A Non-smooth Newton Method for Multibody Dynamics
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.
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…
Fractal aspects and convergence of Newton`s method
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.
[Isaac Newton's Anguli Contactus method].
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.
[Isaac Newton's Anguli Contactus method].
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. PMID:25033525
Subsampled Hessian Newton Methods for Supervised Learning.
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.
A combined modification of Newton`s method for systems of nonlinear equations
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.
Spatial Interpolation Methods for Integrating Newton's Equation
NASA Astrophysics Data System (ADS)
Gueron, Shay; Shalloway, David
1996-11-01
Numerical integration of Newton's equation in multiple dimensions plays an important role in many fields such as biochemistry and astrophysics. Currently, some of the most important practical questions in these areas cannot be addressed because the large dimensionality of the variable space and complexity of the required force evaluations precludes integration over sufficiently large time intervals. Improving the efficiency of algorithms for this purpose is therefore of great importance. Standard numerical integration schemes (e.g., leap-frog and Runge-Kutta) ignore the special structure of Newton's equation that, for conservative systems, constrains the force to be the gradient of a scalar potential. We propose a new class of "spatial interpolation" (SI) integrators that exploit this property by interpolating the force in space rather than (as with standard methods) in time. Since the force is usually a smoother function of space than of time, this can improve algorithmic efficiency and accuracy. In particular, an SI integrator solves the one- and two-dimensional harmonic oscillators exactly with one force evaluation per step. A simple type of time-reversible SI algorithm is described and tested. Significantly improved performance is achieved on one- and multi-dimensional benchmark problems.
Newton-Krylov methods applied to nonequilibrium radiation diffusion
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.
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...
Newton-Krylov-Schwarz methods in unstructured grid Euler flow
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.
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.
Low-rank Quasi-Newton updates for Robust Jacobian lagging in Newton methods
Brown, J.; Brune, P.
2013-07-01
Newton-Krylov methods are standard tools for solving nonlinear problems. A common approach is to 'lag' the Jacobian when assembly or preconditioner setup is computationally expensive, in exchange for some degradation in the convergence rate and robustness. We show that this degradation may be partially mitigated by using the lagged Jacobian as an initial operator in a quasi-Newton method, which applies unassembled low-rank updates to the Jacobian until the next full reassembly. We demonstrate the effectiveness of this technique on problems in glaciology and elasticity. (authors)
Choosing the forcing terms in an inexact Newton method
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.
An improved generalized Newton method for absolute value equations.
Feng, Jingmei; Liu, Sanyang
2016-01-01
In this paper, we suggest and analyze an improved generalized Newton method for solving the NP-hard absolute value equations [Formula: see text] when the singular values of A exceed 1. We show that the global and local quadratic convergence of the proposed method. Numerical experiments show the efficiency of the method and the high accuracy of calculation. PMID:27462490
Implicit Newton-Krylov methods for modeling blast furnace stoves
Howse, J.W.; Hansen, G.A.; Cagliostro, D.J.; Muske, K.R.
1998-03-01
In this paper the authors discuss the use of an implicit Newton-Krylov method to solve a set of partial differential equations representing a physical model of a blast furnace stove. The blast furnace stove is an integral part of the iron making process in the steel industry. These stoves are used to heat air which is then used in the blast furnace to chemically reduce iron ore to iron metal. The solution technique used to solve the discrete representations of the model and control PDE`s must be robust to linear systems with disparate eigenvalues, and must converge rapidly without using tuning parameters. The disparity in eigenvalues is created by the different time scales for convection in the gas, and conduction in the brick; combined with a difference between the scaling of the model and control PDE`s. A preconditioned implicit Newton-Krylov solution technique was employed. The procedure employs Newton`s method, where the update to the current solution at each stage is computed by solving a linear system. This linear system is obtained by linearizing the discrete approximation to the PDE`s, using a numerical approximation for the Jacobian of the discretized system. This linear system is then solved for the needed update using a preconditioned Krylov subspace projection method.
Global convergence of inexact Newton methods for transonic flow
NASA Technical Reports Server (NTRS)
Young, David P.; Melvin, Robin G.; Bieterman, Michael B.; Johnson, Forrester T.; Samant, Satish S.
1990-01-01
In computational fluid dynamics, nonlinear differential equations are essential to represent important effects such as shock waves in transonic flow. Discretized versions of these nonlinear equations are solved using iterative methods. In this paper an inexact Newton method using the GMRES algorithm of Saad and Schultz is examined in the context of the full potential equation of aerodynamics. In this setting, reliable and efficient convergence of Newton methods is difficult to achieve. A poor initial solution guess often leads to divergence or very slow convergence. This paper examines several possible solutions to these problems, including a standard local damping strategy for Newton's method and two continuation methods, one of which utilizes interpolation from a coarse grid solution to obtain the initial guess on a finer grid. It is shown that the continuation methods can be used to augment the local damping strategy to achieve convergence for difficult transonic flow problems. These include simple wings with shock waves as well as problems involving engine power effects. These latter cases are modeled using the assumption that each exhaust plume is isentropic but has a different total pressure and/or temperature than the freestream.
Newton's method for large bound-constrained optimization problems.
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.
Newton's method with a model trust-region modification
Sorensen, D C
1980-09-01
A modified Newton method for unconstrained minimization is presented and analyzed. The modification is based upon the model trust region approach. This report contains a thorough analysis of the locally constrained quadratic minimizations that arise as subproblems in the modified Newton iteration. Several promising alternatives are presented for solving these subproblems in ways that overcome certain theoretical difficulties exposed by this analysis. Very strong convergence results are presented concerning the minimization algorithm. In particular, the explicit use of second-order information is justified by demonstrating that the iterates converge to a point that satisfies the second-order necessary conditions for minimization. With the exception of very pathological cases this convergence occurs whenever the algorithm is applied to problems with continuous second partial derivatives.
NASA Astrophysics Data System (ADS)
Hohage, Thorsten
1997-10-01
Convergence and logarithmic convergence rates of the iteratively regularized Gauss - Newton method in a Hilbert space setting are proven provided a logarithmic source condition is satisfied. This method is applied to an inverse potential and an inverse scattering problem, and the source condition is interpreted as a smoothness condition in terms of Sobolev spaces for the case where the domain is a circle. Numerical experiments yield convergence and convergence rates of the form expected by our general convergence theorem.
Smoothing Methods for Estimating Test Score Distributions.
ERIC Educational Resources Information Center
Kolen, Michael J.
1991-01-01
Estimation/smoothing methods that are flexible enough to fit a wide variety of test score distributions are reviewed: kernel method, strong true-score model-based method, and method that uses polynomial log-linear models. Applications of these methods include describing/comparing test score distributions, estimating norms, and estimating…
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.
Multiple predictor smoothing methods for sensitivity analysis.
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.
Method for producing smooth inner surfaces
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.
Smooth electrode and method of fabricating same
Weaver, Stanton Earl; Kennerly, Stacey Joy; Aimi, Marco Francesco
2012-08-14
A smooth electrode is provided. The smooth electrode includes at least one metal layer having thickness greater than about 1 micron; wherein an average surface roughness of the smooth electrode is less than about 10 nm.
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.
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.
An adaptive Newton-method based on a dynamical systems approach
NASA Astrophysics Data System (ADS)
Amrein, Mario; Wihler, Thomas P.
2014-09-01
The traditional Newton method for solving nonlinear operator equations in Banach spaces is discussed within the context of the continuous Newton method. This setting makes it possible to interpret the Newton method as a discrete dynamical system and thereby to cast it in the framework of an adaptive step size control procedure. In so doing, our goal is to reduce the chaotic behavior of the original method without losing its quadratic convergence property close to the roots. The performance of the modified scheme is illustrated with various examples from algebraic and differential equations.
On the semilocal convergence of inexact Newton methods in Banach spaces
NASA Astrophysics Data System (ADS)
Argyros, Ioannis K.
2009-06-01
We provide two types of semilocal convergence theorems for approximating a solution of an equation in a Banach space setting using an inexact Newton method [I.K. Argyros, Relation between forcing sequences and inexact Newton iterates in Banach spaces, Computing 63 (2) (1999) 134-144; I.K. Argyros, A new convergence theorem for the inexact Newton method based on assumptions involving the second Fréchet-derivative, Comput. Appl. Math. 37 (7) (1999) 109-115; I.K. Argyros, Forcing sequences and inexact Newton iterates in Banach space, Appl. Math. Lett. 13 (1) (2000) 77-80; I.K. Argyros, Local convergence of inexact Newton-like iterative methods and applications, Comput. Math. Appl. 39 (2000) 69-75; I.K. Argyros, Computational Theory of Iterative Methods, in: C.K. Chui, L. Wuytack (Eds.), in: Studies in Computational Mathematics, vol. 15, Elsevier Publ. Co., New York, USA, 2007; X. Guo, On semilocal convergence of inexact Newton methods, J. Comput. Math. 25 (2) (2007) 231-242]. By using more precise majorizing sequences than before [X. Guo, On semilocal convergence of inexact Newton methods, J. Comput. Math. 25 (2) (2007) 231-242; Z.D. Huang, On the convergence of inexact Newton method, J. Zheijiang University, Nat. Sci. Ed. 30 (4) (2003) 393-396; L.V. Kantorovich, G.P. Akilov, Functional Analysis, Pergamon Press, Oxford, 1982; X.H. Wang, Convergence on the iteration of Halley family in weak condition, Chinese Sci. Bull. 42 (7) (1997) 552-555; T.J. Ypma, Local convergence of inexact Newton methods, SIAM J. Numer. Anal. 21 (3) (1984) 583-590], we provide (under the same computational cost) under the same or weaker hypotheses: finer error bounds on the distances involved; an at least as precise information on the location of the solution. Moreover if the splitting method is used, we show that a smaller number of inner/outer iterations can be obtained.
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.
Zhou, Fangqin
2014-01-01
We present a local convergence analysis of inexact Newton method for solving singular systems of equations. Under the hypothesis that the derivative of the function associated with the singular systems satisfies a majorant condition, we obtain that the method is well defined and converges. Our analysis provides a clear relationship between the majorant function and the function associated with the singular systems. It also allows us to obtain an estimate of convergence ball for inexact Newton method and some important special cases.
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.
Solving Nonlinear Solid Mechanics Problems with the Jacobian-Free Newton Krylov Method
J. D. Hales; S. R. Novascone; R. L. Williamson; D. R. Gaston; M. R. Tonks
2012-06-01
The solution of the equations governing solid mechanics is often obtained via Newton's method. This approach can be problematic if the determination, storage, or solution cost associated with the Jacobian is high. These challenges are magnified for multiphysics applications with many coupled variables. Jacobian-free Newton-Krylov (JFNK) methods avoid many of the difficulties associated with the Jacobian by using a finite difference approximation. BISON is a parallel, object-oriented, nonlinear solid mechanics and multiphysics application that leverages JFNK methods. We overview JFNK, outline the capabilities of BISON, and demonstrate the effectiveness of JFNK for solid mechanics and solid mechanics coupled to other PDEs using a series of demonstration problems.
Flux vector splitting and approximate Newton methods. [for solution of steady Euler equations
NASA Technical Reports Server (NTRS)
Jespersen, D. C.; Pulliam, T. H.
1983-01-01
In the present investigation, the basic approach is employed to view an iterative scheme as Newton's method or as a modified Newton's method. Attention is given to various modified Newton methods which can arise from differencing schemes for the Euler equations. Flux vector splitting is considered as the basic spatial differencing technique. This technique is based on the partition of a flux vector into groups which have certain properties. The Euler equations fluxes can be split into two groups, the first group having a flux Jacobian with all positive eigenvalues, and the second group having a flux Jacobian with all negative eigenvalues. Flux vector splitting based on a velocity-sound speed split is considered along with the use of numerical techniques to analyze nonlinear systems, and the steady Euler equations for quasi-one-dimensional flow in a nozzle. Results are given for steady flows with shocks.
A high-order fast method for computing convolution integral with smooth kernel
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.
A second degree Newton method for an inverse obstacle scattering problem
NASA Astrophysics Data System (ADS)
Kress, Rainer; Lee, Kuo-Ming
2011-08-01
A regularized second degree Newton method is proposed and implemented for the inverse problem for scattering of time-harmonic acoustic waves from a sound-soft obstacle. It combines ideas due to Johansson and Sleeman [18] and Hettlich and Rundell [8] and reconstructs the obstacle from the far field pattern for scattering of one incident plane wave.
A multigrid Newton-Krylov method for flux-limited radiation diffusion
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.
NASA Astrophysics Data System (ADS)
Antipin, A. S.; Vasil'Ev, F. P.; Stukalov, A. S.
2007-01-01
Unstable equilibrium problems are examined in which the objective function and the set where the equilibrium point is sought are specified inexactly. A regularized Newton method, combined with penalty functions, is proposed for solving such problems, and its convergence is analyzed. A regularizing operator is constructed.
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
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
Sato, Y; Yamada, T; Matsumoto, M; Wakitani, Y; Hasegawa, T; Yoshimura, T; Murayama, H; Oda, K; Sato, T; Unno, Y; Yunoki, A
2012-09-01
A tritium radioactivity source was measured by triple-to-double coincidence ratio (TDCR) equipment of the National Metrology Institute of Japan (NMIJ), and measured data were fitted using polynomial approximation and the Newton-Raphson method, a technique whereby equations are solved numerically by successive approximations. The method used to obtain the activity minimizes the difference between statistically calculated data and experimental data. In the fitting, since calculated statistical efficiency and TDCR values are discrete, the calculated efficiencies are approximated by quadratic functions around experimental values and the Newton-Raphson method is used for convergence at the minimal difference between experimental data and calculated data. In this way, the activity of tritium was successfully obtained.
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.
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…
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.
Comparing three methods for teaching Newton's third law
NASA Astrophysics Data System (ADS)
Smith, Trevor I.; Wittmann, Michael C.
2007-12-01
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 University of Washington style tutorial materials, but the different curricula have not been compared against each other. Our study examines three tutorials designed to improve student understanding of Newton’s third law: the University of Washington’s Tutorials in Introductory Physics (TIP), the University of Maryland’s Activity-Based Tutorials (ABT), and the Open Source Tutorials (OST) also developed at the University of Maryland. Each tutorial was designed with different goals and agendas, and each employs different methods to help students understand the physics. We analyzed pretest and post-test data, including course examinations and data from the Force and Motion Conceptual Evaluation (FMCE). Using both FMCE and course data, we find that students using the OST version of the tutorial perform better than students using either of the other two.
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.
Application of smoothed particle hydrodynamics method in aerodynamics
NASA Astrophysics Data System (ADS)
Cortina, Miguel
2014-11-01
Smoothed Particle Hydrodynamics (SPH) is a meshless Lagrangian method in which the domain is represented by particles. Each particle is assigned properties such as mass, pressure, density, temperature, and velocity. These properties are then evaluated at the particle positions using a smoothing kernel that integrates over the values of the surrounding particles. In the present study the SPH method is first used to obtain numerical solutions for fluid flows over a cylinder and then we are going to apply the same principle over an airfoil obstacle.
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.
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.
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.…
Acceleration of k-Eigenvalue / Criticality Calculations using the Jacobian-Free Newton-Krylov Method
Dana Knoll; HyeongKae Park; Chris Newman
2011-02-01
We present a new approach for the $k$--eigenvalue problem using a combination of classical power iteration and the Jacobian--free Newton--Krylov method (JFNK). The method poses the $k$--eigenvalue problem as a fully coupled nonlinear system, which is solved by JFNK with an effective block preconditioning consisting of the power iteration and algebraic multigrid. We demonstrate effectiveness and algorithmic scalability of the method on a 1-D, one group problem and two 2-D two group problems and provide comparison to other efforts using silmilar algorithmic approaches.
A speciation solver for cement paste modeling and the semismooth Newton method
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.
NASA Astrophysics Data System (ADS)
Moschetti, M. P.; Mueller, C. S.; Boyd, O. S.; Petersen, M. D.
2013-12-01
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
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
NASA Astrophysics Data System (ADS)
Mizutani, E.
2015-09-01
In this journal, Pantoja has described a deterministic optimal control problem in which his stagewise Newton procedure yields an exact optimal solution whereas differential dynamic programming (DDP) does not. This problem is also quoted by Coleman and Liao (in another journal) as a correct instance with some emphasis on the advantage of Pantoja's procedure over DDP. Pantoja argues that the problem involves nonlinear dynamics in his terminal-cost problem formulation, and therefore DDP and stagewise Newton methods are different. The purpose of this paper is to show that, while for a general nonlinear optimal control problem DDP and Pantoja's method differ, his problem has a special structure such that it is a false example of this claim; more specifically, the reason is twofold. First, he made an obvious algebraic error in his computation. Second, his example is equivalent to a problem of linear dynamics and quadratic criterion (LQ in short). It is true that when a general LQ that involves quadratic stage costs is transformed to a terminal-cost problem, the nonlinear (quadratic) state dynamics would result from each quadratic stage cost of the LQ. Yet the LQ-solution procedure remains the same, i.e., with the same discrete (Riccati) recurrence equations that can be derived by classical dynamic programming. This means that DDP obtains the exact minimum point of the transformed terminal-cost criterion just as does the Newton method. Using a standard LQ of general type, we formally prove this equivalence in its terminal-cost version even with nonlinear state dynamics.
Convergence Properties of the Regularized Newton Method for the Unconstrained Nonconvex Optimization
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.
Chemical method for producing smooth surfaces on silicon wafers
Yu, Conrad
2003-01-01
An improved method for producing optically smooth surfaces in silicon wafers during wet chemical etching involves a pre-treatment rinse of the wafers before etching and a post-etching rinse. The pre-treatment with an organic solvent provides a well-wetted surface that ensures uniform mass transfer during etching, which results in optically smooth surfaces. The post-etching treatment with an acetic acid solution stops the etching instantly, preventing any uneven etching that leads to surface roughness. This method can be used to etch silicon surfaces to a depth of 200 .mu.m or more, while the finished surfaces have a surface roughness of only 15-50 .ANG. (RMS).
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.
Exact Jacobians in an implicit Newton method for two-phase flow in porous media
NASA Astrophysics Data System (ADS)
Büsing, H.; Clauser, C.
2012-04-01
Geological storage of CO2 is one option for mitigating the effects of CO2 emissions on global warming. Since extensive on-site monitoring of the CO2 plume propagation is expensive, numerical simulations are an attractive alternative for gaining deeper insight in the dynamics of this system. We consider a model for two-phase flow in porous media for representing the injection stage of a CO2 sequestration scenario, when the plume propagation is dominated by advection. The porous medium filled by the two phases CO2 and brine is modelled as an initial-boundary-value problem consisting of two nonlinear, coupled partial differential equations, which are complemented by appropriate boundary and initial conditions. We present a new numerical approach to solve this fully coupled system using exact Jacobians. The method is based on the finite element, finite volume, box method [Huber & Helmig(2000)] for the space discretization and, since stability of the method is one of the main concerns, the fully implicit Euler method for the time discretization. A simple first order upwind method takes into account advective contributions. The resulting system of nonlinear algebraic equations is linearized by Newton's method. The required Jacobians can be obtained elegantly by automatic differentiation (AD) [Griewank & Walther(2008), Rall(1981)], a source code transformation giving exact derivatives of the discretized equations with respect to primary variables. The resulting system of linear equations is then solved by an iterative method (BiCGStab) with ILU0 preconditioning in every Newton step. We compare the forward AD differentiation mode to the standard finite difference method in terms of precision and performance. It turns out that AD performs favourable in both aspects. We also illustrate the advantages of exact Jacobians for two-phase flow in a sequestration scenario investigating the evolution of pressure and saturation.
Method for smoothing the surface of a protective coating
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.
Flexibility-based structural damage identification using Gauss-Newton method
NASA Astrophysics Data System (ADS)
Chen, Bilei; Nagarajaiah, Satish
2007-04-01
Structural damage will change the dynamic characteristics, including natural frequencies, modal shapes, damping ratios and modal flexibility matrix of the structure. Modal flexibility matrix is a function of natural frequencies and mode shapes and can be used for structural damage detection and health monitoring. In this paper, experimental modal flexibility matrix is obtained from the first few lower measured natural frequencies and incomplete modal shapes. The optimization problem is then constructed by minimizing Frobenius norm of the change of flexibility matrix. Gauss- Newton method is used to solve the optimization problem, where the sensitivity of flexibility matrix with respect to structural parameters is calculated iteratively by only using the first few lower modes. The optimal solution corresponds to structural parameters which can be used to identify damage sites and extent. Numerical results show that flexibility-based method can be successfully applied to identify the damage elements and is robust to measurement noise.
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.
Optimal control with accelerated convergence: Combining the Krotov and quasi-Newton methods
Eitan, Reuven; Mundt, Michael; Tannor, David J.
2011-05-15
One of the most popular methods for solving numerical optimal control problems is the Krotov method, adapted for quantum control by Tannor and coworkers. The Krotov method has the following three appealing properties: (1) monotonic increase of the objective with iteration number, (2) no requirement for a line search, leading to a significant savings over gradient (first-order) methods, and (3) macrosteps at each iteration, resulting in significantly faster growth of the objective at early iterations than in gradient methods where small steps are required. The principal drawback of the Krotov method is slow convergence at later iterations, which is particularly problematic when high fidelity is desired. We show here that, near convergence, the Krotov method degenerates to a first-order gradient method. We then present a variation on the Krotov method that has all the advantages of the original Krotov method but with significantly enhanced convergence (second-order or quasi-Newton) as the optimal solution is approached. We illustrate the method by controlling the three-dimensional dynamics of the valence electron in the Na atom.
Dana A. Knoll; H. Park; Kord Smith
2011-02-01
The use of the Jacobian-free Newton-Krylov (JFNK) method within the context of nonlinear diffusion acceleration (NDA) of source iteration is explored. The JFNK method is a synergistic combination of Newton's method as the nonlinear solver and Krylov methods as the linear solver. JFNK methods do not form or store the Jacobian matrix, and Newton's method is executed via probing the nonlinear discrete function to approximate the required matrix-vector products. Current application of NDA relies upon a fixed-point, or Picard, iteration to resolve the nonlinearity. We show that the JFNK method can be used to replace this Picard iteration with a Newton iteration. The Picard linearization is retained as a preconditioner. We show that the resulting JFNK-NDA capability provides benefit in some regimes. Furthermore, we study the effects of a two-grid approach, and the required intergrid transfers when the higher-order transport method is solved on a fine mesh compared to the low-order acceleration problem.
Multi-scale crystal growth computations via an approximate block Newton method
NASA Astrophysics Data System (ADS)
Yeckel, Andrew; Lun, Lisa; Derby, Jeffrey J.
2010-04-01
Multi-scale and multi-physics simulations, such as the computational modeling of crystal growth processes, will benefit from the modular coupling of existing codes rather than the development of monolithic, single-application software. An effective coupling approach, the approximate block Newton approach (ABN), is developed and applied to the steady-state computation of crystal growth in an electrodynamic gradient freeze system. Specifically, the code CrysMAS is employed for furnace-scale heat transfer computations and is coupled with the code Cats2D to calculate melt fluid dynamics and phase-change phenomena. The ABN coupling strategy proves to be vastly more reliable and cost efficient than simpler coupling methods for this problem and is a promising approach for future crystal growth models.
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.
NASA Astrophysics Data System (ADS)
Yeckel, Andrew; Lun, Lisa; Derby, Jeffrey J.
2009-12-01
A new, approximate block Newton (ABN) method is derived and tested for the coupled solution of nonlinear models, each of which is treated as a modular, black box. Such an approach is motivated by a desire to maintain software flexibility without sacrificing solution efficiency or robustness. Though block Newton methods of similar type have been proposed and studied, we present a unique derivation and use it to sort out some of the more confusing points in the literature. In particular, we show that our ABN method behaves like a Newton iteration preconditioned by an inexact Newton solver derived from subproblem Jacobians. The method is demonstrated on several conjugate heat transfer problems modeled after melt crystal growth processes. These problems are represented by partitioned spatial regions, each modeled by independent heat transfer codes and linked by temperature and flux matching conditions at the boundaries common to the partitions. Whereas a typical block Gauss-Seidel iteration fails about half the time for the model problem, quadratic convergence is achieved by the ABN method under all conditions studied here. Additional performance advantages over existing methods are demonstrated and discussed.
Zhou, Fangqin
2014-01-01
We study the local convergence properties of inexact Newton-Gauss method for singular systems of equations. Unified estimates of radius of convergence balls for one kind of singular systems of equations with constant rank derivatives are obtained. Application to the Smale point estimate theory is provided and some important known results are extended and/or improved.
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…
The methods for the generation of smoothness in dental ceramics.
Yilmaz, Kerem; Ozkan, Pelin
2010-01-01
Occlusal corrections, acidulated phosphate fluoride applications, carbonated beverages, or air-powder abrasion procedures can roughen the surface of restorations. Once deteriorated, porcelain surfaces need to be repolished. These surfaces can be reglazed or polished through various intraoral and extraoral polishing kits. Although clinicians often seek studies on the effect of repeated firings on coherence between metal and ceramic, the color of the porcelain, fluorescence, microstructure, and brightness, only a limited number of studies are available in the literature. This article reviews the available literature and presents methods for generating a smooth surface and assessing surface roughness. It also discusses the differences between glazing and mechanical polishing, highlighting the importance of mechanical polishing of dental ceramics.
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.
A hybrid Newton-type method for censored survival data using double weights in linear models.
Yu, Menggang; Nan, Bin
2006-09-01
As an alternative to the Cox model, the rank-based estimating method for censored survival data has been studied extensively since it was proposed by Tsiatis [Tsiatis AA (1990) Ann Stat 18:354-372] among others. Due to the discontinuity feature of the estimating function, a significant amount of work in the literature has been focused on numerical issues. In this article, we consider the computational aspects of a family of doubly weighted rank-based estimating functions. This family is rich enough to include both estimating functions of Tsiatis (1990) for the randomly observed data and of Nan et al. [Nan B, Yu M, Kalbfleisch JD (2006) Biometrika (to appear)] for the case-cohort data as special examples. The latter belongs to the biased sampling problems. We show that the doubly weighted rank-based discontinuous estimating functions are monotone, a property established for the randomly observed data in the literature, when the generalized Gehan-type weights are used. Though the estimating problem can be formulated to a linear programming problem as that for the randomly observed data, due to its easily uncontrollable large scale even for a moderate sample size, we instead propose a Newton-type iterated method to search for an approximate solution of the (system of) discontinuous monotone estimating equation(s). Simulation results provide a good demonstration of the proposed method. We also apply our method to a real data example. PMID:16917733
General purpose nonlinear system solver based on Newton-Krylov method.
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].
Owusu-Edusei, Kwame; Owens, Chantelle J
2009-01-01
Background Chlamydia continues to be the most prevalent disease in the United States. Effective spatial monitoring of chlamydia incidence is important for successful implementation of control and prevention programs. The objective of this study is to apply Bayesian smoothing and exploratory spatial data analysis (ESDA) methods to monitor Texas county-level chlamydia incidence rates by examining spatiotemporal patterns. We used county-level data on chlamydia incidence (for all ages, gender and races) from the National Electronic Telecommunications System for Surveillance (NETSS) for 2004 and 2005. Results Bayesian-smoothed chlamydia incidence rates were spatially dependent both in levels and in relative changes. Erath county had significantly (p < 0.05) higher smoothed rates (> 300 cases per 100,000 residents) than its contiguous neighbors (195 or less) in both years. Gaines county experienced the highest relative increase in smoothed rates (173% – 139 to 379). The relative change in smoothed chlamydia rates in Newton county was significantly (p < 0.05) higher than its contiguous neighbors. Conclusion Bayesian smoothing and ESDA methods can assist programs in using chlamydia surveillance data to identify outliers, as well as relevant changes in chlamydia incidence in specific geographic units. Secondly, it may also indirectly help in assessing existing differences and changes in chlamydia surveillance systems over time. PMID:19245686
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
Recovery Discontinuous Galerkin Jacobian-free Newton-Krylov Method for all-speed flows
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.
Regularized Newton methods for x-ray phase contrast and general imaging problems
NASA Astrophysics Data System (ADS)
Maretzke, Simon; Bartels, Matthias; Krenkel, Martin; Salditt, Tim; Hohage, Thorsten
2016-03-01
Like many other advanced imaging methods, x-ray phase contrast imaging and tomography require mathematical inversion of the observed data to obtain real-space information. While an accurate forward model describing the generally nonlinear image formation from a given object to the observations is often available, explicit inversion formulas are typically not known. Moreover, the measured data might be insufficient for stable image reconstruction, in which case it has to be complemented by suitable a priori information. In this work, regularized Newton methods are presented as a general framework for the solution of such ill-posed nonlinear imaging problems. For a proof of principle, the approach is applied to x-ray phase contrast imaging in the near-field propagation regime. Simultaneous recovery of the phase- and amplitude from a single near-field diffraction pattern without homogeneity constraints is demonstrated for the first time. The presented methods further permit all-at-once phase contrast tomography, i.e. simultaneous phase retrieval and tomographic inversion. We demonstrate the potential of this approach by three-dimensional imaging of a colloidal crystal at 95 nm isotropic resolution.
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.
NASA Astrophysics Data System (ADS)
Muthuvalu, Mohana Sundaram; Aruchunan, Elayaraja; Koh, Wei Sin; Akhir, Mohd Kamalrulzaman Md; Sulaiman, Jumat; Karim, Samsul Ariffin Abdul
2014-07-01
In this paper, the application of the Accelerated Over-Relaxation (AOR) iterative method is extended to solve first order composite closed Newton-Cotes quadrature (1-CCNC) algebraic equations arising from second kind linear Fredholm integral equations. The formulation and implementation of the method are also discussed. In addition, numerical results by solving several test problems are included and compared with the conventional iterative methods.
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.
Projected Newton method for l/sub p/ norm location problems
Calamai, P.H.; Conn, A.R.
1985-08-01
This paper is concerned with the numerical solution of continuous minisum multifacility location problems involving the l/sub p/ norm, where 1 < p < infinity. This class of problems is potentially difficult to solve because the objective function is not everywhere differentiable. After developing conditions that characterize the minimum of the problems under consideration, a second-order algorithm is presented. This algorithm is based on the solution of a finite sequence of linearly constrained subproblems. Descent directions for these subproblems are obtained by projecting the Newton direction onto the corresponding constraint manifold. Univariate minimization is achieved via a specialized linesearch which recognizes the possibility of first derivative discontinuity (and second derivative unboundedness) at points along the search direction. The algorithm, motivated by Calamai and Calamai and Conn and related to methods recently described by Overton and Dax, is shown to possess both global and quadratic convergence properties. Degeneracy can complicate the numerical solution of the subproblems. This degeneracy is identified, and a method for handling this degeneracy is outlined. An implementation of the algorithm, that exploits the intrinsic structure of the location problem formulation, is then described along with a discussion of numerical results. 35 refs., 7 tabs.
A Jacobian-free Newton Krylov method for mortar-discretized thermomechanical contact problems
NASA Astrophysics Data System (ADS)
Hansen, Glen
2011-07-01
Multibody contact problems are common within the field of multiphysics simulation. Applications involving thermomechanical contact scenarios are also quite prevalent. Such problems can be challenging to solve due to the likelihood of thermal expansion affecting contact geometry which, in turn, can change the thermal behavior of the components being analyzed. This paper explores a simple model of a light water reactor nuclear fuel rod, which consists of cylindrical pellets of uranium dioxide (UO 2) fuel sealed within a Zircalloy cladding tube. The tube is initially filled with helium gas, which fills the gap between the pellets and cladding tube. The accurate modeling of heat transfer across the gap between fuel pellets and the protective cladding is essential to understanding fuel performance, including cladding stress and behavior under irradiated conditions, which are factors that affect the lifetime of the fuel. The thermomechanical contact approach developed here is based on the mortar finite element method, where Lagrange multipliers are used to enforce weak continuity constraints at participating interfaces. In this formulation, the heat equation couples to linear mechanics through a thermal expansion term. Lagrange multipliers are used to formulate the continuity constraints for both heat flux and interface traction at contact interfaces. The resulting system of nonlinear algebraic equations are cast in residual form for solution of the transient problem. A Jacobian-free Newton Krylov method is used to provide for fully-coupled solution of the coupled thermal contact and heat equations.
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.
NASA Astrophysics Data System (ADS)
Hendry, Archibald W.
2007-05-01
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 recollections of events did not always match known facts. However, one thing is certain-falling objects were to play a key part in Newton's eventual understanding of how objects move.
Weighted Wilcoxon-type Smoothly Clipped Absolute Deviation Method
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
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
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.
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.
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…
Methods and electrolytes for electrodeposition of smooth films
Zhang, Jiguang; Xu, Wu; Graff, Gordon L; Chen, Xilin; Ding, Fei; Shao, Yuyan
2015-03-17
Electrodeposition involving an electrolyte having a surface-smoothing additive can result in self-healing, instead of self-amplification, of initial protuberant tips that give rise to roughness and/or dendrite formation on the substrate and/or film surface. For electrodeposition of a first conductive material (C1) on a substrate from one or more reactants in an electrolyte solution, the electrolyte solution is characterized by a surface-smoothing additive containing cations of a second conductive material (C2), wherein cations of C2 have an effective electrochemical reduction potential in the solution lower than that of the reactants.
Impact of beam smoothing method on direct drive target performance for the NIF
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.
NASA Astrophysics Data System (ADS)
Fisz, J. J.; Buczkowski, M.; Budziński, M. P.; Kolenderski, P.
2005-05-01
The application of genetic algorithms (GA) optimization approach supported by the first-order derivative (FOD) and Newton-Raphson (NR) methods to time-resolved polarized fluorescence spectroscopy, is discussed. It is demonstrated that the application of both methods to χ2 function reduces the number of adjustable model parameters. The combination of GA-optimizer with the FOD and NR methods improves considerably the efficiency of global analysis of kinetic and polarized fluorescence decays for solutions and organized media, including the case of excited-state processes.
Yuan, Zhen; Wang, Qiang; Jiang, Huabei
2007-12-24
We describe a novel reconstruction method that allows for quantitative recovery of optical absorption coefficient maps of heterogeneous media using tomographic photoacoustic measurements. Images of optical absorption coefficient are obtained from a diffusion equation based regularized Newton method where the absorbed energy density distribution from conventional photoacoustic tomography serves as the measured field data. We experimentally demonstrate this new method using tissue-mimicking phantom measurements and simulations. The reconstruction results show that the optical absorption coefficient images obtained are quantitative in terms of the shape, size, location and optical property values of the heterogeneities examined.
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.
Suppression of stochastic pulsation in laser-plasma interaction by smoothing methods
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.
Quasi-Newton methods for parameter estimation in functional differential equations
NASA Technical Reports Server (NTRS)
Brewer, Dennis W.
1988-01-01
A state-space approach to parameter estimation in linear functional differential equations is developed using the theory of linear evolution equations. A locally convergent quasi-Newton type algorithm is applied to distributed systems with particular emphasis on parameters that induce unbounded perturbations of the state. The algorithm is computationally implemented on several functional differential equations, including coefficient and delay estimation in linear delay-differential equations.
Stochastic quasi-Newton method: application to minimal model for proteins.
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>T(θ), where T(θ) is the collapse temperature. Second, S-QN simulations for several initial structures at very low temperature (T=0.01
NASA Astrophysics Data System (ADS)
Dadić, Martin
2013-06-01
The increased interest in vacuum tube audio amplifiers led to an increased interest in mathematical modelling of such kind of amplifiers. The main purpose of this paper is to develop a novel global numerical approach in calculation of the harmonic distortion (HD) and intermodulation distortion (IM) of vacuum-triode audio amplifiers, suitable for applications using brute-force of modern computers. Since the 3/2 power law gives only the transcharacteristic inverse of a vacuum triode amplifier, unknown plate currents are determined in this paper iteratively using Newton's method. Using the resulting input/output pairs, harmonic distortions and intermodulations are calculated using discrete Fourier transform and three different analytical methods.
Yuan, Zhen; Jiang, Huabei
2007-05-10
What we believe to be a novel 3D diffuse optical tomography scheme is developed to reconstruct images of both absorption and scattering coefficients of finger joint systems. Compared with our previous reconstruction method, the improved 3D algorithm employs both modified Newton methods and an enhanced initial value optimization scheme to recover the optical properties of highly heterogeneous media. The developed approach is tested using simulated, phantom, and in vivo measurement data. The recovered results suggest that the improved approach is able to provide quantitatively better images than our previous algorithm for optical tomography reconstruction.
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.
Alternative methods to smooth the Earth's gravity field
NASA Technical Reports Server (NTRS)
Jekeli, C.
1981-01-01
Convolutions on the sphere with corresponding convolution theorems are developed for one and two dimensional functions. Some of these results are used in a study of isotropic smoothing operators or filters. Well known filters in Fourier spectral analysis, such as the rectangular, Gaussian, and Hanning filters, are adapted for data on a sphere. The low-pass filter most often used on gravity data is the rectangular (or Pellinen) filter. However, its spectrum has relatively large sidelobes; and therefore, this filter passes a considerable part of the upper end of the gravity spectrum. The spherical adaptations of the Gaussian and Hanning filters are more efficient in suppressing the high-frequency components of the gravity field since their frequency response functions are strongly field since their frequency response functions are strongly tapered at the high frequencies with no, or small, sidelobes. Formulas are given for practical implementation of these new filters.
NASA Astrophysics Data System (ADS)
Lemieux, Jean-François; Price, Stephen F.; Evans, Katherine J.; Knoll, Dana; Salinger, Andrew G.; Holland, David M.; Payne, Antony J.
2011-07-01
We have implemented the Jacobian-free Newton-Krylov (JFNK) method for solving the first-order ice sheet momentum equation in order to improve the numerical performance of the Glimmer-Community Ice Sheet Model (Glimmer-CISM), the land ice component of the Community Earth System Model (CESM). Our JFNK implementation is based on significant re-use of existing code. For example, our physics-based preconditioner uses the original Picard linear solver in Glimmer-CISM. For several test cases spanning a range of geometries and boundary conditions, our JFNK implementation is 1.8-3.6 times more efficient than the standard Picard solver in Glimmer-CISM. Importantly, this computational gain of JFNK over the Picard solver increases when refining the grid. Global convergence of the JFNK solver has been significantly 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.
Smoothing methods comparison for CMB E- and B-mode separation
NASA Astrophysics Data System (ADS)
Wang, Yi-Fan; Wang, Kai; Zhao, Wen
2016-04-01
The anisotropies of the B-mode polarization in the cosmic microwave background radiation play a crucial role in the study of the very early Universe. However, in real observations, a mixture of the E-mode and B-mode can be caused by partial sky surveys, which must be separated before being applied to a cosmological explanation. The separation method developed by Smith (2006) has been widely adopted, where the edge of the top-hat mask should be smoothed to avoid numerical errors. In this paper, we compare three different smoothing methods and investigate leakage residuals of the E-B mixture. We find that, if less information loss is needed and a smaller region is smoothed in the analysis, the sin- and cos-smoothing methods are better. However, if we need a cleanly constructed B-mode map, the larger region around the mask edge should be smoothed. In this case, the Gaussian-smoothing method becomes much better. In addition, we find that the leakage caused by numerical errors in the Gaussian-smoothing method is mostly concentrated in two bands, which is quite easy to reduce for further E-B separations.
A numerical study of the Regge calculus and smooth lattice methods on a Kasner cosmology
NASA Astrophysics Data System (ADS)
Brewin, Leo
2015-10-01
Two lattice based methods for numerical relativity, the Regge calculus and the smooth lattice relativity, will be compared with respect to accuracy and computational speed in a full 3+1 evolution of initial data representing a standard Kasner cosmology. It will be shown that both methods provide convergent approximations to the exact Kasner cosmology. It will also be shown that the Regge calculus is of the order of 110 times slower than the smooth lattice method.
Effect of spatial smoothing on the performance of MUSIC and the minimum-norm method
NASA Astrophysics Data System (ADS)
Rao, B. D.; Hari, K. V. S.
1990-12-01
The effect of using a spatially smoothed forward-backward covariance matrix on the statistical performance of two eigendecomposition-based methods, MUSIC and the minimum-norm method, is analyzed. It is shown that, in general, for all subspace methods the forward-backward smoothing approach is preferable to the forward smoothing approach. The error in the signal zeros obtained using MUSIC is shown to follow a different trend compared to the error in the direction of arrival (DOA) estimates, leading to difficulty in interpreting the spatial spectrum. On the other hand, it is shown that for the minimum-norm method the errors in the signal zeros exhibit the same trend as the DOA estimates so that no such problem is created. It is also shown that proper spatial smoothing enables the performance of the minimum-norm method to be made comparable to that of MUSIC.
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.
The two-level Newton method and its application to electronic simulation.
Hoekstra, Robert John; Waters, Lon J.; Rankin, Eric Lamont; Hutchinson, Scott Alan; Keiter, Eric Richard; Russo, Thomas V.
2004-06-01
Coupling between transient simulation codes of different fidelity can often be performed at the nonlinear solver level, if the time scales of the two codes are similar. A good example is electrical mixed-mode simulation, in which an analog circuit simulator is coupled to a PDE-based semiconductor device simulator. Semiconductor simulation problems, such as single-event upset (SEU), often require the fidelity of a mesh-based device simulator but are only meaningful when dynamically coupled with an external circuit. For such problems a mixed-level simulator is desirable, but the two types of simulation generally have different (somewhat conflicting) numerical requirements. To address these considerations, we have investigated variations of the two-level Newton algorithm, which preserves tight coupling between the circuit and the PDE device, while optimizing the numerics for both. The research was done within Xyce, a massively parallel electronic simulator under development at Sandia National Laboratories.
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.
New method for fast detection of railway track smoothness by fiber optic gyro
NASA Astrophysics Data System (ADS)
Wang, Lixin; Liang, Lei; Hu, Wenbin
2000-05-01
In this article, the conducting schemes for fiber optic gyro (FOG) used int he fast detecting of the smoothness of rail track has been proposed from the practical use point of view. The relevant approximate method of calculating has been given. The experiments in lab have been carried out, and the factors to influence the detecting precision of the smoothness of rail track such as the precision of FOG have been analyzed.
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.
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.
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.
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)
Yang, Zhongming; Wang, Kailiang; Cheng, Jinlong; Gao, Zhishan; Yuan, Qun
2016-06-10
We have proposed a virtual quadratic Newton rings phase-shifting moiré-fringes measurement method in a nonnull interferometer to measure the large radius of curvature for a spherical surface. In a quadratic polar coordinate system, linear carrier testing Newton rings interferogram and virtual Newton rings interferogram form the moiré fringes. It is possible to retrieve the wavefront difference data between the testing and standard spherical surface from the moiré fringes after low-pass filtering. Based on the wavefront difference data, we deduced a precise formula to calculate the radius of curvature in the quadratic polar coordinate system. We calculated the retrace error in the nonnull interferometer using the multi-configuration model of the nonnull interferometric system in ZEMAX. Our experimental results indicate that the measurement accuracy is better than 0.18% for a spherical mirror with a radius of curvature of 41,400 mm.
Melnikov Method for a Class of Planar Hybrid Piecewise-Smooth Systems
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 periodic perturbed planar hybrid piecewise-smooth systems. In this class, the switching manifold is a straight line which divides the plane into two zones, and the dynamics in each zone is governed by a smooth system. When a trajectory reaches the separation line, then a reset map is applied instantaneously before entering the trajectory in the other zone. We assume that the unperturbed system is a piecewise Hamiltonian system which possesses a piecewise-smooth homoclinic solution transversally crossing the switching manifold. Then, we study the persistence of the homoclinic orbit under a nonautonomous periodic perturbation and the reset map. To achieve this objective, we obtain the Melnikov function to measure the distance of the perturbed stable and unstable manifolds and present the theorem for homoclinic bifurcations for the class of planar hybrid piecewise-smooth systems. Furthermore, we employ the obtained Melnikov function to detect the chaotic boundaries for a concrete planar hybrid piecewise-smooth system.
Nonequilibrium flows with smooth particle applied mechanics
Kum, O.
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 (u{rho}) and (T{rho}), 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.
A relaxation method for minimizing a smooth function on a generalized spherical segment
NASA Astrophysics Data System (ADS)
Dulliev, A. M.
2014-02-01
The minimization of a smooth functional on a generalized spherical segment of a finite-dimensional Euclidean space is examined. A relaxation method that involves successive projections of the antigradient onto auxiliary sets of a simpler structure is proposed. It is shown that, under certain natural assumptions, this method converges to a stationary point.
Code of Federal Regulations, 2014 CFR
2014-07-01
... practices to minimize air pollution emission during malfunctions) has not been superseded. 4. Continuous... Demonstrating Compliance With 40 CFR 60.43 for the Newton Power Station of Central Illinois Public Service... Appendix G to Part 60—Provisions for an Alternative Method of Demonstrating Compliance With 40 CFR...
Code of Federal Regulations, 2012 CFR
2012-07-01
... air pollution emission during malfunctions) has not been superseded. 4. Continuous Emission Monitoring... Demonstrating Compliance With 40 CFR 60.43 for the Newton Power Station of Central Illinois Public Service... Appendix G to Part 60—Provisions for an Alternative Method of Demonstrating Compliance With 40 CFR...
Code of Federal Regulations, 2013 CFR
2013-07-01
... air pollution emission during malfunctions) has not been superseded. 4. Continuous Emission Monitoring... Demonstrating Compliance With 40 CFR 60.43 for the Newton Power Station of Central Illinois Public Service... Appendix G to Part 60—Provisions for an Alternative Method of Demonstrating Compliance With 40 CFR...
Code of Federal Regulations, 2011 CFR
2011-07-01
... air pollution emission during malfunctions) has not been superseded. 4. Continuous Emission Monitoring... Demonstrating Compliance With 40 CFR 60.43 for the Newton Power Station of Central Illinois Public Service... Appendix G to Part 60—Provisions for an Alternative Method of Demonstrating Compliance With 40 CFR...
Code of Federal Regulations, 2010 CFR
2010-07-01
... Demonstrating Compliance With 40 CFR 60.43 for the Newton Power Station of Central Illinois Public Service... PROGRAMS (CONTINUED) STANDARDS OF PERFORMANCE FOR NEW STATIONARY SOURCES (CONTINUED) Pt. 60, App. G Appendix G to Part 60—Provisions for an Alternative Method of Demonstrating Compliance With 40 CFR...
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
A Meshfree Cell-based Smoothed Point Interpolation Method for Solid Mechanics Problems
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
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
A Monte Carlo method for variance estimation for estimators based on induced smoothing
Jin, Zhezhen; Shao, Yongzhao; Ying, Zhiliang
2015-01-01
An important issue in statistical inference for semiparametric models is how to provide reliable and consistent variance estimation. Brown and Wang (2005. Standard errors and covariance matrices for smoothed rank estimators. Biometrika 92, 732–746) proposed a variance estimation procedure based on an induced smoothing for non-smooth estimating functions. Herein a Monte Carlo version is developed that does not require any explicit form for the estimating function itself, as long as numerical evaluation can be carried out. A general convergence theory is established, showing that any one-step iteration leads to a consistent variance estimator and continuation of the iterations converges at an exponential rate. The method is demonstrated through the Buckley–James estimator and the weighted log-rank estimators for censored linear regression, and rank estimation for multiple event times data. PMID:24812418
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.
A Newton-CG method for large-scale three-dimensional elastic full-waveform seismic inversion
NASA Astrophysics Data System (ADS)
Epanomeritakis, I.; Akçelik, V.; Ghattas, O.; Bielak, J.
2008-06-01
We present a nonlinear optimization method for large-scale 3D elastic full-waveform seismic inversion. The method combines outer Gauss-Newton nonlinear iterations with inner conjugate gradient linear iterations, globalized by an Armijo backtracking line search, solved on a sequence of finer grids and higher frequencies to remain in the vicinity of the global optimum, inexactly terminated to prevent oversolving, preconditioned by L-BFGS/Frankel, regularized by a total variation operator to capture sharp interfaces, finely discretized by finite elements in the Lamé parameter space to provide flexibility and avoid bias, implemented in matrix-free fashion with adjoint-based computation of reduced gradient and reduced Hessian-vector products, checkpointed to avoid full spacetime waveform storage, and partitioned spatially across processors to parallelize the solutions of the forward and adjoint wave equations and the evaluation of gradient-like information. Several numerical examples demonstrate the grid independence of linear and nonlinear iterations, the effectiveness of the preconditioner, the ability to solve inverse problems with up to 17 million inversion parameters on up to 2048 processors, the effectiveness of multiscale continuation in keeping iterates in the basin of attraction of the global minimum, and the ability to fit the observational data while reconstructing the model with reasonable resolution and capturing sharp interfaces.
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
NASA Astrophysics Data System (ADS)
Danilewicz, Andrzej; Sikora, Zbigniew
2015-02-01
A theoretical base of SPH method, including the governing equations, discussion of importance of the smoothing function length, contact formulation, boundary treatment and finally utilization in hydrocode simulations are presented. An application of SPH to a real case of large penetrations (crater creating) into the soil caused by falling mass in Dynamic Replacement Method is discussed. An influence of particles spacing on method accuracy is presented. An example calculated by LS-DYNA software is discussed. Chronological development of Smooth Particle Hydrodynamics is presented. Theoretical basics of SPH method stability and consistency in SPH formulation, artificial viscosity and boundary treatment are discussed. Time integration techniques with stability conditions, SPH+FEM coupling, constitutive equation and equation of state (EOS) are presented as well.
NASA Astrophysics Data System (ADS)
McHugh, P. R.; Knoll, D. A.
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. 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 is employed. 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.
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.
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.
Testing local anisotropy using the method of smoothed residuals I — methodology
Appleby, Stephen; Shafieloo, Arman E-mail: arman@apctp.org
2014-03-01
We discuss some details regarding the method of smoothed residuals, which has recently been used to search for anisotropic signals in low-redshift distance measurements (Supernovae). In this short note we focus on some details regarding the implementation of the method, particularly the issue of effectively detecting signals in data that are inhomogeneously distributed on the sky. Using simulated data, we argue that the original method proposed in Colin et al. [1] will not detect spurious signals due to incomplete sky coverage, and that introducing additional Gaussian weighting to the statistic as in [2] can hinder its ability to detect a signal. Issues related to the width of the Gaussian smoothing are also discussed.
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
Direct estimation of Cole parameters in multifrequency EIT using a regularized Gauss-Newton method.
Brandstätter, Bernhard; Hollaus, Karl; Hutten, Helmut; Mayer, Michael; Merwa, Robert; Scharfetter, Hermann
2003-05-01
A major drawback of electrical impedance tomography is the poor quality of the conductivity images, i.e., the low spatial resolution as well as large errors in the reconstructed conductivity values. The main reason is the necessity for regularization of the ill-conditioned inverse problem which results in excessive spatial low-pass filtering. A novel regularization method (SMORR (spectral modelling regularized reconstructor)) is proposed, which is based on the inclusion of spectral a priori information in the form of appropriate tissue models (e.g. Cole models). This approach reduces the ill-posedness of the inverse problem, when multifrequency data are available. An additional advantage is the direct reconstruction of the (physiological) tissue parameters of interest instead of the conductivities. SMORR was compared with posterior fitting of a Cole model to the conductivity spectra obtained with a classical iterative reconstruction scheme at various frequencies. SMORR performed significantly better than the reference method concerning robustness against noise in the data.
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.
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.
Simple parameterized coordinate transformation method for deep- and smooth-profile gratings.
Xu, Xihong; Li, Lifeng
2014-12-01
A simple variable transformation that consists of two joined straight-line segments per grating period is proposed for the parameterized coordinate transformation method (the C method). With this bilinear parameterization, the C method can produce convergent numerical results for gratings of deep and smooth profiles with a groove depth-to-period ratio as high as 10, which to date has been far out of reach of the C method. The danger of getting divergent results due to inadvertently using an overly large truncation number is also practically eliminated.
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
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
Methods for Least Squares Data Smoothing by Adjustment of Divided Differences
NASA Astrophysics Data System (ADS)
Demetriou, I. C.
2008-09-01
A brief survey is presented for the main methods that are used in least squares data smoothing by adjusting the signs of divided differences of the smoothed values. The most distinctive feature of the smoothing approach is that it provides automatically a piecewise monotonic or a piecewise convex/concave fit to the data. The data are measured values of a function of one variable that contain random errors. As a consequence of the errors, the number of sign alterations in the sequence of mth divided differences is usually unacceptably large, where m is a prescribed positive integer. Therefore, we make the least sum of squares change to the measurements by requiring the sequence of the divided differences of order m to have at most k-1 sign changes, for some positive integer k. Although, it is a combinatorial problem, whose solution can require about O(nk) quadratic programming calculations in n variables and n-m constraints, where n is the number of data, very efficient algorithms have been developed for the cases when m = 1 or m = 2 and k is arbitrary, as well as when m>2 for small values of k. Attention is paid to the purpose of each method instead of to its details. Some software packages make the methods publicly accessible through library systems.
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.
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.
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.
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.
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
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.
Smoothed Particle Inference: A Kilo-Parametric Method for X-ray Galaxy Cluster Modeling
Peterson, John R.; Marshall, P.J.; Andersson, K.; /Stockholm U. /SLAC
2005-08-05
We propose an ambitious new method that models the intracluster medium in clusters of galaxies as a set of X-ray emitting smoothed particles of plasma. Each smoothed particle is described by a handful of parameters including temperature, location, size, and elemental abundances. Hundreds to thousands of these particles are used to construct a model cluster of galaxies, with the appropriate complexity estimated from the data quality. This model is then compared iteratively with X-ray data in the form of adaptively binned photon lists via a two-sample likelihood statistic and iterated via Markov Chain Monte Carlo. The complex cluster model is propagated through the X-ray instrument response using direct sampling Monte Carlo methods. Using this approach the method can reproduce many of the features observed in the X-ray emission in a less assumption-dependent way that traditional analyses, and it allows for a more detailed characterization of the density, temperature, and metal abundance structure of clusters. Multi-instrument X-ray analyses and simultaneous X-ray, Sunyaev-Zeldovich (SZ), and lensing analyses are a straight-forward extension of this methodology. Significant challenges still exist in understanding the degeneracy in these models and the statistical noise induced by the complexity of the models.
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.
NASA Astrophysics Data System (ADS)
Li, Fang; Wang, Shoudong; Chen, Xiaohong; Liu, Guochang; Zheng, Qiang
2014-04-01
Deconvolution is an important part of seismic processing tool for improving the resolution. One of the key assumptions made in most deconvolutional methods is that the seismic data is stationary. However, due to the anelastic absorption, the seismic data is usually nonstationary. In this paper, a novel nonstationary deconvolution approach is proposed based on spectral modeling and variable-step sampling (VSS) hyperbolic smoothing. To facilitate our method, firstly, we apply the Gabor transform to perform a time-frequency decomposition of the nonstationary seismic trace. Secondly, we estimate the source wavelet amplitude spectrum by spectral modeling. Thirdly, smoothing the Gabor magnitude spectrum of seismic data along hyperbolic paths with VSS can obtain the magnitude of the attenuation function, and can also eliminate the effect of source wavelet. Fourthly, by assuming that the source wavelet and attenuation function are minimum phase, their phases can be determined by Hilbert transform. Finally, the estimated two factors are removed by dividing them into the Gabor spectrum of the trace to estimate the Gabor spectrum of the reflectivity. An inverse Gabor transform gives the time-domain reflectivity estimate. Tests on synthetic and field data show that the presented method is an effective tool that not only has the advantages of stationary deconvolution, but also can compensate for the energy absorption, without knowing or estimating the quality factor Q.
Method of adiabatic modes in studying problems of smoothly irregular open waveguide structures
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.
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.
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
Kerfriden, P.; Gosselet, P.; Adhikari, S.; Bordas, S.
2013-01-01
This article describes a bridge between POD-based model order reduction techniques and the classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, “on-the-fly”, the reduced order modelling of highly nonlinear problems undergoing strong topological changes. Damage initiation problems are addressed and tackle via a corrected hyperreduction method. It is shown that the relevancy of reduced order model can be significantly improved with reasonable additional costs when using this algorithm, even when strong topological changes are involved. PMID:27076688
HyeongKae Park; Robert R. Nourgaliev; Richard C. Martineau; Dana A. Knoll
2008-09-01
We present high-order accurate spatiotemporal discretization of all-speed flow solvers using Jacobian-free Newton Krylov framework. One of the key developments in this work is the physics-based preconditioner for the all-speed flow, which makes use of traditional semi-implicit schemes. The physics-based preconditioner is developed in the primitive variable form, which allows a straightforward separation of physical phenomena. Numerical examples demonstrate that the developed preconditioner effectively reduces the number of the Krylov iterations, and the efficiency is independent of the Mach number and mesh sizes under a fixed CFL condition.
NASA Astrophysics Data System (ADS)
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.
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.
NASA Astrophysics Data System (ADS)
Sugio, Tetsuya; Yamamoto, Masayoshi; Funabiki, Shigeyuki
The use of an SMES (Superconducting Magnetic Energy Storage) for smoothing power fluctuations in a railway substation has been discussed. This paper proposes a smoothing control method based on fuzzy reasoning for reducing the SMES capacity at substations along high-speed railways. The proposed smoothing control method comprises three countermeasures for reduction of the SMES capacity. The first countermeasure involves modification of rule 1 for smoothing out the fluctuating electric power to its average value. The other countermeasures involve the modification of the central value of the stored energy control in the SMES and revision of the membership function in rule 2 for reduction of the SMES capacity. The SMES capacity in the proposed smoothing control method is reduced by 49.5% when compared to that in the nonrevised control method. It is confirmed by computer simulations that the proposed control method is suitable for smoothing out power fluctuations in substations along high-speed railways and for reducing the SMES capacity.
An incompressible smoothed particle hydrodynamics method for the motion of rigid bodies in fluids
NASA Astrophysics Data System (ADS)
Tofighi, N.; Ozbulut, M.; Rahmat, A.; Feng, J. J.; Yildiz, M.
2015-09-01
A two-dimensional incompressible smoothed particle hydrodynamics scheme is presented for simulation of rigid bodies moving through Newtonian fluids. The scheme relies on combined usage of the rigidity constraints and the viscous penalty method to simulate rigid body motion. Different viscosity ratios and interpolation schemes are tested by simulating a rigid disc descending in quiescent medium. A viscosity ratio of 100 coupled with weighted harmonic averaging scheme has been found to provide satisfactory results. The performance of the resulting scheme is systematically tested for cases with linear motion, rotational motion and their combination. The test cases include sedimentation of a single and a pair of circular discs, sedimentation of an elliptic disc and migration and rotation of a circular disc in linear shear flow. Comparison with previous results at various Reynolds numbers indicates that the proposed method captures the motion of rigid bodies driven by flow or external body forces accurately.
NASA Astrophysics Data System (ADS)
Yang, G.; Han, X.; Hu, D. A.
2015-11-01
Modified cylindrical smoothed particle hydrodynamics (MCSPH) approximation equations are derived for hydrodynamics with material strength in axisymmetric cylindrical coordinates. The momentum equation and internal energy equation are represented to be in the axisymmetric form. The MCSPH approximation equations are applied to simulate the process of explosively driven metallic tubes, which includes strong shock waves, large deformations and large inhomogeneities, etc. The meshless and Lagrangian character of the MCSPH method offers the advantages in treating the difficulties embodied in these physical phenomena. Two test cases, the cylinder test and the metallic tube driven by two head-on colliding detonation waves, are presented. Numerical simulation results show that the new form of the MCSPH method can predict the detonation process of high explosives and the expansion process of metallic tubes accurately and robustly.
NASA Astrophysics Data System (ADS)
Mozdgir, A.; Mahdavi, Iraj; Seyyedi, I.; Shiraqei, M. E.
2011-06-01
An assembly line is a flow-oriented production system where the productive units performing the operations, referred to as stations, are aligned in a serial manner. The assembly line balancing problem arises and has to be solved when an assembly line has to be configured or redesigned. The so-called simple assembly line balancing problem (SALBP), a basic version of the general problem, has attracted attention of researchers and practitioners of operations research for almost half a century. There are four types of objective functions which are considered to this kind of problem. The versions of SALBP may be complemented by a secondary objective which consists of smoothing station loads. Many heuristics have been proposed for the assembly line balancing problem due to its computational complexity and difficulty in identifying an optimal solution and so many heuristic solutions are supposed to solve this problem. In this paper a differential evolution algorithm is developed to minimize workload smoothness index in SALBP-2 and the algorithm parameters are optimized using Taguchi method.
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.
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)
Experiments with "Newton's Cradle."
ERIC Educational Resources Information Center
Ehrlich, Robert
1996-01-01
Outlines the use of the toy popularly known as Newton's Cradle or Newton's Balls in illustrating the laws of conservation of momentum and mechanical energy. Discusses in detail the joint effects of elasticity, friction, and ball alignment on the rate of damping of this apparatus. (JRH)
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.
Coupling of Smoothed Particle Hydrodynamics with Finite Volume method for free-surface flows
NASA Astrophysics Data System (ADS)
Marrone, S.; Di Mascio, A.; Le Touzé, D.
2016-04-01
A new algorithm for the solution of free surface flows with large front deformation and fragmentation is presented. The algorithm is obtained by coupling a classical Finite Volume (FV) approach, that discretizes the Navier-Stokes equations on a block structured Eulerian grid, with an approach based on the Smoothed Particle Hydrodynamics (SPH) method, implemented in a Lagrangian framework. The coupling procedure is formulated in such a way that each solver is applied in the region where its intrinsic characteristics can be exploited in the most efficient and accurate way: the FV solver is used to resolve the bulk flow and the wall regions, whereas the SPH solver is implemented in the free surface region to capture details of the front evolution. The reported results clearly prove that the combined use of the two solvers is convenient from the point of view of both accuracy and computing time.
Wu, Wei; Fan, Qinwei; Zurada, Jacek M; Wang, Jian; Yang, Dakun; Liu, Yan
2014-02-01
The aim of this paper is to develop a novel method to prune feedforward neural networks by introducing an L1/2 regularization term into the error function. This procedure forces weights to become smaller during the training and can eventually removed after the training. The usual L1/2 regularization term involves absolute values and is not differentiable at the origin, which typically causes oscillation of the gradient of the error function during the training. A key point of this paper is to modify the usual L1/2 regularization term by smoothing it at the origin. This approach offers the following three advantages: First, it removes the oscillation of the gradient value. Secondly, it gives better pruning, namely the final weights to be removed are smaller than those produced through the usual L1/2 regularization. Thirdly, it makes it possible to prove the convergence of the training. Supporting numerical examples are also provided.
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.
NASA Astrophysics Data System (ADS)
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
NASA Astrophysics Data System (ADS)
Wang, Liang; Chen, Dong; Cheng, Tinghai; He, Pu; Lu, Xiaohui; Zhao, Hongwei
2016-08-01
The smooth impact drive mechanism (SIDM) is a type of piezoelectric actuator that has been developed for several decades. As a kind of driving method for the SIDM, the traditional sawtooth (TS) wave is always employed. The kinetic friction force during the rapid contraction stage usually results in the generation of a backward motion. A friction regulation hybrid (FRH) driving method realized by a composite waveform for the backward motion restraint of the SIDM is proposed in this paper. The composite waveform is composed of a sawtooth driving (SD) wave and a sinusoidal friction regulation (SFR) wave which is applied to the rapid deformation stage of the SD wave. A prototype of the SIDM was fabricated and its output performance under the excitation of the FRH driving method and the TS wave driving method was tested. The results indicate that the backward motion can be restrained obviously using the FRH driving method. Compared with the driving effect of the TS wave, the backward rates of the prototype in forward and reverse motions are decreased by 83% and 85%, respectively.
NASA Technical Reports Server (NTRS)
Tsiveriotis, K.; Brown, R. A.
1993-01-01
A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.
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
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.
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 factor…
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
ERIC Educational Resources Information Center
Erlichson, Herman
1995-01-01
Discusses Newton's apparent oversight of the role of energy considerations in collisions between two spherical bodies related to the third corollary of his "Laws of Motion." Investigates several theories that provide solutions to the mysterious oversight. (LZ)
NASA Astrophysics Data System (ADS)
Dyachkov, S. A.; Parshikov, A. N.; Zhakhovsky, V. V.
2015-11-01
Experimental methods of observation of early stage of shock-induced ejecta from metal surface with micrometer-sized perturbations are still limited in terms of following a complete sequence of processes having microscale dimensions and nanoscale times. Therefore, simulations by the smoothed particle hydrodynamics (SPH) and molecular dynamics (MD) methods can shed of light on details of micro-jet evolution. The size of simulated sample is too restricted in MD, but the simulations with large enough number of atoms can be scaled well to the sizes of realistic samples. To validate such scaling the comparative MD and SPH simulations of tin samples are performed. SPH simulation takes the realistic experimental sizes, while MD uses the proportionally scaled sizes of samples. It is shown that the velocity and mass distributions along the jets simulated by MD and SPH are in a good agreement. The observed difference in velocity of spikes between MD and experiments can be partially explained by a profound effect of surface tension on jets ejected from the small-scale samples.
MASS TRANSFER IN BINARY STARS USING SMOOTHED PARTICLE HYDRODYNAMICS. I. NUMERICAL METHOD
Lajoie, Charles-Philippe; Sills, Alison E-mail: asills@mcmaster.ca
2011-01-10
Close interactions and mass transfer in binary stars can lead to the formation of many different exotic stellar populations, but detailed modeling of mass transfer is a computationally challenging problem. Here, we present an alternate smoothed particle hydrodynamics approach to the modeling of mass transfer in binary systems that allows a better resolution of the flow of matter between main-sequence stars. Our approach consists of modeling only the outermost layers of the stars using appropriate boundary conditions and ghost particles. We arbitrarily set the radius of the boundary and find that our boundary treatment behaves physically and conserves energy well. In particular, when used with our binary relaxation procedure, our treatment of boundary conditions is also shown to evolve circular binaries properly for many orbits. The results of our first simulation of mass transfer are also discussed and used to assess the strengths and limitations of our method. We conclude that it is well suited for the modeling of interacting binary stars. The method presented here represents a convenient alternative to previous hydrodynamical techniques aimed at modeling mass transfer in binary systems since it can be used to model both the donor and the accretor while maintaining the density profiles taken from realistic stellar models.
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.
Newton and scholastic philosophy.
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.
Newton and scholastic philosophy.
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. PMID:26593733
Method reduces computer time for smoothing functions and derivatives through ninth order polynomials
NASA Technical Reports Server (NTRS)
Glauz, R. D.; Wilgus, C. A.
1969-01-01
Analysis presented is an efficient technique to adjust previously calculated orthogonal polynomial coefficients for an odd number of equally spaced data points. The adjusting technique derivation is for a ninth order polynomial. It reduces computer time for smoothing functions.
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.
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.
NASA Astrophysics Data System (ADS)
Zouch, Wassim; Slima, Mohamed Ben; Feki, Imed; Derambure, Philippe; Taleb-Ahmed, Abdelmalik; Hamida, Ahmed Ben
2010-12-01
A new nonparametric method, based on the smooth weighted-minimum-norm (WMN) focal underdetermined-system solver (FOCUSS), for electrical cerebral activity localization using electroencephalography measurements is proposed. This method iteratively adjusts the spatial sources by reducing the size of the lead-field and the weighting matrix. Thus, an enhancement of source localization is obtained, as well as a reduction of the computational complexity. The performance of the proposed method, in terms of localization errors, robustness, and computation time, is compared with the WMN-FOCUSS and nonshrinking smooth WMN-FOCUSS methods as well as with standard generalized inverse methods (unweighted minimum norm, WMN, and FOCUSS). Simulation results for single-source localization confirm the effectiveness and robustness of the proposed method with respect to the reconstruction accuracy of a simulated single dipole.
Mazza, G; Roßmanith, E; Lang-Olip, I; Pfeiffer, D
2016-08-01
Even though umbilical cord arteries are a common source of vascular smooth muscle cells, the lack of reliable marker profiles have not facilitated the isolation of human umbilical artery smooth muscle cells (HUASMC). For accurate characterization of HUASMC and cells in their environment, the expression of smooth muscle and mesenchymal markers was analyzed in umbilical cord tissue sections. The resulting marker profile was then used to evaluate the quality of HUASMC isolation and culture methods. HUASMC and perivascular-Wharton's jelly stromal cells (pv-WJSC) showed positive staining for α-smooth muscle actin (α-SMA), smooth muscle myosin heavy chain (SM-MHC), desmin, vimentin and CD90. Anti-CD10 stained only pv-WJSC. Consequently, HUASMC could be characterized as α-SMA+ , SM-MHC+ , CD10- cells, which are additionally negative for endothelial markers (CD31 and CD34). Enzymatic isolation provided primary HUASMC batches with 90-99 % purity, yet, under standard culture conditions, contaminant CD10+ cells rapidly constituted more than 80 % of the total cell population. Contamination was mainly due to the poor adhesion of HUASMC to cell culture plates, regardless of the different protein coatings (fibronectin, collagen I or gelatin). HUASMC showed strong attachment and long-term viability only in 3D matrices. The explant isolation method achieved cultures with only 13-40 % purity with considerable contamination by CD10+ cells. CD10+ cells showed spindle-like morphology and up-regulated expression of α-SMA and SM-MHC upon culture in smooth muscle differentiation medium. Considering the high contamination risk of HUASMC cultures by CD10+ neighboring cells and their phenotypic similarities, precise characterization is mandatory to avoid misleading results.
NITSOL: A Newton iterative solver for nonlinear systems
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.
NASA Astrophysics Data System (ADS)
Voznyuk, I.; Litman, A.; Tortel, H.
2015-08-01
A Quasi-Newton method for reconstructing the constitutive parameters of three-dimensional (3D) penetrable scatterers from scattered field measurements is presented. This method is adapted for handling large-scale electromagnetic problems while keeping the memory requirement and the time flexibility as low as possible. The forward scattering problem is solved by applying the finite-element tearing and interconnecting full-dual-primal (FETI-FDP2) method which shares the same spirit as the domain decomposition methods for finite element methods. The idea is to split the computational domain into smaller non-overlapping sub-domains in order to simultaneously solve local sub-problems. Various strategies are proposed in order to efficiently couple the inversion algorithm with the FETI-FDP2 method: a separation into permanent and non-permanent subdomains is performed, iterative solvers are favorized for resolving the interface problem and a marching-on-in-anything initial guess selection further accelerates the process. The computational burden is also reduced by applying the adjoint state vector methodology. Finally, the inversion algorithm is confronted to measurements extracted from the 3D Fresnel database.
Methods and energy storage devices utilizing electrolytes having surface-smoothing additives
Xu, Wu; Zhang, Jiguang; Graff, Gordon L; Chen, Xilin; Ding, Fei
2015-11-12
Electrodeposition and energy storage devices utilizing an electrolyte having a surface-smoothing additive can result in self-healing, instead of self-amplification, of initial protuberant tips that give rise to roughness and/or dendrite formation on the substrate and anode surface. For electrodeposition of a first metal (M1) on a substrate or anode from one or more cations of M1 in an electrolyte solution, the electrolyte solution is characterized by a surface-smoothing additive containing cations of a second metal (M2), wherein cations of M2 have an effective electrochemical reduction potential in the solution lower than that of the cations of M1.
Induced Pluripotent Stem Cell-derived Vascular Smooth Muscle Cells: Methods and Application
Dash, Biraja C.; Jiang, Zhengxin; Suh, Carol; Qyang, Yibing
2015-01-01
Vascular smooth muscle cells (VSMCs) play a major role in the pathophysiology of cardiovascular diseases. The advent of induced pluripotent stem cell (iPSC) technology and their capability to differentiation into virtually every cell type in the human body make this field a ray of hope for vascular regenerative therapy and for understanding disease mechanism. In this review, we first discuss the recent iPSC technology and vascular smooth muscle development from embryo and then examine different methodology to derive VSMCs from iPSCs and their applications in regenerative therapy and disease modeling. PMID:25559088
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.
"To Improve upon Hints of Things": Illustrating Isaac Newton.
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. PMID:27071300
"To Improve upon Hints of Things": Illustrating Isaac Newton.
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.
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)
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.
Kalita, Dhruba Jyoti; Gupta, Ashish K
2010-10-01
A study of the multiphoton dissociation of H(2)(+) in intense laser field using the smooth exterior scaling method to calculate resonance states is presented. This method is very attractive as it does not disturb the interaction region. The wave functions calculated with this method provide indisputable proof in support of the mechanisms of the different phenomena happening during photodissociation. Wave functions corresponding to the "vibrationally trapped" (bond-hardening) states are found. A unequivocal mechanism for "bond-softening" is provided. It is observed that with an increase in intensity, the lifetime of low vibrational level increases. The mechanism for this novel phenomenon is also explained.
NASA Astrophysics Data System (ADS)
Maris, Virginie
An existing 3-D magnetotelluric (MT) inversion program written for a single processor personal computer (PC) has been modified and parallelized using OpenMP, in order to run the program efficiently on a multicore workstation. The program uses the Gauss-Newton inversion algorithm based on a staggered-grid finite-difference forward problem, requiring explicit calculation of the Frechet derivatives. The most time-consuming tasks are calculating the derivatives and determining the model parameters at each iteration. Forward modeling and derivative calculations are parallelized by assigning the calculations for each frequency to separate threads, which execute concurrently. Model parameters are obtained by factoring the Hessian using the LDLT method, implemented using a block-cyclic algorithm and compact storage. MT data from 102 tensor stations over the East Flank of the Coso Geothermal Field, California are inverted. Less than three days are required to invert the dataset for ˜ 55,000 inversion parameters on a 2.66 GHz 8-CPU PC with 16 GB of RAM. Inversion results, recovered from a halfspace rather than initial 2-D inversions, qualitatively resemble models from massively parallel 3-D inversion by other researchers and overall, exhibit an improved fit. A steeply west-dipping conductor under the western East Flank is tentatively correlated with a zone of high-temperature ionic fluids based on known well production and lost circulation intervals. Beneath the Main Field, vertical and north-trending shallow conductors are correlated with geothermal producing intervals as well.
Modeling the propagation of volcanic debris avalanches by a Smoothed Particle Hydrodynamics method
NASA Astrophysics Data System (ADS)
Sosio, Rosanna; Battista Crosta, Giovanni
2010-05-01
Hazard from collapses of volcanic edifices threatens million of people which currently live on top of volcanic deposits or around volcanoes prone to fail. Nevertheless, no much effort has been dedicated for the evaluation of the hazard posed by volcanic debris avalanches (e.g. emergency plans, hazard zoning maps). This work focuses at evaluating the exceptional mobility of volcanic debris avalanches for hazard analyses purposes by providing a set of calibrated cases. We model the propagation of eight debris avalanche selected among the best known historical events originated from sector collapses of volcanic edifices. The events have large volumes (ranging from 0.01-0.02 km3 to 25 km3) and are well preserved so that their main features are recognizable from satellite images. The events developed in a variety of settings and condition and they vary with respect to their morphological constrains, materials, styles of failure. The modeling has been performed using a Lagragian numerical method adapted from Smoothed Particle Hydrodynamics to solve the depth averaged quasi-3D equation for motion (McDougall and Hungr 2004). This code has been designed and satisfactorily used to simulate rock and debris avalanches in non-volcanic settings (McDougall and Hungr, 2004). Its use is here extended to model volcanic debris avalanches which may differ from non-volcanic ones by dimensions, water content and by possible thermodynamic effects or degassing caused by active volcanic processes. The resolution of the topographic data is generally low for remote areas like the ones considered in this study, while the pre event topographies are more often not available. The effect of the poor topographic resolution on the final results has been evaluated by replicating the modeling on satellite-derived topographical grids with varying cell size (from 22 m to 90 m). The event reconstructions and the back analyses are based on the observations available from the literature. We test the
Simulation of wave mitigation by coastal vegetation using smoothed particle hydrodynamics method
NASA Astrophysics Data System (ADS)
Iryanto; Gunawan, P. H.
2016-02-01
Vegetation in coastal area lead to wave mitigation has been studied by some researchers recently. The effect of vegetation forest in coastal area is minimizing the negative impact of wave propagation. In order to describe the effect of vegetation resistance into the water flow, the modified model of framework smoothed hydrodynamics particle has been constructed. In the Lagrangian framework, the Darcy, Manning, and laminar viscosity resistances are added. The effect of each resistances is given in some results of numerical simulations. Simulation of wave mitigation on sloping beach is also given.
Airway mechanics and methods used to visualize smooth muscle dynamics in vitro.
Cooper, P R; McParland, B E; Mitchell, H W; Noble, P B; Politi, A Z; Ressmeyer, A R; West, A R
2009-10-01
Contraction of airway smooth muscle (ASM) is regulated by the physiological, structural and mechanical environment in the lung. We review two in vitro techniques, lung slices and airway segment preparations, that enable in situ ASM contraction and airway narrowing to be visualized. Lung slices and airway segment approaches bridge a gap between cell culture and isolated ASM, and whole animal studies. Imaging techniques enable key upstream events involved in airway narrowing, such as ASM cell signalling and structural and mechanical events impinging on ASM, to be investigated.
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.
Newton polyhedron and applications
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.
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.
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.
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
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
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.
NASA Astrophysics Data System (ADS)
Fessant, Françoise; Pierret, Catherine; Lantos, Pierre
1996-10-01
In this paper we propose a comparison between two methods for the problem of long-term prediction of the smoothed sunspot index. These two methods are first the classical method of McNish and Lincoln (as improved by Stewart and Ostrow), and second a neural network method. The results of these two methods are compared in two periods, during the ascending and the declining phases of the current cycle 22 (1986 1996). The predictions with neural networks are much better than with the McNish and Lincoln method for the atypical ascending phase of cycle 22. During the second period the predictions are very similar, and in agreement with observations, when the McNish and Lincoln method is based on the data of declining phases of the cycles.
Isaac Newton and the astronomical refraction.
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.
The Unknown Detective Career of Isaac Newton
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.
An implicit Smooth Particle Hydrodynamic code
Charles E. Knapp
2000-04-01
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.
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.
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…
Kawato, M; Isobe, M; Maeda, Y; Suzuki, R
1988-01-01
In order to control visually-guided voluntary movements, the central nervous system (CNS) must solve the following three computational problems at different levels: (1) determination of a desired trajectory in the visual coordinates, (2) transformation of the coordinates of the desired trajectory to the body coordinates and (3) generation of motor command. In this paper, the second and the third problems are treated at computational, representational and hardware levels of Marr. We first study the problems at the computational level, and then propose an iterative learning scheme as a possible algorithm. This is a trial and error type learning such as repetitive training of golf swing. The amount of motor command needed to coordinate activities of many muscles is not determined at once, but in a step-wise, trial and error fashion in the course of a set of repetitions. Actually, the motor command in the (n + 1)-th iteration is a sum of the motor command in the n-th iteration plus two modification terms which are, respectively, proportional to acceleration and speed errors between the desired trajectory and the realized trajectory in the n-th iteration. We mathematically formulate this iterative learning control as a Newton-like method in functional spaces and prove its convergence under appropriate mathematical conditions with use of dynamical system theory and functional analysis. Computer simulations of this iterative learning control of a robotic manipulator in the body or visual coordinates are shown. Finally, we propose that areas 2, 5, and 7 of the sensory association cortex are possible sites of this learning control. Further we propose neural network model which acquires transformation matrices from acceleration or velocity to motor command, which are used in these schemes. PMID:3179342
Kawato, M; Isobe, M; Maeda, Y; Suzuki, R
1988-01-01
In order to control visually-guided voluntary movements, the central nervous system (CNS) must solve the following three computational problems at different levels: (1) determination of a desired trajectory in the visual coordinates, (2) transformation of the coordinates of the desired trajectory to the body coordinates and (3) generation of motor command. In this paper, the second and the third problems are treated at computational, representational and hardware levels of Marr. We first study the problems at the computational level, and then propose an iterative learning scheme as a possible algorithm. This is a trial and error type learning such as repetitive training of golf swing. The amount of motor command needed to coordinate activities of many muscles is not determined at once, but in a step-wise, trial and error fashion in the course of a set of repetitions. Actually, the motor command in the (n + 1)-th iteration is a sum of the motor command in the n-th iteration plus two modification terms which are, respectively, proportional to acceleration and speed errors between the desired trajectory and the realized trajectory in the n-th iteration. We mathematically formulate this iterative learning control as a Newton-like method in functional spaces and prove its convergence under appropriate mathematical conditions with use of dynamical system theory and functional analysis. Computer simulations of this iterative learning control of a robotic manipulator in the body or visual coordinates are shown. Finally, we propose that areas 2, 5, and 7 of the sensory association cortex are possible sites of this learning control. Further we propose neural network model which acquires transformation matrices from acceleration or velocity to motor command, which are used in these schemes.
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
Modelling shear flows with smoothed particle hydrodynamics and grid-based methods
NASA Astrophysics Data System (ADS)
Junk, Veronika; Walch, Stefanie; Heitsch, Fabian; Burkert, Andreas; Wetzstein, Markus; Schartmann, Marc; Price, Daniel
2010-09-01
Given the importance of shear flows for astrophysical gas dynamics, we study the evolution of the Kelvin-Helmholtz instability (KHI) analytically and numerically. We derive the dispersion relation for the two-dimensional KHI including viscous dissipation. The resulting expression for the growth rate is then used to estimate the intrinsic viscosity of four numerical schemes depending on code-specific as well as on physical parameters. Our set of numerical schemes includes the Tree-SPH code VINE, an alternative smoothed particle hydrodynamics (SPH) formulation developed by Price and the finite-volume grid codes FLASH and PLUTO. In the first part, we explicitly demonstrate the effect of dissipation-inhibiting mechanisms such as the Balsara viscosity on the evolution of the KHI. With VINE, increasing density contrasts lead to a continuously increasing suppression of the KHI (with complete suppression from a contrast of 6:1 or higher). The alternative SPH formulation including an artificial thermal conductivity reproduces the analytically expected growth rates up to a density contrast of 10:1. The second part addresses the shear flow evolution with FLASH and PLUTO. Both codes result in a consistent non-viscous evolution (in the equal as well as in the different density case) in agreement with the analytical prediction. The viscous evolution studied with FLASH shows minor deviations from the analytical prediction.
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
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
NASA Astrophysics Data System (ADS)
Sohn, Dongwoo; Im, Seyoung
2013-06-01
In this paper, novel finite elements that include an arbitrary number of additional nodes on each edge of a quadrilateral element are proposed to achieve compatible connection of neighboring nonmatching meshes in plate and shell analyses. The elements, termed variable-node plate elements, are based on two-dimensional variable-node elements with point interpolation and on the Mindlin-Reissner plate theory. Subsequently the flat shell elements, termed variable-node shell elements, are formulated by further extending the plate elements. To eliminate a transverse shear locking phenomenon, the assumed natural strain method is used for plate and shell analyses. Since the variable-node plate and shell elements allow an arbitrary number of additional nodes and overcome locking problems, they make it possible to connect two nonmatching meshes and to provide accurate solutions in local mesh refinement. In addition, the curvature and strain smoothing methods through smoothed integration are adopted to improve the element performance. Several numerical examples are presented to demonstrate the effectiveness of the elements in terms of the accuracy and efficiency of the analyses.
NASA Astrophysics Data System (ADS)
Nassauer, Benjamin; Liedke, Thomas; Kuna, Meinhard
2016-03-01
In the present paper, the direct coupling of a discrete element method (DEM) with polyhedral particles and smoothed particle hydrodynamics (SPH) is presented. The two simulation techniques are fully coupled in both ways through interaction forces between the solid DEM particles and the fluid SPH particles. Thus this simulation method provides the possibility to simulate the individual movement of polyhedral, sharp-edged particles as well as the flow field around these particles in fluid-saturated granular matter which occurs in many technical processes e.g. wire sawing, grinding or lapping. The coupled method is exemplified and validated by the simulation of a particle in a shear flow, which shows good agreement with analytical solutions.
Critical Parameters of the In Vitro Method of Vascular Smooth Muscle Cell Calcification
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
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.
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)
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…
ERIC Educational Resources Information Center
Westfall, Richard S.
1973-01-01
Newton's contribution to measure a phenomenon quantitatively and explain results along the lines of mechanical philosophy has been accepted as a common approach of science. Describes many of the mathematical relationships based on these lines that Newton found about different phenomena. (PS)
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…
MODFLOW-NWT, A Newton formulation for MODFLOW-2005
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
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.
Computing modified Newton directions using a partial Cholesky factorization
Forsgren, A.; Gill, P.E.; Murray, W.
1993-03-01
The effectiveness of Newton`s method for finding an unconstrained minimizer of a strictly convex twice continuously differentiable function has prompted the proposal of various modified Newton inetliods for the nonconvex case. Linesearch modified Newton methods utilize a linear combination of a descent direction and a direction of negative curvature. If these directions are sufficient in a certain sense, and a suitable linesearch is used, the resulting method will generate limit points that satisfy the second-order necessary conditions for optimality. We propose an efficient method for computing a descent direction and a direction of negative curvature that is based on a partial Cholesky factorization of the Hessian. This factorization not only gives theoretically satisfactory directions, but also requires only a partial pivoting strategy, i.e., the equivalent of only two rows of the Schur complement need be examined at each step.
PEOPLE IN PHYSICS: Newton's apple
NASA Astrophysics Data System (ADS)
Sandford Smith, Daniel
1997-03-01
This essay has a long history. It was triggered at university by one of my tutors describing the dispute between Robert Hooke and Isaac Newton. He conjured up an image of Newton sitting at his desk doing calculations while Hooke went down mineshafts trying to detect a change in the strength of gravity. To someone who was finding the maths content of a physics degree somewhat challenging this was a symbolic image. I believe that the story of Newton and the apple illustrates the complex nature of scientific discovery.
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…
NASA Astrophysics Data System (ADS)
Belenkiy, Ari
2007-08-01
Among the Newtonian manuscripts, owned by the Jewish National and University Library at Jerusalem and known as MS Yahuda 24, there is a proposal for the reform of the Julian and Ecclesiastical calendars, written in three drafts in early 1700. This was Newton's response to the challenge suggested by Continental mathematicians and astronomers, G.W. Leibniz in particular. This calendar, if implemented in England, would have become a formidable rival to the Gregorian calendar. Despite having a different algorithm, its solar part agrees with the latter until 2400 AD and is more precise in the long run, within a period of 5,000 years. Its lunar algorithm is simpler than the Gregorian, but remained incomplete. Though the calendar was buried under a pile of theological papers, were it now to be implemented it would have a glorious future, since it includes the most characteristic features of the Christian, Jewish, and Muslim calendars and can aspire to become the universal calendar. Looking for the best astronomical parameters Newton attempted to compute the length of the tropical year using the ancient equinox observations reported by Hipparchus of Rhodes. Though Newton had a very thin sample of data, he obtained a tropical year only a few seconds longer than the correct length. We show that the reason lies in Newton's application of a technique similar (though not identical) to the modern ordinary least squares method. Newton also had a clear understanding of qualitative variables. Open historic-astronomical problems related to inclination of the Earth's axis of rotation are discussed. In particular, ignorance about the long-range variation in inclination and nutation is likely responsible for the wide variety in the lengths of the tropical year assigned by different 17th century astronomers - the problem that led Newton to Hipparchus.
Joshi, Anand A.; Shattuck, David W.; Thompson, Paul M.; Leahy, Richard M.
2009-01-01
Neuroimaging data, such as 3-D maps of cortical thickness or neural activation, can often be analyzed more informatively with respect to the cortical surface rather than the entire volume of the brain. Any cortical surface-based analysis should be carried out using computations in the intrinsic geometry of the surface rather than using the metric of the ambient 3-D space. We present parameterization-based numerical methods for performing isotropic and anisotropic filtering on triangulated surface geometries. In contrast to existing FEM-based methods for triangulated geometries, our approach accounts for the metric of the surface. In order to discretize and numerically compute the isotropic and anisotropic geometric operators, we first parameterize the surface using a p-harmonic mapping. We then use this parameterization as our computational domain and account for the surface metric while carrying out isotropic and anisotropic filtering. To validate our method, we compare our numerical results to the analytical expression for isotropic diffusion on a spherical surface. We apply these methods to smoothing of mean curvature maps on the cortical surface, a step commonly required for analysis of gyrification or for registering surface-based maps across subjects. PMID:19423447
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)
Adaptive particle refinement and derefinement applied to the smoothed particle hydrodynamics method
NASA Astrophysics Data System (ADS)
Barcarolo, D. A.; Le Touzé, D.; Oger, G.; de Vuyst, F.
2014-09-01
SPH simulations are usually performed with a uniform particle distribution. New techniques have been recently proposed to enable the use of spatially varying particle distributions, which encouraged the development of automatic adaptivity and particle refinement/derefinement algorithms. All these efforts resulted in very interesting and promising procedures leading to more efficient and faster SPH simulations. In this article, a family of particle refinement techniques is reviewed and a new derefinement technique is proposed and validated through several test cases involving both free-surface and viscous flows. Besides, this new procedure allows higher resolutions in the regions requiring increased accuracy. Moreover, several levels of refinement can be used with this new technique, as often encountered in adaptive mesh refinement techniques in mesh-based methods.
[Malthus's Essay and Newton's Principia].
Nakanishi, Y
1989-05-01
The author examines a natural scientific approach to demography using the example of Malthus's "Essay on the Principle of Population." The work is analyzed and compared to Newton's "Philosophiae Naturalis Principia Mathematica."
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
Newton solution of inviscid and viscous problems
NASA Technical Reports Server (NTRS)
Venkatakrishnan, V.
1988-01-01
The application of Newton iteration to inviscid and viscous airfoil calculations is examined. Spatial discretization is performed using upwind differences with split fluxes. The system of linear equations which arises as a result of linearization in time is solved directly using either a banded matrix solver or a sparse matrix solver. In the latter case, the solver is used in conjunction with the nested dissection strategy, whose implementation for airfoil calculations is discussed. The boundary conditions are also implemented in a fully implicit manner, thus yielding quadratic convergence. Complexities such as the ordering of cell nodes and the use of a far field vortex to correct freestream for a lifting airfoil are addressed. Various methods to accelerate convergence and improve computational efficiency while using Newton iteration are discussed. Results are presented for inviscid, transonic nonlifting and lifting airfoils and also for laminar viscous cases.
Space and motion in nature and Scripture: Galileo, Descartes, Newton.
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.
Space and motion in nature and Scripture: Galileo, Descartes, Newton.
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. PMID:26227236
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
NASA Astrophysics Data System (ADS)
Suwa, T.; Imamura, F.; Sugawara, D.; Ogasawara, K.; Watanabe, M.; Hirahara, T.
2014-12-01
A tsunami simulator integrating a 3-D fluid simulation technology that runs on large-scale parallel computers using smoothed-particle hydrodynamics (SPH) method has been developed together with a 2-D tsunami propagation simulation technique using a nonlinear shallow water wave model. We use the 2-D simulation to calculate tsunami propagation of scale of about 1000km from epicenter to near shore. The 3-D SPH method can be used to calculate the water surface and hydraulic force that a tsunami can exert on a building, and to simulate flooding patterns at urban area of at most km scale. With our simulator we can also see three dimensional fluid feature such as complex changes a tsunami undergoes as it interacts with coastal topography or structures. As a result it is hoped that, e.g. , effect of the structures to dissipate waves energy passing over it can be elucidated. The authors utilize the simulator in the third of five fields of the Strategic Programs for Innovative Research, "Advanced Prediction Researches for Natural Disaster Prevention and Reduction," or the theme "Improvement of the tsunami forecasting system on the HPCI computer." The results of tsunami simulation using the K computer will be reported. We are going to apply it to a real problem of the disaster prevention in future.
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.
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
NASA Astrophysics Data System (ADS)
Ginzburg, Vitalii L.
1987-01-01
The first edition of Newton's "Philosophiae Naturalis Principia Mathematica" was published in 1687. The present paper is dedicated to the tricentenary of this event, which is important not just in the history of physics, but of science generally. After the Introduction, the paper continues with the following Sections: Before Newton, Principia, Principia and the method of principles, The nature of gravitation, Critique of Newtonian mechanics and its subsequent development, On Newton, Concluding remarks.
The Cartwheel galaxy with XMM-Newton
NASA Astrophysics Data System (ADS)
Crivellari, E.; Wolter, A.; Trinchieri, G.
2009-07-01
Aims: The extreme environment provided by the Cartwheel ring is analyzed to study its X-ray and optical-UV properties. We compare the Cartwheel with the other members of its group and study the system as a whole in the X-ray band. Methods: We analyze the data of the Cartwheel galaxy obtained with XMM-Newton in two different periods (December 2004 and May 2005). We focus on the X-ray properties of the system and use the OM data to obtain additional information in the optical and UV bands. Each dataset is analyzed separately to study source variability and summed together to study fainter and extended sources. Results: We detect a total of 8 sources associated with the Cartwheel galaxy and three in its vicinity, including G1 and G2, all at LX ≥ 1039 erg s-1, that is the Ultra Luminous X-ray (ULX) source range. The brightest ULX source has been already discussed elsewhere. The spectra of the next three brightest ULX are well fitted by a power-law model with a mean photon index of 2. We compare the XMM-Newton and Chandra datasets to study the long-term variability of the sources. At least three sources vary in the 5 months between the two XMM-Newton observations and at least four in the 4-year timeframe between Chandra and XMM-Newton observations. One Chandra source disappears and a new one is detected by XMM-Newton in the ring. Optical-UV colors of the Cartwheel ring are consistent with a burst of star formation that is close to reaching its maximum, yielding a mean stellar age of about 40 Myr. The inferred variability and age suggest that high mass X-ray binaries are the counterparts to the ULX sources. The 3 companion galaxies have luminosities in the range 1039-40 erg/s consistent with expectations. The hot gas of the Cartwheel galaxy is luminous and abundant (a few 108 {M⊙}) and is found both in the outer ring, and in the inner part of the galaxy, behind the shock wave front. We also detect gas in the group with LX 1040 erg s-1.
Computing modified Newton directions using a partial Cholesky factorization
Forsgren, A. . Dept. of Mathematics); Gill, P.E. ); Murray, W. . Systems Optimization Lab.)
1993-03-01
The effectiveness of Newton's method for finding an unconstrained minimizer of a strictly convex twice continuously differentiable function has prompted the proposal of various modified Newton inetliods for the nonconvex case. Linesearch modified Newton methods utilize a linear combination of a descent direction and a direction of negative curvature. If these directions are sufficient in a certain sense, and a suitable linesearch is used, the resulting method will generate limit points that satisfy the second-order necessary conditions for optimality. We propose an efficient method for computing a descent direction and a direction of negative curvature that is based on a partial Cholesky factorization of the Hessian. This factorization not only gives theoretically satisfactory directions, but also requires only a partial pivoting strategy, i.e., the equivalent of only two rows of the Schur complement need be examined at each step.
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.
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)
NASA Astrophysics Data System (ADS)
Shaw, Mike
2012-11-01
Would you like to build an inexpensive, highly visible, quickly assembled device that dramatically illustrates Newton's three laws of motion? This model incorporates sturdiness, high-profile visibility, and a student interest component that is sure to capture and hold their attention.
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…
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…
Mathiowetz, A M; Jain, A; Karasawa, N; Goddard, W A
1994-11-01
Two new methods developed for molecular dynamics simulations of very large proteins are applied to a series of proteins ranging up to the protein capsid of tomato bushy stunt virus (TBSV). For molecular dynamics of very large proteins and polymers, it is useful to carry out the dynamics using internal coordinates (say, torsions only) rather than Cartesian coordinates. This allows larger time steps, eliminates problems with the classical description of high energy modes, and focuses on the important degrees of freedom. The resulting equation of motion has the form. [formula: see text] where for T is the vector of generalized forces, M(theta) is the moments of inertia tensor, theta is the vector of torsions, and C is a vector containing Coriolis forces and nonbond forces. The problem is that to calculate the acceleration vector theta from M, C, and T requires inverting M(theta), an order N3 calculation. Since the number of degrees of freedom might be 300,000 for a million atom system, solving these equations every time step is impractical, restricting internal coordinate methods to small systems. The new method, Newton-Euler Inverse Mass Operator (NEIMO) dynamics, constructs the torsional accelerations vector theta = M-1 (T-C) directly by an order N process, allowing internal-coordinate dynamics to be solved for super larger (million atom) systems. The first use of the NEIMO method for molecular dynamics of proteins is presented here. A second serious difficulty for large proteins is calculation of the nonbond forces. We report here the first application to proteins of the new Cell Multipole Method (CMM) to evaluate the Coulomb and van der Waals interactions. The costs of CMM scales linearly with the number of particles while retaining an accuracy significantly better than standard nonbond methods (involving cutoffs). Results for NEIMO and CMM are given for simulations of a wide range of peptide and protein systems, including the protein capsid of TBSV with 488
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)
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.
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.
Keynes, Newton and the Royal Society: the events of 1942 and 1943.
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.
Keynes, Newton and the Royal Society: the events of 1942 and 1943
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
The Use of Kruskal-Newton Diagrams for Differential Equations
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.
Hooke, orbital motion, and Newton's Principia
NASA Astrophysics Data System (ADS)
Nauenberg, Michael
1994-04-01
A detailed analysis is given of a 1685 graphical construction by Robert Hooke for the polygonal path of a body moving in a periodically pulsed radial field of force. In this example the force varies linearly with the distance from the center. Hooke's method is based directly on his original idea from the mid-1660s that the orbital motion of a planet is determined by compounding its tangential velocity with a radial velocity impressed by the gravitational attraction of the sun at the center. This hypothesis corresponds to the second law of motion, as formulated two decades later by Newton, and its geometrical implementation constitutes the cornerstone of Newton's Principia. Hooke's diagram represents the first known accurate graphical evaluation of an orbit in a central field of force, and it gives evidence that he demonstrated that his resulting discrete orbit is an approximate ellipse centered at the origin of the field of force. A comparable calculation to obtain orbits for an inverse square force, which Hooke had conjectured to be the gravitational force, has not been found among his unpublished papers. Such a calculation is carried out here numerically with the Newton-Hooke geometrical construction. It is shown that for orbits of comparable or larger eccentricity than Hooke's example, a graphical approach runs into convergence difficulties due to the singularity of the gravitational force at the origin. This may help resolve the long-standing mystery why Hooke never published his controversial claim that he had demonstrated that an attractive force, which is ``...in a duplicate proportion to the Distance from the Center Reciprocall...'' implies elliptic orbits.
NASA Astrophysics Data System (ADS)
Chartas, George
2003-03-01
A recent XMM-Newton observation of BALQSO PG1115+080(z1.72) has detected strong absorption lines in the Fe line region. A comparison between this and an earlier Chandra observation of PG1115+080 separated by 19~weeks resulted in a weak constraint on the variability of these absorption lines due to the low S/N of the Chandra spectrum.The proposed XMM-Newton observations will allow us to (a) monitor the variability of the Fe lines,(b) test the correctness of the present interpretation of these lines,and (c) constrain the kinematic,ionization and absorbing properties of the quasar outflow.These constraints will allow us to determine the contribution of outflows to the enrichment of the IGM,and provide insights of the connection between black hole and bulge growth in the host galaxy.
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.
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
An analytical approach to the Schrödinger-Newton equations
NASA Astrophysics Data System (ADS)
Tod, Paul; Moroz, Irene M.
1999-03-01
In this paper we present the second part of a study of spherically-symmetric solutions of the Schrödinger-Newton equations for a single particle (Penrose R 1998 Quantum computation, entanglement and state reduction Phil. Trans. R. Soc. 356 1-13). We show that there exists an infinite family of normalizable, finite energy solutions which are characterized by being smooth and bounded for all values of the radial coordinate. We therefore provide analytical support for our earlier numerical integrations (Moroz I M et al 1998 Spherically-symmetric solutions of the Schrödinger-Newton equations Classical and Quantum Gravity 1998 15 2733-42).
Bantroch, S; Bühler, T; Lam, J S
1994-01-01
Smooth, rough, and neutral forms of lipopolysaccharide (LPS) from Pseudomonas aeruginosa were used to assess the appropriate conditions for effective enzyme-linked immunosorbent assay (ELISA) of LPS. Each of these forms of well-defined LPS was tested for the efficiency of antigen coating by various methods as well as to identify an appropriate type of microtiter plate to use. For smooth LPS, the standard carbonate-bicarbonate buffer method was as efficient as the other sensitivity-enhancing plate-coating methods compared. The rough LPS, which has an overall hydrophobic characteristic, was shown to adhere effectively, regardless of the coating method used, to only one type of microtiter plate, CovaLink. This type of plate has secondary amine groups attached on its polystyrene surface by carbon chain spacers, which likely favors hydrophobic interactions between the rough LPS and the well surfaces. Dehydration methods were effective for coating microtiter plates with the neutral LPS examined, which is composed predominantly of a D-rhamnan. For the two dehydration procedures, LPS suspended in water or the organic solvent chloroform-ethanol was added directly to the wells, and the solvent was allowed to dehydrate or evaporate overnight. Precoating of plates with either polymyxin or poly-L-lysine did not give any major improvement in coating with the various forms of LPS. The possibility of using proteinase K- and sodium dodecyl sulfate-treated LPS preparations for ELISAs was also investigated. Smooth LPS prepared by this method was as effective in ELISA as LPS prepared by the hot water-phenol method, while the rough and neutral LPSs prepared this way were not satisfactory for ELISA. PMID:7496923
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
Conservative smoothing versus artificial viscosity
Guenther, C.; Hicks, D.L.; Swegle, J.W.
1994-08-01
This report was stimulated by some recent investigations of S.P.H. (Smoothed Particle Hydrodynamics method). Solid dynamics computations with S.P.H. show symptoms of instabilities which are not eliminated by artificial viscosities. Both analysis and experiment indicate that conservative smoothing eliminates the instabilities in S.P.H. computations which artificial viscosities cannot. Questions were raised as to whether conservative smoothing might smear solutions more than artificial viscosity. Conservative smoothing, properly used, can produce more accurate solutions than the von Neumann-Richtmyer-Landshoff artificial viscosity which has been the standard for many years. The authors illustrate this using the vNR scheme on a test problem with known exact solution involving a shock collision in an ideal gas. They show that the norms of the errors with conservative smoothing are significantly smaller than the norms of the errors with artificial viscosity.
Newton-like equations for a radiating particle
NASA Astrophysics Data System (ADS)
Cabo Montes de Oca, A.; Cabo Bizet, N. G.
2015-01-01
Second-order Newton equations of motion for a radiating particle are presented. It is argued that the trajectories obeying them also satisfy the Abraham-Lorentz-Dirac (ALD) equations for general 3D motions in the nonrelativistic and relativistic limits. The case of forces depending on only the proper time is here considered. For these properties to hold, it is sufficient that the external force be infinitely smooth and that a Landau-Lifshitz series formed with its time derivatives converges. This series defines in a special local way the effective forces entering the Newton equations. When the external force vanishes in an open vicinity of a given time, the effective one also becomes null. Thus, the proper solutions of the effective equations cannot show runaway or preacceleration effects. The Newton equations are numerically solved for a pulsed force given by an analytic function along the proper time axis. The simultaneous satisfaction of the ALD equations is numerically checked. Furthermore, a set of modified ALD equations for almost everywhere infinitely smooth forces, but including steplike discontinuities in some points, is also presented. The form of the equations supports the statement argued in a previous work, that the causal Lienard-Wiechert field solution surrounding a radiating particle implies that the effective force on the particle should instantaneously vanish when the external force is retired. The modified ALD equations proposed in the previous work are here derived in a generalized way including the same effect also when the force is instantly connected. The possibility of deriving a pointlike model showing a finite mass and an infinite electromagnetic energy from a reasonable Lagrangian theory is also started to be investigated here.
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…
Coherence imaging by use of a Newton rings sampling function.
Podoleanu, A G; Dobre, G M; Webb, D J; Jackson, D A
1996-11-01
We show that, with suitable optics in the arm of a Michelson interferometer, orthogonal galvo-scanning mirrors build a sampling function in the form of Newton rings when the two interferometer arms are matched. Using a low-coherence source, one can obtain transversal depth-resolved images. A fast display procedure using a storage oscilloscope was devised based on this method.
A Comparison of Inexact Newton and Coordinate Descent Meshoptimization Technqiues
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.
Rule-governed Approaches to Physics--Newton's Third Law.
ERIC Educational Resources Information Center
Maloney, David P.
1984-01-01
Describes an approach to assessing the use of rules in solving problems related to Newton's third law of motion. Discusses the problems used, method of questioning, scoring of problem sets, and a general overview of the use of the technique in aiding the teacher in dealing with student's conceptual levels. (JM)
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
Numerical conformal mapping methods for exterior and doubly connected regions
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.
NASA Astrophysics Data System (ADS)
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.
NASA Astrophysics Data System (ADS)
Kajzer, A.; Pozorski, J.; Szewc, K.
2014-08-01
In the paper we present Large-eddy simulation (LES) results of 3D Taylor- Green vortex obtained by the three different computational approaches: Smoothed Particle Hydrodynamics (SPH), Lattice Boltzmann Method (LBM) and Finite Volume Method (FVM). The Smagorinsky model was chosen as a subgrid-scale closure in LES for all considered methods and a selection of spatial resolutions have been investigated. The SPH and LBM computations have been carried out with the use of the in-house codes executed on GPU and compared, for validation purposes, with the FVM results obtained using the open-source CFD software OpenFOAM. A comparative study in terms of one-point statistics and turbulent energy spectra shows a good agreement of LES results for all methods. An analysis of the GPU code efficiency and implementation difficulties has been made. It is shown that both SPH and LBM may offer a significant advantage over mesh-based CFD methods.
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).
Happy Balls, Unhappy Balls, and Newton's Cradle
NASA Astrophysics Data System (ADS)
Kagan, David
2010-03-01
The intricacies of Newton's Cradle are well covered in the literature2-4 going as far back as the time of Newton!5 These discussions generally center on the highly elastic collisions of metal spheres. Thanks to the invention of happy and unhappy balls,6 you can build and study the interaction of less elastic systems (see Fig. 1).
Newtons Wissenschaftslehre als Basis der Quantenphysik
NASA Astrophysics Data System (ADS)
Bopp, Fritz
Es ist richtig zu sagen, die Quantenphysik folge nicht aus der auf Newtons Prinzipien beruhenden klassischen Physik. Es ist aber auch richtig, daß Newtons Wissenschaftslehre, die eng mit der Platonschen zusammenhängt und über diese hinausgeht, von der Quantenphysik nicht berührt wird, wie an anderer Stelle gezeigt ist. Hier wird Newtons Wissenschaftslehre genauer analysiert und der Unterschied zur kartesischen herausgearbeitet, was durch die Newtontradition verschleiert wird. Am Ende werden die Ergebnisse an Beispielen aus der Quantenoptik erläutert.Translated AbstractNewton's Epistemology as Basic Concept of Quantum PhysicsIt is correct to say that quantum physics cannot be derived from classical physics, which is founded on Newton's principles. However, it is also correct that Newton's epistemology, a more developed Platonian one, can be considered as basic for quantum physics. That is previously shown. Here, we remember Newton's epistemology more thoroughly, and consider particularly the difference to the Cartesian epistemology, a difference often veiled in the Newton tradition. Finally, we apply the result on some phenomena of quantum optics.
A new Newton's law of cooling?
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."
An improved Newton iteration for the generalized inverse of a matrix, with applications
NASA Technical Reports Server (NTRS)
Pan, Victor; Schreiber, Robert
1990-01-01
The purpose here is to clarify and illustrate the potential for the use of variants of Newton's method of solving problems of practical interest on highly personal computers. The authors show how to accelerate the method substantially and how to modify it successfully to cope with ill-conditioned matrices. The authors conclude that Newton's method can be of value for some interesting computations, especially in parallel and other computing environments in which matrix products are especially easy to work with.
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…
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.
Newtonian cosmology Newton would understand
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.
NASA Astrophysics Data System (ADS)
Barnard, Robin
2003-03-01
A Z-source candidate has been identified in the core of M31 using data from existing XMM-Newton observations. Z-sources are perhaps the most extreme form of neutron star binary; powered by Roche lobe overflow from a low mass secondary via disc accretion, their X-ray luminosities can reach 10^39 erg/s,and exhibit complex correlations between luminosity and X-ray spectra so thatthey trace out Z-shapes in colour-colour diagrams over a few days. We propose a programme of four 20 ks observations over 4 days to trace the Z-track, which will conclusively prove whether or not the candidate is a Z-source. Also, the programme would access for the first time variability over time-scales of a few days in the 120 sources in the field of view.
NASA Astrophysics Data System (ADS)
Verbunt, Frank
2003-03-01
The radius of neutron stars can be determined from their X-ray spectrum. Quiescent soft X-ray transients are the best candidates for this, provided their interstellar absorption and distance are independently known. We propose to observe such a system, well outside the core of globular cluster NGC 1904, which has extremely low interstellar absorption (E(B-V)0.01), and is not contaminated by nearby other sources. We aim at a better than 10 percent accuracy. This source is also interesting from a dynamical point of view, since it must have been catapulted from the cluster core. As a bonus we observe the core of the cluster. The XMM-Newton source position will enable us to look for an optical counterpart in archival HST/WFPC2 data.
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.
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.
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)
XMM-Newton observation of Mrk 110
NASA Astrophysics Data System (ADS)
Boller, Th.; Balestra, I.; Kollatschny, W.
2007-04-01
Context: We report on the first XMM-Newton observation of the bright narrow-line Seyfert 1 galaxy Mrk 110. Aims: Our analysis is aimed to study the properties of the X-ray spectrum of Mrk 110 and compare them with those inferred from optical spectroscopy. Methods: We make use of detailed timing and spectral analysis as well as high resolution X-ray spectroscopy with the XMM-Newton gratings. Results: We find a narrow Fe K fluorescent line, a broad component (FWHM≃16 500 km s-1) of the O VII triplet, either due to infall motions or gravitational redshift effects in the vicinity of the central black hole, a Comptonized accretion disk layer, and a strong starburst component. Conclusions: .We found that Mrk 110 has a complex X-ray spectrum, exhibiting relatively strong broadening of the O VII emission line, probably associated with X-ray emission from the Broad Line Region (BLR), which might be correlated with the optical gravitationally redshifted, asymmetric line profiles. Spectral fits including a Gaussian line or a discline give the same statistical significance. If the broad redshifted soft X-ray components are due to gravitational redshift effects, the distance of the line-emitting regions ranges between about 0.2 and 1 light day with respect to the central black hole. In addition, the EPIC pn spectrum shows a double power-law and a strong starburst component. One power-law component exhibits a photon index slope of 1.401.501.38, while the second is much steeper with a power law slope of 2.502.632.48. The second power-law is most probably due to thermal Comptonization of a hot electron layer above the accretion disk. Mrk 110 is another example of extragalactic sources showing Comptonization effects in the accretion disc and its properties are very similar to the narrow-line Seyfert 1 Galaxy Ton S 180.
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.
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.
NASA Astrophysics Data System (ADS)
Dobson, G. J.
1998-07-01
Newton's treatment of the precession of the equinoxes in his Philosophiae Naturalis Principia Mathematica was recognised by d'Alembert in 1749 as being faulty, despite the very close agreement between Newton's calculated value for the rate of precesion and the observed value. Here, the author presents an analysis of Newton's geometrical methods applied in his treatment of precession and claims that it was basically flawed because Newton lacked knowledge of the principles of rigid body dynamics and, in particular, was unaware of the idea of angular momentum.
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.
Stabilized quasi-Newton optimization of noisy potential energy surfaces
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.
Stabilized quasi-Newton optimization of noisy potential energy surfaces.
Schaefer, Bastian; Alireza Ghasemi, S; Roy, Shantanu; Goedecker, Stefan
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.
Why Goethe rejected Newton's theory of light.
Treisman, M
1996-01-01
Observations that he himself had made persuaded Goethe to reject Newton's theory of light and to put forward an alternative theory of the colour phenomena seen with a prism. Duck has argued that Goethe's attack on Newton's theory rested on valid experimental observations that appeared to present a difficulty for Newton's theory but to support his own views on colour. Duck has also proposed that these observations may be accounted for as an instance of the Bezold-Brücke phenomenon. It is argued here that this explanation is invalid and that two other features of colour processing can explain Goethe's observations.
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.
Smooth halos in the cosmic web
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.
NASA Astrophysics Data System (ADS)
Li, Zhe; Leduc, Julien; Nunez-Ramirez, Jorge; Combescure, Alain; Marongiu, Jean-Christophe
2015-04-01
We propose a non-intrusive numerical coupling method for transient fluid-structure interaction (FSI) problems simulated by means of different discretization methods: smoothed particle hydrodynamics (SPH) and finite element (FE) methods for the fluid and the solid sub-domains, respectively. As a partitioned coupling method, the present algorithm can ensure a zero interface energy during the whole period of numerical simulation, even in the presence of large interface motion. In other words, the time integrations of the two sub-domains (second order Runge-Kutta scheme for fluid and Newmark integrator for solid) are synchronized. Thanks to this energy-conserving feature, one can preserve the minimal order of accuracy in time and the numerical stability of the FSI simulations, which are validated with a 1D and a 2D trivial numerical test cases. Additionally, some other 2D FSI simulations involving large interface motion have also been carried out with the proposed SPH-FE coupling method. Finally, an example of aquaplaning problem is given in order to show the feasibility of such coupling method in multi-dimensional applications with complicated structural geometries.
NASA Astrophysics Data System (ADS)
Tune, D. D.; Stolz, B. W.; Pfohl, M.; Flavel, B. S.
2016-02-01
We show that the application of lateral shear force on a randomly oriented thin film of carbon nanotubes, in the dry state, causes significant reordering of the nanotubes at the film surface. This new technique of dry shear aligning is applicable to carbon nanotube thin films produced by many of the established methods.We show that the application of lateral shear force on a randomly oriented thin film of carbon nanotubes, in the dry state, causes significant reordering of the nanotubes at the film surface. This new technique of dry shear aligning is applicable to carbon nanotube thin films produced by many of the established methods. Electronic supplementary information (ESI) available: Detailed experimental methods, table of nanotube details, absorption spectra, further SEM data, plots of sheet resistance, DC to optical conductivity, and 2D order parameter as a function of transmittance. See DOI: 10.1039/c5nr08784h
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…
Newton and the American Political Tradition
ERIC Educational Resources Information Center
Arons, A. B.
1975-01-01
Traces the historical sequence that establishes a clear line of connection from Newton and Locke through the philosophy of the Enlightenment and the evolution of deism to the American political tradition. (Author/GS)
Demonstrating Newton's Third Law: Changing Aristotelian Viewpoints.
ERIC Educational Resources Information Center
Roach, Linda E.
1992-01-01
Suggests techniques to help eliminate students' misconceptions involving Newton's Third Law. Approaches suggested include teaching physics from a historical perspective, using computer programs with simulations, rewording the law, drawing free-body diagrams, and using demonstrations and examples. (PR)
NASA Astrophysics Data System (ADS)
Schartel, N.
2008-02-01
Some key numbers about the XMM-Newton users, usage of the mission and the scientific outcome are provided. The background for selecting the topic, the preparation work, the organization and the corresponding committees are briefly described.
GOES-West Movie of Hurricane Newton
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...
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)
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)
Traveling and Standing Waves in Coupled Pendula and Newton's Cradle
NASA Astrophysics Data System (ADS)
García-Azpeitia, Carlos
2016-06-01
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.
An Alternative Realization of Gauss-Newton for Frequency-Domain Acoustic Waveform Inversion
NASA Astrophysics Data System (ADS)
Liu, Y.; Yang, J.; Chi, B.; Dong, L.
2014-12-01
Since FWI was studied under the least-square misfit optimization proposed by Tarantola (1984) in time domain, it has been greatly improved by many researchers. Pratt (1998) developed FWI in frequency domain using a Gauss-Newton optimization. In recent years, FWI has been widely studied under the framework of adjoint-state methods, as summarized by Plessix (2006). Preconditioning and high order gradients are important for FWI. Many researches have focused on the Newton optimization, in which the calculation of inverse Hessian is the key problem. Pseudo Hessian such as the diagonal Hessian was firstly used to approximate inverse Hessian (Choi & Shin, 2007). Then Gauss-Newton or l-BFGS method was widely studied to iteratively calculate the inverse approximate Hessian Haor full Hessian (Sheen et al., 2006). Full Hessian is the base of the exact Newton optimization. Fichtner and Trampert (2011) presented an extension of the adjoint-state method to directly compute the full Hessian; Métivier et al. (2012) proposed a general second-order adjoint-state formula for Hessian-vector product to tackle Gauss-Newton and exact Newton. Liu et al. (2014) proposed a matrix-decomposition FWI (MDFWI) based on Born kernel. They used the Born Fréchet kernel to explicitly calculate the gradient of the objective function through matrix decomposition, no full Fréchet kernel being stored in memory beforehand. However, they didn't give a method to calculate the Gauss-Newton. In this paper, We propose a method based on Born Fréchet kernel to calculate the Gauss-Newton for acoustic full waveform inversion (FWI). The Gauss-Newton is iteratively constructed without needing to store the huge approximate Hessian (Ha) or Fréchet kernel beforehand, and the inverse of Ha is not need to be calculated either. This procedure can be efficiently accomplished through matrix decomposition. More resolved result and faster convergence are obtained when this Gauss-Newton is applied in FWI based on the Born
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.
Smoothing spline ANOVA frailty model for recurrent event data.
Du, Pang; Jiang, Yihua; Wang, Yuedong
2011-12-01
Gap time hazard estimation is of particular interest in recurrent event data. This article proposes a fully nonparametric approach for estimating the gap time hazard. Smoothing spline analysis of variance (ANOVA) decompositions are used to model the log gap time hazard as a joint function of gap time and covariates, and general frailty is introduced to account for between-subject heterogeneity and within-subject correlation. We estimate the nonparametric gap time hazard function and parameters in the frailty distribution using a combination of the Newton-Raphson procedure, the stochastic approximation algorithm (SAA), and the Markov chain Monte Carlo (MCMC) method. The convergence of the algorithm is guaranteed by decreasing the step size of parameter update and/or increasing the MCMC sample size along iterations. Model selection procedure is also developed to identify negligible components in a functional ANOVA decomposition of the log gap time hazard. We evaluate the proposed methods with simulation studies and illustrate its use through the analysis of bladder tumor data.
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.
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.
Glosup, J.
1992-07-23
The class of gene linear models is extended to develop a class of nonparametric regression models known as generalized smooth models. The technique of local scoring is used to estimate a generalized smooth model and the estimation procedure based on locally weighted regression is shown to produce local likelihood estimates. The asymptotically correct distribution of the deviance difference is derived and its use in comparing the fits of generalized linear models and generalized smooth models is illustrated. The relationship between generalized smooth models and generalized additive models is discussed, also.
Polarization smoothing for the National Ignition Facility
Rothenberg, J F
1998-08-13
Polarization smoothing (PS) is the illumination of the target with two distinct and orthogonally polarized speckle patterns. Since these two polarizations do not interfere, the intensity patterns add incoherently and thus the contrast of the intensity nonuniformity can be reduced by a factor of {radical}2 in addition to any reduction achieved by temporal smoothing techniques. Smoothing by PS is completely effective on an instantaneous basis and is therefore of particular interest for the suppression of laser plasma instabilities, which have a very rapid response time. The various implementations of PS are considered and their impact, in conjunction with temporal smoothing methods, on the spatial spectrum of the target illumination is analyzed.
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.
Technology Transfer Automated Retrieval System (TEKTRAN)
Vascular smooth muscle cells (SMCs) originate from multiple types of progenitor cells. In the embryo, the most well-studied SMC progenitor is the cardiac neural crest stem cell. Smooth muscle differentiation in the neural crest lineage is controlled by a combination of cell intrinsic factors, includ...
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.
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?"
NASA Astrophysics Data System (ADS)
Mehta, Dhagash; Chen, Tianran; Morgan, John W. R.; Wales, David J.
2015-12-01
The comment notes that the Newton homotopy (NH) and Newton trajectory (NT) methods are related. By describing recent implementations of the NH method, we clarify the similarities and differences between the two approaches. The possible synergy between NH, NT and other flow methods could suggest further developments in mathematics and chemistry.
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.
Disformal transformation in Newton-Cartan geometry
NASA Astrophysics Data System (ADS)
Huang, Peng; Yuan, Fang-Fang
2016-08-01
Newton-Cartan geometry has played a central role in recent discussions of the non-relativistic holography and condensed matter systems. Although the conformal transformation in non-relativistic holography can easily be rephrased in terms of Newton-Cartan geometry, we show that it requires a nontrivial procedure to arrive at the consistent form of anisotropic disformal transformation in this geometry. Furthermore, as an application of the newly obtained transformation, we use it to induce a geometric structure which may be seen as a particular non-relativistic version of the Weyl integrable geometry.
Facemyer, K C; Cremo, C R
1992-01-01
We present a new method to specifically and stably label proteins by attaching extrinsic probes to amino acids that are thiophosphorylated by protein kinases and ATP gamma S. The method was demonstrated for labeling of a thiophosphorylatable serine of the isolated regulatory light chain of smooth muscle myosin. We stoichiometrically blocked the single thiol (Cys-108) either by forming a reversible intermolecular disulfide bond or by reacting with iodoacetic acid. The protein was stoichiometrically thiophosphorylated at Ser-19 by myosin light chain kinase and ATP gamma S. The nucleophilic sulfur of the protein phosphorothioate was coupled at pH 7.9 and 25 degrees C to the fluorescent haloacetate [3H]-5-[[2-[(iodoacetyl)-amino]ethyl]amino]naphthalene-1- sulfonic acid ([3H]IAEDANS) by displacement of the iodide. Typical labeling efficiencies were 70-100%. The labeling was specific for the thiophosphorylated Ser-19, as determined from the sequences of two labeled peptides isolated from a tryptic digest of the labeled protein. [3H]IAEDANS attached to the thiophosphorylated Ser-19 was stable at pH 3-10 at 25 degrees C, and to boiling in high concentrations of reductant. The labeled light chains were efficiently exchanged for unlabeled regulatory light chains of the whole myosin molecule. The resulting labeled myosin had normal ATPase activities in the absence of actin, indicating that the modification of Ser-19 and the exchange of the labeled light chain into myosin did not significantly disrupt the protein. The labeled myosin partially retained the elevated actin-activated Mg(2+)-ATPase activity which is characteristic of thiophosphorylated myosin. This indicates that labeling of the thiophosphate group with [3H]IAEDANS did not completely disrupt the functional properties of the thiophosphorylated protein in the presence of actin.
Newton and Colour: The Complex Interplay of Theory and Experiment.
ERIC Educational Resources Information Center
Martins, Roberto De Andrade; Silva, Cibelle Celestino
2001-01-01
Elucidates some aspects of Newton's theory of light and colors, specifically as presented in his first optical paper in 1672. Analyzes Newton's main experiments intended to show that light is a mixture of rays with different refrangibilities. (SAH)
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
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.
Discrete square root smoothing.
NASA Technical Reports Server (NTRS)
Kaminski, P. G.; Bryson, A. E., Jr.
1972-01-01
The basic techniques applied in the square root least squares and square root filtering solutions are applied to the smoothing problem. Both conventional and square root solutions are obtained by computing the filtered solutions, then modifying the results to include the effect of all measurements. A comparison of computation requirements indicates that the square root information smoother (SRIS) is more efficient than conventional solutions in a large class of fixed interval smoothing problems.
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.
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)
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…
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 "Getting Started," which…
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)
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.
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…
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…
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)
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…
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...
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...
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...
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...
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...
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…
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
Newton, laplace, and the epistemology of systems biology.
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. PMID:23170064
Newton, laplace, and the epistemology of systems biology.
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.
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.
Smoothed particle hydrodynamics with smoothed pseudo-density
NASA Astrophysics Data System (ADS)
Yamamoto, Satoko; Saitoh, Takayuki R.; Makino, Junichiro
2015-06-01
In this paper, we present a new formulation of smoothed particle hydrodynamics (SPH), which, unlike the standard SPH (SSPH), is well behaved at the contact discontinuity. The SSPH scheme cannot handle discontinuities in density (e.g., the contact discontinuity and the free surface), because it requires that the density of fluid is positive and continuous everywhere. Thus there is inconsistency in the formulation of the SSPH scheme at discontinuities of the fluid density. To solve this problem, we introduce a new quantity associated with particles and the "density" of that quantity. This "density" evolves through the usual continuity equation with an additional artificial diffusion term, in order to guarantee the continuity of the "density." We use this "density," or pseudo-density, instead of the mass density, to formulate our SPH scheme. We call our new method SPH with smoothed pseudo-density, and we show that it is physically consistent and can handle discontinuities quite well.
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.
Improved beam smoothing with SSD using generalized phase modulation
Rothenberg, J.E.
1997-01-01
The smoothing of the spatial illumination of an inertial confinement fusion target is examined by its spatial frequency content. It is found that the smoothing by spectral dispersion method, although efficient for glass lasers, can yield poor smoothing at low spatial frequency. The dependence of the smoothed spatial spectrum on the characteristics of phase modulation and dispersion is examined for both sinusoidal and more general phase modulation. It is shown that smoothing with non-sinusoidal phase modulation can result in spatial spectra which are substantially identical to that obtained with the induced spatial incoherence or similar method where random phase plates are present in both methods and identical beam divergence is assumed.
A multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations
NASA Technical Reports Server (NTRS)
Yoon, Seokkwan; Jameson, Antony
1986-01-01
A new efficient relaxation scheme in conjunction with a multigrid method is developed for the Euler equations. The LU SSOR scheme is based on a central difference scheme and does not need flux splitting for Newton iteration. Application to transonic flow shows that the new method surpasses the performance of the LU implicit scheme.
Newton's laws beyond the classroom walls
NASA Astrophysics Data System (ADS)
Pugh, Kevin J.
2004-03-01
One of the most profound qualities of science is its potential to transform and enrich students' experiences with the world. In prior work, I have conceptualized this quality of science in the construct of transformative experience. In order to illustrate the difference between transformative and nontransformative experience, this article presents the contrasting experiences of two students learning Newton's Laws in a seventh-grade general science class. One student exemplifies engagement in a transformative experience - the learning of Newton's Laws enriches his experience with events of motion in his everyday, out-of-school life. The other student exemplifies the good student who is engaged in the class and learns the content, but does not undergo a transformative experience. The experiences of these two students are analyzed and discussed. Recommendations include a need to focus on student experience outside the classroom and engagement with content (as opposed to engagement with peripheral things, such as humor or mere activity).
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.
Magnetic Levitation and Newton's Third Law
NASA Astrophysics Data System (ADS)
Aguilar, Horacio Munguía
2007-05-01
Newton's third law is often misunderstood by students and even their professors, as has already been pointed out in the literature.1,2 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 act can be muddied by the concept of "action at a distance." While some experiments have been described3,4 illustrating Newton's third law in magnetic situations, these do not offer the student a clear way of evaluating his/her own preconceptions. The experiment we present shows how easily the student, and even the graduate student, can fail to apply the third law correctly in an electromagnetic situation. The experiment described here employs a magnetic levitator and shows the difficulty in recognizing action and reaction forces.
Newton's third law on a scale balance
NASA Astrophysics Data System (ADS)
Nopparatjamjomras, Suchai; Panijpan, Bhinyo; Huntula, Jiradawan
2009-09-01
We propose a series of experiments involving balance readings of an object naturally floating or forced to be partially or fully immersed in water contained in a beaker sitting on an electronic scale balance. Students were asked to predict, observe and explain each case. The teacher facilitated the learning by asking probing questions, giving hints and helping in the drawing of the free body diagrams. From this guided enquiry, students improved their understanding of the involvement of Newton's third law in each experiment.
ERIC Educational Resources Information Center
Yeo, Shelley; Zadnik, Marjin
2000-01-01
Describes the difficulties that high school and university students have in thinking about force, identifying forces, and drawing force diagrams. Finds that students using a computer tutoring program made limited progress in learning to construct free-body diagrams because of their alternative conceptions and faulty teaching methods. Offers…
Life after Newton: an ecological metaphysic.
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.
Development of a next generation short range gravity experiment NEWTON-V, using digital microscope
NASA Astrophysics Data System (ADS)
Saiba, Shuntaro; Ando, Hiroaki; Hatori, Mirei; Inaba, Shoki; Ninomiya, Kazufumi; Sakuta, Tomomi; Shinozaki, Natsumi; Murata, Jiro; Newton Collaboration
2014-09-01
According to a large extra dimensional model, a deviation from Newton's inverse square law is expected at sub-millimeter range. Current NEWTON-IVh project aims to test the inverse-square law at millimeter scale, using a torsion pendulum. In order to examine the gravitational force at around micrometer distances, we are developing the new apparatus NEWTON-V, using a digital microscope. This experiment is going to measure gravity between two wires of around 10 to 100 micrometer, which are separated by distances in the range of 100 micrometer. One wire is used as a cantilever for the force sensing, which motion is measured by a pico-precision displacement sensor. This method was originally developed for the micron precision optical alignment system (OASys) for the PHENIX muon tracking chambers at RHIC, using digital image analysis technique. In this presentation, development status and preliminary results will be reported.
A Newton-Krylov solution to the porous medium equations in the agree code
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)
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).
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.
Supporting the learning of Newton's laws with graphical data
NASA Astrophysics Data System (ADS)
Piggott, David
Teaching physics provides the opportunity for a very unique interaction between students and instructor that is not found in chemistry or biology. Physics has a heavy emphasis on trying to alter students' misconceptions about how things work in the real word. In chemistry and microbiology this is not an issue because the topics of discussion in those classes are a new experience for the students. In the case of physics the students have everyday experience with the different concepts discussed. This causes the students to build incorrect mental models explaining how different things work. In order to correct these mental models physics teachers must first get the students to vocalize these misconceptions. Then the teacher must confront the students with an example that exposes the false nature of their model. Finally, the teacher must help the student resolve these discrepancies and form the correct model. This study attempts to resolve these discrepancies by giving the students concrete evidence via graphs of Newton's laws. The results reported here indicate that this method of eliciting the misconception, confronting the misconception, and resolving the misconception is successful with Newton's third law, but only marginally successful for first and second laws.
Scalable parallel Newton-Krylov solvers for discontinuous Galerkin discretizations
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.
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.
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)
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…
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…
Backward smoothing for precise GNSS applications
NASA Astrophysics Data System (ADS)
Vaclavovic, Pavel; Dousa, Jan
2015-10-01
The Extended Kalman filter is widely used for its robustness and simple implementation. Parameters estimated for solving dynamical systems usually require certain time to converge and need to be smoothed by a dedicated algorithms. The purpose of our study was to implement smoothing algorithms for processing both code and carrier phase observations with Precise Point Positioning method. We implemented and used the well known Rauch-Tung-Striebel smoother (RTS). It has been found out that the RTS suffer from significant numerical instability in smoothed state covariance matrix determination. We improved the processing with algorithms based on Singular Value Decomposition, which was more robust. Observations from many permanent stations have been processed with final orbits and clocks provided by the International GNSS service (IGS), and the smoothing improved stability and precision in every cases. Moreover, (re)convergence of the parameters were always successfully eliminated.
Selvan, S Easter; George, S Thomas; Balakrishnan, R
2015-03-01
Independent component analysis (ICA) aims at separating a multivariate signal into independent nongaussian signals by optimizing a contrast function with no knowledge on the mixing mechanism. Despite the availability of a constellation of contrast functions, a Hartley-entropy-based ICA contrast endowed with the discriminacy property makes it an appealing choice as it guarantees the absence of mixing local optima. Fueled by an outstanding source separation performance of this contrast function in practical instances, a succession of optimization techniques has recently been adopted to solve the ICA problem. Nevertheless, the nondifferentiability of the considered contrast restricts the choice of the optimizer to the class of derivative-free methods. On the contrary, this letter concerns a Riemannian quasi-Newton scheme involving an explicit expression for the gradient to optimize the contrast function that is differentiable almost everywhere. Furthermore, the inexact line search insisting on the weak Wolfe condition and a terminating criterion befitting the partly smooth function optimization have been generalized to manifold settings, leaving the previous results intact. The investigations with diversified images and the electroencephalographic (EEG) data acquired from 45 focal epileptic subjects demonstrate the efficacy of our approach in terms of computational savings and reliable EEG source localization, respectively. Additional experimental results are available in the online supplement.
An error in Isaac Newton's determination of planetary properties
NASA Astrophysics Data System (ADS)
Garisto, Robert
1991-01-01
Isaac Newton introduced his theory of gravitation in Book III of the Principia. To demonstrate the power of his new theory, Newton for the first time calculated the mass, surface gravity, and density of Jupiter, Saturn, and the Earth (relative to the Sun). In the final printing of the Principia, an error appears in Newton's calculation of the mass of the Earth and its origin is traced. In the course of reconstructing the source of the error, several other minor inconsistencies are resolved.
From Newton's laws to Einstein's theory of relativity.
NASA Astrophysics Data System (ADS)
Fang, L.; Chu, Y.
Contents: 1. From Aristotle to Newton. 2. Space, time and motion. 3. From the classical composition of velocities to the constant speed of light. 4. From Galileo's principle of relativity to the special theory of relativity. 5. The relativity and absoluteness ofa rod and a clock. 6. Dynamic problems. 7. From the leaning tower of Pisa to the general theory of relativity. 8. From Newton to post-Newton. 9. From classical gravitational collapse to the black hole. 10. Theconfirmation of gravitational waves. 11. From Newton's universe to the expanding universe. 12. After Einstein.
Is violation of Newton's second law possible?
Ignatiev, A Yu
2007-03-01
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. PMID:17358522
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.
High degree interpolation polynomial in Newton form
NASA Technical Reports Server (NTRS)
Tal-Ezer, Hillel
1988-01-01
Polynomial interpolation is an essential subject in numerical analysis. Dealing with a real interval, it is well known that even if f(x) is an analytic function, interpolating at equally spaced points can diverge. On the other hand, interpolating at the zeroes of the corresponding Chebyshev polynomial will converge. Using the Newton formula, this result of convergence is true only on the theoretical level. It is shown that the algorithm which computes the divided differences is numerically stable only if: (1) the interpolating points are arranged in a different order, and (2) the size of the interval is 4.
The Mathematical Papers of Isaac Newton
NASA Astrophysics Data System (ADS)
Newton, Isaac; Whiteside, D. T.; Hoskin, With M. A.
2008-01-01
Part I. Researches in Pure and Analytical Geometry 1667-1668: 1. Analysis of the Properties of Cubic Curves and their Classification by Species; 2. Researches into the General Properties of Curves; 3. Researches in the Organic Construction of Curves; Part II. Researches in Calculus: 1. Curve Problems and Further Logarithmic Computations; 2. Miscellaneous Researches; 3. The 'De Analysi Per Æquationes Infinitas'; Part III. Researches in Algebra and the Construction of Equations: 1.Kinckhuysen's Algebra and Newton's 'Observationes'; 2.Researches in the Geometrical Construction of Equations; Index of Names
Is violation of Newton's second law possible?
Ignatiev, A Yu
2007-03-01
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.
... 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 ...
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
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
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.
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.
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.
On topological modifications of Newton's law
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.
Extending Newton's Universal Theory of Gravity
NASA Astrophysics Data System (ADS)
Aisenberg, Sol
2011-11-01
This should remove the mystery of Dark Matter. Newton's universal theory of gravity only used the observations of the motion of planets in our solar system. Hubble later used observations of fixed stars in the universe, and showed that the fixed stars were actually galaxies with very large numbers of stars. Newton's universal law of gravity could not explain these new observations without the mystery of dark matter for the additional gravity. In science, when a theory is not able to explain new observations it is necessary to modify the theory or abandon the theory. Rubin observed flat (constant velocity) rotation curves for stars in spiral galaxies. Dark matter was proposed to provide the missing gravity. The equation balancing gravitational force and centripetal force is M*G=v*v*r and for the observed constant velocity v this requires M*G to be a linear function of distance r. If the linear dependence is instead assigned to G instead of M to give a new value for Gn as G+A*r, this will explain the observations in the cosmos and also in our solar system for small r. See ``The Misunderstood Universe'' for more details.
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).
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…
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)
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…
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…
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…
The XMM-Newton Wide Angle Survey (XWAS)
NASA Astrophysics Data System (ADS)
Esquej, P.; Page, M.; Carrera, F. J.; Mateos, S.; Tedds, J.; Watson, M. G.; Corral, A.; Ebrero, J.; Krumpe, M.; Rosen, S. R.; Ceballos, M. T.; Schwope, A.; Page, C. G.; Alonso-Herrero, A.; Caccianiga, A.; Della Ceca, R.; González-Martín, O.; Lamer, G.; Severgnini, P.
2013-09-01
Aims: This programme is aimed at obtaining one of the largest X-ray selected samples of identified active galactic nuclei to date in order to characterise such a population at intermediate fluxes, where most of the Universe's accretion power originates. We present the XMM-Newton Wide Angle Survey (XWAS), a new catalogue of almost a thousand X-ray sources spectroscopically identified through optical observations. Methods: A sample of X-ray sources detected in 68 XMM-Newton pointed observations was selected for optical multi-fibre spectroscopy. Optical counterparts and corresponding photometry of the X-ray sources were obtained from the SuperCOSMOS Sky Survey. Candidates for spectroscopy were initially selected with magnitudes down to R ~ 21, with preference for X-ray sources having a flux F0.5-4.5 keV ≥ 10-14 erg s-1 cm-2. Optical spectroscopic observations were made using the Two Degree Field of the Anglo Australian Telescope, and the resulting spectra were classified based on optical emission lines. Results: We have identified through optical spectroscopy 940 X-ray sources over Ω ~ 11.8 deg2 of the sky. Source populations in our sample can be summarised as 65% broad line active galactic nuclei (BLAGN), 16% narrow emission line galaxies (NELGs), 6% absorption line galaxies (ALGs) and 13% stars. An active nucleus is also likely to be present in the large majority of the X-ray sources spectroscopically classified as NELGs or ALGs. Sources lie in high-galactic latitude (|b| > 20 deg) XMM-Newton fields mainly in the southern hemisphere. Owing to the large parameter space in redshift (0 ≤ z ≤ 4.25) and flux (10-15 ≤ F0.5 - 4.5 keV ≤ 10-12 erg s-1 cm-2) covered by the XWAS this work provides an excellent resource for the further study of subsamples and particular cases. The overall properties of the extragalactic objects are presented in this paper. These include the redshift and luminosity distributions, optical and X-ray colours and X-ray-to-optical flux
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....
Improved metabolite profile smoothing for flux estimation.
Dromms, Robert A; Styczynski, Mark P
2015-09-01
As genome-scale metabolic models become more sophisticated and dynamic, one significant challenge in using these models is to effectively integrate increasingly prevalent systems-scale metabolite profiling data into them. One common data processing step when integrating metabolite data is to smooth experimental time course measurements: the smoothed profiles can be used to estimate metabolite accumulation (derivatives), and thus the flux distribution of the metabolic model. However, this smoothing step is susceptible to the (often significant) noise in experimental measurements, limiting the accuracy of downstream model predictions. Here, we present several improvements to current approaches for smoothing metabolite time course data using defined functions. First, we use a biologically-inspired mathematical model function taken from transcriptional profiling and clustering literature that captures the dynamics of many biologically relevant transient processes. We demonstrate that it is competitive with, and often superior to, previously described fitting schemas, and may serve as an effective single option for data smoothing in metabolic flux applications. We also implement a resampling-based approach to buffer out sensitivity to specific data sets and allow for more accurate fitting of noisy data. We found that this method, as well as the addition of parameter space constraints, yielded improved estimates of concentrations and derivatives (fluxes) in previously described fitting functions. These methods have the potential to improve the accuracy of existing and future dynamic metabolic models by allowing for the more effective integration of metabolite profiling data.
Newton`s iteration for inversion of Cauchy-like and other structured matrices
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.
Newton`s third law: a criterion for particle behavior of extended bodies.
NASA Astrophysics Data System (ADS)
Newburgh, R.
This paper examines the validity of Newton's third law when the two bodies involved are not point masses. Newton himself, assuming perfectly rigid bodies and infinite velocity for signal propagation, set forth the axiom of equality of action and reaction. When dealing with extended bodies and recognizing that propagation velocities must be finite, one finds that there is a breakdown of the third law. One also finds clues to reestablishing its validity in studying reversible and isentropic processes. At relativistic speeds one must consider Born rigid motions as well. By determining a characteristic time from the dimensions of a body and the signal propagation velocity, one arrives at a principle of minimum time. This principle establishes the conditions under which an extended body can act as a particle.
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.
Intermediate dynamics between Newton and Langevin.
Bao, Jing-Dong; Zhuo, Yi-Zhong; Oliveira, Fernando A; Hänggi, Peter
2006-12-01
A dynamics between Newton and Langevin formalisms is elucidated within the framework of the generalized Langevin equation. For thermal noise yielding a vanishing zero-frequency friction the corresponding non-Markovian Brownian dynamics exhibits anomalous behavior which is characterized by ballistic diffusion and accelerated transport. We also investigate the role of a possible initial correlation between the system degrees of freedom and the heat-bath degrees of freedom for the asymptotic long-time behavior of the system dynamics. As two test beds we investigate (i) the anomalous energy relaxation of free non-Markovian Brownian motion that is driven by a harmonic velocity noise and (ii) the phenomenon of a net directed acceleration in noise-induced transport of an inertial rocking Brownian motor.
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.
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.
A Newton-Krylov Solver for Implicit Solution of Hydrodynamics in Core Collapse Supernovae
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.
SIMS: computation of a smooth invariant molecular surface.
Vorobjev, Y N; Hermans, J
1997-01-01
SIMS, a new method of calculating a smooth invariant molecular dot surface, is presented. The SIMS method generates the smooth molecular surface by rolling two probe spheres. A solvent probe sphere is rolled over the molecule and produces a Richards-Connolly molecular surface (MS), which envelops the solvent-excluded volume of the molecule. In deep crevices, Connolly's method of calculating the MS has two deficiencies. First, it produces self-intersecting parts of the molecular surface, which must be removed to obtain the correct MS. Second, the correct MS is not smooth, i.e., the direction of the normal vector of the MS is not continuous, and some points of the MS are singular. We present an exact method for removing self-intersecting parts and smoothing the singular regions of the MS. The singular MS is smoothed by rolling a smoothing probe sphere over the inward side of the singular MS. The MS in the vicinity of singularities is replaced with the reentrant surface of the smoothing probe sphere. The smoothing method does not disturb the topology of a singular MS, and the smooth MS is a better approximation of the dielectric border between high dielectric solvent and the low dielectric molecular interior. The SIMS method generates a smooth molecular dot surface, which has a quasi-uniform dot distribution in two orthogonal directions on the molecular surface, which is invariant with molecular rotation and stable under changes in the molecular conformation, and which can be used in a variety of implicit methods of modeling solvent effects. The SIMS program is faster than the Connolly MS program, and in a matter of seconds generates a smooth dot MS of a 200-residue protein. The program is available from the authors on request (see http:@femto.med.unc.edu/SIMS). PMID:9251789
Dark Matter, the Correction to Newton's Law in a Disk
NASA Astrophysics Data System (ADS)
Heymann, Yuri
2016-09-01
The dark matter problem in the context of spiral galaxies refers to the discrepancy between the galactic mass estimated from luminosity measurements of galaxies with a given mass-to-luminosity ratio and the galactic mass measured from the rotational speed of stars using the Newton's law. Newton's law fails when applied to a star in a spiral galaxy. The problem stems from the fact that Newton's law is applicable to masses represented as points by their barycenter. As spiral galaxies have shapes similar to a disk, we shall correct Newton's law accordingly. We found that the Newton's force exerted by the interior mass of a disk on an adjacent mass shall be multiplied by the coefficient ηdisk estimated to be 7.44±0.83 at a 99% confidence level. The corrective coefficient for the gravitational force exerted by a homogeneous sphere at it's surface is 1.00±0.01 at a 99% confidence level, meaning that Newton's law is not modified for a spherical geometry. This result was proven a long time ago by Newton in the shell theorem.
Correlation-based smoothing model for optical polishing.
Shu, Yong; Kim, Dae Wook; Martin, Hubert M; Burge, James H
2013-11-18
A generalized model is developed to quantitatively describe the smoothing effects from different polishing tools used for optical surfaces. The smoothing effect naturally corrects mid-to-high spatial frequency errors that have features small compared to the size of the polishing lap. The original parametric smoothing model provided a convenient way to compare smoothing efficiency of different polishing tools for the case of sinusoidal surface irregularity, providing the ratio of surface improvement via smoothing to the bulk material removal. A new correlation-based smoothing model expands the capability to quantify smoothing using general surface data with complex irregularity. For this case, we define smoothing as a band-limited correlated component of the change in the surface and original surface. Various concepts and methods, such as correlation screening, have been developed and verified to manipulate the data for the calculation of smoothing factor. Data from two actual polishing runs from the Giant Magellan Telescope off-axis segment and the Large Synoptic Survey Telescope monolithic primary-tertiary mirror were processed, and a quantitative evaluation for the smoothing efficiency of a large pitch lap and a conformal lap with polishing pads is provided.
Newton-Krylov-Schwarz algorithms for the 2D full potential equation
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.
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.
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.
Smooth PARAFAC Decomposition for Tensor Completion
NASA Astrophysics Data System (ADS)
Yokota, Tatsuya; Zhao, Qibin; Cichocki, Andrzej
2016-10-01
In recent years, low-rank based tensor completion, which is a higher-order extension of matrix completion, has received considerable attention. However, the low-rank assumption is not sufficient for the recovery of visual data, such as color and 3D images, where the ratio of missing data is extremely high. In this paper, we consider "smoothness" constraints as well as low-rank approximations, and propose an efficient algorithm for performing tensor completion that is particularly powerful regarding visual data. The proposed method admits significant advantages, owing to the integration of smooth PARAFAC decomposition for incomplete tensors and the efficient selection of models in order to minimize the tensor rank. Thus, our proposed method is termed as "smooth PARAFAC tensor completion (SPC)." In order to impose the smoothness constraints, we employ two strategies, total variation (SPC-TV) and quadratic variation (SPC-QV), and invoke the corresponding algorithms for model learning. Extensive experimental evaluations on both synthetic and real-world visual data illustrate the significant improvements of our method, in terms of both prediction performance and efficiency, compared with many state-of-the-art tensor completion methods.
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.
Catch a falling apple: Isaac Newton and myths of genius.
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.
Anisotropic Smoothing Improves DT-MRI-Based Muscle Fiber Tractography
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
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.
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
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
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.
Newton-based optimization for Kullback-Leibler nonnegative tensor factorizations
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.
Newton-based optimization for Kullback-Leibler nonnegative tensor factorizations
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
rpSPH: a novel smoothed particle hydrodynamics algorithm
NASA Astrophysics Data System (ADS)
Abel, Tom
2011-05-01
We suggest a novel discretization of the momentum equation for smoothed particle hydrodynamics (SPH) and show that it significantly improves the accuracy of the obtained solutions. Our new formulation which we refer to as relative pressure SPH, rpSPH, evaluates the pressure force with respect to the local pressure. It respects Newton's first law of motion and applies forces to particles only when there is a net force acting upon them. This is in contrast to standard SPH which explicitly uses Newton's third law of motion continuously applying equal but opposite forces between particles. rpSPH does not show the unphysical particle noise, the clumping or banding instability, unphysical surface tension and unphysical scattering of different mass particles found for standard SPH. At the same time, it uses fewer computational operations and only changes a single line in existing SPH codes. We demonstrate its performance on isobaric uniform density distributions, uniform density shearing flows, the Kelvin-Helmholtz and Rayleigh-Taylor instabilities, the Sod shock tube, the Sedov-Taylor blast wave and a cosmological integration of the Santa Barbara galaxy cluster formation test. rpSPH is an improvement in these cases. The improvements come at the cost of giving up exact momentum conservation of the scheme. Consequently, one can also obtain unphysical solutions particularly at low resolutions.
A Catalogue of XMM-Newton BL Lacs
NASA Astrophysics Data System (ADS)
Racero, E.; De la Calle, I.; Rouco Escorial, A.
2015-05-01
A catalogue of XMM-Newton BL Lac is presented based on a cross-correlation with the 1374 BL Lac objects listed in the 13th edition of the Veron-Cetty and Veron (2010) catalogue. X-ray counterparts were searched for in the field of view of more than 10000 pointed observations available in the XMM-Newton Archive (XSA) that were public before June 2012. The cross-correlation yielded around 250 XMM-Newton observations, which correspond to 162 different sources. X-ray data from the three EPIC cameras and Optical Monitor data were uniformly analyzed using the latest XMM-Newton Science Analysis System (SAS) version. The catalogue collects X-ray spectral properties, including flux variability, of the sample in the 0.2--10 KeV energy band. All the catalogue products will be made publicly available to the scientific community.
Gravitational Bohr's model with Newton's and Weber's potentials
NASA Astrophysics Data System (ADS)
Tiandho, Yuant; Triyanta
2015-09-01
Similarity between Newtonian gravitational force and Coulomb's force leads one to define gravitational electric and magnetic fields or gravito-electromagnetic fields. Also, one may define a gravitational Bohr's theory in analogy with the electromagnetic Bohr's theory for which the latter is quite successful in explaining some properties of hydrogen atom. Unlike to the Coulomb's force, the Newton`s force is believed to be an approximated theory of gravity as it is unable to explain the Mercury's orbit. This paper discusses the gravitational Bohr's theory by taking into account the Newton's potential and Weber's potential; the later is a modified Newton's gravitational potential that conforms, to some degrees, to the anomaly of the Mercury's orbit.
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.
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. PMID:26089129
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.
Systemic venous drainage: can we help Newton?
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.
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.
Newton-Cartan, Galileo-Maxwell and Kaluza-Klein
NASA Astrophysics Data System (ADS)
Van den Bleeken, Dieter; Yunus, Çağin
2016-07-01
We study Kaluza-Klein reduction in Newton-Cartan gravity. In particular we show that dimensional reduction and the nonrelativistic limit commute. The resulting theory contains Galilean electromagnetism and a nonrelativistic scalar. It provides the first example of back-reacted couplings of scalar and vector matter to Newton-Cartan gravity. This back-reaction is interesting as it sources the spatial Ricci curvature, providing an example where nonrelativistic gravity is more than just a Newtonian potential.
Laboratory Test of Newton's Second Law for Small Accelerations
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}.
Laboratory test of Newton's second law for small accelerations.
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).
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.
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.
XMM-Newton Education and Public Outreach Program
NASA Astrophysics Data System (ADS)
Plait, P.; Silva, S.; Graves, T.; Simonnet, G.; Spear, S.; Slater, G.; Borders, T.; Cominsky, L.
2003-12-01
XMM-Newton is a joint NASA-European Space Agency (ESA) orbiting observatory, designed to observe high energy X-rays emitted from exotic astronomical objects such as pulsars, black holes, and active galaxies. It was launched on December 10, 1999 from the ESA base at Kourou, French Guiana and continues to make observations today. In 2003, The NASA E/PO Group at Sonoma State University took the lead for the US portion of the XMM-Newton Education and Public Outreach (E/PO) program. This program is using the mission science to engage students in science and math learning. Currently we are working on developing curriculum materials for grades 6-12. One such product, developed with our new partners at Gettysburg College in Gettysburg, PA, is a Contemporary Laboratory Experiences in Astronomy (CLEA) exercise on X-ray spectroscopy of a supernova remnant. The XMM-Newton E/PO program has also partnered with the GLAST Telescope Network (GTN) and the AAVSO to help coordinate observations of magnetic white dwarfs called polars. This year, the XMM-Newton outreach program will begin the development of a Starlab Planetarium show which will depict the X-ray sky. In addition, the outreach program has created a website (mirrored at NASA's Goddard Space Flight Center) designed to enhance the XMM-Newton mission's science education. More educational materials and information about the XMM-Newton E/PO program can be found at http://xmm.sonoma.edu.
Study of the X-ray activity of Sagittarius A* during the 2011 XMM-Newton campaign
NASA Astrophysics Data System (ADS)
Mossoux, Enmanuelle; Grosso, Nicolas; Vincent, Frédéric H.; Porquet, Delphine
2015-01-01
Context. At the dynamical center of the Milky Way, there is the closest supermassive black hole: Sgr A*. Its non-flaring luminosity is several orders of magnitude lower than the Eddington luminosity, but flares can be observed in the infrared and X-rays. This flaring activity can help us to understand radiation mechanisms from Sgr A*. Aims: Our aim is to investigate the X-ray flaring activity of Sgr A* and to constrain the physical properties of the X-ray flares and their origin. Methods: In March and April 2011, we observed Sgr A* with XMM-Newton with a total exposure of ≈226 ks in coordination with the 1.3 mm Very-Long-Baseline Interferometry array. We performed timing analysis of the X-ray emission from Sgr A* using a Bayesian-blocks algorithm to detect X-ray flares observed with XMM-Newton. Furthermore, we computed X-ray smoothed light curves observed in this campaign in order to have better accuracy on the position and the amplitude of the flares. Results: We detected two X-ray flares on March 30 and April 3, 2011, which for comparison have a peak detection level of 6.8 and 5.9σ in the XMM-Newton/EPIC (pn+MOS1+MOS2) light curve in the 2-10 keV energy range with a 300 s bin. The former is characterized by two sub-flares: the first one is very short (~458 s) with a peak luminosity of Lunabs2-10~keV ~9.4 × 1034 erg s-1, whereas the second one is longer (~1542 s) with a lower peak luminosity (Lunabs2-10~keV ~6.8 × 1034 erg s-1). The comparison with the sample of X-ray flares detected during the 2012 Chandra XVP campaign favors the hypothesis that the 2011 March 30 flare is a single flare rather than two distinct subflares. We model the light curve of this flare with the gravitational lensing of a simple hotspot-like structure, but we cannot satisfactorily reproduce the large decay of the light curve between the two subflares with this model. From magnetic energy heating during the rise phase of the first subflare and assuming an X-ray photons production
NASA Astrophysics Data System (ADS)
Cardozo Dias, Penha Maria; Stuchi, T. J.
2013-11-01
In a letter to Robert Hooke, Isaac Newton drew the orbit of a mass moving under a constant attracting central force. The drawing of the orbit may indicate how and when Newton developed dynamic categories. Some historians claim that Newton used a method contrived by Hooke; others that he used some method of curvature. We prove that Hooke’s method is a second-order symplectic area-preserving algorithm, and the method of curvature is a first-order algorithm without special features; then we integrate the Hamiltonian equations. Integration by the method of curvature can also be done, exploring the geometric properties of curves. We compare three methods: Hooke’s method, the method of curvature and a first-order method. A fourth-order algorithm sets a standard of comparison. We analyze which of these methods best explains Newton’s drawing.
Smooth Muscle Strips for Intestinal Tissue Engineering
Walthers, Christopher M.; Lee, Min; Wu, Benjamin M.; Dunn, James C. Y.
2014-01-01
Functionally contracting smooth muscle is an essential part of the engineered intestine that has not been replicated in vitro. The purpose of this study is to produce contracting smooth muscle in culture by maintaining the native smooth muscle organization. We employed intact smooth muscle strips and compared them to dissociated smooth muscle cells in culture for 14 days. Cells isolated by enzymatic digestion quickly lost maturity markers for smooth muscle cells and contained few enteric neural and glial cells. Cultured smooth muscle strips exhibited periodic contraction and maintained neural and glial markers. Smooth muscle strips cultured for 14 days also exhibited regular fluctuation of intracellular calcium, whereas cultured smooth muscle cells did not. After implantation in omentum for 14 days on polycaprolactone scaffolds, smooth muscle strip constructs expressed high levels of smooth muscle maturity markers as well as enteric neural and glial cells. Intact smooth muscle strips may be a useful component for engineered intestinal smooth muscle. PMID:25486279
DARK MATTER SEARCH USING XMM-NEWTON OBSERVATIONS OF WILLMAN 1
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.
Notes on Newton-Krylov based Incompressible Flow Projection Solver
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.
Smooth Sailing with Contract Services.
ERIC Educational Resources Information Center
Fickes, Michael
2001-01-01
Discusses how to make the contract services relationship work smoothly for educational facilities. Covers topics of food, child care, and transportation services, along with a brief explanation of the benefits of outsourcing on-campus amenities. (GR)
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.
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.
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.
Exotic smoothness and quantum gravity
NASA Astrophysics Data System (ADS)
Asselmeyer-Maluga, T.
2010-08-01
Since the first work on exotic smoothness in physics, it was folklore to assume a direct influence of exotic smoothness to quantum gravity. Thus, the negative result of Duston (2009 arXiv:0911.4068) was a surprise. A closer look into the semi-classical approach uncovered the implicit assumption of a close connection between geometry and smoothness structure. But both structures, geometry and smoothness, are independent of each other. In this paper we calculate the 'smoothness structure' part of the path integral in quantum gravity assuming that the 'sum over geometries' is already given. For that purpose we use the knot surgery of Fintushel and Stern applied to the class E(n) of elliptic surfaces. We mainly focus our attention to the K3 surfaces E(2). Then we assume that every exotic smoothness structure of the K3 surface can be generated by knot or link surgery in the manner of Fintushel and Stern. The results are applied to the calculation of expectation values. Here we discuss the two observables, volume and Wilson loop, for the construction of an exotic 4-manifold using the knot 52 and the Whitehead link Wh. By using Mostow rigidity, we obtain a topological contribution to the expectation value of the volume. Furthermore, we obtain a justification of area quantization.
Correction of the continual scanning record of radioactivity distribution I: Smoothing
NASA Astrophysics Data System (ADS)
Tykva, Richard; Jisl, Rudolf
1986-10-01
A method is described of smoothing the graphical record of the counting rate obtained in measuring the radioactivity distribution during continual scanning of a plane sample by the detector. The smoothing is based on using a smoothing operator with coefficients optimized according to the recorded curve. The method enables on-line smoothing if the curves are similar in shape. Its use is demonstrated on the example of the simultaneous determination of the distribution of 14C and 32P.
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.
Frank, K. A.; Peterson, J. R.; Andersson, K.; Fabian, A. C.; Sanders, J. S.
2013-02-10
We measure the intracluster medium (ICM) temperature distributions for 62 galaxy clusters in the HIFLUGCS, an X-ray flux-limited sample, with available X-ray data from XMM-Newton. We search for correlations between the width of the temperature distributions and other cluster properties, including median cluster temperature, luminosity, size, presence of a cool core, active galactic nucleus (AGN) activity, and dynamical state. We use a Markov Chain Monte Carlo analysis, which models the ICM as a collection of X-ray emitting smoothed particles of plasma. Each smoothed particle is given its own set of parameters, including temperature, spatial position, redshift, size, and emission measure. This allows us to measure the width of the temperature distribution, median temperature, and total emission measure of each cluster. We find that none of the clusters have a temperature width consistent with isothermality. Counterintuitively, we also find that the temperature distribution widths of disturbed, non-cool-core, and AGN-free clusters tend to be wider than in other clusters. A linear fit to {sigma} {sub kT}-kT {sub med} finds {sigma} {sub kT} {approx} 0.20kT {sub med} + 1.08, with an estimated intrinsic scatter of {approx}0.55 keV, demonstrating a large range in ICM thermal histories.
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.
Kuriyama, H; Tomita, T
1970-02-01
The configuration of the electrotonic potential and the action potential observed by the double sucrose-gap method was similar to that observed with a microelectrode inserted into a cell in the center pool between the gaps. In the taenia and the ureter, the evoked spike was larger in low Na or in Na-free (sucrose substitute) solution than in normal solution. However, the plateau component in the ureter was suppressed in the absence of Na. In Ca-free solution containing Mg (3-5 mM) and Na (137 mM), the membrane potential and membrane resistance were normal, but no spike could be elicited in both the taenia and ureter. Replacement of Ca with Sr did not affect the spike in the taenia, nor the spike component of the ureter but prolonged the plateau component. The prolonged plateau disappeared on removal of Na, while repetitive spikes could still be evoked. It was concluded that the spike activity in the taenia and in the ureter of the guinea pig is due to Ca entry, that the plateau component in the ureter is due to an increase in the Na conductance of the membrane, and that both mechanisms, for the spike and for the plateau, are separately controlled by Ca bound in the membrane.
A multigrid method for variational inequalities
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.
HIGH-RESOLUTION XMM-NEWTON SPECTROSCOPY OF THE COOLING FLOW CLUSTER A3112
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.
XMM-Newton and Swift observations of WZ Sagittae: spectral and timing analysis
NASA Astrophysics Data System (ADS)
Nucita, A. A.; Kuulkers, E.; De Paolis, F.; Mukai, K.; Ingrosso, G.; Maiolo, B. M. T.
2014-06-01
Context. WZ Sagittae is the prototype object of a subclass of dwarf novae with rare and long (super)outbursts, in which a white dwarf primary accretes matter from a low mass companion. High-energy observations offer the possibility of a better understanding of the disk-accretion mechanism in WZ Sge-like binaries. Aims: We used archival XMM-Newton and Swift data to characterize the X-ray spectral and temporal properties of WZ Sge in quiescence. Methods: We performed a detailed timing analysis of the simultaneous X-ray and UV light curves obtained with the EPIC and OM instruments on board XMM-Newton in 2003. We employed several techniques in this study, including a correlation study between the two curves. We also performed an X-ray spectral analysis using the EPIC data and Swift/XRT data obtained in 2011. Results: We find that the X-ray intensity is clearly modulated at a period of ≃28.96 s, confirming previously published preliminary results. We find that the X-ray spectral shape of WZ Sge remains practically unchanged between the XMM-Newton and Swift observations. However, after correcting for interstellar absorption, the intrinsic luminosity is estimated to be LXUna = (2.65 ± 0.06) × 1030 erg s-1 and LXUna = (1.57 ± 0.03) × 1030 erg s-1 in 2003 and 2011, respectively. During the Swift/XRT observation, the observed flux is a factor ≃2 lower than that observed by XMM-Newton but is similar to the quiescent levels that are observed various times before the 2001 outburst.
A BeppoSAX and XMM-Newton spectral study of 4U 1735-44
NASA Astrophysics Data System (ADS)
Mück, B.; Piraino, S.; Santangelo, A.
2013-07-01
Context. Low-mass X-ray binary systems consist of a neutron star and a main-sequence companion star. The compact object accretes matter via Roche-lobe overflow, which leads to an accretion disk. In addition to a broad-band continuum emission of a thermal component and a Comptonization part, evidence for a broad iron Kα line is found in several sources. Some of them show an asymmetric line profile as well, which could originate from relativistic effects. Aims: To understand the spectral behavior of the system 4U 1735-44, we study the broad-band spectrum and especially the iron line feature between 6.4 and 6.97 keV. The shape of the line allows one to determine the region where the line is produced. Together with the continuum models, a geometrical model of the source can be proposed. Furthermore, the effects of pile-up in the XMM-Newton observation are investigated. Methods: We analyzed data obtained with the X-ray satellites BeppoSAX and XMM-Newton. The XMM-Newton data were analyzed, specifically taking into account pile-up effects. With the help of the data of these two satellites, we performed a detailed spectral study in an energy range from 0.2-24 keV. Results: During the observations, the source was in the so-called banana state of an atoll source. Fitting the BeppoSAX data, we found line features that we were able to model with a reflection model, whereas the continuum was modeled with a combination of a thermal component and a Comptonization part. The analysis of the XMM-Newton data gave evidence for a broad but not asymmetric iron line. We found no broadening or asymmetry of the line because of pile-up.
Reduction of noise in diffusion tensor images using anisotropic smoothing.
Ding, Zhaohua; Gore, John C; Anderson, Adam W
2005-02-01
To improve the accuracy of tissue structural and architectural characterization with diffusion tensor imaging, a novel smoothing technique is developed for reducing noise in diffusion tensor images. The technique extends the traditional anisotropic diffusion filtering method by allowing isotropic smoothing within homogeneous regions and anisotropic smoothing along structure boundaries. This is particularly useful for smoothing diffusion tensor images in which direction information contained in the tensor needs to be restored following noise corruption and preserved around tissue boundaries. The effectiveness of this technique is quantitatively studied with experiments on simulated and human in vivo diffusion tensor data. Illustrative results demonstrate that the anisotropic smoothing technique developed can significantly reduce the impact of noise on the direction as well as anisotropy measures of the diffusion tensor images.
Stabilizing S.P.H. with conservative smoothing
Wen, Y.; Hicks, D.L.; Swegle, J.W.
1994-08-01
There is an instability in certain S.P.H. (Smoothed Particle Hydrodynamics method) material dynamics computations. Evidence from analyses and experiments suggests that the instabilities in S.P.H. are not removable with artificial viscosities. However, the analysis shows that a type of conservative smoothing does remove the instability. Also, numerical experiments, on certain test problems, show that SPHCS, and S.P.H. code with conservative smoothing, compares well in accuracy with computations based on the von Neumann-Richtmyer method.
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.
Compressive Sensing via Nonlocal Smoothed Rank Function.
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. PMID:27583683
Compressive Sensing via Nonlocal Smoothed Rank Function
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
Compressive Sensing via Nonlocal Smoothed Rank Function.
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.
Bohlin transformation: the hidden symmetry that connects Hooke to Newton
NASA Astrophysics Data System (ADS)
Saggio, Maria Luisa
2013-01-01
Hooke's name is familiar to students of mechanics thanks to the law of force that bears his name. Less well-known is the influence his findings had on the founder of mechanics, Isaac Newton. In a lecture given some twenty years ago, W Arnol'd pointed out the outstanding contribution to science made by Hooke, and also noted the controversial issue of the attribution of important discoveries to Newton that were actually inspired by Hooke. It therefore seems ironic that the two most famous force laws, named after Hooke and Newton, are two geometrical aspects of the same law. This relationship, together with other illuminating aspects of Newtonian mechanics, is described in Arnol'd's book and is worth remembering in standard physics courses. In this didactical paper the duality of the two forces is expounded and an account of the more recent contributions to the subject is given.
Non-Relativistic Twistor Theory and Newton-Cartan Geometry
NASA Astrophysics Data System (ADS)
Dunajski, Maciej; Gundry, James
2016-03-01
We develop a non-relativistic twistor theory, in which Newton-Cartan structures of Newtonian gravity correspond to complex three-manifolds with a four-parameter family of rational curves with normal bundle O oplus O(2)}. We show that the Newton-Cartan space-times are unstable under the general Kodaira deformation of the twistor complex structure. The Newton-Cartan connections can nevertheless be reconstructed from Merkulov's generalisation of the Kodaira map augmented by a choice of a holomorphic line bundle over the twistor space trivial on twistor lines. The Coriolis force may be incorporated by holomorphic vector bundles, which in general are non-trivial on twistor lines. The resulting geometries agree with non-relativistic limits of anti-self-dual gravitational instantons.
Room-temperature wafer scale bonding using smoothed Au seal ring surfaces for hermetic sealing
NASA Astrophysics Data System (ADS)
Kurashima, Yuichi; Maeda, Atsuhiko; Takagi, Hideki
2016-01-01
We evaluated room-temperature bonding characteristics of electroplated Au surfaces smoothed by the lift-off and imprint methods. As a result, we found that smoothed surfaces enable strong bonding; on the other hand, electroplated rough surfaces result in very weak bonding. In transmission electron microscopy observations, no delamination was observed at the bonding interface bonded at room temperature using a smooth surface prepared by the lift-off method. Moreover, the hermeticity of the bonding interface prepared using smoothed surfaces was evaluated using diaphragm structures. As a result, we confirmed that good hermetic sealing was achieved using the electroplated Au surface smoothed by the lift-off method.
Isaac Newton and the problem of the Earth's shape.
NASA Astrophysics Data System (ADS)
Greenberg, J. L.
1996-04-01
The author discusses the theory of the Earth's shape presented by Isaac Newton in Book III of his "Principia". It is shown that the theory struck even the most reputable continental mathematicians of the day as incomprehensible. The author examines the many obstacles to understanding the theory which the reader faced - the gaps, the underived equations, the unproven assertions, the dependence upon corollaries to practically incomprehensible theorems in Book I of the "Principia" and the ambiguities of these corollaries, the conjectures without explanations of their bases and so forth. The author explains why these apparent drawbacks are, historically considered, strengths of Newton's theory of the Earth's shape, not weaknesses.
PEOPLE IN PHYSICS: 'Lady Newton' - an eighteenth century Marquise
NASA Astrophysics Data System (ADS)
Badilescu, Simona
1996-07-01
The contribution of Voltaire and Mme du ChÃ¢telet to the diffusion of Newtonian physics in eighteenth century France is outlined. Their most important writings in the realm of physics (Philosophical Letters, Elements de la philosophie de Newton, Institutions de Physique) are analysed and the impact of the new ideas on the traditional Cartesian physics is emphasized. The genesis of the first French translation of Newton's Principia is described. The usefulness of the historically connected stories in the teaching of physics is envisaged.
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…
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…
7 CFR 51.768 - Smooth texture.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 2 2011-01-01 2011-01-01 false Smooth texture. 51.768 Section 51.768 Agriculture... Standards for Grades of Florida Grapefruit Definitions § 51.768 Smooth texture. Smooth texture means that the skin is thin and smooth for the variety and size of the fruit. “Thin” means that the...
7 CFR 51.698 - Smooth texture.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 2 2013-01-01 2013-01-01 false Smooth texture. 51.698 Section 51.698 Agriculture..., California, and Arizona) Definitions § 51.698 Smooth texture. Smooth texture means that the skin is thin and smooth for the variety and size of the fruit....
7 CFR 51.1159 - Smooth texture.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Smooth texture. 51.1159 Section 51.1159 Agriculture... Standards for Grades of Florida Oranges and Tangelos Definitions § 51.1159 Smooth texture. Smooth texture means that the skin is thin and smooth for the variety and size of the fruit....
7 CFR 51.636 - Smooth texture.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 2 2014-01-01 2014-01-01 false Smooth texture. 51.636 Section 51.636 Agriculture... Florida, California, and Arizona) Definitions § 51.636 Smooth texture. Smooth texture means that the skin is thin and smooth for the variety and size of the fruit....
7 CFR 51.636 - Smooth texture.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 2 2011-01-01 2011-01-01 false Smooth texture. 51.636 Section 51.636 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing...) Definitions § 51.636 Smooth texture. Smooth texture means that the skin is thin and smooth for the variety...
7 CFR 51.1159 - Smooth texture.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 2 2013-01-01 2013-01-01 false Smooth texture. 51.1159 Section 51.1159 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... § 51.1159 Smooth texture. Smooth texture means that the skin is thin and smooth for the variety...
7 CFR 51.698 - Smooth texture.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 2 2012-01-01 2012-01-01 false Smooth texture. 51.698 Section 51.698 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... § 51.698 Smooth texture. Smooth texture means that the skin is thin and smooth for the variety and...
7 CFR 51.698 - Smooth texture.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 2 2011-01-01 2011-01-01 false Smooth texture. 51.698 Section 51.698 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... § 51.698 Smooth texture. Smooth texture means that the skin is thin and smooth for the variety and...
7 CFR 51.768 - Smooth texture.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Smooth texture. 51.768 Section 51.768 Agriculture... Standards for Grades of Florida Grapefruit Definitions § 51.768 Smooth texture. Smooth texture means that the skin is thin and smooth for the variety and size of the fruit. “Thin” means that the...
7 CFR 51.768 - Smooth texture.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 2 2013-01-01 2013-01-01 false Smooth texture. 51.768 Section 51.768 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Smooth texture. Smooth texture means that the skin is thin and smooth for the variety and size of...
7 CFR 51.1159 - Smooth texture.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 2 2011-01-01 2011-01-01 false Smooth texture. 51.1159 Section 51.1159 Agriculture... Standards for Grades of Florida Oranges and Tangelos Definitions § 51.1159 Smooth texture. Smooth texture means that the skin is thin and smooth for the variety and size of the fruit....
7 CFR 51.768 - Smooth texture.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 2 2012-01-01 2012-01-01 false Smooth texture. 51.768 Section 51.768 Agriculture... Standards for Grades of Florida Grapefruit Definitions § 51.768 Smooth texture. Smooth texture means that the skin is thin and smooth for the variety and size of the fruit. “Thin” means that the...
7 CFR 51.698 - Smooth texture.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 2 2014-01-01 2014-01-01 false Smooth texture. 51.698 Section 51.698 Agriculture..., California, and Arizona) Definitions § 51.698 Smooth texture. Smooth texture means that the skin is thin and smooth for the variety and size of the fruit....
7 CFR 51.1159 - Smooth texture.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 2 2012-01-01 2012-01-01 false Smooth texture. 51.1159 Section 51.1159 Agriculture... Standards for Grades of Florida Oranges and Tangelos Definitions § 51.1159 Smooth texture. Smooth texture means that the skin is thin and smooth for the variety and size of the fruit....
7 CFR 51.698 - Smooth texture.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Smooth texture. 51.698 Section 51.698 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... § 51.698 Smooth texture. Smooth texture means that the skin is thin and smooth for the variety and...
7 CFR 51.636 - Smooth texture.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Smooth texture. 51.636 Section 51.636 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing...) Definitions § 51.636 Smooth texture. Smooth texture means that the skin is thin and smooth for the variety...
7 CFR 51.636 - Smooth texture.
Code of Federal Regulations, 2013 CFR
2013-01-01
... 7 Agriculture 2 2013-01-01 2013-01-01 false Smooth texture. 51.636 Section 51.636 Agriculture... Florida, California, and Arizona) Definitions § 51.636 Smooth texture. Smooth texture means that the skin is thin and smooth for the variety and size of the fruit....
7 CFR 51.636 - Smooth texture.
Code of Federal Regulations, 2012 CFR
2012-01-01
... 7 Agriculture 2 2012-01-01 2012-01-01 false Smooth texture. 51.636 Section 51.636 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing...) Definitions § 51.636 Smooth texture. Smooth texture means that the skin is thin and smooth for the variety...
7 CFR 51.1159 - Smooth texture.
Code of Federal Regulations, 2014 CFR
2014-01-01
... 7 Agriculture 2 2014-01-01 2014-01-01 false Smooth texture. 51.1159 Section 51.1159 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... § 51.1159 Smooth texture. Smooth texture means that the skin is thin and smooth for the variety...
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. PMID:25750143
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. PMID:25455541
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.
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.
Communication: Newton homotopies for sampling stationary points of potential energy landscapes
NASA Astrophysics Data System (ADS)
Mehta, Dhagash; Chen, Tianran; Hauenstein, Jonathan D.; Wales, David J.
2014-09-01
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 ϕ4 model and atomic clusters.
Communication: Newton homotopies for sampling stationary points of potential energy landscapes
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.
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
Smooth local subspace projection for nonlinear noise reduction
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.
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...
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…
Join Newton's Apple on a Global Science Adventure!
ERIC Educational Resources Information Center
Vespy, Linda
1996-01-01
Describes Newton's Apple, the PBS family science show that explores how biology, chemistry, physics, and other sciences are integral parts of everyday life and includes demonstrations, activities, and inquiry-based discussions that encourage students to discover science for themselves. Presents highlights of the show for the year and contact…
Effect of written text on usage of newton's third law
NASA Astrophysics Data System (ADS)
Boyle, Rosemary K.; Maloney, David P.
This article reports on a study that investigated novice students' rules for determining which of two objects exerted the greater force on the other. Subjects worked five paper-and-pencil task sets depicting different objects interacting with each other. For each situation they were asked to identify which of the two objects was exerting the stronger force on the other. Each subject worked the task sets under one of three conditions: with no aid, with a written statement describing forces as interactions that always occur in pairs, or with a written statement of Newton's third law. The vast majority of the subjects in the study used procedures (rules) which could be identified. There were significant differences in the patterns of usage of the various rules between those who received no written statement and those who received the statement of Newton's third law. The primary difference between the two groups was in the usage of a rule (All Equal) which produced the same response sequence as Newton's third law. However, only 29% of those who received the Newton's third law handout used the All Equal rule on all five task sets. There were no significant differences in usage of the All Equal rule between those who had had high school physics and those who had not. Strong evidence was found to contradict the idea that the subjects who failed to used the All Equal rule simply did not read the written statement properly. The results of this study have implications for learning from text.
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…
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…
Rediscovering Kepler's laws using Newton's gravitation law and NASA data
NASA Astrophysics Data System (ADS)
Springsteen, Paul; Keith, Jason
2010-03-01
Kepler's three laws of planetary motion were originally discovered by using data acquired from Tycho Brache's naked eye observations of the planets. We show how Kepler's third law can be reproduced using planetary data from NASA. We will also be using Newton's Gravitational law to explain why Kepler's three laws exist as they do.
Microlensing, Newton-Einstein gravity, and conformal gravity
NASA Astrophysics Data System (ADS)
Mannheim, Philip D.
1995-07-01
We discuss some implications of the current round of galactic dark matter searches for galactic rotation curve systematics and dynamics, and show that these new data do not invalidate the conformal gravity program of Mannheim and Kazanas which has been advanced as a candidate alternative to both the standard second order Newton-Einstein theory and the need for dark matter. .