourier spectral methods: The case of smooth solutions

    SciTech Connect

    Garcia-Archilla, B.; Novo, J.; Titi, E.S.

    1998-11-01

    A postprocessing technique to improve the accuracy of Galerkin methods, when applied to dissipative partial differential equations, is examined in the particular case of smooth solutions. Pseudospectral methods are shown to perform poorly. This performance is analyzed and a refined postprocessing technique is proposed.

  14. A speciation solver for cement paste modeling and the semismooth Newton method

    SciTech Connect

    Georget, Fabien; Prévost, Jean H.; Vanderbei, Robert J.

    2015-02-15

    The mineral assemblage of a cement paste may vary considerably with its environment. In addition, the water content of a cement paste is relatively low and the ionic strength of the interstitial solution is often high. These conditions are extreme conditions with respect to the common assumptions made in speciation problem. Furthermore the common trial and error algorithm to find the phase assemblage does not provide any guarantee of convergence. We propose a speciation solver based on a semismooth Newton method adapted to the thermodynamic modeling of cement paste. The strong theoretical properties associated with these methods offer practical advantages. Results of numerical experiments indicate that the algorithm is reliable, robust, and efficient.

  15. A method of smoothed particle hydrodynamics using spheroidal kernels

    NASA Technical Reports Server (NTRS)

    Fulbright, Michael S.; Benz, Willy; Davies, Melvyn B.

    1995-01-01

    We present a new method of three-dimensional smoothed particle hydrodynamics (SPH) designed to model systems dominated by deformation along a preferential axis. These systems cause severe problems for SPH codes using spherical kernels, which are best suited for modeling systems which retain rough spherical symmetry. Our method allows the smoothing length in the direction of the deformation to evolve independently of the smoothing length in the perpendicular plane, resulting in a kernel with a spheroidal shape. As a result the spatial resolution in the direction of deformation is significantly improved. As a test case we present the one-dimensional homologous collapse of a zero-temperature, uniform-density cloud, which serves to demonstrate the advantages of spheroidal kernels. We also present new results on the problem of the tidal disruption of a star by a massive black hole.

  16. Likelihood Methods for Adaptive Filtering and Smoothing. Technical Report #455.

    ERIC Educational Resources Information Center

    Butler, Ronald W.

    The dynamic linear model or Kalman filtering model provides a useful methodology for predicting the past, present, and future states of a dynamic system, such as an object in motion or an economic or social indicator that is changing systematically with time. Recursive likelihood methods for adaptive Kalman filtering and smoothing are developed.…

  17. Convergence Properties of the Regularized Newton Method for the Unconstrained Nonconvex Optimization

    SciTech Connect

    Ueda, Kenji Yamashita, Nobuo

    2010-08-15

    The regularized Newton method (RNM) is one of the efficient solution methods for the unconstrained convex optimization. It is well-known that the RNM has good convergence properties as compared to the steepest descent method and the pure Newton's method. For example, Li, Fukushima, Qi and Yamashita showed that the RNM has a quadratic rate of convergence under the local error bound condition. Recently, Polyak showed that the global complexity bound of the RNM, which is the first iteration k such that -parallel {nabla}f(x{sub k})-parallel {<=}{epsilon}, is O({epsilon}{sup -4}), where f is the objective function and {epsilon} is a given positive constant. In this paper, we consider a RNM extended to the unconstrained 'nonconvex' optimization. We show that the extended RNM (E-RNM) has the following properties. (a) The E-RNM has a global convergence property under appropriate conditions. (b) The global complexity bound of the E-RNM is O({epsilon}{sup -2}) if {nabla}{sup 2}f is Lipschitz continuous on a certain compact set. (c) The E-RNM has a superlinear rate of convergence under the local error bound condition.

  18. Comparison of smoothing methods for the development of a smoothed seismicity model for Alaska and the implications for seismic hazard

    USGS Publications Warehouse

    Moschetti, Morgan P.; Mueller, Charles S.; Boyd, Oliver S.; Petersen, Mark D.

    2014-01-01

    In anticipation of the update of the Alaska seismic hazard maps (ASHMs) by the U. S. Geological Survey, we report progress on the comparison of smoothed seismicity models developed using fixed and adaptive smoothing algorithms, and investigate the sensitivity of seismic hazard to the models. While fault-based sources, such as those for great earthquakes in the Alaska-Aleutian subduction zone and for the ~10 shallow crustal faults within Alaska, dominate the seismic hazard estimates for locations near to the sources, smoothed seismicity rates make important contributions to seismic hazard away from fault-based sources and where knowledge of recurrence and magnitude is not sufficient for use in hazard studies. Recent developments in adaptive smoothing methods and statistical tests for evaluating and comparing rate models prompt us to investigate the appropriateness of adaptive smoothing for the ASHMs. We develop smoothed seismicity models for Alaska using fixed and adaptive smoothing methods and compare the resulting models by calculating and evaluating the joint likelihood test. We use the earthquake catalog, and associated completeness levels, developed for the 2007 ASHM to produce fixed-bandwidth-smoothed models with smoothing distances varying from 10 to 100 km and adaptively smoothed models. Adaptive smoothing follows the method of Helmstetter et al. and defines a unique smoothing distance for each earthquake epicenter from the distance to the nth nearest neighbor. The consequence of the adaptive smoothing methods is to reduce smoothing distances, causing locally increased seismicity rates, where seismicity rates are high and to increase smoothing distances where seismicity is sparse. We follow guidance from previous studies to optimize the neighbor number (n-value) by comparing model likelihood values, which estimate the likelihood that the observed earthquake epicenters from the recent catalog are derived from the smoothed rate models. We compare likelihood

  19. Newton's method applied to finite-difference approximations for the steady-state compressible Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Bailey, Harry E.; Beam, Richard M.

    1991-01-01

    Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.

  20. A majorized Newton-CG augmented Lagrangian-based finite element method for 3D restoration of geological models

    NASA Astrophysics Data System (ADS)

    Tang, Peipei; Wang, Chengjing; Dai, Xiaoxia

    2016-04-01

    In this paper, we propose a majorized Newton-CG augmented Lagrangian-based finite element method for 3D elastic frictionless contact problems. In this scheme, we discretize the restoration problem via the finite element method and reformulate it to a constrained optimization problem. Then we apply the majorized Newton-CG augmented Lagrangian method to solve the optimization problem, which is very suitable for the ill-conditioned case. Numerical results demonstrate that the proposed method is a very efficient algorithm for various large-scale 3D restorations of geological models, especially for the restoration of geological models with complicated faults.

  1. REGIONALLY SMOOTHED META-ANALYSIS METHODS FOR GWAS DATASETS

    PubMed Central

    Begum, Ferdouse; Sharker, Monir H.; Sherman, Stephanie L.; Tseng, George C.; Feingold, Eleanor

    2015-01-01

    Genome-wide association studies (GWAS) are proven tools for finding disease genes, but it is often necessary to combine many cohorts into a meta-analysis to detect statistically significant genetic effects. Often the component studies are performed by different investigators on different populations, using different chips with minimal SNPs overlap. In some cases, raw data are not available for imputation so that only the genotyped SNP results can be used in meta-analysis. Even when SNP sets are comparable, different cohorts may have peak association signals at different SNPs within the same gene due to population differences in linkage disequilibrium or environmental interactions. We hypothesize that the power to detect statistical signals in these situations will improve by using a method that simultaneously meta-analyzes and smooths the signal over nearby markers. In this study we propose regionally smoothed meta-analysis (RSM) methods and compare their performance on real and simulated data. PMID:26707090

  2. Smoothed particle hydrodynamics method from a large eddy simulation perspective

    NASA Astrophysics Data System (ADS)

    Di Mascio, A.; Antuono, M.; Colagrossi, A.; Marrone, S.

    2017-03-01

    The Smoothed Particle Hydrodynamics (SPH) method, often used for the modelling of the Navier-Stokes equations by a meshless Lagrangian approach, is revisited from the point of view of Large Eddy Simulation (LES). To this aim, the LES filtering procedure is recast in a Lagrangian framework by defining a filter that moves with the positions of the fluid particles at the filtered velocity. It is shown that the SPH smoothing procedure can be reinterpreted as a sort of LES Lagrangian filtering, and that, besides the terms coming from the LES convolution, additional contributions (never accounted for in the SPH literature) appear in the equations when formulated in a filtered fashion. Appropriate closure formulas are derived for the additional terms and a preliminary numerical test is provided to show the main features of the proposed LES-SPH model.

  3. Systems identification using a modified Newton-Raphson method: A FORTRAN program

    NASA Technical Reports Server (NTRS)

    Taylor, L. W., Jr.; Iliff, K. W.

    1972-01-01

    A FORTRAN program is offered which computes a maximum likelihood estimate of the parameters of any linear, constant coefficient, state space model. For the case considered, the maximum likelihood estimate can be identical to that which minimizes simultaneously the weighted mean square difference between the computed and measured response of a system and the weighted square of the difference between the estimated and a priori parameter values. A modified Newton-Raphson or quasilinearization method is used to perform the minimization which typically requires several iterations. A starting technique is used which insures convergence for any initial values of the unknown parameters. The program and its operation are described in sufficient detail to enable the user to apply the program to his particular problem with a minimum of difficulty.

  4. Preconditioning strategies for nonlinear conjugate gradient methods, based on quasi-Newton updates

    NASA Astrophysics Data System (ADS)

    Andrea, Caliciotti; Giovanni, Fasano; Massimo, Roma

    2016-10-01

    This paper reports two proposals of possible preconditioners for the Nonlinear Conjugate Gradient (NCG) method, in large scale unconstrained optimization. On one hand, the common idea of our preconditioners is inspired to L-BFGS quasi-Newton updates, on the other hand we aim at explicitly approximating in some sense the inverse of the Hessian matrix. Since we deal with large scale optimization problems, we propose matrix-free approaches where the preconditioners are built using symmetric low-rank updating formulae. Our distinctive new contributions rely on using information on the objective function collected as by-product of the NCG, at previous iterations. Broadly speaking, our first approach exploits the secant equation, in order to impose interpolation conditions on the objective function. In the second proposal we adopt and ad hoc modified-secant approach, in order to possibly guarantee some additional theoretical properties.

  5. Method for smoothing the surface of a protective coating

    DOEpatents

    Sangeeta, D.; Johnson, Curtis Alan; Nelson, Warren Arthur

    2001-01-01

    A method for smoothing the surface of a ceramic-based protective coating which exhibits roughness is disclosed. The method includes the steps of applying a ceramic-based slurry or gel coating to the protective coating surface; heating the slurry/gel coating to remove volatile material; and then further heating the slurry/gel coating to cure the coating and bond it to the underlying protective coating. The slurry/gel coating is often based on yttria-stabilized zirconia, and precursors of an oxide matrix. Related articles of manufacture are also described.

  6. Effectiveness in Learning Newton's Second Law of Motion in Secondary School Physics Using Three Methods of Learning.

    ERIC Educational Resources Information Center

    Geiger, H. Bruce

    Compared were inductive programed, deductive programed, and conventional lecture-question methods of instruction related to Newton's Second Law of Motion on outcome gains including recall of factual information, ability to solve mathematical problems, and retention. Some 266 students in three schools participated and were compared for…

  7. Fracture characterization by hybrid enumerative search and Gauss-Newton least-squares inversion methods

    NASA Astrophysics Data System (ADS)

    Alkharji, Mohammed N.

    Most fracture characterization methods provide a general description of the fracture parameters as part of the reservoirs parameters; the fracture interaction and geometry within the reservoir is given less attention. T-Matrix and Linear Slip effective medium fracture models are implemented to invert the elastic tensor for the parameters and geometries of the fractures within the reservoir. The fracture inverse problem has an ill-posed, overdetermined, underconstrained rank-deficit system of equations. Least-squares inverse methods are used to solve the problem. A good starting initial model for the parameters is a key factor in the reliability of the inversion. Most methods assume that the starting parameters are close to the solution to avoid inaccurate local minimum solutions. The prior knowledge of the fracture parameters and their geometry is not available. We develop a hybrid, enumerative and Gauss-Newton, method that estimates the fracture parameters and geometry from the elastic tensor with no prior knowledge of the initial parameter values. The fracture parameters are separated into two groups. The first group contains the fracture parameters with no prior information, and the second group contains the parameters with known prior information. Different models are generated from the first group parameters by sampling the solution space over a predefined range of possible solutions for each parameter. Each model generated by the first group is fixed and used as a starting model to invert for the second group of parameters using the Gauss-Newton method. The least-squares residual between the observed elastic tensor and the estimated elastic tensor is calculated for each model. The model parameters that yield the least-squares residual corresponds to the correct fracture reservoir parameters and geometry. Two synthetic examples of fractured reservoirs with oil and gas saturations were inverted with no prior information about the fracture properties. The

  8. Arima model and exponential smoothing method: A comparison

    NASA Astrophysics Data System (ADS)

    Wan Ahmad, Wan Kamarul Ariffin; Ahmad, Sabri

    2013-04-01

    This study shows the comparison between Autoregressive Moving Average (ARIMA) model and Exponential Smoothing Method in making a prediction. The comparison is focused on the ability of both methods in making the forecasts with the different number of data sources and the different length of forecasting period. For this purpose, the data from The Price of Crude Palm Oil (RM/tonne), Exchange Rates of Ringgit Malaysia (RM) in comparison to Great Britain Pound (GBP) and also The Price of SMR 20 Rubber Type (cents/kg) with three different time series are used in the comparison process. Then, forecasting accuracy of each model is measured by examinethe prediction error that producedby using Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE), and Mean Absolute deviation (MAD). The study shows that the ARIMA model can produce a better prediction for the long-term forecasting with limited data sources, butcannot produce a better prediction for time series with a narrow range of one point to another as in the time series for Exchange Rates. On the contrary, Exponential Smoothing Method can produce a better forecasting for Exchange Rates that has a narrow range of one point to another for its time series, while itcannot produce a better prediction for a longer forecasting period.

  9. Modeling Electrokinetic Flows by the Smoothed Profile Method

    PubMed Central

    Luo, Xian; Beskok, Ali; Karniadakis, George Em

    2010-01-01

    We propose an efficient modeling method for electrokinetic flows based on the Smoothed Profile Method (SPM) [1–4] and spectral element discretizations. The new method allows for arbitrary differences in the electrical conductivities between the charged surfaces and the the surrounding electrolyte solution. The electrokinetic forces are included into the flow equations so that the Poisson-Boltzmann and electric charge continuity equations are cast into forms suitable for SPM. The method is validated by benchmark problems of electroosmotic flow in straight channels and electrophoresis of charged cylinders. We also present simulation results of electrophoresis of charged microtubules, and show that the simulated electrophoretic mobility and anisotropy agree with the experimental values. PMID:20352076

  10. Low-rank approximations with sparse factors II: Penalized methods with discrete Newton-like iterations

    SciTech Connect

    Zhang, Zhenyue; Zha, Hongyuan; Simon, Horst

    2006-07-31

    In this paper, we developed numerical algorithms for computing sparse low-rank approximations of matrices, and we also provided a detailed error analysis of the proposed algorithms together with some numerical experiments. The low-rank approximations are constructed in a certain factored form with the degree of sparsity of the factors controlled by some user-specified parameters. In this paper, we cast the sparse low-rank approximation problem in the framework of penalized optimization problems. We discuss various approximation schemes for the penalized optimization problem which are more amenable to numerical computations. We also include some analysis to show the relations between the original optimization problem and the reduced one. We then develop a globally convergent discrete Newton-like iterative method for solving the approximate penalized optimization problems. We also compare the reconstruction errors of the sparse low-rank approximations computed by our new methods with those obtained using the methods in the earlier paper and several other existing methods for computing sparse low-rank approximations. Numerical examples show that the penalized methods are more robust and produce approximations with factors which have fewer columns and are sparser.

  11. Smoothing Forecasting Methods for Academic Library Circulations: An Evaluation and Recommendation.

    ERIC Educational Resources Information Center

    Brooks, Terrence A.; Forys, John W., Jr.

    1986-01-01

    Circulation time-series data from 50 midwest academic libraries were used to test 110 variants of 8 smoothing forecasting methods. Data and methodologies and illustrations of two recommended methods--the single exponential smoothing method and Brown's one-parameter linear exponential smoothing method--are given. Eight references are cited. (EJS)

  12. Employing a Monte Carlo algorithm in Newton-type methods for restricted maximum likelihood estimation of genetic parameters.

    PubMed

    Matilainen, Kaarina; Mäntysaari, Esa A; Lidauer, Martin H; Strandén, Ismo; Thompson, Robin

    2013-01-01

    Estimation of variance components by Monte Carlo (MC) expectation maximization (EM) restricted maximum likelihood (REML) is computationally efficient for large data sets and complex linear mixed effects models. However, efficiency may be lost due to the need for a large number of iterations of the EM algorithm. To decrease the computing time we explored the use of faster converging Newton-type algorithms within MC REML implementations. The implemented algorithms were: MC Newton-Raphson (NR), where the information matrix was generated via sampling; MC average information(AI), where the information was computed as an average of observed and expected information; and MC Broyden's method, where the zero of the gradient was searched using a quasi-Newton-type algorithm. Performance of these algorithms was evaluated using simulated data. The final estimates were in good agreement with corresponding analytical ones. MC NR REML and MC AI REML enhanced convergence compared to MC EM REML and gave standard errors for the estimates as a by-product. MC NR REML required a larger number of MC samples, while each MC AI REML iteration demanded extra solving of mixed model equations by the number of parameters to be estimated. MC Broyden's method required the largest number of MC samples with our small data and did not give standard errors for the parameters directly. We studied the performance of three different convergence criteria for the MC AI REML algorithm. Our results indicate the importance of defining a suitable convergence criterion and critical value in order to obtain an efficient Newton-type method utilizing a MC algorithm. Overall, use of a MC algorithm with Newton-type methods proved feasible and the results encourage testing of these methods with different kinds of large-scale problem settings.

  13. General purpose nonlinear system solver based on Newton-Krylov method.

    SciTech Connect

    2013-12-01

    KINSOL is part of a software family called SUNDIALS: SUite of Nonlinear and Differential/Algebraic equation Solvers [1]. KINSOL is a general-purpose nonlinear system solver based on Newton-Krylov and fixed-point solver technologies [2].

  14. Multi-Focusing Procedure based on the Inexact-Newton Method for Electromagnetic Subsurface Prospecting

    NASA Astrophysics Data System (ADS)

    Salucci, Marco; Oliveri, Giacomo; Massa, Andrea; Randazzo, Andrea; Pastorino, Matteo

    2014-05-01

    Ground penetrating radars (GPRs) are key instruments for subsurface monitoring and imaging. They can be used in different applicative fields, e.g., for the assessment of the structural stability of concrete structures and for the detection of targets buried inside inaccessible materials. In this framework, imaging systems based on the solution of the underlying inverse electromagnetic scattering problem have been acquiring an ever growing interest in the scientific community. In fact, they are able - at least in principle - to provide a quantitative reconstruction of the distributions of the dielectric properties (e.g., the dielectric permittivity and the electric conductivity) of the investigated scenario. Although good results have been obtained in recent years, there is still the need of further research, especially concerning the development of inversion procedure able to deal with the limitations arising from the non-linearity and ill-posedness of the underlying electromagnetic imaging formulation. In this work, a novel electromagnetic inverse scattering method is proposed for the reconstruction of shallow buried objects. The inversion procedure is based on the combination of different imaging modalities. In particular, an iterative multi-scaling approach [1] is adopted for focusing the reconstruction only on limited subdomains of the original investigation region. The data inversion is performed by applying an inexact-Newton method (which exhibits very good regularization properties) within the second-order Born approximation [2]. The use of this approximation allows a reduction of the problem unknowns and a mitigation of the nonlinear effects. The proposed approach has been validated by means of several numerical simulations. In particular, the reconstruction performances have been evaluated in terms of accuracy, robustness, noise levels, and computational efficiency, with particular emphasis on the comparisons with the results obtained by using the standard

  15. A Newton method with adaptive finite elements for solving phase-change problems with natural convection

    NASA Astrophysics Data System (ADS)

    Danaila, Ionut; Moglan, Raluca; Hecht, Frédéric; Le Masson, Stéphane

    2014-10-01

    We present a new numerical system using finite elements with mesh adaptivity for the simulation of solid-liquid phase change systems. In the liquid phase, the natural convection flow is simulated by solving the incompressible Navier-Stokes equations with Boussinesq approximation. A variable viscosity model allows the velocity to progressively vanish in the solid phase, through an intermediate mushy region. The phase change is modeled by introducing an implicit enthalpy source term in the heat equation. The final system of equations describing the liquid-solid system by a single domain approach is solved using a Newton iterative algorithm. The space discretization is based on a P2-P1 Taylor-Hood finite elements and mesh adaptivity by metric control is used to accurately track the solid-liquid interface or the density inversion interface for water flows. The numerical method is validated against classical benchmarks that progressively add strong non-linearities in the system of equations: natural convection of air, natural convection of water, melting of a phase-change material and water freezing. Very good agreement with experimental data is obtained for each test case, proving the capability of the method to deal with both melting and solidification problems with convection. The presented numerical method is easy to implement using FreeFem++ software using a syntax close to the mathematical formulation.

  16. Recovery Discontinuous Galerkin Jacobian-free Newton-Krylov Method for all-speed flows

    SciTech Connect

    HyeongKae Park; Robert Nourgaliev; Vincent Mousseau; Dana Knoll

    2008-07-01

    There is an increasing interest to develop the next generation simulation tools for the advanced nuclear energy systems. These tools will utilize the state-of-art numerical algorithms and computer science technology in order to maximize the predictive capability, support advanced reactor designs, reduce uncertainty and increase safety margins. In analyzing nuclear energy systems, we are interested in compressible low-Mach number, high heat flux flows with a wide range of Re, Ra, and Pr numbers. Under these conditions, the focus is placed on turbulent heat transfer, in contrast to other industries whose main interest is in capturing turbulent mixing. Our objective is to develop singlepoint turbulence closure models for large-scale engineering CFD code, using Direct Numerical Simulation (DNS) or Large Eddy Simulation (LES) tools, requireing very accurate and efficient numerical algorithms. The focus of this work is placed on fully-implicit, high-order spatiotemporal discretization based on the discontinuous Galerkin method solving the conservative form of the compressible Navier-Stokes equations. The method utilizes a local reconstruction procedure derived from weak formulation of the problem, which is inspired by the recovery diffusion flux algorithm of van Leer and Nomura [?] and by the piecewise parabolic reconstruction [?] in the finite volume method. The developed methodology is integrated into the Jacobianfree Newton-Krylov framework [?] to allow a fully-implicit solution of the problem.

  17. A convergence rates result for an iteratively regularized Gauss-Newton-Halley method in Banach space

    NASA Astrophysics Data System (ADS)

    Kaltenbacher, B.

    2015-01-01

    The use of second order information on the forward operator often comes at a very moderate additional computational price in the context of parameter identification problems for differential equation models. On the other hand the use of general (non-Hilbert) Banach spaces has recently found much interest due to its usefulness in many applications. This motivates us to extend the second order method from Kaltenbacher (2014 Numer. Math. at press), (see also Hettlich and Rundell 2000 SIAM J. Numer. Anal. 37 587620) to a Banach space setting and analyze its convergence. We here show rates results for a particular source condition and different exponents in the formulation of Tikhonov regularization in each step. This includes a complementary result on the (first order) iteratively regularized Gauss-Newton method in case of a one-homogeneous data misfit term, which corresponds to exact penalization. The results clearly show the possible advantages of using second order information, which get most pronounced in this exact penalization case. Numerical simulations for an inverse source problem for a nonlinear elliptic PDE illustrate the theoretical findings.

  18. On the convergence of Newton-type methods under mild differentiability conditions

    NASA Astrophysics Data System (ADS)

    Argyros, Ioannis; Hilout, Saïd

    2009-12-01

    We introduce the new idea of recurrent functions to provide a new semilocal convergence analysis for Newton-type methods, under mild differentiability conditions. It turns out that our sufficient convergence conditions are weaker, and the error bounds are tighter than in earlier studies in some interesting cases (Chen, Ann Inst Stat Math 42:387-401, 1990; Chen, Numer Funct Anal Optim 10:37-48, 1989; Cianciaruso, Numer Funct Anal Optim 24:713-723, 2003; Cianciaruso, Nonlinear Funct Anal Appl 2009; Dennis 1971; Deuflhard 2004; Deuflhard, SIAM J Numer Anal 16:1-10, 1979; Gutiérrez, J Comput Appl Math 79:131-145, 1997; Hernández, J Optim Theory Appl 109:631-648, 2001; Hernández, J Comput Appl Math 115:245-254, 2000; Huang, J Comput Appl Math 47:211-217, 1993; Kantorovich 1982; Miel, Numer Math 33:391-396, 1979; Miel, Math Comput 34:185-202, 1980; Moret, Computing 33:65-73, 1984; Potra, Libertas Mathematica 5:71-84, 1985; Rheinboldt, SIAM J Numer Anal 5:42-63, 1968; Yamamoto, Numer Math 51: 545-557, 1987; Zabrejko, Numer Funct Anal Optim 9:671-684, 1987; Zinc̆ko 1963). Applications and numerical examples, involving a nonlinear integral equation of Chandrasekhar-type, and a differential equation are also provided in this study.

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

    SciTech Connect

    HyeongKae Park; Robert Nourgaliev; Vincent Mousseau; Dana Knoll

    2008-07-01

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

  20. Newton-Krylov-Schwarz methods for aerodynamics problems : compressible and incompressible flows on unstructured grids.

    SciTech Connect

    Kaushik, D. K.; Keyes, D. E.; Smith, B. F.

    1999-02-24

    We review and extend to the compressible regime an earlier parallelization of an implicit incompressible unstructured Euler code [9], and solve for flow over an M6 wing in subsonic, transonic, and supersonic regimes. While the parallelization philosophy of the compressible case is identical to the incompressible, we focus here on the nonlinear and linear convergence rates, which vary in different physical regimes, and on comparing the performance of currently important computational platforms. Multiple-scale problems should be marched out at desired accuracy limits, and not held hostage to often more stringent explicit stability limits. In the context of inviscid aerodynamics, this means evolving transient computations on the scale of the convective transit time, rather than the acoustic transit time, or solving steady-state problems with local CFL numbers approaching infinity. Whether time-accurate or steady, we employ Newton's method on each (pseudo-) timestep. The coupling of analysis with design in aerodynamic practice is another motivation for implicitness. Design processes that make use of sensitivity derivatives and the Hessian matrix require operations with the Jacobian matrix of the state constraints (i.e., of the governing PDE system); if the Jacobian is available for design, it may be employed with advantage in a nonlinearly implicit analysis, as well.

  1. Rapid springback compensation for age forming based on quasi Newton method

    NASA Astrophysics Data System (ADS)

    Xiong, Wei; Gan, Zhong; Xiong, Shipeng; Xia, Yushan

    2014-05-01

    Iterative methods based on finite element simulation are effective approaches to design mold shape to compensate springback in sheet metal forming. However, convergence rate of iterative methods is difficult to improve greatly. To increase the springback compensate speed of designing age forming mold, process of calculating springback for a certain mold with finite element method is analyzed. Springback compensation is abstracted as finding a solution for a set of nonlinear functions and a springback compensation algorithm is presented on the basis of quasi Newton method. The accuracy of algorithm is verified by developing an ABAQUS secondary development program with MATLAB. Three rectangular integrated panels of dimensions 710 mm ×750 mm integrated panels with intersected ribs of 10 mm are selected to perform case studies. The algorithm is used to compute mold contours for the panels with cylinder, sphere and saddle contours respectively and it takes 57%, 22% and 33% iterations as compared to that of displacement adjustment (DA) method. At the end of iterations, maximum deviations on the three panels are 0.618 4 mm, 0.624 1 mm and 0.342 0 mm that are smaller than the deviations determined by DA method (0.740 8 mm, 0.740 8 mm and 0.713 7 mm respectively). In following experimental verification, mold contour for another integrated panel with 400 mm×380 mm size is designed by the algorithm. Then the panel is age formed in an autoclave and measured by a three dimensional digital measurement devise. Deviation between measuring results and the panel's design contour is less than 1 mm. Finally, the iterations with different mesh sizes (40 mm, 35 mm, 30 mm, 25 mm, 20 mm) in finite element models are compared and found no considerable difference. Another possible compensation method, Broyden-Fletcher-Shanmo method, is also presented based on the solving nonlinear functions idea. The Broyden-Fletcher-Shanmo method is employed to compute mold contour for the second panel

  2. Convergence of the gradient projection method and Newton's method as applied to optimization problems constrained by intersection of a spherical surface and a convex closed set

    NASA Astrophysics Data System (ADS)

    Chernyaev, Yu. A.

    2016-10-01

    The gradient projection method and Newton's method are generalized to the case of nonconvex constraint sets representing the set-theoretic intersection of a spherical surface with a convex closed set. Necessary extremum conditions are examined, and the convergence of the methods is analyzed.

  3. Numerical performance of half-sweep SOR method for solving second order composite closed Newton-Cotes system

    NASA Astrophysics Data System (ADS)

    Muthuvalu, Mohana Sundaram; Aruchunan, Elayaraja; Akhir, Mohd Kamalrulzaman Md; Sulaiman, Jumat; Karim, Samsul Ariffin Abdul

    2014-10-01

    In this paper, application of the Half-Sweep Successive Over-Relaxation (HSSOR) iterative method is extended by solving second order composite closed Newton-Cotes quadrature (2-CCNC) system. The performance of HSSOR method in solving 2-CCNC system is comparatively studied by their application on linear Fredholm integral equations of the second kind. The derivation and implementation of the method are discussed. In addition, numerical results by solving two test problems are included and compared with the standard Gauss-Seidel (GS) and Successive Over-Relaxation (SOR) methods. Numerical results demonstrate that HSSOR method is an efficient method among the tested methods.

  4. Newton's Apple

    ERIC Educational Resources Information Center

    Hendry, Archibald W.

    2007-01-01

    Isaac Newton may have seen an apple fall, but it was Robert Hooke who had a better idea of where it would land. No one really knows whether or not Isaac Newton actually saw an apple fall in his garden. Supposedly it took place in 1666, but it was a tale he told in his old age more than 60 years later, a time when his memory was failing and his…

  5. One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure

    NASA Technical Reports Server (NTRS)

    Amar, Adam J.; Blackwell, Ben F.; Edwards, Jack R.

    2007-01-01

    The development and verification of a one-dimensional material thermal response code with ablation is presented. The implicit time integrator, control volume finite element spatial discretization, and Newton's method for nonlinear iteration on the entire system of residual equations have been implemented and verified for the thermochemical ablation of internally decomposing materials. This study is a continuation of the work presented in "One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure" (AIAA-2006-2910), which described the derivation, implementation, and verification of the constant density solid energy equation terms and boundary conditions. The present study extends the model to decomposing materials including decomposition kinetics, pyrolysis gas flow through the porous char layer, and a mixture (solid and gas) energy equation. Verification results are presented for the thermochemical ablation of a carbon-phenolic ablator which involves the solution of the entire system of governing equations.

  6. Efficient recovery-based error estimation for the smoothed finite element method for smooth and singular linear elasticity

    NASA Astrophysics Data System (ADS)

    González-Estrada, Octavio A.; Natarajan, Sundararajan; Ródenas, Juan José; Nguyen-Xuan, Hung; Bordas, Stéphane P. A.

    2013-07-01

    An error control technique aimed to assess the quality of smoothed finite element approximations is presented in this paper. Finite element techniques based on strain smoothing appeared in 2007 were shown to provide significant advantages compared to conventional finite element approximations. In particular, a widely cited strength of such methods is improved accuracy for the same computational cost. Yet, few attempts have been made to directly assess the quality of the results obtained during the simulation by evaluating an estimate of the discretization error. Here we propose a recovery type error estimator based on an enhanced recovery technique. The salient features of the recovery are: enforcement of local equilibrium and, for singular problems a "smooth + singular" decomposition of the recovered stress. We evaluate the proposed estimator on a number of test cases from linear elastic structural mechanics and obtain efficient error estimations whose effectivities, both at local and global levels, are improved compared to recovery procedures not implementing these features.

  7. Weighted Wilcoxon-type Smoothly Clipped Absolute Deviation Method

    PubMed Central

    Wang, Lan; Li, Runze

    2009-01-01

    Summary Shrinkage-type variable selection procedures have recently seen increasing applications in biomedical research. However, their performance can be adversely influenced by outliers in either the response or the covariate space. This paper proposes a weighted Wilcoxon-type smoothly clipped absolute deviation (WW-SCAD) method, which deals with robust variable selection and robust estimation simultaneously. The new procedure can be conveniently implemented with the statistical software R. We establish that the WW-SCAD correctly identifies the set of zero coefficients with probability approaching one and estimates the nonzero coefficients with the rate n−1/2. Moreover, with appropriately chosen weights the WW-SCAD is robust with respect to outliers in both the x and y directions. The important special case with constant weights yields an oracle-type estimator with high efficiency at the presence of heavier-tailed random errors. The robustness of the WW-SCAD is partly justified by its asymptotic performance under local shrinking contamination. We propose a BIC-type tuning parameter selector for the WW-SCAD. The performance of the WW-SCAD is demonstrated via simulations and by an application to a study that investigates the effects of personal characteristics and dietary factors on plasma beta-carotene level. PMID:18647294

  8. Evaluation of Two New Smoothing Methods in Equating: The Cubic B-Spline Presmoothing Method and the Direct Presmoothing Method

    ERIC Educational Resources Information Center

    Cui, Zhongmin; Kolen, Michael J.

    2009-01-01

    This article considers two new smoothing methods in equipercentile equating, the cubic B-spline presmoothing method and the direct presmoothing method. Using a simulation study, these two methods are compared with established methods, the beta-4 method, the polynomial loglinear method, and the cubic spline postsmoothing method, under three sample…

  9. Immersed Boundary Smooth Extension (IBSE): A high-order method for solving incompressible flows in arbitrary smooth domains

    NASA Astrophysics Data System (ADS)

    Stein, David B.; Guy, Robert D.; Thomases, Becca

    2017-04-01

    The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet for fluid problems it only achieves first-order spatial accuracy near embedded boundaries for the velocity field and fails to converge pointwise for elements of the stress tensor. In a previous work we introduced the Immersed Boundary Smooth Extension (IBSE) method, a variation of the IB method that achieves high-order accuracy for elliptic PDE by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations. In this work, we extend the IBSE method to allow for the imposition of a divergence constraint, and demonstrate high-order convergence for the Stokes and incompressible Navier-Stokes equations: up to third-order pointwise convergence for the velocity field, and second-order pointwise convergence for all elements of the stress tensor. The method is flexible to the underlying discretization: we demonstrate solutions produced using both a Fourier spectral discretization and a standard second-order finite-difference discretization.

  10. Stochastic quasi-Newton method: Application to minimal model for proteins

    NASA Astrophysics Data System (ADS)

    Chau, C. D.; Sevink, G. J. A.; Fraaije, J. G. E. M.

    2011-01-01

    Knowledge of protein folding pathways and inherent structures is of utmost importance for our understanding of biological function, including the rational design of drugs and future treatments against protein misfolds. Computational approaches have now reached the stage where they can assess folding properties and provide data that is complementary to or even inaccessible by experimental imaging techniques. Minimal models of proteins, which make possible the simulation of protein folding dynamics by (systematic) coarse graining, have provided understanding in terms of descriptors for folding, folding kinetics, and folded states. Here we focus on the efficiency of equilibration on the coarse-grained level. In particular, we applied a new regularized stochastic quasi-Newton (S-QN) method, developed for accelerated configurational space sampling while maintaining thermodynamic consistency, to analyze the folding pathway and inherent structures of a selected protein, where regularization was introduced to improve stability. The adaptive compound mobility matrix B in S-QN, determined by a factorized secant update, gives rise to an automated scaling of all modes in the protein, in particular an acceleration of protein domain dynamics or principal modes and a slowing down of fast modes or “soft” bond constraints, similar to lincs/shake algorithms, when compared to conventional Langevin dynamics. We used and analyzed a two-step strategy. Owing to the enhanced sampling properties of S-QN and increased barrier crossing at high temperatures (in reduced units), a hierarchy of inherent protein structures is first efficiently determined by applying S-QN for a single initial structure and T=1>Tθ, where Tθ is the collapse temperature. Second, S-QN simulations for several initial structures at very low temperature (T=0.01

  11. Impact of beam smoothing method on direct drive target performance for the NIF

    SciTech Connect

    Rothenberg, J.E.; Weber, S.V.

    1997-01-01

    The impact of smoothing method on the performance of a direct drive target is modeled and examined in terms of its 1-mode spectrum. In particular, two classes of smoothing methods are compared, smoothing by spectral dispersion (SSD) and the induced spatial incoherence (ISI) method. It is found that SSD using sinusoidal phase modulation (FM) results in poor smoothing at low 1-modes and therefore inferior target performance at both peak velocity and ignition. This disparity is most notable if the effective imprinting integration time of the target is small. However, using SSD with more generalized phase modulation can result in smoothing at low l-modes which is identical to that obtained with ISI. For either smoothing method, the calculations indicate that at peak velocity the surface perturbations are about 100 times larger than that which leads to nonlinear hydrodynamics. Modeling of the hydrodynamic nonlinearity shows that saturation can reduce the amplified nonuniformities to the level required to achieve ignition for either smoothing method. The low l- mode behavior at ignition is found to be strongly dependent on the induced divergence of the smoothing method. For the NIF parameters the target performance asymptotes for smoothing divergence larger than {approximately}100 {mu}rad.

  12. Calculation of 10 MV x-ray spectra emitted by a medical linear accelerator using the BFGS quasi-Newton method.

    PubMed

    Shimozato, T; Tabushi, K; Kitoh, S; Shiota, Y; Hirayama, C; Suzuki, S

    2007-01-21

    To calculate photon spectra for a 10 MV x-ray beam emitted by a medical linear accelerator, we performed numerical analysis using the aluminium transmission data obtained along the central axis of the beam under the narrow beam condition corresponding to a 3x3 cm2 field at a 100 cm distance from the source. We used the BFGS quasi-Newton method based on a general nonlinear optimization technique for the numerical analysis. The attenuation coefficients, aluminium thicknesses and measured transmission data are necessary inputs for the numerical analysis. The calculated x-ray spectrum shape was smooth in the lower to higher energy regions without any angular components. The x-ray spectrum acquired by the employed method was evaluated by comparing the measurements along the central axis percentage depth dose in a water phantom and by a Monte Carlo simulation code, the electron gamma shower code. The values of the calculated percentage depth doses for a 10x10 cm2 field at a 100 cm source-to-surface distance in a water phantom were obtained using the same geometry settings as those of the water phantom measurement. The differences in the measured and calculated values were less than +/-1.0% for a broad region from the shallow part near the surface to deep parts of up to 25 cm in the water phantom.

  13. A solution to the Navier-Stokes equations based upon the Newton Kantorovich method

    NASA Technical Reports Server (NTRS)

    Davis, J. E.; Gabrielsen, R. E.; Mehta, U. B.

    1977-01-01

    An implicit finite difference scheme based on the Newton-Kantorovich technique was developed for the numerical solution of the nonsteady, incompressible, two-dimensional Navier-Stokes equations in conservation-law form. The algorithm was second-order-time accurate, noniterative with regard to the nonlinear terms in the vorticity transport equation except at the earliest few time steps, and spatially factored. Numerical results were obtained with the technique for a circular cylinder at Reynolds number 15. Results indicate that the technique is in excellent agreement with other numerical techniques for all geometries and Reynolds numbers investigated, and indicates a potential for significant reduction in computation time over current iterative techniques.

  14. Suppression of stochastic pulsation in laser-plasma interaction by smoothing methods

    NASA Astrophysics Data System (ADS)

    Hora, Heinrich; Aydin, Meral

    1992-04-01

    The control of the very complex behavior of a plasma with laser interaction by smoothing with induced spatial incoherence or other methods was related to improving the lateral uniformity of the irradiation. While this is important, it is shown from numerical hydrodynamic studies that the very strong temporal pulsation (stuttering) will mostly be suppressed by these smoothing methods too.

  15. Suppression of stochastic pulsation in laser-plasma interaction by smoothing methods

    SciTech Connect

    Hora, H. ); Aydin, M. )

    1992-04-15

    The control of the very complex behavior of a plasma with laser interaction by smoothing with induced spatial incoherence or other methods was related to improving the lateral uniformity of the irradiation. While this is important, it is shown from numerical hydrodynamic studies that the very strong temporal pulsation (stuttering) will mostly be suppressed by these smoothing methods too.

  16. Deconvolution of positron annihilation coincidence Doppler broadening spectra using an iterative projected Newton method with non-negativity constraints

    NASA Astrophysics Data System (ADS)

    Ho, K. F.; Beling, C. D.; Fung, S.; Cheng, Vincent K. W.; Ng, Michael K.; Yip, A. M.

    2003-11-01

    A generalized least-square method with Tikonov-Miller regularization and non-negativity constraints has been developed for deconvoluting two-dimensional coincidence Doppler broadening spectroscopy (CDBS) spectra. A projected Newton algorithm is employed to solve the generalized least-square problem. The algorithm has been tested on Monte Carlo generated spectra to find the best regularization parameters for different simulated experimental conditions. Good retrieval of the underlying positron-electron momentum distributions in the low momentum region is demonstrated. The algorithm has been successfully used to deconvolute experimental CDBS data from aluminum.

  17. Lattice-Boltzmann method combined with smoothed-profile method for particulate suspensions

    NASA Astrophysics Data System (ADS)

    Jafari, Saeed; Yamamoto, Ryoichi; Rahnama, Mohamad

    2011-02-01

    We developed a simulation scheme based on the coupling of the lattice-Boltzmann method with the smoothed-profile method (SPM) to predict the dynamic behavior of colloidal dispersions. The SPM provides a coupling scheme between continuum fluid dynamics and rigid-body dynamics through a smoothed profile of the fluid-particle interface. In this approach, the flow is computed on fixed Eulerian grids which are also used for the particles. Owing to the use of the same grids for simulation of fluid flow and particles, this method is highly efficient. Furthermore, an external boundary is used to impose the no-slip boundary condition at the fluid-particle interface. In addition, the operations in the present method are local; it can be easily programmed for parallel machines. The methodology is validated by comparing with previously published data.

  18. Lattice-Boltzmann method combined with smoothed-profile method for particulate suspensions.

    PubMed

    Jafari, Saeed; Yamamoto, Ryoichi; Rahnama, Mohamad

    2011-02-01

    We developed a simulation scheme based on the coupling of the lattice-Boltzmann method with the smoothed-profile method (SPM) to predict the dynamic behavior of colloidal dispersions. The SPM provides a coupling scheme between continuum fluid dynamics and rigid-body dynamics through a smoothed profile of the fluid-particle interface. In this approach, the flow is computed on fixed Eulerian grids which are also used for the particles. Owing to the use of the same grids for simulation of fluid flow and particles, this method is highly efficient. Furthermore, an external boundary is used to impose the no-slip boundary condition at the fluid-particle interface. In addition, the operations in the present method are local; it can be easily programmed for parallel machines. The methodology is validated by comparing with previously published data.

  19. Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

    NASA Astrophysics Data System (ADS)

    Yang, Haijian; Sun, Shuyu; Yang, Chao

    2017-03-01

    Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.

  20. Electro-optical deflectors as a method of beam smoothing for Inertial Confinement Fusion

    SciTech Connect

    Rothenberg, J.E.

    1997-01-01

    The electro-optic deflector is analyzed and compared to smoothing by spectral dispersion for efficacy as a beam smoothing method for ICF. It is found that the electro-optic deflector is inherently somewhat less efficient when compared either on the basis of equal peak phase modulation or equal generated bandwidth.

  1. SKRYN: A fast semismooth-Krylov-Newton method for controlling Ising spin systems

    NASA Astrophysics Data System (ADS)

    Ciaramella, G.; Borzì, A.

    2015-05-01

    The modeling and control of Ising spin systems is of fundamental importance in NMR spectroscopy applications. In this paper, two computer packages, ReHaG and SKRYN, are presented. Their purpose is to set-up and solve quantum optimal control problems governed by the Liouville master equation modeling Ising spin-1/2 systems with pointwise control constraints. In particular, the MATLAB package ReHaG allows to compute a real matrix representation of the master equation. The MATLAB package SKRYN implements a new strategy resulting in a globalized semismooth matrix-free Krylov-Newton scheme. To discretize the real representation of the Liouville master equation, a norm-preserving modified Crank-Nicolson scheme is used. Results of numerical experiments demonstrate that the SKRYN code is able to provide fast and accurate solutions to the Ising spin quantum optimization problem.

  2. An adaptive segment method for smoothing lidar signal based on noise estimation

    NASA Astrophysics Data System (ADS)

    Wang, Yuzhao; Luo, Pingping

    2014-10-01

    An adaptive segmentation smoothing method (ASSM) is introduced in the paper to smooth the signal and suppress the noise. In the ASSM, the noise is defined as the 3σ of the background signal. An integer number N is defined for finding the changing positions in the signal curve. If the difference of adjacent two points is greater than 3Nσ, the position is recorded as an end point of the smoothing segment. All the end points detected as above are recorded and the curves between them will be smoothed separately. In the traditional method, the end points of the smoothing windows in the signals are fixed. The ASSM creates changing end points in different signals and the smoothing windows could be set adaptively. The windows are always set as the half of the segmentations and then the average smoothing method will be applied in the segmentations. The Iterative process is required for reducing the end-point aberration effect in the average smoothing method and two or three times are enough. In ASSM, the signals are smoothed in the spacial area nor frequent area, that means the frequent disturbance will be avoided. A lidar echo was simulated in the experimental work. The echo was supposed to be created by a space-born lidar (e.g. CALIOP). And white Gaussian noise was added to the echo to act as the random noise resulted from environment and the detector. The novel method, ASSM, was applied to the noisy echo to filter the noise. In the test, N was set to 3 and the Iteration time is two. The results show that, the signal could be smoothed adaptively by the ASSM, but the N and the Iteration time might be optimized when the ASSM is applied in a different lidar.

  3. An inexact Newton method for fully-coupled solution of the Navier-Stokes equations with heat and mass transport

    SciTech Connect

    Shadid, J.N.; Tuminaro, R.S.; Walker, H.F.

    1997-02-01

    The solution of the governing steady transport equations for momentum, heat and mass transfer in flowing fluids can be very difficult. These difficulties arise from the nonlinear, coupled, nonsymmetric nature of the system of algebraic equations that results from spatial discretization of the PDEs. In this manuscript the authors focus on evaluating a proposed nonlinear solution method based on an inexact Newton method with backtracking. In this context they use a particular spatial discretization based on a pressure stabilized Petrov-Galerkin finite element formulation of the low Mach number Navier-Stokes equations with heat and mass transport. The discussion considers computational efficiency, robustness and some implementation issues related to the proposed nonlinear solution scheme. Computational results are presented for several challenging CFD benchmark problems as well as two large scale 3D flow simulations.

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

    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.

  5. The Enigma of Newton

    ERIC Educational Resources Information Center

    Nunan, E.

    1973-01-01

    Presents a brief biography of Sir Isaac Newton, lists contemporary scientists and scientific developments and discusses Newton's optical research and conceptual position concerning the nature of light. (JR)

  6. An efficient method for correcting the edge artifact due to smoothing.

    PubMed

    Maisog, J M; Chmielowska, J

    1998-01-01

    Spatial smoothing is a common pre-processing step in the analysis of functional brain imaging data. It can increase sensitivity to signals of specific shapes and sizes (Rosenfeld and Kak [1982]: Digital Picture Processing, vol. 2. Orlando, Fla.: Academic; Worsley et al. [1996]: Hum Brain Mapping 4:74-90). Also, some amount of spatial smoothness is required if methods from the theory of Gaussian random fields are to be used (Holmes [1994]: Statistical Issues in Functional Brain Mapping. PhD thesis, University of Glasgow). Smoothing is most often implemented as a convolution of the imaging data with a smoothing kernel, and convolution is most efficiently performed using the Convolution Theorem and the Fast Fourier Transform (Cooley and Tukey [1965]: Math Comput 19:297-301; Priestly [1981]: Spectral Analysis and Time Series. San Diego: Academic; Press et al. [1992]: Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. Cambridge: Cambridge University Press). An undesirable side effect of smoothing is an artifact along the edges of the brain, where brain voxels become smoothed with non-brain voxels. This results in a dark rim which might be mistaken for hypoactivity. In this short methodological paper, we present a method for correcting functional brain images for the edge artifact due to smoothing, while retaining the use of the Convolution Theorem and the Fast Fourier Transform for efficient calculation of convolutions.

  7. Smooth connection method of segment test data in road surface profile measurement

    NASA Astrophysics Data System (ADS)

    Duan, Hu-Ming; Ma, Ying; Shi, Feng; Zhang, Kai-Bin; Xie, Fei

    2011-12-01

    It's reviewed that the measurement system of road surface profile and the calculation method of segment road test data have been introduced. Because of there are sudden vertical steps at the connection points of segment data which will influence the application of road surface data in automotive engineering. So a new smooth connection method of segment test data is proposed which revised the sudden vertical steps connection by the Signal Local Baseline Adjustment (SLBA) method. Besides, there is an actual example which mentioned the detailed process of the smooth connection of segment test data by the SLBA method and the adjusting results at these connection points. The application and calculation results show that the SLBA method is simple and has achieved obvious effect in smooth connection of the segment road test data. The method of SLBA can be widely applied to segment road surface data processing or the long period vibration signal processing.

  8. Smooth connection method of segment test data in road surface profile measurement

    NASA Astrophysics Data System (ADS)

    Duan, Hu-Ming; Ma, Ying; Shi, Feng; Zhang, Kai-Bin; Xie, Fei

    2012-01-01

    It's reviewed that the measurement system of road surface profile and the calculation method of segment road test data have been introduced. Because of there are sudden vertical steps at the connection points of segment data which will influence the application of road surface data in automotive engineering. So a new smooth connection method of segment test data is proposed which revised the sudden vertical steps connection by the Signal Local Baseline Adjustment (SLBA) method. Besides, there is an actual example which mentioned the detailed process of the smooth connection of segment test data by the SLBA method and the adjusting results at these connection points. The application and calculation results show that the SLBA method is simple and has achieved obvious effect in smooth connection of the segment road test data. The method of SLBA can be widely applied to segment road surface data processing or the long period vibration signal processing.

  9. CANM, a program for numerical solution of a system of nonlinear equations using the continuous analog of Newton's method

    NASA Astrophysics Data System (ADS)

    Abrashkevich, Alexander; Puzynin, I. V.

    2004-01-01

    A FORTRAN program is presented which solves a system of nonlinear simultaneous equations using the continuous analog of Newton's method (CANM). The user has the option of either to provide a subroutine which calculates the Jacobian matrix or allow the program to calculate it by a forward-difference approximation. Five iterative schemes using different algorithms of determining adaptive step size of the CANM process are implemented in the program. Program summaryTitle of program: CANM Catalogue number: ADSN Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADSN Program available from: CPC Program Library, Queen's University of Belfast, Northern Ireland Licensing provisions: none Computer for which the program is designed and others on which it has been tested: Computers: IBM RS/6000 Model 320H, SGI Origin2000, SGI Octane, HP 9000/755, Intel Pentium IV PC Installation: Department of Chemistry, University of Toronto, Toronto, Canada Operating systems under which the program has been tested: IRIX64 6.1, 6.4 and 6.5, AIX 3.4, HP-UX 9.01, Linux 2.4.7 Programming language used: FORTRAN 90 Memory required to execute with typical data: depends on the number of nonlinear equations in a system. Test run requires 80 KB No. of bits in distributed program including test data, etc.: 15283 Distribution format: tar gz format No. of lines in distributed program, including test data, etc.: 1794 Peripherals used: line printer, scratch disc store External subprograms used: DGECO and DGESL [1] Keywords: nonlinear equations, Newton's method, continuous analog of Newton's method, continuous parameter, evolutionary differential equation, Euler's method Nature of physical problem: System of nonlinear simultaneous equations F i(x 1,x 2,…,x n)=0,1⩽i⩽n, is numerically solved. It can be written in vector form as F( X)= 0, X∈ Rn, where F : Rn→ Rn is a twice continuously differentiable function with domain and range in n-dimensional Euclidean space. The solutions of such systems of

  10. Comparison of Exponential Smoothing Methods in Forecasting Palm Oil Real Production

    NASA Astrophysics Data System (ADS)

    Siregar, B.; Butar-Butar, I. A.; Rahmat, RF; Andayani, U.; Fahmi, F.

    2017-01-01

    Palm oil has important role for the plantation subsector. Forecasting of the real palm oil production in certain period is needed by plantation companies to maintain their strategic management. This study compared several methods based on exponential smoothing (ES) technique such as single ES, double exponential smoothing holt, triple exponential smoothing, triple exponential smoothing additive and multiplicative to predict the palm oil production. We examined the accuracy of forecasting models of production data and analyzed the characteristics of the models. Programming language R was used with selected constants for double ES (α and β) and triple ES (α, β, and γ) evaluated by the technique of minimizing the root mean squared prediction error (RMSE). Our result showed that triple ES additives had lowest error rate compared to the other models with RMSE of 0.10 with a combination of parameters α = 0.6, β = 0.02, and γ = 0.02.

  11. A high-order Immersed Boundary method for solving fluid problems on arbitrary smooth domains

    NASA Astrophysics Data System (ADS)

    Stein, David; Guy, Robert; Thomases, Becca

    2015-11-01

    We present a robust, flexible, and high-order Immersed Boundary method for solving the equations of fluid motion on domains with smooth boundaries using FFT-based spectral methods. The solution to the PDE is coupled with an equation for a smooth extension of the unknown solution; high-order accuracy is a natural consequence of this additional global regularity. The method retains much of the simplicity of the original Immersed Boundary method, and enables the use of simple implicit and implicit/explicit timestepping schemes to be used to solve a wide range of problems. We show results for the Stokes, Navier-Stokes, and Oldroyd-B equations.

  12. Joint inversion of seismic velocities and source location without rays using the truncated Newton and the adjoint-state method

    NASA Astrophysics Data System (ADS)

    Virieux, J.; Bretaudeau, F.; Metivier, L.; Brossier, R.

    2013-12-01

    Simultaneous inversion of seismic velocities and source parameters have been a long standing challenge in seismology since the first attempts to mitigate trade-off between very different parameters influencing travel-times (Spencer and Gubbins 1980, Pavlis and Booker 1980) since the early development in the 1970s (Aki et al 1976, Aki and Lee 1976, Crosson 1976). There is a strong trade-off between earthquake source positions, initial times and velocities during the tomographic inversion: mitigating these trade-offs is usually carried empirically (Lemeur et al 1997). This procedure is not optimal and may lead to errors in the velocity reconstruction as well as in the source localization. For a better simultaneous estimation of such multi-parametric reconstruction problem, one may take benefit of improved local optimization such as full Newton method where the Hessian influence helps balancing between different physical parameter quantities and improving the coverage at the point of reconstruction. Unfortunately, the computation of the full Hessian operator is not easily computed in large models and with large datasets. Truncated Newton (TCN) is an alternative optimization approach (Métivier et al. 2012) that allows resolution of the normal equation H Δm = - g using a matrix-free conjugate gradient algorithm. It only requires to be able to compute the gradient of the misfit function and Hessian-vector products. Traveltime maps can be computed in the whole domain by numerical modeling (Vidale 1998, Zhao 2004). The gradient and the Hessian-vector products for velocities can be computed without ray-tracing using 1st and 2nd order adjoint-state methods for the cost of 1 and 2 additional modeling step (Plessix 2006, Métivier et al. 2012). Reciprocity allows to compute accurately the gradient and the full Hessian for each coordinates of the sources and for their initial times. Then the resolution of the problem is done through two nested loops. The model update Δm is

  13. Nonequilibrium flows with smooth particle applied mechanics

    SciTech Connect

    Kum, Oyeon

    1995-07-01

    Smooth particle methods are relatively new methods for simulating solid and fluid flows through they have a 20-year history of solving complex hydrodynamic problems in astrophysics, such as colliding planets and stars, for which correct answers are unknown. The results presented in this thesis evaluate the adaptability or fitness of the method for typical hydrocode production problems. For finite hydrodynamic systems, boundary conditions are important. A reflective boundary condition with image particles is a good way to prevent a density anomaly at the boundary and to keep the fluxes continuous there. Boundary values of temperature and velocity can be separately controlled. The gradient algorithm, based on differentiating the smooth particle expression for (uρ) and (Tρ), does not show numerical instabilities for the stress tensor and heat flux vector quantities which require second derivatives in space when Fourier`s heat-flow law and Newton`s viscous force law are used. Smooth particle methods show an interesting parallel linking to them to molecular dynamics. For the inviscid Euler equation, with an isentropic ideal gas equation of state, the smooth particle algorithm generates trajectories isomorphic to those generated by molecular dynamics. The shear moduli were evaluated based on molecular dynamics calculations for the three weighting functions, B spline, Lucy, and Cusp functions. The accuracy and applicability of the methods were estimated by comparing a set of smooth particle Rayleigh-Benard problems, all in the laminar regime, to corresponding highly-accurate grid-based numerical solutions of continuum equations. Both transient and stationary smooth particle solutions reproduce the grid-based data with velocity errors on the order of 5%. The smooth particle method still provides robust solutions at high Rayleigh number where grid-based methods fails.

  14. Generalization of Taylor's theorem and Newton's method via a new family of determinantal interpolation formulas and its applications

    NASA Astrophysics Data System (ADS)

    Kalantari, Bahman

    2000-12-01

    The general form of Taylor's theorem for a function f : K-->K, where K is the real line or the complex plane, gives the formula, f=Pn+Rn, where Pn is the Newton interpolating polynomial computed with respect to a confluent vector of nodes, and Rn is the remainder. Whenever f'[not equal to]0, for each m=2,...,n+1, we describe a "determinantal interpolation formula", f=Pm,n+Rm,n, where Pm,n is a rational function in x and f itself. These formulas play a dual role in the approximation of f or its inverse. For m=2, the formula is Taylor's and for m=3 is a new expansion formula and a Padé approximant. By applying the formulas to Pn, for each m[greater-or-equal, slanted]2, Pm,m-1,...,Pm,m+n-2 is a set of n rational approximations that includes Pn, and may provide a better approximation to f, than Pn. Hence each Taylor polynomial unfolds into an infinite spectrum of rational approximations. The formulas also give an infinite spectrum of rational inverse approximations, as well as a fundamental k-point iteration function Bm(k), for each k[less-than-or-equals, slant]m, defined as the ratio of two determinants that depend on the first m-k derivatives. Application of our formulas have motivated several new results obtained in sequel papers: (i) theoretical analysis of the order of Bm(k), k=1,...,m, proving that it ranges from m to the limiting ratio of generalized Fibonacci numbers of order m; (ii) computational results with the first few members of Bm(k) indicating that they outperform traditional root finding methods, e.g., Newton's; (iii) a novel polynomial rootfinding method requiring only a single input and the evaluation of the sequence of iteration functions Bm(1) at that input. This amounts to the evaluation of special Toeplitz determinants that are also computable via a recursive formula; (iv) a new strategy for general root finding; (v) new formulas for approximation of [pi],e, and other special numbers.

  15. Analysis of vadose zone inhomogeneity toward distinguishing recharge rates: Solving the nonlinear interface problem with Newton method

    NASA Astrophysics Data System (ADS)

    Steward, David R.

    2016-11-01

    Recharge from surface to groundwater is an important component of the hydrological cycle, yet its rate is difficult to quantify. Percolation through two-dimensional circular inhomogeneities in the vadose zone is studied where one soil type is embedded within a uniform background, and nonlinear interface conditions in the quasilinear formulation are solved using Newton's method with the Analytic Element Method. This numerical laboratory identifies detectable variations in pathline and pressure head distributions that manifest due to a shift in recharge rate through in a heterogeneous media. Pathlines either diverge about or converge through coarser and finer grained materials with inverse patterns forming across lower and upper elevations; however, pathline geometry is not significantly altered by recharge. Analysis of pressure head in lower regions near groundwater identifies a new phenomenon: its distribution is not significantly impacted by an inhomogeneity soil type, nor by its placement nor by recharge rate. Another revelation is that pressure head for coarser grained inhomogeneities in upper regions is completely controlled by geometry and conductivity contrasts; a shift in recharge generates a difference Δp that becomes an additive constant with the same value throughout this region. In contrast, shifts in recharge for finer grained inhomogeneities reveal patterns with abrupt variations across their interfaces. Consequently, measurements aimed at detecting shifts in recharge in a heterogeneous vadose zone by deciphering the corresponding patterns of change in pressure head should focus on finer grained inclusions well above a groundwater table.

  16. A new flux conserving Newton's method scheme for the two-dimensional, steady Navier-Stokes equations

    NASA Technical Reports Server (NTRS)

    Scott, James R.; Chang, Sin-Chung

    1993-01-01

    A new numerical method is developed for the solution of the two-dimensional, steady Navier-Stokes equations. The method that is presented differs in significant ways from the established numerical methods for solving the Navier-Stokes equations. The major differences are described. First, the focus of the present method is on satisfying flux conservation in an integral formulation, rather than on simulating conservation laws in their differential form. Second, the present approach provides a unified treatment of the dependent variables and their unknown derivatives. All are treated as unknowns together to be solved for through simulating local and global flux conservation. Third, fluxes are balanced at cell interfaces without the use of interpolation or flux limiters. Fourth, flux conservation is achieved through the use of discrete regions known as conservation elements and solution elements. These elements are not the same as the standard control volumes used in the finite volume method. Fifth, the discrete approximation obtained on each solution element is a functional solution of both the integral and differential form of the Navier-Stokes equations. Finally, the method that is presented is a highly localized approach in which the coupling to nearby cells is only in one direction for each spatial coordinate, and involves only the immediately adjacent cells. A general third-order formulation for the steady, compressible Navier-Stokes equations is presented, and then a Newton's method scheme is developed for the solution of incompressible, low Reynolds number channel flow. It is shown that the Jacobian matrix is nearly block diagonal if the nonlinear system of discrete equations is arranged approximately and a proper pivoting strategy is used. Numerical results are presented for Reynolds numbers of 100, 1000, and 2000. Finally, it is shown that the present scheme can resolve the developing channel flow boundary layer using as few as six to ten cells per channel

  17. A Meshfree Cell-based Smoothed Point Interpolation Method for Solid Mechanics Problems

    SciTech Connect

    Zhang Guiyong; Liu Guirong

    2010-05-21

    In the framework of a weakened weak (W{sup 2}) formulation using a generalized gradient smoothing operation, this paper introduces a novel meshfree cell-based smoothed point interpolation method (CS-PIM) for solid mechanics problems. The W{sup 2} formulation seeks solutions from a normed G space which includes both continuous and discontinuous functions and allows the use of much more types of methods to create shape functions for numerical methods. When PIM shape functions are used, the functions constructed are in general not continuous over the entire problem domain and hence are not compatible. Such an interpolation is not in a traditional H{sup 1} space, but in a G{sup 1} space. By introducing the generalized gradient smoothing operation properly, the requirement on function is now further weakened upon the already weakened requirement for functions in a H{sup 1} space and G{sup 1} space can be viewed as a space of functions with weakened weak (W{sup 2}) requirement on continuity. The cell-based smoothed point interpolation method (CS-PIM) is formulated based on the W{sup 2} formulation, in which displacement field is approximated using the PIM shape functions, which possess the Kronecker delta property facilitating the enforcement of essential boundary conditions [3]. The gradient (strain) field is constructed by the generalized gradient smoothing operation within the cell-based smoothing domains, which are exactly the triangular background cells. A W{sup 2} formulation of generalized smoothed Galerkin (GS-Galerkin) weak form is used to derive the discretized system equations. It was found that the CS-PIM possesses the following attractive properties: (1) It is very easy to implement and works well with the simplest linear triangular mesh without introducing additional degrees of freedom; (2) it is at least linearly conforming; (3) this method is temporally stable and works well for dynamic analysis; (4) it possesses a close-to-exact stiffness, which is much

  18. Fully implicit solutions of the benchmark backward facing step problem using finite element discretization and inexact Newton's method

    SciTech Connect

    McHugh, P.R.; Knoll, D.A.

    1992-01-01

    A fully implicit solution algorithm based on Newton's method is used to solve the steady, incompressible Navier-Stokes and energy equations. An efficiently evaluated numerical Jacobian is used to simplify implementation, and mesh sequencing is used to increase the radius of convergence of the algorithm. We employ finite volume discretization using the power law scheme of Patankar to solve the benchmark backward facing step problem defined by the ASME K-12 Aerospace Heat Transfer Committee. LINPACK banded Gaussian elimination and the preconditioned transpose-free quasi-minimal residual (TFQMR) algorithm of Freund are studied as possible linear equation solvers. Implementation of the preconditioned TFQMR algorithm requires use of the switched evolution relaxation algorithm of Mulder and Van Leer to ensure convergence. The preconditioned TFQMR algorithm is more memory efficient than the direct solver, but our implementation is not as CPU efficient. Results show that for the level of grid refinement used, power law differencing was not adequate to yield the desired accuracy for this problem.

  19. Newton's method as applied to the Riemann problem for media with general equations of state

    NASA Astrophysics Data System (ADS)

    Moiseev, N. Ya.; Mukhamadieva, T. A.

    2008-06-01

    An approach based on Newton’s method is proposed for solving the Riemann problem for media with normal equations of state. The Riemann integrals are evaluated using a cubic approximation of an isentropic curve that is superior to the Simpson method in terms of accuracy, convergence rate, and efficiency. The potentials of the approach are demonstrated by solving problems for media obeying the Mie-Grüneisen equation of state. The algebraic equation of the isentropic curve and some exact solutions for configurations with rarefaction waves are explicitly given.

  20. On the accuracy of analytical methods for turbulent flows near smooth walls

    NASA Astrophysics Data System (ADS)

    Absi, Rafik; Di Nucci, Carmine

    2012-09-01

    This Note presents two methods for mean streamwise velocity profiles of fully-developed turbulent pipe and channel flows near smooth walls. The first is the classical approach where the mean streamwise velocity is obtained by solving the momentum equation with an eddy viscosity formulation [R. Absi, A simple eddy viscosity formulation for turbulent boundary layers near smooth walls, C. R. Mecanique 337 (2009) 158-165]. The second approach presents a formulation of the velocity profile based on an analogy with an electric field distribution [C. Di Nucci, E. Fiorucci, Mean velocity profiles of fully-developed turbulent flows near smooth walls, C. R. Mecanique 339 (2011) 388-395] and a formulation for the turbulent shear stress. However, this formulation for the turbulent shear stress shows a weakness. A corrected formulation is presented. Comparisons with DNS data show that the classical approach with the eddy viscosity formulation provides more accurate profiles for both turbulent shear stress and velocity gradient.

  1. Using the Gauss-Newton Method to Invert for Brune Model Moment, Corner Frequency, and Kappa Parameters: Results from the Canterbury, New Zealand Earthquake Sequence

    NASA Astrophysics Data System (ADS)

    Neighbors, C.; Cochran, E. S.; Ryan, K. J.; Kaiser, A. E.

    2015-12-01

    The seismic spectrum can be modeled by assuming a Brune spectrum and estimating the parameters of seismic moment (M0), corner frequency (fc), and the high frequency site attenuation (κ). Traditionally studies either hold fixed or use a predefined set of trial values for one of the parameters (e.g., fc) and then solve for the remaining parameters. Here, we use the Gauss-Newton nonlinear least-squares method to simultaneously determine the M0, fc, and high-frequency κ for each event-station pair. We use data collected during the Canterbury, New Zealand earthquake sequence. The seismic stations include the permanent GeoNet accelerometer network as well as a dense network of nearly 200 Quake-Catcher Network (QCN) MEMs accelerometers installed following the 3 September 2010 M 7.1 Darfield earthquake. We examine over 180 aftershocks ≥ Mw3.5 that occurred from 9 September 2010 to 31 July 2011 and are captured by both networks. We use Fourier-transformed S-wave windows that include 80% of the S-wave energy and fit the acceleration spectra between 0.5 and 20 Hz. We apply a path and site correction to the data as described in Oth and Kaiser (2014). Then, the records are smoothed using a Konno and Omachi (1998) filter and uniformly resampled in log space. Initial "best guesses" for M0 and fc are determined from GNS catalog magnitudes and by assuming a 100 bar (10 MPa) stress drop and an initial κ is determined from an automated high-frequency fit method. We use a parametric inversion technique that requires a single M0 and fc for each event, while κ is allowed to vary by station to reflect varying site conditions. Final solutions for M0, fc, and κ are iteratively calculated by minimizing the residual function. After Brune (1970, 1971), the stress drop is determined from the best-fit fc. Moment magnitudes determined agree well with the GNS catalog, with a median difference of 0.12 Mw and 0.20 Mw for GeoNet and QCN inversions, respectively. Stress drop results are within

  2. A Newton/upwind method and numerical study of shock wave/boundary layer interactions

    NASA Technical Reports Server (NTRS)

    Liou, Meng-Sing

    1989-01-01

    The objective of the paper is two-fold. First, an upwind/central differencing method for solving the steady Navier-Stokes equations is described. The symmetric line relation method is used to solve the resulting algebraic system to achieve high computational efficiency. The grid spacings used in the calculations are determined from the triple-deck theory, in terms of Mach and Reynolds numbers and other flow parameters. Thus the accuracy of the numerical solutions is improved by comparing them with experimental, analytical, and other computational results. Secondly, the shock wave/boundary layer interactions are studied numerically, with special attention given to the flow separation. The concept of free interaction is confirmed. Although the separated region varies with Mach and Reynolds numbers, it is found that the transverse velocity component behind the incident shock, which has not been identified heretofore, is also an important parameter. A small change of this quantity is sufficient to eliminate the flow separation entirely.

  3. A Newton-Raphson Method Approach to Adjusting Multi-Source Solar Simulators

    NASA Technical Reports Server (NTRS)

    Snyder, David B.; Wolford, David S.

    2012-01-01

    NASA Glenn Research Center has been using an in house designed X25 based multi-source solar simulator since 2003. The simulator is set up for triple junction solar cells prior to measurements b y adjusting the three sources to produce the correct short circuit current, lsc, in each of three AM0 calibrated sub-cells. The past practice has been to adjust one source on one sub-cell at a time, iterating until all the sub-cells have the calibrated Isc. The new approach is to create a matrix of measured lsc for small source changes on each sub-cell. A matrix, A, is produced. This is normalized to unit changes in the sources so that Ax(delta)s = (delta)isc. This matrix can now be inverted and used with the known Isc differences from the AM0 calibrated values to indicate changes in the source settings, (delta)s = A ·'x.(delta)isc This approach is still an iterative one, but all sources are changed during each iteration step. It typically takes four to six steps to converge on the calibrated lsc values. Even though the source lamps may degrade over time, the initial matrix evaluation i s not performed each time, since measurement matrix needs to be only approximate. Because an iterative approach is used the method will still continue to be valid. This method may become more important as state-of-the-art solar cell junction responses overlap the sources of the simulator. Also, as the number of cell junctions and sources increase, this method should remain applicable.

  4. A Novel Method for Modeling Neumann and Robin Boundary Conditions in Smoothed Particle Hydrodynamics

    SciTech Connect

    Ryan, Emily M.; Tartakovsky, Alexandre M.; Amon, Cristina

    2010-08-26

    In this paper we present an improved method for handling Neumann or Robin boundary conditions in smoothed particle hydrodynamics. The Neumann and Robin boundary conditions are common to many physical problems (such as heat/mass transfer), and can prove challenging to model in volumetric modeling techniques such as smoothed particle hydrodynamics (SPH). A new SPH method for diffusion type equations subject to Neumann or Robin boundary conditions is proposed. The new method is based on the continuum surface force model [1] and allows an efficient implementation of the Neumann and Robin boundary conditions in the SPH method for geometrically complex boundaries. The paper discusses the details of the method and the criteria needed to apply the model. The model is used to simulate diffusion and surface reactions and its accuracy is demonstrated through test cases for boundary conditions describing different surface reactions.

  5. Newton'Principia for the Common Reader

    NASA Astrophysics Data System (ADS)

    Chandrasekhar, S.

    1995-07-01

    Representing a decade's work from one of the world's most distinguished physicists, this major publication is, as far as is known, the first comprehensive analysis of Newton's Principia without recourse to secondary sources. Chandrasekhar analyses some 150 propositions which form a direct chain leading to Newton's formulation of his universal law of gravitation. In each case, Newton's proofs are arranged in a linear sequence of equations and arguments, avoiding the need to unravel the necessarily convoluted style of Newton's connected prose. In almost every case, a modern version of the proofs is given to bring into sharp focus the beauty, clarity, and breathtaking economy of Newton's methods. This book will stimulate great interest and debate among the scientific community, illuminating the brilliance of Newton's work under the steady gaze of Chandrasekhar's rare perception.

  6. XMM-Newton large program on SN1006 - I. Methods and initial results of spatially resolved spectroscopy

    NASA Astrophysics Data System (ADS)

    Li, Jiang-Tao; Decourchelle, Anne; Miceli, Marco; Vink, Jacco; Bocchino, Fabrizio

    2015-11-01

    Based on our newly developed methods and the XMM-Newton large program of SN1006, we extract and analyse the spectra from 3596 tessellated regions of this supernova remnant (SNR) each with 0.3-8 keV counts >104. For the first time, we map out multiple physical parameters, such as the temperature (kT), electron density (ne), ionization parameter (net), ionization age (tion), metal abundances, as well as the radio-to-X-ray slope (α) and cutoff frequency (νcutoff) of the synchrotron emission. We construct probability distribution functions of kT and net, and model them with several Gaussians, in order to characterize the average thermal and ionization states of such an extended source. We construct equivalent width (EW) maps based on continuum interpolation with the spectral model of each region. We then compare the EW maps of O VII, O VIII, O VII Kδ - ζ, Ne, Mg, Si XIII, Si XIV, and S lines constructed with this method to those constructed with linear interpolation. We further extract spectra from larger regions to confirm the features revealed by parameter and EW maps, which are often not directly detectable on X-ray intensity images. For example, O abundance is consistent with solar across the SNR, except for a low-abundance hole in the centre. This `O hole' has enhanced O VII Kδ - ζ and Fe emissions, indicating recently reverse shocked ejecta, but also has the highest net, indicating forward shocked interstellar medium (ISM). Therefore, a multitemperature model is needed to decompose these components. The asymmetric metal distributions suggest there is either an asymmetric explosion of the supernova or an asymmetric distribution of the ISM.

  7. Newton and comets

    NASA Astrophysics Data System (ADS)

    Bork, Alfred

    1987-12-01

    The publication of Isaac Newton's ``notions about motion'' 300 years ago was a major moment in the history of science. In the period just before 1687 Newton's correspondence was much concerned with comets. In this period two bright comets were seen. These comets appear to have been a major stimulation to Newton's work on mechanics.

  8. A method for smoothing segmented lung boundary in chest CT images

    NASA Astrophysics Data System (ADS)

    Yim, Yeny; Hong, Helen

    2007-03-01

    To segment low density lung regions in chest CT images, most of methods use the difference in gray-level value of pixels. However, radiodense pulmonary vessels and pleural nodules that contact with the surrounding anatomy are often excluded from the segmentation result. To smooth lung boundary segmented by gray-level processing in chest CT images, we propose a new method using scan line search. Our method consists of three main steps. First, lung boundary is extracted by our automatic segmentation method. Second, segmented lung contour is smoothed in each axial CT slice. We propose a scan line search to track the points on lung contour and find rapidly changing curvature efficiently. Finally, to provide consistent appearance between lung contours in adjacent axial slices, 2D closing in coronal plane is applied within pre-defined subvolume. Our method has been applied for performance evaluation with the aspects of visual inspection, accuracy and processing time. The results of our method show that the smoothness of lung contour was considerably increased by compensating for pulmonary vessels and pleural nodules.

  9. Computing Modified Newton Directions Using a Partial Cholesky Factorization.

    DTIC Science & Technology

    1993-03-01

    Newton method for unconstrained minimization’ Department of Operations Research, Stanford University, 1989. Any opinions, findings, and conclusions or...Technical Report SOL 93-1 § March 1993 Abstract The effectiveness of Newton’s method for finding an unconstrained mini- mizer of a strictly convex...twice continuously differentiable function has prompted the proposal of various modified Newton methods for the nonconvex case. Linesearch modified Newton

  10. Is Newton's second law really Newton's?

    NASA Astrophysics Data System (ADS)

    Pourciau, Bruce

    2011-10-01

    When we call the equation f = ma "Newton's second law," how much historical truth lies behind us? Many textbooks on introductory physics and classical mechanics claim that the Principia's second law becomes f = ma, once Newton's vocabulary has been translated into more familiar terms. But there is nothing in the Principia's second law about acceleration and nothing about a rate of change. If the Principia's second law does not assert f = ma, what does it assert, and is there some other axiom or some proposition in the Principia that does assert f = ma? Is there any historical truth behind us when we call f = ma "Newton's second law"? This article answers these questions.

  11. Melnikov Method for a Three-Zonal Planar Hybrid Piecewise-Smooth System and Application

    NASA Astrophysics Data System (ADS)

    Li, Shuangbao; Ma, Wensai; Zhang, Wei; Hao, Yuxin

    In this paper, we extend the well-known Melnikov method for smooth systems to a class of planar hybrid piecewise-smooth systems, defined in three domains separated by two switching manifolds x = a and x = b. The dynamics in each domain is governed by a smooth system. When an orbit reaches the separation lines, then a reset map describing an impacting rule applies instantaneously before the orbit enters into another domain. We assume that the unperturbed system has a continuum of periodic orbits transversally crossing the separation lines. Then, we wish to study the persistence of the periodic orbits under an autonomous perturbation and the reset map. To achieve this objective, we first choose four appropriate switching sections and build a Poincaré map, after that, we present a displacement function and carry on the Taylor expansion of the displacement function to the first-order in the perturbation parameter ɛ near ɛ = 0. We denote the first coefficient in the expansion as the first-order Melnikov function whose zeros provide us the persistence of periodic orbits under perturbation. Finally, we study periodic orbits of a concrete planar hybrid piecewise-smooth system by the obtained Melnikov function.

  12. Evaluation of kinetic constants of biomolecular interaction on optical surface plasmon resonance sensor with Newton Iteration Method

    NASA Astrophysics Data System (ADS)

    Zhao, Yuanyuan; Jiang, Guoliang; Hu, Jiandong; Hu, Fengjiang; Wei, Jianguang; Shi, Liang

    2010-10-01

    of biomolecular interaction by using Newton Iteration Method and Least Squares Method. First, the pseudo first order kinetic model of biomolecular interaction was established. Then the data of molecular interaction of HBsAg and HBsAb was obtained by bioanalyzer. Finally, we used the optical SPR bioanalyzer software which was written by ourselves to make nonlinear fit about the association and dissociation curves. The correlation coefficient R-squared is 0.99229 and 0.99593, respectively. Furthermore, the kinetic parameters and affinity constants were evaluated using the obtained data from the fitting results.

  13. Analysis of the incomplete Galerkin method for modelling of smoothly-irregular transition between planar waveguides

    NASA Astrophysics Data System (ADS)

    Divakov, D.; Sevastianov, L.; Nikolaev, N.

    2017-01-01

    The paper deals with a numerical solution of the problem of waveguide propagation of polarized light in smoothly-irregular transition between closed regular waveguides using the incomplete Galerkin method. This method consists in replacement of variables in the problem of reduction of the Helmholtz equation to the system of differential equations by the Kantorovich method and in formulation of the boundary conditions for the resulting system. The formulation of the boundary problem for the ODE system is realized in computer algebra system Maple. The stated boundary problem is solved using Maples libraries of numerical methods.

  14. A Nonlinear Framework of Delayed Particle Smoothing Method for Vehicle Localization under Non-Gaussian Environment

    PubMed Central

    Xiao, Zhu; Havyarimana, Vincent; Li, Tong; Wang, Dong

    2016-01-01

    In this paper, a novel nonlinear framework of smoothing method, non-Gaussian delayed particle smoother (nGDPS), is proposed, which enables vehicle state estimation (VSE) with high accuracy taking into account the non-Gaussianity of the measurement and process noises. Within the proposed method, the multivariate Student’s t-distribution is adopted in order to compute the probability distribution function (PDF) related to the process and measurement noises, which are assumed to be non-Gaussian distributed. A computation approach based on Ensemble Kalman Filter (EnKF) is designed to cope with the mean and the covariance matrix of the proposal non-Gaussian distribution. A delayed Gibbs sampling algorithm, which incorporates smoothing of the sampled trajectories over a fixed-delay, is proposed to deal with the sample degeneracy of particles. The performance is investigated based on the real-world data, which is collected by low-cost on-board vehicle sensors. The comparison study based on the real-world experiments and the statistical analysis demonstrates that the proposed nGDPS has significant improvement on the vehicle state accuracy and outperforms the existing filtering and smoothing methods. PMID:27187405

  15. A strategy to couple the material point method (MPM) and smoothed particle hydrodynamics (SPH) computational techniques

    NASA Astrophysics Data System (ADS)

    Raymond, Samuel J.; Jones, Bruce; Williams, John R.

    2016-12-01

    A strategy is introduced to allow coupling of the material point method (MPM) and smoothed particle hydrodynamics (SPH) for numerical simulations. This new strategy partitions the domain into SPH and MPM regions, particles carry all state variables and as such no special treatment is required for the transition between regions. The aim of this work is to derive and validate the coupling methodology between MPM and SPH. Such coupling allows for general boundary conditions to be used in an SPH simulation without further augmentation. Additionally, as SPH is a purely particle method, and MPM is a combination of particles and a mesh. This coupling also permits a smooth transition from particle methods to mesh methods, where further coupling to mesh methods could in future provide an effective farfield boundary treatment for the SPH method. The coupling technique is introduced and described alongside a number of simulations in 1D and 2D to validate and contextualize the potential of using these two methods in a single simulation. The strategy shown here is capable of fully coupling the two methods without any complicated algorithms to transform information from one method to another.

  16. An immersed boundary method for smoothed particle hydrodynamics of self-propelled swimmers

    NASA Astrophysics Data System (ADS)

    Hieber, S. E.; Koumoutsakos, P.

    2008-10-01

    We present a novel particle method, combining remeshed Smoothed Particle Hydrodynamics with Immersed Boundary and Level Set techniques for the simulation of flows past complex deforming geometries. The present method retains the Lagrangian adaptivity of particle methods and relies on the remeshing of particle locations in order to ensure the accuracy of the method. In fact this remeshing step enables the introduction of Immersed Boundary Techniques used in grid based methods. The method is applied to simulations of flows of isothermal and compressible fluids past steady and unsteady solid boundaries that are described using a particle Level Set formulation. The method is validated with two and three-dimensional benchmark problems of flows past cylinders and spheres and it is shown to be well suited to simulations of large scale simulations using tens of millions of particles, on flow-structure interaction problems as they pertain to self-propelled anguilliform swimmers.

  17. Incomplete iterations in multistep backward difference methods for parabolic problems with smooth and nonsmooth data

    SciTech Connect

    Bramble, J. H.; Pasciak, J. E.; Sammon, P. H.; Thomee, V.

    1989-04-01

    Backward difference methods for the discretization of parabolic boundary value problems are considered in this paper. In particular, we analyze the case when the backward difference equations are only solved 'approximately' by a preconditioned iteration. We provide an analysis which shows that these methods remain stable and accurate if a suitable number of iterations (often independent of the spatial discretization and time step size) are used. Results are provided for the smooth as well as nonsmooth initial data cases. Finally, the results of numerical experiments illustrating the algorithms' performance on model problems are given.

  18. Image reconstruction for 3D light microscopy with a regularized linear method incorporating a smoothness prior

    NASA Astrophysics Data System (ADS)

    Preza, Chrysanthe; Miller, Michael I.; Conchello, Jose-Angel

    1993-07-01

    We have shown that the linear least-squares (LLS) estimate of the intensities of a 3-D object obtained from a set of optical sections is unstable due to the inversion of small and zero-valued eigenvalues of the point-spread function (PSF) operator. The LLS solution was regularized by constraining it to lie in a subspace spanned by the eigenvectors corresponding to a selected number of the largest eigenvalues. In this paper we extend the regularized LLS solution to a maximum a posteriori (MAP) solution induced by a prior formed from a 'Good's like' smoothness penalty. This approach also yields a regularized linear estimator which reduces noise as well as edge artifacts in the reconstruction. The advantage of the linear MAP (LMAP) estimate over the current regularized LLS (RLLS) is its ability to regularize the inverse problem by smoothly penalizing components in the image associated with small eigenvalues. Computer simulations were performed using a theoretical PSF and a simple phantom to compare the two regularization techniques. It is shown that the reconstructions using the smoothness prior, give superior variance and bias results compared to the RLLS reconstructions. Encouraging reconstructions obtained with the LMAP method from real microscopical images of a 10 micrometers fluorescent bead, and a four-cell Volvox embryo are shown.

  19. A Fast Variational Method for the Construction of Resolution Adaptive C-Smooth Molecular Surfaces.

    PubMed

    Bajaj, Chandrajit L; Xu, Guoliang; Zhang, Qin

    2009-05-01

    We present a variational approach to smooth molecular (proteins, nucleic acids) surface constructions, starting from atomic coordinates, as available from the protein and nucleic-acid data banks. Molecular dynamics (MD) simulations traditionally used in understanding protein and nucleic-acid folding processes, are based on molecular force fields, and require smooth models of these molecular surfaces. To accelerate MD simulations, a popular methodology is to employ coarse grained molecular models, which represent clusters of atoms with similar physical properties by psuedo- atoms, resulting in coarser resolution molecular surfaces. We consider generation of these mixed-resolution or adaptive molecular surfaces. Our approach starts from deriving a general form second order geometric partial differential equation in the level-set formulation, by minimizing a first order energy functional which additionally includes a regularization term to minimize the occurrence of chemically infeasible molecular surface pockets or tunnel-like artifacts. To achieve even higher computational efficiency, a fast cubic B-spline C(2) interpolation algorithm is also utilized. A narrow band, tri-cubic B-spline level-set method is then used to provide C(2) smooth and resolution adaptive molecular surfaces.

  20. 40 CFR Appendix G to Part 60 - Provisions for an Alternative Method of Demonstrating Compliance With 40 CFR 60.43 for the Newton...

    Code of Federal Regulations, 2012 CFR

    2012-07-01

    ... Demonstrating Compliance With 40 CFR 60.43 for the Newton Power Station of Central Illinois Public Service... for the Newton Power Station of Central Illinois Public Service Company 1. Designation of Affected...) Newton Power Station in Jasper County, Illinois. Each of these units is subject to the Standards...

  1. 40 CFR Appendix G to Part 60 - Provisions for an Alternative Method of Demonstrating Compliance With 40 CFR 60.43 for the Newton...

    Code of Federal Regulations, 2011 CFR

    2011-07-01

    ... Demonstrating Compliance With 40 CFR 60.43 for the Newton Power Station of Central Illinois Public Service... for the Newton Power Station of Central Illinois Public Service Company 1. Designation of Affected...) Newton Power Station in Jasper County, Illinois. Each of these units is subject to the Standards...

  2. 40 CFR Appendix G to Part 60 - Provisions for an Alternative Method of Demonstrating Compliance With 40 CFR 60.43 for the Newton...

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... Demonstrating Compliance With 40 CFR 60.43 for the Newton Power Station of Central Illinois Public Service... for the Newton Power Station of Central Illinois Public Service Company 1. Designation of Affected...) Newton Power Station in Jasper County, Illinois. Each of these units is subject to the Standards...

  3. Nonequilibrium Flows with Smooth Particle Applied Mechanics.

    NASA Astrophysics Data System (ADS)

    Kum, Oyeon

    Smooth particle methods are relatively new methods for simulating solid and fluid flows though they have a 20-year history of solving complex hydrodynamic problems in astrophysics, such as colliding planets and stars, for which correct answers are unknown. The results presented in this thesis evaluate the adaptability or fitness of the method for typical hydrocode production problems. For finite hydrodynamic systems, boundary conditions are important. A reflective boundary condition with image particles is a good way to prevent a density anomaly at the boundary and to keep the fluxes continuous there. Boundary values of temperature and velocity can be separately controlled. The gradient algorithm, based on differentiating the smooth particle expressions for (urho) and (Trho), does not show numerical instabilities for the stress tensor and heat flux vector quantities which require second derivatives in space when Fourier's heat -flow law and Newton's viscous force law are used. Smooth particle methods show an interesting parallel linking them to molecular dynamics. For the inviscid Euler equation, with an isentropic ideal gas equation of state, the smooth particle algorithm generates trajectories isomorphic to those generated by molecular dynamics. The shear moduli were evaluated based on molecular dynamics calculations for the three weighting functions, B spline, Lucy, and Cusp functions. The accuracy and applicability of the methods were estimated by comparing a set of smooth particle Rayleigh -Benard problems, all in the laminar regime, to corresponding highly-accurate grid-based numerical solutions of continuum equations. Both transient and stationary smooth particle solutions reproduce the grid-based data with velocity errors on the order of 5%. The smooth particle method still provides robust solutions at high Rayleigh number where grid-based methods fails. Considerably fewer smooth particles are required than atoms in a corresponding molecular dynamics

  4. An adaptive kernel smoothing method for classifying Austrosimulium tillyardianum (Diptera: Simuliidae) larval instars.

    PubMed

    Cen, Guanjun; Yu, Yonghao; Zeng, Xianru; Long, Xiuzhen; Wei, Dewei; Gao, Xuyuan; Zeng, Tao

    2015-01-01

    In insects, the frequency distribution of the measurements of sclerotized body parts is generally used to classify larval instars and is characterized by a multimodal overlap between instar stages. Nonparametric methods with fixed bandwidths, such as histograms, have significant limitations when used to fit this type of distribution, making it difficult to identify divisions between instars. Fixed bandwidths have also been chosen somewhat subjectively in the past, which is another problem. In this study, we describe an adaptive kernel smoothing method to differentiate instars based on discontinuities in the growth rates of sclerotized insect body parts. From Brooks' rule, we derived a new standard for assessing the quality of instar classification and a bandwidth selector that more accurately reflects the distributed character of specific variables. We used this method to classify the larvae of Austrosimulium tillyardianum (Diptera: Simuliidae) based on five different measurements. Based on head capsule width and head capsule length, the larvae were separated into nine instars. Based on head capsule postoccipital width and mandible length, the larvae were separated into 8 instars and 10 instars, respectively. No reasonable solution was found for antennal segment 3 length. Separation of the larvae into nine instars using head capsule width or head capsule length was most robust and agreed with Crosby's growth rule. By strengthening the distributed character of the separation variable through the use of variable bandwidths, the adaptive kernel smoothing method could identify divisions between instars more effectively and accurately than previous methods.

  5. An Adaptive Kernel Smoothing Method for Classifying Austrosimulium tillyardianum (Diptera: Simuliidae) Larval Instars

    PubMed Central

    Cen, Guanjun; Zeng, Xianru; Long, Xiuzhen; Wei, Dewei; Gao, Xuyuan; Zeng, Tao

    2015-01-01

    In insects, the frequency distribution of the measurements of sclerotized body parts is generally used to classify larval instars and is characterized by a multimodal overlap between instar stages. Nonparametric methods with fixed bandwidths, such as histograms, have significant limitations when used to fit this type of distribution, making it difficult to identify divisions between instars. Fixed bandwidths have also been chosen somewhat subjectively in the past, which is another problem. In this study, we describe an adaptive kernel smoothing method to differentiate instars based on discontinuities in the growth rates of sclerotized insect body parts. From Brooks’ rule, we derived a new standard for assessing the quality of instar classification and a bandwidth selector that more accurately reflects the distributed character of specific variables. We used this method to classify the larvae of Austrosimulium tillyardianum (Diptera: Simuliidae) based on five different measurements. Based on head capsule width and head capsule length, the larvae were separated into nine instars. Based on head capsule postoccipital width and mandible length, the larvae were separated into 8 instars and 10 instars, respectively. No reasonable solution was found for antennal segment 3 length. Separation of the larvae into nine instars using head capsule width or head capsule length was most robust and agreed with Crosby’s growth rule. By strengthening the distributed character of the separation variable through the use of variable bandwidths, the adaptive kernel smoothing method could identify divisions between instars more effectively and accurately than previous methods. PMID:26546689

  6. The multiscale restriction smoothed basis method for fractured porous media (F-MsRSB)

    NASA Astrophysics Data System (ADS)

    Shah, Swej; Møyner, Olav; Tene, Matei; Lie, Knut-Andreas; Hajibeygi, Hadi

    2016-08-01

    A novel multiscale method for multiphase flow in heterogeneous fractured porous media is devised. The discrete fine-scale system is described using an embedded fracture modeling approach, in which the heterogeneous rock (matrix) and highly-conductive fractures are represented on independent grids. Given this fine-scale discrete system, the method first partitions the fine-scale volumetric grid representing the matrix and the lower-dimensional grids representing fractures into independent coarse grids. Then, basis functions for matrix and fractures are constructed by restricted smoothing, which gives a flexible and robust treatment of complex geometrical features and heterogeneous coefficients. From the basis functions one constructs a prolongation operator that maps between the coarse- and fine-scale systems. The resulting method allows for general coupling of matrix and fracture basis functions, giving efficient treatment of a large variety of fracture conductivities. In addition, basis functions can be adaptively updated using efficient global smoothing strategies to account for multiphase flow effects. The method is conservative and because it is described and implemented in algebraic form, it is straightforward to employ it to both rectilinear and unstructured grids. Through a series of challenging test cases for single and multiphase flow, in which synthetic and realistic fracture maps are combined with heterogeneous petrophysical matrix properties, we validate the method and conclude that it is an efficient and accurate approach for simulating flow in complex, large-scale, fractured media.

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

    SciTech Connect

    HyeongKae Park; Robert R. Nourgaliev; Richard C. Martineau; Dana A. Knoll

    2008-09-01

    We present high-order accurate spatiotemporal discretization of all-speed flow solvers using Jacobian-free Newton Krylov framework. One of the key developments in this work is the physics-based preconditioner for the all-speed flow, which makes use of traditional semi-implicit schemes. The physics-based preconditioner is developed in the primitive variable form, which allows a straightforward separation of physical phenomena. Numerical examples demonstrate that the developed preconditioner effectively reduces the number of the Krylov iterations, and the efficiency is independent of the Mach number and mesh sizes under a fixed CFL condition.

  8. Application of MSOR iteration with Newton scheme for solutions of 1D nonlinear porous medium equations

    NASA Astrophysics Data System (ADS)

    Chew, J. V. L.; Sulaiman, J.

    2016-06-01

    This paper considers Newton-MSOR iterative method for solving 1D nonlinear porous medium equation (PME). The basic concept of proposed iterative method is derived from a combination of one step nonlinear iterative method which known as Newton method with Modified Successive Over Relaxation (MSOR) method. The reliability of Newton-MSOR to obtain approximate solution for several PME problems is compared with Newton-Gauss-Seidel (Newton-GS) and Newton-Successive Over Relaxation (Newton-SOR). In this paper, the formulation and implementation of these three iterative methods have also been presented. From four examples of PME problems, numerical results showed that Newton-MSOR method requires lesser number of iterations and computational time as compared with Newton-GS and Newton-SOR methods.

  9. From Newton to Einstein.

    ERIC Educational Resources Information Center

    Ryder, L. H.

    1987-01-01

    Discusses the history of scientific thought in terms of the theories of inertia and absolute space, relativity and gravitation. Describes how Sir Isaac Newton used the work of earlier scholars in his theories and how Albert Einstein used Newton's theories in his. (CW)

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

    SciTech Connect

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

    2011-01-01

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

  11. The CACAO Method for Smoothing, Gap Filling, and Characterizing Seasonal Anomalies in Satellite Time Series

    NASA Technical Reports Server (NTRS)

    Verger, Aleixandre; Baret, F.; Weiss, M.; Kandasamy, S.; Vermote, E.

    2013-01-01

    Consistent, continuous, and long time series of global biophysical variables derived from satellite data are required for global change research. A novel climatology fitting approach called CACAO (Consistent Adjustment of the Climatology to Actual Observations) is proposed to reduce noise and fill gaps in time series by scaling and shifting the seasonal climatological patterns to the actual observations. The shift and scale CACAO parameters adjusted for each season allow quantifying shifts in the timing of seasonal phenology and inter-annual variations in magnitude as compared to the average climatology. CACAO was assessed first over simulated daily Leaf Area Index (LAI) time series with varying fractions of missing data and noise. Then, performances were analyzed over actual satellite LAI products derived from AVHRR Long-Term Data Record for the 1981-2000 period over the BELMANIP2 globally representative sample of sites. Comparison with two widely used temporal filtering methods-the asymmetric Gaussian (AG) model and the Savitzky-Golay (SG) filter as implemented in TIMESAT-revealed that CACAO achieved better performances for smoothing AVHRR time series characterized by high level of noise and frequent missing observations. The resulting smoothed time series captures well the vegetation dynamics and shows no gaps as compared to the 50-60% of still missing data after AG or SG reconstructions. Results of simulation experiments as well as confrontation with actual AVHRR time series indicate that the proposed CACAO method is more robust to noise and missing data than AG and SG methods for phenology extraction.

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

    SciTech Connect

    Luanjing Guo; Hai Huang; Derek Gaston; Cody Permann; David Andrs; George Redden; Chuan Lu; Don Fox; Yoshiko Fujita

    2013-03-01

    Modeling large multicomponent reactive transport systems in porous media is particularly challenging when the governing partial differential algebraic equations (PDAEs) are highly nonlinear and tightly coupled due to complex nonlinear reactions and strong solution-media interactions. Here we present a preconditioned Jacobian-Free Newton-Krylov (JFNK) solution approach to solve the governing PDAEs in a fully coupled and fully implicit manner. A well-known advantage of the JFNK method is that it does not require explicitly computing and storing the Jacobian matrix during Newton nonlinear iterations. Our approach further enhances the JFNK method by utilizing physics-based, block preconditioning and a multigrid algorithm for efficient inversion of the preconditioner. This preconditioning strategy accounts for self- and optionally, cross-coupling between primary variables using diagonal and off-diagonal blocks of an approximate Jacobian, respectively. Numerical results are presented demonstrating the efficiency and massive scalability of the solution strategy for reactive transport problems involving strong solution-mineral interactions and fast kinetics. We found that the physics-based, block preconditioner significantly decreases the number of linear iterations, directly reducing computational cost; and the strongly scalable algebraic multigrid algorithm for approximate inversion of the preconditioner leads to excellent parallel scaling performance.

  13. Method of adiabatic modes in studying problems of smoothly irregular open waveguide structures

    SciTech Connect

    Sevastianov, L. A.; Egorov, A. A.; Sevastyanov, A. L.

    2013-02-15

    Basic steps in developing an original method of adiabatic modes that makes it possible to solve the direct and inverse problems of simulating and designing three-dimensional multilayered smoothly irregular open waveguide structures are described. A new element in the method is that an approximate solution of Maxwell's equations is made to obey 'inclined' boundary conditions at the interfaces between themedia being considered. These boundary conditions take into account the obliqueness of planes tangent to nonplanar boundaries between the media and lead to new equations for coupled vector quasiwaveguide hybrid adiabatic modes. Solutions of these equations describe the phenomenon of 'entanglement' of two linear polarizations of an irregular multilayered waveguide, the appearance of a new mode in an entangled state, and the effect of rotation of the polarization plane of quasiwaveguide modes. The efficiency of the method is demonstrated by considering the example of numerically simulating a thin-film generalized waveguide Lueneburg lens.

  14. A method for the accurate and smooth approximation of standard thermodynamic functions

    NASA Astrophysics Data System (ADS)

    Coufal, O.

    2013-01-01

    A method is proposed for the calculation of approximations of standard thermodynamic functions. The method is consistent with the physical properties of standard thermodynamic functions. This means that the approximation functions are, in contrast to the hitherto used approximations, continuous and smooth in every temperature interval in which no phase transformations take place. The calculation algorithm was implemented by the SmoothSTF program in the C++ language which is part of this paper. Program summaryProgram title:SmoothSTF Catalogue identifier: AENH_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENH_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 3807 No. of bytes in distributed program, including test data, etc.: 131965 Distribution format: tar.gz Programming language: C++. Computer: Any computer with gcc version 4.3.2 compiler. Operating system: Debian GNU Linux 6.0. The program can be run in operating systems in which the gcc compiler can be installed, see http://gcc.gnu.org/install/specific.html. RAM: 256 MB are sufficient for the table of standard thermodynamic functions with 500 lines Classification: 4.9. Nature of problem: Standard thermodynamic functions (STF) of individual substances are given by thermal capacity at constant pressure, entropy and enthalpy. STF are continuous and smooth in every temperature interval in which no phase transformations take place. The temperature dependence of STF as expressed by the table of its values is for further application approximated by temperature functions. In the paper, a method is proposed for calculating approximation functions which, in contrast to the hitherto used approximations, are continuous and smooth in every temperature interval. Solution method: The approximation functions are

  15. Immersed smoothed finite element method for fluid-structure interaction simulation of aortic valves

    NASA Astrophysics Data System (ADS)

    Yao, Jianyao; Liu, G. R.; Narmoneva, Daria A.; Hinton, Robert B.; Zhang, Zhi-Qian

    2012-12-01

    This paper presents a novel numerical method for simulating the fluid-structure interaction (FSI) problems when blood flows over aortic valves. The method uses the immersed boundary/element method and the smoothed finite element method and hence it is termed as IS-FEM. The IS-FEM is a partitioned approach and does not need a body-fitted mesh for FSI simulations. It consists of three main modules: the fluid solver, the solid solver and the FSI force solver. In this work, the blood is modeled as incompressible viscous flow and solved using the characteristic-based-split scheme with FEM for spacial discretization. The leaflets of the aortic valve are modeled as Mooney-Rivlin hyperelastic materials and solved using smoothed finite element method (or S-FEM). The FSI force is calculated on the Lagrangian fictitious fluid mesh that is identical to the moving solid mesh. The octree search and neighbor-to-neighbor schemes are used to detect efficiently the FSI pairs of fluid and solid cells. As an example, a 3D idealized model of aortic valve is modeled, and the opening process of the valve is simulated using the proposed IS-FEM. Numerical results indicate that the IS-FEM can serve as an efficient tool in the study of aortic valve dynamics to reveal the details of stresses in the aortic valves, the flow velocities in the blood, and the shear forces on the interfaces. This tool can also be applied to animal models studying disease processes and may ultimately translate to a new adaptive methods working with magnetic resonance images, leading to improvements on diagnostic and prognostic paradigms, as well as surgical planning, in the care of patients.

  16. Finding the transition state of quasi-barrierless reactions by a growing string method for newton trajectories: application to the dissociation of methylenecyclopropene and cyclopropane.

    PubMed

    Quapp, Wolfgang; Kraka, Elfi; Cremer, Dieter

    2007-11-08

    A method for finding a transition state (TS) between a reactant minimum and a quasi-flat, high dissociation plateau on the potential energy surface is described. The method is based on the search of a growing string (GS) along reaction pathways defined by different Newton trajectories (NT). Searches with the GS-NT method always make it possible to identify the TS region because monotonically increasing NTs cross at the TS or, if not monotonically increasing, possess turning points that are located in the TS region. The GS-NT method is applied to quasi-barrierless and truly barrierless chemical reactions. Examples are the dissociation of methylenecyclopropene to acetylene and vinylidene, for which a small barrier far out in the exit channel is found, and the cycloaddition of singlet methylene and ethene, which is barrierless for a broad reaction channel with Cs-symmetry reminiscent of a mountain cirque formed by a glacier.

  17. Numerical study of a multigrid method with four smoothing methods for the incompressible Navier-Stokes equations in general coordinates

    NASA Technical Reports Server (NTRS)

    Zeng, S.; Wesseling, P.

    1993-01-01

    The performance of a linear multigrid method using four smoothing methods, called SCGS (Symmetrical Coupled GauBeta-Seidel), CLGS (Collective Line GauBeta-Seidel), SILU (Scalar ILU), and CILU (Collective ILU), is investigated for the incompressible Navier-Stokes equations in general coordinates, in association with Galerkin coarse grid approximation. Robustness and efficiency are measured and compared by application to test problems. The numerical results show that CILU is the most robust, SILU the least, with CLGS and SCGS in between. CLGS is the best in efficiency, SCGS and CILU follow, and SILU is the worst.

  18. Perturbation theory for anisotropic dielectric interfaces, and application to subpixel smoothing of discretized numerical methods.

    PubMed

    Kottke, Chris; Farjadpour, Ardavan; Johnson, Steven G

    2008-03-01

    We derive a correct first-order perturbation theory in electromagnetism for cases where an interface between two anisotropic dielectric materials is slightly shifted. Most previous perturbative methods give incorrect results for this case, even to lowest order, because of the complicated discontinuous boundary conditions on the electric field at such an interface. Our final expression is simply a surface integral, over the material interface, of the continuous field components from the unperturbed structure. The derivation is based on a "localized" coordinate-transformation technique, which avoids both the problem of field discontinuities and the challenge of constructing an explicit coordinate transformation by taking the limit in which the coordinate perturbation is infinitesimally localized around the boundary. Not only is our result potentially useful in evaluating boundary perturbations, e.g., from fabrication imperfections, in highly anisotropic media such as many metamaterials, but it also has a direct application in numerical electromagnetism. In particular, we show how it leads to a subpixel smoothing scheme to ameliorate staircasing effects in discretized simulations of anisotropic media, in such a way as to greatly reduce the numerical errors compared to other proposed smoothing schemes.

  19. Invariant measures of smooth dynamical systems, generalized functions and summation methods

    NASA Astrophysics Data System (ADS)

    Kozlov, V. V.

    2016-04-01

    We discuss conditions for the existence of invariant measures of smooth dynamical systems on compact manifolds. If there is an invariant measure with continuously differentiable density, then the divergence of the vector field along every solution tends to zero in the Cesàro sense as time increases unboundedly. Here the Cesàro convergence may be replaced, for example, by any Riesz summation method, which can be arbitrarily close to ordinary convergence (but does not coincide with it). We give an example of a system whose divergence tends to zero in the ordinary sense but none of its invariant measures is absolutely continuous with respect to the `standard' Lebesgue measure (generated by some Riemannian metric) on the phase space. We give examples of analytic systems of differential equations on analytic phase spaces admitting invariant measures of any prescribed smoothness (including a measure with integrable density), but having no invariant measures with positive continuous densities. We give a new proof of the classical Bogolyubov-Krylov theorem using generalized functions and the Hahn-Banach theorem. The properties of signed invariant measures are also discussed.

  20. Calculation of smooth potential energy surfaces using local electron correlation methods

    NASA Astrophysics Data System (ADS)

    Mata, Ricardo A.; Werner, Hans-Joachim

    2006-11-01

    The geometry dependence of excitation domains in local correlation methods can lead to noncontinuous potential energy surfaces. We propose a simple domain merging procedure which eliminates this problem in many situations. The method is applied to heterolytic bond dissociations of ketene and propadienone, to SN2 reactions of Cl- with alkylchlorides, and in a quantum mechanical/molecular mechanical study of the chorismate mutase enzyme. It is demonstrated that smooth potentials are obtained in all cases. Furthermore, basis set superposition error effects are reduced in local calculations, and it is found that this leads to better basis set convergence when computing barrier heights or weak interactions. When the electronic structure strongly changes between reactants or products and the transition state, the domain merging procedure leads to a balanced description of all structures and accurate barrier heights.

  1. Calculation of smooth potential energy surfaces using local electron correlation methods

    SciTech Connect

    Mata, Ricardo A.; Werner, Hans-Joachim

    2006-11-14

    The geometry dependence of excitation domains in local correlation methods can lead to noncontinuous potential energy surfaces. We propose a simple domain merging procedure which eliminates this problem in many situations. The method is applied to heterolytic bond dissociations of ketene and propadienone, to SN2 reactions of Cl{sup -} with alkylchlorides, and in a quantum mechanical/molecular mechanical study of the chorismate mutase enzyme. It is demonstrated that smooth potentials are obtained in all cases. Furthermore, basis set superposition error effects are reduced in local calculations, and it is found that this leads to better basis set convergence when computing barrier heights or weak interactions. When the electronic structure strongly changes between reactants or products and the transition state, the domain merging procedure leads to a balanced description of all structures and accurate barrier heights.

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

    PubMed

    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

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

    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.

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

    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

  5. Application of Holt exponential smoothing and ARIMA method for data population in West Java

    NASA Astrophysics Data System (ADS)

    Supriatna, A.; Susanti, D.; Hertini, E.

    2017-01-01

    One method of time series that is often used to predict data that contains trend is Holt. Holt method using different parameters used in the original data which aims to smooth the trend value. In addition to Holt, ARIMA method can be used on a wide variety of data including data pattern containing a pattern trend. Data actual of population from 1998-2015 contains the trends so can be solved by Holt and ARIMA method to obtain the prediction value of some periods. The best method is measured by looking at the smallest MAPE and MAE error. The result using Holt method is 47.205.749 populations in 2016, 47.535.324 populations in 2017, and 48.041.672 populations in 2018, with MAPE error is 0,469744 and MAE error is 189.731. While the result using ARIMA method is 46.964.682 populations in 2016, 47.342.189 in 2017, and 47.899.696 in 2018, with MAPE error is 0,4380 and MAE is 176.626.

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

    SciTech Connect

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

    2010-10-20

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

  7. Ultrasonic Newton's rings

    SciTech Connect

    Hsu, D.K. ); Dayal, V. )

    1992-03-09

    Interference fringes due to bondline thickness variation were observed in ultrasonic scans of the reflected echo amplitude from the bondline of adhesively joined aluminum skins. To demonstrate that full-field interference patterns are observable in point-by-point ultrasonic scans, an optical setup for Newton's rings was scanned ultrasonically in a water immersion tank. The ultrasonic scan showed distinct Newton's rings whose radii were in excellent agreement with the prediction.

  8. A DAFT DL_POLY distributed memory adaptation of the Smoothed Particle Mesh Ewald method

    NASA Astrophysics Data System (ADS)

    Bush, I. J.; Todorov, I. T.; Smith, W.

    2006-09-01

    The Smoothed Particle Mesh Ewald method [U. Essmann, L. Perera, M.L. Berkowtz, T. Darden, H. Lee, L.G. Pedersen, J. Chem. Phys. 103 (1995) 8577] for calculating long ranged forces in molecular simulation has been adapted for the parallel molecular dynamics code DL_POLY_3 [I.T. Todorov, W. Smith, Philos. Trans. Roy. Soc. London 362 (2004) 1835], making use of a novel 3D Fast Fourier Transform (DAFT) [I.J. Bush, The Daresbury Advanced Fourier transform, Daresbury Laboratory, 1999] that perfectly matches the Domain Decomposition (DD) parallelisation strategy [W. Smith, Comput. Phys. Comm. 62 (1991) 229; M.R.S. Pinches, D. Tildesley, W. Smith, Mol. Sim. 6 (1991) 51; D. Rapaport, Comput. Phys. Comm. 62 (1991) 217] of the DL_POLY_3 code. In this article we describe software adaptations undertaken to import this functionality and provide a review of its performance.

  9. A multiscale restriction-smoothed basis method for high contrast porous media represented on unstructured grids

    SciTech Connect

    Møyner, Olav Lie, Knut-Andreas

    2016-01-01

    A wide variety of multiscale methods have been proposed in the literature to reduce runtime and provide better scaling for the solution of Poisson-type equations modeling flow in porous media. We present a new multiscale restricted-smoothed basis (MsRSB) method that is designed to be applicable to both rectilinear grids and unstructured grids. Like many other multiscale methods, MsRSB relies on a coarse partition of the underlying fine grid and a set of local prolongation operators (multiscale basis functions) that map unknowns associated with the fine grid cells to unknowns associated with blocks in the coarse partition. These mappings are constructed by restricted smoothing: Starting from a constant, a localized iterative scheme is applied directly to the fine-scale discretization to compute prolongation operators that are consistent with the local properties of the differential operators. The resulting method has three main advantages: First of all, both the coarse and the fine grid can have general polyhedral geometry and unstructured topology. This means that partitions and good prolongation operators can easily be constructed for complex models involving high media contrasts and unstructured cell connections introduced by faults, pinch-outs, erosion, local grid refinement, etc. In particular, the coarse partition can be adapted to geological or flow-field properties represented on cells or faces to improve accuracy. Secondly, the method is accurate and robust when compared to existing multiscale methods and does not need expensive recomputation of local basis functions to account for transient behavior: Dynamic mobility changes are incorporated by continuing to iterate a few extra steps on existing basis functions. This way, the cost of updating the prolongation operators becomes proportional to the amount of change in fluid mobility and one reduces the need for expensive, tolerance-based updates. Finally, since the MsRSB method is formulated on top of a cell

  10. Newton and scholastic philosophy.

    PubMed

    Levitin, Dmitri

    2016-03-01

    This article examines Isaac Newton's engagement with scholastic natural philosophy. In doing so, it makes two major historiographical interventions. First of all, the recent claim that Newton's use of the concepts of analysis and synthesis was derived from the Aristotelian regressus tradition is challenged on the basis of bibliographical, palaeographical and intellectual evidence. Consequently, a new, contextual explanation is offered for Newton's use of these concepts. Second, it will be shown that some of Newton's most famous pronouncements - from the General Scholium appended to the second edition of the Principia (1713) and from elsewhere - are simply incomprehensible without an understanding of specific scholastic terminology and its later reception, and that this impacts in quite significant ways on how we understand Newton's natural philosophy more generally. Contrary to the recent historiographical near-consensus, Newton did not hold an elaborate metaphysics, and his seemingly 'metaphysical' statements were in fact anti-scholastic polemical salvoes. The whole investigation will permit us a brief reconsideration of the relationship between the self-proclaimed 'new' natural philosophy and its scholastic predecessors.

  11. The truncated Newton using 1st and 2nd order adjoint-state method: a new approach for traveltime tomography without rays

    NASA Astrophysics Data System (ADS)

    Bretaudeau, F.; Metivier, L.; Brossier, R.; Virieux, J.

    2013-12-01

    Traveltime tomography algorithms generally use ray tracing. The use of rays in tomography may not be suitable for handling very large datasets and perform tomography in very complex media. Traveltime maps can be computed through finite-difference approach (FD) and avoid complex ray-tracing algorithm for the forward modeling (Vidale 1998, Zhao 2004). However, rays back-traced from receiver to source following the gradient of traveltime are still used to compute the Fréchet derivatives. As a consequence, the sensitivity information computed using back-traced rays is not numerically consistent with the FD modeling used (the derivatives are only a rough approximation of the true derivatives of the forward modeling). Leung & Quian (2006) proposed a new approach that avoid ray tracing where the gradient of the misfit function is computed using the adjoint-state method. An adjoint-state variable is thus computed simultaneously for all receivers using a numerical method consistent with the forward modeling, and for the computational cost of one forward modeling. However, in their formulation, the receivers have to be located at the boundary of the investigated model, and the optimization approach is limited to simple gradient-based method (i.e. steepest descent, conjugate gradient) as only the gradient is computed. However, the Hessian operator has an important role in gradient-based reconstruction methods, providing the necessary information to rescale the gradient, correct for illumination deficit and remove artifacts. Leung & Quian (2006) uses LBFGS, a quasi-Newton method that provides an improved estimation of the influence of the inverse Hessian. Lelievre et al. (2011) also proposed a tomography approach in which the Fréchet derivatives are computed directly during the forward modeling using explicit symbolic differentiation of the modeling equations, resulting in a consistent Gauss-Newton inversion. We are interested here in the use of a new optimization approach

  12. Different shades of Newton: Herman Boerhaave on Newton mathematicus, philosophus, and optico-chemicus.

    PubMed

    Ducheyne, Steffen

    2017-03-29

    In this paper I will probe into Herman Boerhaave's (1668-1738) appropriation of Isaac Newton's natural philosophy. It will be shown that Newton's work served multiple purposes in Boerhaave's oeuvre, for he appropriated Newton's work differently in different contexts and in different episodes in his career. Three important episodes in, and contexts of, Boerhaave's appropriation of Newton's natural philosophical ideas and methods will be considered: 1710-11, the time of his often neglected lectures on the place of physics in medicine; 1715, when he delivered his most famous rectorial address; and, finally, 1731/2, in publishing his Elementa chemiae. Along the way, I will spell out the implications of Boerhaave's case for our understanding of the reception, or use, of Newton's ideas more generally.

  13. Compactness vs. Smoothness: Methods for regularizing fault slip inversions with application to subduction zone earthquakes.

    NASA Astrophysics Data System (ADS)

    Lohman, R. B.; Simons, M.

    2004-12-01

    We examine inversions of geodetic data for fault slip and discuss how inferred results are affected by choices of regularization. The final goal of any slip inversion is to enhance our understanding of the dynamics governing fault zone processes through kinematic descriptions of fault zone behavior at various temporal and spatial scales. Important kinematic observations include ascertaining whether fault slip is correlated with topographic and gravitational anomalies, whether coseismic and postseismic slip occur on complementary or overlapping regions of the fault plane, and how aftershock distributions compare with areas of coseismic and postseismic slip. Fault slip inversions are generally poorly-determined inverse problems requiring some sort of regularization. Attempts to place inversion results in the context of understanding fault zone processes should be accompanied by careful treatment of how the applied regularization affects characteristics of the inferred slip model. Most regularization techniques involve defining a metric that quantifies the solution "simplicity". A frequently employed method defines a "simple" slip distribution as one that is spatially smooth, balancing the fit to the data vs. the spatial complexity of the slip distribution. One problem related to the use of smoothing constraints is the "smearing" of fault slip into poorly-resolved areas on the fault plane. In addition, even if the data is fit well by a point source, the fact that a point source is spatially "rough" will force the inversion to choose a smoother model with slip over a broader area. Therefore, when we interpret the area of inferred slip we must ask whether the slipping area is truly constrained by the data, or whether it could be fit equally well by a more spatially compact source with larger amplitudes of slip. We introduce an alternate regularization technique for fault slip inversions, where we seek an end member model that is the smallest region of fault slip that

  14. GPUs, a new tool of acceleration in CFD: efficiency and reliability on smoothed particle hydrodynamics methods.

    PubMed

    Crespo, Alejandro C; Dominguez, Jose M; Barreiro, Anxo; Gómez-Gesteira, Moncho; Rogers, Benedict D

    2011-01-01

    Smoothed Particle Hydrodynamics (SPH) is a numerical method commonly used in Computational Fluid Dynamics (CFD) to simulate complex free-surface flows. Simulations with this mesh-free particle method far exceed the capacity of a single processor. In this paper, as part of a dual-functioning code for either central processing units (CPUs) or Graphics Processor Units (GPUs), a parallelisation using GPUs is presented. The GPU parallelisation technique uses the Compute Unified Device Architecture (CUDA) of nVidia devices. Simulations with more than one million particles on a single GPU card exhibit speedups of up to two orders of magnitude over using a single-core CPU. It is demonstrated that the code achieves different speedups with different CUDA-enabled GPUs. The numerical behaviour of the SPH code is validated with a standard benchmark test case of dam break flow impacting on an obstacle where good agreement with the experimental results is observed. Both the achieved speed-ups and the quantitative agreement with experiments suggest that CUDA-based GPU programming can be used in SPH methods with efficiency and reliability.

  15. GPUs, a New Tool of Acceleration in CFD: Efficiency and Reliability on Smoothed Particle Hydrodynamics Methods

    PubMed Central

    Crespo, Alejandro C.; Dominguez, Jose M.; Barreiro, Anxo; Gómez-Gesteira, Moncho; Rogers, Benedict D.

    2011-01-01

    Smoothed Particle Hydrodynamics (SPH) is a numerical method commonly used in Computational Fluid Dynamics (CFD) to simulate complex free-surface flows. Simulations with this mesh-free particle method far exceed the capacity of a single processor. In this paper, as part of a dual-functioning code for either central processing units (CPUs) or Graphics Processor Units (GPUs), a parallelisation using GPUs is presented. The GPU parallelisation technique uses the Compute Unified Device Architecture (CUDA) of nVidia devices. Simulations with more than one million particles on a single GPU card exhibit speedups of up to two orders of magnitude over using a single-core CPU. It is demonstrated that the code achieves different speedups with different CUDA-enabled GPUs. The numerical behaviour of the SPH code is validated with a standard benchmark test case of dam break flow impacting on an obstacle where good agreement with the experimental results is observed. Both the achieved speed-ups and the quantitative agreement with experiments suggest that CUDA-based GPU programming can be used in SPH methods with efficiency and reliability. PMID:21695185

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

    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.

  17. A method for anisotropic spatial smoothing of functional magnetic resonance images using distance transformation of a structural image

    NASA Astrophysics Data System (ADS)

    Nam, Haewon; Lee, Dongha; Doo Lee, Jong; Park, Hae-Jeong

    2011-08-01

    Spatial smoothing using isotropic Gaussian kernels to remove noise reduces spatial resolution and increases the partial volume effect of functional magnetic resonance images (fMRI), thereby reducing localization power. To minimize these limitations, we propose a novel anisotropic smoothing method for fMRI data. To extract an anisotropic tensor for each voxel of the functional data, we derived an intensity gradient using the distance transformation of the segmented gray matter of the fMRI-coregistered T1-weighted image. The intensity gradient was then used to determine the anisotropic smoothing kernel at each voxel of the fMRI data. Performance evaluations on both real and simulated data showed that the proposed method had 10% higher statistical power and about 20% higher gray matter localization compared to isotropic smoothing and robustness to the registration errors (up to 4 mm translations and 4° rotations) between T1 structural images and fMRI data. The proposed method also showed higher performance than the anisotropic smoothing with diffusion gradients derived from the fMRI intensity data.

  18. Enrollment Forecasting with Double Exponential Smoothing: Two Methods for Objective Weight Factor Selection. AIR Forum 1980 Paper.

    ERIC Educational Resources Information Center

    Gardner, Don E.

    The merits of double exponential smoothing are discussed relative to other types of pattern-based enrollment forecasting methods. The difficulties associated with selecting an appropriate weight factor are discussed, and their potential effects on prediction results are illustrated. Two methods for objectively selecting the "best" weight…

  19. A novel method for modeling of complex wall geometries in smoothed particle hydrodynamics

    NASA Astrophysics Data System (ADS)

    Eitzlmayr, Andreas; Koscher, Gerold; Khinast, Johannes

    2014-10-01

    Smoothed particle hydrodynamics (SPH) has become increasingly important during recent decades. Its meshless nature, inherent representation of convective transport and ability to simulate free surface flows make SPH particularly promising with regard to simulations of industrial mixing devices for high-viscous fluids, which often have complex rotating geometries and partially filled regions (e.g., twin-screw extruders). However, incorporating the required geometries remains a challenge in SPH since the most obvious and most common ways to model solid walls are based on particles (i.e., boundary particles and ghost particles), which leads to complications with arbitrarily-curved wall surfaces. To overcome this problem, we developed a systematic method for determining an adequate interaction between SPH particles and a continuous wall surface based on the underlying SPH equations. We tested our new approach by using the open-source particle simulator "LIGGGHTS" and comparing the velocity profiles to analytical solutions and SPH simulations with boundary particles. Finally, we followed the evolution of a tracer in a twin-cam mixer during the rotation, which was experimentally and numerically studied by several other authors, and ascertained good agreement with our results. This supports the validity of our newly-developed wall interaction method, which constitutes a step forward in SPH simulations of complex geometries.

  20. NITSOL: A Newton iterative solver for nonlinear systems

    SciTech Connect

    Pernice, M.; Walker, H.F.

    1996-12-31

    Newton iterative methods, also known as truncated Newton methods, are implementations of Newton`s method in which the linear systems that characterize Newton steps are solved approximately using iterative linear algebra methods. Here, we outline a well-developed Newton iterative algorithm together with a Fortran implementation called NITSOL. The basic algorithm is an inexact Newton method globalized by backtracking, in which each initial trial step is determined by applying an iterative linear solver until an inexact Newton criterion is satisfied. In the implementation, the user can specify inexact Newton criteria in several ways and select an iterative linear solver from among several popular {open_quotes}transpose-free{close_quotes} Krylov subspace methods. Jacobian-vector products used by the Krylov solver can be either evaluated analytically with a user-supplied routine or approximated using finite differences of function values. A flexible interface permits a wide variety of preconditioning strategies and allows the user to define a preconditioner and optionally update it periodically. We give details of these and other features and demonstrate the performance of the implementation on a representative set of test problems.

  1. Fast numerical design of spatial-selective rf pulses in MRI using Krotov and quasi-Newton based optimal control methods.

    PubMed

    Vinding, Mads S; Maximov, Ivan I; Tošner, Zdenĕk; Nielsen, Niels Chr

    2012-08-07

    The use of increasingly strong magnetic fields in magnetic resonance imaging (MRI) improves sensitivity, susceptibility contrast, and spatial or spectral resolution for functional and localized spectroscopic imaging applications. However, along with these benefits come the challenges of increasing static field (B(0)) and rf field (B(1)) inhomogeneities induced by radial field susceptibility differences and poorer dielectric properties of objects in the scanner. Increasing fields also impose the need for rf irradiation at higher frequencies which may lead to elevated patient energy absorption, eventually posing a safety risk. These reasons have motivated the use of multidimensional rf pulses and parallel rf transmission, and their combination with tailoring of rf pulses for fast and low-power rf performance. For the latter application, analytical and approximate solutions are well-established in linear regimes, however, with increasing nonlinearities and constraints on the rf pulses, numerical iterative methods become attractive. Among such procedures, optimal control methods have recently demonstrated great potential. Here, we present a Krotov-based optimal control approach which as compared to earlier approaches provides very fast, monotonic convergence even without educated initial guesses. This is essential for in vivo MRI applications. The method is compared to a second-order gradient ascent method relying on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method, and a hybrid scheme Krotov-BFGS is also introduced in this study. These optimal control approaches are demonstrated by the design of a 2D spatial selective rf pulse exciting the letters "JCP" in a water phantom.

  2. Development of a Smooth Trajectory Maneuver Method to Accommodate the Ares I Flight Control Constraints

    NASA Technical Reports Server (NTRS)

    Pinson, Robin M.; Schmitt, Terri L.; Hanson, John M.

    2008-01-01

    Six degree-of-freedom (DOF) launch vehicle trajectories are designed to follow an optimized 3-DOF reference trajectory. A vehicle has a finite amount of control power that it can allocate to performing maneuvers. Therefore, the 3-DOF trajectory must be designed to refrain from using 100% of the allowable control capability to perform maneuvers, saving control power for handling off-nominal conditions, wind gusts and other perturbations. During the Ares I trajectory analysis, two maneuvers were found to be hard for the control system to implement; a roll maneuver prior to the gravity turn and an angle of attack maneuver immediately after the J-2X engine start-up. It was decided to develop an approach for creating smooth maneuvers in the optimized reference trajectories that accounts for the thrust available from the engines. A feature of this method is that no additional angular velocity in the direction of the maneuver has been added to the vehicle after the maneuver completion. This paper discusses the equations behind these new maneuvers and their implementation into the Ares I trajectory design cycle. Also discussed is a possible extension to adjusting closed-loop guidance.

  3. Using two soft computing methods to predict wall and bed shear stress in smooth rectangular channels

    NASA Astrophysics Data System (ADS)

    Khozani, Zohreh Sheikh; Bonakdari, Hossein; Zaji, Amir Hossein

    2017-03-01

    Two soft computing methods were extended in order to predict the mean wall and bed shear stress in open channels. The genetic programming (GP) and Genetic Algorithm Artificial Neural Network (GAA) were investigated to determine the accuracy of these models in estimating wall and bed shear stress. The GP and GAA model results were compared in terms of testing dataset in order to find the best model. In modeling both bed and wall shear stress, the GP model performed better with RMSE of 0.0264 and 0.0185, respectively. Then both proposed models were compared with equations for rectangular open channels, trapezoidal channels and ducts. According to the results, the proposed models performed the best in predicting wall and bed shear stress in smooth rectangular channels. The obtained equation for rectangular channels could estimate values closer to experimental data, but the equations for ducts had poor, inaccurate results in predicting wall and bed shear stress. The equation presented for trapezoidal channels did not have acceptable accuracy in predicting wall and bed shear stress either.

  4. Turning around Newton's Second Law

    ERIC Educational Resources Information Center

    Goff, John Eric

    2004-01-01

    Conceptual and quantitative difficulties surrounding Newton's second law often arise among introductory physics students. Simply turning around how one expresses Newton's second law may assist students in their understanding of a deceptively simple-looking equation.

  5. "To Improve upon Hints of Things": Illustrating Isaac Newton.

    PubMed

    Schilt, Cornelis J

    2016-01-01

    When Isaac Newton died in 1727 he left a rich legacy in terms of draft manuscripts, encompassing a variety of topics: natural philosophy, mathematics, alchemy, theology, and chronology, as well as papers relating to his career at the Mint. One thing that immediately strikes us is the textuality of Newton's legacy: images are sparse. Regarding his scholarly endeavours we witness the same practice. Newton's extensive drafts on theology and chronology do not contain a single illustration or map. Today we have all of Newton's draft manuscripts as witnesses of his working methods, as well as access to a significant number of books from his own library. Drawing parallels between Newton's reading practices and his natural philosophical and scholarly work, this paper seeks to understand Newton's recondite writing and publishing politics.

  6. Isaac Newton Olympics.

    ERIC Educational Resources Information Center

    Cox, Carol

    2001-01-01

    Presents the Isaac Newton Olympics in which students complete a hands-on activity at seven stations and evaluate what they have learned in the activity and how it is related to real life. Includes both student and teacher instructions for three of the activities. (YDS)

  7. Optimizing seeding and culture methods to engineer smooth muscle tissue on biodegradable polymer matrices.

    PubMed

    Kim, B S; Putnam, A J; Kulik, T J; Mooney, D J

    1998-01-05

    The engineering of functional smooth muscle (SM) tissue is critical if one hopes to successfully replace the large number of tissues containing an SM component with engineered equivalents. This study reports on the effects of SM cell (SMC) seeding and culture conditions on the cellularity and composition of SM tissues engineered using biodegradable matrices (5 x 5 mm, 2-mm thick) of polyglycolic acid (PGA) fibers. Cells were seeded by injecting a cell suspension into polymer matrices in tissue culture dishes (static seeding), by stirring polymer matrices and a cell suspension in spinner flasks (stirred seeding), or by agitating polymer matrices and a cell suspension in tubes with an orbital shaker (agitated seeding). The density of SMCs adherent to these matrices was a function of cell concentration in the seeding solution, but under all conditions a larger number (approximately 1 order of magnitude) and more uniform distribution of SMCs adherent to the matrices were obtained with dynamic versus static seeding methods. The dynamic seeding methods, as compared to the static method, also ultimately resulted in new tissues that had a higher cellularity, more uniform cell distribution, and greater elastin deposition. The effects of culture conditions were next studied by culturing cell-polymer constructs in a stirred bioreactor versus static culture conditions. The stirred culture of SMC-seeded polymer matrices resulted in tissues with a cell density of 6.4 +/- 0.8 x 10(8) cells/cm3 after 5 weeks, compared to 2.0 +/- 1.1 x 10(8) cells/cm3 with static culture. The elastin and collagen synthesis rates and deposition within the engineered tissues were also increased by culture in the bioreactors. The elastin content after 5-week culture in the stirred bioreactor was 24 +/- 3%, and both the elastin content and the cellularity of these tissues are comparable to those of native SM tissue. New tissues were also created in vivo when dynamically seeded polymer matrices were

  8. Astronomers against Newton.

    PubMed

    Higgitt, Rebekah

    2004-03-01

    Francis Baily's publication of the manuscripts of John Flamsteed, the first Astronomer Royal, provoked a furious response. Flamsteed had quarrelled with Isaac Newton, and described him in terms unforgivable to those who claimed him as a paragon of all virtues, both moral and scientific. Baily was condemned for putting Flamsteed's complaints in the public sphere. However, his supporters saw his work as a critique of the excessive hero-worship accorded to Newton. Written when the word 'scientist' had been newly coined, this work and the debates it provoked gives us an insight into contemporary views of the role of the man of science and of the use of science to back political, religious and moral positions.

  9. Newton in Space

    NASA Technical Reports Server (NTRS)

    Herbert, Dexter (Editor)

    1992-01-01

    In this 'Liftoff to Learning' series video, astronauts (Charles Veach, Gregory Harbaugh, Donald McMonagle, Michael Coats, L. Blaine Hammond, Guion Bluford, Richard Hieb) from the STS-39 Mission use physical experiments and computer animation to explain how weightlessness and gravity affects everything and everyone onboard the Space Shuttle. The physics behind the differences between weight and mass, and the concepts of 'free fall', are demonstrated along with explanations and experiments of Sir Issac Newton's three laws of motion.

  10. Newton polyhedron and applications

    SciTech Connect

    Bruno, A.D.

    1994-12-31

    We give a simple presentation of an algorithm of selecting asymptotical first approximations of equations (algebraic and ordinary differential and partial differential). Here the first approximation of a solution of the initial equation is a solution of the corresponding first approximation of the equation. The algorithm is based on the geometry of power exponents including the Newton polyhedron. We give also a survey of applications of the algorithm in problems of Celestial Mechanics and Hydrodynamics.

  11. Newton in space

    NASA Astrophysics Data System (ADS)

    Herbert, Dexter

    1992-03-01

    In this 'Liftoff to Learning' series video, astronauts (Charles Veach, Gregory Harbaugh, Donald McMonagle, Michael Coats, L. Blaine Hammond, Guion Bluford, Richard Hieb) from the STS-39 Mission use physical experiments and computer animation to explain how weightlessness and gravity affects everything and everyone onboard the Space Shuttle. The physics behind the differences between weight and mass, and the concepts of 'free fall', are demonstrated along with explanations and experiments of Sir Issac Newton's three laws of motion.

  12. Globally convergent techniques in nonlinear Newton-Krylov

    NASA Technical Reports Server (NTRS)

    Brown, Peter N.; Saad, Youcef

    1989-01-01

    Some convergence theory is presented for nonlinear Krylov subspace methods. The basic idea of these methods is to use variants of Newton's iteration in conjunction with a Krylov subspace method for solving the Jacobian linear systems. These methods are variants of inexact Newton methods where the approximate Newton direction is taken from a subspace of small dimensions. The main focus is to analyze these methods when they are combined with global strategies such as linesearch techniques and model trust region algorithms. Most of the convergence results are formulated for projection onto general subspaces rather than just Krylov subspaces.

  13. Isaac Newton and the astronomical refraction.

    PubMed

    Lehn, Waldemar H

    2008-12-01

    In a short interval toward the end of 1694, Isaac Newton developed two mathematical models for the theory of the astronomical refraction and calculated two refraction tables, but did not publish his theory. Much effort has been expended, starting with Biot in 1836, in the attempt to identify the methods and equations that Newton used. In contrast to previous work, a closed form solution is identified for the refraction integral that reproduces the table for his first model (in which density decays linearly with elevation). The parameters of his second model, which includes the exponential variation of pressure in an isothermal atmosphere, have also been identified by reproducing his results. The implication is clear that in each case Newton had derived exactly the correct equations for the astronomical refraction; furthermore, he was the first to do so.

  14. The Unknown Detective Career of Isaac Newton

    SciTech Connect

    Levenson, Thomas

    2010-03-17

    Isaac Newton's fame is such that it would seem that almost nothing remains to be discovered about his deeds or his methods. But very little attention has been paid to the three decades Newton spent in charge of the Royal Mint, and especially to the first of those years, in which he supervised the remaking of England's entire silver money supply, all the while investigating, prosecuting, and executing the nation's currency criminals. That story provides unique perspectives on both his own habits of mind and on how what has come to be called the scientific revolution played out, not just in the minds of the great, but on the mean streets of London.

  15. Examination of tear film smoothness on corneae after refractive surgeries using a noninvasive interferometric method

    NASA Astrophysics Data System (ADS)

    Szczesna, Dorota H.; Kulas, Zbigniew; Kasprzak, Henryk T.; Stenevi, Ulf

    2009-11-01

    A lateral shearing interferometer was used to examine the smoothness of the tear film. The information about the distribution and stability of the precorneal tear film is carried out by the wavefront reflected from the surface of tears and coded in interference fringes. Smooth and regular fringes indicate a smooth tear film surface. On corneae after laser in situ keratomileusis (LASIK) or radial keratotomy (RK) surgery, the interference fringes are seldom regular. The fringes are bent on bright lines, which are interpreted as tear film breakups. The high-intensity pattern seems to appear in similar location on the corneal surface after refractive surgery. Our purpose was to extract information about the pattern existing under the interference fringes and calculate its shape reproducibility over time and following eye blinks. A low-pass filter was applied and correlation coefficient was calculated to compare a selected fragment of the template image to each of the following frames in the recorded sequence. High values of the correlation coefficient suggest that irregularities of the corneal epithelium might influence tear film instability and that tear film breakup may be associated with local irregularities of the corneal topography created after the LASIK and RK surgeries.

  16. Jacobian Free-Newton Krylov Discontinuous Galerkin Method and Physics-Based Preconditioning for Nuclear Reactor Simulations

    SciTech Connect

    HyeongKae Park; R. Nourgaliev; Richard C. Martineau; Dana A. Knoll

    2008-09-01

    Multidimensional, higher-order (2nd and higher) numerical methods have come to the forefront in recent years due to significant advances of computer technology and numerical algorithms, and have shown great potential as viable design tools for realistic applications. To achieve this goal, implicit high-order accurate coupling of the multiphysics simulations is a critical component. One of the issues that arise from multiphysics simulation is the necessity to resolve multiple time scales. For example, the dynamical time scales of neutron kinetics, fluid dynamics and heat conduction significantly differ (typically >1010 magnitude), with the dominant (fastest) physical mode also changing during the course of transient [Pope and Mousseau, 2007]. This leads to the severe time step restriction for stability in traditional multiphysics (i.e. operator split, semi-implicit discretization) simulations. The lower order methods suffer from an undesirable numerical dissipation. Thus implicit, higher order accurate scheme is necessary to perform seamlessly-coupled multiphysics simulations that can be used to analyze the “what-if” regulatory accident scenarios, or to design and optimize engineering systems.

  17. Preconditioning Techniques for a Newton-Krylov Algorithm for the Compressible Navier-Stokes Equations

    NASA Astrophysics Data System (ADS)

    Gatsis, John

    An investigation of preconditioning techniques is presented for a Newton-Krylov algorithm that is used for the computation of steady, compressible, high Reynolds number flows about airfoils. A second-order centred-difference method is used to discretize the compressible Navier-Stokes (NS) equations that govern the fluid flow. The one-equation Spalart-Allmaras turbulence model is used. The discretized equations are solved using Newton's method and the generalized minimal residual (GMRES) Krylov subspace method is used to approximately solve the linear system. These preconditioning techniques are first applied to the solution of the discretized steady convection-diffusion equation. Various orderings, iterative block incomplete LU (BILU) preconditioning and multigrid preconditioning are explored. The baseline preconditioner is a BILU factorization of a lower-order discretization of the system matrix in the Newton linearization. An ordering based on the minimum discarded fill (MDF) ordering is developed and compared to the widely popular reverse Cuthill-McKee ordering. An evolutionary algorithm is used to investigate and enhance this ordering. For the convection-diffusion equation, the MDF-based ordering performs well and RCM is superior for the NS equations. Experiments for inviscid, laminar and turbulent cases are presented to show the effectiveness of iterative BILU preconditioning in terms of reducing the number of GMRES iterations, and hence the memory requirements of the Newton-Krylov algorithm. Multigrid preconditioning also reduces the number of GMRES iterations. The framework for the iterative BILU and BILU-smoothed multigrid preconditioning algorithms is presented in detail.

  18. Integrating Scientific Methods and Knowledge into the Teaching of Newton's Theory of Gravitation: An Instructional Sequence for Teachers' and Students' Nature of Science Education

    ERIC Educational Resources Information Center

    Develaki, Maria

    2012-01-01

    The availability of teaching units on the nature of science (NOS) can reinforce classroom instruction in the subject, taking into account the related deficiencies in textbook material and teacher training. We give a sequence of teaching units in which the teaching of Newton's gravitational theory is used as a basis for reflecting on the…

  19. An implicit Smooth Particle Hydrodynamic code

    SciTech Connect

    Knapp, Charles E.

    2000-05-01

    An implicit version of the Smooth Particle Hydrodynamic (SPH) code SPHINX has been written and is working. In conjunction with the SPHINX code the new implicit code models fluids and solids under a wide range of conditions. SPH codes are Lagrangian, meshless and use particles to model the fluids and solids. The implicit code makes use of the Krylov iterative techniques for solving large linear-systems and a Newton-Raphson method for non-linear corrections. It uses numerical derivatives to construct the Jacobian matrix. It uses sparse techniques to save on memory storage and to reduce the amount of computation. It is believed that this is the first implicit SPH code to use Newton-Krylov techniques, and is also the first implicit SPH code to model solids. A description of SPH and the techniques used in the implicit code are presented. Then, the results of a number of tests cases are discussed, which include a shock tube problem, a Rayleigh-Taylor problem, a breaking dam problem, and a single jet of gas problem. The results are shown to be in very good agreement with analytic solutions, experimental results, and the explicit SPHINX code. In the case of the single jet of gas case it has been demonstrated that the implicit code can do a problem in much shorter time than the explicit code. The problem was, however, very unphysical, but it does demonstrate the potential of the implicit code. It is a first step toward a useful implicit SPH code.

  20. A smooth dissipative particle dynamics method for domains with arbitrary-geometry solid boundaries

    NASA Astrophysics Data System (ADS)

    Gatsonis, Nikolaos A.; Potami, Raffaele; Yang, Jun

    2014-01-01

    A smooth dissipative particle dynamics method with dynamic virtual particle allocation (SDPD-DV) for modeling and simulation of mesoscopic fluids in wall-bounded domains is presented. The physical domain in SDPD-DV may contain external and internal solid boundaries of arbitrary geometries, periodic inlets and outlets, and the fluid region. The SDPD-DV method is realized with fluid particles, boundary particles, and dynamically allocated virtual particles. The internal or external solid boundaries of the domain can be of arbitrary geometry and are discretized with a surface grid. These boundaries are represented by boundary particles with assigned properties. The fluid domain is discretized with fluid particles of constant mass and variable volume. Conservative and dissipative force models due to virtual particles exerted on a fluid particle in the proximity of a solid boundary supplement the original SDPD formulation. The dynamic virtual particle allocation approach provides the density and the forces due to virtual particles. The integration of the SDPD equations is accomplished with a velocity-Verlet algorithm for the momentum and a Runge-Kutta for the entropy equation. The velocity integrator is supplemented by a bounce-forward algorithm in cases where the virtual particle force model is not able to prevent particle penetration. For the incompressible isothermal systems considered in this work, the pressure of a fluid particle is obtained by an artificial compressibility formulation for liquids and the ideal gas law for gases. The self-diffusion coefficient is obtained by an implementation of the generalized Einstein and the Green-Kubo relations. Field properties are obtained by sampling SDPD-DV outputs on a post-processing grid that allows harnessing the particle information on desired spatiotemporal scales. The SDPD-DV method is verified and validated with simulations in bounded and periodic domains that cover the hydrodynamic and mesoscopic regimes for

  1. A nonparametric mean-variance smoothing method to assess Arabidopsis cold stress transcriptional regulator CBF2 overexpression microarray data.

    PubMed

    Hu, Pingsha; Maiti, Tapabrata

    2011-01-01

    Microarray is a powerful tool for genome-wide gene expression analysis. In microarray expression data, often mean and variance have certain relationships. We present a non-parametric mean-variance smoothing method (NPMVS) to analyze differentially expressed genes. In this method, a nonlinear smoothing curve is fitted to estimate the relationship between mean and variance. Inference is then made upon shrinkage estimation of posterior means assuming variances are known. Different methods have been applied to simulated datasets, in which a variety of mean and variance relationships were imposed. The simulation study showed that NPMVS outperformed the other two popular shrinkage estimation methods in some mean-variance relationships; and NPMVS was competitive with the two methods in other relationships. A real biological dataset, in which a cold stress transcription factor gene, CBF2, was overexpressed, has also been analyzed with the three methods. Gene ontology and cis-element analysis showed that NPMVS identified more cold and stress responsive genes than the other two methods did. The good performance of NPMVS is mainly due to its shrinkage estimation for both means and variances. In addition, NPMVS exploits a non-parametric regression between mean and variance, instead of assuming a specific parametric relationship between mean and variance. The source code written in R is available from the authors on request.

  2. Isaac Newton: Man, Myth, and Mathematics.

    ERIC Educational Resources Information Center

    Rickey, V. Frederick

    1987-01-01

    This article was written in part to celebrate the anniversaries of landmark mathematical works by Newton and Descartes. It's other purpose is to dispel some myths about Sir Isaac Newton and to encourage readers to read Newton's works. (PK)

  3. Accurate and efficient method for smoothly space-variant Gaussian blurring.

    PubMed

    Popkin, Timothy; Cavallaro, Andrea; Hands, David

    2010-05-01

    This paper presents a computationally efficient algorithm for smoothly space-variant Gaussian blurring of images. The proposed algorithm uses a specialized filter bank with optimal filters computed through principal component analysis. This filter bank approximates perfect space-variant Gaussian blurring to arbitrarily high accuracy and at greatly reduced computational cost compared to the brute force approach of employing a separate low-pass filter at each image location. This is particularly important for spatially variant image processing such as foveated coding. Experimental results show that the proposed algorithm provides typically 10 to 15 dB better approximation of perfect Gaussian blurring than the blended Gaussian pyramid blurring approach when using a bank of just eight filters.

  4. Newton-Krylov-Schwarz: An implicit solver for CFD

    NASA Technical Reports Server (NTRS)

    Cai, Xiao-Chuan; Keyes, David E.; Venkatakrishnan, V.

    1995-01-01

    Newton-Krylov methods and Krylov-Schwarz (domain decomposition) methods have begun to become established in computational fluid dynamics (CFD) over the past decade. The former employ a Krylov method inside of Newton's method in a Jacobian-free manner, through directional differencing. The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that relies primarily on local information, for data-parallel concurrency. They may be composed as Newton-Krylov-Schwarz (NKS) methods, which seem particularly well suited for solving nonlinear elliptic systems in high-latency, distributed-memory environments. We give a brief description of this family of algorithms, with an emphasis on domain decomposition iterative aspects. We then describe numerical simulations with Newton-Krylov-Schwarz methods on aerodynamics applications emphasizing comparisons with a standard defect-correction approach, subdomain preconditioner consistency, subdomain preconditioner quality, and the effect of a coarse grid.

  5. Edme Mariotte and Newton's Cradle

    ERIC Educational Resources Information Center

    Cross, Rod

    2012-01-01

    The first recorded experiments describing the phenomena made popular by Newton's cradle appear to be those conducted by Edme Mariotte around 1670. He was quoted in Newton's "Principia," along with Wren, Wallis, and Huygens, as having conducted pioneering experiments on the collisions of pendulum balls. Each of these authors concluded that momentum…

  6. Telecommunications Handbook: Connecting to Newton.

    ERIC Educational Resources Information Center

    Baker, Christopher; And Others

    This handbook was written by the Argonne National Laboratory for use with their electronic bulletin board system (BBS) called Newton. Newton is an educational BBS for use by teachers, students, and parents. Topics range from discussions of science fair topics to online question and answer sessions with scientists. Future capabilities will include…

  7. Newton's Cradle in Physics Education

    ERIC Educational Resources Information Center

    Gauld, Colin F.

    2006-01-01

    Newton's Cradle is a series of bifilar pendulums used in physics classrooms to demonstrate the role of the principles of conservation of momentum and kinetic energy in elastic collisions. The paper reviews the way in which textbooks use Newton's Cradle and points out the unsatisfactory nature of these treatments in almost all cases. The literature…

  8. A computational method for three-dimensional reconstruction of the microarchitecture of myometrial smooth muscle from histological sections

    PubMed Central

    Lutton, E. Josiah; Lammers, Wim J. E. P.; James, Sean

    2017-01-01

    Background The fibrous structure of the myometrium has previously been characterised at high resolutions in small tissue samples (< 100 mm3) and at low resolutions (∼500 μm per voxel edge) in whole-organ reconstructions. However, no high-resolution visualisation of the myometrium at the organ level has previously been attained. Methods and results We have developed a technique to reconstruct the whole myometrium from serial histological slides, at a resolution of approximately 50 μm per voxel edge. Reconstructions of samples taken from human and rat uteri are presented here, along with histological verification of the reconstructions and detailed investigation of the fibrous structure of these uteri, using a range of tools specifically developed for this analysis. These reconstruction techniques enable the high-resolution rendering of global structure previously observed at lower resolution. Moreover, structures observed previously in small portions of the myometrium can be observed in the context of the whole organ. The reconstructions are in direct correspondence with the original histological slides, which allows the inspection of the anatomical context of any features identified in the three-dimensional reconstructions. Conclusions and significance The methods presented here have been used to generate a faithful representation of myometrial smooth muscle at a resolution of ∼50 μm per voxel edge. Characterisation of the smooth muscle structure of the myometrium by means of this technique revealed a detailed view of previously identified global structures in addition to a global view of the microarchitecture. A suite of visualisation tools allows researchers to interrogate the histological microarchitecture. These methods will be applicable to other smooth muscle tissues to analyse fibrous microarchitecture. PMID:28301486

  9. MODFLOW-NWT, A Newton formulation for MODFLOW-2005

    USGS Publications Warehouse

    Niswonger, Richard G.; Panday, Sorab; Ibaraki, Motomu

    2011-01-01

    This report documents a Newton formulation of MODFLOW-2005, called MODFLOW-NWT. MODFLOW-NWT is a standalone program that is intended for solving problems involving drying and rewetting nonlinearities of the unconfined groundwater-flow equation. MODFLOW-NWT must be used with the Upstream-Weighting (UPW) Package for calculating intercell conductances in a different manner than is done in the Block-Centered Flow (BCF), Layer Property Flow (LPF), or Hydrogeologic-Unit Flow (HUF; Anderman and Hill, 2000) Packages. The UPW Package treats nonlinearities of cell drying and rewetting by use of a continuous function of groundwater head, rather than the discrete approach of drying and rewetting that is used by the BCF, LPF, and HUF Packages. This further enables application of the Newton formulation for unconfined groundwater-flow problems because conductance derivatives required by the Newton method are smooth over the full range of head for a model cell. The NWT linearization approach generates an asymmetric matrix, which is different from the standard MODFLOW formulation that generates a symmetric matrix. Because all linear solvers presently available for use with MODFLOW-2005 solve only symmetric matrices, MODFLOW-NWT includes two previously developed asymmetric matrix-solver options. The matrix-solver options include a generalized-minimum-residual (GMRES) Solver and an Orthomin / stabilized conjugate-gradient (CGSTAB) Solver. The GMRES Solver is documented in a previously published report, such that only a brief description and input instructions are provided in this report. However, the CGSTAB Solver (called XMD) is documented in this report. Flow-property input for the UPW Package is designed based on the LPF Package and material-property input is identical to that for the LPF Package except that the rewetting and vertical-conductance correction options of the LPF Package are not available with the UPW Package. Input files constructed for the LPF Package can be used

  10. [Methods to smooth mortality indicators: application to analysis of inequalities in mortality in Spanish cities [the MEDEA Project

    PubMed

    Barceló, M Antònia; Saez, Marc; Cano-Serral, Gemma; Martínez-Beneito, Miguel Angel; Martínez, José Miguel; Borrell, Carme; Ocaña-Riola, Ricardo; Montoya, Imanol; Calvo, Montse; López-Abente, Gonzalo; Rodríguez-Sanz, Maica; Toro, Silvia; Alcalá, José Tomás; Saurina, Carme; Sánchez-Villegas, Pablo; Figueiras, Adolfo

    2008-01-01

    Although there is some experience in the study of mortality inequalities in Spanish cities, there are large urban centers that have not yet been investigated using the census tract as the unit of territorial analysis. The coordinated project was designed to fill this gap, with the participation of 10 groups of researchers in Andalusia, Aragon, Catalonia, Galicia, Madrid, Valencia, and the Basque Country. The MEDEA project has four distinguishing features: a) the census tract is used as the basic geographical area; b) statistical methods that include the geographical structure of the region under study are employed for risk estimation; c) data are drawn from three complementary data sources (information on air pollution, information on industrial pollution, and the records of mortality registrars), and d) a coordinated, large-scale analysis, favored by the implantation of coordinated research networks, is carried out. The main objective of the present study was to explain the methods for smoothing mortality indicators in the context of the MEDEA project. This study focusses on the methodology and the results of the Besag, York and Mollié model (BYM) in disease mapping. In the MEDEA project, standardized mortality ratios (SMR), corresponding to 17 large groups of causes of death and 28 specific causes, were smoothed by means of the BYM model; however, in the present study this methodology was applied to mortality due to cancer of the trachea, bronchi and lung in men and women in the city of Barcelona from 1996 to 2003. As a result of smoothing, a different geographical pattern for SMR in both genders was observed. In men, a SMR higher than unity was found in highly deprived areas. In contrast, in women, this pattern was observed in more affluent areas.

  11. Fourth-order solutions of nonlinear two-point boundary value problems by Newton-HSSOR iteration

    NASA Astrophysics Data System (ADS)

    Sulaiman, Jumat; Hasan, Mohd. Khatim; Othman, Mohamed; Karim, Samsul Ariffin Abdul

    2014-06-01

    In this paper, the Half-Sweep Successive Over-Relaxation (HSSOR) iterative method together with Newton scheme namely Newton-HSSOR is investigated in solving the nonlinear systems generated from the fourth-order half-sweep finite difference approximation equation for nonlinear two-point boundary value problems. The Newton scheme is proposed to linearize the nonlinear system into the form of linear system. On top of that, we also present the basic formulation and implementation of Newton-HSSOR iterative method. For comparison purpose, combinations between the Full-Sweep Gauss-Seidel (FSGS) and Full-Sweep Successive Over-Relaxation (FSSOR) iterative methods with Newton scheme, which are indicated as Newton-FSGS and Newton-FSSOR methods respectively have been implemented numerically. Numerical experiments of two problems are given to illustrate that the Newton-HSSOR method is more superior compared with the tested methods.

  12. A comparison of methods for smoothing and gap filling time series of remote sensing observations - application to MODIS LAI products

    NASA Astrophysics Data System (ADS)

    Kandasamy, S.; Baret, F.; Verger, A.; Neveux, P.; Weiss, M.

    2013-06-01

    Moderate resolution satellite sensors including MODIS (Moderate Resolution Imaging Spectroradiometer) already provide more than 10 yr of observations well suited to describe and understand the dynamics of earth's surface. However, these time series are associated with significant uncertainties and incomplete because of cloud cover. This study compares eight methods designed to improve the continuity by filling gaps and consistency by smoothing the time course. It includes methods exploiting the time series as a whole (iterative caterpillar singular spectrum analysis (ICSSA), empirical mode decomposition (EMD), low pass filtering (LPF) and Whittaker smoother (Whit)) as well as methods working on limited temporal windows of a few weeks to few months (adaptive Savitzky-Golay filter (SGF), temporal smoothing and gap filling (TSGF), and asymmetric Gaussian function (AGF)), in addition to the simple climatological LAI yearly profile (Clim). Methods were applied to the MODIS leaf area index product for the period 2000-2008 and over 25 sites showed a large range of seasonal patterns. Performances were discussed with emphasis on the balance achieved by each method between accuracy and roughness depending on the fraction of missing observations and the length of the gaps. Results demonstrate that the EMD, LPF and AGF methods were failing because of a significant fraction of gaps (more than 20%), while ICSSA, Whit and SGF were always providing estimates for dates with missing data. TSGF (Clim) was able to fill more than 50% of the gaps for sites with more than 60% (80%) fraction of gaps. However, investigation of the accuracy of the reconstructed values shows that it degrades rapidly for sites with more than 20% missing data, particularly for ICSSA, Whit and SGF. In these conditions, TSGF provides the best performances that are significantly better than the simple Clim for gaps shorter than about 100 days. The roughness of the reconstructed temporal profiles shows large

  13. A comparison of methods for smoothing and gap filling time series of remote sensing observations: application to MODIS LAI products

    NASA Astrophysics Data System (ADS)

    Kandasamy, S.; Baret, F.; Verger, A.; Neveux, P.; Weiss, M.

    2012-12-01

    Moderate resolution satellite sensors including MODIS already provide more than 10 yr of observations well suited to describe and understand the dynamics of the Earth surface. However, these time series are incomplete because of cloud cover and associated with significant uncertainties. This study compares eight methods designed to improve the continuity by filling gaps and the consistency by smoothing the time course. It includes methods exploiting the time series as a whole (Iterative caterpillar singular spectrum analysis (ICSSA), empirical mode decomposition (EMD), low pass filtering (LPF) and Whittaker smoother (Whit)) as well as methods working on limited temporal windows of few weeks to few months (Adaptive Savitzky-Golay filter (SGF), temporal smoothing and gap filling (TSGF) and asymmetric Gaussian function (AGF)) in addition to the simple climatological LAI yearly profile (Clim). Methods were applied to MODIS leaf area index product for the period 2000-2008 over 25 sites showing a large range of seasonal patterns. Performances were discussed with emphasis on the balance achieved by each method between accuracy and roughness depending on the fraction of missing observations and the length of the gaps. Results demonstrate that EMD, LPF and AGF methods were failing in case of significant fraction of gaps (%Gap > 20%), while ICSSA, Whit and SGF were always providing estimates for dates with missing data. TSGF (respectively Clim) was able to fill more than 50% of the gaps for sites with more than 60% (resp. 80%) fraction of gaps. However, investigation of the accuracy of the reconstructed values shows that it degrades rapidly for sites with more than 20% missing data, particularly for ICSSA, Whit and SGF. In these conditions, TSGF provides the best performances significantly better than the simple Clim for gaps shorter than about 100 days. The roughness of the reconstructed temporal profiles shows large differences between the several methods, with a decrease

  14. Smooth particle hydrodynamics method for modeling cavitation-induced fracture of a fluid under shock-wave loading

    NASA Astrophysics Data System (ADS)

    Davydov, M. N.; Kedrinskii, V. K.

    2013-11-01

    It is demonstrated that the method of smoothed particle hydrodynamics can be used to study the flow structure in a cavitating medium with a high concentration of the gas phase and to describe the process of inversion of the two-phase state of this medium: transition from a cavitating fluid to a system consisting of a gas and particles. A numerical analysis of the dynamics of the state of a hemispherical droplet under shock-wave loading shows that focusing of the shock wave reflected from the free surface of the droplet leads to the formation of a dense, but rapidly expanding cavitation cluster at the droplet center. By the time t = 500 µs, the bubbles at the cluster center not only coalesce and form a foam-type structure, but also transform to a gas-particle system, thus, forming an almost free rapidly expanding zone. The mechanism of this process defined previously as an internal "cavitation explosion" of the droplet is validated by means of mathematical modeling of the problem by the smoothed particle hydrodynamics method. The deformation of the cavitating droplet is finalized by its decomposition into individual fragments and particles.

  15. Automatic estimation of sleep level for nap based on conditional probability of sleep stages and an exponential smoothing method.

    PubMed

    Wang, Bei; Wang, Xingyu; Zhang, Tao; Nakamura, Masatoshi

    2013-01-01

    An automatic sleep level estimation method was developed for monitoring and regulation of day time nap sleep. The recorded nap data is separated into continuous 5-second segments. Features are extracted from EEGs, EOGs and EMG. A parameter of sleep level is defined which is estimated based on the conditional probability of sleep stages. An exponential smoothing method is applied for the estimated sleep level. There were totally 12 healthy subjects, with an averaged age of 22 yeas old, participated into the experimental work. Comparing with sleep stage determination, the presented sleep level estimation method showed better performance for nap sleep interpretation. Real time monitoring and regulation of nap is realizable based on the developed technique.

  16. A novel smooth impact drive mechanism actuation method with dual-slider for a compact zoom lens system.

    PubMed

    Lee, Jonghyun; Kwon, Won Sik; Kim, Kyung-Soo; Kim, Soohyun

    2011-08-01

    In this paper, a novel actuation method for a smooth impact drive mechanism that positions dual-slider by a single piezo-element is introduced and applied to a compact zoom lens system. A mode chart that determines the state of the slider at the expansion or shrinkage periods of the piezo-element is presented, and the design guide of a driving input profile is proposed. The motion of dual-slider holding lenses is analyzed at each mode, and proper modes for zoom functions are selected for the purpose of positioning two lenses. Because the proposed actuation method allows independent movement of two lenses by a single piezo-element, the zoom lens system can be designed to be compact. For a feasibility test, a lens system composed of an afocal zoom system and a focusing lens was developed, and the passive auto-focus method was implemented.

  17. Critical Parameters of the In Vitro Method of Vascular Smooth Muscle Cell Calcification

    PubMed Central

    Hortells, Luis; Sosa, Cecilia; Millán, Ángel; Sorribas, Víctor

    2015-01-01

    Background Vascular calcification (VC) is primarily studied using cultures of vascular smooth muscle cells. However, the use of very different protocols and extreme conditions can provide findings unrelated to VC. In this work we aimed to determine the critical experimental parameters that affect calcification in vitro and to determine the relevance to calcification in vivo. Experimental Procedures and Results Rat VSMC calcification in vitro was studied using different concentrations of fetal calf serum, calcium, and phosphate, in different types of culture media, and using various volumes and rates of change. The bicarbonate content of the media critically affected pH and resulted in supersaturation, depending on the concentration of Ca2+ and Pi. Such supersaturation is a consequence of the high dependence of bicarbonate buffers on CO2 vapor pressure and bicarbonate concentration at pHs above 7.40. Such buffer systems cause considerable pH variations as a result of minor experimental changes. The variations are more critical for DMEM and are negligible when the bicarbonate concentration is reduced to ¼. Particle nucleation and growth were observed by dynamic light scattering and electron microscopy. Using 2mM Pi, particles of ~200nm were observed at 24 hours in MEM and at 1 hour in DMEM. These nuclei grew over time, were deposited in the cells, and caused osteogene expression or cell death, depending on the precipitation rate. TEM observations showed that the initial precipitate was amorphous calcium phosphate (ACP), which converts into hydroxyapatite over time. In blood, the scenario is different, because supersaturation is avoided by a tightly controlled pH of 7.4, which prevents the formation of PO43--containing ACP. Conclusions The precipitation of ACP in vitro is unrelated to VC in vivo. The model needs to be refined through controlled pH and the use of additional procalcifying agents other than Pi in order to reproduce calcium phosphate deposition in vivo

  18. An Inexact Newton-Krylov Algorithm for Constrained Diffeomorphic Image Registration.

    PubMed

    Mang, Andreas; Biros, George

    We propose numerical algorithms for solving large deformation diffeomorphic image registration problems. We formulate the nonrigid image registration problem as a problem of optimal control. This leads to an infinite-dimensional partial differential equation (PDE) constrained optimization problem. The PDE constraint consists, in its simplest form, of a hyperbolic transport equation for the evolution of the image intensity. The control variable is the velocity field. Tikhonov regularization on the control ensures well-posedness. We consider standard smoothness regularization based on H(1)- or H(2)-seminorms. We augment this regularization scheme with a constraint on the divergence of the velocity field (control variable) rendering the deformation incompressible (Stokes regularization scheme) and thus ensuring that the determinant of the deformation gradient is equal to one, up to the numerical error. We use a Fourier pseudospectral discretization in space and a Chebyshev pseudospectral discretization in time. The latter allows us to reduce the number of unknowns and enables the time-adaptive inversion for nonstationary velocity fields. We use a preconditioned, globalized, matrix-free, inexact Newton-Krylov method for numerical optimization. A parameter continuation is designed to estimate an optimal regularization parameter. Regularity is ensured by controlling the geometric properties of the deformation field. Overall, we arrive at a black-box solver that exploits computational tools that are precisely tailored for solving the optimality system. We study spectral properties of the Hessian, grid convergence, numerical accuracy, computational efficiency, and deformation regularity of our scheme. We compare the designed Newton-Krylov methods with a globalized Picard method (preconditioned gradient descent). We study the influence of a varying number of unknowns in time. The reported results demonstrate excellent numerical accuracy, guaranteed local deformation

  19. Quantum State Smoothing

    NASA Astrophysics Data System (ADS)

    Guevara, Ivonne; Wiseman, Howard

    2015-10-01

    Smoothing is an estimation method whereby a classical state (probability distribution for classical variables) at a given time is conditioned on all-time (both earlier and later) observations. Here we define a smoothed quantum state for a partially monitored open quantum system, conditioned on an all-time monitoring-derived record. We calculate the smoothed distribution for a hypothetical unobserved record which, when added to the real record, would complete the monitoring, yielding a pure-state "quantum trajectory." Averaging the pure state over this smoothed distribution yields the (mixed) smoothed quantum state. We study how the choice of actual unraveling affects the purity increase over that of the conventional (filtered) state conditioned only on the past record.

  20. Quantum State Smoothing.

    PubMed

    Guevara, Ivonne; Wiseman, Howard

    2015-10-30

    Smoothing is an estimation method whereby a classical state (probability distribution for classical variables) at a given time is conditioned on all-time (both earlier and later) observations. Here we define a smoothed quantum state for a partially monitored open quantum system, conditioned on an all-time monitoring-derived record. We calculate the smoothed distribution for a hypothetical unobserved record which, when added to the real record, would complete the monitoring, yielding a pure-state "quantum trajectory." Averaging the pure state over this smoothed distribution yields the (mixed) smoothed quantum state. We study how the choice of actual unraveling affects the purity increase over that of the conventional (filtered) state conditioned only on the past record.

  1. Newton and the Second Law of Motion

    ERIC Educational Resources Information Center

    Gauld, C. F.

    1975-01-01

    Deals generally with historical errors in science teaching and specifically with Newton's conception of his second law of motion. With reference to Newton's "Principia", the author concludes that Newton would not understand what we today refer to as "Newton's Second Law." (MLH)

  2. A Parallel Implementation of a Smoothed Particle Hydrodynamics Method on Graphics Hardware Using the Compute Unified Device Architecture

    SciTech Connect

    Wong Unhong; Wong Honcheng; Tang Zesheng

    2010-05-21

    The smoothed particle hydrodynamics (SPH), which is a class of meshfree particle methods (MPMs), has a wide range of applications from micro-scale to macro-scale as well as from discrete systems to continuum systems. Graphics hardware, originally designed for computer graphics, now provide unprecedented computational power for scientific computation. Particle system needs a huge amount of computations in physical simulation. In this paper, an efficient parallel implementation of a SPH method on graphics hardware using the Compute Unified Device Architecture is developed for fluid simulation. Comparing to the corresponding CPU implementation, our experimental results show that the new approach allows significant speedups of fluid simulation through handling huge amount of computations in parallel on graphics hardware.

  3. On the constrained minimization of smooth Kurdyka—Łojasiewicz functions with the scaled gradient projection method

    NASA Astrophysics Data System (ADS)

    Prato, Marco; Bonettini, Silvia; Loris, Ignace; Porta, Federica; Rebegoldi, Simone

    2016-10-01

    The scaled gradient projection (SGP) method is a first-order optimization method applicable to the constrained minimization of smooth functions and exploiting a scaling matrix multiplying the gradient and a variable steplength parameter to improve the convergence of the scheme. For a general nonconvex function, the limit points of the sequence generated by SGP have been proved to be stationary, while in the convex case and with some restrictions on the choice of the scaling matrix the sequence itself converges to a constrained minimum point. In this paper we extend these convergence results by showing that the SGP sequence converges to a limit point provided that the objective function satisfies the Kurdyka-Łojasiewicz property at each point of its domain and its gradient is Lipschitz continuous.

  4. XMM-Newton publication statistics

    NASA Astrophysics Data System (ADS)

    Ness, J.-U.; Parmar, A. N.; Valencic, L. A.; Smith, R.; Loiseau, N.; Salama, A.; Ehle, M.; Schartel, N.

    2014-02-01

    We assessed the scientific productivity of XMM-Newton by examining XMM-Newton publications and data usage statistics. We analyse 3272 refereed papers, published until the end of 2012, that directly use XMM-Newton data. The SAO/NASA Astrophysics Data System (ADS) was used to provide additional information on each paper including the number of citations. For each paper, the XMM-Newton observation identifiers and instruments used to provide the scientific results were determined. The identifiers were used to access the XMM-{Newton} Science Archive (XSA) to provide detailed information on the observations themselves and on the original proposals. The information obtained from these sources was then combined to allow the scientific productivity of the mission to be assessed. Since around three years after the launch of XMM-Newton there have been around 300 refereed papers per year that directly use XMM-Newton data. After more than 13 years in operation, this rate shows no evidence that it is decreasing. Since 2002, around 100 scientists per year become lead authors for the first time on a refereed paper which directly uses XMM-Newton data. Each refereed XMM-Newton paper receives around four citations per year in the first few years with a long-term citation rate of three citations per year, more than five years after publication. About half of the articles citing XMM-Newton articles are not primarily X-ray observational papers. The distribution of elapsed time between observations taken under the Guest Observer programme and first article peaks at 2 years with a possible second peak at 3.25 years. Observations taken under the Target of Opportunity programme are published significantly faster, after one year on average. The fraction of science time taken until the end of 2009 that has been used in at least one article is {˜ 90} %. Most observations were used more than once, yielding on average a factor of two in usage on available observing time per year. About 20 % of

  5. Poles tracking of weakly nonlinear structures using a Bayesian smoothing method

    NASA Astrophysics Data System (ADS)

    Stephan, Cyrille; Festjens, Hugo; Renaud, Franck; Dion, Jean-Luc

    2017-02-01

    This paper describes a method for the identification and the tracking of poles of a weakly nonlinear structure from its free responses. This method is based on a model of multichannel damped sines whose parameters evolve over time. Their variations are approximated in discrete time by a nonlinear state space model. States are estimated by an iterative process which couples a two-pass Bayesian smoother with an Expectation-Maximization (EM) algorithm. The method is applied on numerical and experimental cases. As a result, accurate frequency and damping estimates are obtained as a function of amplitude.

  6. Including State Excitation in the Fixed-Interval Smoothing Algorithm and Implementation of the Maneuver Detection Method Using Error Residuals

    DTIC Science & Technology

    1990-12-01

    N is taken as the first smoothed estimate, P, must be equal to P,,, at this last data point. This can be seen graphically in Figure 4. Meditch [Ref...D-A246 336 NAVAL POSTGRADUATE SCHOOL Monterey , California R AWDTIC ELECTIE THESIS INCLUDING STATE EXCITATION IN THE FIXED-INTERVAL SMOOTHING ...Filter, Smoothing , Noise Process, Maneuver Detection. 19 Abstract (continue on reverse f necessary and idcntify by block number) The effects of the state

  7. Space and motion in nature and Scripture: Galileo, Descartes, Newton.

    PubMed

    Janiak, Andrew

    2015-06-01

    In the Scholium to the Definitions in Principia mathematica, Newton departs from his main task of discussing space, time and motion by suddenly mentioning the proper method for interpreting Scripture. This is surprising, and it has long been ignored by scholars. In this paper, I argue that the Scripture passage in the Scholium is actually far from incidental: it reflects Newton's substantive concern, one evident in correspondence and manuscripts from the 1680s, that any general understanding of space, time and motion must enable readers to recognize the veracity of Biblical claims about natural phenomena, including the motion of the earth. This substantive concern sheds new light on an aspect of Newton's project in the Scholium. It also underscores Newton's originality in dealing with the famous problem of reconciling theological and philosophical conceptions of nature in the seventeenth century.

  8. A comparative study of energy minimization methods for Markov random fields with smoothness-based priors.

    PubMed

    Szeliski, Richard; Zabih, Ramin; Scharstein, Daniel; Veksler, Olga; Kolmogorov, Vladimir; Agarwala, Aseem; Tappen, Marshall; Rother, Carsten

    2008-06-01

    Among the most exciting advances in early vision has been the development of efficient energy minimization algorithms for pixel-labeling tasks such as depth or texture computation. It has been known for decades that such problems can be elegantly expressed as Markov random fields, yet the resulting energy minimization problems have been widely viewed as intractable. Recently, algorithms such as graph cuts and loopy belief propagation (LBP) have proven to be very powerful: for example, such methods form the basis for almost all the top-performing stereo methods. However, the tradeoffs among different energy minimization algorithms are still not well understood. In this paper we describe a set of energy minimization benchmarks and use them to compare the solution quality and running time of several common energy minimization algorithms. We investigate three promising recent methods graph cuts, LBP, and tree-reweighted message passing in addition to the well-known older iterated conditional modes (ICM) algorithm. Our benchmark problems are drawn from published energy functions used for stereo, image stitching, interactive segmentation, and denoising. We also provide a general-purpose software interface that allows vision researchers to easily switch between optimization methods. Benchmarks, code, images, and results are available at http://vision.middlebury.edu/MRF/.

  9. Smoothed Particle Hydrodynamics Continuous Boundary Force method for Navier-Stokes equations subject to Robin boundary condition

    SciTech Connect

    Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre M.

    2014-02-15

    Robin boundary condition for the Navier-Stokes equations is used to model slip conditions at the fluid-solid boundaries. A novel Continuous Boundary Force (CBF) method is proposed for solving the Navier-Stokes equations subject to Robin boundary condition. In the CBF method, the Robin boundary condition at boundary is replaced by the homogeneous Neumann boundary condition at the boundary and a volumetric force term added to the momentum conservation equation. Smoothed Particle Hydrodynamics (SPH) method is used to solve the resulting Navier-Stokes equations. We present solutions for two-dimensional and three-dimensional flows in domains bounded by flat and curved boundaries subject to various forms of the Robin boundary condition. The numerical accuracy and convergence are examined through comparison of the SPH-CBF results with the solutions of finite difference or finite element method. Taken the no-slip boundary condition as a special case of slip boundary condition, we demonstrate that the SPH-CBF method describes accurately both no-slip and slip conditions.

  10. Smooth Sailing.

    ERIC Educational Resources Information Center

    Price, Beverley; Pincott, Maxine; Rebman, Ashley; Northcutt, Jen; Barsanti, Amy; Silkunas, Betty; Brighton, Susan K.; Reitz, David; Winkler, Maureen

    1999-01-01

    Presents discipline tips from several teachers to keep classrooms running smoothly all year. Some of the suggestions include the following: a bear-cave warning system, peer mediation, a motivational mystery, problem students acting as the teacher's assistant, a positive-behavior-reward chain, a hallway scavenger hunt (to ensure quiet passage…

  11. An equatorially enhanced grid with smooth resolution distribution generated by a spring dynamics method

    NASA Astrophysics Data System (ADS)

    Iga, Shin-ichi

    2017-02-01

    An equatorially enhanced grid is applicable to atmospheric general circulation simulations with better representations of the cumulus convection active in the tropics. This study improved the topology of previously proposed equatorially enhanced grids (Iga, 2015) [1], which had extremely large grid intervals around the poles. The proposed grids in this study are of a triangular mesh and are generated by a spring dynamics method with stretching around singular points, which are connected to five or seven neighboring grid points. The latitudinal distribution of resolution is nearly proportional to the combination of the map factors of the Mercator, Lambert conformal conic, and polar stereographic projections. The resolution contrast between the equator and pole is 2.3 ∼ 4.5 for the sampled cases, which is much smaller than that for the LML grids. This improvement requires only a small amount of additional grid resources, less than 11% of the total. The proposed grids are also examined with shallow water tests, and were found to perform better than the previous LML grids.

  12. Smoothed Biasing Forces Yield Unbiased Free Energies with the Extended-System Adaptive Biasing Force Method.

    PubMed

    Lesage, Adrien; Lelièvre, Tony; Stoltz, Gabriel; Hénin, Jérôme

    2016-12-27

    We report a theoretical description and numerical tests of the extended-system adaptive biasing force method (eABF), together with an unbiased estimator of the free energy surface from eABF dynamics. Whereas the original ABF approach uses its running estimate of the free energy gradient as the adaptive biasing force, eABF is built on the idea that the exact free energy gradient is not necessary for efficient exploration, and that it is still possible to recover the exact free energy separately with an appropriate estimator. eABF does not directly bias the collective coordinates of interest, but rather fictitious variables that are harmonically coupled to them; therefore is does not require second derivative estimates, making it easily applicable to a wider range of problems than ABF. Furthermore, the extended variables present a smoother, coarse-grain-like sampling problem on a mollified free energy surface, leading to faster exploration and convergence. We also introduce CZAR, a simple, unbiased free energy estimator from eABF trajectories. eABF/CZAR converges to the physical free energy surface faster than standard ABF for a wide range of parameters.

  13. A smoothed finite element method for analysis of anisotropic large deformation of passive rabbit ventricles in diastole.

    PubMed

    Jiang, Chen; Liu, Gui-Rong; Han, Xu; Zhang, Zhi-Qian; Zeng, Wei

    2015-01-01

    The smoothed FEM (S-FEM) is firstly extended to explore the behavior of 3D anisotropic large deformation of rabbit ventricles during the passive filling process in diastole. Because of the incompressibility of myocardium, a special method called selective face-based/node-based S-FEM using four-node tetrahedral elements (FS/NS-FEM-TET4) is adopted in order to avoid volumetric locking. To validate the proposed algorithms of FS/NS-FEM-TET4, the 3D Lame problem is implemented. The performance contest results show that our FS/NS-FEM-TET4 is accurate, volumetric locking-free and insensitive to mesh distortion than standard linear FEM because of absence of isoparametric mapping. Actually, the efficiency of FS/NS-FEM-TET4 is comparable with higher-order FEM, such as 10-node tetrahedral elements. The proposed method for Holzapfel myocardium hyperelastic strain energy is also validated by simple shear tests through the comparison outcomes reported in available references. Finally, the FS/NS-FEM-TET4 is applied in the example of the passive filling of MRI-based rabbit ventricles with fiber architecture derived from rule-based algorithm to demonstrate its efficiency. Hence, we conclude that FS/NS-FEM-TET4 is a promising alternative other than FEM in passive cardiac mechanics.

  14. Investigation of calcium antagonist-L-type calcium channel interactions by a vascular smooth muscle cell membrane chromatography method.

    PubMed

    Du, Hui; He, Jianyu; Wang, Sicen; He, Langchong

    2010-07-01

    The dissociation equilibrium constant (K(D)) is an important affinity parameter for studying drug-receptor interactions. A vascular smooth muscle (VSM) cell membrane chromatography (CMC) method was developed for determination of the K(D) values for calcium antagonist-L-type calcium channel (L-CC) interactions. VSM cells, by means of primary culture with rat thoracic aortas, were used for preparation of the cell membrane stationary phase in the VSM/CMC model. All measurements were performed with spectrophotometric detection (237 nm) at 37 degrees C. The K(D) values obtained using frontal analysis were 3.36 x 10(-6) M for nifedipine, 1.34 x 10(-6) M for nimodipine, 6.83 x 10(-7) M for nitrendipine, 1.23 x 10(-7) M for nicardipine, 1.09 x 10(-7) M for amlodipine, and 8.51 x 10(-8) M for verapamil. This affinity rank order obtained from the VSM/CMC method had a strong positive correlation with that obtained from radioligand binding assay. The location of the binding region was examined by displacement experiments using nitrendipine as a mobile-phase additive. It was found that verapamil occupied a class of binding sites on L-CCs different from those occupied by nitrendipine. In addition, nicardipine, amlodipine, and nitrendipine had direct competition at a single common binding site. The studies showed that CMC can be applied to the investigation of drug-receptor interactions.

  15. A Real-Time Orbit Determination Method for Smooth Transition from Optical Tracking to Laser Ranging of Debris

    PubMed Central

    Li, Bin; Sang, Jizhang; Zhang, Zhongping

    2016-01-01

    A critical requirement to achieve high efficiency of debris laser tracking is to have sufficiently accurate orbit predictions (OP) in both the pointing direction (better than 20 arc seconds) and distance from the tracking station to the debris objects, with the former more important than the latter because of the narrow laser beam. When the two line element (TLE) is used to provide the orbit predictions, the resultant pointing errors are usually on the order of tens to hundreds of arc seconds. In practice, therefore, angular observations of debris objects are first collected using an optical tracking sensor, and then used to guide the laser beam pointing to the objects. The manual guidance may cause interrupts to the laser tracking, and consequently loss of valuable laser tracking data. This paper presents a real-time orbit determination (OD) and prediction method to realize smooth and efficient debris laser tracking. The method uses TLE-computed positions and angles over a short-arc of less than 2 min as observations in an OD process where simplified force models are considered. After the OD convergence, the OP is performed from the last observation epoch to the end of the tracking pass. Simulation and real tracking data processing results show that the pointing prediction errors are usually less than 10″, and the distance errors less than 100 m, therefore, the prediction accuracy is sufficient for the blind laser tracking. PMID:27347958

  16. POEMS in Newton's Aerodynamic Frustum

    ERIC Educational Resources Information Center

    Sampedro, Jaime Cruz; Tetlalmatzi-Montiel, Margarita

    2010-01-01

    The golden mean is often naively seen as a sign of optimal beauty but rarely does it arise as the solution of a true optimization problem. In this article we present such a problem, demonstrating a close relationship between the golden mean and a special case of Newton's aerodynamical problem for the frustum of a cone. Then, we exhibit a parallel…

  17. Newton's Law of Cooling Revisited

    ERIC Educational Resources Information Center

    Vollmer, M.

    2009-01-01

    The cooling of objects is often described by a law, attributed to Newton, which states that the temperature difference of a cooling body with respect to the surroundings decreases exponentially with time. Such behaviour has been observed for many laboratory experiments, which led to a wide acceptance of this approach. However, the heat transfer…

  18. Atomism from Newton to Dalton.

    ERIC Educational Resources Information Center

    Schofield, Robert E.

    1981-01-01

    Indicates that although Newton's achievements were rooted in an atomistic theory of matter resembling aspects of modern nuclear physics, Dalton developed his chemical atomism on the basis of the character of the gross behavior of substances rather than their particulate nature. (Author/SK)

  19. Integrating Scientific Methods and Knowledge into the Teaching of Newton's Theory of Gravitation: An Instructional Sequence for Teachers' and Students' Nature of Science Education

    NASA Astrophysics Data System (ADS)

    Develaki, Maria

    2012-06-01

    The availability of teaching units on the nature of science (NOS) can reinforce classroom instruction in the subject, taking into account the related deficiencies in textbook material and teacher training. We give a sequence of teaching units in which the teaching of Newton's gravitational theory is used as a basis for reflecting on the fundamental factors that enter into the cognitive and evaluative processes of science, such as creativity, empirical data, theorising, substantiating and modelling tactics. Distinguishing phases in the evolution of a theory (initial conception and formation, testing, scope and limits of the theory) helps show how the importance of these factors varies from phase to phase, while they continue to interact throughout the whole process. Our concept of how to teach NOS is based on the introduction of such special units, containing direct instruction in NOS elements incorporated into curricular science content, thus giving an initial theoretical basis with which epistemological points of other course material can be correlated during the usual classroom teaching of the subject throughout the school year. The sequence is presented in the form of teaching units that can also be used in teachers' NOS education, extended in this case by more explicit instruction in basic philosophical views of the nature of science and how they relate to and impact on teaching.

  20. Smoothed particle hydrodynamics method applied to pulsatile flow inside a rigid two-dimensional model of left heart cavity.

    PubMed

    Shahriari, S; Kadem, L; Rogers, B D; Hassan, I

    2012-11-01

    This paper aims to extend the application of smoothed particle hydrodynamics (SPH), a meshfree particle method, to simulate flow inside a model of the heart's left ventricle (LV). This work is considered the first attempt to simulate flow inside a heart cavity using a meshfree particle method. Simulating this kind of flow, characterized by high pulsatility and moderate Reynolds number using SPH is challenging. As a consequence, validation of the computational code using benchmark cases is required prior to simulating the flow inside a model of the LV. In this work, this is accomplished by simulating an unsteady oscillating flow (pressure amplitude: A = 2500 N ∕ m(3) and Womersley number: W(o)  = 16) and the steady lid-driven cavity flow (Re = 3200, 5000). The results are compared against analytical solutions and reference data to assess convergence. Then, both benchmark cases are combined and a pulsatile jet in a cavity is simulated and the results are compared with the finite volume method. Here, an approach to deal with inflow and outflow boundary conditions is introduced. Finally, pulsatile inlet flow in a rigid model of the LV is simulated. The results demonstrate the ability of SPH to model complex cardiovascular flows and to track the history of fluid properties. Some interesting features of SPH are also demonstrated in this study, including the relation between particle resolution and sound speed to control compressibility effects and also order of convergence in SPH simulations, which is consistently demonstrated to be between first-order and second-order at the moderate Reynolds numbers investigated.

  1. NEWTPOIS- NEWTON POISSON DISTRIBUTION PROGRAM

    NASA Technical Reports Server (NTRS)

    Bowerman, P. N.

    1994-01-01

    The cumulative poisson distribution program, NEWTPOIS, is one of two programs which make calculations involving cumulative poisson distributions. Both programs, NEWTPOIS (NPO-17715) and CUMPOIS (NPO-17714), can be used independently of one another. NEWTPOIS determines percentiles for gamma distributions with integer shape parameters and calculates percentiles for chi-square distributions with even degrees of freedom. It can be used by statisticians and others concerned with probabilities of independent events occurring over specific units of time, area, or volume. NEWTPOIS determines the Poisson parameter (lambda), that is; the mean (or expected) number of events occurring in a given unit of time, area, or space. Given that the user already knows the cumulative probability for a specific number of occurrences (n) it is usually a simple matter of substitution into the Poisson distribution summation to arrive at lambda. However, direct calculation of the Poisson parameter becomes difficult for small positive values of n and unmanageable for large values. NEWTPOIS uses Newton's iteration method to extract lambda from the initial value condition of the Poisson distribution where n=0, taking successive estimations until some user specified error term (epsilon) is reached. The NEWTPOIS program is written in C. It was developed on an IBM AT with a numeric co-processor using Microsoft C 5.0. Because the source code is written using standard C structures and functions, it should compile correctly on most C compilers. The program format is interactive, accepting epsilon, n, and the cumulative probability of the occurrence of n as inputs. It has been implemented under DOS 3.2 and has a memory requirement of 30K. NEWTPOIS was developed in 1988.

  2. Demonstrating Newton's Second Law.

    ERIC Educational Resources Information Center

    Fricker, H. S.

    1994-01-01

    Describes an apparatus for demonstrating the second law of motion. Provides sample data and discusses the merits of this method over traditional methods of supplying a constant force. The method produces empirical best-fit lines which convincingly demonstrate that for a fixed mass, acceleration is proportional to force. (DDR)

  3. Smoothed Particle Inference Analysis of SNR RCW 103

    NASA Astrophysics Data System (ADS)

    Frank, Kari A.; Burrows, David N.; Dwarkadas, Vikram

    2016-04-01

    We present preliminary results of applying a novel analysis method, Smoothed Particle Inference (SPI), to an XMM-Newton observation of SNR RCW 103. SPI is a Bayesian modeling process that fits a population of gas blobs ("smoothed particles") such that their superposed emission reproduces the observed spatial and spectral distribution of photons. Emission-weighted distributions of plasma properties, such as abundances and temperatures, are then extracted from the properties of the individual blobs. This technique has important advantages over analysis techniques which implicitly assume that remnants are two-dimensional objects in which each line of sight encompasses a single plasma. By contrast, SPI allows superposition of as many blobs of plasma as are needed to match the spectrum observed in each direction, without the need to bin the data spatially. This RCW 103 analysis is part of a pilot study for the larger SPIES (Smoothed Particle Inference Exploration of SNRs) project, in which SPI will be applied to a sample of 12 bright SNRs.

  4. A method for three-dimensional quantification of vascular smooth muscle orientation: application in viable murine carotid arteries.

    PubMed

    Spronck, Bart; Megens, Remco T A; Reesink, Koen D; Delhaas, Tammo

    2016-04-01

    When studying in vivo arterial mechanical behaviour using constitutive models, smooth muscle cells (SMCs) should be considered, while they play an important role in regulating arterial vessel tone. Current constitutive models assume a strictly circumferential SMC orientation, without any dispersion. We hypothesised that SMC orientation would show considerable dispersion in three dimensions and that helical dispersion would be greater than transversal dispersion. To test these hypotheses, we developed a method to quantify the 3D orientation of arterial SMCs. Fluorescently labelled SMC nuclei of left and right carotid arteries of ten mice were imaged using two-photon laser scanning microscopy. Arteries were imaged at a range of luminal pressures. 3D image processing was used to identify individual nuclei and their orientations. SMCs showed to be arranged in two distinct layers. Orientations were quantified by fitting a Bingham distribution to the observed orientations. As hypothesised, orientation dispersion was much larger helically than transversally. With increasing luminal pressure, transversal dispersion decreased significantly, whereas helical dispersion remained unaltered. Additionally, SMC orientations showed a statistically significant (p < 0.05) mean right-handed helix angle in both left and right arteries and in both layers, which is a relevant finding from a developmental biology perspective. In conclusion, vascular SMC orientation (1) can be quantified in 3D; (2) shows considerable dispersion, predominantly in the helical direction; and (3) has a distinct right-handed helical component in both left and right carotid arteries. The obtained quantitative distribution data are instrumental for constitutive modelling of the artery wall and illustrate the merit of our method.

  5. Student conception and perception of Newton's law

    NASA Astrophysics Data System (ADS)

    Handhika, Jeffry; Cari, C.; Soeparmi, A.; Sunarno, Widha

    2016-02-01

    This research aims to reveal the student's conception and perception of Newton's Law. Method of this research is qualitative with the sample is taken using purposive sampling consist of second semester (25 students), fourth semester (26 students), sixth semester VI (25 students), and eight semester (18 students) IKIP PGRI MADIUN, which have taken the first basic physics and mechanics courses The data was collected with essay questions, interview, and FCI test. It can be concluded that Mathematical language (symbol and visual) perception and intuition influence students conception. The results of analysis showed that an incorrect conception arises because students do not understand the language of physics and mathematics correctly.

  6. Keynes, Newton and the Royal Society: the events of 1942 and 1943.

    PubMed

    Kuehn, Daniel

    2013-03-20

    Most discussions of John Maynard Keynes's activities in connection with Newton are restricted to the sale in 1936 at Sotheby's of Newton's Portsmouth Papers and to Keynes's 1946 essay 'Newton, the Man'. This paper provides a history of Keynes's Newton-related work in the interim, highlighting especially the events of 1942 and 1943, which were particularly relevant to the Royal Society's role in the domestic and international promotion of Newton's legacy. During this period, Keynes lectured twice on Newton, leaving notes that would later be read by his brother Geoffrey in the famous commemoration of the Newton tercentenary in 1946. In 1943 Keynes assisted the Royal Society in its recognition of the Soviet celebrations and in the acquisition and preservation of more of the Newton library. In each instance Keynes took the opportunity to promote his interpretation of Newton as 'the last of the magicians': a scientist who had one foot in the pre-modern world and whose approach to understanding the world was as much intuitive as it was methodical.

  7. Keynes, Newton and the Royal Society: the events of 1942 and 1943

    PubMed Central

    Kuehn, Daniel

    2013-01-01

    Most discussions of John Maynard Keynes's activities in connection with Newton are restricted to the sale in 1936 at Sotheby's of Newton's Portsmouth Papers and to Keynes's 1946 essay ‘Newton, the Man’. This paper provides a history of Keynes's Newton-related work in the interim, highlighting especially the events of 1942 and 1943, which were particularly relevant to the Royal Society's role in the domestic and international promotion of Newton's legacy. During this period, Keynes lectured twice on Newton, leaving notes that would later be read by his brother Geoffrey in the famous commemoration of the Newton tercentenary in 1946. In 1943 Keynes assisted the Royal Society in its recognition of the Soviet celebrations and in the acquisition and preservation of more of the Newton library. In each instance Keynes took the opportunity to promote his interpretation of Newton as ‘the last of the magicians’: a scientist who had one foot in the pre-modern world and whose approach to understanding the world was as much intuitive as it was methodical. PMID:24686919

  8. The Use of Kruskal-Newton Diagrams for Differential Equations

    SciTech Connect

    T. Fishaleck and R.B. White

    2008-02-19

    The method of Kruskal-Newton diagrams for the solution of differential equations with boundary layers is shown to provide rapid intuitive understanding of layer scaling and can result in the conceptual simplification of some problems. The method is illustrated using equations arising in the theory of pattern formation and in plasma physics.

  9. Newton's Principia: Myth and Reality

    NASA Astrophysics Data System (ADS)

    Smith, George

    2016-03-01

    Myths about Newton's Principia abound. Some of them, such as the myth that the whole book was initially developed using the calculus and then transformed into a geometric mathematics, stem from remarks he made during the priority controversy with Leibniz over the calculus. Some of the most persistent, and misleading, arose from failures to read the book with care. Among the latter are the myth that he devised his theory of gravity in order to explain the already established ``laws'' of Kepler, and that in doing so he took himself to be establishing that Keplerian motion is ``absolute,'' if not with respect to ``absolute space,'' then at least with respect to the fixed stars taken as what came later to be known as an inertial frame. The talk will replace these two myths with the reality of what Newton took himself to have established.

  10. Newton filtrations, graded algebras and codimension of non-degenerate ideals

    NASA Astrophysics Data System (ADS)

    Bivià-Ausina, Carles; Fukui, Toshizumi; Saia, Marcelo José

    2002-07-01

    We investigate a generalization of the method introduced by Kouchnirenko to compute the codimension (colength) of an ideal under a certain non-degeneracy condition on a given system of generators of I. We also discuss Newton non-degenerate ideals and give characterizations using the notion of reductions and Newton polyhedra of ideals.

  11. The XMM-Newton serendipitous survey. VII. The third XMM-Newton serendipitous source catalogue

    NASA Astrophysics Data System (ADS)

    Rosen, S. R.; Webb, N. A.; Watson, M. G.; Ballet, J.; Barret, D.; Braito, V.; Carrera, F. J.; Ceballos, M. T.; Coriat, M.; Della Ceca, R.; Denkinson, G.; Esquej, P.; Farrell, S. A.; Freyberg, M.; Grisé, F.; Guillout, P.; Heil, L.; Koliopanos, F.; Law-Green, D.; Lamer, G.; Lin, D.; Martino, R.; Michel, L.; Motch, C.; Nebot Gomez-Moran, A.; Page, C. G.; Page, K.; Page, M.; Pakull, M. W.; Pye, J.; Read, A.; Rodriguez, P.; Sakano, M.; Saxton, R.; Schwope, A.; Scott, A. E.; Sturm, R.; Traulsen, I.; Yershov, V.; Zolotukhin, I.

    2016-05-01

    Context. Thanks to the large collecting area (3 ×~1500 cm2 at 1.5 keV) and wide field of view (30' across in full field mode) of the X-ray cameras on board the European Space Agency X-ray observatory XMM-Newton, each individual pointing can result in the detection of up to several hundred X-ray sources, most of which are newly discovered objects. Since XMM-Newton has now been in orbit for more than 15 yr, hundreds of thousands of sources have been detected. Aims: Recently, many improvements in the XMM-Newton data reduction algorithms have been made. These include enhanced source characterisation and reduced spurious source detections, refined astrometric precision of sources, greater net sensitivity for source detection, and the extraction of spectra and time series for fainter sources, both with better signal-to-noise. Thanks to these enhancements, the quality of the catalogue products has been much improved over earlier catalogues. Furthermore, almost 50% more observations are in the public domain compared to 2XMMi-DR3, allowing the XMM-Newton Survey Science Centre to produce a much larger and better quality X-ray source catalogue. Methods: The XMM-Newton Survey Science Centre has developed a pipeline to reduce the XMM-Newton data automatically. Using the latest version of this pipeline, along with better calibration, a new version of the catalogue has been produced, using XMM-Newton X-ray observations made public on or before 2013 December 31. Manual screening of all of the X-ray detections ensures the highest data quality. This catalogue is known as 3XMM. Results: In the latest release of the 3XMM catalogue, 3XMM-DR5, there are 565 962 X-ray detections comprising 396 910 unique X-ray sources. Spectra and lightcurves are provided for the 133 000 brightest sources. For all detections, the positions on the sky, a measure of the quality of the detection, and an evaluation of the X-ray variability is provided, along with the fluxes and count rates in 7 X-ray energy

  12. A TWO-DIMENSIONAL METHOD OF MANUFACTURED SOLUTIONS BENCHMARK SUITE BASED ON VARIATIONS OF LARSEN'S BENCHMARK WITH ESCALATING ORDER OF SMOOTHNESS OF THE EXACT SOLUTION

    SciTech Connect

    Sebastian Schunert; Yousry Y. Azmy

    2011-05-01

    The quantification of the discretization error associated with the spatial discretization of the Discrete Ordinate(DO) equations in multidimensional Cartesian geometries is the central problem in error estimation of spatial discretization schemes for transport theory as well as computer code verification. Traditionally fine mesh solutions are employed as reference, because analytical solutions only exist in the absence of scattering. This approach, however, is inadequate when the discretization error associated with the reference solution is not small compared to the discretization error associated with the mesh under scrutiny. Typically this situation occurs if the mesh of interest is only a couple of refinement levels away from the reference solution or if the order of accuracy of the numerical method (and hence the reference as well) is lower than expected. In this work we present a Method of Manufactured Solutions (MMS) benchmark suite with variable order of smoothness of the underlying exact solution for two-dimensional Cartesian geometries which provides analytical solutions aver- aged over arbitrary orthogonal meshes for scattering and non-scattering media. It should be emphasized that the developed MMS benchmark suite first eliminates the aforementioned limitation of fine mesh reference solutions since it secures knowledge of the underlying true solution and second that it allows for an arbitrary order of smoothness of the underlying ex- act solution. The latter is of importance because even for smooth parameters and boundary conditions the DO equations can feature exact solution with limited smoothness. Moreover, the degree of smoothness is crucial for both the order of accuracy and the magnitude of the discretization error for any spatial discretization scheme.

  13. Visualizing and Understanding the Components of Lagrange and Newton Interpolation

    ERIC Educational Resources Information Center

    Yang, Yajun; Gordon, Sheldon P.

    2016-01-01

    This article takes a close look at Lagrange and Newton interpolation by graphically examining the component functions of each of these formulas. Although interpolation methods are often considered simply to be computational procedures, we demonstrate how the components of the polynomial terms in these formulas provide insight into where these…

  14. A Comparison of Inexact Newton and Coordinate Descent Meshoptimization Technqiues

    SciTech Connect

    Diachin, L F; Knupp, P; Munson, T; Shontz, S

    2004-07-08

    We compare inexact Newton and coordinate descent methods for optimizing the quality of a mesh by repositioning the vertices, where quality is measured by the harmonic mean of the mean-ratio metric. The effects of problem size, element size heterogeneity, and various vertex displacement schemes on the performance of these algorithms are assessed for a series of tetrahedral meshes.

  15. Isaac Newton: Eighteenth-century Perspectives

    NASA Astrophysics Data System (ADS)

    Hall, A. Rupert

    1999-05-01

    This new product of the ever-flourishing Newton industry seems a bit far-fetched at first sight: who but a few specialists would be interested in the historiography of Newton biography in the eighteenth century? On closer inspection, this book by one of the most important Newton scholars of our day turns out to be of interest to a wider audience as well. It contains several biographical sketches of Newton, written in the decades after his death. The two most important ones are the Eloge by the French mathematician Bernard de Fontenelle and the Italian scholar Paolo Frisi's Elogio. The latter piece was hitherto unavailable in English translation. Both articles are well-written, interesting and sometimes even entertaining. They give us new insights into the way Newton was revered throughout Europe and how not even the slightest blemish on his personality or work could be tolerated. An example is the way in which Newton's famous controversy with Leibniz is treated: Newton is without hesitation presented as the wronged party. Hall has provided very useful historical introductions to the memoirs as well as footnotes where needed. Among the other articles discussed is a well-known memoir by John Conduitt, who was married to Newton's niece. This memoir, substantial parts of which are included in this volume, has been a major source of personal information for Newton biographers up to this day. In a concluding chapter, Hall gives a very interesting overview of the later history of Newton biography, in which he describes the gradual change from adoration to a more critical approach in Newton's various biographers. In short, this is a very useful addition to the existing biographical literature on Newton. A J Kox

  16. Two-ball Newton's cradle.

    PubMed

    Glendinning, Paul

    2011-12-01

    Newton's cradle for two balls with Hertzian interactions is considered as a hybrid system, and this makes it possible to derive return maps for the motion between collisions in an exact form despite the fact that the three-halves interaction law cannot be solved in closed form. The return maps depend on a constant whose value can only be determined numerically, but solutions can be written down explicitly in terms of this parameter, and we compare this with the results of simulations. The results are in fact independent of the details of the interaction potential.

  17. Numerical conformal mapping methods for exterior and doubly connected regions

    SciTech Connect

    DeLillo, T.K.; Pfaltzgraff, J.A.

    1996-12-31

    Methods are presented and analyzed for approximating the conformal map from the exterior of the disk to the exterior a smooth, simple closed curve and from an annulus to a bounded, doubly connected region with smooth boundaries. The methods are Newton-like methods for computing the boundary correspondences and conformal moduli similar to Fornberg`s method for the interior of the disk. We show that the linear systems are discretizations of the identity plus a compact operator and, hence, that the conjugate gradient method converges superlinearly.

  18. A new parameter identification method to obtain change in smooth musclecontraction state due to mechanical skin irritation

    NASA Astrophysics Data System (ADS)

    Bauer, Daniela

    2005-03-01

    A light scratch with a needle induces histamine and neuropetide release on the line of stroke and in the surrounding tissue. Histamine and neuropeptides are vasodilaters. They create vasodilation by changing the contraction state of the vascular smooth muscles and hence vessel compliance. Smooth muscle contraction state is very difficult to measure. We propose an identification procedure that determines change in compliance. The procedure is based on numerical and experimental results. Blood flow is measured by Laser Doppler Velocimetry. Numerical data is obtained by a continuous model of hierarchically arranged porous media of the vascular network [1]. We show that compliance increases after the stroke in the entire tissue. Then, compliance decreases in the surrounding tissue, while it keeps increasing on the line of stroke. Hence, blood is transported from the surrounding tissue to the line of stroke. Thus, higher blood volume on the line of stroke is obtained. [1] Bauer, D., Grebe, R. Ehrlacher, A., 2004. A three layer continuous model of porous media to describe the first phase of skin irritation. J. Theoret. Bio. in press

  19. The Schrödinger-Newton equations beyond Newton

    NASA Astrophysics Data System (ADS)

    Manfredi, Giovanni

    2015-02-01

    The scope of this paper is twofold. First, we derive rigorously a low-velocity and Galilei-covariant limit of the gravitoelectromagnetic (GEM) equations. Subsequently, these reduced GEM equations are coupled to the Schrödinger equation with gravitoelectric and gravitomagnetic potentials. The resulting extended Schrödinger-Newton equations constitute a minimal model where the three fundamental constants of nature (, and ) appear naturally. We show that the relativistic correction coming from the gravitomagnetic potential scales as the ratio of the mass of the system to the Planck mass, and that it reinforces the standard Newtonian (gravitoelectric) attraction. The theory is further generalized to many particles through a Wigner function approach.

  20. An eigenvalue inequality of the Newton potential

    NASA Astrophysics Data System (ADS)

    Suragan, Durvudkhan

    2016-12-01

    In this short conference paper we prove an isoperimetric inequality for the second eigenvalue of the Newton potential. In turn, the Newton potential can be related to the Laplacian with a non-local type boundary condition, so we obtain an isoperimetric result for its second eigenvalue as well.

  1. A new Newton's law of cooling?

    PubMed

    Kleiber, M

    1972-12-22

    Several physiologists confuse Fourier's law of animal heat flow with Newton's law of cooling. A critique of this error in 1932 remained ineffective. In 1969 Molnar tested Newton's cooling law. In 1971 Strunk found Newtonian cooling unrealistic for animals. Unfortunately, he called the Fourier formulation of animal heat flow, requiring post-Newtonian observations, a "contemporary Newtonian law of cooling."

  2. Happy Balls, Unhappy Balls, and Newton's Cradle

    ERIC Educational Resources Information Center

    Kagan, David

    2010-01-01

    The intricacies of Newton's Cradle are well covered in the literature going as far back as the time of Newton! These discussions generally center on the highly elastic collisions of metal spheres. Thanks to the invention of happy and unhappy balls, you can build and study the interaction of less elastic systems (see Fig. 1).

  3. Improving smoothing efficiency of rigid conformal polishing tool using time-dependent smoothing evaluation model

    NASA Astrophysics Data System (ADS)

    Song, Chi; Zhang, Xuejun; Zhang, Xin; Hu, Haifei; Zeng, Xuefeng

    2017-01-01

    A rigid conformal (RC) lap can smooth mid-spatial-frequency (MSF) errors, which are naturally smaller than the tool size, while still removing large-scale errors in a short time. However, the RC-lap smoothing efficiency performance is poorer than expected, and existing smoothing models cannot explicitly specify the methods to improve this efficiency. We presented an explicit time-dependent smoothing evaluation model that contained specific smoothing parameters directly derived from the parametric smoothing model and the Preston equation. Based on the time-dependent model, we proposed a strategy to improve the RC-lap smoothing efficiency, which incorporated the theoretical model, tool optimization, and efficiency limit determination. Two sets of smoothing experiments were performed to demonstrate the smoothing efficiency achieved using the time-dependent smoothing model. A high, theory-like tool influence function and a limiting tool speed of 300 RPM were o

  4. Effectiveness of Analytic Smoothing in Equipercentile Equating.

    ERIC Educational Resources Information Center

    Kolen, Michael J.

    1984-01-01

    An analytic procedure for smoothing in equipercentile equating using cubic smoothing splines is described and illustrated. The effectiveness of the procedure is judged by comparing the results from smoothed equipercentile equating with those from other equating methods using multiple cross-validations for a variety of sample sizes. (Author/JKS)

  5. Dark Valley in Newton Crater

    NASA Technical Reports Server (NTRS)

    2003-01-01

    MGS MOC Release No. MOC2-418, 11 July 2003

    This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) high resolution image shows part of a dark-floored valley system in northern Newton Crater. The valley might have been originally formed by liquid water; the dark material is probably sand that has blown into the valley in more recent times. The picture was acquired earlier this week on July 6, 2003, and is located near 39.2oS, 157.9oW. The picture covers an area 2.3 km (1.4 mi) across; sunlight illuminates the scene from the upper left.

  6. XMM-Newton Proposal 03016512

    NASA Astrophysics Data System (ADS)

    Georgantopoulos, Ioannis

    2004-10-01

    Recent X-ray surveys have shown a dramatic deficit of obscured AGN at high redshift. This comes in contrast with the situation in the nearby Universe which shows a huge fraction of heavily absorbed objects. However, this discrepancy may arise because the column density information locally is ill-determined. Here, we propose to obtain snapshot (10 ksec) observations of an optically selected sample (12) of nearby Seyfert galaxies from the Ho et al.catalogue. Together with the galaxies which have been already observed, our survey will cover ALL the Sy galaxies in the above sample. The superb quality XMM-Newton spectra will accurately probe the column densities and will provide the least biased measurement of the AGN column density distribution locally.

  7. Origins of Newton's First Law

    NASA Astrophysics Data System (ADS)

    Hecht, Eugene

    2015-02-01

    Anyone who has taught introductory physics should know that roughly a third of the students initially believe that any object at rest will remain at rest, whereas any moving body not propelled by applied forces will promptly come to rest. Likewise, about half of those uninitiated students believe that any object moving at a constant speed must be continually pushed if it is to maintain its motion.1 That's essentially Aristotle's law of motion and it is so "obviously" borne out by experience that it was accepted by scholars for 2000 years, right through the Copernican Revolution. But, of course, it's fundamentally wrong. This paper tells the story of how the correct understanding, the law of inertia, evolved and how Newton came to make it his first law.

  8. Newtonian cosmology Newton would understand

    SciTech Connect

    Lemons, D.S.

    1988-06-01

    Isaac Newton envisioned a static, infinite, and initially uniform, zero field universe that was gravitationally unstable to local condensations of matter. By postulating the existence of such a universe and using it as a boundary condition on Newtonian gravity, a new field equation for gravity is derived, which differs from the classical one by a time-dependent cosmological term proportional to the average mass density of the universe. The new field equation not only makes Jeans' analysis of the gravitational instability of a Newtonian universe consistent, but also gives rise to a family of Newtonian evolutionary cosmologies parametrized by a time-invariant expansion velocity. This Newtonian cosmology contrasts with both 19th-century ones and with post general relativity Newtonian cosmology.

  9. XMM-Newton Proposal 02066102

    NASA Astrophysics Data System (ADS)

    Breitschwerdt, Dieter

    2003-03-01

    The densest and closest absorbers of the soft X-ray background (SXRB) in the Milky Way are Bok globules, located just outside the Local Bubble in the Pipe Nebula at a distance of 125pc. With column densities of up to log(NH)~23, they are ideal targets for shadowing the SXRB in the energy range 0.3 - 2 keV, thus giving important information on the spatial and spectral variation of the foreground X-ray intensity on small scales. We propose Barnard 59 due to an extinction gradient of A_V~50 mag and the Fest 1-457 region due to strong small scale NH-variations for a detailed spectral study with XMM-Newton. Together with already existing XMM data of Barnard 68, this will allow to determine the ionization structure of the Local and Loop I superbubbles.

  10. Newton's cradle versus nonbinary collisions.

    PubMed

    Sekimoto, Ken

    2010-03-26

    Newton's cradle is a classical example of a one-dimensional impact problem. In the early 1980s the naive perception of its behavior was corrected: For example, the impact of a particle does not exactly cause the release of the farthest particle of the target particle train, if the target particles have been just in contact with their own neighbors. It is also known that the naive picture would be correct if the whole process consisted of purely binary collisions. Our systematic study of particle systems with truncated power-law repulsive force shows that the quasibinary collision is recovered in the limit of hard core repulsion, or a very large exponent. In contrast, a discontinuous steplike repulsive force mimicking a hard contact, or a very small exponent, leads to a completely different process: the impacting cluster and the targeted cluster act, respectively, as if they were nondeformable blocks.

  11. Illustrating Newton's Second Law with the Automobile Coast-Down Test.

    ERIC Educational Resources Information Center

    Bryan, Ronald A.; And Others

    1988-01-01

    Describes a run test of automobiles for applying Newton's second law of motion and the concept of power. Explains some automobile thought-experiments and provides the method and data of an actual coast-down test. (YP)

  12. First XMM-Newton Observations of an Isolated Neutron Star: RXJ0720.4-3125

    NASA Technical Reports Server (NTRS)

    Paerels, Frits; Mori, Kaya; Motch, Christian; Haberl, Frank; Zavlin, Vyacheslav E.; Zane, Silvia; Ramsay, Gavin; Cropper, Mark

    2000-01-01

    We present the high resolution spectrum of the isolated neutron star RXJ0720.4-3125, obtained with the Reflection Grating Spectrometer on XMM-Newton, complemented with the broad band spectrum observed with the EPIC PN camera. The spectrum appears smooth, with no evidence for strong photospheric absorption or emission features. We briefly discuss the implications of our failure to detect structure in the spectrum.

  13. Stabilized quasi-Newton optimization of noisy potential energy surfaces

    SciTech Connect

    Schaefer, Bastian; Goedecker, Stefan; Alireza Ghasemi, S.; Roy, Shantanu

    2015-01-21

    Optimizations of atomic positions belong to the most commonly performed tasks in electronic structure calculations. Many simulations like global minimum searches or characterizations of chemical reactions require performing hundreds or thousands of minimizations or saddle computations. To automatize these tasks, optimization algorithms must not only be efficient but also very reliable. Unfortunately, computational noise in forces and energies is inherent to electronic structure codes. This computational noise poses a severe problem to the stability of efficient optimization methods like the limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm. We here present a technique that allows obtaining significant curvature information of noisy potential energy surfaces. We use this technique to construct both, a stabilized quasi-Newton minimization method and a stabilized quasi-Newton saddle finding approach. We demonstrate with the help of benchmarks that both the minimizer and the saddle finding approach are superior to comparable existing methods.

  14. Stabilized quasi-Newton optimization of noisy potential energy surfaces

    NASA Astrophysics Data System (ADS)

    Schaefer, Bastian; Ghasemi, S. Alireza; Roy, Shantanu; Goedecker, Stefan; Goedecker Group Team

    Optimizations of atomic positions belong to the most frequently performed tasks in electronic structure calculations. Many simulations like global minimum searches or the identification of chemical reaction pathways can require the computation of hundreds or thousands of minimizations or saddle points. To automatize these tasks, optimization algorithms must not only be efficient but also very reliable. Unfortunately, computational noise in forces and energies is inherent to electronic structure codes. This computational noise poses a severe problem to the stability of efficient optimization methods like the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. In this talk a recently published technique that allows to obtain significant curvature information of noisy potential energy surfaces is presented. This technique was used to construct both, a stabilized quasi-Newton minimization method and a stabilized quasi-Newton saddle finding approach. With the help of benchmarks both the minimizer and the saddle finding approach were demonstrated to be superior to comparable existing methods.

  15. Stabilized quasi-Newton optimization of noisy potential energy surfaces

    NASA Astrophysics Data System (ADS)

    Schaefer, Bastian; Alireza Ghasemi, S.; Roy, Shantanu; Goedecker, Stefan

    2015-01-01

    Optimizations of atomic positions belong to the most commonly performed tasks in electronic structure calculations. Many simulations like global minimum searches or characterizations of chemical reactions require performing hundreds or thousands of minimizations or saddle computations. To automatize these tasks, optimization algorithms must not only be efficient but also very reliable. Unfortunately, computational noise in forces and energies is inherent to electronic structure codes. This computational noise poses a severe problem to the stability of efficient optimization methods like the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. We here present a technique that allows obtaining significant curvature information of noisy potential energy surfaces. We use this technique to construct both, a stabilized quasi-Newton minimization method and a stabilized quasi-Newton saddle finding approach. We demonstrate with the help of benchmarks that both the minimizer and the saddle finding approach are superior to comparable existing methods.

  16. Smoothing and Equating Methods Applied to Different Types of Test Score Distributions and Evaluated with Respect to Multiple Equating Criteria. Research Report. ETS RR-11-20

    ERIC Educational Resources Information Center

    Moses, Tim; Liu, Jinghua

    2011-01-01

    In equating research and practice, equating functions that are smooth are typically assumed to be more accurate than equating functions with irregularities. This assumption presumes that population test score distributions are relatively smooth. In this study, two examples were used to reconsider common beliefs about smoothing and equating. The…

  17. Torsional Newton-Cartan geometry from Galilean gauge theory

    NASA Astrophysics Data System (ADS)

    Banerjee, Rabin; Mukherjee, Pradip

    2016-11-01

    Using the recently advanced Galilean gauge theory (GGT) we give a comprehensive construction of torsional Newton-Cartan (NC) geometry. The coupling of a Galilean symmetric model with background NC geometry following GGT is illustrated by a free nonrelativistic scalar field theory. The issue of spatial diffeomorphism (Son and Wingate 2006 Ann. Phys. 321 197-224 Banerjee et al 2015 Phys. Rev. D 91 084021) is focussed from a new angle. The expression of the torsionful connection is worked out, which is in complete parallel with the relativistic theory. Also, smooth transition of the connection to its well known torsionless expression is demonstrated. A complete (implicit) expression of the torsion tensor for the NC spacetime is provided where the first-order variables occur in a suggestive way. The well known result for the temporal part of torsion is reproduced from our expression.

  18. Apparatus for Teaching Physics: Giant Newton's Rings.

    ERIC Educational Resources Information Center

    Cheung, Kai-yin; Mak, Se-yuen

    1996-01-01

    Describes a modification of the traditional demonstration of Newton's rings that magnifies the scale of the interference pattern so that the demonstration can be used for the whole class or for semiquantitative measurements in any high school laboratory. (JRH)

  19. GOES-West Movie of Hurricane Newton

    NASA Video Gallery

    This animation of infrared and visible images from NOAA's GOES-West satellite shows the development and movement of Hurricane Newton from Sept. 4 through Sept. 6 at 10 a.m. EDT (1400 UTC) toward Ba...

  20. Discovery Science: Newton All around You.

    ERIC Educational Resources Information Center

    Prigo, Robert; Humphrey, Gregg

    1993-01-01

    Presents activities for helping elementary students learn about Newton's third law of motion. Several activity cards demonstrate the concept of the law of action and reaction. The activities require only inexpensive materials that can be found around the house. (SM)

  1. On Time-II: Newton's Time.

    ERIC Educational Resources Information Center

    Raju, C. K.

    1991-01-01

    A study of time in Newtonian physics is presented. Newton's laws of motion, falsifiability and physical theories, laws of motion and law of gravitation, and Laplace's demon are discussed. Short bibliographic sketches of Laplace and Karl Popper are included. (KR)

  2. Iteration of Complex Functions and Newton's Method

    ERIC Educational Resources Information Center

    Dwyer, Jerry; Barnard, Roger; Cook, David; Corte, Jennifer

    2009-01-01

    This paper discusses some common iterations of complex functions. The presentation is such that similar processes can easily be implemented and understood by undergraduate students. The aim is to illustrate some of the beauty of complex dynamics in an informal setting, while providing a couple of results that are not otherwise readily available in…

  3. Mathematical modelling for the drying method and smoothing drying rate using cubic spline for seaweed Kappaphycus Striatum variety Durian in a solar dryer

    SciTech Connect

    M Ali, M. K. E-mail: eutoco@gmail.com; Ruslan, M. H. E-mail: eutoco@gmail.com; Muthuvalu, M. S. E-mail: jumat@ums.edu.my; Wong, J. E-mail: jumat@ums.edu.my; Sulaiman, J. E-mail: hafidzruslan@eng.ukm.my; Yasir, S. Md. E-mail: hafidzruslan@eng.ukm.my

    2014-06-19

    The solar drying experiment of seaweed using Green V-Roof Hybrid Solar Drier (GVRHSD) was conducted in Semporna, Sabah under the metrological condition in Malaysia. Drying of sample seaweed in GVRHSD reduced the moisture content from about 93.4% to 8.2% in 4 days at average solar radiation of about 600W/m{sup 2} and mass flow rate about 0.5 kg/s. Generally the plots of drying rate need more smoothing compared moisture content data. Special cares is needed at low drying rates and moisture contents. It is shown the cubic spline (CS) have been found to be effective for moisture-time curves. The idea of this method consists of an approximation of data by a CS regression having first and second derivatives. The analytical differentiation of the spline regression permits the determination of instantaneous rate. The method of minimization of the functional of average risk was used successfully to solve the problem. This method permits to obtain the instantaneous rate to be obtained directly from the experimental data. The drying kinetics was fitted with six published exponential thin layer drying models. The models were fitted using the coefficient of determination (R{sup 2}), and root mean square error (RMSE). The modeling of models using raw data tested with the possible of exponential drying method. The result showed that the model from Two Term was found to be the best models describe the drying behavior. Besides that, the drying rate smoothed using CS shows to be effective method for moisture-time curves good estimators as well as for the missing moisture content data of seaweed Kappaphycus Striatum Variety Durian in Solar Dryer under the condition tested.

  4. Mathematical modelling for the drying method and smoothing drying rate using cubic spline for seaweed Kappaphycus Striatum variety Durian in a solar dryer

    NASA Astrophysics Data System (ADS)

    M Ali, M. K.; Ruslan, M. H.; Muthuvalu, M. S.; Wong, J.; Sulaiman, J.; Yasir, S. Md.

    2014-06-01

    The solar drying experiment of seaweed using Green V-Roof Hybrid Solar Drier (GVRHSD) was conducted in Semporna, Sabah under the metrological condition in Malaysia. Drying of sample seaweed in GVRHSD reduced the moisture content from about 93.4% to 8.2% in 4 days at average solar radiation of about 600W/m2 and mass flow rate about 0.5 kg/s. Generally the plots of drying rate need more smoothing compared moisture content data. Special cares is needed at low drying rates and moisture contents. It is shown the cubic spline (CS) have been found to be effective for moisture-time curves. The idea of this method consists of an approximation of data by a CS regression having first and second derivatives. The analytical differentiation of the spline regression permits the determination of instantaneous rate. The method of minimization of the functional of average risk was used successfully to solve the problem. This method permits to obtain the instantaneous rate to be obtained directly from the experimental data. The drying kinetics was fitted with six published exponential thin layer drying models. The models were fitted using the coefficient of determination (R2), and root mean square error (RMSE). The modeling of models using raw data tested with the possible of exponential drying method. The result showed that the model from Two Term was found to be the best models describe the drying behavior. Besides that, the drying rate smoothed using CS shows to be effective method for moisture-time curves good estimators as well as for the missing moisture content data of seaweed Kappaphycus Striatum Variety Durian in Solar Dryer under the condition tested.

  5. Traveling and Standing Waves in Coupled Pendula and Newton's Cradle

    NASA Astrophysics Data System (ADS)

    García-Azpeitia, Carlos

    2016-12-01

    The existence of traveling and standing waves is investigated for chains of coupled pendula with periodic boundary conditions. The results are proven by applying topological methods to subspaces of symmetric solutions. The main advantage of this approach comes from the fact that only properties of the linearized forces are required. This allows to cover a wide range of models such as Newton's cradle, the Fermi-Pasta-Ulam lattice, and the Toda lattice.

  6. Smooth halos in the cosmic web

    NASA Astrophysics Data System (ADS)

    Gaite, José

    2015-04-01

    Dark matter halos can be defined as smooth distributions of dark matter placed in a non-smooth cosmic web structure. This definition of halos demands a precise definition of smoothness and a characterization of the manner in which the transition from smooth halos to the cosmic web takes place. We introduce entropic measures of smoothness, related to measures of inequality previously used in economy and with the advantage of being connected with standard methods of multifractal analysis already used for characterizing the cosmic web structure in cold dark matter N-body simulations. These entropic measures provide us with a quantitative description of the transition from the small scales portrayed as a distribution of halos to the larger scales portrayed as a cosmic web and, therefore, allow us to assign definite sizes to halos. However, these ``smoothness sizes'' have no direct relation to the virial radii. Finally, we discuss the influence of N-body discreteness parameters on smoothness.

  7. Smooth halos in the cosmic web

    SciTech Connect

    Gaite, José

    2015-04-01

    Dark matter halos can be defined as smooth distributions of dark matter placed in a non-smooth cosmic web structure. This definition of halos demands a precise definition of smoothness and a characterization of the manner in which the transition from smooth halos to the cosmic web takes place. We introduce entropic measures of smoothness, related to measures of inequality previously used in economy and with the advantage of being connected with standard methods of multifractal analysis already used for characterizing the cosmic web structure in cold dark matter N-body simulations. These entropic measures provide us with a quantitative description of the transition from the small scales portrayed as a distribution of halos to the larger scales portrayed as a cosmic web and, therefore, allow us to assign definite sizes to halos. However, these ''smoothness sizes'' have no direct relation to the virial radii. Finally, we discuss the influence of N-body discreteness parameters on smoothness.

  8. Numerical discretization-based estimation methods for ordinary differential equation models via penalized spline smoothing with applications in biomedical research.

    PubMed

    Wu, Hulin; Xue, Hongqi; Kumar, Arun

    2012-06-01

    Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches.

  9. Numerical Discretization-Based Estimation Methods for Ordinary Differential Equation Models via Penalized Spline Smoothing with Applications in Biomedical Research

    PubMed Central

    Wu, Hulin; Xue, Hongqi; Kumar, Arun

    2012-01-01

    Summary Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this paper, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler’s method, trapezoidal rule and Runge-Kutta method. A higher order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators (DBE) are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods to an HIV study to further illustrate the usefulness of the proposed approaches. PMID:22376200

  10. XMM-Newton: Longevity through continued modification

    NASA Astrophysics Data System (ADS)

    Jansen, F.

    2014-07-01

    While the XMM-Newton observatory was built with a design lifetime of 10 years, a number of activities have been necessary during recent years to guarantee, from a resource and hardware point of view, the extension of an, otherwise limited, lifetime. This has required involving the original designers, project team members and companies where the relevant hardware elements were built to define, test and upload on board software which had not been changed in some 14 years. This, amongst others, has led to the implementation of attitude control based on simultaneous use of 4 reaction wheels - a method which has not only generated significant fuel savings, but also helped to address some performance issues with one of the reaction wheels. In the next few years a few other projects/updates will need to be implemented on-board. Not only the hardware is an item to be addressed in trying to achieve mission longevity, but also analysis software changes and calibration consolidation are items which have to be considered to keep on operating under increasing budget pressure while maintaining scientific proficiency.

  11. Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.; Scheid, R. E., Jr.

    1987-01-01

    This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.

  12. The history of Newton's apple tree

    NASA Astrophysics Data System (ADS)

    Keesing, R. G.

    1998-05-01

    This article contains a brief introduction to Newton's early life to put into context the subsequent events in this narrative. It is followed by a summary of accounts of Newton's famous story of his discovery of universal gravitation which was occasioned by the fall of an apple in the year 1665/6. Evidence of Newton's friendship with a prosperous Yorkshire family who planted an apple tree arbour in the early years of the eighteenth century to celebrate his discovery is presented. A considerable amount of new and unpublished pictorial and documentary material is included relating to a particular apple tree which grew in the garden of Woolsthorpe Manor (Newton's birthplace) and which blew down in a storm before the year 1816. Evidence is then presented which describes how this tree was chosen to be the focus of Newton's account. Details of the propagation of the apple tree growing in the garden at Woolsthorpe in the early part of the last century are then discussed, and the results of a dendrochronological study of two of these trees is presented. It is then pointed out that there is considerable evidence to show that the apple tree presently growing at Woolsthorpe and known as 'Newton's apple tree' is in fact the same specimen which was identified in the middle of the eighteenth century and which may now be 350 years old. In conclusion early results from a radiocarbon dating study being carried out at the University of Oxford on core samples from the Woolsthorpe tree lend support to the contention that the present tree is one and the same as that identified as Newton's apple tree more than 200 years ago. Very recently genetic fingerprinting techniques have been used in an attempt to identify from which sources the various 'Newton apple trees' planted throughout the world originate. The tentative result of this work suggests that there are two separate varieties of apple tree in existence which have been accepted as 'the tree'. One may conclude that at least some of

  13. The XMM-Newton Survey of the Small Magellanic Cloud

    NASA Technical Reports Server (NTRS)

    Haberl, F.; Sturm, R.; Ballet, J.; Bomans, D. J.; Buckley, D. A. H.; Coe, M. J.; Corbet, R.; Ehle, M.; Filipovic, M. D.; Gilfanov, M.; Hatzidimitriou, D.; La Palombara, N.; Mereghetti, S.; Pietsch, W.; Snowden, S.; Tiengo, A.

    2012-01-01

    Context. Although numerous archival XMM-Newton observations existed towards the Small Magellanic Cloud (SMC) before 2009, only a fraction of the whole galaxy had been covered. Aims. Between May 2009 and March 2010, we carried out an XMM-Newton survey of the SMC, to ensure a complete coverage of both its bar and wing. Thirty-three observations of 30 different fields with a total exposure of about one Ms filled the previously missing parts. Methods. We systematically processed all available SMC data from the European Photon Imaging Camera. After rejecting observations with very high background, we included 53 archival and the 33 survey observations. We produced images in five different energy bands. We applied astrometric boresight corrections using secure identifications of X-ray sources and combined all the images to produce a mosaic covering the main body of the SMC. Results. We present an overview of the XMM-Newton observations, describe their analysis, and summarize our first results, which will be presented in detail in follow-up papers. Here, we mainly focus on extended X-ray sources, such as supernova remnants (SNRs) and clusters of galaxies, that are seen in our X-ray images. Conclusions. Our XMM-Newton survey represents the deepest complete survey of the SMC in the 0.15-12.0 keV X-ray band. We propose three new SNRs that have low surface brightnesses of a few 10-14 erg cm-2 s-1 arcmin-2 and large extents. In addition, several known remnants appear larger than previously measured at either X-rays or other wavelengths extending the size distribution of SMC SNRs to larger values.

  14. 3, 2, 1 … Discovering Newton's Laws

    NASA Astrophysics Data System (ADS)

    Lutz, Joe; Sylvester, Kevin; Oliver, Keith; Herrington, Deborah

    2017-03-01

    "For every action there is an equal and opposite reaction." "Except when a bug hits your car window, the car must exert more force on the bug because Newton's laws only apply in the physics classroom, right?" Students in our classrooms were able to pick out definitions as well as examples of Newton's three laws; they could recite the laws and even solve for force, mass, and acceleration. However, when given "real world" questions, they would quickly revert to naive explanations. This frustration led to an examination of our approach to teaching Newton's laws. Like many, we taught Newton's laws in their numerical order—first, second, and then third. Students read about the laws, copied definitions, and became proficient with vocabulary before they applied the laws in a lab setting. This paper discusses how we transformed our teaching of Newton's laws by flipping the order (3, 2, 1) and putting the activity before concept, as well as how these changes affected student outcomes.

  15. An investigation of particles suspension using smoothed particle hydrodynamics

    NASA Astrophysics Data System (ADS)

    Pazouki, Arman; Negrut, Dan

    2013-11-01

    This contribution outlines a method for the direct numerical simulation of rigid body suspensions in a Lagrangian-Lagrangian framework using extended Smoothed Particle Hydrodynamics (XSPH) method. The dynamics of the arbitrarily shaped rigid bodies is fully resolved via Boundary Condition Enforcing (BCE) markers and updated according to the general Newton-Euler equations of motion. The simulation tool, refered to herien as Chrono::Fluid, relies on a parallel implementation that runs on Graphics Processing Unit (GPU) cards. The simulation results obtained for transient Poiseuille flow, migration of cylinder and sphere in Poiseuille flow, and distribution of particles at different cross sections of the laminar flow of dilute suspension were respectively within 0.1%, 1%, and 5% confidence interval of analytical and experimental results reported in the literature. It was shown that at low Reynolds number, Re = O(1), the radial migration (a) behaves non-monotonically as the particles relative distance (distance over diameter) increases from zero to two; and (b) decreases as the particle skewness and size increases. The scaling of Chrono::Fluid was demonstrated in conjunction with a suspension dynamics analysis in which the number of ellipsoids went up to 3e4. Financial support was provided in part by National Science Foundation grant NSF CMMI-084044.

  16. Fourier smoothing of digital photographic spectra

    NASA Astrophysics Data System (ADS)

    Anupama, G. C.

    1990-03-01

    Fourier methods of smoothing one-dimensional data are discussed with particular reference to digital photographic spectra. Data smoothed using lowpass filters with different cut-off frequencies are intercompared. A method to scale densities in order to remove the dependence of grain noise on density is described. Optimal filtering technique which models signal and noise in Fourier domain is also explained.

  17. Smooth eigenvalue correction

    NASA Astrophysics Data System (ADS)

    Hendrikse, Anne; Veldhuis, Raymond; Spreeuwers, Luuk

    2013-12-01

    Second-order statistics play an important role in data modeling. Nowadays, there is a tendency toward measuring more signals with higher resolution (e.g., high-resolution video), causing a rapid increase of dimensionality of the measured samples, while the number of samples remains more or less the same. As a result the eigenvalue estimates are significantly biased as described by the Marčenko Pastur equation for the limit of both the number of samples and their dimensionality going to infinity. By introducing a smoothness factor, we show that the Marčenko Pastur equation can be used in practical situations where both the number of samples and their dimensionality remain finite. Based on this result we derive methods, one already known and one new to our knowledge, to estimate the sample eigenvalues when the population eigenvalues are known. However, usually the sample eigenvalues are known and the population eigenvalues are required. We therefore applied one of the these methods in a feedback loop, resulting in an eigenvalue bias correction method. We compare this eigenvalue correction method with the state-of-the-art methods and show that our method outperforms other methods particularly in real-life situations often encountered in biometrics: underdetermined configurations, high-dimensional configurations, and configurations where the eigenvalues are exponentially distributed.

  18. Analyzing Collisions in Terms of Newton's Laws

    NASA Astrophysics Data System (ADS)

    Roeder, John L.

    2003-02-01

    Although the principle of momentum conservation is a consequence of Newton's second and third laws of motion, as recognized by Newton himself, this principle is typically applied in analyzing collisions as if it is a separate concept of its own. This year I sought to integrate my treatment of collisions with my coverage of Newton's laws by asking students to calculate the effect on the motion of two particles due to the forces they exerted for a specified time interval on each other. For example, "A 50-kg crate slides across the ice at 3 m/s and collides with a 25-kg crate at rest. During the collision process the 50-kg crate exerts a 500 N time-averaged force on the 25 kg for 0.1 s. What are the accelerations of the crates during the collision, and what are their velocities after the collision? What are the momenta of the crates before and after collision?"

  19. Smooth, seamless, and structured grid generation with flexibility in resolution distribution on a sphere based on conformal mapping and the spring dynamics method

    NASA Astrophysics Data System (ADS)

    Iga, Shin-ichi

    2015-09-01

    A generation method for smooth, seamless, and structured triangular grids on a sphere with flexibility in resolution distribution is proposed. This method is applicable to many fields that deal with a sphere on which the required resolution is not uniform. The grids were generated using the spring dynamics method, and adjustments were made using analytical functions. The mesh topology determined its resolution distribution, derived from a combination of conformal mapping factors: polar stereographic projection (PSP), Lambert conformal conic projection (LCCP), and Mercator projection (MP). Their combination generated, for example, a tropically fine grid that had a nearly constant high-resolution belt around the equator, with a gradual decrease in resolution distribution outside of the belt. This grid can be applied to boundary-less simulations of tropical meteorology. The other example involves a regionally fine grid with a nearly constant high-resolution circular region and a gradually decreasing resolution distribution outside of the region. This is applicable to regional atmospheric simulations without grid nesting. The proposed grids are compatible with computer architecture because they possess a structured form. Each triangle of the proposed grids was highly regular, implying a high local isotropy in resolution. Finally, the proposed grids were examined by advection and shallow water simulations.

  20. XMM-Newton Mobile Web Application

    NASA Astrophysics Data System (ADS)

    Ibarra, A.; Kennedy, M.; Rodríguez, P.; Hernández, C.; Saxton, R.; Gabriel, C.

    2013-10-01

    We present the first XMM-Newton web mobile application, coded using new web technologies such as HTML5, the Query mobile framework, and D3 JavaScript data-driven library. This new web mobile application focuses on re-formatted contents extracted directly from the XMM-Newton web, optimizing the contents for mobile devices. The main goals of this development were to reach all kind of handheld devices and operating systems, while minimizing software maintenance. The application therefore has been developed as a web mobile implementation rather than a more costly native application. New functionality will be added regularly.

  1. Development and Implementation of a Newton-BICGSTAB Iterative Solver in the FORMOSA-B BWR Core Simulator Code

    SciTech Connect

    Kastanya, Doddy Yozef Febrian; Turinsky, Paul J.

    2005-05-15

    A Newton-Krylov iterative solver has been developed to reduce the CPU execution time of boiling water reactor (BWR) core simulators implemented in the core simulator part of the Fuel Optimization for Reloads Multiple Objectives by Simulated Annealing for BWR (FORMOSA-B) code, which is an in-core fuel management optimization code for BWRs. This new solver utilizes Newton's method to explicitly treat strong nonlinearities in the problem, replacing the traditionally used nested iterative approach. Newton's method provides the solver with a higher-than-linear convergence rate, assuming that good initial estimates of the unknowns are provided. Within each Newton iteration, an appropriately preconditioned Krylov solver is utilized for solving the linearized system of equations. Taking advantage of the higher convergence rate provided by Newton's method and utilizing an efficient preconditioned Krylov solver, we have developed a Newton-Krylov solver to evaluate the three-dimensional, two-group neutron diffusion equations coupled with a two-phase flow model within a BWR core simulator. Numerical tests on the new solver have shown that speedups ranging from 1.6 to 2.1, with reference to the traditional approach of employing nested iterations to treat the nonlinear feedbacks, can be achieved. However, if a preconditioned Krylov solver is employed to complete the inner iterations of the traditional approach, negligible CPU time differences are noted between the Newton-Krylov and traditional (Krylov) approaches.

  2. Newton's Metaphysics of Space as God's Emanative Effect

    NASA Astrophysics Data System (ADS)

    Jacquette, Dale

    2014-09-01

    In several of his writings, Isaac Newton proposed that physical space is God's "emanative effect" or "sensorium," revealing something interesting about the metaphysics underlying his mathematical physics. Newton's conjectures depart from Plato and Aristotle's metaphysics of space and from classical and Cambridge Neoplatonism. Present-day philosophical concepts of supervenience clarify Newton's ideas about space and offer a portrait of Newton not only as a mathematical physicist but an independent-minded rationalist philosopher.

  3. Magnetic Levitation and Newton's Third Law

    ERIC Educational Resources Information Center

    Aguilar, Horacio Munguia

    2007-01-01

    Newton's third law is often misunderstood by students and even their professors, as has already been pointed out in the literature. Application of the law in the context of electromagnetism can be especially problematic, because the idea that the forces of "action" and "reaction" are equal and opposite independent of the medium through which they…

  4. Infinity and Newton's Three Laws of Motion

    NASA Astrophysics Data System (ADS)

    Lee, Chunghyoung

    2011-12-01

    It is shown that the following three common understandings of Newton's laws of motion do not hold for systems of infinitely many components. First, Newton's third law, or the law of action and reaction, is universally believed to imply that the total sum of internal forces in a system is always zero. Several examples are presented to show that this belief fails to hold for infinite systems. Second, two of these examples are of an infinitely divisible continuous body with finite mass and volume such that the sum of all the internal forces in the body is not zero and the body accelerates due to this non-null net internal force. So the two examples also demonstrate the breakdown of the common understanding that according to Newton's laws a body under no external force does not accelerate. Finally, these examples also make it clear that the expression `impressed force' in Newton's formulations of his first and second laws should be understood not as `external force' but as `exerted force' which is the sum of all the internal and external forces acting on a given body, if the body is infinitely divisible.

  5. Quantum physics explains Newton's laws of motion

    NASA Astrophysics Data System (ADS)

    Ogborn, Jon; Taylor, Edwin F.

    2005-01-01

    Newton was obliged to give his laws of motion as fundamental axioms. But today we know that the quantum world is fundamental, and Newton’s laws can be seen as consequences of fundamental quantum laws. This article traces this transition from fundamental quantum mechanics to derived classical mechanics.

  6. Newtons's Thermometry: The Role of Radiation.

    ERIC Educational Resources Information Center

    French, A. P.

    1993-01-01

    Discusses Newton's idea of predicting very high temperatures of objects by observing the time needed for the object to cool to some standard reference temperature. This article discusses experimental deviations from this idea and provides explanations for the observed results. (MVL)

  7. Newton's First Law: A Learning Cycle Approach

    ERIC Educational Resources Information Center

    McCarthy, Deborah

    2005-01-01

    To demonstrate how Newton's first law of motion applies to students' everyday lives, the author developed a learning cycle series of activities on inertia. The discrepant event at the heart of these activities is sure to elicit wide-eyed stares and puzzled looks from students, but also promote critical thinking and help bring an abstract concept…

  8. Newton's Law: Not so Simple after All

    ERIC Educational Resources Information Center

    Robertson, William C.; Gallagher, Jeremiah; Miller, William

    2004-01-01

    One of the most basic concepts related to force and motion is Newton's first law, which essentially states, "An object at rest tends to remain at rest unless acted on by an unbalanced force. An object in motion in a straight line tends to remain in motion in a straight line unless acted upon by an unbalanced force." Judging by the time and space…

  9. A Class Inquiry into Newton's Cooling Curve

    ERIC Educational Resources Information Center

    Bartholow, Martin

    2007-01-01

    Newton's cooling curve was chosen for the four-part laboratory inquiry into conditions affecting temperature change. The relationship between time and temperature is not foreseen by the average high school student before the first session. However, during several activities students examine the classic relationship, T = A exp[superscript -Ct] + B…

  10. Sonic Beam Model of Newton's Cradle

    ERIC Educational Resources Information Center

    Menger, Fredric M.; Rizvi, Syed A. A.

    2016-01-01

    The motions of Newton's cradle, consisting of several steel balls hanging side-by-side, have been analysed in terms of a sound pulse that travels via points of contact among the balls. This presupposes a focused energy beam. When the pulse reaches the fifth and final ball, the energy disperses and dislocates the ball with a trajectory equivalent…

  11. Bernoulli and Newton in Fluid Mechanics

    ERIC Educational Resources Information Center

    Smith, Norman F.

    1972-01-01

    Bernoulli's theorem can be better understood with the aid of Newton's laws and the law of conservation of energy. Application of this theorem should involve only cases dealing with an interchange of velocity and pressure within a fluid under isentropic conditions. (DF)

  12. NEWTON'S APPLE 14th Season Teacher's Guide.

    ERIC Educational Resources Information Center

    Wichmann, Sue, Ed.

    This guide was developed to help teachers use the 14th season of NEWTON'S APPLE in their classrooms and contains lessons formatted to follow the National Science Education Standards. The "Overview,""Main Activity," and "Try-This" sections were created with inquiry-based learning in mind. Each lesson page begins with…

  13. Three Hundred Years of Newton's Principia.

    ERIC Educational Resources Information Center

    Dolby, R. G. A.

    1987-01-01

    Discusses how the reputation of "Principia" was created and maintained. Indicates the difficulties of identifying a single unambiguous meaning for the text. Shows that knowledge of Sir Isaac Newton makes little difference to understanding the later impact of the work. (CW)

  14. Smoothing error pitfalls

    NASA Astrophysics Data System (ADS)

    von Clarmann, T.

    2014-04-01

    The difference due to the content of a priori information between a constrained retrieval and the true atmospheric state is usually represented by the so-called smoothing error. In this paper it is shown that the concept of the smoothing error is questionable because it is not compliant with Gaussian error propagation. The reason for this is that the smoothing error does not represent the expected deviation of the retrieval from the true state but the expected deviation of the retrieval from the atmospheric state sampled on an arbitrary grid, which is itself a smoothed representation of the true state. The idea of a sufficiently fine sampling of this reference atmospheric state is untenable because atmospheric variability occurs on all scales, implying that there is no limit beyond which the sampling is fine enough. Even the idealization of infinitesimally fine sampling of the reference state does not help because the smoothing error is applied to quantities which are only defined in a statistical sense, which implies that a finite volume of sufficient spatial extent is needed to meaningfully talk about temperature or concentration. Smoothing differences, however, which play a role when measurements are compared, are still a useful quantity if the involved a priori covariance matrix has been evaluated on the comparison grid rather than resulting from interpolation. This is, because the undefined component of the smoothing error, which is the effect of smoothing implied by the finite grid on which the measurements are compared, cancels out when the difference is calculated.

  15. 27 CFR 9.152 - Malibu-Newton Canyon.

    Code of Federal Regulations, 2013 CFR

    2013-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2013-04-01 2013-04-01 false Malibu-Newton Canyon. 9... Malibu-Newton Canyon. (a) Name. The name of the viticultural area described in this petition is “Malibu-Newton Canyon.” (b) Approved maps. The appropriate map for determining the boundary of the...

  16. 27 CFR 9.152 - Malibu-Newton Canyon.

    Code of Federal Regulations, 2010 CFR

    2010-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2010-04-01 2010-04-01 false Malibu-Newton Canyon. 9... Malibu-Newton Canyon. (a) Name. The name of the viticultural area described in this petition is “Malibu-Newton Canyon.” (b) Approved maps. The appropriate map for determining the boundary of the...

  17. 27 CFR 9.152 - Malibu-Newton Canyon.

    Code of Federal Regulations, 2011 CFR

    2011-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2011-04-01 2011-04-01 false Malibu-Newton Canyon. 9... Malibu-Newton Canyon. (a) Name. The name of the viticultural area described in this petition is “Malibu-Newton Canyon.” (b) Approved maps. The appropriate map for determining the boundary of the...

  18. 27 CFR 9.152 - Malibu-Newton Canyon.

    Code of Federal Regulations, 2012 CFR

    2012-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2012-04-01 2012-04-01 false Malibu-Newton Canyon. 9... Malibu-Newton Canyon. (a) Name. The name of the viticultural area described in this petition is “Malibu-Newton Canyon.” (b) Approved maps. The appropriate map for determining the boundary of the...

  19. Constructs and Attributes in Test Validity: Reflections on Newton's Account

    ERIC Educational Resources Information Center

    Markus, Keith A.

    2012-01-01

    I congratulate Paul E. Newton on a thoughtful and evenhanded contribution to test validity theory. I especially appreciate the evident care that went into interpreting the various authors whose work Newton discusses. I found many useful insights along with the few minor points with which I might quibble. I comment on three aspects of Newton's…

  20. 27 CFR 9.152 - Malibu-Newton Canyon.

    Code of Federal Regulations, 2014 CFR

    2014-04-01

    ... 27 Alcohol, Tobacco Products and Firearms 1 2014-04-01 2014-04-01 false Malibu-Newton Canyon. 9... Malibu-Newton Canyon. (a) Name. The name of the viticultural area described in this petition is “Malibu-Newton Canyon.” (b) Approved maps. The appropriate map for determining the boundary of the...

  1. Diamond Smoothing Tools

    NASA Technical Reports Server (NTRS)

    Voronov, Oleg

    2007-01-01

    Diamond smoothing tools have been proposed for use in conjunction with diamond cutting tools that are used in many finish-machining operations. Diamond machining (including finishing) is often used, for example, in fabrication of precise metal mirrors. A diamond smoothing tool according to the proposal would have a smooth spherical surface. For a given finish machining operation, the smoothing tool would be mounted next to the cutting tool. The smoothing tool would slide on the machined surface left behind by the cutting tool, plastically deforming the surface material and thereby reducing the roughness of the surface, closing microcracks and otherwise generally reducing or eliminating microscopic surface and subsurface defects, and increasing the microhardness of the surface layer. It has been estimated that if smoothing tools of this type were used in conjunction with cutting tools on sufficiently precise lathes, it would be possible to reduce the roughness of machined surfaces to as little as 3 nm. A tool according to the proposal would consist of a smoothing insert in a metal holder. The smoothing insert would be made from a diamond/metal functionally graded composite rod preform, which, in turn, would be made by sintering together a bulk single-crystal or polycrystalline diamond, a diamond powder, and a metallic alloy at high pressure. To form the spherical smoothing tip, the diamond end of the preform would be subjected to flat grinding, conical grinding, spherical grinding using diamond wheels, and finally spherical polishing and/or buffing using diamond powders. If the diamond were a single crystal, then it would be crystallographically oriented, relative to the machining motion, to minimize its wear and maximize its hardness. Spherically polished diamonds could also be useful for purposes other than smoothing in finish machining: They would likely also be suitable for use as heat-resistant, wear-resistant, unlubricated sliding-fit bearing inserts.

  2. Epidemiological analysis of hemorrhagic fever with renal syndrome in China with the seasonal-trend decomposition method and the exponential smoothing model

    PubMed Central

    Ke, Guibao; Hu, Yao; Huang, Xin; Peng, Xuan; Lei, Min; Huang, Chaoli; Gu, Li; Xian, Ping; Yang, Dehua

    2016-01-01

    Hemorrhagic fever with renal syndrome (HFRS) is one of the most common infectious diseases globally. With the most reported cases in the world, the epidemic characteristics are still remained unclear in China. This paper utilized the seasonal-trend decomposition (STL) method to analyze the periodicity and seasonality of the HFRS data, and used the exponential smoothing model (ETS) model to predict incidence cases from July to December 2016 by using the data from January 2006 to June 2016. Analytic results demonstrated a favorable trend of HFRS in China, and with obvious periodicity and seasonality, the peak of the annual reported cases in winter concentrated on November to January of the following year, and reported in May and June also constituted another peak in summer. Eventually, the ETS (M, N and A) model was adopted for fitting and forecasting, and the fitting results indicated high accuracy (Mean absolute percentage error (MAPE) = 13.12%). The forecasting results also demonstrated a gradual decreasing trend from July to December 2016, suggesting that control measures for hemorrhagic fever were effective in China. The STL model could be well performed in the seasonal analysis of HFRS in China, and ETS could be effectively used in the time series analysis of HFRS in China. PMID:27976704

  3. A Simple Method for the Growth of Very Smooth and Ultra-Thin GaSb Films on GaAs (111) Substrate by MOCVD

    NASA Astrophysics Data System (ADS)

    Ni, Pei-Nan; Tong, Jin-Chao; Tobing, Landobasa Y. M.; Qiu, Shu-Peng; Xu, Zheng-Ji; Tang, Xiao-Hong; Zhang, Dao-Hua

    2017-02-01

    We present a simple thermal treatment with the antimony source for the metal-organic chemical vapor deposition of thin GaSb films on GaAs (111) substrates for the first time. The properties of the as-grown GaSb films are systematically analyzed by scanning electron microscopy, atomic force microscopy, x-ray diffraction, photo-luminescence (PL) and Hall measurement. It is found that the as-grown GaSb films by the proposed method can be as thin as 35 nm and have a very smooth surface with the root mean square roughness as small as 0.777 nm. Meanwhile, the grown GaSb films also have high crystalline quality, of which the full width at half maximum of the rocking-curve is as small as 218 arcsec. Moreover, the good optical quality of the GaSb films has been demonstrated by the low-temperature PL. This work provides a simple and feasible buffer-free strategy for the growth of high-quality GaSb films directly on GaAs substrates and the strategy may also be applicable to the growth on other substrates and the hetero-growth of other materials.

  4. A Newton-Krylov Approach to Aerodynamic Shape Optimization in Three Dimensions

    NASA Astrophysics Data System (ADS)

    Leung, Timothy Man-Ming

    A Newton-Krylov algorithm is presented for aerodynamic shape optimization in three dimensions using the Euler equations. An inexact-Newton method is used in the flow solver, a discrete-adjoint method to compute the gradient, and the quasi-Newton optimizer to find the optimum. A Krylov subspace method with approximate-Schur preconditioning is used to solve both the flow equation and the adjoint equation. Basis spline surfaces are used to parameterize the geometry, and a fast algebraic algorithm is used for grid movement. Accurate discrete- adjoint gradients can be obtained in approximately one-fourth the time required for a converged flow solution. Single- and multi-point lift-constrained drag minimization optimization cases are presented for wing design at transonic speeds. In all cases, the optimizer is able to efficiently decrease the objective function and gradient for problems with hundreds of design variables.

  5. The use of Newton's rings for characterising ophthalmic lenses.

    PubMed

    Illueca, C; Vazquez, C; Hernández, C; Viqueira, V

    1998-07-01

    The interference technique of Newton's Rings is widely used for the quality control of optical surfaces because the precision obtained with this method proves to be very satisfactory. The dimensions of the rings permits calculation of the radii of curvature of the analysed surfaces and deformation of the interference pattern can be utilised to calculate other parameters, such as astigmatism. We describe the study of progressive surfaces by means of this technique, whereby the analysis of the various points of the progressive corridor is made, and also include information on the power function for these lenses, as well as the addition and corridor length.

  6. Asymptotic analysis of Bayesian generalization error with Newton diagram.

    PubMed

    Yamazaki, Keisuke; Aoyagi, Miki; Watanabe, Sumio

    2010-01-01

    Statistical learning machines that have singularities in the parameter space, such as hidden Markov models, Bayesian networks, and neural networks, are widely used in the field of information engineering. Singularities in the parameter space determine the accuracy of estimation in the Bayesian scenario. The Newton diagram in algebraic geometry is recognized as an effective method by which to investigate a singularity. The present paper proposes a new technique to plug the diagram in the Bayesian analysis. The proposed technique allows the generalization error to be clarified and provides a foundation for an efficient model selection. We apply the proposed technique to mixtures of binomial distributions.

  7. Newton, laplace, and the epistemology of systems biology.

    PubMed

    Bittner, Michael L; Dougherty, Edward R

    2012-01-01

    For science, theoretical or applied, to significantly advance, researchers must use the most appropriate mathematical methods. A century and a half elapsed between Newton's development of the calculus and Laplace's development of celestial mechanics. One cannot imagine the latter without the former. Today, more than three-quarters of a century has elapsed since the birth of stochastic systems theory. This article provides a perspective on the utilization of systems theory as the proper vehicle for the development of systems biology and its application to complex regulatory diseases such as cancer.

  8. A quasi-Newton approach to optimization problems with probability density constraints. [problem solving in mathematical programming

    NASA Technical Reports Server (NTRS)

    Tapia, R. A.; Vanrooy, D. L.

    1976-01-01

    A quasi-Newton method is presented for minimizing a nonlinear function while constraining the variables to be nonnegative and sum to one. The nonnegativity constraints were eliminated by working with the squares of the variables and the resulting problem was solved using Tapia's general theory of quasi-Newton methods for constrained optimization. A user's guide for a computer program implementing this algorithm is provided.

  9. Astrophysical smooth particle hydrodynamics

    NASA Astrophysics Data System (ADS)

    Rosswog, Stephan

    2009-04-01

    The paper presents a detailed review of the smooth particle hydrodynamics (SPH) method with particular focus on its astrophysical applications. We start by introducing the basic ideas and concepts and thereby outline all ingredients that are necessary for a practical implementation of the method in a working SPH code. Much of SPH's success relies on its excellent conservation properties and therefore the numerical conservation of physical invariants receives much attention throughout this review. The self-consistent derivation of the SPH equations from the Lagrangian of an ideal fluid is the common theme of the remainder of the text. We derive a modern, Newtonian SPH formulation from the Lagrangian of an ideal fluid. It accounts for changes of the local resolution lengths which result in corrective, so-called "grad-h-terms". We extend this strategy to special relativity for which we derive the corresponding grad-h equation set. The variational approach is further applied to a general-relativistic fluid evolving in a fixed, curved background space-time. Particular care is taken to explicitly derive all relevant equations in a coherent way.

  10. A new method for direct detection of the sites of actin polymerization in intact cells and its application to differentiated vascular smooth muscle.

    PubMed

    Kim, Hak Rim; Leavis, Paul C; Graceffa, Philip; Gallant, Cynthia; Morgan, Kathleen G

    2010-11-01

    Here we report and validate a new method, suitable broadly, for use in differentiated cells and tissues, for the direct visualization of actin polymerization under physiological conditions. We have designed and tested different versions of fluorescently labeled actin, reversibly attached to the protein transduction tag TAT, and have introduced this novel reagent into intact differentiated vascular smooth muscle cells (dVSMCs). A thiol-reactive version of the TAT peptide was synthesized by adding the amino acids glycine and cysteine to its NH(2)-terminus and forming a thionitrobenzoate adduct: viz. TAT-Cys-S-STNB. This peptide reacts readily with G-actin, and the complex is rapidly taken up by freshly enzymatically isolated dVSMC, as indicated by the fluorescence of a FITC tag on the TAT peptide. By comparing different versions of the construct, we determined that the optimal construct for biological applications is a nonfluorescently labeled TAT peptide conjugated to rhodamine-labeled actin. When TAT-Cys-S-STNB-tagged rhodamine actin (TSSAR) was added to live, freshly enzymatically isolated cells, we observed punctae of incorporated actin at the cortex of the cell. The punctae are indistinguishable from those we have previously reported to occur in the same cell type when rhodamine G-actin is added to permeabilized cells. Thus this new method allows the delivery of labeled G-actin into intact cells without disrupting the native state and will allow its further use to study the effect of physiological intracellular Ca(2+) concentration transients and signal transduction on actin dynamics in intact cells.

  11. Molecular method for sex identification of half-smooth tongue sole (Cynoglossus semilaevis) using a novel sex-linked microsatellite marker.

    PubMed

    Liao, Xiaolin; Xu, Genbo; Chen, Song-Lin

    2014-07-22

    Half-smooth tongue sole (Cynoglossus semilaevis) is one of the most important flatfish species for aquaculture in China. To produce a monosex population, we attempted to develop a marker-assisted sex control technique in this sexually size dimorphic fish. In this study, we identified a co-dominant sex-linked marker (i.e., CyseSLM) by screening genomic microsatellites and further developed a novel molecular method for sex identification in the tongue sole. CyseSLM has a sequence similarity of 73%-75% with stickleback, medaka, Fugu and Tetraodon. At this locus, two alleles (i.e., A244 and A234) were amplified from 119 tongue sole individuals with primer pairs CyseSLM-F1 and CyseSLM-R. Allele A244 was present in all individuals, while allele A234 (female-associated allele, FAA) was mostly present in females with exceptions in four male individuals. Compared with the sequence of A244, A234 has a 10-bp deletion and 28 SNPs. A specific primer (CyseSLM-F2) was then designed based on the A234 sequence, which amplified a 204 bp fragment in all females and four males with primer CyseSLM-R. A time-efficient multiplex PCR program was developed using primers CyseSLM-F2, CyseSLM-R and the newly designed primer CyseSLM-F3. The multiplex PCR products with co-dominant pattern could be detected by agarose gel electrophoresis, which accurately identified the genetic sex of the tongue sole. Therefore, we have developed a rapid and reliable method for sex identification in tongue sole with a newly identified sex-linked microsatellite marker.

  12. Computer assisted expansion of 1/Delta series with Newton iteration. [for Jovian satellite perturbation

    NASA Technical Reports Server (NTRS)

    Chao, C. C.; Broucke, R. A.

    1976-01-01

    The Newton iteration method has been widely applied to the solution of various equations such as Kepler's equation. In this study it is used in planetary and satellite theory as a general procedure for Fourier series inversion. The method is used for the construction of the 1/Delta series either in literal form or in numerical form with small eccentricities and inclinations substituted in advance. This usually results in very compact series. With the Newton iteration procedure and a computerized series manipulation technique, the Fourier series of 1/Delta of the mutual perturbations among most natural satellites can be easily constructed.

  13. A Novel Method for Differentiation of Human Mesenchymal Stem Cells into Smooth Muscle-Like Cells on Clinically Deliverable Thermally Induced Phase Separation Microspheres

    PubMed Central

    Parmar, Nina; Ahmadi, Raheleh

    2015-01-01

    Muscle degeneration is a prevalent disease, particularly in aging societies where it has a huge impact on quality of life and incurs colossal health costs. Suitable donor sources of smooth muscle cells are limited and minimally invasive therapeutic approaches are sought that will augment muscle volume by delivering cells to damaged or degenerated areas of muscle. For the first time, we report the use of highly porous microcarriers produced using thermally induced phase separation (TIPS) to expand and differentiate adipose-derived mesenchymal stem cells (AdMSCs) into smooth muscle-like cells in a format that requires minimal manipulation before clinical delivery. AdMSCs readily attached to the surface of TIPS microcarriers and proliferated while maintained in suspension culture for 12 days. Switching the incubation medium to a differentiation medium containing 2 ng/mL transforming growth factor beta-1 resulted in a significant increase in both the mRNA and protein expression of cell contractile apparatus components caldesmon, calponin, and myosin heavy chains, indicative of a smooth muscle cell-like phenotype. Growth of smooth muscle cells on the surface of the microcarriers caused no change to the integrity of the polymer microspheres making them suitable for a cell-delivery vehicle. Our results indicate that TIPS microspheres provide an ideal substrate for the expansion and differentiation of AdMSCs into smooth muscle-like cells as well as a microcarrier delivery vehicle for the attached cells ready for therapeutic applications. PMID:25205072

  14. A combination method for solving nonlinear equations

    NASA Astrophysics Data System (ADS)

    Silalahi, B. P.; Laila, R.; Sitanggang, I. S.

    2017-01-01

    This paper discusses methods for finding solutions of nonlinear equations: the Newton method, the Halley method and the combination of the Newton method, the Newton inverse method and the Halley method. Computational results in terms of the accuracy, the number of iterations and the running time for solving some given problems are presented.

  15. XMM Newton Observations of Toothbrush Cluster

    NASA Astrophysics Data System (ADS)

    Kara, Sinancan; Nihal Ercan, Enise; De Plaa, Jelle; Mernier, Francois

    2016-07-01

    Galaxy clusters are the largest gravitationally-bound objects in the universe. The member galaxies are embedded in a hot X-ray emitting Intra-Cluster Medium (ICM) that has been enriched over time with metals produced by supernovae. In this presentation we show new results from XMM-Newton regarding the merging cluster 1RXSJ0603.3+4213. This cluster, also known as the Toothbrush cluster, shows a large toothbrush-shaped radio relic associated with a merger shock North of the cluster core. We show the distribution and the abundances of the metals in this merging cluster in relation to the merger shock. The results are derived from spatially resolved X-ray spectra from the EPIC instrument aboard XMM-Newton.

  16. Cancer Therapeutics Following Newton's Third Law.

    PubMed

    Arbab, Ali S; Jain, Meenu; Achyut, Bhagelu R

    2016-01-01

    Cancer is a wound that never heals. This is suggested by the data produced after several years of cancer research and therapeutic interventions done worldwide. There is a strong similarity between Newton's third law and therapeutic behavior of tumor. According to Newton's third law "for every action, there is an equal and opposite reaction". In cancer therapeutics, tumor exerts strong pro-tumor response against applied treatment and imposes therapeutic resistance, one of the major problems seen in preclinical and clinical studies. There is an urgent need to understand the tumor biology of therapy resistant tumors following the therapy. Here, we have discussed the problem and provided possible path for future studies to treat cancer.

  17. A low-complexity 2-point step size gradient projection method with selective function evaluations for smoothed total variation based CBCT reconstructions

    NASA Astrophysics Data System (ADS)

    Song, Bongyong; Park, Justin C.; Song, William Y.

    2014-11-01

    The Barzilai-Borwein (BB) 2-point step size gradient method is receiving attention for accelerating Total Variation (TV) based CBCT reconstructions. In order to become truly viable for clinical applications, however, its convergence property needs to be properly addressed. We propose a novel fast converging gradient projection BB method that requires ‘at most one function evaluation’ in each iterative step. This Selective Function Evaluation method, referred to as GPBB-SFE in this paper, exhibits the desired convergence property when it is combined with a ‘smoothed TV’ or any other differentiable prior. This way, the proposed GPBB-SFE algorithm offers fast and guaranteed convergence to the desired 3DCBCT image with minimal computational complexity. We first applied this algorithm to a Shepp-Logan numerical phantom. We then applied to a CatPhan 600 physical phantom (The Phantom Laboratory, Salem, NY) and a clinically-treated head-and-neck patient, both acquired from the TrueBeam™ system (Varian Medical Systems, Palo Alto, CA). Furthermore, we accelerated the reconstruction by implementing the algorithm on NVIDIA GTX 480 GPU card. We first compared GPBB-SFE with three recently proposed BB-based CBCT reconstruction methods available in the literature using Shepp-Logan numerical phantom with 40 projections. It is found that GPBB-SFE shows either faster convergence speed/time or superior convergence property compared to existing BB-based algorithms. With the CatPhan 600 physical phantom, the GPBB-SFE algorithm requires only 3 function evaluations in 30 iterations and reconstructs the standard, 364-projection FDK reconstruction quality image using only 60 projections. We then applied the algorithm to a clinically-treated head-and-neck patient. It was observed that the GPBB-SFE algorithm requires only 18 function evaluations in 30 iterations. Compared with the FDK algorithm with 364 projections, the GPBB-SFE algorithm produces visibly equivalent quality CBCT

  18. A low-complexity 2-point step size gradient projection method with selective function evaluations for smoothed total variation based CBCT reconstructions.

    PubMed

    Song, Bongyong; Park, Justin C; Song, William Y

    2014-11-07

    The Barzilai-Borwein (BB) 2-point step size gradient method is receiving attention for accelerating Total Variation (TV) based CBCT reconstructions. In order to become truly viable for clinical applications, however, its convergence property needs to be properly addressed. We propose a novel fast converging gradient projection BB method that requires 'at most one function evaluation' in each iterative step. This Selective Function Evaluation method, referred to as GPBB-SFE in this paper, exhibits the desired convergence property when it is combined with a 'smoothed TV' or any other differentiable prior. This way, the proposed GPBB-SFE algorithm offers fast and guaranteed convergence to the desired 3DCBCT image with minimal computational complexity. We first applied this algorithm to a Shepp-Logan numerical phantom. We then applied to a CatPhan 600 physical phantom (The Phantom Laboratory, Salem, NY) and a clinically-treated head-and-neck patient, both acquired from the TrueBeam™ system (Varian Medical Systems, Palo Alto, CA). Furthermore, we accelerated the reconstruction by implementing the algorithm on NVIDIA GTX 480 GPU card. We first compared GPBB-SFE with three recently proposed BB-based CBCT reconstruction methods available in the literature using Shepp-Logan numerical phantom with 40 projections. It is found that GPBB-SFE shows either faster convergence speed/time or superior convergence property compared to existing BB-based algorithms. With the CatPhan 600 physical phantom, the GPBB-SFE algorithm requires only 3 function evaluations in 30 iterations and reconstructs the standard, 364-projection FDK reconstruction quality image using only 60 projections. We then applied the algorithm to a clinically-treated head-and-neck patient. It was observed that the GPBB-SFE algorithm requires only 18 function evaluations in 30 iterations. Compared with the FDK algorithm with 364 projections, the GPBB-SFE algorithm produces visibly equivalent quality CBCT image for

  19. Life after Newton: an ecological metaphysic.

    PubMed

    Ulanowicz, R E

    1999-05-01

    Ecology may indeed be 'deep', as some have maintained, but perhaps much of the mystery surrounding it owes more simply to the dissonance between ecological notions and the fundamentals of the modern synthesis. Comparison of the axioms supporting the Newtonian world view with those underlying the organicist and stochastic metaphors that motivate much of ecosystems science reveals strong disagreements--especially regarding the nature of the causes of events and the scalar domains over which these causes can operate. The late Karl Popper held that the causal closure forced by our mechanical perspective on nature frustrates our attempts to achieve an 'evolutionary theory of knowledge.' He suggested that the Newtonian concept of 'force' must be generalized to encompass the contingencies that arise in evolutionary processes. His reformulation of force as 'propensity' leads quite naturally to a generalization of Newton's laws for ecology. The revised tenets appear, however, to exhibit more scope and allow for change to arise from within a system. Although Newton's laws survive (albeit in altered form) within a coalescing ecological metaphysic, the axioms that Enlightenment thinkers appended to Newton's work seem ill-suited for ecology and perhaps should yield to a new and coherent set of assumptions on how to view the processes of nature.

  20. Cosmological Conundrums and Discoveries Since Newton

    NASA Astrophysics Data System (ADS)

    Topper, David R.

    Cosmology is key branch of astronomy, dealing with questions around the structure of the universe. The ancient cosmos - systematically codified by Aristotle, and later given empirical support, especially by Ptolemy - was geocentric, geostatic, and finite. Based on a common sense view of the world being as it appears to our senses, the ancient model prevailed well into the seventeenth century. The subsequent scientific revolution, however, bequeathed to the eighteenth century and after a radically different cosmic model. The radical change came in two stages. First Copernicus in the fifteenth century moved the Sun to Earth's previous place at the center of the universe, an idea adopted by Galileo, Kepler, and a few other key thinkers up to Newton. The second stage, often called the "breaking of the sphere," replaced the sphere of a few thousand stars at the edge of the finite universe with myriad stars extending into an infinite universe, filled with Newton's invisible gravity, and with our Earth being the third planet from the Sun in our solar system somewhere within that Euclidean space. Two planets were added to our solar system (one in the eighteenth and one in the nineteenth centuries), but the overall structure remained essentially as conceived by Newton when he died in 1727. This was the universe Einstein was born into in 1879.

  1. Spline-Based Smoothing of Airfoil Curvatures

    NASA Technical Reports Server (NTRS)

    Li, W.; Krist, S.

    2008-01-01

    Constrained fitting for airfoil curvature smoothing (CFACS) is a splinebased method of interpolating airfoil surface coordinates (and, concomitantly, airfoil thicknesses) between specified discrete design points so as to obtain smoothing of surface-curvature profiles in addition to basic smoothing of surfaces. CFACS was developed in recognition of the fact that the performance of a transonic airfoil is directly related to both the curvature profile and the smoothness of the airfoil surface. Older methods of interpolation of airfoil surfaces involve various compromises between smoothing of surfaces and exact fitting of surfaces to specified discrete design points. While some of the older methods take curvature profiles into account, they nevertheless sometimes yield unfavorable results, including curvature oscillations near end points and substantial deviations from desired leading-edge shapes. In CFACS as in most of the older methods, one seeks a compromise between smoothing and exact fitting. Unlike in the older methods, the airfoil surface is modified as little as possible from its original specified form and, instead, is smoothed in such a way that the curvature profile becomes a smooth fit of the curvature profile of the original airfoil specification. CFACS involves a combination of rigorous mathematical modeling and knowledge-based heuristics. Rigorous mathematical formulation provides assurance of removal of undesirable curvature oscillations with minimum modification of the airfoil geometry. Knowledge-based heuristics bridge the gap between theory and designers best practices. In CFACS, one of the measures of the deviation of an airfoil surface from smoothness is the sum of squares of the jumps in the third derivatives of a cubicspline interpolation of the airfoil data. This measure is incorporated into a formulation for minimizing an overall deviation- from-smoothness measure of the airfoil data within a specified fitting error tolerance. CFACS has been

  2. Analytic elements of smooth shapes

    NASA Astrophysics Data System (ADS)

    Strack, Otto D. L.; Nevison, Patrick R.

    2015-10-01

    We present a method for producing analytic elements of a smooth shape, obtained using conformal mapping. Applications are presented for a case of impermeable analytic elements as well as for head-specified ones. The mathematical operations necessary to use the elements in practical problems can be carried out before modeling of flow problems begins. A catalog of shapes, along with pre-determined coefficients could be established on the basis of the approach presented here, making applications in the field straight forward.

  3. Smoothing error pitfalls

    NASA Astrophysics Data System (ADS)

    von Clarmann, T.

    2014-09-01

    The difference due to the content of a priori information between a constrained retrieval and the true atmospheric state is usually represented by a diagnostic quantity called smoothing error. In this paper it is shown that, regardless of the usefulness of the smoothing error as a diagnostic tool in its own right, the concept of the smoothing error as a component of the retrieval error budget is questionable because it is not compliant with Gaussian error propagation. The reason for this is that the smoothing error does not represent the expected deviation of the retrieval from the true state but the expected deviation of the retrieval from the atmospheric state sampled on an arbitrary grid, which is itself a smoothed representation of the true state; in other words, to characterize the full loss of information with respect to the true atmosphere, the effect of the representation of the atmospheric state on a finite grid also needs to be considered. The idea of a sufficiently fine sampling of this reference atmospheric state is problematic because atmospheric variability occurs on all scales, implying that there is no limit beyond which the sampling is fine enough. Even the idealization of infinitesimally fine sampling of the reference state does not help, because the smoothing error is applied to quantities which are only defined in a statistical sense, which implies that a finite volume of sufficient spatial extent is needed to meaningfully discuss temperature or concentration. Smoothing differences, however, which play a role when measurements are compared, are still a useful quantity if the covariance matrix involved has been evaluated on the comparison grid rather than resulting from interpolation and if the averaging kernel matrices have been evaluated on a grid fine enough to capture all atmospheric variations that the instruments are sensitive to. This is, under the assumptions stated, because the undefined component of the smoothing error, which is the

  4. Smoothing analysis of HLSII storage ring magnets

    NASA Astrophysics Data System (ADS)

    Wang, Wei; He, Xiao-Ye; Tang, Zheng; Yao, Qiu-Yang

    2016-12-01

    Hefei Light Source (HLS) has been upgraded to improve the quality and stability of the synchrotron light, and the new facility is named HLSII. However, a final accurate adjustment is required to smooth the beam orbit after the initial instalment and alignment of the magnets. We implement a reliable smoothing method for the beam orbit of the HLSII storage ring. In addition to greatly smoothing and stabilizing the beam orbit, this method also doubles the work efficiency and significantly reduces the number of magnets adjusted and the range of the adjustments. Supported by National Natural Science Foundation of China (11275192) and the Upgrade Project of Hefei Light Source

  5. Conjugate gradient and steepest descent approach on quasi-Newton search direction

    NASA Astrophysics Data System (ADS)

    Sofi, A. Z. M.; Mamat, M.; Mohd, I.; Ibrahim, M. A. H.

    2014-07-01

    An approach of using conjugate gradient and classic steepest descent search direction onto quasi-Newton search direction had been proposed in this paper and we called it as 'scaled CGSD-QN' search direction. A new coefficient formula had been successfully constructed for being used in the 'scaled CGSD-QN' search direction and proven here that the coefficient formula is globally converge to the minimizer. The Hessian update formula that has been used in the quasi-Newton algorithm is DFP update formula. This new search direction approach was testes with some some standard unconstrained optimization test problems and proven that this new search direction approach had positively affect quasi-Newton method by using DFP update formula.

  6. A Newton-Krylov solution to the porous medium equations in the agree code

    SciTech Connect

    Ward, A. M.; Seker, V.; Xu, Y.; Downar, T. J.

    2012-07-01

    In order to improve the convergence of the AGREE code for porous medium, a Newton-Krylov solver was developed for steady state problems. The current three-equation system was expanded and then coupled using Newton's Method. Theoretical behavior predicts second order convergence, while actual behavior was highly nonlinear. The discontinuous derivatives found in both closure and empirical relationships prevented true second order convergence. Agreement between the current solution and new Exact Newton solution was well below the convergence criteria. While convergence time did not dramatically decrease, the required number of outer iterations was reduced by approximately an order of magnitude. GMRES was also used to solve problem, where ILU without fill-in was used to precondition the iterative solver, and the performance was slightly slower than the direct solution. (authors)

  7. Analysis of XMM-Newton Data from Extended Sources and the Diffuse X-Ray Background

    NASA Technical Reports Server (NTRS)

    Snowden, Steven

    2011-01-01

    Reduction of X-ray data from extended objects and the diffuse background is a complicated process that requires attention to the details of the instrumental response as well as an understanding of the multiple background components. We present methods and software that we have developed to reduce data from XMM-Newton EPIC imaging observations for both the MOS and PN instruments. The software has now been included in the Science Analysis System (SAS) package available through the XMM-Newton Science Operations Center (SOC).

  8. XMM-Newton closes in on space's exotic matter

    NASA Astrophysics Data System (ADS)

    2002-11-01

    search. The way they got this measurement is a first in astronomical observations and it is considered a huge achievement. The method consists of determining the compactness of the neutron star in an indirect way. The gravitational pull of a neutron star is immense - thousands of million times stronger than the Earth’s. This makes the light particles emitted by the neutron star lose energy. This energy loss is called a gravitational 'red shift'. The measurement of this red shift by XMM-Newton indicated the strength of the gravitational pull, and revealed the star’s compactness. "This is a highly precise measurement that we could not have made without both the high sensitivity of XMM-Newton and its ability to distinguish details," says Fred Jansen, ESA's XMM-Newton Project Scientist. According to the main author of the discovery, Jean Cottam of NASA’s Goddard Space Flight Center, “attempts to measure the gravitational red shift were made right after Einstein published the General Theory of Relativity, but no one had ever been able to measure the effect in a neutron star, where it was supposed to be huge. This has now been confirmed." Note to editors The result was obtained by observations of the neutron star EXO 0748-676. XMM-Newton detected the light in the form of X-rays. In particular, thanks to analysis of this X-ray radiation, the astronomers were able to identify some chemical elements, namely iron, present in the material surrounding the neutron star. They then compared the distorted signal emitted by the iron atoms in the neutron star with the one produced by iron atoms in the laboratory. In this way, they could measure the actual degree of distortion due to the gravity of EXO 0748-676. The result is published in the 7 November 2002 issue of Nature. The lead author is Jean Cottam, of NASA’s Goddard Space Flight Center (Greenbelt, United States). Other authors are Mariano Mendez, of the National Institute for Space Research, SRON (The Netherlands); and

  9. Stochastic modification of the Schrödinger-Newton equation

    NASA Astrophysics Data System (ADS)

    Bera, Sayantani; Mohan, Ravi; Singh, Tejinder P.

    2015-07-01

    The Schrödinger-Newton (SN) equation describes the effect of self-gravity on the evolution of a quantum system, and it has been proposed that gravitationally induced decoherence drives the system to one of the stationary solutions of the SN equation. However, the equation itself lacks a decoherence mechanism, because it does not possess any stochastic feature. In the present work we derive a stochastic modification of the Schrödinger-Newton equation, starting from the Einstein-Langevin equation in the theory of stochastic semiclassical gravity. We specialize this equation to the case of a single massive point particle, and by using Karolyhazy's phase variance method, we derive the Diósi-Penrose criterion for the decoherence time. We obtain a (nonlinear) master equation corresponding to this stochastic SN equation. This equation is, however, linear at the level of the approximation we use to prove decoherence; hence, the no-signaling requirement is met. Lastly, we use physical arguments to obtain expressions for the decoherence length of extended objects.

  10. The Optimal Degree of Smoothing in Equipercentile Equating with Postsmoothing.

    ERIC Educational Resources Information Center

    Zeng, Lingjia

    1995-01-01

    The effects of different degrees of smoothing on results of equipercentile equating in random groups design using a postsmoothing method based on cubic splines were investigated, and a computer-based procedure was introduced for selecting a desirable degree of smoothing. Results suggest that no particular degree of smoothing was always optimal.…

  11. Recursive Newton-Euler formulation of manipulator dynamics

    NASA Technical Reports Server (NTRS)

    Nasser, M. G.

    1989-01-01

    A recursive Newton-Euler procedure is presented for the formulation and solution of manipulator dynamical equations. The procedure includes rotational and translational joints and a topological tree. This model was verified analytically using a planar two-link manipulator. Also, the model was tested numerically against the Walker-Orin model using the Shuttle Remote Manipulator System data. The hinge accelerations obtained from both models were identical. The computational requirements of the model vary linearly with the number of joints. The computational efficiency of this method exceeds that of Walker-Orin methods. This procedure may be viewed as a considerable generalization of Armstrong's method. A six-by-six formulation is adopted which enhances both the computational efficiency and simplicity of the model.

  12. Scalable parallel Newton-Krylov solvers for discontinuous Galerkin discretizations

    SciTech Connect

    Persson, P.-O.

    2008-12-31

    We present techniques for implicit solution of discontinuous Galerkin discretizations of the Navier-Stokes equations on parallel computers. While a block-Jacobi method is simple and straight-forward to parallelize, its convergence properties are poor except for simple problems. Therefore, we consider Newton-GMRES methods preconditioned with block-incomplete LU factorizations, with optimized element orderings based on a minimum discarded fill (MDF) approach. We discuss the difficulties with the parallelization of these methods, but also show that with a simple domain decomposition approach, most of the advantages of the block-ILU over the block-Jacobi preconditioner are still retained. The convergence is further improved by incorporating the matrix connectivities into the mesh partitioning process, which aims at minimizing the errors introduced from separating the partitions. We demonstrate the performance of the schemes for realistic two- and three-dimensional flow problems.

  13. Toward milli-Newton electro- and magneto-static microactuators

    NASA Technical Reports Server (NTRS)

    Fan, Long-Sheng

    1993-01-01

    Microtechnologies can potentially push integrated electro- and magnetostatic actuators toward the regime where constant forces in the order of milli-Newton (or torques in the order of micro-Newton meter) can be generated with constant inputs within a volume of 1.0 x 1.0 x 0.02 mm with 'conventional' technology. 'Micro' actuators are, by definition, actuators with dimensions confined within a millimeter cube. Integrated microactuators based on electrostatics typically have force/torque in the order of sub-micro-Newton (sub-nano-Newton meter). These devices are capable of moving small objects at MHz frequencies. On the other hand, suppose we want to move a one cubic millimeter object around with 100 G acceleration; a few milli-Newton force will be required. Thus, milli-Newton microactuators are very desirable for some immediate applications, and it challenges micromechanical researchers to develop new process technologies, designs, and materials toward this goal.

  14. Toward milli-Newton electro- and magneto-static microactuators

    NASA Astrophysics Data System (ADS)

    Fan, Long-Sheng

    1993-06-01

    Microtechnologies can potentially push integrated electro- and magnetostatic actuators toward the regime where constant forces in the order of milli-Newton (or torques in the order of micro-Newton meter) can be generated with constant inputs within a volume of 1.0 x 1.0 x 0.02 mm with 'conventional' technology. 'Micro' actuators are, by definition, actuators with dimensions confined within a millimeter cube. Integrated microactuators based on electrostatics typically have force/torque in the order of sub-micro-Newton (sub-nano-Newton meter). These devices are capable of moving small objects at MHz frequencies. On the other hand, suppose we want to move a one cubic millimeter object around with 100 G acceleration; a few milli-Newton force will be required. Thus, milli-Newton microactuators are very desirable for some immediate applications, and it challenges micromechanical researchers to develop new process technologies, designs, and materials toward this goal.

  15. The Effect of Group Work on Misconceptions of 9th Grade Students about Newton's Laws

    ERIC Educational Resources Information Center

    Ergin, Serap

    2016-01-01

    In this study, the effect of group work and traditional method on 9th grade students' misconceptions about Newton Laws was investigated. The study was conducted in three classes in an Anatolian Vocational High School in Ankara/Turkey in the second term of the 2014-2015 academic year. Two of these classes were chosen as the experimental group and…

  16. A Simple Gauss-Newton Procedure for Covariance Structure Analysis with High-Level Computer Languages.

    ERIC Educational Resources Information Center

    Cudeck, Robert; And Others

    1993-01-01

    An implementation of the Gauss-Newton algorithm for the analysis of covariance structure that is specifically adapted for high-level computer languages is reviewed. This simple method for estimating structural equation models is useful for a variety of standard models, as is illustrated. (SLD)

  17. Development and Application of a Rubric for Evaluating Students' Performance on Newton's Laws of Motion

    ERIC Educational Resources Information Center

    Kocakulah, Mustafa Sabri

    2010-01-01

    This study aims to develop and apply a rubric to evaluate the solutions of pre-service primary science teachers to questions about Newton's Laws of Motion. Two groups were taught the topic using the same teaching methods and administered four questions before and after teaching. Furthermore, 76 students in the experiment group were instructed…

  18. Smoothly deformed light

    NASA Technical Reports Server (NTRS)

    Stenholm, Stig

    1993-01-01

    A single mode cavity is deformed smoothly to change its electromagnetic eigenfrequency. The system is modeled as a simple harmonic oscillator with a varying period. The Wigner function of the problem is obtained exactly by starting with a squeezed initial state. The result is evaluated for a linear change of the cavity length. The approach to the adiabatic limit is investigated. The maximum squeezing is found to occur for smooth change lasting only a fraction of the oscillational period. However, only a factor of two improvement over the adiabatic result proves to be possible. The sudden limit cannot be investigated meaningfully within the model.

  19. Newton’s Rotating Water Bucket: A Simple Model

    DTIC Science & Technology

    2013-01-01

    University of America Press, Washington, DC Abstract Isaac Newton proposed hanging a bucket of water by a cord in the Principia. If the cord is...Acad. Sci. 99, 15 (Summer 2013) 14. ABSTRACT Isaac Newton proposed hanging a bucket of water by a cord in the Principia. If the cord is twisted and...As the bucket spins faster, the water level drops in the center and rises up near the walls, as Newton noted. 18 Washington Academy of Sciences

  20. Is violation of Newton's second law possible?

    PubMed

    Ignatiev, A Yu

    2007-03-09

    Astrophysical observations (usually explained by dark matter) suggest that classical mechanics could break down when the acceleration becomes extremely small [the approach known as modified Newtonian dynamics (MOND)]. I present the first analysis of MOND manifestations in terrestrial (rather than astrophysical) settings. A new effect is reported: around each equinox date, 2 spots emerge on the Earth where static bodies experience spontaneous acceleration due to the possible violation of Newton's second law. Preliminary estimates indicate that an experimental search for this effect can be feasible.

  1. C. N. Yang on Einstein and Newton

    NASA Astrophysics Data System (ADS)

    2015-11-01

    In Professor C. N. Yang’s view, Einstein’s strength was in his ability to distinguish what was truly important and to investigate it. Also, Einstein was unique in that he was able to zoom in as well as zoom out, just like a film which has both close-up and long shots. Many people are only able to have one view, either close-up or from afar, and cannot switch between the two. Professor C. N. Yang feels that, in the history of physics, only Newton can be compared with Einstein. Although Maxwell and Boltzmann were prominent physicists, their influence was not as great as Einstein’s.

  2. Smoothed Particle Hydrodynamic Simulator

    SciTech Connect

    2016-10-05

    This code is a highly modular framework for developing smoothed particle hydrodynamic (SPH) simulations running on parallel platforms. The compartmentalization of the code allows for rapid development of new SPH applications and modifications of existing algorithms. The compartmentalization also allows changes in one part of the code used by many applications to instantly be made available to all applications.

  3. Stirring Astronomy into Theology: Sir Isaac Newton on the Date of the Passion of Christ

    NASA Astrophysics Data System (ADS)

    Belenkiy, Ari; Echagüe, Eduardo Vila

    2007-08-01

    It is known that Sir Isaac Newton suggested a date for the Passion of Christ in the posthumously published Observations upon the Prophecies of Daniel and the Apocalypse of St. John (1733). [This fact was revived recently in Quarterly Journal of the Royal Astronomical Society, 32, Sept 1991]. What was not known is that the first attempts to find that date were made during the early period of his life. The Jewish National and University Library in Jerusalem contains two drafts in Latin, grouped as Yahuda MS 24E under the same title, Rules for the Determination of Easter, which cast some light on Newton's life in the late 1660s - early 1670s. The earlier draft contains multiple references to the virtually forgotten De Annis Christi (1649), written by Villem Lange, the 17th century Danish astronomer and theologian, who might have been Newton's first mentor on the Jewish calendar tradition. The second draft shows not only Newton's close acquaintance with Maimonides' theory of lunar visibility, but also his attempts to simplify the latter's criteria by introducing different parameters. These “astronomical exercises”, announced in a 1673 book, were intended to appear as an appendix to Nicholas Mercator's 1676 book. Both of Yahuda 24E's drafts carry an astronomical table with the solar and lunar positions for the years 30-37 AD, which Newton used to decide on the date of the Passion. The Ordinary Least Squares regression method sends a dubious message; applied to the table's lunar data, OLS strongly suggests a pre-Tychonic origin. The table shows little correlation with solar data coming from Ptolemy, al-Battani, Tycho Brahe, Johannes Kepler, Philip van Lansbergen, Thomas Streete, John Flamsteed, or Newton's own 1702 lunar theory; however, its lunar positions display very high correlations with the Prutenic tables, which were based on Copernicus' De Revolutionibus. Surprisingly, the solar table comes from either 1651 Harmonicon Coeleste or 1669 Astronomia Britannica by

  4. Numerical Convergence In Smoothed Particle Hydrodynamics

    NASA Astrophysics Data System (ADS)

    Zhu, Qirong; Hernquist, Lars; Li, Yuexing

    2015-02-01

    We study the convergence properties of smoothed particle hydrodynamics (SPH) using numerical tests and simple analytic considerations. Our analysis shows that formal numerical convergence is possible in SPH only in the joint limit N → ∞, h → 0, and Nnb → ∞, where N is the total number of particles, h is the smoothing length, and Nnb is the number of neighbor particles within the smoothing volume used to compute smoothed estimates. Previous work has generally assumed that the conditions N → ∞ and h → 0 are sufficient to achieve convergence, while holding Nnb fixed. We demonstrate that if Nnb is held fixed as the resolution is increased, there will be a residual source of error that does not vanish as N → ∞ and h → 0. Formal numerical convergence in SPH is possible only if Nnb is increased systematically as the resolution is improved. Using analytic arguments, we derive an optimal compromise scaling for Nnb by requiring that this source of error balance that present in the smoothing procedure. For typical choices of the smoothing kernel, we find Nnb vpropN 0.5. This means that if SPH is to be used as a numerically convergent method, the required computational cost does not scale with particle number as O(N), but rather as O(N 1 + δ), where δ ≈ 0.5, with a weak dependence on the form of the smoothing kernel.

  5. Approximation of Bivariate Functions via Smooth Extensions

    PubMed Central

    Zhang, Zhihua

    2014-01-01

    For a smooth bivariate function defined on a general domain with arbitrary shape, it is difficult to do Fourier approximation or wavelet approximation. In order to solve these problems, in this paper, we give an extension of the bivariate function on a general domain with arbitrary shape to a smooth, periodic function in the whole space or to a smooth, compactly supported function in the whole space. These smooth extensions have simple and clear representations which are determined by this bivariate function and some polynomials. After that, we expand the smooth, periodic function into a Fourier series or a periodic wavelet series or we expand the smooth, compactly supported function into a wavelet series. Since our extensions are smooth, the obtained Fourier coefficients or wavelet coefficients decay very fast. Since our extension tools are polynomials, the moment theorem shows that a lot of wavelet coefficients vanish. From this, with the help of well-known approximation theorems, using our extension methods, the Fourier approximation and the wavelet approximation of the bivariate function on the general domain with small error are obtained. PMID:24683316

  6. Eye-openers from XMM-Newton

    NASA Astrophysics Data System (ADS)

    2000-02-01

    many years of work. They are all that we hoped they would be. In the LMC we can see the elements, which go to make up new stars and planets, being released in giant stellar explosions. We can even see the creation of new stars going on, using elements scattered through space by previous stellar explosions. This is what we built the EPIC cameras for and they are really fulfilling their promise" Multiwavelength views of Hickson Group 16 The HCG-16 viewed by EPIC and by the Optical Monitor in the visible and ultraviolet wavelengths is one of approximately a hundred compact galaxy clusters listed by Canadian astronomer Paul Hickson in the 1980s. The criteria for the Hickson cluster groups included their compactness, their isolation from other galaxies and a limited magnitude range between their members. Most Hicksons are very faint, but a few can be observed with modest aperture telescopes. Galaxies in Hickson groups have a high probability of interacting. Their study has shed light on the question of galactic evolution and the effects of interaction. Investigation into their gravitational behaviour has also significantly contributed to our understanding of "dark matter", the mysterious matter that most astronomers feel comprises well over 90% of our universe. Observation of celestial objects from space over a range of X-ray, ultraviolet and visible wavelengths, is a unique feature of the XMM-Newton mission. The EPIC-PN view of the Hickson 16 group shows a handful of bright X-sources and in the background more than a hundred faint X-ray sources that XMM-Newton is revealing for the first time. Juxtaposing the X-ray view of HCG 16 with that of the Optical Monitor reveals one of the great strengths of XMM-Newton in being able to routinely compare the optical, ultraviolet and X-ray properties of objects. Many of the X-ray sources are revealed as elongated "fuzzy blobs" coincident with some of the optical galaxies. Routine access to ultraviolet images is a first for the mission

  7. Arakelian 564: An XMM-Newton View

    NASA Technical Reports Server (NTRS)

    Vignali, Cristian; Brandt, W. N.; Boller, Th.; Fabian, A. C.; Vaughan, Simon

    2003-01-01

    We report on two XMM-Newton observations of the bright narrow-line Seyfert 1 galaxy Ark 564 taken one year apart (2000 June and 2001 June). The 0.6-10 keV continuum is well described by a soft blackbody component (kTau approximately equal 140-150 eV) plus a steep power law (Tau approximately equal to 2.50-2.55). No significant spectral changes are observed between the two observations, although the X-ray flux in the second observation is approximately equal to 40-50 per cent lower. In both observations we detect a significant absorption edge at a rest-frame energy of approximately equal to 0.73 keV, corresponding to O VII. The presence of the absorption feature is confirmed by a simultaneous Chandra grating observation in 2000 June, although the best-fitting edge threshold is at a slightly lower energy in the Chandra data, possibly because of a different parameterization of the underlying X-ray continuum. We find tentative evidence for a broad iron emission line in the 2000 June observation. The results from an analysis of the power spectral density (PSD) function are also presented. The present XMM-Newton data support the idea that the PSD shown two breads, although the location of the high-frequency break requires further constraints.

  8. Newtons Universum. Materialien zur Geschichte des Kraftbegriffes.

    NASA Astrophysics Data System (ADS)

    Mit einem Vorwort von E. Seibold und einer Einführung von W. Neuser. This book is a selection of 15 articles published in the journal "Spektrum der Wissenschaft". The original English versions of the papers were first published in "Scientific American". Contents: 1. Impetustheorie und Intuition in der Physik (M. McCloskey). 2. Mittelalterliche Ursprünge der industriellen Revolution (T. S. Reynolds). 3. Leonardo da Vincis Beiträge zur theoretischen Mechanik (V. Foley, W. Soedel). 4. Nikolaus Kopernikus und Tycho Brahe (O. Gingerich). 5. Keplers Entdeckung der ersten beiden Planetengesetze (C. Wilson). 6. Galileis Entdeckung des Fallgesetzes (S. Drake). 7. Galileis Beobachtung des Neptun (S. Drake, C. T. Kowal). 8. Galileo Galilei und der Schatten des Giordano Bruno (L. S. Lerner, E. A. Gosselin). 9. Der Fall Galilei (O. Gingerich). 10. Newtons Apfel und Galileis "Dialog" (S. Drake). 11. Newtons Gravitationsgesetz - aus Formeln wird eine Idee (I. B. Cohen). 12. Christopher Wren: Astronom und Architekt (H. Dorn, R. Mark). 13. Atomismus und Kräfte in der Geschichte (L. Holliday). 14. Ein Elitezirkel vor 200 Jahren: Die Lunar Society von Birmingham (L. Ritchie-Calder). 15. Sadi Carnot: Technik und Theorie der Dampfmaschine (S. S. Wilson).

  9. XMM-Newton: The Next Decade

    NASA Astrophysics Data System (ADS)

    Ness, Jan-Uwe

    2016-06-01

    The recent generation of high energy observatories has enabled unprecedented progress to be made in our understanding of astrophysics in the X-ray domain. Current technical evaluations suggest that the XMM-Newton spacecraft and its scientific instruments may continue to provide first class X-ray observations well into the next decade. Other X-ray missions are planned to be launched soon, including Astro-H and e-ROSITA. Coupled with new ground-based developments, this will open up new exciting opportunities for multi-wavelength and follow-up observations, to which XMM-Newton is ideally placed to play a major role. This workshop will summarise the state of our current knowledge derived from X-ray astrophysics. We will discuss some of the major achievements over the past years, and identify a set of fundamental questions still to be addressed. Within this context a primary aim of the workshop will be to define the key scientific topics which will have the highest scientific importance and impact. We will seek to identify observing programs of maximum long-term value to the entire astronomical community. Many of these programs are likely to require large amounts of observing time on only a few carefully selected targets or sky areas. We strongly encourage innovative ideas for applications, and the formation of well organised major collaborations.

  10. On topological modifications of Newton's law

    SciTech Connect

    Floratos, E.G.; Leontaris, G.K. E-mail: leonta@uoi.gr

    2012-04-01

    Recent cosmological data for very large distances challenge the validity of the standard cosmological model. Motivated by the observed spatial flatness the accelerating expansion and the various anisotropies with preferred axes in the universe we examine the consequences of the simple hypothesis that the three-dimensional space has a global R{sup 2} × S{sup 1} topology. We take the radius of the compactification to be the observed cosmological scale beyond which the accelerated expansion starts. We derive the induced corrections to the Newton's gravitational potential and we find that for distances smaller than the S{sup 1} radius the leading 1/r-term is corrected by convergent power series of multipole form in the polar angle making explicit the induced anisotropy by the compactified third dimension. On the other hand, for distances larger than the compactification scale the asymptotic behavior of the potential exhibits a logarithmic dependence with exponentially small corrections. The change of Newton's force from 1/r{sup 2} to 1/r behavior implies a weakening of the deceleration for the expanding universe. Such topologies can also be created locally by standard Newtonian axially symmetric mass distributions with periodicity along the symmetry axis. In such cases we can use our results to obtain measurable modifications of Newtonian orbits for small distances and flat rotation spectra, for large distances at the galactic level.

  11. Smoothing spline primordial power spectrum reconstruction

    SciTech Connect

    Sealfon, Carolyn; Verde, Licia; Jimenez, Raul

    2005-11-15

    We reconstruct the shape of the primordial power spectrum (PPS) using a smoothing spline. Our adapted smoothing spline technique provides a complementary method to existing efforts to search for smooth features in the PPS, such as a running spectral index. With this technique we find no significant indication with Wilkinson Microwave Anisotropy Probe first-year data that the PPS deviates from a Harrison-Zeldovich spectrum and no evidence for loss of power on large scales. We also examine the effect on the cosmological parameters of the additional PPS freedom. Smooth variations in the PPS are not significantly degenerate with other cosmological parameters, but the spline reconstruction greatly increases the errors on the optical depth and baryon fraction.

  12. Consequences That Cannot Be Avoided: A Response to Paul Newton

    ERIC Educational Resources Information Center

    Bennett, Randy Elliot

    2012-01-01

    This article presents the author's response to Paul E. Newton's paper titled "Clarifying the Consensus Definition of Validity" ("Measurement: Interdisciplinary Research and Perspectives," 2012). Newton's paper offers an interesting and constructive discussion about how people think about validity. In this reaction, the author comments on some of…

  13. Newton's First Law: Text, Translations, Interpretations and Physics Education.

    ERIC Educational Resources Information Center

    Galili, Igal; Tzeitlin, Michael

    2003-01-01

    Considers the translation from Latin of Newton's First Law (NFL) in an historical perspective. Shows that Newton's original yields two versions of complimentary meanings, one temporal and the other quantitative. Reviews the presentation of NFL in physics textbooks and notes a decline in the status of NFL in the physics curriculum. (Contains 72…

  14. Newton's Path to Universal Gravitation: The Role of the Pendulum

    ERIC Educational Resources Information Center

    Boulos, Pierre J.

    2006-01-01

    Much attention has been given to Newton's argument for Universal Gravitation in Book III of the "Principia". Newton brings an impressive array of phenomena, along with the three laws of motion, and his rules for reasoning to deduce Universal Gravitation. At the centre of this argument is the famous "moon test". Here it is the empirical evidence…

  15. Essential nature of Newton's constant in unimodular gravity

    NASA Astrophysics Data System (ADS)

    Benedetti, Dario

    2016-05-01

    We point out that in unimodular gravity Newton's constant is an essential coupling, i.e. it is independent of field redefinitions. We illustrate the consequences of this fact by a calculation in a standard simple approximation, showing that in this case the renormalization group flow of Newton's constant is gauge and parametrization independent.

  16. On the Shoulders of Sir Isaac Newton and Arthur Storer

    ERIC Educational Resources Information Center

    Martin, Helen E.; Evans-Gondo, Bonita

    2013-01-01

    Helen E. Martin, the author of this article, is a retired National Board Certified Teacher who has been researching Sir Isaac Newton's unpublished manuscripts for over three decades. While researching the work of Newton, a teacher she was mentoring asked for some hands-on activities to study planetary motion. The description of the activity…

  17. Why Did Newton See Indigo in the Spectrum?

    ERIC Educational Resources Information Center

    Biernson, George

    1972-01-01

    The arrangement of colors in Newton's color circle suggests that it was derived from paint mixtures, not light mixtures. If this is true it may be concluded that what Newton called indigo represents violet in modern terminology, and what he called violet represents purple. (Author/TS)

  18. Newton's 1679/80 solution of the constant gravity problem

    NASA Astrophysics Data System (ADS)

    Erlichson, Herman

    1991-08-01

    In his letter of 6 January 1679/80 Hooke wrote to Newton ``in truth I agree with You that the Explicating the Curve in which a body Descending to the Center of the Earth, would circumgyrate were a Speculation of noe Use yet'' [The Correspondence of Isaac Newton, edited by H. W. Turnbull (Cambridge U.P., Cambridge, 1960), Vol. 2, p. 309]. In these words, Hooke referred to a hypothetical problem which he was discussing in a correspondence with Newton. The problem was that of determining the orbit of a body moving inside a narrow cut made centrally across the Earth. This was perhaps the very first inverse central force problem to be attacked by Newton. Newton seems to have used his instantaneous impulse technique to provide a drawing of a solution that was almost exact. This paper explores this fascinating early solution of an inverse central force problem.

  19. 75 FR 41277 - Central of Georgia Railroad Company-Discontinuance of Service Exemption-Newton County, GA; Great...

    Federal Register 2010, 2011, 2012, 2013, 2014

    2010-07-15

    ...--Newton County, GA; Great Walton Railroad Company-- Discontinuance of Operations Exemption--Newton County... Newton, Ga., and the end of the line at milepost E 80.70 at Covington, Ga., in Newton County, Ga....

  20. Anti-smooth muscle antibody

    MedlinePlus

    ... gov/ency/article/003531.htm Anti-smooth muscle antibody To use the sharing features on this page, please enable JavaScript. Anti-smooth muscle antibody is a blood test that detects the presence ...

  1. Newton`s iteration for inversion of Cauchy-like and other structured matrices

    SciTech Connect

    Pan, V.Y.; Zheng, Ailong; Huang, Xiaohan; Dias, O.

    1996-12-31

    We specify some initial assumptions that guarantee rapid refinement of a rough initial approximation to the inverse of a Cauchy-like matrix, by mean of our new modification of Newton`s iteration, where the input, output, and all the auxiliary matrices are represented with their short generators defined by the associated scaling operators. The computations are performed fast since they are confined to operations with short generators of the given and computed matrices. Because of the known correlations among various structured matrices, the algorithm is immediately extended to rapid refinement of rough initial approximations to the inverses of Vandermonde-like, Chebyshev-Vandermonde-like and Toeplitz-like matrices, where again, the computations are confined to operations with short generators of the involved matrices.

  2. Testing Newton's Gravitational Inverse-Square Law

    NASA Astrophysics Data System (ADS)

    Hagedorn, Charles

    2015-04-01

    Newton's inverse-square law of gravitation is the oldest standing mathematical description of a fundamental interaction. Experimental tests of gravity's distance-dependence define a frontier between our understanding of gravity and many proposed forms of new physics. These experiments constrain the size of possible extra dimensions, bound attempted resolution of the cosmological-constant problem, search for self-interacting chameleons, make direct measurements at the dark-energy length-scale, and more. As gravity is ~1040 times weaker than electromagnetism, gravity remains hidden by experimental backgrounds at distances smaller than the diameter of a fine human hair. This talk will survey the past, present, and near-future of the experimental field, with substantial emphasis on precision sub-millimeter laboratory experiments.

  3. Beam-smoothing investigation on Heaven I

    NASA Astrophysics Data System (ADS)

    Xiang, Yi-huai; Gao, Zhi-xing; Tong, Xiao-hui; Dai, Hui; Tang, Xiu-zhang; Shan, Yu-sheng

    2007-01-01

    Directly driven targets for inertial confinement fusion (ICF) require laser beams with extremely smooth irradiance profiles to prevent hydrodynamic instabilities that destroy the spherical symmetry of the target during implosion. Such instabilities can break up and mix together the target's wall and fuel material, preventing it from reaching the density and temperature required for fusion ignition. 1,2 Measurements in the equation of state (EOS) experiments require laser beams with flat-roofed profiles to generate uniform shockwave 3. Some method for beam smooth, is thus needed. A technique called echelon-free induced spatial incoherence (EFISI) is proposed for producing smooth target beam profiles with large KrF lasers. The idea is basically an image projection technique that projects the desired time-averaged spatial profile onto the target via the laser system, using partially coherent broadband lighe. Utilize the technique, we developing beam- smoothing investigation on "Heaven I". At China Institute of Atomic Energy , a new angular multiplexing providing with beam-smoothing function has been developed, the total energy is 158J, the stability of energy is 4%, the pulse duration is 25ns, the effective diameter of focusing spot is 400um, and the ununiformity is about 1.6%, the power density on the target is about 3.7×10 12W/cm2. At present, the system have provided steady and smooth laser irradiation for EOS experiments.

  4. s-SMOOTH: Sparsity and Smoothness Enhanced EEG Brain Tomography

    PubMed Central

    Li, Ying; Qin, Jing; Hsin, Yue-Loong; Osher, Stanley; Liu, Wentai

    2016-01-01

    EEG source imaging enables us to reconstruct current density in the brain from the electrical measurements with excellent temporal resolution (~ ms). The corresponding EEG inverse problem is an ill-posed one that has infinitely many solutions. This is due to the fact that the number of EEG sensors is usually much smaller than that of the potential dipole locations, as well as noise contamination in the recorded signals. To obtain a unique solution, regularizations can be incorporated to impose additional constraints on the solution. An appropriate choice of regularization is critically important for the reconstruction accuracy of a brain image. In this paper, we propose a novel Sparsity and SMOOthness enhanced brain TomograpHy (s-SMOOTH) method to improve the reconstruction accuracy by integrating two recently proposed regularization techniques: Total Generalized Variation (TGV) regularization and ℓ1−2 regularization. TGV is able to preserve the source edge and recover the spatial distribution of the source intensity with high accuracy. Compared to the relevant total variation (TV) regularization, TGV enhances the smoothness of the image and reduces staircasing artifacts. The traditional TGV defined on a 2D image has been widely used in the image processing field. In order to handle 3D EEG source images, we propose a voxel-based Total Generalized Variation (vTGV) regularization that extends the definition of second-order TGV from 2D planar images to 3D irregular surfaces such as cortex surface. In addition, the ℓ1−2 regularization is utilized to promote sparsity on the current density itself. We demonstrate that ℓ1−2 regularization is able to enhance sparsity and accelerate computations than ℓ1 regularization. The proposed model is solved by an efficient and robust algorithm based on the difference of convex functions algorithm (DCA) and the alternating direction method of multipliers (ADMM). Numerical experiments using synthetic data demonstrate the

  5. XMM-Newton study of the Draco dwarf spheroidal galaxy

    NASA Astrophysics Data System (ADS)

    Saeedi, Sara; Sasaki, Manami; Ducci, Lorenzo

    2016-02-01

    Aims: We present the results of the analysis of five XMM-Newton observations of the Draco dwarf spheroidal galaxy (dSph). The aim of the work is the study of the X-ray population in the field of the Draco dSph. Methods: We classified the sources on the basis of spectral analysis, hardness ratios, X-ray-to-optical flux ratio, X-ray variability, and cross-correlation with available catalogues in X-ray, optical, infrared, and radio wavelengths. Results: We detected 70 X-ray sources in the field of the Draco dSph in the energy range of 0.2 - 12 keV and classified 18 AGNs, 9 galaxies and galaxy candidates, 6 sources as foreground stars, 4 low-mass X-ray binary candidates, 1 symbiotic star, and 2 binary system candidates. We also identified 9 sources as hard X-ray sources in the field of the galaxy. We derived the X-ray luminosity function of X-ray sources in the Draco dSph in the 2 - 10 keV and 0.5 - 2 keV energy bands. Using the X-ray luminosity function in the energy range of 0.5 - 2 keV, we estimate that ~10 X-ray sources are objects in the Draco dSph. We have also estimated the dark matter halo mass that would be needed to keep the low-mass X-ray binaries gravitationally bound to the galaxy. Based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA.

  6. A 3D Contact Smoothing Method based on Quasi-C1 Interpolation and Normal voting —Application to 3D Forging and Rolling

    NASA Astrophysics Data System (ADS)

    Hachani, Maha; Fourment, Lionel

    2010-06-01

    This paper describes the effect of tool discretization accuracy on the simulation of forming processes, especially for processes where the contact area is quite small with respect to the component size. For smoothing contact surface discretized by linear triangles, an algorithm is followed to develop a higher order quadratic interpolation of the curved surface from the positions and normal vectors of the nodes, as proposed by Nagata. Normal vectors are calculated at each node from the existing discretized surface by considering a patch of surrounding elements. This is accomplished by the mean of normal voting strategy. The efficiency and reliability of the resulting contact model are checked through several examples like indenting and ironing a bulk parallelepiped. It is also applied to complex ring rolling, form rolling and extrusion problems.

  7. Resolving galaxy cluster gas properties at z ∼ 1 with XMM-Newton and Chandra

    NASA Astrophysics Data System (ADS)

    Bartalucci, I.; Arnaud, M.; Pratt, G. W.; Démoclès, J.; van der Burg, R. F. J.; Mazzotta, P.

    2017-02-01

    Massive, high-redshift, galaxy clusters are useful laboratories to test cosmological models and to probe structure formation and evolution, but observations are challenging due to cosmological dimming and angular distance effects. Here we present a pilot X-ray study of the five most massive (M500 > 5 × 1014M⊙), distant (z 1), clusters detected via the Sunyaev-Zel'Dovich effect. We optimally combine XMM-Newton and Chandra X-ray observations by leveraging the throughput of XMM-Newton to obtain spatially-resolved spectroscopy, and the spatial resolution of Chandra to probe the bright inner parts and to detect embedded point sources. Capitalising on the excellent agreement in flux-related measurements, we present a new method to derive the density profiles, which are constrained in the centre by Chandra and in the outskirts by XMM-Newton. We show that the Chandra-XMM-Newton combination is fundamental for morphological analysis at these redshifts, the Chandra resolution being required to remove point source contamination, and the XMM-Newton sensitivity allowing higher significance detection of faint substructures. Measuring the morphology using images from both instruments, we found that the sample is dominated by dynamically disturbed objects. We use the combined Chandra-XMM-Newton density profiles and spatially-resolved temperature profiles to investigate thermodynamic quantities including entropy and pressure. From comparison of the scaled profiles with the local REXCESS sample, we find no significant departure from standard self-similar evolution, within the dispersion, at any radius, except for the entropy beyond 0.7 R500. The baryon mass fraction tends towards the cosmic value, with a weaker dependence on mass than that observed in the local Universe. We make a comparison with the predictions from numerical simulations. The present pilot study demonstrates the utility and feasibility of spatially-resolved analysis of individual objects at high-redshift through

  8. Fast and exact Newton and Bidirectional fitting of Active Appearance Models.

    PubMed

    Kossaifi, Jean; Tzimiropoulos, Yorgos; Pantic, Maja

    2016-12-21

    Active Appearance Models (AAMs) are generative models of shape and appearance that have proven very attractive for their ability to handle wide changes in illumination, pose and occlusion when trained in the wild, while not requiring large training dataset like regression-based or deep learning methods. The problem of fitting an AAM is usually formulated as a non-linear least squares one and the main way of solving it is a standard Gauss-Newton algorithm. In this paper we extend Active Appearance Models in two ways: we first extend the Gauss-Newton framework by formulating a bidirectional fitting method that deforms both the image and the template to fit a new instance. We then formulate a second order method by deriving an efficient Newton method for AAMs fitting. We derive both methods in a unified framework for two types of Active Appearance Models, holistic and part-based, and additionally show how to exploit the structure in the problem to derive fast yet exact solutions. We perform a thorough evaluation of all algorithms on three challenging and recently annotated inthe- wild datasets, and investigate fitting accuracy, convergence properties and the influence of noise in the initialisation. We compare our proposed methods to other algorithms and show that they yield state-of-the-art results, out-performing other methods while having superior convergence properties.

  9. A Newton-Krylov Solver for Implicit Solution of Hydrodynamics in Core Collapse Supernovae

    SciTech Connect

    Reynolds, D R; Swesty, F D; Woodward, C S

    2008-06-12

    This paper describes an implicit approach and nonlinear solver for solution of radiation-hydrodynamic problems in the context of supernovae and proto-neutron star cooling. The robust approach applies Newton-Krylov methods and overcomes the difficulties of discontinuous limiters in the discretized equations and scaling of the equations over wide ranges of physical behavior. We discuss these difficulties, our approach for overcoming them, and numerical results demonstrating accuracy and efficiency of the method.

  10. INTERMEDIATE FILAMENTS IN SMOOTH MUSCLE

    PubMed Central

    Tang, Dale D.

    2008-01-01

    The intermediate filament (IF) network is one of the three cytoskeletal systems in smooth muscle. The type III IF proteins vimentin and desmin are major constituents of the network in smooth muscle cells and tissues. Lack of vimentin or desmin impairs contractile ability of various smooth muscle preparations, implying their important role for smooth muscle force development. The IF framework has long been viewed as a fixed cytostructure that solely provides mechanical integrity for the cell. However, recent studies suggest that the IF cytoskeleton is dynamic in mammalian cells in response to various external stimulation. In this review, the structure and biological properties of IF proteins in smooth muscle are summarized. The role of IF proteins in the modulation of smooth muscle force development and redistribution/translocation of signaling partners (such as p130 Crk-associated substrate, CAS) is depicted. This review also summarizes our latest understanding on how the IF network may be regulated in smooth muscle. PMID:18256275

  11. Efficient solution of liquid state integral equations using the Newton-GMRES algorithm

    NASA Astrophysics Data System (ADS)

    Booth, Michael J.; Schlijper, A. G.; Scales, L. E.; Haymet, A. D. J.

    1999-06-01

    We present examples of the accurate, robust and efficient solution of Ornstein-Zernike type integral equations which describe the structure of both homogeneous and inhomogeneous fluids. In this work we use the Newton-GMRES algorithm as implemented in the public-domain nonlinear Krylov solvers NKSOL [ P. Brown, Y. Saad, SIAM J. Sci. Stat. Comput. 11 (1990) 450] and NITSOL [ M. Pernice, H.F. Walker, SIAM J. Sci. Comput. 19 (1998) 302]. We compare and contrast this method with more traditional approaches in the literature, using Picard iteration (successive-substitution) and hybrid Newton-Raphson and Picard methods, and a recent vector extrapolation method [ H.H.H. Homeier, S. Rast, H. Krienke, Comput. Phys. Commun. 92 (1995) 188]. We find that both the performance and ease of implementation of these nonlinear solvers recommend them for the solution of this class of problem.

  12. Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation

    NASA Technical Reports Server (NTRS)

    Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E.; Melvin, Robin G.; Young, David P.

    1996-01-01

    We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, is robust and, economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.

  13. Newton-Krylov-Schwarz algorithms for the 2D full potential equation

    SciTech Connect

    Cai, Xiao-Chuan; Gropp, W.D.; Keyes, D.E.

    1996-12-31

    We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The main algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, can be made robust for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report favorable choices for numerical convergence rate and overall execution time on a distributed-memory parallel computer.

  14. Catch a falling apple: Isaac Newton and myths of genius.

    PubMed

    Fara, P

    1999-01-01

    Newton has become a legendary figure belonging to the distant past rather than a historical person who lived at a specific time. Historians and scientists have constantly reinterpreted many anecdotal tales describing Newton's achievements and behaviour, but the most famous concerns the falling apple in his country garden. Newton's apple conjures up multiple allegorical resonances, and examining its historical accuracy is less important than uncovering the mythical truths embedded within this symbol. Because interest groups fashion different collective versions of the past, analysing mythical tales can reveal fundamental yet conflicting attitudes towards science and its practices.

  15. Solutions of relativistic Newton's equations for nonconstant fields

    NASA Astrophysics Data System (ADS)

    Wooten, R. E.; Macek, J. H.

    2004-08-01

    Newton's second law can be readily solved for many forces, but few situations can be solved for the relativistic form of Newton's second law. The only problems directly solvable are those involving charged particles in constant electromagnetic fields. If the external field represents a light pulse, Dirac's relativistic equation can be solved, as done by Volkov in 1935. Classical solutions based on Volkov's work employ the Hamilton-Jacobi equations. We discuss the solution of this problem using Newton's equations, thereby making the solution more accessible.

  16. A Residuals Approach to Filtering, Smoothing and Identification for Static Distributed Systems

    NASA Technical Reports Server (NTRS)

    Rodriguez, G.

    1985-01-01

    An approach for state estimation and identification of spatially distributed parameters embedded in static distributed (elliptic) system models is advanced. The method of maximum likelihood is used to find parameter values that maximize a likelihood functional for the system model, or equivalently, that minimize the negative logarithm of this functional. To find the minimum, a Newton-Raphson search is conducted that from an initial estimate generates a convergent sequence of parameter estimates. For simplicity, a Gauss-Markov approach is used to approximate the Hessian in terms of products of first derivatives. The gradient and approximate Hessian are computed by first arranging the negative log likelihood functional into a form based on the square root factorization of the predicted covariance of the measurement process. The resulting data processing approach, referred to here by the new term of predicted data covariance square root filtering, makes the gradient and approximate Hessian calculations very simple. A closely related set of state estimates is also produced by the maximum likelihood method: smoothed estimates that are optimal in a conditional mean sense and filtered estimates that emerge from the predicted data covariance square root filter.

  17. Application of a XMM-Newton EPIC Monte Carlo to Analysis And Interpretation of Data for Abell 1689, RXJ0658-55 And the Centaurus Clusters of Galaxies

    SciTech Connect

    Andersson, Karl E.; Peterson, J.R.; Madejski, G.M.; /SLAC /KIPAC, Menlo Park

    2007-04-17

    We propose a new Monte Carlo method to study extended X-ray sources with the European Photon Imaging Camera (EPIC) aboard XMM Newton. The Smoothed Particle Inference (SPI) technique, described in a companion paper, is applied here to the EPIC data for the clusters of galaxies Abell 1689, Centaurus and RXJ 0658-55 (the ''bullet cluster''). We aim to show the advantages of this method of simultaneous spectral-spatial modeling over traditional X-ray spectral analysis. In Abell 1689 we confirm our earlier findings about structure in temperature distribution and produce a high resolution temperature map. We also confirm our findings about velocity structure within the gas. In the bullet cluster, RXJ 0658-55, we produce the highest resolution temperature map ever to be published of this cluster allowing us to trace what looks like the motion of the bullet in the cluster. We even detect a south to north temperature gradient within the bullet itself. In the Centaurus cluster we detect, by dividing up the luminosity of the cluster in bands of gas temperatures, a striking feature to the north-east of the cluster core. We hypothesize that this feature is caused by a subcluster left over from a substantial merger that slightly displaced the core. We conclude that our method is very powerful in determining the spatial distributions of plasma temperatures and very useful for systematic studies in cluster structure.

  18. Tornadogenesis Versus Newton's Third Law of Motion

    NASA Astrophysics Data System (ADS)

    Hardwig, R. B.

    2015-12-01

    For over 90 years scientists have tried to explain how tornadoes form and function. The present general consensus is that a tornado is just a function of the thunderstorm. Much research has been done to find the answer and numerous articles and papers have been written, all to no avail. This research explores the fact that a tornado cannot be just a function of a thunderstorm, as there is no opposite force within the thunderstorm to the air drawn up by the tornado, so there must be some external force involved in a tornado's formation. To have compliance with Newton's Third Law of Motion we must see an equal downforce or some other force within the thunderstorm, to that drawn up by the tornado. And if there was a downforce, that force would be virtually as damaging as the tornado itself. But we don't see this downforce or any other opposing force within the thunderstorm. Therefore, we must look for some other force that could cause a tornado's formation. And if that opposing force is not within the thunderstorm we need to be looking for some external force, outside the thunderstorm, that could cause a tornado. Also the fact that we have Waterspouts, Landspouts and Gustnadoes all without a thunderstorm, but since they all look and function just like a tornado, tells us that there must be some other force that is responsible for causing a tornado just like a Waterspout, Landspout or Gustnado. My research shows that there is one other force of energy that could cause all of these vortexes and is most likely the source of energy for a tornado's formation. That force is the High Velocity Overhead Jet Stream. My research shows a direct relationship between the High Velocity Overhead Jet Stream and Tornadogenesis as well as Waterspouts, Landspouts and Gustnadoes. Therefore, with the High Velocity Overhead Jet Stream providing the Action, at its interface with the tornado in the stratosphere, the Reaction is what we see on the ground as a tornado. With this explanation we

  19. From Schawlow to Newton: An educational return

    NASA Astrophysics Data System (ADS)

    Sathe, D.

    Newton's laws of motion and his theory of gravitation are known for over 300 years. However, investigations of educators, from various countries and carried out in the last quarter of the 20t h century, show that the Aristotelian ideas keep persisting among students - in spite of learning thes e topics in schools and colleges. In the traditional examinations students do give answers in accordance with Newton's laws but in questionnaires of educators they ignore Newtonian laws unknowingly, and quite naturally give answers along the Aristotelian line of thought. Why do they give such contrasting answers? Should we take for granted that their understanding of Newtonian laws is satisfactory because of their correct answers in traditional exams, though not in questionnaires? Can these contrasting views affect their interest in physics? These are some questions that warrant our attention earnestly, as we gear up for the research and teaching in 21s t century. The author felt the need of focusing attention on the logical aspects of the subject, due to the global character of said problem. His decision was strengthened greatly, in late1970s, by the philosophy of Dennis Sciama and hence author's dedication of a letter to the editor to his memory, in the COSPAR Info. Bulletin /1/. Being a trained biochemist, author started looking for points, missed by the earlier educators - that means author started following the advice of Arthur Schawlow /2/ in late 1970s, though unknowingly. Sadly, author came to know of it after dedicating a lecture to the memory of Abdus Salam in a symposium in Samarkand, Uzbekistan. Therefore he is dedicating this presentation to the memory of Arthur Schawlow. According to the present author, the persistence of Aristotelian ideas and consequent contrasting performances of students are due to the logical conflicts between the basic concepts of physics itself. For example, the conflict between the treatment of uniform circular motion and the concept of

  20. A comparison of Picard and Newton iteration in the numerical solution of multidimensional variably saturated flow problems

    NASA Astrophysics Data System (ADS)

    Paniconi, Claudio; Putti, Mario

    1994-12-01

    Picard iteration is a widely used procedure for solving the nonlinear equation governing flow in variably saturated porous media. The method is simple to code and computationally cheap, but has been known to fail or converge slowly. The Newton method is more complex and expensive (on a per-iteration basis) than Picard, and as such has not received very much attention. Its robustness and higher rate of convergence, however, make it an attractive alternative to the Picard method, particularly for strongly nonlinear problems. In this paper the Picard and Newton schemes are implemented and compared in one-, two-, and three-dimensional finite element simulations involving both steady state and transient flow. The eight test cases presented highlight different aspects of the performance of the two iterative methods and the different factors that can affect their convergence and efficiency, including problem size, spatial and temporal discretization, initial solution estimates, convergence error norm, mass lumping, time weighting, conductivity and moisture content characteristics, boundary conditions, seepage faces, and the extent of fully saturated zones in the soil. Previous strategies for enhancing the performance of the Picard and Newton schemes are revisited, and new ones are suggested. The strategies include chord slope approximations for the derivatives of the characteristic equations, relaxing convergence requirements along seepage faces, dynamic time step control, nonlinear relaxation, and a mixed Picard-Newton approach. The tests show that the Picard or relaxed Picard schemes are often adequate for solving Richards' equation, but that in cases where these fail to converge or converge slowly, the Newton method should be used. The mixed Picard-Newton approach can effectively overcome the Newton scheme's sensitivity to initial solution estimates, while comparatively poor performance is reported for the various chord slope approximations. Finally, given the

  1. NUMERICAL CONVERGENCE IN SMOOTHED PARTICLE HYDRODYNAMICS

    SciTech Connect

    Zhu, Qirong; Li, Yuexing; Hernquist, Lars

    2015-02-10

    We study the convergence properties of smoothed particle hydrodynamics (SPH) using numerical tests and simple analytic considerations. Our analysis shows that formal numerical convergence is possible in SPH only in the joint limit N → ∞, h → 0, and N{sub nb} → ∞, where N is the total number of particles, h is the smoothing length, and N{sub nb} is the number of neighbor particles within the smoothing volume used to compute smoothed estimates. Previous work has generally assumed that the conditions N → ∞ and h → 0 are sufficient to achieve convergence, while holding N{sub nb} fixed. We demonstrate that if N{sub nb} is held fixed as the resolution is increased, there will be a residual source of error that does not vanish as N → ∞ and h → 0. Formal numerical convergence in SPH is possible only if N{sub nb} is increased systematically as the resolution is improved. Using analytic arguments, we derive an optimal compromise scaling for N{sub nb} by requiring that this source of error balance that present in the smoothing procedure. For typical choices of the smoothing kernel, we find N{sub nb} ∝N {sup 0.5}. This means that if SPH is to be used as a numerically convergent method, the required computational cost does not scale with particle number as O(N), but rather as O(N {sup 1} {sup +} {sup δ}), where δ ≈ 0.5, with a weak dependence on the form of the smoothing kernel.

  2. Newton-based optimization for Kullback-Leibler nonnegative tensor factorizations

    SciTech Connect

    Plantenga, Todd; Kolda, Tamara G.; Hansen, Samantha

    2015-04-30

    Tensor factorizations with nonnegativity constraints have found application in analysing data from cyber traffic, social networks, and other areas. We consider application data best described as being generated by a Poisson process (e.g. count data), which leads to sparse tensors that can be modelled by sparse factor matrices. In this paper, we investigate efficient techniques for computing an appropriate canonical polyadic tensor factorization based on the Kullback–Leibler divergence function. We propose novel subproblem solvers within the standard alternating block variable approach. Our new methods exploit structure and reformulate the optimization problem as small independent subproblems. We employ bound-constrained Newton and quasi-Newton methods. Finally, we compare our algorithms against other codes, demonstrating superior speed for high accuracy results and the ability to quickly find sparse solutions.

  3. Newton-based optimization for Kullback-Leibler nonnegative tensor factorizations

    DOE PAGES

    Plantenga, Todd; Kolda, Tamara G.; Hansen, Samantha

    2015-04-30

    Tensor factorizations with nonnegativity constraints have found application in analysing data from cyber traffic, social networks, and other areas. We consider application data best described as being generated by a Poisson process (e.g. count data), which leads to sparse tensors that can be modelled by sparse factor matrices. In this paper, we investigate efficient techniques for computing an appropriate canonical polyadic tensor factorization based on the Kullback–Leibler divergence function. We propose novel subproblem solvers within the standard alternating block variable approach. Our new methods exploit structure and reformulate the optimization problem as small independent subproblems. We employ bound-constrained Newton andmore » quasi-Newton methods. Finally, we compare our algorithms against other codes, demonstrating superior speed for high accuracy results and the ability to quickly find sparse solutions.« less

  4. "Yugoslavia" Branch of the International Astronomical Institute "Isaac Newton"

    NASA Astrophysics Data System (ADS)

    Dimitrijević, Milan S.; Popović, Luka Č.; Simić, Zoran; Jovanović, Predrag; Milovanović, Nenad; Bon, Edi

    2005-10-01

    Isaac Newton Institute of Chile in Eastern Europe and Eurasia and its president and founder Gonzalo Alcaino Barros have been presented as well as the foundation and activities of its "Yugoslavia" branch.

  5. Neural Generalized Predictive Control: A Newton-Raphson Implementation

    NASA Technical Reports Server (NTRS)

    Soloway, Donald; Haley, Pamela J.

    1997-01-01

    An efficient implementation of Generalized Predictive Control using a multi-layer feedforward neural network as the plant's nonlinear model is presented. In using Newton-Raphson as the optimization algorithm, the number of iterations needed for convergence is significantly reduced from other techniques. The main cost of the Newton-Raphson algorithm is in the calculation of the Hessian, but even with this overhead the low iteration numbers make Newton-Raphson faster than other techniques and a viable algorithm for real-time control. This paper presents a detailed derivation of the Neural Generalized Predictive Control algorithm with Newton-Raphson as the minimization algorithm. Simulation results show convergence to a good solution within two iterations and timing data show that real-time control is possible. Comments about the algorithm's implementation are also included.

  6. Suzanne Newton's "I Will Call it Georgie's Blues".

    ERIC Educational Resources Information Center

    Scales, Pat

    1998-01-01

    Summarizes Suzanne Newton's children's book, "I Will Call It Georgie's Blues." Includes discussion questions about the book, and a list of activities. Provides an annotated bibliography of fiction, picture books, nonfiction, and biography titles about jazz and jazz musicians. (AEF)

  7. Systemic venous drainage: can we help Newton?

    PubMed

    Corno, Antonio F

    2007-06-01

    In recent years substantial progress occurred in the techniques of cardiopulmonary bypass, but the factor potentially limiting the flexibility of cardiopulmonary bypass remains the drainage of the systemic venous return. In the daily clinical practice of cardiac surgery, the amount of systemic venous return on cardiopulmonary bypass is directly correlated with the amount of the pump flow. As a consequence, the pump flow is limited by the amount of venous return that the pump is receiving. On cardiopulmonary bypass the amount of venous drainage depends upon the central venous pressure, the height differential between patient and inlet of the venous line into the venous reservoir, and the resistance in the venous cannula(s) and circuit. The factors determining the venous return to be taken into consideration in cardiac surgery are the following: (a) characteristics of the individual patient; (b) type of planned surgical procedure; (c) type of venous cannula(s); (d) type of circuit for cardiopulmonary bypass; (e) strategy of cardiopulmonary bypass; (f) use of accessory mechanical systems to increased the systemic venous return. The careful pre-operative evaluation of all the elements affecting the systemic venous drainage, including the characteristics of the individual patient and the type of required surgical procedure, the choice of the best strategy of cardiopulmonary bypass, and the use of the most advanced materials and tools, can provide a systemic venous drainage substantially better than what it would be allowed by the simple "Law of universal gravitation" by Isaac Newton.

  8. Insect Flight: From Newton's Law to Neurons

    NASA Astrophysics Data System (ADS)

    Wang, Z. Jane

    2016-03-01

    Why do animals move the way they do? Bacteria, insects, birds, and fish share with us the necessity to move so as to live. Although each organism follows its own evolutionary course, it also obeys a set of common laws. At the very least, the movement of animals, like that of planets, is governed by Newton's law: All things fall. On Earth, most things fall in air or water, and their motions are thus subject to the laws of hydrodynamics. Through trial and error, animals have found ways to interact with fluid so they can float, drift, swim, sail, glide, soar, and fly. This elementary struggle to escape the fate of falling shapes the development of motors, sensors, and mind. Perhaps we can deduce parts of their neural computations by understanding what animals must do so as not to fall. Here I discuss recent developments along this line of inquiry in the case of insect flight. Asking how often a fly must sense its orientation in order to balance in air has shed new light on the role of motor neurons and steering muscles responsible for flight stability.

  9. Optomechanical test of the Schrödinger-Newton equation

    NASA Astrophysics Data System (ADS)

    Großardt, André; Bateman, James; Ulbricht, Hendrik; Bassi, Angelo

    2016-05-01

    The Schrödinger-Newton equation has been proposed as an experimentally testable alternative to quantum gravity, accessible at low energies. It contains self-gravitational terms, which slightly modify the quantum dynamics. Here we show that it distorts the spectrum of a harmonic system. Based on this effect, we propose an optomechanical experiment with a trapped microdisc to test the Schrödinger-Newton equation, and we show that it can be realized with existing technology.

  10. Laboratory test of Newton's second law for small accelerations.

    PubMed

    Gundlach, J H; Schlamminger, S; Spitzer, C D; Choi, K-Y; Woodahl, B A; Coy, J J; Fischbach, E

    2007-04-13

    We have tested the proportionality of force and acceleration in Newton's second law, F=ma, in the limit of small forces and accelerations. Our tests reach well below the acceleration scales relevant to understanding several current astrophysical puzzles such as the flatness of galactic rotation curves, the Pioneer anomaly, and the Hubble acceleration. We find good agreement with Newton's second law at accelerations as small as 5 x 10(-14) m/s(2).

  11. Laboratory Test of Newton's Second Law for Small Accelerations

    SciTech Connect

    Gundlach, J. H.; Schlamminger, S.; Spitzer, C. D.; Choi, K.-Y.; Woodahl, B. A.; Coy, J. J.; Fischbach, E.

    2007-04-13

    We have tested the proportionality of force and acceleration in Newton's second law, F=ma, in the limit of small forces and accelerations. Our tests reach well below the acceleration scales relevant to understanding several current astrophysical puzzles such as the flatness of galactic rotation curves, the Pioneer anomaly, and the Hubble acceleration. We find good agreement with Newton's second law at accelerations as small as 5x10{sup -14} m/s{sup 2}.

  12. Laboratory Test of Newton's Second Law for Small Accelerations

    NASA Astrophysics Data System (ADS)

    Woodahl, Brian; Gundlach, Jens; Schlamminger, Stephan; Spitzer, Chris; Choi, Ki; Coy, Jen; Fischbach, Ephraim

    2009-10-01

    We have tested the proportionality of force and acceleration in Newton's second law, F=ma, in the limit of small forces and accelerations. Our tests reach well below the acceleration scales relevant to understanding several current astrophysical puzzles such as the flatness of galactic rotation curves, the Pioneer anomaly, and the Hubble acceleration. We find good agreement with Newton's second law at accelerations as small as 5 x 10-14 m/s^2.

  13. Issac Newton: A passion to learn and understand

    NASA Astrophysics Data System (ADS)

    French, A. P.

    1988-10-01

    The work of Isaac Newton is an enduring tribute to his genius for observation, investigation and analysis. Although most of his work was done over three hundred years ago, it is replete with examples of current value to our role as teachers of physics. The purpose of this paper is both to pay homage to Newton, on the tercentenary of the Principia, and to suggest the much of that what he did can translate directly into our classrooms.

  14. Astronomie et chronoligie chez Newton - arguments astronomiques à l'appui de la chronologie de Newton (Astronomical arguments in Newton's Chronology)

    NASA Astrophysics Data System (ADS)

    Nazé, Yaël

    2012-12-01

    In his Chronology, Newton uses astronomical "evidence" to support its extreme rejuvenation of ancient times. These elements, having a scientific varnish, provide some credibility to the work. They have been fiercely debated for a century, with a gradual undermining of Newton's assumptions. However, this has not dented the prestige of the English scientist. Dans sa Chronologie, Newton utilise des "preuves" astronomiques pour appuyer son rajeunissement extreme des epoques anciennes. Ces elements, au vernis scientifique, donnent une credibilite certaine a l'ensemble. Ils ont donc ete aprement discutes, les debats sapant petit a petit les hypotheses du savant anglais pour finalement porter un coup mortel a l'ensemble. Cela n'a toutefois pas entame le prestige du savant anglais.

  15. Autoregressive smoothing of GOMOS transmittances

    NASA Astrophysics Data System (ADS)

    Fussen, D.; Vanhellemont, F.; Bingen, C.; Kyrölä, B.; Tamminen, J.; Sofieva, V.; Hassinen, S.; Seppälä, A.; Verronen, P. T.; Bertaux, J. L.; Hauchecorne, A.; Dalaudier, F.; d'Andon, O. Fanton; Barrot, G.; Mangin, A.; Theodore, B.; Guirlet, M.; Renard, J. B.; Fraisse, R.; Snoeij, P.; Koopman, R.; Saavedra, L.

    GOMOS is a stellar occultation instrument onboard ENVISAT. It has already measured several hundreds of thousands occultations since March 2002. In some circumstances, the obliqueness of the star setting causes the remote sounding of possible horizontal turbulence that cannot be adequately corrected by using the fast photometer signals, leading to the presence of residual scintillation in the atmospheric transmittance. We investigate the mechanism that produces this spurious signal that may cause the retrieval of wavy constituent profiles. A special algorithm of vertical autoregressive smoothing (VAS) is proposed that takes into account the physical correlation between adjacent measurements at different tangent altitudes. A regularization parameter of the method may be optimized on basis of the minimal correlation between the residuals as prescribed by the Durbin-Watson statistics. The improvements obtained in the retrieval of both O 3 and NO 2 number density profiles is presented and discussed with respect to the results of the official data processing model.

  16. Newton law in covariant unimodular F(R) gravity

    NASA Astrophysics Data System (ADS)

    Nojiri, S.; Odintsov, S. D.; Oikonomou, V. K.

    2016-09-01

    We investigate the Newton law in the unimodular F(R) gravity. In the standard F(R) gravity, due to the extra scalar mode, there often appear the large corrections to the Newton law and such models are excluded by the experiments and/or the observations. In the unimodular F(R) gravity, however, the extra scalar mode become not to be dynamical due to the unimodular constraint and there is not any correction to the Newton law. Even in the unimodular Einstein gravity, the Newton law is reproduced but the mechanism is a little bit different from that in the unimodular F(R) gravity. We also investigate the unimodular F(R) gravity in the covariant formulation. In the covariant formulation, we include the three-form field. We show that the three-form field could not have any unwanted property, like ghost nor correction to the Newton law. In the covariant formulation, however, the above extra scalar mode becomes dynamical and could give a correction to the Newton law. We also show that there are no difference in the Friedmann-Robertson-Walker (FRW) dynamics in the non-covariant and covariant formulation.

  17. Structured mesh generation with smoothness controls

    NASA Astrophysics Data System (ADS)

    Zhang, Yaoxin; Jia, Yafei; Wang, Sam S. Y.

    2006-08-01

    In geometrically complex domains, the Ryskin and Leal (RL) orthogonal mesh generation system may cause mesh distortion and overlapping problems when using the weak constraint method with specified boundary point distribution for all boundaries. To resolve these problems, an improved RL system with automatic smoothness control is proposed. In this improved RL system, the automatic smoothness control mechanism is based on five types of smoothness conditions and includes the self-adjustment mechanism and the auto-evaluation mechanism for an empirical parameter. The proposed system is illustrated using several test examples. Several applications to natural domains are also demonstrated. It is shown that the improved RL system is capable of resolving the above problems at little cost of orthogonality.

  18. Impact modeling with Smooth Particle Hydrodynamics

    SciTech Connect

    Stellingwerf, R.F.; Wingate, C.A.

    1992-01-01

    Smooth Particle Hydrodynamics (SPH) is a new computational technique uniquely suited to computation of hypervelocity impact phenomena. This paper reviews the characteristics, philosophy, and a bit of the derivation of the method. As illustrations of the technique, several test case computations and several application computations are shown.

  19. Impact modeling with Smooth Particle Hydrodynamics

    SciTech Connect

    Stellingwerf, R.F.; Wingate, C.A.

    1992-09-01

    Smooth Particle Hydrodynamics (SPH) is a new computational technique uniquely suited to computation of hypervelocity impact phenomena. This paper reviews the characteristics, philosophy, and a bit of the derivation of the method. As illustrations of the technique, several test case computations and several application computations are shown.

  20. Anisotropic Smoothing Improves DT-MRI-Based Muscle Fiber Tractography

    PubMed Central

    Buck, Amanda K. W.; Ding, Zhaohua; Elder, Christopher P.; Towse, Theodore F.; Damon, Bruce M.

    2015-01-01

    Purpose To assess the effect of anisotropic smoothing on fiber tracking measures, including pennation angle, fiber tract length, and fiber tract number in the medial gastrocnemius (MG) muscle in healthy subjects using diffusion-weighted magnetic resonance imaging (DW-MRI). Materials and Methods 3T DW-MRI data were used for muscle fiber tractography in the MG of healthy subjects. Anisotropic smoothing was applied at three levels (5%, 10%, 15%), and pennation angle, tract length, fiber tract number, fractional anisotropy, and principal eigenvector orientation were quantified for each smoothing level. Results Fiber tract length increased with pre-fiber tracking smoothing, and local heterogeneities in fiber direction were reduced. However, pennation angle was not affected by smoothing. Conclusion Modest anisotropic smoothing (10%) improved fiber-tracking results, while preserving structural features. PMID:26010830

  1. DARK MATTER SEARCH USING XMM-NEWTON OBSERVATIONS OF WILLMAN 1

    SciTech Connect

    Loewenstein, Michael; Kusenko, Alexander

    2012-06-01

    We report the results of a search for an emission line from radiatively decaying dark matter in the ultra-faint dwarf spheroidal galaxy Willman 1 based on analysis of spectra extracted from XMM-Newton X-ray Observatory data. The observation follows up our analysis of Chandra data of Willman 1 that resulted in line flux upper limits over the Chandra bandpass and evidence of a 2.5 keV feature at a significance below the 99% confidence threshold used to define the limits. The higher effective area of the XMM-Newton detectors, combined with application of recently developing methods for extended-source analysis, allows us to derive improved constraints on the combination of mass and mixing angle of the sterile neutrino dark matter candidate. We do not confirm the Chandra evidence for a 2.5 keV emission line.

  2. Student's preconception and anxiety when they solve multi representation concepts in Newton laws and it's application

    NASA Astrophysics Data System (ADS)

    Cari, C.; Suparmi, A.; Handhika, J.

    2016-11-01

    The purpose of this study was to describe of preconceptions and anxieties students in solving the representation concepts in newton laws and it's application. This research was conducted for junior undergraduate student's in physics department (36 Students) and physics education (31 Students). The method used in this study is a qualitative descriptive. The data was collection using test for multirepresentation concept, questionnaires for anxiety, and interviews. Based on the analysis it can be concluded that (1) the higher is anxiety, the higher is unconsistency (67,16%), (2) the higher is anxiety, the higher is consistency but wrong answer (29,85%), (3) the lower is anxiety, the higher is consistency of right answer (2,98%). Mostly students have understood fewer physics concept in newtons laws.

  3. Newton Leibniz integration for ket bra operators in quantum mechanics and derivation of entangled state representations

    NASA Astrophysics Data System (ADS)

    Fan, Hong-yi; Lu, Hai-liang; Fan, Yue

    2006-02-01

    Newton-Leibniz integration rule only applies to commuting functions of continuum variables, while operators made of Dirac's symbols (ket versus bra, e.g., | q>< q| of continuous parameter q) in quantum mechanics are usually not commutative. Therefore, integrations over the operators of type |><| cannot be directly performed by Newton-Leibniz rule. We invented an innovative technique of integration within an ordered product (IWOP) of operators that made the integration of non-commutative operators possible. The IWOP technique thus bridges this mathematical gap between classical mechanics and quantum mechanics, and further reveals the beauty and elegance of Dirac's symbolic method and transformation theory. Various applications of the IWOP technique, including constructing the entangled state representations and their applications, are presented.

  4. Notes on Newton-Krylov based Incompressible Flow Projection Solver

    SciTech Connect

    Robert Nourgaliev; Mark Christon; J. Bakosi

    2012-09-01

    The purpose of the present document is to formulate Jacobian-free Newton-Krylov algorithm for approximate projection method used in Hydra-TH code. Hydra-TH is developed by Los Alamos National Laboratory (LANL) under the auspices of the Consortium for Advanced Simulation of Light-Water Reactors (CASL) for thermal-hydraulics applications ranging from grid-to-rod fretting (GTRF) to multiphase flow subcooled boiling. Currently, Hydra-TH is based on the semi-implicit projection method, which provides an excellent platform for simulation of transient single-phase thermalhydraulics problems. This algorithm however is not efficient when applied for very slow or steady-state problems, as well as for highly nonlinear multiphase problems relevant to nuclear reactor thermalhydraulics with boiling and condensation. These applications require fully-implicit tightly-coupling algorithms. The major technical contribution of the present report is the formulation of fully-implicit projection algorithm which will fulfill this purpose. This includes the definition of non-linear residuals used for GMRES-based linear iterations, as well as physics-based preconditioning techniques.

  5. New smooth hybrid inflation

    SciTech Connect

    Lazarides, George; Vamvasakis, Achilleas

    2007-10-15

    We consider the extension of the supersymmetric Pati-Salam model which solves the b-quark mass problem of supersymmetric grand unified models with exact Yukawa unification and universal boundary conditions and leads to the so-called new shifted hybrid inflationary scenario. We show that this model can also lead to a new version of smooth hybrid inflation based only on renormalizable interactions provided that a particular parameter of its superpotential is somewhat small. The potential possesses valleys of minima with classical inclination, which can be used as inflationary paths. The model is consistent with the fitting of the three-year Wilkinson microwave anisotropy probe data by the standard power-law cosmological model with cold dark matter and a cosmological constant. In particular, the spectral index turns out to be adequately small so that it is compatible with the data. Moreover, the Pati-Salam gauge group is broken to the standard model gauge group during inflation and, thus, no monopoles are formed at the end of inflation. Supergravity corrections based on a nonminimal Kaehler potential with a convenient choice of a sign keep the spectral index comfortably within the allowed range without generating maxima and minima of the potential on the inflationary path. So, unnatural restrictions on the initial conditions for inflation can be avoided.

  6. Ceramic coatings on smooth surfaces

    NASA Technical Reports Server (NTRS)

    Miller, R. A. (Inventor); Brindley, W. J. (Inventor); Rouge, C. J. (Inventor)

    1991-01-01

    A metallic coating is plasma sprayed onto a smooth surface of a metal alloy substitute or on a bond coating. An initial thin ceramic layer is low pressure sprayed onto the smooth surface of the substrate or bond coating. Another ceramic layer is atmospheric plasma sprayed onto the initial ceramic layer.

  7. Ryanodine receptors in smooth muscle.

    PubMed

    Guerrero-Hernández, Agustín; Gómez-Viquez, Leticia; Guerrero-Serna, Guadalupe; Rueda, Angélica

    2002-07-01

    The sarcoplasmic reticulum (SR) of smooth muscle is endowed with two different types of Ca2+ release channels, i.e. inositol 1,4,5-trisphosphate receptors (IP3Rs) and ryanodine receptors (RyRs). In general, both release channels mobilize Ca2+ from the same internal store in smooth muscle. While the importance of IP3Rs in agonist-induced contraction is well established, the role of RyRs in excitation-contraction coupling of smooth muscle is not clear. The participation of smooth muscle RyRs in the amplification of Ca2+ transients induced by either opening of Ca2+-permeable channels or IP3-triggered Ca2+ release has been studied. The efficacy of both processes to activate RyRs by calcium-induced calcium release (CICR) is highly variable and not widely present in smooth muscle. Although RyRs in smooth muscle generate Ca2+ sparks that are similar to those observed in striated muscles, the contribution of these local Ca2+ events to depolarization-induced global rise in [Ca2+]i is rather limited. Recent data suggest that RyRs are involved in regulating the luminal [Ca2+] of SR and also in smooth muscle relaxation. This review summarizes studies that were carried out mainly in muscle strips or in freshly isolated myocytes, and that were aimed to determine the physiological role of RyRs in smooth muscle.

  8. Synthesis of NIR-Responsive NaYF₄:Yb,Er Upconversion Fluorescent Nanoparticles Using an Optimized Solvothermal Method and Their Applications in Enhanced Development of Latent Fingerprints on Various Smooth Substrates.

    PubMed

    Wang, Meng; Zhu, Ye; Mao, Chuanbin

    2015-06-30

    Fingerprints at crime scenes are usually latent. The powder-dusting method is the most commonly used procedure for developing latent fingerprints in forensic science. However, the traditional powder-dusting method has characteristics of low sensitivity, low contrast, high background noise, and high autofluorescence interference. To overcome the drawbacks faced by the traditional method, we first optimized an oleic acid-based solvothermal approach for the synthesis of NaYF4:Yb,Er fluorescent upconversion nanoparticles (UCNPs) with the highest possible fluorescence intensity under near-infrared (NIR) irradiation. To optimize the synthesis, we studied the effects of the reaction time, reaction temperature, and volume of oleic acid on the size, phase composition, and UC fluorescence intensity of the UCNPs. We then used the resultant UCNPs to fluorescently label the fingerprints on various smooth substrates to improve the development of latent fingerprints because the UCNPs could undergo excitation under 980 nm NIR light to emit visible light. Latent fingerprints on three major types of smooth substrates were studied, including those with a single background color (transparent glass, white ceramic tiles, and black marbles), with multiple background colors (marbles with different complex surface patterns) and with strong background autofluorescence (note papers, Chinese paper money, and plastic plates). Compared with fingerprint development using traditional powders such as bronze powder, magnetic powder, and green fluorescent powder, our development procedure using UCNPs is facile and exhibits very high sensitivity, high contrast, low background interference, and low autofluorescence interference. This work shows that UCNPs synthesized under optimized conditions are a versatile fluorescent label for the facile development of fingerprints and can find their practical applications in forensic sciences.

  9. Aircraft automatic-flight-control system with inversion of the model in the feed-forward path using a Newton-Raphson technique for the inversion

    NASA Technical Reports Server (NTRS)

    Smith, G. A.; Meyer, G.; Nordstrom, M.

    1986-01-01

    A new automatic flight control system concept suitable for aircraft with highly nonlinear aerodynamic and propulsion characteristics and which must operate over a wide flight envelope was investigated. This exact model follower inverts a complete nonlinear model of the aircraft as part of the feed-forward path. The inversion is accomplished by a Newton-Raphson trim of the model at each digital computer cycle time of 0.05 seconds. The combination of the inverse model and the actual aircraft in the feed-forward path alloys the translational and rotational regulators in the feedback path to be easily designed by linear methods. An explanation of the model inversion procedure is presented. An extensive set of simulation data for essentially the full flight envelope for a vertical attitude takeoff and landing aircraft (VATOL) is presented. These data demonstrate the successful, smooth, and precise control that can be achieved with this concept. The trajectory includes conventional flight from 200 to 900 ft/sec with path accelerations and decelerations, altitude changes of over 6000 ft and 2g and 3g turns. Vertical attitude maneuvering as a tail sitter along all axes is demonstrated. A transition trajectory from 200 ft/sec in conventional flight to stationary hover in the vertical attitude includes satisfactory operation through lift-cure slope reversal as attitude goes from horizontal to vertical at constant altitude. A vertical attitude takeoff from stationary hover to conventional flight is also demonstrated.

  10. A Catalog of Galaxy Clusters Observed by XMM-Newton

    NASA Technical Reports Server (NTRS)

    Snowden, S. L.; Mushotzky, R. M.; Kuntz, K. D.; Davis, David S.

    2007-01-01

    Images and the radial profiles of the temperature, abundance, and brightness for 70 clusters of galaxies observed by XMM-Newton are presented along with a detailed discussion of the data reduction and analysis methods, including background modeling, which were used in the processing. Proper consideration of the various background components is vital to extend the reliable determination of cluster parameters to the largest possible cluster radii. The various components of the background including the quiescent particle background, cosmic diffuse emission, soft proton contamination, and solar wind charge exchange emission are discussed along with suggested means of their identification, filtering, and/or their modeling and subtraction. Every component is spectrally variable, sometimes significantly so, and all components except the cosmic background are temporally variable as well. The distributions of the events over the FOV vary between the components, and some distributions vary with energy. The scientific results from observations of low surface brightness objects and the diffuse background itself can be strongly affected by these background components and therefore great care should be taken in their consideration.

  11. HIGH-RESOLUTION XMM-NEWTON SPECTROSCOPY OF THE COOLING FLOW CLUSTER A3112

    SciTech Connect

    Bulbul, G. Esra; Smith, Randall K.; Foster, Adam; Cottam, Jean; Loewenstein, Michael; Mushotzky, Richard; Shafer, Richard

    2012-03-01

    We examine high signal-to-noise XMM-Newton European Photon Imaging Camera (EPIC) and Reflection Grating Spectrometer (RGS) observations to determine the physical characteristics of the gas in the cool core and outskirts of the nearby rich cluster A3112. The XMM-Newton Extended Source Analysis Software data reduction and background modeling methods were used to analyze the XMM-Newton EPIC data. From the EPIC data, we find that the iron and silicon abundance gradients show significant increase toward the center of the cluster while the oxygen abundance profile is centrally peaked but has a shallower distribution than that of iron. The X-ray mass modeling is based on the temperature and deprojected density distributions of the intracluster medium determined from EPIC observations. The total mass of A3112 obeys the M-T scaling relations found using XMM-Newton and Chandra observations of massive clusters at r{sub 500}. The gas mass fraction f{sub gas} = 0.149{sup +0.036}{sub -0.032} at r{sub 500} is consistent with the seven-year Wilkinson Microwave Anisotropy Probe results. The comparisons of line fluxes and flux limits on the Fe XVII and Fe XVIII lines obtained from high-resolution RGS spectra indicate that there is no spectral evidence for cooler gas associated with the cluster with temperature below 1.0 keV in the central <38'' ({approx}52 kpc) region of A3112. High-resolution RGS spectra also yield an upper limit to the turbulent motions in the compact core of A3112 (206 km s{sup -1}). We find that the contribution of turbulence to total energy is less than 6%. This upper limit is consistent with the energy contribution measured in recent high-resolution simulations of relaxed galaxy clusters.

  12. Students’ misconceptions about Newton's second law in outer space

    NASA Astrophysics Data System (ADS)

    Temiz, B. K.; Yavuz, A.

    2014-07-01

    Students’ misconceptions about Newton's second law in frictionless outer space were investigated. The research was formed according to an epistemic game theoretical framework. The term ‘epistemic’ refers to students’ participation in problem-solving activities as a means of constructing new knowledge. The term ‘game’ refers to a coherent activity that consists of moves and rules. A set of questions in which students are asked to solve two similar Newton's second law problems, one of which is on the Earth and the other in outer space, was administered to 116 undergraduate students. The findings indicate that there is a significant difference between students’ epistemic game preferences and race-type (outer space or frictional surface) question. So students who used Newton's second law on the ground did not apply this law and used primitive reasoning when it came to space. Among these students, voluntary interviews were conducted with 18 students. Analysis of interview transcripts showed that: (1) the term ‘space’ causes spontaneity among students that prevents the use of the law; (2) students hesitate to apply Newton's second law in space due to the lack of a condition—the friction; (3) students feel that Newton's second law is not valid in space for a variety of reasons, but mostly for the fact that the body in space is not in contact with a surface.

  13. Simple Robust Fixed Lag Smoothing

    DTIC Science & Technology

    1988-12-02

    SIMPLE ROBUST FIXED LAG SMOOTHING by ~N. D. Le R.D. Martin 4 TECHNICAL RlEPORT No. 149 December 1988 Department of Statistics, GN-22 Accesion For...frLsD1ist Special A- Z Simple Robust Fixed Lag Smoothing With Application To Radar Glint Noise * N. D. Le R. D. Martin Department of Statistics, GN...smoothers. The emphasis here is on fixed-lag smoothing , as opposed to the use of existing robust fixed interval smoothers (e.g., as in Martin, 1979

  14. A multigrid method for variational inequalities

    SciTech Connect

    Oliveira, S.; Stewart, D.E.; Wu, W.

    1996-12-31

    Multigrid methods have been used with great success for solving elliptic partial differential equations. Penalty methods have been successful in solving finite-dimensional quadratic programs. In this paper these two techniques are combined to give a fast method for solving obstacle problems. A nonlinear penalized problem is solved using Newton`s method for large values of a penalty parameter. Multigrid methods are used to solve the linear systems in Newton`s method. The overall numerical method developed is based on an exterior penalty function, and numerical results showing the performance of the method have been obtained.

  15. Analytic Smoothing for Equipercentile Equating under the Common Item Nonequivalent Populations Design.

    ERIC Educational Resources Information Center

    Kolen, Michael J.; Jarjoura, David

    1987-01-01

    A cubic spline method for smoothing equipercentile equating relationships under the common item nonequivalent populations design is described. Statistical techniques based on bootstrap estimation are presented for choosing an equating method/degree of smoothing. Smoothing decreases the estimate of random error but results in an increase in…

  16. Relating constrained motion to force through Newton's second law

    NASA Astrophysics Data System (ADS)

    Roithmayr, Carlos M.

    When a mechanical system is subject to constraints its motion is in some way restricted. In accordance with Newton's second law, motion is a direct result of forces acting on a system; hence, constraint is inextricably linked to force. The presence of a constraint implies the application of particular forces needed to compel motion in accordance with the constraint; absence of a constraint implies the absence of such forces. The objective of this thesis is to formulate a comprehensive, consistent, and concise method for identifying a set of forces needed to constrain the behavior of a mechanical system modeled as a set of particles and rigid bodies. The goal is accomplished in large part by expressing constraint equations in vector form rather than entirely in terms of scalars. The method developed here can be applied whenever constraints can be described at the acceleration level by a set of independent equations that are linear in acceleration. Hence, the range of applicability extends to servo-constraints or program constraints described at the velocity level with relationships that are nonlinear in velocity. All configuration constraints, and an important class of classical motion constraints, can be expressed at the velocity level by using equations that are linear in velocity; therefore, the associated constraint equations are linear in acceleration when written at the acceleration level. Two new approaches are presented for deriving equations governing motion of a system subject to constraints expressed at the velocity level with equations that are nonlinear in velocity. By using partial accelerations instead of the partial velocities normally employed with Kane's method, it is possible to form dynamical equations that either do or do not contain evidence of the constraint forces, depending on the analyst's interests.

  17. Laboratory Test of Newton's Second Law for Small Accelerations

    NASA Astrophysics Data System (ADS)

    Woodahl, Brian; Gundlach, Jens; Schlamminger, Stephan; Spitzer, Chris; Choi, Ki; Coy, Jennifer; Fischbach, Ephraim

    2007-05-01

    We have tested the proportionality of force and acceleration in Newton's second law, F=ma, in the limit of small forces and accelerations. Our tests reach well below the acceleration scales relevant to understanding several current astrophysical puzzles such as the flatness of galactic rotation curves, the Pioneer anomaly, and the Hubble acceleration. We find good agreement with Newton's second law at accelerations as small as 5 x 10-14 m/s^2. To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2007.OSS07.P1.15

  18. The architecture of Newton, a general-purpose dynamics simulator

    NASA Technical Reports Server (NTRS)

    Cremer, James F.; Stewart, A. James

    1989-01-01

    The architecture for Newton, a general-purpose system for simulating the dynamics of complex physical objects, is described. The system automatically formulates and analyzes equations of motion, and performs automatic modification of this system equations when necessitated by changes in kinematic relationships between objects. Impact and temporary contact are handled, although only using simple models. User-directed influence of simulations is achieved using Newton's module, which can be used to experiment with the control of many-degree-of-freedom articulated objects.

  19. Self-adaptive incremental Newton-Raphson algorithms

    NASA Technical Reports Server (NTRS)

    Padovan, J.

    1980-01-01

    Multilevel self-adaptive Newton-Raphson type strategies are developed to improve the solution efficiency of nonlinear finite element simulations of statically loaded structures. The overall strategy involves three basic levels. The first level involves preliminary solution tunneling via primative operators. Secondly, the solution is constantly monitored via quality/convergence/nonlinearity tests. Lastly, the third level involves self-adaptive algorithmic update procedures aimed at improving the convergence characteristics of the Newton-Raphson strategy. Numerical experiments are included to illustrate the results of the procedure.

  20. Radar data smoothing filter study

    NASA Technical Reports Server (NTRS)

    White, J. V.

    1984-01-01

    The accuracy of the current Wallops Flight Facility (WFF) data smoothing techniques for a variety of radars and payloads is examined. Alternative data reduction techniques are given and recommendations are made for improving radar data processing at WFF. A data adaptive algorithm, based on Kalman filtering and smoothing techniques, is also developed for estimating payload trajectories above the atmosphere from noisy time varying radar data. This algorithm is tested and verified using radar tracking data from WFF.

  1. Active controls for ride smoothing

    NASA Technical Reports Server (NTRS)

    Conner, D. W.; Thompson, G. O.

    1976-01-01

    Active controls technology offers great promise for significantly smoothing the ride, and thus improving public and air carrier acceptance, of certain types of transport aircraft. Recent findings which support this promise are presented in the following three pertinent areas: (1) Ride quality versus degree of traveler satisfaction; (2) significant findings from a feasibility study of a ride smoothing system; and (3) potential ride problems identified for several advanced transport concepts.

  2. High-order implicit residual smoothing time scheme for direct and large eddy simulations of compressible flows

    NASA Astrophysics Data System (ADS)

    Cinnella, P.; Content, C.

    2016-12-01

    Restrictions on the maximum allowable time step of explicit time integration methods for direct and large eddy simulations of compressible turbulent flows at high Reynolds numbers can be very severe, because of the extremely small space steps used close to solid walls to capture tiny and elongated boundary layer structures. A way of increasing stability limits is to use implicit time integration schemes. However, the price to pay is a higher computational cost per time step, higher discretization errors and lower parallel scalability. In quest for an implicit time scheme for scale-resolving simulations providing the best possible compromise between these opposite requirements, we develop a Runge-Kutta implicit residual smoothing (IRS) scheme of fourth-order accuracy, based on a bilaplacian operator. The implicit operator involves the inversion of scalar pentadiagonal systems, for which efficient parallel algorithms are available. The proposed method is assessed against two explicit and two implicit time integration techniques in terms of computational cost required to achieve a threshold level of accuracy. Precisely, the proposed time scheme is compared to four-stages and six-stages low-storage Runge-Kutta method, to the second-order IRS and to a second-order backward scheme solved by means of matrix-free quasi-exact Newton subiterations. Numerical results show that the proposed IRS scheme leads to reductions in computational time by a factor 3 to 5 for an accuracy comparable to that of the corresponding explicit Runge-Kutta scheme.

  3. There is grandeur in this view of Newton: Charles Darwin, Isaac Newton and Victorian conceptions of scientific virtue.

    PubMed

    Bellon, Richard

    2014-01-01

    For Victorian men of science, the scientific revolution of the seventeenth century represented a moral awakening. Great theoretical triumphs of inductive science flowed directly from a philosophical spirit that embraced the virtues of self-discipline, courage, patience and humility. Isaac Newton exemplified this union of moral and intellectual excellence. This, at least, was the story crafted by scientific leaders like David Brewster, Thomas Chalmers, John Herschel, Adam Sedgwick and William Whewell. Not everyone accepted this reading of history. Evangelicals who decried the 'materialism' of mainstream science assigned a different meaning to Newton's legacy on behalf of their 'scriptural' alternative. High-church critics of science like John Henry Newman, on the other hand, denied that Newton's secular achievements carried any moral significance at all. These debates over Newtonian standards of philosophical behavior had a decisive influence on Charles Darwin as he developed his theory of evolution by natural selection.

  4. Newton shows the light: a commentary on Newton (1672) 'A letter … containing his new theory about light and colours…'.

    PubMed

    Fara, Patricia

    2015-04-13

    Isaac Newton's reputation was initially established by his 1672 paper on the refraction of light through a prism; this is now seen as a ground-breaking account and the foundation of modern optics. In it, he claimed to refute Cartesian ideas of light modification by definitively demonstrating that the refrangibility of a ray is linked to its colour, hence arguing that colour is an intrinsic property of light and does not arise from passing through a medium. Newton's later significance as a world-famous scientific genius and the apparent confirmation of his experimental results have tended to obscure the realities of his reception at the time. This paper explores the rhetorical strategies Newton deployed to convince his audience that his conclusions were certain and unchallengeable. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

  5. Smooth Passage For The Jetfoil

    NASA Technical Reports Server (NTRS)

    1978-01-01

    The Flying Princess is a Boeing Jetfoil, one of a family of commercial waterjets built by Boeing Marine Systems, a division of The Boeing Company, Seattle, Washington. The new Jetfoil offers a number of advantages over earlier hydrofoils, a major one being a smooth ride in rough waters. NASA technology contributed to jolt-free passenger comfort. Hydrofoils skim the surface at speeds considerably greater than those of conventional ships because there is little friction between hull and water. Hulls are raised above the water by the lift of the foils, which resemble and function like an airplane wing. The foils are attached to the hull by rigid struts, which ordinarily cause a vessel operating in coastal seas to follow the contour of the waves. In wind-whipped waters, this makes for a rough ride. Seeking to increase passenger acceptance, Boeing Marine System engineers looked for ways to improve rough-water ride quality. Langley Research Center conducts continuing ride quality research. Initially, it was aimed at improving aircraft ride; it was later expanded to include all modes of transportation. Research includes studies of vibration, acceleration, temperature, humidity, passenger seats and posture, and the psychological aspects of passenger reaction to vehicle ride. As part of the program, Langley developed instrumentation, ride quality models and methods of data analysis.

  6. Communication: Newton homotopies for sampling stationary points of potential energy landscapes

    SciTech Connect

    Mehta, Dhagash; Chen, Tianran; Hauenstein, Jonathan D.; Wales, David J.

    2014-09-28

    One of the most challenging and frequently arising problems in many areas of science is to find solutions of a system of multivariate nonlinear equations. There are several numerical methods that can find many (or all if the system is small enough) solutions but they all exhibit characteristic problems. Moreover, traditional methods can break down if the system contains singular solutions. Here, we propose an efficient implementation of Newton homotopies, which can sample a large number of the stationary points of complicated many-body potentials. We demonstrate how the procedure works by applying it to the nearest-neighbor ϕ{sup 4} model and atomic clusters.

  7. An Approximate Newton Method for Coupled Nonlinear Systems.

    DTIC Science & Technology

    1984-02-01

    ANM that, at the solution zo, d, = -(Nt - Nv) - 1N.S, d,= -1- (No - N.v)-N.t. Combining these results gives the following: Lamna Ui. At the solution z...most cases is much less than 1. Therefore, to simplify the analysis, we shall take c 0 from now on. This assumption should have a relatively minor

  8. Newton Methods for Large Scale Problems in Machine Learning

    ERIC Educational Resources Information Center

    Hansen, Samantha Leigh

    2014-01-01

    The focus of this thesis is on practical ways of designing optimization algorithms for minimizing large-scale nonlinear functions with applications in machine learning. Chapter 1 introduces the overarching ideas in the thesis. Chapters 2 and 3 are geared towards supervised machine learning applications that involve minimizing a sum of loss…

  9. Newton's Method and the Wada Property: A Graphical Approach

    ERIC Educational Resources Information Center

    Frame, Michael; Neger, Nial

    2007-01-01

    Imagine trying to paint a picture with three colors--say red, blue, and yellow--with a blue region between any red and yellow regions, a red region between any blue and yellow regions, and a yellow region between any red and blue regions, down to infinitely fine details. Regions arranged in this way satisfy what is called the Wada property. At…

  10. Multiscale Optimization of a Truncated Newton Minimization Algorithm and Application to Proteins and Protein-Ligand Complexes.

    PubMed

    Zhu, Kai; Shirts, Michael R; Friesner, Richard A; Jacobson, Matthew P

    2007-03-01

    We optimize a truncated Newton (TN) minimization algorithm and computer package, TNPACK, developed for macromolecular minimizations by applying multiscale methods, analogous to those used in molecular dynamics (e.g., r-RESPA). The molecular mechanics forces are divided into short- and long-range components, with the long-range forces updated only intermittently in the iterative evaluations. This algorithm, which we refer to as MSTN, is implemented as a modification to the TNPACK package and is tested on energy minimizations of protein loops, entire proteins, and protein-ligand complexes and compared with the unmodified truncated Newton algorithm, a quasi-Newton algorithm (LBFGS), and a conjugate gradient algorithm (CG+). In vacuum minimizations, the speedup of MSTN relative to the unmodified TN algorithm (TNPACK) depends on system size and the distance cutoffs used for defining the short- and long-range interactions and the long-range force updating frequency, but it is 4 to 5 times greater in the work reported here. This algorithm works best for the minimization of small portions of a protein and shows some degradation (speedup factor of 2-3) for the minimization of entire proteins. The MSTN algorithm is faster than the quasi-Newton and conjugate gradient algorithms by approximately 1 order of magnitude. We also present a modification of the algorithm which permits minimizations with a generalized Born implicit solvent model, using a self-consistent procedure that increases the computational expense, relative to a vacuum, by only a small factor (∼3-4).

  11. Symmetric smoothing filters from global consistency constraints.

    PubMed

    Haque, Sheikh Mohammadul; Pai, Gautam P; Govindu, Venu Madhav

    2015-05-01

    Many patch-based image denoising methods can be viewed as data-dependent smoothing filters that carry out a weighted averaging of similar pixels. It has recently been argued that these averaging filters can be improved using their doubly stochastic approximation, which are symmetric and stable smoothing operators. In this paper, we introduce a simple principle of consistency that argues that the relative similarities between pixels as imputed by the averaging matrix should be preserved in the filtered output. The resultant consistency filter has the theoretically desirable properties of being symmetric and stable, and is a generalized doubly stochastic matrix. In addition, we can also interpret our consistency filter as a specific form of Laplacian regularization. Thus, our approach unifies two strands of image denoising methods, i.e., symmetric smoothing filters and spectral graph theory. Our consistency filter provides high-quality image denoising and significantly outperforms the doubly stochastic version. We present a thorough analysis of the properties of our proposed consistency filter and compare its performance with that of other significant methods for image denoising in the literature.

  12. Assessment and Learning of Qualitative Physics in Newton's Playground

    ERIC Educational Resources Information Center

    Shute, Valerie J.; Ventura, Matthew; Kim, Yoon Jeon

    2013-01-01

    Digital games are very popular in modern culture. The authors are examining ways to leverage these engaging environments to assess and support student competencies. The authors examine gameplay and learning using a physics game they developed called Newton's Playground. The sample consisted of 167 eighth- and ninth-grade students who played…

  13. Telecommunications Handbook: Connecting to NEWTON. Version 1.4.

    ERIC Educational Resources Information Center

    Baker, Christopher; And Others

    This handbook was written for use with the Argonne National Laboratory's electronic bulletin board system (BBS) called NEWTON, which is designed to create an electronic network that will link scientists, teachers, and students with the many diversified resources of the Argonne National Laboratory. The link to Argonne will include such resources as…

  14. James Newton Howard: JAMs with TRI-M.

    ERIC Educational Resources Information Center

    Reninger, Rosemary D.

    2000-01-01

    Presents an interview with James Newton Howard, a film composer. Provides background information on Howard. Addresses topics such as his most challenging and rewarding scores, his musical background, and the benefits of being associated with the American Society of Composers, Authors, and Publishers (ASCAP). (CMK)

  15. Newton Minow's Global View: Television and the National Interest.

    ERIC Educational Resources Information Center

    Curtin, Michael

    Newton Minow, chair of the Federal Communications Commission (FCC) during John Kennedy's presidency, considered his plan for the organization of international television--one that gave a new priority to broadcasting without fundamentally altering the legal framework of regulation--as one of the major accomplishments of his tenure. Yet historians…

  16. Snowboard Jumping, Newton's Second Law and the Force on Landing

    ERIC Educational Resources Information Center

    O'Shea, Michael J.

    2004-01-01

    An application of Newton's second law to a snowboarder dropping off a vertical ledge shows that the average normal force during landing (force exerted by the ground on the snowboarder) is determined by four factors. It is shown that the flexing of the legs, the softness of the snow, the angle of the landing surface and the forward motion of the…

  17. Newton's Apple: 15th Season. Free Educational Materials.

    ERIC Educational Resources Information Center

    Twin Cities Public Television, St. Paul, MN.

    This guide helps teachers use the 15th season of the television program "Newton's Apple" in the classroom and lists show segments on asthma, car engines, glacier climbing, glass blowing, glaucoma, gliders, gold mine, greenhouse effect, kids on Mars, lightning, "Lost World" dinosaurs, mammoth dig, NASA robots, Novocain (TM),…

  18. Demonstrating Kinematics and Newton's Laws in a Jump

    ERIC Educational Resources Information Center

    Kamela, Martin

    2007-01-01

    When students begin the study of Newton's laws they are generally comfortable with static equilibrium type problems, but dynamic examples where forces are not constant are more challenging. The class exercise presented here helps students to develop an intuitive grasp of both the position-velocity-acceleration relation and the force-acceleration…

  19. Dramatic (and Simple!) Demonstration of Newton's Third Law

    ERIC Educational Resources Information Center

    Feldman, Gerald

    2011-01-01

    An operational understanding of Newton's third law is often elusive for students. Typical examples of this concept are given for contact forces that are closer to the students' everyday experience. While this is a good thing in general, the reaction force can sometimes be taken for granted, and the students can miss the opportunity to really think…

  20. Newton's Laws, Euler's Laws and the Speed of Light

    ERIC Educational Resources Information Center

    Whitaker, Stephen

    2009-01-01

    Chemical engineering students begin their studies of mechanics in a department of physics where they are introduced to the mechanics of Newton. The approach presented by physicists differs in both perspective and substance from that encountered in chemical engineering courses where Euler's laws provide the foundation for studies of fluid and solid…

  1. Gamow on Newton: Another Look at Centripetal Acceleration

    ERIC Educational Resources Information Center

    Corrao, Christian

    2012-01-01

    Presented here is an adaptation of George Gamow's derivation of the centripetal acceleration formula as it applies to Earth's orbiting Moon. The derivation appears in Gamows short but engaging book "Gravity", first published in 1962, and is essentially a distillation of Newton's work. While "TPT" contributors have offered several insightful…

  2. A Magnetic Set-Up to Help Teach Newton's Laws

    ERIC Educational Resources Information Center

    Panijpan, Bhinyo; Sujarittham, Thanida; Arayathanitkul, Kwan; Tanamatayarat, Jintawat; Nopparatjamjomras, Suchai

    2009-01-01

    A set-up comprising a magnetic disc, a solenoid and a mechanical balance was used to teach first-year physics students Newton's third law with the help of a free body diagram. The image of a floating magnet immobilized by the solenoid's repulsive force should help dispel a common misconception of students as regards the first law: that stationary…

  3. Newton Algorithms for Analytic Rotation: An Implicit Function Approach

    ERIC Educational Resources Information Center

    Boik, Robert J.

    2008-01-01

    In this paper implicit function-based parameterizations for orthogonal and oblique rotation matrices are proposed. The parameterizations are used to construct Newton algorithms for minimizing differentiable rotation criteria applied to "m" factors and "p" variables. The speed of the new algorithms is compared to that of existing algorithms and to…

  4. Can Newton's Third Law Be "Derived" from the Second?

    NASA Astrophysics Data System (ADS)

    Gangopadhyaya, Asim; Harrington, James

    2017-04-01

    Newton's laws have engendered much discussion over several centuries. Today, the internet is awash with a plethora of information on this topic. We find many references to Newton's laws, often discussions of various types of misunderstandings and ways to explain them. Here we present an intriguing example that shows an assumption hidden in Newton's third law that is often overlooked. As is well known, the first law defines an inertial frame of reference and the second law determines the acceleration of a particle in such a frame due to an external force. The third law describes forces exerted on each other in a two-particle system, and allows us to extend the second law to a system of particles. Students are often taught that the three laws are independent. Here we present an example that challenges this assumption. At first glance, it seems to show that, at least for a special case, the third law follows from the second law. However, a careful examination of the assumptions demonstrates that is not quite the case. Ultimately, the example does illustrate the significance of the concept of mass in linking Newton's dynamical principles.

  5. Proving Newton Right or Wrong with Blur Photography

    ERIC Educational Resources Information Center

    Davidhazy, Andrew

    2012-01-01

    Sir Isaac Newton determined that the acceleration constant for gravity was 32 ft./per/sec/sec. This is a fact that most students become familiar with over time and through various means. This article describes how this can be demonstrated in a technology classroom using simple photographic equipment. (Contains 5 figures.)

  6. Newton's Apple 13th Season. Free Educational Materials.

    ERIC Educational Resources Information Center

    Twin Cities Public Television, St. Paul, MN.

    This educational materials packet was designed to help teachers use the Public Broadcasting Service's (PBS) program called "Newton's Apple" in the classroom. This book contains information on how these materials support the latest science standards; an index to the 13th season lesson pages and an index to the past three seasons; a…

  7. Newton's Radii, Maupertuis' Arc Length, and Voltaire's Giant

    ERIC Educational Resources Information Center

    Simoson, Andrew J.

    2011-01-01

    Given two arc length measurements along the perimeter of an ellipse--one taken near the long diameter, the other taken anywhere else--how do you find the lengths of major and minor axes? This was a problem of great interest from the time of Newton's "Principia" until the mid-eighteenth century when France launched twin geodesic…

  8. The Cooling Law and the Search for a Good Temperature Scale, from Newton to Dalton

    ERIC Educational Resources Information Center

    Besson, Ugo

    2011-01-01

    The research on the cooling law began with an article by Newton published in 1701. Later, many studies were performed by other scientists confirming or confuting Newton's law. This paper presents a description and an interpretation of Newton's article, provides a short overview of the research conducted on the topic during the 18th century, and…

  9. How Two Differing Portraits of Newton Can Teach Us about the Cultural Context of Science

    ERIC Educational Resources Information Center

    Tucci, Pasquale

    2015-01-01

    Like several scientists, Isaac Newton has been represented many times over many different periods, and portraits of Newton were often commissioned by the scientist himself. These portraits tell us a lot about the scientist, the artist and the cultural context. This article examines two very different portraits of Newton that were realized more…

  10. Problem in Two Unknowns: Robert Hooke and a Worm in Newton's Apple.

    ERIC Educational Resources Information Center

    Weinstock, Robert

    1992-01-01

    Discusses the place that Robert Hooke has in science history versus the scientific contributions he made. Examines the relationship between Hooke and his contemporary, Isaac Newton, and Hooke's claims that Newton built on his ideas without receiving Newton's recognition. (26 references) (MDH)

  11. Compressive Sensing via Nonlocal Smoothed Rank Function

    PubMed Central

    Fan, Ya-Ru; Liu, Jun; Zhao, Xi-Le

    2016-01-01

    Compressive sensing (CS) theory asserts that we can reconstruct signals and images with only a small number of samples or measurements. Recent works exploiting the nonlocal similarity have led to better results in various CS studies. To better exploit the nonlocal similarity, in this paper, we propose a non-convex smoothed rank function based model for CS image reconstruction. We also propose an efficient alternating minimization method to solve the proposed model, which reduces a difficult and coupled problem to two tractable subproblems. Experimental results have shown that the proposed method performs better than several existing state-of-the-art CS methods for image reconstruction. PMID:27583683

  12. Compressive Sensing via Nonlocal Smoothed Rank Function.

    PubMed

    Fan, Ya-Ru; Huang, Ting-Zhu; Liu, Jun; Zhao, Xi-Le

    2016-01-01

    Compressive sensing (CS) theory asserts that we can reconstruct signals and images with only a small number of samples or measurements. Recent works exploiting the nonlocal similarity have led to better results in various CS studies. To better exploit the nonlocal similarity, in this paper, we propose a non-convex smoothed rank function based model for CS image reconstruction. We also propose an efficient alternating minimization method to solve the proposed model, which reduces a difficult and coupled problem to two tractable subproblems. Experimental results have shown that the proposed method performs better than several existing state-of-the-art CS methods for image reconstruction.

  13. A smoothing algorithm using cubic spline functions

    NASA Technical Reports Server (NTRS)

    Smith, R. E., Jr.; Price, J. M.; Howser, L. M.

    1974-01-01

    Two algorithms are presented for smoothing arbitrary sets of data. They are the explicit variable algorithm and the parametric variable algorithm. The former would be used where large gradients are not encountered because of the smaller amount of calculation required. The latter would be used if the data being smoothed were double valued or experienced large gradients. Both algorithms use a least-squares technique to obtain a cubic spline fit to the data. The advantage of the spline fit is that the first and second derivatives are continuous. This method is best used in an interactive graphics environment so that the junction values for the spline curve can be manipulated to improve the fit.

  14. Young Mid-latitude Martian Valleys: Evidence from Newton and Gorgonum Basins

    NASA Astrophysics Data System (ADS)

    Howard, A. D.; Moore, J. M.

    2009-12-01

    The mid-latitudes of Mars feature distinctive landforms, including extensive mantling deposits, glacial and periglacial landforms, very young gullies on steep slopes, and sparse, shallowly-incised, fresh-appearing valleys discussed here. These mid-latitude valleys (MLVs) are distinct from the older, late Noachian to early Hesperian valley systems which are deeply dissected, generally of much larger spatial extent and which feature multiple tributaries. The older valley systems extend from equatorial to near-polar latitudes and are much more degraded than the MLVs. Although some MLVs involve rejuvenation of older valley networks, many MLVs are eroded into smooth or rolling slopes and intercrater terrain. The MLVs range from a few meters to more than 300 m in width, with nearly parallel valley walls and planforms that are locally sinuous. Valley floors appear to be nearly flat, sometimes exhibiting faint lineations. These features suggest that the MLVs in many cases are incised channels that were occupied at least intermittently by flows over the entire valley bottom. Particularly diagnostic MLVs occupy parts of the floors of the ~ 300 km Newton and the ~240 km Gorgonum basins on the southern highlands. In Newton basin the MLVs are sourced from the upper basin walls and flow radially inwards towards the basin center, extending across the smooth basin floor (which may have been the site of an earlier paleolake). Incised and depositional sections sometimes alternate in response to variations in basin slope. The valleys terminate in small fans. In some places the valleys appear to anastomose, but it is likely that the multiple valleys record successive flow diversions. There is no evidence that the valleys terminated in standing water in the basin center. MLVs in Gorgonum basin likewise are sourced from the upper basin walls and flow inward, but in this case the valleys disappear at the edge of what has previously been hypothesized to be a late stage, ice-covered lake

  15. Newton's laws of motion in the form of a Riccati equation.

    PubMed

    Nowakowski, Marek; Rosu, Haret C

    2002-04-01

    We discuss two applications of a Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential V(r)=kr(epsilon). For zero total energy we show that the equation of motion can be cast in the Riccati form. We briefly show here an analogy to barotropic Friedmann-Robertson-Lemaitre cosmology where the expansion of the universe can be also shown to obey a Riccati equation. A second application in classical mechanics, where again the Riccati equation appears naturally, are problems involving quadratic friction. We use methods reminiscent to nonrelativistic supersymmetry to generalize and solve such problems.

  16. Special features of Newton-type fringe formation in a diffraction interferometer

    SciTech Connect

    Koronkevich, Voldemar P.; Lenkova, Galina A.; Matochkin, Aleksey E

    2006-01-01

    An interferometer with a Fresnel zone plate located in the center of curvature of a concave mirror was studied. Attention was paid to the unique features of the interference field, which has a special point at which the path difference is equal to zero, thereby allowing for the observation of Newton-type fringes in white and quasi-monochromatic light. The conditions necessary for reducing the instrumental error to values less than lambda/20 were determined. Methods for suppressing noise and destructive interference patterns were also found. Metrological tests were carried out, and they proved the possibility of using this interferometer for industrial testing of spherical and parabolic mirrors.

  17. Adaptive quasi-Newton algorithm for source extraction via CCA approach.

    PubMed

    Zhang, Wei-Tao; Lou, Shun-Tian; Feng, Da-Zheng

    2014-04-01

    This paper addresses the problem of adaptive source extraction via the canonical correlation analysis (CCA) approach. Based on Liu's analysis of CCA approach, we propose a new criterion for source extraction, which is proved to be equivalent to the CCA criterion. Then, a fast and efficient online algorithm using quasi-Newton iteration is developed. The stability of the algorithm is also analyzed using Lyapunov's method, which shows that the proposed algorithm asymptotically converges to the global minimum of the criterion. Simulation results are presented to prove our theoretical analysis and demonstrate the merits of the proposed algorithm in terms of convergence speed and successful rate for source extraction.

  18. Income Smoothing: Methodology and Models.

    DTIC Science & Technology

    1986-05-01

    that managers desire a pattern % of income that has low variability relative to a linear time trend. 2. Industry Trend. Target 2 assumes that firms...R167 55? INCOME SMOOTHING: METHODOLOGY ND NODELS(U) UMVL in1POSTGRADUATE SCHOOL MONTEREY CA 0 D HOSES "AY S6 UNCLASSIFIED NP5-604FO53 E * I* vu...California oCiD ELEC fl MAY 12 986 INCOME SMOOTHING - METHODOLOGY AND MODELS by 0. Douglas Moses May 1986 *Approved frpublic release; ditibto uniie

  19. Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD

    NASA Technical Reports Server (NTRS)

    Gropp, W. D.; Keyes, D. E.; McInnes, L. C.; Tidriri, M. D.

    1998-01-01

    Implicit solution methods are important in applications modeled by PDEs with disparate temporal and spatial scales. Because such applications require high resolution with reasonable turnaround, "routine" parallelization is essential. The pseudo-transient matrix-free Newton-Krylov-Schwarz (Psi-NKS) algorithmic framework is presented as an answer. We show that, for the classical problem of three-dimensional transonic Euler flow about an M6 wing, Psi-NKS can simultaneously deliver: globalized, asymptotically rapid convergence through adaptive pseudo- transient continuation and Newton's method-, reasonable parallelizability for an implicit method through deferred synchronization and favorable communication-to-computation scaling in the Krylov linear solver; and high per- processor performance through attention to distributed memory and cache locality, especially through the Schwarz preconditioner. Two discouraging features of Psi-NKS methods are their sensitivity to the coding of the underlying PDE discretization and the large number of parameters that must be selected to govern convergence. We therefore distill several recommendations from our experience and from our reading of the literature on various algorithmic components of Psi-NKS, and we describe a freely available, MPI-based portable parallel software implementation of the solver employed here.

  20. Globalized Newton-Krylov-Schwarz algorithms and software for parallel implicit CFD.

    SciTech Connect

    Gropp, W. D.; Keyes, D. E.; McInnes, L. C.; Tidriri, M. D.; Mathematics and Computer Science; Old Dominion Univ.; Iowa State Univ.

    2000-01-01

    Implicit solution methods are important in applications modeled by PDEs with disparate temporal and spatial scales. Because such applications require high resolution with reasonable turnaround, parallelization is essential. The pseudo-transient matrix-free Newton-Krylov-Schwarz ({psi}NKS) algorithmic framework is presented as a widely applicable answer. This article shows that for the classical problem of three-dimensional transonic Euler flow about an M6 wing, {psi}NKS can simultaneously deliver globalized, asymptotically rapid convergence through adaptive pseudo-transient continuation and Newton's method; reasonable parallelizability for an implicit method through deferred synchronization and favorable communication-to-computation scaling in the Krylov linear solver; and high per processor performance through attention to distributed memory and cache locality, especially through the Schwarz preconditioner. Two discouraging features of {psi}NKS methods are their sensitivity to the coding of the underlying PDE discretization and the large number of parameters that must be selected to govern convergence. The authors therefore distill several recommendations from their experience and reading of the literature on various algorithmic components of {psi}NKS, and they describe a freely available MPI-based portable parallel software implementation of the solver employed here.

  1. A Parallel Newton-Krylov-Schur Algorithm for the Reynolds-Averaged Navier-Stokes Equations

    NASA Astrophysics Data System (ADS)

    Osusky, Michal

    Aerodynamic shape optimization and multidisciplinary optimization algorithms have the potential not only to improve conventional aircraft, but also to enable the design of novel configurations. By their very nature, these algorithms generate and analyze a large number of unique shapes, resulting in high computational costs. In order to improve their efficiency and enable their use in the early stages of the design process, a fast and robust flow solution algorithm is necessary. This thesis presents an efficient parallel Newton-Krylov-Schur flow solution algorithm for the three-dimensional Navier-Stokes equations coupled with the Spalart-Allmaras one-equation turbulence model. The algorithm employs second-order summation-by-parts (SBP) operators on multi-block structured grids with simultaneous approximation terms (SATs) to enforce block interface coupling and boundary conditions. The discrete equations are solved iteratively with an inexact-Newton method, while the linear system at each Newton iteration is solved using the flexible Krylov subspace iterative method GMRES with an approximate-Schur parallel preconditioner. The algorithm is thoroughly verified and validated, highlighting the correspondence of the current algorithm with several established flow solvers. The solution for a transonic flow over a wing on a mesh of medium density (15 million nodes) shows good agreement with experimental results. Using 128 processors, deep convergence is obtained in under 90 minutes. The solution of transonic flow over the Common Research Model wing-body geometry with grids with up to 150 million nodes exhibits the expected grid convergence behavior. This case was completed as part of the Fifth AIAA Drag Prediction Workshop, with the algorithm producing solutions that compare favourably with several widely used flow solvers. The algorithm is shown to scale well on over 6000 processors. The results demonstrate the effectiveness of the SBP-SAT spatial discretization, which can

  2. SMACK - SMOOTHING FOR AIRCRAFT KINEMATICS

    NASA Technical Reports Server (NTRS)

    Bach, R.

    1994-01-01

    The computer program SMACK (SMoothing for AirCraft Kinematics) is designed to provide flightpath reconstruction of aircraft forces and motions from measurements that are noisy or incomplete. Additionally, SMACK provides a check on instrument accuracy and data consistency. The program can be used to analyze data from flight-test experiments prior to their use in performance, stability and control, or aerodynamic modeling calculations. It can also be used in the analysis of aircraft accidents, where the actual forces and motions may have to be determined from a very limited data set. Application of a state-estimation method for flightpath reconstruction is possible because aircraft forces and motions are related by well-known equations of motion. The task of postflight state estimation is known as a nonlinear, fixed-interval smoothing problem. SMACK utilizes a backward-filter, forward-smoother algorithm to solve the problem. The equations of motion are used to produce estimates that are compared with their corresponding measurement time histories. The procedure is iterative, providing improved state estimates until a minimum squared-error measure is achieved. In the SMACK program, the state and measurement models together represent a finite-difference approximation for the six-degree-of-freedom dynamics of a rigid body. The models are used to generate time histories which are likely to be found in a flight-test measurement set. These include onboard variables such as Euler angles, angular rates, and linear accelerations as well as tracking variables such as slant range, bearing, and elevation. Any bias or scale-factor errors associated with the state or measurement models are appended to the state vector and treated as constant but unknown parameters. The SMACK documentation covers the derivation of the solution algorithm, describes the state and measurement models, and presents several application examples that should help the analyst recognize the potential

  3. Smooth local subspace projection for nonlinear noise reduction

    SciTech Connect

    Chelidze, David

    2014-03-15

    Many nonlinear or chaotic time series exhibit an innate broad spectrum, which makes noise reduction difficult. Local projective noise reduction is one of the most effective tools. It is based on proper orthogonal decomposition (POD) and works for both map-like and continuously sampled time series. However, POD only looks at geometrical or topological properties of data and does not take into account the temporal characteristics of time series. Here, we present a new smooth projective noise reduction method. It uses smooth orthogonal decomposition (SOD) of bundles of reconstructed short-time trajectory strands to identify smooth local subspaces. Restricting trajectories to these subspaces imposes temporal smoothness on the filtered time series. It is shown that SOD-based noise reduction significantly outperforms the POD-based method for continuously sampled noisy time series.

  4. The XXL Survey. I. Scientific motivations - XMM-Newton observing plan - Follow-up observations and simulation programme

    NASA Astrophysics Data System (ADS)

    Pierre, M.; Pacaud, F.; Adami, C.; Alis, S.; Altieri, B.; Baran, N.; Benoist, C.; Birkinshaw, M.; Bongiorno, A.; Bremer, M. N.; Brusa, M.; Butler, A.; Ciliegi, P.; Chiappetti, L.; Clerc, N.; Corasaniti, P. S.; Coupon, J.; De Breuck, C.; Democles, J.; Desai, S.; Delhaize, J.; Devriendt, J.; Dubois, Y.; Eckert, D.; Elyiv, A.; Ettori, S.; Evrard, A.; Faccioli, L.; Farahi, A.; Ferrari, C.; Finet, F.; Fotopoulou, S.; Fourmanoit, N.; Gandhi, P.; Gastaldello, F.; Gastaud, R.; Georgantopoulos, I.; Giles, P.; Guennou, L.; Guglielmo, V.; Horellou, C.; Husband, K.; Huynh, M.; Iovino, A.; Kilbinger, M.; Koulouridis, E.; Lavoie, S.; Le Brun, A. M. C.; Le Fevre, J. P.; Lidman, C.; Lieu, M.; Lin, C. A.; Mantz, A.; Maughan, B. J.; Maurogordato, S.; McCarthy, I. G.; McGee, S.; Melin, J. B.; Melnyk, O.; Menanteau, F.; Novak, M.; Paltani, S.; Plionis, M.; Poggianti, B. M.; Pomarede, D.; Pompei, E.; Ponman, T. J.; Ramos-Ceja, M. E.; Ranalli, P.; Rapetti, D.; Raychaudury, S.; Reiprich, T. H.; Rottgering, H.; Rozo, E.; Rykoff, E.; Sadibekova, T.; Santos, J.; Sauvageot, J. L.; Schimd, C.; Sereno, M.; Smith, G. P.; Smolčić, V.; Snowden, S.; Spergel, D.; Stanford, S.; Surdej, J.; Valageas, P.; Valotti, A.; Valtchanov, I.; Vignali, C.; Willis, J.; Ziparo, F.

    2016-06-01

    Context. The quest for the cosmological parameters that describe our universe continues to motivate the scientific community to undertake very large survey initiatives across the electromagnetic spectrum. Over the past two decades, the Chandra and XMM-Newton observatories have supported numerous studies of X-ray-selected clusters of galaxies, active galactic nuclei (AGNs), and the X-ray background. The present paper is the first in a series reporting results of the XXL-XMM survey; it comes at a time when the Planck mission results are being finalised. Aims: We present the XXL Survey, the largest XMM programme totaling some 6.9 Ms to date and involving an international consortium of roughly 100 members. The XXL Survey covers two extragalactic areas of 25 deg2 each at a point-source sensitivity of ~5 × 10-15 erg s-1 cm-2 in the [0.5-2] keV band (completeness limit). The survey's main goals are to provide constraints on the dark energy equation of state from the space-time distribution of clusters of galaxies and to serve as a pathfinder for future, wide-area X-ray missions. We review science objectives, including cluster studies, AGN evolution, and large-scale structure, that are being conducted with the support of approximately 30 follow-up programmes. Methods: We describe the 542 XMM observations along with the associated multi-λ and numerical simulation programmes. We give a detailed account of the X-ray processing steps and describe innovative tools being developed for the cosmological analysis. Results: The paper provides a thorough evaluation of the X-ray data, including quality controls, photon statistics, exposure and background maps, and sky coverage. Source catalogue construction and multi-λ associations are briefly described. This material will be the basis for the calculation of the cluster and AGN selection functions, critical elements of the cosmological and science analyses. Conclusions: The XXL multi-λ data set will have a unique lasting legacy

  5. Registration of 'Newell' Smooth Bromegrass

    Technology Transfer Automated Retrieval System (TEKTRAN)

    ‘Newell’ (Reg. No. CV-xxxx, PI 671851) smooth bromegrass (Bromus inermis Leyss.) is a steppe or southern type cultivar that is primarily adapted in the USA to areas north of 40o N lat. and east of 100o W long. that have 500 mm or more annual precipitation or in areas that have similar climate cond...

  6. Computer programs for smoothing and scaling airfoil coordinates

    NASA Technical Reports Server (NTRS)

    Morgan, H. L., Jr.

    1983-01-01

    Detailed descriptions are given of the theoretical methods and associated computer codes of a program to smooth and a program to scale arbitrary airfoil coordinates. The smoothing program utilizes both least-squares polynomial and least-squares cubic spline techniques to smooth interatively the second derivatives of the y-axis airfoil coordinates with respect to a transformed x-axis system which unwraps the airfoil and stretches the nose and trailing-edge regions. The corresponding smooth airfoil coordinates are then determined by solving a tridiagonal matrix of simultaneous cubic-spline equations relating the y-axis coordinates and their corresponding second derivatives. A technique for computing the camber and thickness distribution of the smoothed airfoil is also discussed. The scaling program can then be used to scale the thickness distribution generated by the smoothing program to a specific maximum thickness which is then combined with the camber distribution to obtain the final scaled airfoil contour. Computer listings of the smoothing and scaling programs are included.

  7. Calibration and in-orbit performance of the reflection grating spectrometer onboard XMM-Newton

    NASA Astrophysics Data System (ADS)

    de Vries, C. P.; den Herder, J. W.; Gabriel, C.; Gonzalez-Riestra, R.; Ibarra, A.; Kaastra, J. S.; Pollock, A. M. T.; Raassen, A. J. J.; Paerels, F. B. S.

    2015-01-01

    Context. XMM-Newton was launched on 10 December 1999 and has been operational since early 2000. One of the instruments onboard XMM-Newton is the reflection grating spectrometer (RGS). Two identical RGS instruments are available, with each RGS combining a reflection grating assembly and a camera with charge-coupled devices to record the spectra. Aims: We describe the calibration and in-orbit performance of the RGS instrument. By combining the preflight calibration with appropriate inflight calibration data including the changes in detector performance over time, we aim at profound knowledge about the accuracy in the calibration. This will be crucial for any correct scientific interpretation of spectral features for a wide variety of objects. Methods: Ground calibrations alone are not able to fully characterize the instrument. Dedicated inflight measurements and constant monitoring are essential for a full understanding of the instrument and the variations of the instrument response over time. Physical models of the instrument are tuned to agree with calibration measurements and are the basis from which the actual instrument response can be interpolated over the full parameter space. Results: Uncertainties in the instrument response have been reduced to <10% for the effective area and <6 mÅ for the wavelength scale (in the range from 8 Å to 34 Å). The remaining systematic uncertainty in the detection of weak absorption features has been estimated to be 1.5%. Conclusions: Based on a large set of inflight calibration data and comparison with other instruments onboard XMM-Newton, the calibration accuracy of the RGS instrument has been improved considerably over the preflight calibrations.

  8. NEW APPROACHES: Newton's laws and conservation of mass

    NASA Astrophysics Data System (ADS)

    Puri, Avinash

    1996-07-01

    In an exposition of Newton's second law, F = dp/dt is commonly viewed as the fundamental relation and the equation F = ma as a mere special case when m is constant, it being implied that, when analysing bodies with a variable mass, some fuller machinery contained in F = dp/dt is needed. Paradoxically, one is also likely to be told that the conservation of mass of a body is a presupposition in Newtonian theory, or again, that it is a consequence of his laws. The following note is an attempt at sorting out the mess that ensues: it examines some of the logical interlinks between Newton's laws of motion, mass conservation and the notion of a 'body'.

  9. Gullies and Layers in Crater Wall in Newton

    NASA Technical Reports Server (NTRS)

    2002-01-01

    This dramatic view of gullies emergent from layered outcrops occurs on the wall of a crater within the much larger impact basin, Newton. Newton Crater and its surrounding terrain exhibit many examples of gullies on the walls of craters and troughs. The gullies exhibit meandering channels with fan-shaped aprons of debris located downslope. The gullies are considered to have been formed by erosion--both from a fluid (such as water) running downslope, and by slumping and landsliding processes driven by the force of gravity. This picture was obtained by the Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) in March 2001; it is illuminated from the upper left and covers an area 3 km (1.9 mi) across.

  10. Torsional Newton-Cartan geometry from the Noether procedure

    NASA Astrophysics Data System (ADS)

    Festuccia, Guido; Hansen, Dennis; Hartong, Jelle; Obers, Niels A.

    2016-11-01

    We apply the Noether procedure for gauging space-time symmetries to theories with Galilean symmetries, analyzing both massless and massive (Bargmann) realizations. It is shown that at the linearized level the Noether procedure gives rise to (linearized) torsional Newton-Cartan geometry. In the case of Bargmann theories the Newton-Cartan form Mμ couples to the conserved mass current. We show that even in the case of theories with massless Galilean symmetries it is necessary to introduce the form Mμ and that it couples to a topological current. Further, we show that the Noether procedure naturally gives rise to a distinguished affine (Christoffel type) connection that is linear in Mμ and torsionful. As an application of these techniques we study the coupling of Galilean electrodynamics to TNC geometry at the linearized level.

  11. On Newton's third law and its symmetry-breaking effects

    NASA Astrophysics Data System (ADS)

    Pinheiro, Mario J.

    2011-11-01

    The law of action-reaction, considered by Ernst Mach as the cornerstone of physics, is thoroughly used to derive the conservation laws of linear and angular momentum. However, the conflict between momentum conservation law and Newton's third law, on experimental and theoretical grounds, calls for more attention. We give a background survey of several questions raised by the action-reaction law and, in particular, the role of the physical vacuum is shown to provide an appropriate framework for clarifying the occurrence of possible violations of the action-reaction law. Then, in the framework of statistical mechanics, using a maximizing entropy procedure, we obtain an expression for the general linear momentum of a body particle. The new approach presented here shows that Newton's third law is not verified in systems out of equilibrium due to an additional entropic gradient term present in the particle's momentum.

  12. Smooth Vibrotactile Flow Generation Using Two Piezoelectric Actuators.

    PubMed

    Jeonggoo Kang; Jongsuh Lee; Heewon Kim; Kwangsu Cho; Semyung Wang; Jeha Ryu

    2012-01-01

    This paper proposes a method for generating a smooth directional vibrotactile flow on a thin plate. While actuating two piezoelectric actuators spatially across the plate, temporal sweeping of the input excitation frequency from zero to the first mode of the resonance frequency can smooth the perceived directional vibrotactile flow, as compared to a vibrotactile flow generated by conventional apparent tactile movement and phantom sensation methods. In order to ascertain important factors in the excitation pattern, a user study was conducted for three factors (amplitude (constant versus modulated), frequency (constant versus swept), and ending shape (sharp versus smooth)). The results showed that frequency sweeping in addition to amplitude modulation and smooth ending were the most important factors in smoothing vibrotactile flows. Moreover, an excitation signal with a smooth ending shape was important for generating nonspiky flows at the midpoint. In this study, a vibration isolation design is also proposed in order to substantially decrease the transmission of the actuator vibration to the mockup housing. As such, it is expected that the proposed vibrotactile flow generation method and vibration isolation design may be useful in applications including generating directional information in navigation maps or for identifying callers in mobile devices.

  13. The Architecture of Newton, a General-Purpose Dynamics Simulator

    DTIC Science & Technology

    1989-01-01

    11 N The Architecture of Newton, a General-Purpose Dynamics 0 Simulator OTIC James F. Cremer ELECTE A. James Stewart JUL 141989f l Computer Science...173SS, ONR grant N00t4.SK-0281 and DARPA grant N0014-OOK.0S91 Support for James Stewart is provided in part by U.S. Army Math-4.3 Control matica Sciences

  14. Implementing WebQuest Based Instruction on Newton's Second Law

    ERIC Educational Resources Information Center

    Gokalp, Muhammed Sait; Sharma, Manjula; Johnston, Ian; Sharma, Mia

    2013-01-01

    The purpose of this study was to investigate how WebQuests can be used in physics classes for teaching specific concepts. The study had three stages. The first stage was to develop a WebQuest on Newton's second law. The second stage involved developing a lesson plan to implement the WebQuest in class. In the final stage, the WebQuest was…

  15. Derivation of special relativity from Maxwell and Newton.

    PubMed

    Dunstan, D J

    2008-05-28

    Special relativity derives directly from the principle of relativity and from Newton's laws of motion with a single undetermined parameter, which is found from Faraday's and Ampère's experimental work and from Maxwell's own introduction of the displacement current to be the -c(-2) term in the Lorentz transformations. The axiom of the constancy of the speed of light is quite unnecessary. The behaviour and the mechanism of the propagation of light are not at the foundations of special relativity.

  16. SAS: Science Analysis System for XMM-Newton observatory

    NASA Astrophysics Data System (ADS)

    SAS development Team

    2014-04-01

    The Science Analysis System (SAS) is an extensive suite of software tasks developed to process the data collected by the XMM-Newton Observatory. The SAS extracts standard (spectra, light curves) and/or customized science products, and allows reproductions of the reduction pipelines run to get the PPS products from the ODFs files. SAS includes a powerful and extensive suite of FITS file manipulation packages based on the Data Access Layer library.

  17. When Newton's cooling law doesn't hold

    SciTech Connect

    Tarnow, E. )

    1994-01-01

    What is the fastest way to cool something If the object is macroscopic it is to lower the surrounding temperature as much as possible and let Newton's cooling law take effect. If we enter the microscopic world where quantum mechanics rules, this procedure may no longer be the best. This is shown in a simple example where we calculate the optimum cooling rate for an asymmetric two-state system.

  18. XMM-Newton, powerful AGN winds and galaxy feedback

    NASA Astrophysics Data System (ADS)

    Pounds, K.; King, A.

    2016-06-01

    The discovery that ultra-fast ionized winds - sufficiently powerful to disrupt growth of the host galaxy - are a common feature of luminous AGN is major scientific breakthrough led by XMM-Newton. An extended observation in 2014 of the prototype UFO, PG1211+143, has revealed an unusually complex outflow, with distinct and persisting velocities detected in both hard and soft X-ray spectra. While the general properties of UFOs are consistent with being launched - at the local escape velocity - from the inner disc where the accretion rate is modestly super-Eddington (King and Pounds, Ann Rev Astron Astro- phys 2015), these more complex flows have raised questions about the outflow geometry and the importance of shocks and enhanced cooling. XMM-Newton seems likely to remain the best Observatory to study UFOs prior to Athena, and further extended observations, of PG1211+143 and other bright AGN, have the exciting potential to establish the typical wind dynamics, while providing new insights on the accretion geometry and continuum source structure. An emphasis on such large, coordinated observing programmes with XMM-Newton over the next decade will continue the successful philosophy pioneered by EXOSAT, while helping to inform the optimum planning for Athena

  19. Deviations from Newton's law in supersymmetric large extra dimensions

    NASA Astrophysics Data System (ADS)

    Callin, P.; Burgess, C. P.

    2006-09-01

    Deviations from Newton's inverse-squared law at the micron length scale are smoking-gun signals for models containing supersymmetric large extra dimensions (SLEDs), which have been proposed as approaches for resolving the cosmological constant problem. Just like their non-supersymmetric counterparts, SLED models predict gravity to deviate from the inverse-square law because of the advent of new dimensions at sub-millimeter scales. However SLED models differ from their non-supersymmetric counterparts in three important ways: (i) the size of the extra dimensions is fixed by the observed value of the dark energy density, making it impossible to shorten the range over which new deviations from Newton's law must be seen; (ii) supersymmetry predicts there to be more fields in the extra dimensions than just gravity, implying different types of couplings to matter and the possibility of repulsive as well as attractive interactions; and (iii) the same mechanism which is purported to keep the cosmological constant naturally small also keeps the extra-dimensional moduli effectively massless, leading to deviations from general relativity in the far infrared of the scalar-tensor form. We here explore the deviations from Newton's law which are predicted over micron distances, and show the ways in which they differ and resemble those in the non-supersymmetric case.

  20. INTEGRAL and XMM-Newton Spectral Studies of NGC 4388

    NASA Technical Reports Server (NTRS)

    Beckmann, V.; Gehrels, N.; Favre, P.; Walter, R.; Courvoisier, T. J.-L.; Petrucci, P.-O.; Malzac, J.

    2004-01-01

    We present first INTEGRAL and XMM-Newton observations of a Seyfert galaxy, the type 2 AGN NGC 4388. Several INTEGRAL observations performed in 2003 allow us to study the spectrum in the 20 - 300 keV range. In addition two XMM-Newton observations give detailed insight into the 0.2 - 10 keV emission. Comparison with previous observations by BeppoSAX, SIGMA and CGRO/OSSE show that the overall spectrum for soft X-rays up to the gamma-rays can be described by a highly absorbed (N(sub H approx. = 2.7 x 10(exp 23)/sq cm) and variable non-thermal component in addition to constant non-absorbed thermal emission (T approx. = 0.8 keV) of low abundance (Z approx. 5% Z (solar)), plus a constant Fe K a line. The hard X-ray component is well described by a simple power law with a mean photon index of Gamma = 1.7. During the INTEGRAL observations the flux at 100 keV increased by a factor of 1.5. The analysis of XMM-Newton data implies that the emission below 3 keV is decoupled from the AGN and probably due to extended emission as seen in Chandra observations. The constant iron line emission is apparently also decoupled from the direct emission of the central engine and likely to be generated in the obscuring material, e.g. in the molecular torus.