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.
More, J. J.; Sorensen, D. C.
1982-02-01
Newton's method plays a central role in the development of numerical techniques for optimization. In fact, most of the current practical methods for optimization can be viewed as variations on Newton's method. It is therefore important to understand Newton's method as an algorithm in its own right and as a key introduction to the most recent ideas in this area. One of the aims of this expository paper is to present and analyze two main approaches to Newton's method for unconstrained minimization: the line search approach and the trust region approach. The other aim is to present some of the recent developments in the optimization field which are related to Newton's method. In particular, we explore several variations on Newton's method which are appropriate for large scale problems, and we also show how quasi-Newton methods can be derived quite naturally from Newton's method.
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…
Quasi-Newton and multigrid methods for semiconductor device simulation
Slamet, S.
1983-12-01
A finite difference approximation to the semiconductor device equations using the Bernoulli function approximation to the exponential function is described, and the robustness of this approximation is demonstrated. Sheikh's convergence analysis of Gummel's method and quasi-Newton methods is extended to a nonuniform mesh and the Bernoulli function discretization. It is proved that Gummel's method and the quasi-Newton methods for the scaled carrier densities and carrier densities converge locally for sufficiently smooth problems.
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. PMID:25033525
OPF by Newton`s method: A comparison between polar and rectangular formulations
Gutierrez, G.; Guzman, C.R.; Chavez, S.; Madrigal, M.; Tovar, J.H.
1998-12-31
The purpose of an Optimal Power Flow (OPF) is to schedule power system controls which optimizes an objective function while at the same time satisfying a set of nonlinear equality and inequality constraints. This problem has been solved by Newton`s approach using polar coordinates to represent power flow equations. In this paper Newton`s method is used to solve the optimal power flow problem, but using rectangular coordinates. Extensive comparison are made against the polar version. The results show superiority in computing time and robustness of the rectangular coordinates Newton`s OPF.
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.
The Newton Modified Barrier Method for QP Problems
NASA Technical Reports Server (NTRS)
Melman, A.; Polyak, R.
1996-01-01
The Modified Barrier Functions (MBF) have elements of both Classical Lagrangians (CL) and Classical Barrier Functions (CBF). The MBF methods find an unconstrained minimizer of some smooth barrier function in primal space and then update the Lagrange multipliers, while the barrier parameter either remains fixed or can be updated at each step. The numerical realization of the MBF method leads to the Newton MBF method, where the primal minimizer is found by using Newton's method. This minimizer is then used to update the Lagrange multipliers. In this paper, we examine the Newton MBF method for the Quadratic Programming (QP) problem. It will be shown that under standard second-order optimality conditions, there is a ball around the primal solution and a cut cone in the dual space such that for a set of Lagrange multipliers in this cut cone, the method converges quadratically to the primal minimizer from any point in the aforementioned ball, and continues to do so after each Lagrange multiplier update. The Lagrange multipliers remain within the cut cone and converge linearly to their optimal values. Any point in this ball will be called a "hot start". Starting at such a "hot start", at most Omicron(1n 1n epsilon(exp -1)) Newton steps are sufficient to perform the primal minimization which is necessary for the Lagrange multiplier update. Here, epsilon > 0 is the desired accuracy. Because of the linear convergence of the Lagrange multipliers, this means that only Omicron(1n epsilon(exp -1))omicron(ln 1n epsilon(exp-1)) Newton steps are required to reach an epsilon-approximation to the solution from any "hot start". In order to reach the "hot start", one has to perform Omicron(square root(m) 1n C) Newton steps, where m characterizes the size of the problem and C > 0 is the condition number of the QP problem. This condition number will be characterized explicitly in terms of key parameters of the QP problem, which in turn depend on the input data and the size of the problem.
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.
Newton iterative methods for large scale nonlinear systems
Walker, H.F.; Turner, K.
1993-01-01
Objective is to develop robust, efficient Newton iterative methods for general large scale problems well suited for discretizations of partial differential equations, integral equations, and other continuous problems. A concomitant objective is to develop improved iterative linear algebra methods. We first outline research on Newton iterative methods and then review work on iterative linear algebra methods. (DLC)
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.
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.
Convergence of Newton's method for a single real equation
NASA Technical Reports Server (NTRS)
Campbell, C. W.
1985-01-01
Newton's method for finding the zeroes of a single real function is investigated in some detail. Convergence is generally checked using the Contraction Mapping Theorem which yields sufficient but not necessary conditions for convergence of the general single point iteration method. The resulting convergence intervals are frequently considerably smaller than actual convergence zones. For a specific single point iteration method, such as Newton's method, better estimates of regions of convergence should be possible. A technique is described which, under certain conditions (frequently satisfied by well behaved functions) gives much larger zones where convergence is guaranteed.
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
On collinear scaling algorithms that extend quasi-Newton methods
Ariyawansa, K.A.
1994-12-31
Quasi-Newton methods for unconstrained minimization are based on local affine scalings of the domain, and local quadratic approximations to the objective function that interpolate the gradient. Quasi-Newton algorithms have finite termination on quadratic functions, and are invariant under affine scalings. In 1980, Davidon presented a new class of algorithms for unconstrained minimization based on local collinear scalings of the domain, and local conic approximations to the objective function that interpolate both the gradient and function value. We refer to these algorithms as Davidon`s collinear scaling algorithms. Collinear scalings and conic functions generalize affine scalings and quadratic functions respectively, and therefore collinear scaling algorithms extend quasi-Newton algorithms. Davidon`s collinear scaling algorithms have finite termination on conic functions, and are invariant under collinear scalings. In this talk, we present a new derivation of Davidon`s collinear scaling algorithms. It indicates that collinear scaling algorithms extending quasi-Newton methods studied to date are different from those of Davidon. It also explains why it has not been possible to demonstrate that these other collinear scaling algorithms have finite termination on conic functions, and are invariant under collinear scalings.
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.
Puso, M A; Laursen, T A
2002-05-02
Smoothing of contact surfaces can be used to eliminate the chatter typically seen with node on facet contact and give a better representation of the actual contact surface. The latter affect is well demonstrated for problems with interference fits. In this work we present two methods for the smoothing of contact surfaces for 3D finite element contact. In the first method, we employ Gregory patches to smooth the faceted surface in a node on facet implementation. In the second method, we employ a Bezier interpolation of the faceted surface in a mortar method implementation of contact. As is well known, node on facet approaches can exhibit locking due to the failure of the Babuska-Brezzi condition and in some instances fail the patch test. The mortar method implementation is stable and provides optimal convergence in the energy of error. In the this work we demonstrate the superiority of the smoothed versus the non-smoothed node on facet implementations. We also show where the node on facet method fails and some results from the smoothed mortar method implementation.
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.
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'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.
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.
Gauss-Newton method for DEM co-registration
NASA Astrophysics Data System (ADS)
Wang, Kunlun; Zhang, Tonggang
2015-12-01
Digital elevation model (DEM) co-registration is one of the hottest research problems, and it is the critical technology for multi-temporal DEM analysis, which has wide potential application in many fields, such as geological hazards. Currently, the least-squares principle is used in most DEM co-registration methods, in which the matching parameters are obtained by iteration; the surface co-registration is then accomplished. To improve the iterative convergence rate, a Gauss-Newton method for DEM co-registration (G-N) is proposed in this paper. A gradient formula based on a gridded discrete surface is derived in theory, and then the difficulty of applying the Gauss-Newton method to DEM matching is solved. With the G-N algorithm, the surfaces approach each other along the maximal gradient direction, and therefore the iterative convergence and the performance efficiency of the new method can be enhanced greatly. According to experimental results based on the simulated datasets, the average convergence rates of rotation and translation parameters of the G-N algorithm are increased by 40 and 15% compared to those of the ICP algorithm, respectively. The performance efficiency of the G-N algorithm is 74.9% better.
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.
Newton iterative methods for large scale nonlinear systems. Progress report, 1992--1993
Walker, H.F.; Turner, K.
1993-06-01
Objective is to develop robust, efficient Newton iterative methods for general large scale problems well suited for discretizations of partial differential equations, integral equations, and other continuous problems. A concomitant objective is to develop improved iterative linear algebra methods. We first outline research on Newton iterative methods and then review work on iterative linear algebra methods. (DLC)
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.
Recent developments in quasi-Newton methods for structural analysis and synthesis
NASA Technical Reports Server (NTRS)
Kamat, M. P.; Hayduk, R. J.
1981-01-01
Unlike the Newton-Raphson method, quasi-Newton methods by virture of the updates and step length control procedures are globally convergent and hence better suited for the solution of nonlinear problems of structural analysis and synthesis. Extension of quasi-Newton algorithms to large scale problems has led to the development of sparse update algorithms and to economical strategies for evaluating sparse Hessians. Ill-conditioning problems have led to the development of self-scaled variable metric and conjugate gradient algorithms, as well as the use of the singular perturbation theory. This paper emphasizes the effectiveness of such quasi-Newton algorithms for nonlinear structural analysis and synthesis.
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.
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.
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.
Application of Newton's method to the postbuckling of rings under pressure loadings
NASA Technical Reports Server (NTRS)
Thurston, Gaylen A.
1989-01-01
The postbuckling response of circular rings (or long cylinders) is examined. The rings are subjected to four types of external pressure loadings; each type of pressure is defined by its magnitude and direction at points on the buckled ring. Newton's method is applied to the nonlinear differential equations of the exact inextensional theory for the ring problem. A zeroth approximation for the solution of the nonlinear equations, based on the mode shape corresponding to the first buckling pressure, is derived in closed form for each of the four types of pressure. The zeroth approximation is used to start the iteration cycle in Newton's method to compute numerical solutions of the nonlinear equations. The zeroth approximations for the postbuckling pressure-deflection curves are compared with the converged solutions from Newton's method and with similar results reported in the literature.
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.
On a class of Newton-like methods for solving nonlinear equations
NASA Astrophysics Data System (ADS)
Argyros, Ioannis K.
2009-06-01
We provide a semilocal convergence analysis for a certain class of Newton-like methods considered also in [I.K. Argyros, A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space, J. Math. Anal. Appl. 298 (2004) 374-397; I.K. Argyros, Computational theory of iterative methods, in: C.K. Chui, L. Wuytack (Eds.), Series: Studies in Computational Mathematics, vol. 15, Elsevier Publ. Co, New York, USA, 2007; J.E. Dennis, Toward a unified convergence theory for Newton-like methods, in: L.B. Rall (Ed.), Nonlinear Functional Analysis and Applications, Academic Press, New York, 1971], in order to approximate a locally unique solution of an equation in a Banach space. Using a combination of Lipschitz and center-Lipschitz conditions, instead of only Lipschitz conditions [F.A. Potra, Sharp error bounds for a class of Newton-like methods, Libertas Math. 5 (1985) 71-84], we provide an analysis with the following advantages over the work in [F.A. Potra, Sharp error bounds for a class of Newton-like methods, Libertas Math. 5 (1985) 71-84] which improved the works in [W.E. Bosarge, P.L. Falb, A multipoint method of third order, J. Optimiz. Theory Appl. 4 (1969) 156-166; W.E. Bosarge, P.L. Falb, Infinite dimensional multipoint methods and the solution of two point boundary value problems, Numer. Math. 14 (1970) 264-286; J.E. Dennis, On the Kantorovich hypothesis for Newton's method, SIAM J. Numer. Anal. 6 (3) (1969) 493-507; J.E. Dennis, Toward a unified convergence theory for Newton-like methods, in: L.B. Rall (Ed.), Nonlinear Functional Analysis and Applications, Academic Press, New York, 1971; H.J. Kornstaedt, Ein allgemeiner Konvergenzstaz fü r verschä rfte Newton-Verfahrem, in: ISNM, vol. 28, Birkhaü ser Verlag, Basel and Stuttgart, 1975, pp. 53-69; P. Laasonen, Ein überquadratisch konvergenter iterativer algorithmus, Ann. Acad. Sci. Fenn. Ser I 450 (1969) 1-10; F.A. Potra, On a modified secant method, L'analyse num
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.
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.
Markov chain Mote Carlo solution of BK equation through Newton-Kantorovich method
NASA Astrophysics Data System (ADS)
BoŻek, Krzysztof; Kutak, Krzysztof; Placzek, Wieslaw
2013-07-01
We propose a new method for Monte Carlo solution of non-linear integral equations by combining the Newton-Kantorovich method for solving non-linear equations with the Markov Chain Monte Carlo (MCMC) method for solving linear equations. The Newton-Kantorovich method allows to express the non-linear equation as a system of the linear equations which then can be treated by the MCMC (random walk) algorithm. We apply this method to the Balitsky-Kovchegov (BK) equation describing evolution of gluon density at low x. Results of numerical computations show that the MCMC method is both precise and efficient. The presented algorithm may be particularly suited for solving more complicated and higher-dimensional non-linear integral equation, for which traditional methods become unfeasible.
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
A compressible Navier-Stokes flow solver using the Newton-Krylov method on unstructured grids
NASA Astrophysics Data System (ADS)
Wong, Peterson
A Newton-Krylov algorithm is presented for the compressible Navier-Stokes equations on hybrid unstructured grids. The Spalart-Allmaras turbulence model is used for turbulent flows. The spatial discretization is based on a finite-volume matrix dissipation scheme. A preconditioned matrix-free generalized minimal residual method is used to solve the linear system that arises in the Newton iterations. The incomplete lower-upper factorization based on an approximate Jacobian is used as the preconditioner after applying the reverse Cuthill-McKee reordering. Various aspects of the Newton-Krylov algorithm are studied to improve efficiency and reliability. The inexact Newton method is studied to avoid over-solving of the linear system to reduce computational cost. The ILU(1) approach is selected in three dimensions, based on a comparison among various preconditioners. Approximate viscous formulations involving only the nearest neighboring terms are studied to reduce the cost of preconditioning. The resulting preconditioners are found to be effective and provide Newton-type convergence. Scaling of the linear system is studied to improve convergence of the inexact matrix-free approach. Numerical studies are performed for two-dimensional cases as well as flows over the ONERA M6 wing and the DLR-F6 wing-body configuration. A ten-order-of-magnitude residual reduction can be obtained with a computing cost equivalent to 4,000 residual function evaluations for two-dimensional cases, while the same convergence can be obtained in 5,500 and 8,000 function evaluations for the wing and wing-body configuration, respectively, on grids with a half million nodes.
NASA Technical Reports Server (NTRS)
Chapman, G.; Kirk, D.
1974-01-01
The parameter identification scheme being used is a differential correction least squares procedure (Gauss-Newton method). The position, orientation, and derivatives of these quantities with respect to the parameters of interest (i.e., sensitivity coefficients) are determined by digital integration of the equations of motion and the parametric differential equations. The application of this technique to three vastly different sets of data is used to illustrate the versatility of the method and to indicate some of the problems that still remain.
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.
Postprocessing Fourier spectral methods: The case of smooth solutions
Garcia-Archilla, B.; Novo, J.; Titi, E.S.
1998-11-01
A postprocessing technique to improve the accuracy of Galerkin methods, when applied to dissipative partial differential equations, is examined in the particular case of smooth solutions. Pseudospectral methods are shown to perform poorly. This performance is analyzed and a refined postprocessing technique is proposed.
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.
Modeling of hydrogen-assisted cracking in iron crystal using a quasi-Newton method.
Telitchev, Igor Ye; Vinogradov, Oleg
2008-07-01
A Quasi-Newton method was applied in the context of a molecular statics approach to simulate the phenomenon of hydrogen embrittlement of an iron lattice. The atomic system is treated as a truss-type structure. The interatomic forces between the hydrogen-iron and the iron-iron atoms are defined by Morse and modified Morse potential functions, respectively. Two-dimensional hexagonal and 3D bcc crystal structures were subjected to tensile numerical tests. It was shown that the Inverse Broyden's Algorithm-a quasi-Newton method-provides a computationally efficient technique for modeling of the hydrogen-assisted cracking in iron crystal. Simulation results demonstrate that atoms of hydrogen placed near the crack tip produce a strong deformation and crack propagation effect in iron lattice, leading to a decrease in the residual strength of numerically tested samples. PMID:18481119
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.
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.
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.
Hyperbolic Divergence Cleaning Method for Godunov Smoothed Particle Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Iwasaki, K.; Inutsuka, S.-I.
2013-04-01
In this paper, we implement a divergence cleaning method into Godunov smoothed particle magnetohydrodynamics (GSPM). In the GSPM, to describe MHD shocks accurately, a Riemann solver is applied to the SPH method instead of artificial viscosity and resistivity that have been used in previous works. We confirmed that the divergence cleaning method reduces divergence errors significantly. The performance of the method is demonstrated in the numerical simulations of a strongly magnetized gas and bipolar outflow from the first core.
Solving nonlinear heat conduction problems with multigrid preconditioned Newton-Krylov methods
Rider, W.J.; Knoll, D.A.
1997-09-01
Our objective is to investigate the utility of employing multigrid preconditioned Newton-Krylov methods for solving initial value problems. Multigrid based method promise better performance from the linear scaling associated with them. Our model problem is nonlinear heat conduction which can model idealized Marshak waves. Here we will investigate the efficiency of using a linear multigrid method to precondition a Krylov subspace method. In effect we will show that a fixed point nonlinear iterative method provides an effective preconditioner for the nonlinear problem.
Modified Newton-Raphson GRAPE methods for optimal control of spin systems.
Goodwin, D L; Kuprov, Ilya
2016-05-28
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. PMID:27250279
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.
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.…
Smoothness Evaluation of Cotton Nonwovens Using Quality Energy Method
Technology Transfer Automated Retrieval System (TEKTRAN)
Nonwovens are finding enhanced use in next-to-skin application such as wipes. The global wipe industry is estimated somewhere between $6-8 billion. One important attributes of the wipes is its smoothness as it determines it end use applications. Although there are a number of methods and techniques ...
Cooley, R.L.; Hill, M.C.
1992-01-01
Three methods of solving nonlinear least-squares problems were compared for robustness and efficiency using a series of hypothetical and field problems. A modified Gauss-Newton/full Newton hybrid method (MGN/FN) and an analogous method for which part of the Hessian matrix was replaced by a quasi-Newton approximation (MGN/QN) solved some of the problems with appreciably fewer iterations than required using only a modified Gauss-Newton (MGN) method. In these problems, model nonlinearity and a large variance for the observed data apparently caused MGN to converge more slowly than MGN/FN or MGN/QN after the sum of squared errors had almost stabilized. Other problems were solved as efficiently with MGN as with MGN/FN or MGN/QN. Because MGN/FN can require significantly more computer time per iteration and more computer storage for transient problems, it is less attractive for a general purpose algorithm than MGN/QN.
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.
NASA Astrophysics Data System (ADS)
Stein, David B.; Guy, Robert D.; Thomases, Becca
2016-01-01
The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet it only achieves first-order spatial accuracy near embedded boundaries. In this paper, we introduce a new high-order numerical method which we call the Immersed Boundary Smooth Extension (IBSE) method. The IBSE method achieves high-order accuracy by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations (e.g. Fourier spectral methods). The method preserves much of the flexibility and robustness of the original IB method. In particular, it requires minimal geometric information to describe the boundary and relies only on convolution with regularized delta-functions to communicate information between the computational grid and the boundary. We present a fast algorithm for solving elliptic equations, which forms the basis for simple, high-order implicit-time methods for parabolic PDE and implicit-explicit methods for related nonlinear PDE. We apply the IBSE method to solve the Poisson, heat, Burgers', and Fitzhugh-Nagumo equations, and demonstrate fourth-order pointwise convergence for Dirichlet problems and third-order pointwise convergence for Neumann problems.
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
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.
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 Astrophysics Data System (ADS)
Bendinelli, O.; Parmeggiani, G.; Piccioni, A.; Zavatti, F.
1987-10-01
Modification of the Newton-Gauss linearization method in the Tikhonov regularization sense is described. Its ability to give reliable estimates of a large number of parameters is shown by application to the PSF determination from CCD frames. Extension of the Van Altena and Auer star-image model using a weighted sum of two Gaussians, and explicitly taking its integration on the pixel into account, enables the authors to determine the PSF up to about 10 mag below the central value with an error fit in the range 0.01 - 0.03 mag arcsec-2.
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.
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.
Modeling Electrokinetic Flows by the Smoothed Profile Method
Luo, Xian; Beskok, Ali; Karniadakis, George Em
2010-01-01
We propose an efficient modeling method for electrokinetic flows based on the Smoothed Profile Method (SPM) [1–4] and spectral element discretizations. The new method allows for arbitrary differences in the electrical conductivities between the charged surfaces and the the surrounding electrolyte solution. The electrokinetic forces are included into the flow equations so that the Poisson-Boltzmann and electric charge continuity equations are cast into forms suitable for SPM. The method is validated by benchmark problems of electroosmotic flow in straight channels and electrophoresis of charged cylinders. We also present simulation results of electrophoresis of charged microtubules, and show that the simulated electrophoretic mobility and anisotropy agree with the experimental values. PMID:20352076
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.
NASA Astrophysics Data System (ADS)
Hoppe, R. H. W.; Linsenmann, C.
2012-05-01
The immersed boundary method (IB) is known as a powerful technique for the numerical solution of fluid-structure interaction problems as, for instance, the motion and deformation of viscoelastic bodies immersed in an external flow. It is based on the treatment of the flow equations within an Eulerian framework and of the equations of motion of the immersed bodies with respect to a Lagrangian coordinate system including interaction equations providing the transfer between both frames. The classical IB uses finite differences, but the IBM can be set up within a finite element approach in the spatial variables as well (FE-IB). The discretization in time usually relies on the Backward Euler (BE) method for the semidiscretized flow equations and the Forward Euler (FE) method for the equations of motion of the immersed bodies. The BE/FE FE-IB is subject to a CFL-type condition, whereas the fully implicit BE/BE FE-IB is unconditionally stable. The latter one can be solved numerically by Newton-type methods whose convergence properties are dictated by an appropriate choice of the time step size, in particular, if one is faced with sudden changes in the total energy of the system. In this paper, taking advantage of the well developed affine covariant convergence theory for Newton-type methods, we study a predictor-corrector continuation strategy in time with an adaptive choice of the continuation steplength. The feasibility of the approach and its superiority to BE/FE FE-IB is illustrated by two representative numerical examples.
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.
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.
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.
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…
A Particle-Particle Collision Model for Smoothed Profile Method
NASA Astrophysics Data System (ADS)
Mohaghegh, Fazlolah; Mousel, John; Udaykumar, H. S.
2014-11-01
Smoothed Profile Method (SPM) is a type of continuous forcing approach that adds the particles to the fluid using a forcing. The fluid-structure interaction is through a diffuse interface which avoids sudden transition from solid to fluid. The SPM simulation as a monolithic approach uses an indicator function field in the whole domain based on the distance from each particle's boundary where the possible particle-particle interaction can occur. A soft sphere potential based on the indicator function field has been defined to add an artificial pressure to the flow pressure in the potential overlapping regions. Thus, a repulsion force is obtained to avoid overlapping. Study of two particles which impulsively start moving in an initially uniform flow shows that the particle in the wake of the other one will have less acceleration leading to frequent collisions. Various Reynolds numbers and initial distances have been chosen to test the robustness of the method. Study of Drafting-Kissing Tumbling of two cylindrical particles shows a deviation from the benchmarks due to lack of rotation modeling. The method is shown to be accurate enough for simulating particle-particle collision and can easily be extended for particle-wall modeling and for non-spherical particles.
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].
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
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.
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.
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.
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
Impact of beam smoothing method on direct drive target performance for the NIF
Rothenberg, J.E.; Weber, S.V.
1996-11-01
The impact of smoothing method on the performance of a direct drive target is modeled and examined in terms of its l-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 l-modes and therefore inferior target performance at both peak velocity and ignition. Modeling of the hydrodynamic nonlinearity shows that saturation tends to reduce the difference between target performance for the smoothing methods considered. However, using SSD with more generalized phase modulation results in a smoothed spatial spectrum, and therefore target performance, which is identical to that obtained with the ISI or similar method where random phase plates are present in both methods and identical beam divergence is assumed.
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.
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)
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.
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.
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…
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.
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.
Methods for Smoothing Expectancy Tables Applied to the Prediction of Success in College
ERIC Educational Resources Information Center
Perrin, David W.; Whitney, Douglas R.
1976-01-01
The gains in accuracy resulting from applying any of the smoothing methods appear sufficient to justify the suggestion that all expectancy tables used by colleges for admission, guidance, or planning purposes should be smoothed. These methods on the average, reduce the criterion measure (an index of inaccuracy) by 30 percent. (Author/MV)
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
NASA Astrophysics Data System (ADS)
Chau, C. D.; Sevink, G. J. A.; Fraaije, J. G. E. M.
2011-01-01
Knowledge of protein folding pathways and inherent structures is of utmost importance for our understanding of biological function, including the rational design of drugs and future treatments against protein misfolds. Computational approaches have now reached the stage where they can assess folding properties and provide data that is complementary to or even inaccessible by experimental imaging techniques. Minimal models of proteins, which make possible the simulation of protein folding dynamics by (systematic) coarse graining, have provided understanding in terms of descriptors for folding, folding kinetics, and folded states. Here we focus on the efficiency of equilibration on the coarse-grained level. In particular, we applied a new regularized stochastic quasi-Newton (S-QN) method, developed for accelerated configurational space sampling while maintaining thermodynamic consistency, to analyze the folding pathway and inherent structures of a selected protein, where regularization was introduced to improve stability. The adaptive compound mobility matrix B in S-QN, determined by a factorized secant update, gives rise to an automated scaling of all modes in the protein, in particular an acceleration of protein domain dynamics or principal modes and a slowing down of fast modes or “soft” bond constraints, similar to lincs/shake algorithms, when compared to conventional Langevin dynamics. We used and analyzed a two-step strategy. Owing to the enhanced sampling properties of S-QN and increased barrier crossing at high temperatures (in reduced units), a hierarchy of inherent protein structures is first efficiently determined by applying S-QN for a single initial structure and T=1>Tθ, where Tθ is the collapse temperature. Second, S-QN simulations for several initial structures at very low temperature (T=0.01
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.
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.
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 solution to the Navier-Stokes equations based upon the Newton Kantorovich method
NASA Technical Reports Server (NTRS)
Davis, J. E.; Gabrielsen, R. E.; Mehta, U. B.
1977-01-01
An implicit finite difference scheme based on the Newton-Kantorovich technique was developed for the numerical solution of the nonsteady, incompressible, two-dimensional Navier-Stokes equations in conservation-law form. The algorithm was second-order-time accurate, noniterative with regard to the nonlinear terms in the vorticity transport equation except at the earliest few time steps, and spatially factored. Numerical results were obtained with the technique for a circular cylinder at Reynolds number 15. Results indicate that the technique is in excellent agreement with other numerical techniques for all geometries and Reynolds numbers investigated, and indicates a potential for significant reduction in computation time over current iterative techniques.
Rotating vector methods for smooth torque control of a switched reluctance motor drive
Nagel, N.J.; Lorenz, R.D.
2000-04-01
This paper has two primary contributions to switched reluctance motor (SRM) control: a systematic approach to smooth torque production and a high-performance technique for sensorless motion control. The systematic approach to smooth torque production is based on development of novel rotating spatial vectors methods that can be used to predict the torque produced in an arbitrary SRM. This analysis directly leads to explicit, insightful methods to provide smooth torque control of SRM's. The high-performance technique for sensorless motion control is based on a rotating vector method for high bandwidth, high resolution, position, and velocity estimation suitable for both precise torque and motion control. The sensorless control and smooth torque control methods are both verified experimentally.
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.
A new adaptive exponential smoothing method for non-stationary time series with level shifts
NASA Astrophysics Data System (ADS)
Monfared, Mohammad Ali Saniee; Ghandali, Razieh; Esmaeili, Maryam
2014-07-01
Simple exponential smoothing (SES) methods are the most commonly used methods in forecasting and time series analysis. However, they are generally insensitive to non-stationary structural events such as level shifts, ramp shifts, and spikes or impulses. Similar to that of outliers in stationary time series, these non-stationary events will lead to increased level of errors in the forecasting process. This paper generalizes the SES method into a new adaptive method called revised simple exponential smoothing (RSES), as an alternative method to recognize non-stationary level shifts in the time series. We show that the new method improves the accuracy of the forecasting process. This is done by controlling the number of observations and the smoothing parameter in an adaptive approach, and in accordance with the laws of statistical control limits and the Bayes rule of conditioning. We use a numerical example to show how the new RSES method outperforms its traditional counterpart, SES.
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.
Bladder Smooth Muscle Strip Contractility as a Method to Evaluate Lower Urinary Tract Pharmacology
Kullmann, F. Aura; Daugherty, Stephanie L.; de Groat, William C.; Birder, Lori A.
2015-01-01
We describe an in vitro method to measure bladder smooth muscle contractility, and its use for investigating physiological and pharmacological properties of the smooth muscle as well as changes induced by pathology. This method provides critical information for understanding bladder function while overcoming major methodological difficulties encountered in in vivo experiments, such as surgical and pharmacological manipulations that affect stability and survival of the preparations, the use of human tissue, and/or the use of expensive chemicals. It also provides a way to investigate the properties of each bladder component (i.e. smooth muscle, mucosa, nerves) in healthy and pathological conditions. The urinary bladder is removed from an anesthetized animal, placed in Krebs solution and cut into strips. Strips are placed into a chamber filled with warm Krebs solution. One end is attached to an isometric tension transducer to measure contraction force, the other end is attached to a fixed rod. Tissue is stimulated by directly adding compounds to the bath or by electric field stimulation electrodes that activate nerves, similar to triggering bladder contractions in vivo. We demonstrate the use of this method to evaluate spontaneous smooth muscle contractility during development and after an experimental spinal cord injury, the nature of neurotransmission (transmitters and receptors involved), factors involved in modulation of smooth muscle activity, the role of individual bladder components, and species and organ differences in response to pharmacological agents. Additionally, it could be used for investigating intracellular pathways involved in contraction and/or relaxation of the smooth muscle, drug structure-activity relationships and evaluation of transmitter release. The in vitro smooth muscle contractility method has been used extensively for over 50 years, and has provided data that significantly contributed to our understanding of bladder function as well as to
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.
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.
NASA Astrophysics Data System (ADS)
Lala, P.; Thao, Bui Van
1986-11-01
The first step in the treatment of satellite laser ranging data is its smoothing and rejection of incorrect points. The proposed method uses the comparison of observations with ephemerides and iterative matching of corresponding parameters. The method of solution and a program for a minicomputer are described. Examples of results for satellite Starlette are given.
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. PMID:27409038
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)
A Meshfree Cell-based Smoothed Point Interpolation Method for Solid Mechanics Problems
NASA Astrophysics Data System (ADS)
Zhang, Guiyong; Liu, Gui-Rong
2010-05-01
In the framework of a weakened weak (W2) 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 W2 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 [1]. 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 H1 space, but in a G1 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 H1 space and G1 space can be viewed as a space of functions with weakened weak (W2) requirement on continuity [1-3]. The cell-based smoothed point interpolation method (CS-PIM) is formulated based on the W2 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 W2 formulation of generalized smoothed Galerkin (GS-Galerkin) weak form is used to derive the discretized system equations [2]. 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 softer than the overly-stiff FEM model
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
Tests of smoothing methods for topological study of galaxy redshift surveys
NASA Technical Reports Server (NTRS)
Melott, Adrian L.; Dominik, Kurt G.
1993-01-01
Studying the topology of large-scale structure as a way to better understand initial conditions has become more widespread in recent years. Studying topology of simulations (which have periodic boundary conditions) in redshift space produces results compatible with the real topological characteristics of the simulation. Thus we expect we can extract useful information from redshift surveys. However, with nonperiodic boundary conditions, the use of smoothing must result in the loss of information at survey boundaries. In this paper, we test different methods of smoothing samples with nonperiodic boundary conditions to see which most efficiently preserves the topological features of the real distribution. We find that a smoothing method which (unlike most previous published analysis) sums only over cells inside the survey volume produces the best results among the schemes tested.
Code of Federal Regulations, 2013 CFR
2013-07-01
... 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 60.43... accordance with the quality assurance requirements of section 5.1.1 of 40 CFR part 60, appendix F. Each...
Code of Federal Regulations, 2014 CFR
2014-07-01
... Demonstrating Compliance With 40 CFR 60.43 for the Newton Power Station of Central Illinois Public Service... Appendix G to Part 60—Provisions for an Alternative Method of Demonstrating Compliance With 40 CFR 60.43... of 40 CFR part 60, appendix F. Each SO2 and diluent CEMs shall be subject to cylinder gas audits...
Code of Federal Regulations, 2012 CFR
2012-07-01
... Demonstrating Compliance With 40 CFR 60.43 for the Newton Power Station of Central Illinois Public Service... Appendix G to Part 60—Provisions for an Alternative Method of Demonstrating Compliance With 40 CFR 60.43... accordance with the quality assurance requirements of section 5.1.1 of 40 CFR part 60, appendix F. Each...
Code of Federal Regulations, 2011 CFR
2011-07-01
... Demonstrating Compliance With 40 CFR 60.43 for the Newton Power Station of Central Illinois Public Service... Appendix G to Part 60—Provisions for an Alternative Method of Demonstrating Compliance With 40 CFR 60.43... accordance with the quality assurance requirements of section 5.1.1 of 40 CFR part 60, appendix F. Each...
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... Appendix G to Part 60—Provisions for an Alternative Method of Demonstrating Compliance With 40 CFR 60.43... accordance with the quality assurance requirements of section 5.1.1 of 40 CFR part 60, appendix F. Each...
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
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
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 relativistic smoothed particle hydrodynamics method tested with the shock tube
NASA Astrophysics Data System (ADS)
Mann, Patrick J.
1991-12-01
The smoothed particle hydrodynamics method is applied to an ADM 3 + 1 formulation of the equations for relativistic fluid flow. In particular the one-dimensional shock tube is addressed. Three codes are described. The first is a straightforward extension of classic SPH, while the other two are modifications which allow for time-dependent smoothing lengths. The first of these modifications approximates the internal energy density, while the second approximates the total energy density. Two smoothing forms are tested: an artificial viscosity and the direct method of A.J. Baker [Finite Element Computation Fluid Mechanics (Hemisphere, New York, 1983)]. The results indicate that the classic SPH code with particle-particle based artificial viscosity is reasonably accurate and very consistent. It gives quite sharp edges and flat plateaus, but the velocity plateau is significantly overestimated, and an oscillation can appear in the rarefaction wave. The modified versions with Baker smoothing procedure better results for moderate initial conditions, but begin to show spikes when the initial density jump is large. Generally the results are comparable to simple finite element and finite difference methods.
An Imbricate Finite Element Method (I-FEM) using full, reduced, and smoothed integration
NASA Astrophysics Data System (ADS)
Cazes, Fabien; Meschke, Günther
2013-11-01
A method to design finite elements that imbricate with each other while being assembled, denoted as imbricate finite element method, is proposed to improve the smoothness and the accuracy of the approximation based upon low order elements. Although these imbricate elements rely on triangular meshes, the approximation stems from the shape functions of bilinear quadrilateral elements. These elements satisfy the standard requirements of the finite element method: continuity, delta function property, and partition of unity. The convergence of the proposed approximation is investigated by means of two numerical benchmark problems comparing three different schemes for the numerical integration including a cell-based smoothed FEM based on a quadratic shape of the elements edges. The method is compared to related existing methods.
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.
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
Khandogin, Jana; Gregersen, Brent A; Thiel, Walter; York, Darrin M
2005-05-19
The present paper describes the extension of a recently developed smooth conductor-like screening model for solvation to a d-orbital semiempirical framework (MNDO/d-SCOSMO) with analytic gradients that can be used for geometry optimizations, transition state searches, and molecular dynamics simulations. The methodology is tested on the potential energy surfaces for separating ions and the dissociative phosphoryl transfer mechanism of methyl phosphate. The convergence behavior of the smooth COSMO method with respect to discretization level is examined and the numerical stability of the energy and gradient are compared to that from conventional COSMO calculations. The present method is further tested in applications to energy minimum and transition state geometry optimizations of neutral and charged metaphosphates, phosphates, and phosphoranes that are models for stationary points in transphosphorylation reaction pathways of enzymes and ribozymes. The results indicate that the smooth COSMO method greatly enhances the stability of quantum mechanical geometry optimization and transition state search calculations that would routinely fail with conventional solvation methods. The present MNDO/d-SCOSMO method has considerable computational advantages over hybrid quantum mechanical/molecular mechanical methods with explicit solvation, and represents a potentially useful tool in the arsenal of multi-scale quantum models used to study biochemical reactions. PMID:16852180
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.
A new enzymic method for the isolation and culture of human bladder body smooth muscle cells.
Ma, F -H; Higashira, H; Ukai, Y; Hanai, T; Kiwamoto, H; Park, Y C; Kurita, T
2002-01-01
Cultured cells of the human urinary bladder smooth muscle are useful for investigating bladder function, but methods for culturing them are not well developed. We have now established a novel enzymic technique. The smooth muscle layer was separated out and incubated with 0.2% trypsin for 30 min at 37 degrees C. The samples were then minced and incubated with 0.1% collagenase for 30 min and centrifuged at 900 g. The pellets were resuspended in RPMI-1640 medium containing 10% fetal calf serum (FCS) and centrifuged at 250 g. The smooth muscle cells from the supernatant were cultured in RPMI-1640 containing 10% FCS. The cells grew to confluence after 7-10 days, forming the "hills and valleys" growth pattern characteristic of smooth muscle cells. Immunostaining with anti-alpha-actin, anti-myosin, and anti-caldesmon antibodies demonstrated that 99% of the cells were smooth muscle cells. To investigate the pharmacological properties of the cultured cells, we determined the inhibitory effect of muscarinic receptor antagonists on the binding of [3H]N-methylscopolamine to membranes from cultured cells. The pKi values obtained for six antagonists agreed with the corresponding values for transfected cells expressing the human muscarinic M2 subtype. Furthermore, carbachol produced an increase in the concentration of cytoplasmic free Ca2+ an action that was blocked by 4-diphenylacetoxy-N-methylpiperidine methiodide, an M3 selective antagonist. This result suggests that these cells express functional M3 muscarinic receptors, in addition to M2 receptors. The subcultured cells therefore appear to be unaffected by our new isolation method. PMID:11835427
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.
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.
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
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)
Kang, S.; Suh, Y. K.
2011-02-01
The so-called smoothed profile method, originally suggested by Nakayama and Yamamoto and further improved by Luo et al. in 2005 and 2009, respectively, is an efficient numerical solver for fluid-structure interaction problems, which represents the particles by a certain smoothed profile on a fixed grid and constructs some form of body force added into the momentum (Navier-Stokes) equation by ensuring the rigidity of particles. For numerical simulations, the method first advances the flow and pressure fields by integrating the momentum equation except the body-force (momentum impulse) term in time and next updates them by separately taking temporal integration of the body-force term, thus requiring one more Poisson-equation solver for the extra pressure field due to the rigidity of particles to ensure the divergence-free constraint of the total velocity field. In the present study, we propose a simplified version of the smoothed profile method or the one-stage method, which combines the two stages of velocity update (temporal integration) into one to eliminate the necessity for the additional solver and, thus, significantly save the computational cost. To validate the proposed one-stage method, we perform the so-called direct numerical simulations on the two-dimensional motion of multiple inertialess paramagnetic particles in a nonmagnetic fluid subjected to an external uniform magnetic field and compare their results with the existing benchmark solutions. For the validation, we develop the finite-volume version of the direct simulation method by employing the proposed one-stage method. Comparison shows that the proposed one-stage method is very accurate and efficient in direct simulations of such magnetic particulate flows.
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.
Shot noise limit of the optical 3D measurement methods for smooth surfaces
NASA Astrophysics Data System (ADS)
Pavliček, Pavel; Pech, Miroslav
2016-03-01
The measurement uncertainty of optical 3D measurement methods for smooth surfaces caused by shot noise is investigated. The shot noise is a fundamental property of the quantum nature of light. If all noise sources are eliminated, the shot noise represents the ultimate limit of the measurement uncertainty. The measurement uncertainty is calculated for several simple model methods. The analysis shows that the measurement uncertainty depends on the wavelength of used light, the number of photons used for the measurement, and on a factor that is connected with the geometric arrangement of the measurement setup.
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.
A Fast Variational Method for the Construction of Resolution Adaptive C-Smooth Molecular Surfaces.
Bajaj, Chandrajit L; Xu, Guoliang; Zhang, Qin
2009-05-01
We present a variational approach to smooth molecular (proteins, nucleic acids) surface constructions, starting from atomic coordinates, as available from the protein and nucleic-acid data banks. Molecular dynamics (MD) simulations traditionally used in understanding protein and nucleic-acid folding processes, are based on molecular force fields, and require smooth models of these molecular surfaces. To accelerate MD simulations, a popular methodology is to employ coarse grained molecular models, which represent clusters of atoms with similar physical properties by psuedo- atoms, resulting in coarser resolution molecular surfaces. We consider generation of these mixed-resolution or adaptive molecular surfaces. Our approach starts from deriving a general form second order geometric partial differential equation in the level-set formulation, by minimizing a first order energy functional which additionally includes a regularization term to minimize the occurrence of chemically infeasible molecular surface pockets or tunnel-like artifacts. To achieve even higher computational efficiency, a fast cubic B-spline C(2) interpolation algorithm is also utilized. A narrow band, tri-cubic B-spline level-set method is then used to provide C(2) smooth and resolution adaptive molecular surfaces. PMID:19802355
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; 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.
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.
Is Newton's second law really Newton's?
NASA Astrophysics Data System (ADS)
Pourciau, Bruce
2011-10-01
When we call the equation f = ma "Newton's second law," how much historical truth lies behind us? Many textbooks on introductory physics and classical mechanics claim that the Principia's second law becomes f = ma, once Newton's vocabulary has been translated into more familiar terms. But there is nothing in the Principia's second law about acceleration and nothing about a rate of change. If the Principia's second law does not assert f = ma, what does it assert, and is there some other axiom or some proposition in the Principia that does assert f = ma? Is there any historical truth behind us when we call f = ma "Newton's second law"? This article answers these questions.
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.
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.
NASA Astrophysics Data System (ADS)
Rezaee, Mousa; Shaterian-Alghalandis, Vahid; Banan-Nojavani, Ali
2013-04-01
In this paper, the smooth orthogonal decomposition (SOD) method is developed to the light damped systems in which the inputs are time shifted functions of one or more random processes. An example of such practical cases is the vehicle suspension system in which the random inputs due to the road roughness applied to the rear wheels are the shifted functions of the same random inputs on the front wheels with a time lag depending on the vehicle wheelbase as well as its velocity. The developed SOD method is applied to determine the natural frequencies and mode shapes of a certain vehicle suspension system and the results are compared with the true values obtained by the structural eigenvalue problem. The consistency of the results indicates that the SOD method can be applied with a high degree of accuracy to calculate the modal parameters of vibrating systems in which the system inputs are shifted functions of one or more random processes.
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
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.
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
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.
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)
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
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. PMID:24291693
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.
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.
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.
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
Simulation of surface tension in 2D and 3D with smoothed particle hydrodynamics method
NASA Astrophysics Data System (ADS)
Zhang, Mingyu
2010-09-01
The methods for simulating surface tension with smoothed particle hydrodynamics (SPH) method in two dimensions and three dimensions are developed. In 2D surface tension model, the SPH particle on the boundary in 2D is detected dynamically according to the algorithm developed by Dilts [G.A. Dilts, Moving least-squares particle hydrodynamics II: conservation and boundaries, International Journal for Numerical Methods in Engineering 48 (2000) 1503-1524]. The boundary curve in 2D is reconstructed locally with Lagrangian interpolation polynomial. In 3D surface tension model, the SPH particle on the boundary in 3D is detected dynamically according to the algorithm developed by Haque and Dilts [A. Haque, G.A. Dilts, Three-dimensional boundary detection for particle methods, Journal of Computational Physics 226 (2007) 1710-1730]. The boundary surface in 3D is reconstructed locally with moving least squares (MLS) method. By transforming the coordinate system, it is guaranteed that the interface function is one-valued in the local coordinate system. The normal vector and curvature of the boundary surface are calculated according to the reconstructed boundary surface and then surface tension force can be calculated. Surface tension force acts only on the boundary particle. Density correction is applied to the boundary particle in order to remove the boundary inconsistency. The surface tension models in 2D and 3D have been applied to benchmark tests for surface tension. The ability of the current method applying to the simulation of surface tension in 2D and 3D is proved.
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.
NASA Astrophysics Data System (ADS)
Viallet, M.; Goffrey, T.; Baraffe, I.; Folini, D.; Geroux, C.; Popov, M. V.; Pratt, J.; Walder, R.
2016-02-01
This work is a continuation of our efforts to develop an efficient implicit solver for multidimensional hydrodynamics for the purpose of studying important physical processes in stellar interiors, such as turbulent convection and overshooting. We present an implicit solver that results from the combination of a Jacobian-free Newton-Krylov method and a preconditioning technique tailored to the inviscid, compressible equations of stellar hydrodynamics. We assess the accuracy and performance of the solver for both 2D and 3D problems for Mach numbers down to 10-6. Although our applications concern flows in stellar interiors, the method can be applied to general advection and/or diffusion-dominated flows. The method presented in this paper opens up new avenues in 3D modeling of realistic stellar interiors allowing the study of important problems in stellar structure and evolution.
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)
Barnard, R.; Greening, L. Shaw; Kolb, U.
2008-08-01
NGC253 is a local, starbursting spiral galaxy with strong X-ray emission from hot gas, as well as many point sources. We have conducted a spectral survey of the X-ray population of NGC253 using a deep XMM-Newton observation. NGC253 only accounts for ~20 per cent of the XMM-Newton EPIC field of view, allowing us to identify ~100 X-ray sources that are unlikely to be associated with NGC253. Hence, we were able to make a direct estimate of contamination from, for example, foreground stars and background galaxies. X-ray luminosity functions (XLFs) of galaxy populations are often used to characterize their properties. There are several methods for estimating the luminosities of X-ray sources with few photons. We have obtained spectral fits for the brightest 140 sources in the 2003 XMM-Newton observation of NGC253, and compare the best-fitting luminosities of those 69 non-nuclear sources associated with NGC253 with luminosities derived using other methods. We find the luminosities obtained from these various methods to vary systematically by a factor of up to 3 for the same data; this is largely due to differences in absorption. We therefore conclude that assuming Galactic absorption is probably unwise; rather, one should measure the absorption for the population. A remarkable correlation has been reported between the XLFs of galaxies and their star formation rates. However, the XLFs used in that study were obtained using several different methods. If the sample galaxies were revisited and a single method were applied, then this correlation may become stronger still. In addition, we find that standard estimations of the background contribution to the X-ray sources in the field are insufficient. We find that the background active galactic nuclei (AGN) may be systematically more luminous than previously expected. However, the excess in our measured AGN XLF with respect to the expected XLF may be due to an as yet unrecognized population associated with NGC253.
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.
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.
NASA Astrophysics Data System (ADS)
Bernsen, Erik; Dijkstra, Henk A.; Thies, Jonas; Wubs, Fred W.
2010-10-01
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.
Pérez, Isidro A; Sánchez, M Luisa; García, M Ángeles; Pardo, Nuria
2013-07-01
CO₂ concentrations recorded for two years using a Picarro G1301 analyser at a rural site were studied applying two procedures. Firstly, the smoothing kernel method, which to date has been used with one linear and another circular variable, was used with pairs of circular variables: wind direction, time of day, and time of year, providing that the daily cycle was the prevailing cyclical evolution and that the highest concentrations were justified by the influence of one nearby city source, which was only revealed by directional analysis. Secondly, histograms were obtained, and these revealed most observations to be located between 380 and 410 ppm, and that there was a sharp contrast during the year. Finally, histograms were fitted to 14 distributions, the best known using analytical procedures, and the remainder using numerical procedures. RMSE was used as the goodness of fit indicator to compare and select distributions. Most functions provided similar RMSE values. However, the best fits were obtained using numerical procedures due to their greater flexibility, the triangular distribution being the simplest function of this kind. This distribution allowed us to identify directions and months of noticeable CO₂ input (SSE and April-May, respectively) as well as the daily cycle of the distribution symmetry. Among the functions whose parameters were calculated using an analytical expression, Erlang distributions provided satisfactory fits for monthly analysis, and gamma for the rest. By contrast, the Rayleigh and Weibull distributions gave the worst RMSE values. PMID:23602977
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.
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)
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
ERIC Educational Resources Information Center
Kolen, Michael J.; And Others
Six methods for smoothing double-entry expectancy tables (tables that relate two predictor variables to probability of attaining a selected level of success on a criterion) were compared using data for entering students at 85 colleges and universities. ACT composite scores and self-reported high school grade averages were used to construct…
ERIC Educational Resources Information Center
Perrin, David W.; Whitney, Douglas R.
Six methods for smoothing expectancy tables were compared using data for entering students at 86 colleges and universities. Linear regression analyses were applied to ACT scores and high school grades to obtain predicted first term grade point averages (FGPA's) for students entering each institution in 1969-70. Expectancy tables were constructed…
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. PMID:25535117
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.
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
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.
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.
NASA Astrophysics Data System (ADS)
Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre
2013-11-01
A Continuous Boundary Force (CBF) method was developed for implementing Robin (Navier) boundary condition (BC) that can describe no-slip or slip conditions (slip length from zero to infinity) at the fluid-solid interface. In the CBF method the Robin BC is replaced by a homogeneous Neumann BC and an additional volumetric source term in the governing momentum equation. The formulation is derived based on an approximation of the sharp boundary with a diffuse interface of finite thickness, across which the BC is reformulated by means of a smoothed characteristic function. The CBF method is easy to be implemented in Lagrangian particle-based methods. We first implemented it in smoothed particle hydrodynamics (SPH) to solve numerically the Navier-Stokes equations subject to spatial-independent or dependent Robin BC in two and three dimensions. The numerical accuracy and convergence is examined through comparisons with the corresponding finite difference or finite element solutions. The CBF method is further implemented in smoothed dissipative particle dynamics (SDPD), a mesoscale scheme, for modeling slip flows commonly existent in micro/nano channels and microfluidic devices. The authors acknowledge the funding support by the ASCR Program of the Office of Science, U.S. Department of Energy.
2013-01-01
Background To facilitate new drug development, physiologically-based pharmacokinetic (PBPK) modeling methods receive growing attention as a tool to fully understand and predict complex pharmacokinetic phenomena. As the number of parameters to reproduce physiological functions tend to be large in PBPK models, efficient parameter estimation methods are essential. We have successfully applied a recently developed algorithm to estimate a feasible solution space, called Cluster Newton Method (CNM), to reveal the cause of irinotecan pharmacokinetic alterations in two cancer patient groups. Results After improvements in the original CNM algorithm to maintain parameter diversities, a feasible solution space was successfully estimated for 55 or 56 parameters in the irinotecan PBPK model, within ten iterations, 3000 virtual samples, and in 15 minutes (Intel Xeon E5-1620 3.60GHz × 1 or Intel Core i7-870 2.93GHz × 1). Control parameters or parameter correlations were clarified after the parameter estimation processes. Possible causes in the irinotecan pharmacokinetic alterations were suggested, but they were not conclusive. Conclusions Application of CNM achieved a feasible solution space by solving inverse problems of a system containing ordinary differential equations (ODEs). This method may give us reliable insights into other complicated phenomena, which have a large number of parameters to estimate, under limited information. It is also helpful to design prospective studies for further investigation of phenomena of interest. PMID:24555857
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.
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.
NASA Astrophysics Data System (ADS)
Maulina, Hervin; Santoso, Iman; Subama, Emmistasega; Nurwantoro, Pekik; Abraha, Kamsul; Rusydi, Andrivo
2016-04-01
The extraction of the dielectric constant of nanostructured graphene on SiC substrates from spectroscopy ellipsometry measurement using the Gauss-Newton inversion (GNI) method has been done. This study aims to calculate the dielectric constant and refractive index of graphene by extracting the value of ψ and Δ from the spectroscopy ellipsometry measurement using GNI method and comparing them with previous result which was extracted using Drude-Lorentz (DL) model. The results show that GNI method can be used to calculate the dielectric constant and refractive index of nanostructured graphene on SiC substratesmore faster as compared to DL model. Moreover, the imaginary part of the dielectric constant values and coefficient of extinction drastically increases at 4.5 eV similar to that of extracted using known DL fitting. The increase is known due to the process of interband transition and the interaction between the electrons and electron-hole at M-points in the Brillouin zone of graphene.
"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
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)
Élie-Dit-Cosaque, Xavier J.-G.; Gakwaya, Augustin; Naceur, Hakim
2015-01-01
A smoothed finite element method formulation for the resultant eight-node solid-shell element is presented in this paper for geometrical linear analysis. The smoothing process is successfully performed on the element mid-surface to deal with the membrane and bending effects of the stiffness matrix. The strain smoothing process allows replacing the Cartesian derivatives of shape functions by the product of shape functions with normal vectors to the element mid-surface boundaries. The present formulation remains competitive when compared to the classical finite element formulations since no inverse of the Jacobian matrix is calculated. The three dimensional resultant shell theory allows the element kinematics to be defined only with the displacement degrees of freedom. The assumed natural strain method is used not only to eliminate the transverse shear locking problem encountered in thin-walled structures, but also to reduce trapezoidal effects. The efficiency of the present element is presented and compared with that of standard solid-shell elements through various benchmark problems including some with highly distorted meshes.
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.
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
Users manual for Opt-MS : local methods for simplicial mesh smoothing and untangling.
Freitag, L.
1999-07-20
Creating meshes containing good-quality elements is a challenging, yet critical, problem facing computational scientists today. Several researchers have shown that the size of the mesh, the shape of the elements within that mesh, and their relationship to the physical application of interest can profoundly affect the efficiency and accuracy of many numerical approximation techniques. If the application contains anisotropic physics, the mesh can be improved by considering both local characteristics of the approximate application solution and the geometry of the computational domain. If the application is isotropic, regularly shaped elements in the mesh reduce the discretization error, and the mesh can be improved a priori by considering geometric criteria only. The Opt-MS package provides several local node point smoothing techniques that improve elements in the mesh by adjusting grid point location using geometric, criteria. The package is easy to use; only three subroutine calls are required for the user to begin using the software. The package is also flexible; the user may change the technique, function, or dimension of the problem at any time during the mesh smoothing process. Opt-MS is designed to interface with C and C++ codes, ad examples for both two-and three-dimensional meshes are provided.
Ariyawansa, K.A.; Lau, D.T.M.
1988-01-01
A derivation of collinear scaling algorithms for unconstrained minimization was presented. The local conic approximants to the objective function underlying these algorithms are forced to interpolate the value and gradient of the objective function at the two most recent iterates. The class of algorithms derived therein has a free parameter sequence /l brace/b/sub k//r brace/ and for a fixed choice of /l brace/b/sub k//r brace/ it contains collinear scaling algorithms that may be treated as extensions of quasi-Newton methods with Broyden family of updates. In this paper, under standard assumptions, it is shown that if b/sub k/ is set equal to the gradient of the objective function for all k and if /l brace/chemically bond1 /minus/ theta/sub k/chemically bond/r brace/ (where theta/sub k/ is the parameter in the Broyden family) is uniformly bounded, then these collinear scaling algorithms related to the Broyden family are locally and q-superlinearly convergent. 13 refs.
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.
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.
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. PMID:15036924
Renormalization of Newton's constant
NASA Astrophysics Data System (ADS)
Falls, Kevin
2015-12-01
The problem of obtaining a gauge independent beta function for Newton's constant is addressed. By a specific parametrization of metric fluctuations a gauge independent functional integral is constructed for the semiclassical theory around an arbitrary Einstein space. The effective action then has the property that only physical polarizations of the graviton contribute, while all other modes cancel with the functional measure. We are then able to compute a gauge independent beta function for Newton's constant in d dimensions to one-loop order. No Landau pole is present provided Ng<18 , where Ng=d (d -3 )/2 is the number of polarizations of the graviton. While adding a large number of matter fields can change this picture, the absence of a pole persists for the particle content of the standard model in four spacetime dimensions.
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.
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 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.
NASA Astrophysics Data System (ADS)
Zhao, Xujun; Bordas, Stéphane P. A.; Qu, Jianmin
2013-12-01
Interfacial energy plays an important role in equilibrium morphologies of nanosized microstructures of solid materials due to the high interface-to-volume ratio, and can no longer be neglected as it does in conventional mechanics analysis. When designing nanodevices and to understand the behavior of materials at the nano-scale, this interfacial energy must therefore be taken into account. The present work develops an effective numerical approach by means of a hybrid smoothed extended finite element/level set method to model nanoscale inhomogeneities with interfacial energy effect, in which the finite element mesh can be completely independent of the interface geometry. The Gurtin-Murdoch surface elasticity model is used to account for the interface stress effect and the Wachspress interpolants are used for the first time to construct the shape functions in the smoothed extended finite element method. Selected numerical results are presented to study the accuracy and efficiency of the proposed method as well as the equilibrium shapes of misfit particles in elastic solids. The presented results compare very well with those obtained from theoretical solutions and experimental observations, and the computational efficiency of the method is shown to be superior to that of its most advanced competitor.
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.
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.
NASA Astrophysics Data System (ADS)
Zhang, Zhi-Qian; Liu, G. R.; Khoo, Boo Cheong
2013-02-01
A three-dimensional immersed smoothed finite element method (3D IS-FEM) using four-node tetrahedral element is proposed to solve 3D fluid-structure interaction (FSI) problems. The 3D IS-FEM is able to determine accurately the physical deformation of the nonlinear solids placed within the incompressible viscous fluid governed by Navier-Stokes equations. The method employs the semi-implicit characteristic-based split scheme to solve the fluid flows and smoothed finite element methods to calculate the transient dynamics responses of the nonlinear solids based on explicit time integration. To impose the FSI conditions, a novel, effective and sufficiently general technique via simple linear interpolation is presented based on Lagrangian fictitious fluid meshes coinciding with the moving and deforming solid meshes. In the comparisons to the referenced works including experiments, it is clear that the proposed 3D IS-FEM ensures stability of the scheme with the second order spatial convergence property; and the IS-FEM is fairly independent of a wide range of mesh size ratio.
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
NASA Astrophysics Data System (ADS)
Gatsis, John
An investigation of preconditioning techniques is presented for a Newton-Krylov algorithm that is used for the computation of steady, compressible, high Reynolds number flows about airfoils. A second-order centred-difference method is used to discretize the compressible Navier-Stokes (NS) equations that govern the fluid flow. The one-equation Spalart-Allmaras turbulence model is used. The discretized equations are solved using Newton's method and the generalized minimal residual (GMRES) Krylov subspace method is used to approximately solve the linear system. These preconditioning techniques are first applied to the solution of the discretized steady convection-diffusion equation. Various orderings, iterative block incomplete LU (BILU) preconditioning and multigrid preconditioning are explored. The baseline preconditioner is a BILU factorization of a lower-order discretization of the system matrix in the Newton linearization. An ordering based on the minimum discarded fill (MDF) ordering is developed and compared to the widely popular reverse Cuthill-McKee ordering. An evolutionary algorithm is used to investigate and enhance this ordering. For the convection-diffusion equation, the MDF-based ordering performs well and RCM is superior for the NS equations. Experiments for inviscid, laminar and turbulent cases are presented to show the effectiveness of iterative BILU preconditioning in terms of reducing the number of GMRES iterations, and hence the memory requirements of the Newton-Krylov algorithm. Multigrid preconditioning also reduces the number of GMRES iterations. The framework for the iterative BILU and BILU-smoothed multigrid preconditioning algorithms is presented in detail.
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
2013-01-01
Background There is a rising public and political demand for prospective cancer cluster monitoring. But there is little empirical evidence on the performance of established cluster detection tests under conditions of small and heterogeneous sample sizes and varying spatial scales, such as are the case for most existing population-based cancer registries. Therefore this simulation study aims to evaluate different cluster detection methods, implemented in the open soure environment R, in their ability to identify clusters of lung cancer using real-life data from an epidemiological cancer registry in Germany. Methods Risk surfaces were constructed with two different spatial cluster types, representing a relative risk of RR = 2.0 or of RR = 4.0, in relation to the overall background incidence of lung cancer, separately for men and women. Lung cancer cases were sampled from this risk surface as geocodes using an inhomogeneous Poisson process. The realisations of the cancer cases were analysed within small spatial (census tracts, N = 1983) and within aggregated large spatial scales (communities, N = 78). Subsequently, they were submitted to the cluster detection methods. The test accuracy for cluster location was determined in terms of detection rates (DR), false-positive (FP) rates and positive predictive values. The Bayesian smoothing models were evaluated using ROC curves. Results With moderate risk increase (RR = 2.0), local cluster tests showed better DR (for both spatial aggregation scales > 0.90) and lower FP rates (both < 0.05) than the Bayesian smoothing methods. When the cluster RR was raised four-fold, the local cluster tests showed better DR with lower FPs only for the small spatial scale. At a large spatial scale, the Bayesian smoothing methods, especially those implementing a spatial neighbourhood, showed a substantially lower FP rate than the cluster tests. However, the risk increases at this scale were mostly diluted by data
NASA Astrophysics Data System (ADS)
Wang, Li; Sun, Xiaogang; Xing, Jian
2012-12-01
An inversion technique which combines the pattern search algorithm with the Tikhonov smoothing functional for retrieval of particle size distribution (PSD) by light extinction method is proposed. In the unparameterized shape-independent model, we first transform the PSD inversion problem into an optimization problem, with the Tikhonov smoothing functional employed to model the objective function. The optimization problem is then solved by the pattern search algorithm. To ensure good convergence rate and accuracy of the whole retrieval, a competitive strategy for determining the initial point of the pattern search algorithm is also designed. The accuracy and limitations of the proposed technique are tested by the inversion results of synthetic and real standard polystyrene particles immersed in water. In addition, the issues about the objective function and computation time are further discussed. Both simulation and experimental results show that the technique can be successfully applied to retrieve the PSD with high reliability and stability in the presence of random noise. Compared with the Phillips-Twomey method and genetic algorithm, the proposed technique has certain advantages in terms of reaching a more accurate and steady optimal solution with less computational effort, thus making this technique more suitable for quick and accurate measurement of PSD.
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)
Aghamousa, Amir; Shafieloo, Arman
2015-05-01
The observable time delays between multiple images of strong lensing systems with time variable sources can provide us with some valuable information for probing the expansion history of the universe. Estimating these time delays can be very challenging due to complexities in the observed data caused by seasonal gaps, various noises, and systematics such as unknown microlensing effects. In this paper, we introduce a novel approach for estimating the time delays for strong lensing systems, implementing various statistical methods of data analysis including the smoothing and cross-correlation methods. The method we introduce in this paper has recently been used in the TDC0 and TDC1 Strong Lens Time Delay Challenges and has shown its power in providing reliable and precise estimates of time delays dealing with data with different complexities.
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
Wong Unhong; Wong Honcheng; Tang Zesheng
2010-05-21
The smoothed particle hydrodynamics (SPH), which is a class of meshfree particle methods (MPMs), has a wide range of applications from micro-scale to macro-scale as well as from discrete systems to continuum systems. Graphics hardware, originally designed for computer graphics, now provide unprecedented computational power for scientific computation. Particle system needs a huge amount of computations in physical simulation. In this paper, an efficient parallel implementation of a SPH method on graphics hardware using the Compute Unified Device Architecture is developed for fluid simulation. Comparing to the corresponding CPU implementation, our experimental results show that the new approach allows significant speedups of fluid simulation through handling huge amount of computations in parallel on graphics hardware.
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.
Egorov, A A; Sevast'yanov, L A; Sevast'yanov, A L
2014-02-28
We consider the application of the method of adiabatic waveguide modes for calculating the propagation of electromagnetic radiation in three-dimensional (3D) irregular integrated optical waveguides. The method of adiabatic modes takes into account a three-dimensional distribution of quasi-waveguide modes and explicit ('inclined') tangential boundary conditions. The possibilities of the method are demonstrated on the example of numerical research of two major elements of integrated optics: a waveguide of 'horn' type and a thin-film generalised waveguide Luneburg lens by the methods of adiabatic modes and comparative waveguides. (integral optical waveguides)
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)
Telecommunications Handbook: Connecting to Newton.
ERIC Educational Resources Information Center
Baker, Christopher; And Others
This handbook was written by the Argonne National Laboratory for use with their electronic bulletin board system (BBS) called Newton. Newton is an educational BBS for use by teachers, students, and parents. Topics range from discussions of science fair topics to online question and answer sessions with scientists. Future capabilities will include…
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.
Pan, Wenxiao; Bao, Jie; Tartakovsky, Alexandre M.
2014-02-15
Robin boundary condition for the Navier-Stokes equations is used to model slip conditions at the fluid-solid boundaries. A novel Continuous Boundary Force (CBF) method is proposed for solving the Navier-Stokes equations subject to Robin boundary condition. In the CBF method, the Robin boundary condition at boundary is replaced by the homogeneous Neumann boundary condition at the boundary and a volumetric force term added to the momentum conservation equation. Smoothed Particle Hydrodynamics (SPH) method is used to solve the resulting Navier-Stokes equations. We present solutions for two-dimensional and three-dimensional flows in domains bounded by flat and curved boundaries subject to various forms of the Robin boundary condition. The numerical accuracy and convergence are examined through comparison of the SPH-CBF results with the solutions of finite difference or finite element method. Taken the no-slip boundary condition as a special case of slip boundary condition, we demonstrate that the SPH-CBF method describes accurately both no-slip and slip conditions.
A limited-memory, quasi-Newton preconditioner for nonnegatively constrained image reconstruction.
Bardsley, Johnathan M
2004-05-01
Image reconstruction gives rise to some challenging large-scale constrained optimization problems. We consider a convex minimization problem with nonnegativity constraints that arises in astronomical imaging. To solve this problem, we use an efficient hybrid gradient projection-reduced Newton (active-set) method. By "reduced Newton," we mean that we take Newton steps only in the inactive variables. Owing to the large size of our problem, we compute approximate reduced Newton steps by using the conjugate gradient (CG) iteration. We introduce a limited-memory, quasi-Newton preconditioner that speeds up CG convergence. A numerical comparison is presented that demonstrates the effectiveness of this preconditioner. PMID:15139424
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…
Well-tempered metadynamics: a smoothly converging and tunable free-energy method.
Barducci, Alessandro; Bussi, Giovanni; Parrinello, Michele
2008-01-18
We present a method for determining the free-energy dependence on a selected number of collective variables using an adaptive bias. The formalism provides a unified description which has metadynamics and canonical sampling as limiting cases. Convergence and errors can be rigorously and easily controlled. The parameters of the simulation can be tuned so as to focus the computational effort only on the physically relevant regions of the order parameter space. The algorithm is tested on the reconstruction of an alanine dipeptide free-energy landscape. PMID:18232845
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.
A method of smooth bivariate interpolation for data given on a generalized curvilinear grid
NASA Technical Reports Server (NTRS)
Zingg, David W.; Yarrow, Maurice
1992-01-01
A method of locally bicubic interpolation is presented for data given at the nodes of a two-dimensional generalized curvilinear grid. The physical domain is transformed to a computational domain in which the grid is uniform and rectangular by a generalized curvilinear coordinate transformation. The metrics of the transformation are obtained by finite differences in the computational domain. Metric derivatives are determined by repeated application of the chain rule for partial differentiation. Given the metrics and the metric derivatives, the partial derivatives required to determine a locally bicubic interpolant can be estimated at each data point using finite differences in the computational domain. A bilinear transformation is used to analytically transform the individual quadrilateral cells in the physical domain into unit squares, thus allowing the use of simple formulas for bicubic interpolation.
Modern methods for calculating ground-wave field strength over a smooth spherical Earth
NASA Astrophysics Data System (ADS)
Eckert, R. P.
1986-02-01
The report makes available the computer program that produces the proposed new FCC ground-wave propagation prediction curves for the new band of standard broadcast frequencies between 1605 and 1705 kHz. The curves are included in recommendations to the U.S. Department of State in preparation for an International Telecommunication Union Radio Conference. The history of the FCC curves is traced from the early 1930's, when the Federal Radio Commission and later the FFC faced an intensifying need for technical information concerning interference distances. A family of curves satisfactorily meeting this need was published in 1940. The FCC reexamined the matter recently in connection with the planned expansion of the AM broadcast band, and the resulting new curves are a precise representation of the mathematical theory. Mathematical background is furnished so that the computer program can be critically evaluated. This will be particularly valuable to persons implementing the program on other computers or adapting it for special applications. Technical references are identified for each of the formulas used by the program, and the history of the development of mathematical methods is outlined.
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.
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.
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)
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.
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
[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." PMID:12342767
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
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
Spronck, Bart; Megens, Remco T A; Reesink, Koen D; Delhaas, Tammo
2016-04-01
When studying in vivo arterial mechanical behaviour using constitutive models, smooth muscle cells (SMCs) should be considered, while they play an important role in regulating arterial vessel tone. Current constitutive models assume a strictly circumferential SMC orientation, without any dispersion. We hypothesised that SMC orientation would show considerable dispersion in three dimensions and that helical dispersion would be greater than transversal dispersion. To test these hypotheses, we developed a method to quantify the 3D orientation of arterial SMCs. Fluorescently labelled SMC nuclei of left and right carotid arteries of ten mice were imaged using two-photon laser scanning microscopy. Arteries were imaged at a range of luminal pressures. 3D image processing was used to identify individual nuclei and their orientations. SMCs showed to be arranged in two distinct layers. Orientations were quantified by fitting a Bingham distribution to the observed orientations. As hypothesised, orientation dispersion was much larger helically than transversally. With increasing luminal pressure, transversal dispersion decreased significantly, whereas helical dispersion remained unaltered. Additionally, SMC orientations showed a statistically significant ([Formula: see text]) mean right-handed helix angle in both left and right arteries and in both layers, which is a relevant finding from a developmental biology perspective. In conclusion, vascular SMC orientation (1) can be quantified in 3D; (2) shows considerable dispersion, predominantly in the helical direction; and (3) has a distinct right-handed helical component in both left and right carotid arteries. The obtained quantitative distribution data are instrumental for constitutive modelling of the artery wall and illustrate the merit of our method. PMID:26174758
Smooth Programs and Languages.
ERIC Educational Resources Information Center
Foulk, Clinton R.; Juelich, Otto C.
A smooth program is defined to be one which is "go to"-free in the sense that it can be represented by a flowchart consisting only of concatenation, alternation, and interation elements. Three methods of eliminating the "go to" statement from a program have been proposed: (1) the introduction of additional Boolean variables or the equivalent…
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.
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.
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.
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…
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)
Exploration Zone in Newton Crater
NASA Astrophysics Data System (ADS)
Laine, P. E.
2015-10-01
Newton is a large crater (300 km) located in Terra Sirenum. This region is heavily cratered, preserves crustal magnetism, and has ground ice present. Within this EZ there are many potential science and resource ROIs, e.g. indicatives of past water.
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…
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)
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. PMID:24686919
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
Closed Newton-Cotes Trigonometrically-Fitted Formulae for Long-Time Integration of Orbital Problems
NASA Astrophysics Data System (ADS)
Simos, T. E.
2006-10-01
The connection between closed Newton-Cotes, trigonometrically-fitted differential methods and symplectic integrators is investigated in this paper. It is known from the literature that several one step symplectic integrators have been obtained based on symplectic geometry. However, the investigation of multistep symplectic integrators is very poor. Zhu et al.(1996) presented the well known open Newton-Cotes differential methods as multilayer symplectic integrators. Also, Chiou & Wu (1997) investigated the construction of multistep symplectic integrators based on the open Newton-Cotes integration methods. In this paper we investigate the closed Newton-Cotes formulae and we write them as symplectic multilayer structures. After this we construct trigonometrically-fitted symplectic methods which are based on the closed Newton-Cotes formulae. We apply the symplectic schemes in order to solve Hamilton's equations of motion which are linear in position and momentum. We observe that the Hamiltonian energy of the system remains almost constant as integration procceeds.
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.
NASA Astrophysics Data System (ADS)
Budak, V. P.; Korkin, S. V.
2006-12-01
The paper deals with the vectorial radiative transfer equation (VRTE) problem for a homogeneous strongly anisotropic scattering slab illuminated by a plain unidirectional source of light with an arbitrary angle of irradiance and polarization state. The problem is a theoretical base for the polarized satellite remote sensing (POLDER, PARASOL and others). The VRTE boundary problem decomposition allows reducing to the nonreflecting bottom with subsequent including its polarization properties. We give the complete analysis for the solution smooth non-small angle part for the vectorial small angle modification of the spherical harmonics method (VMSH) built upon the smoothness of the spatial spectrum of the light field distribution vector-function caused by mathematical singularities of the top-boundary condition for the VRTE boundary problem and the anisotropy of many natural scattering media (clouds, ocean). The VMSH itself is described as well.
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.
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
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.
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.
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
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.
Effectiveness of Analytic Smoothing in Equipercentile Equating.
ERIC Educational Resources Information Center
Kolen, Michael J.
1984-01-01
An analytic procedure for smoothing in equipercentile equating using cubic smoothing splines is described and illustrated. The effectiveness of the procedure is judged by comparing the results from smoothed equipercentile equating with those from other equating methods using multiple cross-validations for a variety of sample sizes. (Author/JKS)
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…
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)
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.
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
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…
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.
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).
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.
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.
Walker, H.F.
1990-01-01
During the 1986--1989 project period, two major areas of research developed into which most of the work fell: matrix-free'' methods for solving linear systems, by which we mean iterative methods that require only the action of the coefficient matrix on vectors and not the coefficient matrix itself, and Newton-like methods for underdetermined nonlinear systems. In the 1990 project period of the renewal grant, a third major area of research developed: inexact Newton and Newton iterative methods and their applications to large-scale nonlinear systems, especially those arising in discretized problems. An inexact Newton method is any method in which each step reduces the norm of the local linear model of the function of interest. A Newton iterative method is any implementation of Newton's method in which the linear systems that characterize Newton steps (the Newton equations'') are solved only approximately using an iterative linear solver. Newton iterative methods are properly considered special cases of inexact Newton methods. We describe the work in these areas and in other areas in this paper.
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)
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.
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.
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)
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.
NASA Astrophysics Data System (ADS)
Schofield, Robert E.
1981-03-01
Newton's achievements, both in the Principia and the Opticks, were firmly rooted in an atomistic theory of matter, resembling aspects of modern nuclear physics in its emphasis on fundamental particles held in differing arrays by short and long-range forces. Marred by premature sophistication, its parameters of particle size and shape and interparticulate forces could not be quantified. Although it inspired many scientists of the eighteenth century and was further developed into a qualitative theory which intrigued scientists into the twentieth century, Newtonian unitary corpuscular (or atomistic) matter theory was replaced for most investigators by a variety of substances for which the particulate nature was of less concern than the character of their gross behavior. It was on this basis that Dalton developed his new (chemical) atomism, reifying the multiplicity of substances with separate atoms for each, distinguished by operational differences in their chemical atomic weights.
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.
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.
Wu, Hulin; Xue, Hongqi; Kumar, Arun
2012-06-01
Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches. PMID:22376200
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.
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.
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.
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.
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…
Recursive inverse kinematics for robot arms via Kalman filtering and Bryson-Frazier smoothing
NASA Technical Reports Server (NTRS)
Rodriguez, G.; Scheid, R. E., Jr.
1987-01-01
This paper applies linear filtering and smoothing theory to solve recursively the inverse kinematics problem for serial multilink manipulators. This problem is to find a set of joint angles that achieve a prescribed tip position and/or orientation. A widely applicable numerical search solution is presented. The approach finds the minimum of a generalized distance between the desired and the actual manipulator tip position and/or orientation. Both a first-order steepest-descent gradient search and a second-order Newton-Raphson search are developed. The optimal relaxation factor required for the steepest descent method is computed recursively using an outward/inward procedure similar to those used typically for recursive inverse dynamics calculations. The second-order search requires evaluation of a gradient and an approximate Hessian. A Gauss-Markov approach is used to approximate the Hessian matrix in terms of products of first-order derivatives. This matrix is inverted recursively using a two-stage process of inward Kalman filtering followed by outward smoothing. This two-stage process is analogous to that recently developed by the author to solve by means of spatial filtering and smoothing the forward dynamics problem for serial manipulators.
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.
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)
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...
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.
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.
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)
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.
Against Chandrasekhar's interpretation of Newton's treatment of the precession of the equinoxes.
NASA Astrophysics Data System (ADS)
Dobson, G. J.
1999-02-01
The author examines the interpretation of Newton's theory of the precession of the equinoxes presented by Subrahmanyan Chandrasekhar in his book "Newton's Principia for the common reader" (Clarendon Press, 1995; see abstr. 63.003.040). Based on his own analysis of the respective chapters of the "Principia" published in a recent paper (see abstr. 70.004.121), the author ventures to show that Chandrasekhar has seriously misunderstood Newton's procedure. Specifically, the author expounds his own interpretation of the meaning of Lemmas 1, 2, and 3, and of Proposition 39 of the "Principia", and compares this meaning with Chandrasekhar's interpretation. He argues that Chandrasekhar's interpretation of Proposition 39 is based on modern concepts of rigid body dynamics and does not provide a satisfactory representation of Newton's method.
Genet, Martin; Chuan Lee, Lik; Ge, Liang; Acevedo-Bolton, Gabriel; Jeung, Nick; Martin, Alastair; Cambronero, Neil; Boyle, Andrew; Yeghiazarians, Yerem; Kozerke, Sebastian; Guccione, Julius M
2015-08-01
Heart failure is increasing at an alarming rate, making it a worldwide epidemic. As the population ages and life expectancy increases, this trend is not likely to change. Myocardial infarction (MI)-induced adverse left ventricular (LV) remodeling is responsible for nearly 70% of heart failure cases. The adverse remodeling process involves an extension of the border zone (BZ) adjacent to an MI, which is normally perfused but shows myofiber contractile dysfunction. To improve patient-specific modeling of cardiac mechanics, we sought to create a finite element model of the human LV with BZ and MI morphologies integrated directly from delayed-enhancement magnetic resonance (DE-MR) images. Instead of separating the LV into discrete regions (e.g., the MI, BZ, and remote regions) with each having a homogeneous myocardial material property, we assumed a functional relation between the DE-MR image pixel intensity and myocardial stiffness and contractility--we considered a linear variation of material properties as a function of DE-MR image pixel intensity, which is known to improve the accuracy of the model's response. The finite element model was then calibrated using measurements obtained from the same patient--namely, 3D strain measurements-using complementary spatial modulation of magnetization magnetic resonance (CSPAMM-MR) images. This led to an average circumferential strain error of 8.9% across all American Heart Association (AHA) segments. We demonstrate the utility of our method for quantifying smooth regional variations in myocardial contractility using cardiac DE-MR and CSPAMM-MR images acquired from a 78-yr-old woman who experienced an MI approximately 1 yr prior. We found a remote myocardial diastolic stiffness of C(0) = 0.102 kPa, and a remote myocardial contractility of T(max) = 146.9 kPa, which are both in the range of previously published normal human values. Moreover, we found a normalized pixel intensity range of 30% for the BZ, which is consistent with
Walker, H.F.
1990-12-31
During the 1986--1989 project period, two major areas of research developed into which most of the work fell: ``matrix-free`` methods for solving linear systems, by which we mean iterative methods that require only the action of the coefficient matrix on vectors and not the coefficient matrix itself, and Newton-like methods for underdetermined nonlinear systems. In the 1990 project period of the renewal grant, a third major area of research developed: inexact Newton and Newton iterative methods and their applications to large-scale nonlinear systems, especially those arising in discretized problems. An inexact Newton method is any method in which each step reduces the norm of the local linear model of the function of interest. A Newton iterative method is any implementation of Newton`s method in which the linear systems that characterize Newton steps (the ``Newton equations``) are solved only approximately using an iterative linear solver. Newton iterative methods are properly considered special cases of inexact Newton methods. We describe the work in these areas and in other areas in this paper.
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.
Estimations of the smoothing operator response characteristics
NASA Technical Reports Server (NTRS)
Yatskiv, Y. S.
1974-01-01
The mean response characteristic of the graphical smoothing method is discussed. The method is illustrated by analysis of latitude observations at Washington from 1915.9 to 1941.0. Spectral density, frequency distribution, and distribution functions are also discussed.
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.
Liao, Xiaolin; Xu, Genbo; Chen, Song-Lin
2014-01-01
Half-smooth tongue sole (Cynoglossus semilaevis) is one of the most important flatfish species for aquaculture in China. To produce a monosex population, we attempted to develop a marker-assisted sex control technique in this sexually size dimorphic fish. In this study, we identified a co-dominant sex-linked marker (i.e., CyseSLM) by screening genomic microsatellites and further developed a novel molecular method for sex identification in the tongue sole. CyseSLM has a sequence similarity of 73%-75% with stickleback, medaka, Fugu and Tetraodon. At this locus, two alleles (i.e., A244 and A234) were amplified from 119 tongue sole individuals with primer pairs CyseSLM-F1 and CyseSLM-R. Allele A244 was present in all individuals, while allele A234 (female-associated allele, FAA) was mostly present in females with exceptions in four male individuals. Compared with the sequence of A244, A234 has a 10-bp deletion and 28 SNPs. A specific primer (CyseSLM-F2) was then designed based on the A234 sequence, which amplified a 204 bp fragment in all females and four males with primer CyseSLM-R. A time-efficient multiplex PCR program was developed using primers CyseSLM-F2, CyseSLM-R and the newly designed primer CyseSLM-F3. The multiplex PCR products with co-dominant pattern could be detected by agarose gel electrophoresis, which accurately identified the genetic sex of the tongue sole. Therefore, we have developed a rapid and reliable method for sex identification in tongue sole with a newly identified sex-linked microsatellite marker. PMID:25054319
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?"
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
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.
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
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 image for
Stochastic quasi-Newton molecular simulations
NASA Astrophysics Data System (ADS)
Chau, C. D.; Sevink, G. J. A.; Fraaije, J. G. E. M.
2010-08-01
We report a new and efficient factorized algorithm for the determination of the adaptive compound mobility matrix B in a stochastic quasi-Newton method (S-QN) that does not require additional potential evaluations. For one-dimensional and two-dimensional test systems, we previously showed that S-QN gives rise to efficient configurational space sampling with good thermodynamic consistency [C. D. Chau, G. J. A. Sevink, and J. G. E. M. Fraaije, J. Chem. Phys. 128, 244110 (2008)10.1063/1.2943313]. Potential applications of S-QN are quite ambitious, and include structure optimization, analysis of correlations and automated extraction of cooperative modes. However, the potential can only be fully exploited if the computational and memory requirements of the original algorithm are significantly reduced. In this paper, we consider a factorized mobility matrix B=JJT and focus on the nontrivial fundamentals of an efficient algorithm for updating the noise multiplier J . The new algorithm requires O(n2) multiplications per time step instead of the O(n3) multiplications in the original scheme due to Choleski decomposition. In a recursive form, the update scheme circumvents matrix storage and enables limited-memory implementation, in the spirit of the well-known limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method, allowing for a further reduction of the computational effort to O(n) . We analyze in detail the performance of the factorized (FSU) and limited-memory (L-FSU) algorithms in terms of convergence and (multiscale) sampling, for an elementary but relevant system that involves multiple time and length scales. Finally, we use this analysis to formulate conditions for the simulation of the complex high-dimensional potential energy landscapes of interest.
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)
NASA Astrophysics Data System (ADS)
von Clarmann, T.
2014-09-01
The difference due to the content of a priori information between a constrained retrieval and the true atmospheric state is usually represented by a diagnostic quantity called smoothing error. In this paper it is shown that, regardless of the usefulness of the smoothing error as a diagnostic tool in its own right, the concept of the smoothing error as a component of the retrieval error budget is questionable because it is not compliant with Gaussian error propagation. The reason for this is that the smoothing error does not represent the expected deviation of the retrieval from the true state but the expected deviation of the retrieval from the atmospheric state sampled on an arbitrary grid, which is itself a smoothed representation of the true state; in other words, to characterize the full loss of information with respect to the true atmosphere, the effect of the representation of the atmospheric state on a finite grid also needs to be considered. The idea of a sufficiently fine sampling of this reference atmospheric state is problematic because atmospheric variability occurs on all scales, implying that there is no limit beyond which the sampling is fine enough. Even the idealization of infinitesimally fine sampling of the reference state does not help, because the smoothing error is applied to quantities which are only defined in a statistical sense, which implies that a finite volume of sufficient spatial extent is needed to meaningfully discuss temperature or concentration. Smoothing differences, however, which play a role when measurements are compared, are still a useful quantity if the covariance matrix involved has been evaluated on the comparison grid rather than resulting from interpolation and if the averaging kernel matrices have been evaluated on a grid fine enough to capture all atmospheric variations that the instruments are sensitive to. This is, under the assumptions stated, because the undefined component of the smoothing error, which is the
Spline-Based Smoothing of Airfoil Curvatures
NASA Technical Reports Server (NTRS)
Li, W.; Krist, S.
2008-01-01
Constrained fitting for airfoil curvature smoothing (CFACS) is a splinebased method of interpolating airfoil surface coordinates (and, concomitantly, airfoil thicknesses) between specified discrete design points so as to obtain smoothing of surface-curvature profiles in addition to basic smoothing of surfaces. CFACS was developed in recognition of the fact that the performance of a transonic airfoil is directly related to both the curvature profile and the smoothness of the airfoil surface. Older methods of interpolation of airfoil surfaces involve various compromises between smoothing of surfaces and exact fitting of surfaces to specified discrete design points. While some of the older methods take curvature profiles into account, they nevertheless sometimes yield unfavorable results, including curvature oscillations near end points and substantial deviations from desired leading-edge shapes. In CFACS as in most of the older methods, one seeks a compromise between smoothing and exact fitting. Unlike in the older methods, the airfoil surface is modified as little as possible from its original specified form and, instead, is smoothed in such a way that the curvature profile becomes a smooth fit of the curvature profile of the original airfoil specification. CFACS involves a combination of rigorous mathematical modeling and knowledge-based heuristics. Rigorous mathematical formulation provides assurance of removal of undesirable curvature oscillations with minimum modification of the airfoil geometry. Knowledge-based heuristics bridge the gap between theory and designers best practices. In CFACS, one of the measures of the deviation of an airfoil surface from smoothness is the sum of squares of the jumps in the third derivatives of a cubicspline interpolation of the airfoil data. This measure is incorporated into a formulation for minimizing an overall deviation- from-smoothness measure of the airfoil data within a specified fitting error tolerance. CFACS has been
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.
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.
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…
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 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…
A Class Inquiry into Newton's Cooling Curve
ERIC Educational Resources Information Center
Bartholow, Martin
2007-01-01
Newton's cooling curve was chosen for the four-part laboratory inquiry into conditions affecting temperature change. The relationship between time and temperature is not foreseen by the average high school student before the first session. However, during several activities students examine the classic relationship, T = A exp[superscript -Ct] + B…
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…
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)
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…
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)
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)
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…
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, 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...
Newton flow of the Riemann zeta function: separatrices control the appearance of zeros
NASA Astrophysics Data System (ADS)
Neuberger, J. W.; Feiler, C.; Maier, H.; Schleich, W. P.
2014-10-01
A great many phenomena in physics can be traced back to the zeros of a function or a functional. Eigenvalue or variational problems prevalent in classical as well as quantum mechanics are examples illustrating this statement. Continuous descent methods taken with respect to the proper metric are efficient ways to attack such problems. In particular, the continuous Newton method brings out the lines of constant phase of a complex-valued function. Although the patterns created by the Newton flow are reminiscent of the field lines of electrostatics and magnetostatics they cannot be realized in this way since in general they are not curl-free. We apply the continuous Newton method to the Riemann zeta function and discuss the emerging patterns emphasizing especially the structuring of the non-trivial zeros by the separatrices. This approach might open a new road toward the Riemann hypothesis.
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.
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
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.
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.
Newtons Principia Mathematica Philosophia und Plancks Elementarkonstanten
NASA Astrophysics Data System (ADS)
Rompe, R.; Treder, H.-J.
Die Newtonschen Prinzipien, zusammen mit den Planckschen Elementarkonstanten, erweisen sich als gesichertes Fundament der Physik und der exakten Wissenschaften aller Richtungen.Der Begriffsfundus der Physik ist ausreichend für alle physikalischen aber auch weiterreichenden Probleme anderer Naturwissenschaften und Technik. Es zeigt sich, daß die klassische Physik von vornherein so angelegt wurde, daß sie über die Physik der makroskopischen Körper weit hinaus-greifen kann.Translated AbstractNewton's Principia Mathematica Philosophia and Planck's Elementary ConstantsTogether with Planck's elementary constants Newton's principles prove a guaranteed basis of physics and exact sciences of all directions.The conceptions in physics are competent at all physical problems as well as technology too. Classical physics was founded in such a way to reach far beyond the physics of macroscopic bodies.
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. PMID:10367975
The Geometry of Newton's and Einstein's Theories
NASA Astrophysics Data System (ADS)
Hall, Graham S.
The aim of this paper is to present a simple, brief, mathematical discussion of the interplay between geometry and physics in the theories of Newton and Einstein. The reader will be assumed to have some familiarity with classical Newtonian theory, the ideas of special and general relativity theory (and differential geometry), and the axiomatic formulation of Euclidean geometry. An attempt will be made to describe the relationship between Galileo's law of inertia (Newton's first law) and Euclid's geometry, which is based on the idea of Newtonian absolute time. Newton's second law and classical gravitation theory will then be introduced through the elegant idea of Cartan and his space-time connection and space metric. This space metric will then be used to introduce Minkowski's metric in special relativity and its subsequent generalization, by Einstein, to incorporate relativistic gravitational theory. The role of the principles of equivalence and covariance will also be discussed. Finally, a brief discussion of cosmology will be given. Stress will be laid on the (geometrical) concepts involved rather than the details of the mathematics, in so far as this is possible.
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.
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).
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.
XMM-Newton closes in on space's exotic matter
NASA Astrophysics Data System (ADS)
2002-11-01
search. The way they got this measurement is a first in astronomical observations and it is considered a huge achievement. The method consists of determining the compactness of the neutron star in an indirect way. The gravitational pull of a neutron star is immense - thousands of million times stronger than the Earth’s. This makes the light particles emitted by the neutron star lose energy. This energy loss is called a gravitational 'red shift'. The measurement of this red shift by XMM-Newton indicated the strength of the gravitational pull, and revealed the star’s compactness. "This is a highly precise measurement that we could not have made without both the high sensitivity of XMM-Newton and its ability to distinguish details," says Fred Jansen, ESA's XMM-Newton Project Scientist. According to the main author of the discovery, Jean Cottam of NASA’s Goddard Space Flight Center, “attempts to measure the gravitational red shift were made right after Einstein published the General Theory of Relativity, but no one had ever been able to measure the effect in a neutron star, where it was supposed to be huge. This has now been confirmed." Note to editors The result was obtained by observations of the neutron star EXO 0748-676. XMM-Newton detected the light in the form of X-rays. In particular, thanks to analysis of this X-ray radiation, the astronomers were able to identify some chemical elements, namely iron, present in the material surrounding the neutron star. They then compared the distorted signal emitted by the iron atoms in the neutron star with the one produced by iron atoms in the laboratory. In this way, they could measure the actual degree of distortion due to the gravity of EXO 0748-676. The result is published in the 7 November 2002 issue of Nature. The lead author is Jean Cottam, of NASA’s Goddard Space Flight Center (Greenbelt, United States). Other authors are Mariano Mendez, of the National Institute for Space Research, SRON (The Netherlands); and
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.
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…
... 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 ...
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.
Docherty, Paul D; Schranz, Christoph; Chase, J Geoffrey; Chiew, Yeong Shiong; Möller, Knut
2014-05-01
Accurate model parameter identification relies on accurate forward model simulations to guide convergence. However, some forward simulation methodologies lack the precision required to properly define the local objective surface and can cause failed parameter identification. The role of objective surface smoothness in identification of a pulmonary mechanics model was assessed using forward simulation from a novel error-stepping method and a proprietary Runge-Kutta method. The objective surfaces were compared via the identified parameter discrepancy generated in a Monte Carlo simulation and the local smoothness of the objective surfaces they generate. The error-stepping method generated significantly smoother error surfaces in each of the cases tested (p<0.0001) and more accurate model parameter estimates than the Runge-Kutta method in three of the four cases tested (p<0.0001) despite a 75% reduction in computational cost. Of note, parameter discrepancy in most cases was limited to a particular oblique plane, indicating a non-intuitive multi-parameter trade-off was occurring. The error-stepping method consistently improved or equalled the outcomes of the Runge-Kutta time-integration method for forward simulations of the pulmonary mechanics model. This study indicates that accurate parameter identification relies on accurate definition of the local objective function, and that parameter trade-off can occur on oblique planes resulting prematurely halted parameter convergence. PMID:23910223
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.
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
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
Detecting smoothness in noisy time series
Cawley, R.; Hsu, G.; Salvino, L.W.
1996-06-01
We describe the role of chaotic noise reduction in detecting an underlying smoothness in a dataset. We have described elsewhere a general method for assessing the presence of determinism in a time series, which is to test against the class of datasets producing smoothness (i.e., the null hypothesis is determinism). In order to reduce the likelihood of a false call, we recommend this kind of analysis be applied first to a time series whose deterministic origin is at question. We believe this step should be taken before implementing other methods of dynamical analysis and measurement, such as correlation dimension or Lyapounov spectrum. {copyright} {ital 1996 American Institute of Physics.}
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.
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.
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).
An efficient parallel algorithm for mesh smoothing
Freitag, L.; Plassmann, P.; Jones, M.
1995-12-31
Automatic mesh generation and adaptive refinement methods have proven to be very successful tools for the efficient solution of complex finite element applications. A problem with these methods is that they can produce poorly shaped elements; such elements are undesirable because they introduce numerical difficulties in the solution process. However, the shape of the elements can be improved through the determination of new geometric locations for mesh vertices by using a mesh smoothing algorithm. In this paper the authors present a new parallel algorithm for mesh smoothing that has a fast parallel runtime both in theory and in practice. The authors present an efficient implementation of the algorithm that uses non-smooth optimization techniques to find the new location of each vertex. Finally, they present experimental results obtained on the IBM SP system demonstrating the efficiency of this approach.
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…
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)
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 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…
Essential nature of Newton's constant in unimodular gravity
NASA Astrophysics Data System (ADS)
Benedetti, Dario
2016-05-01
We point out that in unimodular gravity Newton's constant is an essential coupling, i.e. it is independent of field redefinitions. We illustrate the consequences of this fact by a calculation in a standard simple approximation, showing that in this case the renormalization group flow of Newton's constant is gauge and parametrization independent.
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…
NUMERICAL CONVERGENCE IN SMOOTHED PARTICLE HYDRODYNAMICS
Zhu, Qirong; Li, Yuexing; Hernquist, Lars
2015-02-10
We study the convergence properties of smoothed particle hydrodynamics (SPH) using numerical tests and simple analytic considerations. Our analysis shows that formal numerical convergence is possible in SPH only in the joint limit N → ∞, h → 0, and N{sub nb} → ∞, where N is the total number of particles, h is the smoothing length, and N{sub nb} is the number of neighbor particles within the smoothing volume used to compute smoothed estimates. Previous work has generally assumed that the conditions N → ∞ and h → 0 are sufficient to achieve convergence, while holding N{sub nb} fixed. We demonstrate that if N{sub nb} is held fixed as the resolution is increased, there will be a residual source of error that does not vanish as N → ∞ and h → 0. Formal numerical convergence in SPH is possible only if N{sub nb} is increased systematically as the resolution is improved. Using analytic arguments, we derive an optimal compromise scaling for N{sub nb} by requiring that this source of error balance that present in the smoothing procedure. For typical choices of the smoothing kernel, we find N{sub nb} ∝N {sup 0.5}. This means that if SPH is to be used as a numerically convergent method, the required computational cost does not scale with particle number as O(N), but rather as O(N {sup 1} {sup +} {sup δ}), where δ ≈ 0.5, with a weak dependence on the form of the smoothing kernel.
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....
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.
SIMS: computation of a smooth invariant molecular surface.
Vorobjev, Y N; Hermans, J
1997-08-01
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
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
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.
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 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.
Hot gas in groups: NGC 5328 and the intriguing case of NGC 4756 with XMM-Newton
NASA Astrophysics Data System (ADS)
Trinchieri, G.; Marino, A.; Mazzei, P.; Rampazzo, R.; Wolter, A.
2012-09-01
Context. Environment appears to have a strong influence on the fundamental properties of galaxies, modifying both their morphologies and their star formation histories. Similarly, galaxies play a role in determining the properties of the hot intergalactic medium in groups, heating and enriching it through a variety of mechanisms. NGC 5238 and NGC 4756 are the brightest unperturbed elliptical galaxies in their respective loose groups, but the analysis of their environment suggests that they may be at different evolutionary stages. Aims: We aim to characterize the properties of the hot gas in both the halos of the brightest galaxy members and in the environment. In NGC 4756, we are also interested in the properties of a substructure identified to the southwest and the region connecting the two structures, to search for a physical connection between the two. However, we have to take into account that the group is projected against the bright, X-ray emitting cluster A1361, which heavily contaminates and confuses the emission from the foreground structure. Methods: We present XMM-Newton observations of the groups and a careful analysis to separate different components. We examine the X-ray morphology, hot gas distribution, and spectral characteristics of both NGC 4756 and NGC 5328 and their companion galaxies. To better characterize the environment, we also present a re-evaluation of the dynamical properties of the systems. Smoothed particle hydrodynamical simulations are used to interpret the results. Results: We find that the X-ray source associated with NGC 4756 indeed sits on top of extended emission from the background cluster A1361, but can be distinguished relatively well from it as a significant excess out to r ~ 150″ (~40 kpc). NGC 4756 has an X-ray luminosity of Lx ~ 1041 erg s-1 due to hot gas, with an average temperature of kT ~ 0.7 keV. We measure a faint diffuse emission in the region of the subclump to the SW, but more interestingly, we detect gas
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.
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.
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.
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.
Smoothed Particle Hydrodynamics with Time Varying, Piecewise Constant Smoothing Length Profiles
NASA Astrophysics Data System (ADS)
Børve, S.; Omang, M.; Trulsen, J.
2000-12-01
Smoothed Particle Hydrodynamics (SPH) has proven to be a very useful numerical tool in studying a number of widely different astrophysical problems. Still, used on many other types of problems the method faces problems concerning efficiency and accuracy compared to that of modern grid-based methods. Essential to efficiency is maintaining a near-optimal particle distribution and smoothing length profile that reflects the physics of the problem. This means, directing computer resources towards those regions and time intervals where the action is taking place and not being wasted where nothing is happening. In the literature researchers have tried to achieve these goals by combining the Lagrangian nature of the SPH method with a smoothing length profile varying smoothly in space and time. To make the SPH method better suited for accurately describing a wider range of problems, a scheme containing two novel features is proposed. First, the scheme assumes a piecewise constant smoothing length profile. To avoid substantial errors near steps in the smoothing length profile, alternative forms of the SPH equations of motion is used. Secondly, a predictive attitude towards optimizing the particle distribution is introduced by activating a mass, momentum and internal energy conservation regularization process at intervals. The main challenge faced by the scheme has been to put the newly optimized smoothing length profile into use without severely altering the underlying physics. To achieve this, the entire set of particles is redefined in the process. The basic ideas behind this scheme is briefly described. Finally, the results from several hydrodynamical and magnetohydrodynamical tests in one and two dimensions are presented. This work is funded by the Research Council of Norway.
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.
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.
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
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
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
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
Changes of smooth muscle contractile filaments in small bowel atresia
Gfroerer, Stefan; Fiegel, Henning; Ramachandran, Priya; Rolle, Udo; Metzger, Roman
2012-01-01
AIM: To investigate morphological changes of intestinal smooth muscle contractile fibres in small bowel atresia patients. METHODS: Resected small bowel specimens from small bowel atresia patients (n = 12) were divided into three sections (proximal, atretic and distal). Standard histology hematoxylin-eosin staining and enzyme immunohistochemistry was performed to visualize smooth muscle contractile markers α-smooth muscle actin (SMA) and desmin using conventional paraffin sections of the proximal and distal bowel. Small bowel from age-matched patients (n = 2) undergoing Meckel’s diverticulum resection served as controls. RESULTS: The smooth muscle coat in the proximal bowel of small bowel atresia patients was thickened compared with control tissue, but the distal bowel was unchanged. Expression of smooth muscle contractile fibres SMA and desmin within the proximal bowel was slightly reduced compared with the distal bowel and control tissue. There were no major differences in the architecture of the smooth muscle within the proximal bowel and the distal bowel. The proximal and distal bowel in small bowel atresia patients revealed only minimal differences regarding smooth muscle morphology and the presence of smooth muscle contractile filament markers. CONCLUSION: Changes in smooth muscle contractile filaments do not appear to play a major role in postoperative motility disorders in small bowel atresia. PMID:22791945
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
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.
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.
Suzanne Newton's "I Will Call it Georgie's Blues".
ERIC Educational Resources Information Center
Scales, Pat
1998-01-01
Summarizes Suzanne Newton's children's book, "I Will Call It Georgie's Blues." Includes discussion questions about the book, and a list of activities. Provides an annotated bibliography of fiction, picture books, nonfiction, and biography titles about jazz and jazz musicians. (AEF)
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). PMID:17501332
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}.
Optomechanical test of the Schrödinger-Newton equation
NASA Astrophysics Data System (ADS)
Großardt, André; Bateman, James; Ulbricht, Hendrik; Bassi, Angelo
2016-05-01
The Schrödinger-Newton equation has been proposed as an experimentally testable alternative to quantum gravity, accessible at low energies. It contains self-gravitational terms, which slightly modify the quantum dynamics. Here we show that it distorts the spectrum of a harmonic system. Based on this effect, we propose an optomechanical experiment with a trapped microdisc to test the Schrödinger-Newton equation, and we show that it can be realized with existing technology.
Issac Newton: A passion to learn and understand
NASA Astrophysics Data System (ADS)
French, A. P.
1988-10-01
The work of Isaac Newton is an enduring tribute to his genius for observation, investigation and analysis. Although most of his work was done over three hundred years ago, it is replete with examples of current value to our role as teachers of physics. The purpose of this paper is both to pay homage to Newton, on the tercentenary of the Principia, and to suggest the much of that what he did can translate directly into our classrooms.
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.
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.
Evaluating the smoothness of color transformations
NASA Astrophysics Data System (ADS)
Aristova, Anna; Wang, Zhaohui; Hardeberg, Jon Y.
2011-01-01
Multi-dimensional look up tables (LUTs) are widely employed for color transformations due to its high accuracy and general applicability. Using the LUT model generally involves the color measurement of a large number of samples. The precision and uncertainty of the color measurement will be mainly represented in the LUTs, and will affect the smoothness of the color transformation. This, in turn, strongly influences the quality of the reproduced color images. To achieve high quality color image reproduction, the color transformation is required to be relatively smooth. In this study, we have investigated the inherent characteristics of LUTs' transformation from color measurement and their effects on the quality of reproduced images. We propose an algorithm to evaluate the smoothness of 3D LUT based color transformations quantitatively, which is based on the analysis of 3D LUTs transformation from RGB to CIELAB and the second derivative of the differences between adjacent points in vertical and horizontal ramps of each LUT entry. The performance of the proposed algorithm was compared with a those proposed in two recent studies on smoothness, and a better performance is reached by the proposed method.
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.
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.
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)
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.
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.
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.
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.
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.
Conservative Smoothing on an Adaptive Quadrilateral Grid
NASA Astrophysics Data System (ADS)
Sun, M.; Takayama, K.
1999-03-01
The Lax-Wendroff scheme can be freed of spurious oscillations by introducing conservative smoothing. In this paper the approach is first tested in 1-D modeling equations and then extended to multidimensional flows by the finite volume method. The scheme is discretized by a space-splitting method on an adaptive quadrilateral grid. The artificial viscosity coefficients in the conservative smoothing step are specially designed to capture slipstreams and vortices. Algorithms are programmed using a vectorizable data structure, under which not only the flow solver but also the adaptation procedure is well vectorized. The good resolution and high efficiency of the approach are demonstrated in calculating both unsteady and steady compressible flows with either weak or strong shock waves.
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
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.
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.
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.
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.
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
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.
A smoothing algorithm using cubic spline functions
NASA Technical Reports Server (NTRS)
Smith, R. E., Jr.; Price, J. M.; Howser, L. M.
1974-01-01
Two algorithms are presented for smoothing arbitrary sets of data. They are the explicit variable algorithm and the parametric variable algorithm. The former would be used where large gradients are not encountered because of the smaller amount of calculation required. The latter would be used if the data being smoothed were double valued or experienced large gradients. Both algorithms use a least-squares technique to obtain a cubic spline fit to the data. The advantage of the spline fit is that the first and second derivatives are continuous. This method is best used in an interactive graphics environment so that the junction values for the spline curve can be manipulated to improve the fit.
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.
Newton force from wave function collapse: speculation and test
NASA Astrophysics Data System (ADS)
Diósi, Lajos
2014-04-01
The Diosi-Penrose model of quantum-classical boundary postulates gravity-related spontaneous wave function collapse of massive degrees of freedom. The decoherence effects of the collapses are in principle detectable if not masked by the overwhelming environmental decoherence. But the DP (or any other, like GRW, CSL) spontaneous collapses are not detectable themselves, they are merely the redundant formalism of spontaneous decoherence. To let DP collapses become testable physics, recently we extended the DP model and proposed that DP collapses are responsible for the emergence of the Newton gravitational force between massive objects. We identified the collapse rate, possibly of the order of 1/ms, with the rate of emergence of the Newton force. A simple heuristic emergence (delay) time was added to the Newton law of gravity. This non-relativistic delay is in peaceful coexistence with Einstein's relativistic theory of gravitation, at least no experimental evidence has so far surfaced against it. We derive new predictions of such a 'lazy' Newton law that will enable decisive laboratory tests with available technologies. The simple equation of 'lazy' Newton law deserves theoretical and experimental studies in itself, independently of the underlying quantum foundational considerations.
On combining Laplacian and optimization-based mesh smoothing techniques
Freitag, L.A.
1997-07-01
Local mesh smoothing algorithms have been shown to be effective in repairing distorted elements in automatically generated meshes. The simplest such algorithm is Laplacian smoothing, which moves grid points to the geometric center of incident vertices. Unfortunately, this method operates heuristically and can create invalid meshes or elements of worse quality than those contained in the original mesh. In contrast, optimization-based methods are designed to maximize some measure of mesh quality and are very effective at eliminating extremal angles in the mesh. These improvements come at a higher computational cost, however. In this article the author proposes three smoothing techniques that combine a smart variant of Laplacian smoothing with an optimization-based approach. Several numerical experiments are performed that compare the mesh quality and computational cost for each of the methods in two and three dimensions. The author finds that the combined approaches are very cost effective and yield high-quality meshes.
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 51.636 - 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, 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...
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 51.698 - 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 51.636 - 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 51.636 - 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 51.698 - 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...
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.
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.
A Catalogue of XMM-Newton BL Lacs
NASA Astrophysics Data System (ADS)
Rouco Escorial, A.; de la Calle, I.; Held, J.; Racero, E.
2014-07-01
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 XMMNewton 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.
The Riemann hypothesis illuminated by the Newton flow of ζ
NASA Astrophysics Data System (ADS)
Neuberger, J. W.; Feiler, C.; Maier, H.; Schleich, W. P.
2015-10-01
We analyze the Newton flow of the Riemann zeta function ζ and rederive in an elementary way the Riemann-von Mangoldt estimate of the number of non-trivial zeros below a given imaginary part. The representation of the flow on the Riemann sphere highlights the importance of the North pole as the starting and turning point of the separatrices, that is of the continental divides of the Newton flow. We argue that the resulting patterns may lead to deeper insight into the Riemann hypothesis. For this purpose we also compare and contrast the Newton flow of ζ with that of a function which in many ways is similar to ζ, but violates the Riemann hypothesis. We dedicate this paper to the memory of Richard Lewis Arnowitt and his many contributions to general relativity and high energy physics.
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
The architecture of Newton, a general-purpose dynamics simulator
NASA Technical Reports Server (NTRS)
Cremer, James F.; Stewart, A. James
1989-01-01
The architecture for Newton, a general-purpose system for simulating the dynamics of complex physical objects, is described. The system automatically formulates and analyzes equations of motion, and performs automatic modification of this system equations when necessitated by changes in kinematic relationships between objects. Impact and temporary contact are handled, although only using simple models. User-directed influence of simulations is achieved using Newton's module, which can be used to experiment with the control of many-degree-of-freedom articulated objects.
On the origin of gravity and the laws of Newton
NASA Astrophysics Data System (ADS)
Verlinde, Erik
2011-04-01
Starting from first principles and general assumptions we present a heuristic argument that shows that Newton's law of gravitation naturally arises in a theory in which space emerges through a holographic scenario. Gravity is identified with an entropic force caused by changes in the information associated with the positions of material bodies. A relativistic generalization of the presented arguments directly leads to the Einstein equations. When space is emergent even Newton's law of inertia needs to be explained. The equivalence principle auggests that it is actually the law of inertia whose origin is entropic.
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...
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.
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.
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…
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
Surface antigens of smooth brucellae.
Diaz, R; Jones, L M; Leong, D; Wilson, J B
1968-10-01
Surface antigens of smooth brucellae were extracted by ether-water, phenol-water, trichloroacetic acid, and saline and examined by immunoelectrophoresis and gel diffusion with antisera from infected and immunized rabbits. Ether-water extracts of Brucella melitensis contained a lipopolysaccharide protein component, which was specific for the surface of smooth brucellae and was correlated with the M agglutinogen of Wilson and Miles, a polysaccharide protein component devoid of lipid which was not restricted to the surface of smooth brucellae and was not correlated with the smooth agglutinogen (component 1), and several protein components which were associated with internal antigens of rough and smooth brucellae. Immunoelectrophoretic analysis of ether-water extracts of B. abortus revealed only two components, a lipopolysaccharide protein component, which was correlated with the A agglutinogen, and component 1. Component 1 from B. melitensis and B. abortus showed identity in gel diffusion tests, whereas component M from B. melitensis and component A from B. abortus showed partial identity with unabsorbed antisera and no cross-reactions with monospecific sera. Attempts to prepare monospecific sera directly by immunization of rabbits with cell walls or ether-water extracts were unsuccessful. Absorption of antisera with heavy fraction of ether-water extracts did not always result in monospecific sera. It was concluded (as has been described before) that the A and M antigens are present on a single antigenic complex, in different proportions depending upon the species and biotype, and that this component is a lipopolysaccharide protein complex of high molecular weight that diffuses poorly through agar gel. Components 1, A, and M were also demonstrated in trichloroacetic acid and phenol-water extracts. With all extracts, B. melitensis antigen showed greater diffusibility in agar than B. abortus antigens. After mild acid hydrolysis, B. abortus ether-water extract was able
Computer programs for smoothing and scaling airfoil coordinates
NASA Technical Reports Server (NTRS)
Morgan, H. L., Jr.
1983-01-01
Detailed descriptions are given of the theoretical methods and associated computer codes of a program to smooth and a program to scale arbitrary airfoil coordinates. The smoothing program utilizes both least-squares polynomial and least-squares cubic spline techniques to smooth interatively the second derivatives of the y-axis airfoil coordinates with respect to a transformed x-axis system which unwraps the airfoil and stretches the nose and trailing-edge regions. The corresponding smooth airfoil coordinates are then determined by solving a tridiagonal matrix of simultaneous cubic-spline equations relating the y-axis coordinates and their corresponding second derivatives. A technique for computing the camber and thickness distribution of the smoothed airfoil is also discussed. The scaling program can then be used to scale the thickness distribution generated by the smoothing program to a specific maximum thickness which is then combined with the camber distribution to obtain the final scaled airfoil contour. Computer listings of the smoothing and scaling programs are included.
Generating Optimal Initial Conditions for Smoothed Particle Hydrodynamics Simulations
NASA Astrophysics Data System (ADS)
Diehl, S.; Rockefeller, G.; Fryer, C. L.; Riethmiller, D.; Statler, T. S.
2015-12-01
We review existing smoothed particle hydrodynamics setup methods and outline their advantages, limitations, and drawbacks. We present a new method for constructing initial conditions for smoothed particle hydrodynamics simulations, which may also be of interest for N-body simulations, and demonstrate this method on a number of applications. This new method is inspired by adaptive binning techniques using weighted Voronoi tessellations. Particles are placed and iteratively moved based on their proximity to neighbouring particles and the desired spatial resolution. This new method can satisfy arbitrarily complex spatial resolution requirements.
Observations of the post-shock break-out emission of SN 2011dh with XMM-Newton
NASA Astrophysics Data System (ADS)
Sasaki, M.; Ducci, L.
2012-10-01
Context. After the occurrence of the type cIIb SN 2011dh in the nearby spiral galaxy M 51 numerous observations were performed with different telescopes in various bands ranging from radio to γ-rays. Aims: We analysed the XMM-Newton and Swift observations taken 3 to 30 days after the SN explosion to study the X-ray spectrum of SN 2011dh. Methods: We extracted spectra from the XMM-Newton observations, which took place ~7 and 11 days after the SN. In addition, we created integrated Swift/XRT spectra of 3 to 10 days and 11 to 30 days. Results: The spectra can be well-fitted with a power-law spectrum absorbed with Galactic foreground absorption. In addition, we find a harder spectral component in the first XMM-Newton spectrum taken at t ≈ 7 d. This component is also detected in the first Swift spectrum of t = 3-10 d. Conclusions: While the persistent component can be explained as inverse Compton emission from radio synchrotron emitting electrons or emission of the reverse shock, the harder component is most likely bremsstrahlung emission from the shocked stellar wind. Therefore, the harder X-ray emission that fades away after t ≈ 10 d can be interpreted as emission from the shocked circumstellar wind of SN 2011dh. Based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA.
Progress in smooth particle hydrodynamics
Wingate, C.A.; Dilts, G.A.; Mandell, D.A.; Crotzer, L.A.; Knapp, C.E.
1998-07-01
Smooth Particle Hydrodynamics (SPH) is a meshless, Lagrangian numerical method for hydrodynamics calculations where calculational elements are fuzzy particles which move according to the hydrodynamic equations of motion. Each particle carries local values of density, temperature, pressure and other hydrodynamic parameters. A major advantage of SPH is that it is meshless, thus large deformation calculations can be easily done with no connectivity complications. Interface positions are known and there are no problems with advecting quantities through a mesh that typical Eulerian codes have. These underlying SPH features make fracture physics easy and natural and in fact, much of the applications work revolves around simulating fracture. Debris particles from impacts can be easily transported across large voids with SPH. While SPH has considerable promise, there are some problems inherent in the technique that have so far limited its usefulness. The most serious problem is the well known instability in tension leading to particle clumping and numerical fracture. Another problem is that the SPH interpolation is only correct when particles are uniformly spaced a half particle apart leading to incorrect strain rates, accelerations and other quantities for general particle distributions. SPH calculations are also sensitive to particle locations. The standard artificial viscosity treatment in SPH leads to spurious viscosity in shear flows. This paper will demonstrate solutions for these problems that they and others have been developing. The most promising is to replace the SPH interpolant with the moving least squares (MLS) interpolant invented by Lancaster and Salkauskas in 1981. SPH and MLS are closely related with MLS being essentially SPH with corrected particle volumes. When formulated correctly, JLS is conservative, stable in both compression and tension, does not have the SPH boundary problems and is not sensitive to particle placement. The other approach to
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…
Telecommunications Handbook: Connecting to NEWTON. Version 1.4.
ERIC Educational Resources Information Center
Baker, Christopher; And Others
This handbook was written for use with the Argonne National Laboratory's electronic bulletin board system (BBS) called NEWTON, which is designed to create an electronic network that will link scientists, teachers, and students with the many diversified resources of the Argonne National Laboratory. The link to Argonne will include such resources as…
Newton's Apple: 15th Season. Free Educational Materials.
ERIC Educational Resources Information Center
Twin Cities Public Television, St. Paul, MN.
This guide helps teachers use the 15th season of the television program "Newton's Apple" in the classroom and lists show segments on asthma, car engines, glacier climbing, glass blowing, glaucoma, gliders, gold mine, greenhouse effect, kids on Mars, lightning, "Lost World" dinosaurs, mammoth dig, NASA robots, Novocain (TM), pack behavior, pet…
Heat kernel for Newton-Cartan trace anomalies
NASA Astrophysics Data System (ADS)
Auzzi, Roberto; Nardelli, Giuseppe
2016-07-01
We compute the leading part of the trace anomaly for a free non-relativistic scalar in 2 + 1 dimensions coupled to a background Newton-Cartan metric. The anomaly is proportional to 1 /m, where m is the mass of the scalar. We comment on the implications of a conjectured a-theorem for non-relativistic theories with boost invariance.
Gamow on Newton: Another Look at Centripetal Acceleration
ERIC Educational Resources Information Center
Corrao, Christian
2012-01-01
Presented here is an adaptation of George Gamow's derivation of the centripetal acceleration formula as it applies to Earth's orbiting Moon. The derivation appears in Gamows short but engaging book "Gravity", first published in 1962, and is essentially a distillation of Newton's work. While "TPT" contributors have offered several insightful…
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. .
15-Years of Science with XMM-Newton
NASA Astrophysics Data System (ADS)
Ehle, Matthias
2014-11-01
With about 300 refereed papers published each year, XMM-Newton is one of the most successful scientific missions of ESA ever. The talk gives an overview of recent scientific highlights and achievements covering all astrophysical areas from stars, over the strong gravitational field in the vicinity of black holes, up to the most distant quasars and clusters of galaxies.
Newton's Radii, Maupertuis' Arc Length, and Voltaire's Giant
ERIC Educational Resources Information Center
Simoson, Andrew J.
2011-01-01
Given two arc length measurements along the perimeter of an ellipse--one taken near the long diameter, the other taken anywhere else--how do you find the lengths of major and minor axes? This was a problem of great interest from the time of Newton's "Principia" until the mid-eighteenth century when France launched twin geodesic expeditions--one to…
Newton's Apple 13th Season. Free Educational Materials.
ERIC Educational Resources Information Center
Twin Cities Public Television, St. Paul, MN.
This educational materials packet was designed to help teachers use the Public Broadcasting Service's (PBS) program called "Newton's Apple" in the classroom. This book contains information on how these materials support the latest science standards; an index to the 13th season lesson pages and an index to the past three seasons; a science subject…
Demonstrating Kinematics and Newton's Laws in a Jump
ERIC Educational Resources Information Center
Kamela, Martin
2007-01-01
When students begin the study of Newton's laws they are generally comfortable with static equilibrium type problems, but dynamic examples where forces are not constant are more challenging. The class exercise presented here helps students to develop an intuitive grasp of both the position-velocity-acceleration relation and the force-acceleration…
James Newton Howard: JAMs with TRI-M.
ERIC Educational Resources Information Center
Reninger, Rosemary D.
2000-01-01
Presents an interview with James Newton Howard, a film composer. Provides background information on Howard. Addresses topics such as his most challenging and rewarding scores, his musical background, and the benefits of being associated with the American Society of Composers, Authors, and Publishers (ASCAP). (CMK)
Snowboard Jumping, Newton's Second Law and the Force on Landing
ERIC Educational Resources Information Center
O'Shea, Michael J.
2004-01-01
An application of Newton's second law to a snowboarder dropping off a vertical ledge shows that the average normal force during landing (force exerted by the ground on the snowboarder) is determined by four factors. It is shown that the flexing of the legs, the softness of the snow, the angle of the landing surface and the forward motion of the…
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…
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…
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…
Proving Newton Right or Wrong with Blur Photography
ERIC Educational Resources Information Center
Davidhazy, Andrew
2012-01-01
Sir Isaac Newton determined that the acceleration constant for gravity was 32 ft./per/sec/sec. This is a fact that most students become familiar with over time and through various means. This article describes how this can be demonstrated in a technology classroom using simple photographic equipment. (Contains 5 figures.)
Newton Algorithms for Analytic Rotation: An Implicit Function Approach
ERIC Educational Resources Information Center
Boik, Robert J.
2008-01-01
In this paper implicit function-based parameterizations for orthogonal and oblique rotation matrices are proposed. The parameterizations are used to construct Newton algorithms for minimizing differentiable rotation criteria applied to "m" factors and "p" variables. The speed of the new algorithms is compared to that of existing algorithms and to…
How Two Differing Portraits of Newton Can Teach Us about the Cultural Context of Science
ERIC Educational Resources Information Center
Tucci, Pasquale
2015-01-01
Like several scientists, Isaac Newton has been represented many times over many different periods, and portraits of Newton were often commissioned by the scientist himself. These portraits tell us a lot about the scientist, the artist and the cultural context. This article examines two very different portraits of Newton that were realized more…
Problem in Two Unknowns: Robert Hooke and a Worm in Newton's Apple.
ERIC Educational Resources Information Center
Weinstock, Robert
1992-01-01
Discusses the place that Robert Hooke has in science history versus the scientific contributions he made. Examines the relationship between Hooke and his contemporary, Isaac Newton, and Hooke's claims that Newton built on his ideas without receiving Newton's recognition. (26 references) (MDH)
The Cooling Law and the Search for a Good Temperature Scale, from Newton to Dalton
ERIC Educational Resources Information Center
Besson, Ugo
2011-01-01
The research on the cooling law began with an article by Newton published in 1701. Later, many studies were performed by other scientists confirming or confuting Newton's law. This paper presents a description and an interpretation of Newton's article, provides a short overview of the research conducted on the topic during the 18th century, and…
Workshop on advances in smooth particle hydrodynamics
Wingate, C.A.; Miller, W.A.
1993-12-31
This proceedings contains viewgraphs presented at the 1993 workshop held at Los Alamos National Laboratory. Discussed topics include: negative stress, reactive flow calculations, interface problems, boundaries and interfaces, energy conservation in viscous flows, linked penetration calculations, stability and consistency of the SPH method, instabilities, wall heating and conservative smoothing, tensors, tidal disruption of stars, breaking the 10,000,000 particle limit, modelling relativistic collapse, SPH without H, relativistic KSPH avoidance of velocity based kernels, tidal compression and disruption of stars near a supermassive rotation black hole, and finally relativistic SPH viscosity and energy.
NASA Technical Reports Server (NTRS)
Chen, W. C.; Jackson, E. D.
1986-01-01
Rotary seal for turbopump combines low leakage of labyrinth seal with high load capacity of smooth-surface annular seal. New seal acts as strong journal bearing that provides high stiffness - about same as that of ball bearings for turbopump shaft. Seal shares load with ball bearings and prolongs their lives. At same time, seal allows minimal leakage of fluid from pump. By combining leakage control and bearing functions, seal makes multiple seals unnecessary and allows compact design.
XMM-Newton Education and Public Outreach Program
NASA Astrophysics Data System (ADS)
Plait, P.; Silva, S.; Graves, T.; Simonnet, A.; Cominsky, L.
2004-08-01
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 learning science and mathematics. Currently we are working on developing an educator's unit for grades 6-12 using supernovae to teach the origin of the chemical elements. With the Contemporary Laboratory Experiences in Astronomy (CLEA) group at Gettysburg College, we are developing an interactive laboratory exploring elemental abundances through the 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. In addition, we are creating a Starlab Planetarium show which will compare and contrast the X-ray and visible light skies. 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.
Vascular smooth muscle in hypertension.
Winquist, R J; Webb, R C; Bohr, D F
1982-06-01
The cause of the elevated arterial pressure in most forms of hypertension is an increase in total peripheral resistance. This brief review is directed toward an assessment of recent investigations contributing information about the factors responsible for this increased vascular resistance. Structural abnormalities in the vasculature that characterize the hypertensive process are 1) changes in the vascular media, 2) rarefication of the resistance vessels, and 3) lesions of the intimal vascular surface. These abnormalities are mainly the result of an adaptive process and are secondary to the increase in wall stress and/or to pathological damage to cellular components in the vessel wall. Functional alterations in the vascular smooth muscle are described as changes in agonist-smooth muscle interaction or plasma membrane permeability. These types of changes appear to play a primary, initiating role in the elevation of vascular resistance of hypertension. These alterations are not the result of an increase in wall stress and they often precede the development of high blood pressure. The functional changes are initiated by abnormal function of neurogenic, humoral, and/or myogenic changes that alter vascular smooth muscle activity. PMID:6282652
A quasi-Newton acceleration for high-dimensional optimization algorithms
Alexander, David; Lange, Kenneth
2010-01-01
In many statistical problems, maximum likelihood estimation by an EM or MM algorithm suffers from excruciatingly slow convergence. This tendency limits the application of these algorithms to modern high-dimensional problems in data mining, genomics, and imaging. Unfortunately, most existing acceleration techniques are ill-suited to complicated models involving large numbers of parameters. The squared iterative methods (SQUAREM) recently proposed by Varadhan and Roland constitute one notable exception. This paper presents a new quasi-Newton acceleration scheme that requires only modest increments in computation per iteration and overall storage and rivals or surpasses the performance of SQUAREM on several representative test problems. PMID:21359052
NASA Astrophysics Data System (ADS)
Martin-Carrillo, A.; Kirsch, M. G. F.; Caballero, I.; Freyberg, M. J.; Ibarra, A.; Kendziorra, E.; Lammers, U.; Mukerjee, K.; Schönherr, G.; Stuhlinger, M.; Saxton, R. D.; Staubert, R.; Suchy, S.; Wellbrock, A.; Webb, N.; Guainazzi, M.
2012-09-01
Aims: Reliable timing calibration is essential for the accurate comparison of XMM-Newton light curves with those from other observatories, to ultimately use them to derive precise physical quantities. The XMM-Newton timing calibration is based on pulsar analysis. However, because pulsars show both timing noise and glitches, it is essential to monitor these calibration sources regularly. To this end, the XMM-Newton observatory performs observations twice a year of the Crab pulsar to monitor the absolute timing accuracy of the EPIC-pn camera in the fast timing and burst modes. We present the results of this monitoring campaign, comparing XMM-Newton data from the Crab pulsar (PSR B0531+21) with radio measurements. In addition, we use five pulsars (PSR J0537-69, PSR B0540-69, PSR B0833-45, PSR B1509-58, and PSR B1055-52) with periods ranging from 16 ms to 197 ms to verify the relative timing accuracy. Methods: We analysed 38 XMM-Newton observations (0.2-12.0 keV) of the Crab taken over the first ten years of the mission and 13 observations from the five complementary pulsars. All data were processed with SAS, the XMM-Newton Scientific Analysis Software, version 9.0. Epoch-folding techniques coupled with χ2 tests were used to derive relative timing accuracies. The absolute timing accuracy was determined using the Crab data and comparing the time shift between the main X-ray and radio peaks in the phase-folded light curves. Results: The relative timing accuracy of XMM-Newton is found to be better than 10-8. The strongest X-ray pulse peak precedes the corresponding radio peak by 306 ± 9 μs, which agrees with other high-energy observatories such as Chandra, INTEGRAL and RXTE. The derived absolute timing accuracy from our analysis is ± 48 μs.
Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD
NASA Technical Reports Server (NTRS)
Gropp, W. D.; Keyes, D. E.; McInnes, L. C.; Tidriri, M. D.
1998-01-01
Implicit solution methods are important in applications modeled by PDEs with disparate temporal and spatial scales. Because such applications require high resolution with reasonable turnaround, "routine" parallelization is essential. The pseudo-transient matrix-free Newton-Krylov-Schwarz (Psi-NKS) algorithmic framework is presented as an answer. We show that, for the classical problem of three-dimensional transonic Euler flow about an M6 wing, Psi-NKS can simultaneously deliver: globalized, asymptotically rapid convergence through adaptive pseudo- transient continuation and Newton's method-, reasonable parallelizability for an implicit method through deferred synchronization and favorable communication-to-computation scaling in the Krylov linear solver; and high per- processor performance through attention to distributed memory and cache locality, especially through the Schwarz preconditioner. Two discouraging features of Psi-NKS methods are their sensitivity to the coding of the underlying PDE discretization and the large number of parameters that must be selected to govern convergence. We therefore distill several recommendations from our experience and from our reading of the literature on various algorithmic components of Psi-NKS, and we describe a freely available, MPI-based portable parallel software implementation of the solver employed here.
A Parallel Newton-Krylov-Schur Algorithm for the Reynolds-Averaged Navier-Stokes Equations
NASA Astrophysics Data System (ADS)
Osusky, Michal
Aerodynamic shape optimization and multidisciplinary optimization algorithms have the potential not only to improve conventional aircraft, but also to enable the design of novel configurations. By their very nature, these algorithms generate and analyze a large number of unique shapes, resulting in high computational costs. In order to improve their efficiency and enable their use in the early stages of the design process, a fast and robust flow solution algorithm is necessary. This thesis presents an efficient parallel Newton-Krylov-Schur flow solution algorithm for the three-dimensional Navier-Stokes equations coupled with the Spalart-Allmaras one-equation turbulence model. The algorithm employs second-order summation-by-parts (SBP) operators on multi-block structured grids with simultaneous approximation terms (SATs) to enforce block interface coupling and boundary conditions. The discrete equations are solved iteratively with an inexact-Newton method, while the linear system at each Newton iteration is solved using the flexible Krylov subspace iterative method GMRES with an approximate-Schur parallel preconditioner. The algorithm is thoroughly verified and validated, highlighting the correspondence of the current algorithm with several established flow solvers. The solution for a transonic flow over a wing on a mesh of medium density (15 million nodes) shows good agreement with experimental results. Using 128 processors, deep convergence is obtained in under 90 minutes. The solution of transonic flow over the Common Research Model wing-body geometry with grids with up to 150 million nodes exhibits the expected grid convergence behavior. This case was completed as part of the Fifth AIAA Drag Prediction Workshop, with the algorithm producing solutions that compare favourably with several widely used flow solvers. The algorithm is shown to scale well on over 6000 processors. The results demonstrate the effectiveness of the SBP-SAT spatial discretization, which can
NASA Astrophysics Data System (ADS)
Pierre, M.; Pacaud, F.; Adami, C.; Alis, S.; Altieri, B.; Baran, N.; Benoist, C.; Birkinshaw, M.; Bongiorno, A.; Bremer, M. N.; Brusa, M.; Butler, A.; Ciliegi, P.; Chiappetti, L.; Clerc, N.; Corasaniti, P. S.; Coupon, J.; De Breuck, C.; Democles, J.; Desai, S.; Delhaize, J.; Devriendt, J.; Dubois, Y.; Eckert, D.; Elyiv, A.; Ettori, S.; Evrard, A.; Faccioli, L.; Farahi, A.; Ferrari, C.; Finet, F.; Fotopoulou, S.; Fourmanoit, N.; Gandhi, P.; Gastaldello, F.; Gastaud, R.; Georgantopoulos, I.; Giles, P.; Guennou, L.; Guglielmo, V.; Horellou, C.; Husband, K.; Huynh, M.; Iovino, A.; Kilbinger, M.; Koulouridis, E.; Lavoie, S.; Le Brun, A. M. C.; Le Fevre, J. P.; Lidman, C.; Lieu, M.; Lin, C. A.; Mantz, A.; Maughan, B. J.; Maurogordato, S.; McCarthy, I. G.; McGee, S.; Melin, J. B.; Melnyk, O.; Menanteau, F.; Novak, M.; Paltani, S.; Plionis, M.; Poggianti, B. M.; Pomarede, D.; Pompei, E.; Ponman, T. J.; Ramos-Ceja, M. E.; Ranalli, P.; Rapetti, D.; Raychaudury, S.; Reiprich, T. H.; Rottgering, H.; Rozo, E.; Rykoff, E.; Sadibekova, T.; Santos, J.; Sauvageot, J. L.; Schimd, C.; Sereno, M.; Smith, G. P.; Smolčić, V.; Snowden, S.; Spergel, D.; Stanford, S.; Surdej, J.; Valageas, P.; Valotti, A.; Valtchanov, I.; Vignali, C.; Willis, J.; Ziparo, F.
2016-06-01
Context. The quest for the cosmological parameters that describe our universe continues to motivate the scientific community to undertake very large survey initiatives across the electromagnetic spectrum. Over the past two decades, the Chandra and XMM-Newton observatories have supported numerous studies of X-ray-selected clusters of galaxies, active galactic nuclei (AGNs), and the X-ray background. The present paper is the first in a series reporting results of the XXL-XMM survey; it comes at a time when the Planck mission results are being finalised. Aims: We present the XXL Survey, the largest XMM programme totaling some 6.9 Ms to date and involving an international consortium of roughly 100 members. The XXL Survey covers two extragalactic areas of 25 deg2 each at a point-source sensitivity of ~5 × 10-15 erg s-1 cm-2 in the [0.5-2] keV band (completeness limit). The survey's main goals are to provide constraints on the dark energy equation of state from the space-time distribution of clusters of galaxies and to serve as a pathfinder for future, wide-area X-ray missions. We review science objectives, including cluster studies, AGN evolution, and large-scale structure, that are being conducted with the support of approximately 30 follow-up programmes. Methods: We describe the 542 XMM observations along with the associated multi-λ and numerical simulation programmes. We give a detailed account of the X-ray processing steps and describe innovative tools being developed for the cosmological analysis. Results: The paper provides a thorough evaluation of the X-ray data, including quality controls, photon statistics, exposure and background maps, and sky coverage. Source catalogue construction and multi-λ associations are briefly described. This material will be the basis for the calculation of the cluster and AGN selection functions, critical elements of the cosmological and science analyses. Conclusions: The XXL multi-λ data set will have a unique lasting legacy
Study of the X-ray activity of Sgr A* during the 2011 XMM-Newton campaign
NASA Astrophysics Data System (ADS)
Mossoux, E.; Grosso, N.; Vincent, F. H.; Porquet, D.
2015-12-01
Sgr A* is the closest supermassive black hole (˜ 4 × 10^6 M_⊙) located at the dynamical center of our galaxy. It has a very low bolometric luminosity (˜ 9.4 × 10^{-9} times the Eddington luminosity) and, consequently, a very low mass accretion rate (˜ 10^{-6} M_⊙/yr) but flaring activity can be observed in near-infrared, X-ray, sub-millimeter and radio. To constrain the origin of such events, it is important to investigate the timing and spectral properties of these flares, especially in X-rays. During the 2011 XMM-Newton campaign (whose total exposure was ˜226 ks) in coordination with the 1.3 mm Very-Long-Baseline Interferometry array, two X-ray flares have been observed in the 2-10 keV energy band. To perform the timing analysis of the light curves, we apply the Bayesian-blocks method to the XMM-Newton event lists, using a two-step algorithm to correct for any detector flaring background. Furthermore, we compute X-ray smoothed light curves in order to have better accuracy on the substructures and the amplitude of the flares. The first X-ray flare was observed on March 30, 2011 with a peak amplitude of about 3 times the non-flaring level. It is characterized by two sub-flares: the first one is very short (˜458 s) with an unabsorbed peak-luminosity of ˜ 9.4 × 10^{34} erg s^{-1}, whereas the second one is longer (˜1542 s) with a lower unabsorbed peak- luminosity (˜ 6.8 × 10^{34} erg s^{-1}). The waiting time between the two sub-flares (˜1000 s) is one of the smallest ever observed. If we compare this value with those observed during the 2012 Chandra XVP campaign, we can favor the hypothesis that this event is a single flare rather than two distinct sub-flares. We developed a hotspot model to explain the double-peaks shape of the light curve of this flare with the gravitational lensing and Doppler boosting. However, the decrease of the flux back to the quiescent level between the two substructures cannot be satisfactorily reproduced with this simple
7 CFR 51.768 - Smooth texture.
Code of Federal Regulations, 2012 CFR
2012-01-01
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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 Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Florida, California, and Arizona) Definitions § 51.636 Smooth texture. Smooth texture means that the...
7 CFR 51.698 - Smooth texture.
Code of Federal Regulations, 2014 CFR
2014-01-01
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7 CFR 51.698 - Smooth texture.
Code of Federal Regulations, 2013 CFR
2013-01-01
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7 CFR 51.768 - Smooth texture.
Code of Federal Regulations, 2011 CFR
2011-01-01
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7 CFR 51.636 - Smooth texture.
Code of Federal Regulations, 2013 CFR
2013-01-01
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7 CFR 51.1159 - Smooth texture.
Code of Federal Regulations, 2012 CFR
2012-01-01
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7 CFR 51.1159 - Smooth texture.
Code of Federal Regulations, 2011 CFR
2011-01-01
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7 CFR 51.1870 - Fairly smooth.
Code of Federal Regulations, 2012 CFR
2012-01-01
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7 CFR 51.1870 - Fairly smooth.
Code of Federal Regulations, 2011 CFR
2011-01-01
... 7 Agriculture 2 2011-01-01 2011-01-01 false Fairly smooth. 51.1870 Section 51.1870 Agriculture... Standards for Fresh Tomatoes 1 Definitions § 51.1870 Fairly smooth. Fairly smooth means that the tomato is not conspicuously ridged or rough....
7 CFR 51.1910 - Fairly smooth.
Code of Federal Regulations, 2013 CFR
2013-01-01
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7 CFR 51.1870 - Fairly smooth.
Code of Federal Regulations, 2013 CFR
2013-01-01
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7 CFR 51.1910 - Fairly smooth.
Code of Federal Regulations, 2014 CFR
2014-01-01
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7 CFR 51.1870 - Fairly smooth.
Code of Federal Regulations, 2014 CFR
2014-01-01
..., CERTIFICATION, AND STANDARDS) United States Standards for Fresh Tomatoes 1 Definitions § 51.1870 Fairly smooth. Fairly smooth means that the tomato is not conspicuously ridged or rough. ... 7 Agriculture 2 2014-01-01 2014-01-01 false Fairly smooth. 51.1870 Section 51.1870...
7 CFR 51.1910 - Fairly smooth.
Code of Federal Regulations, 2010 CFR
2010-01-01
... 7 Agriculture 2 2010-01-01 2010-01-01 false Fairly smooth. 51.1910 Section 51.1910 Agriculture... Consumer Standards for Fresh Tomatoes Definitions § 51.1910 Fairly smooth. Fairly smooth means that the tomato is not conspicuously ridged or rough....