Sometimes "Newton's Method" Always "Cycles"
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…
ON SEMILOCAL CONVERGENCE OF INEXACT NEWTON METHODS
Xueping Guo
2007-01-01
Inexact Newton methods are constructed by combining Newton's method with another iterative method that is used to solve the Newton equations inexactly. In this paper, we establish two semilocal convergence theorems for the inexact Newton methods. When these two theorems are specified to Newton's method, we obtain a different Newton-Kantorovich theorem about Newton's method. When the iterative method for solving the Newton equations is specified to be the splitting method, we get two estimates about the iteration steps for the special inexact Newton methods.
Fractal aspects and convergence of Newton`s method
Drexler, M. [Oxford Univ. Computing Lab. (United Kingdom)
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.
Newton's method in the context of gradients
John W. Neuberger
2007-09-01
Full Text Available This paper gives a common theoretical treatment for gradient and Newton type methods for general classes of problems. First, for Euler-Lagrange equations Newton's method is characterized as an (asymptotically optimal variable steepest descent method. Second, Sobolev gradient type minimization is developed for general problems using a continuous Newton method which takes into account a "boundary condition" operator.
[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.
Newton type methods for solving nonsmooth equations
Gao Yan
2005-01-01
Numerical methods for the solution of nonsmooth equations are studied. A new subdifferential for a locally Lipschitzian function is proposed. Based on this subdifferential, Newton methods for solving nonsmooth equations are developed and their convergence is shown. Since this subdifferential is easy to be computed, the present Newton methods can be executed easily in some applications.
Sleijpen, G.L.G.; Vorst, H.A. van der
1995-01-01
We discuss a new method for the iterative computation of a portion of the spectrum of a large sparse matrix.The matrix may be complex and non-normal.The method also delivers the Schur vectors associated with the computed eigenvalues. The eigenvectors can easily be computed from the Schur vectors,
Sleijpen, G.L.G.; Vorst, H.A. van der
2006-01-01
We discuss a new method for the iterative computation of a portion of the spectrum of a large sparse matrix.The matrix may be complex and non-normal.The method also delivers the Schur vectors associated with the computed eigenvalues. The eigenvectors can easily be computed from the Schur vectors, an
Subsampled Hessian Newton Methods for Supervised Learning.
Wang, Chien-Chih; Huang, Chun-Heng; Lin, Chih-Jen
2015-08-01
Newton methods can be applied in many supervised learning approaches. However, for large-scale data, the use of the whole Hessian matrix can be time-consuming. Recently, subsampled Newton methods have been proposed to reduce the computational time by using only a subset of data for calculating an approximation of the Hessian matrix. Unfortunately, we find that in some situations, the running speed is worse than the standard Newton method because cheaper but less accurate search directions are used. In this work, we propose some novel techniques to improve the existing subsampled Hessian Newton method. The main idea is to solve a two-dimensional subproblem per iteration to adjust the search direction to better minimize the second-order approximation of the function value. We prove the theoretical convergence of the proposed method. Experiments on logistic regression, linear SVM, maximum entropy, and deep networks indicate that our techniques significantly reduce the running time of the subsampled Hessian Newton method. The resulting algorithm becomes a compelling alternative to the standard Newton method for large-scale data classification.
Generalized Newton Method for Energy Formulation in Image Processing
2008-04-01
Blurred (b) - Newton with LH (c) - Standard Newton (d) - Newton with Ls Fig. 5.2. Deblurring of the clown image with different Newton-like methods...proposed method, the inner product can be adapted to the problem at hand. In the second example, Figure 5.2, the 330 × 291 clown image was additionally
A combined modification of Newton`s method for systems of nonlinear equations
Monteiro, M.T.; Fernandes, E.M.G.P. [Universidade do Minho, Braga (Portugal)
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.
A NEWTON MULTIGRID METHOD FOR QUASILINEAR PARABOLIC EQUATIONS
YU Xijun
2005-01-01
A combination of the classical Newton Method and the multigrid method, i.e.,a Newton multigrid method is given for solving quasilinear parabolic equations discretized by finite elements. The convergence of the algorithm is obtained for only one step Newton iteration per level. The asymptotically computational cost for quasilinear parabolic problems is O(NNk) similar to multigrid method for linear parabolic problems.
On the approximate zero of Newton method
黄正达
2003-01-01
A judgment criterion to guarantee a point to be a Chen' s approximate zero of Newton method for solving nonlinear equation is sought by dominating sequence techniques. The criterion is based on the fact that the dominating function may have only one simple positive zero, assuming that the operator is weak Lipschitz continuous, which is much more relaxed and can be checked much more easily than Lipschitz continuous in practice. It is demonstrated that a Chen' s approximate zero may not be a Smale' s approximate zero. The error estimate obtained indicated the convergent order when we use |f(x) | < ε to stop computation in software.The result can also be applied for solving partial derivative and integration equations.
On the approximate zero of Newton method
黄正达
2003-01-01
A judgment criterion to guarantee a point to be a Chen's approximate zero of Newton method for solving nonlinear equation is sought by dominating sequence techniques. The criterion is based on the fact that the dominating function may have only one simple positive zero, assuming that the operator is weak Lipschitz continuous, which is much more relaxed and can be checked much more easily than Lipschitz continuous in practice. It is demonstrated that a Chen's approximate zero may not be a Smale's approximate zero. The error estimate obtained indicated the convergent order when we use |f(x)|<ε to stop computation in software. The result can also be applied for solving partial derivative and integration equations.
Newton-Krylov-Schwarz methods in unstructured grid Euler flow
Keyes, D.E. [Old Dominion Univ., Norfolk, VA (United States)
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.
Various Newton-type iterative methods for solving nonlinear equations
Manoj Kumar
2013-10-01
Full Text Available The aim of the present paper is to introduce and investigate new ninth and seventh order convergent Newton-type iterative methods for solving nonlinear equations. The ninth order convergent Newton-type iterative method is made derivative free to obtain seventh-order convergent Newton-type iterative method. These new with and without derivative methods have efficiency indices 1.5518 and 1.6266, respectively. The error equations are used to establish the order of convergence of these proposed iterative methods. Finally, various numerical comparisons are implemented by MATLAB to demonstrate the performance of the developed methods.
Choosing the forcing terms in an inexact Newton method
Eisenstat, S.C. [Yale Univ., New Haven, CT (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States)
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.
Optimization: NURBS and the quasi-Newton method
Coburn, Todd Dale
Optimization is important in both engineering and mathematics. The Quasi-Newton Method is widely used for optimization due to its speed and efficiency. NonUniform Rational B-Splines (NURBS) are piecewise parametric approximations to curves and surfaces. NURBS have great curve-fitting properties that can be applied to improve optimization performance. This dissertation investigated the use of NURBS in optimization, focusing primarily on the coupling of NURBS with the Quasi-Newton Method. A hybrid optimization procedure dubbed the NURBS-Quasi-Newton (NQN) Method was developed and utilized that can virtually assure that the global minimum will be found. A Method was also developed to implement Pure NURBS Optimization (PNO), which can be used to optimize non-continuous and singular functions as well as functions of point cloud data. It was concluded that NURBS offer significant benefits for optimization, both individually and coupled with Quasi-Newton Methods.
Approximations of continuous Newton's method: An extension of Cayley's problem
Jon Jacobsen
2007-02-01
Full Text Available Continuous Newton's Method refers to a certain dynamical system whose associated flow generically tends to the roots of a given polynomial. An Euler approximation of this system, with step size $h=1$, yields the discrete Newton's method algorithm for finding roots. In this note we contrast Euler approximations with several different approximations of the continuous ODE system and, using computer experiments, consider their impact on the associated fractal basin boundaries of the roots.
A perfect memory makes the continuous Newton method look ahead
Kim, M. B.; Neuberger, J. W.; Schleich, W. P.
2017-08-01
Hauser and Nedić (2005 SIAM J. Optim. 15 915) have pointed out an intriguing property of a perturbed flow line generated by the continuous Newton method: it returns to the unperturbed one once the perturbation ceases to exist. We show that this feature is a direct consequence of the phase being constant along any Newton trajectory, that is, once a phase always that phase.
On Brown's and Newton's methods with convexity hypotheses
Milaszewicz, J. P.
2003-01-01
In the context of the monotone Newton theorem (MNT) it has been conjectured that discretised Brown iterations converge at least as fast as discretised Newton iterations, because such is the case for analytic iterations. With easily verified hypotheses, it is proved here that Brown analytic iterations converge strictly faster than Newton ones. As a consequence, the same result holds for discretised iterations with conveniently small incremental steps. However, in the general context of the MNT, it may happen that Newton's discretised method converges faster than Brown's, but this situation can be remedied in many cases by conveniently shifting the initial value, so that those hypotheses ensuring the reverse are satisfied. Thus, a fairly effective solution is given to the problem stated initially.
On Newton-Like Methods for Solving Nonlinear Equations
无
2006-01-01
In this paper, we present a family of general Newton-like methods with a parametric function for finding a zero of a univariate function, permitting f′(x)=0 in some points. The case of multiple roots is not treated. The methods are proved to be quadratically convergent provided the weak condition. Thus the methods remove the severe condition f′(x)≠0. Based on the general form of the Newton-like methods, a family of new iterative methods with a variable parameter are developed.
Inexact proximal Newton methods for self-concordant functions
Li, Jinchao; Andersen, Martin Skovgaard; Vandenberghe, Lieven
2016-01-01
with an application to L1-regularized covariance selection, in which prior constraints on the sparsity pattern of the inverse covariance matrix are imposed. In the numerical experiments the proximal Newton steps are computed by an accelerated proximal gradient method, and multifrontal algorithms for positive definite......We analyze the proximal Newton method for minimizing a sum of a self-concordant function and a convex function with an inexpensive proximal operator. We present new results on the global and local convergence of the method when inexact search directions are used. The method is illustrated...
A mixed Newton-Tikhonov method for nonlinear ill-posed problems
Chuan-gang KANG; Guo-qiang HE
2009-01-01
Newton type methods are one kind of the efficient methods to solve nonlinear ill-posed problems,which have attracted extensive attention.However,computational cost of Newton type methods is high because practical problems are complicated.We propose a mixed Newton-Tikhonov method,i.e.,one step Newton-Tikhonov method with several other steps of simplified Newton-Tikhonov method.Convergence and stability of this method are proved under some conditions.Numerical experiments show that the proposed method has obvious advantages over the classical Newton method in terms of computational costs.
Derivation of special relativity from Maxwell and Newton.
Dunstan, D J
2008-05-28
Special relativity derives directly from the principle of relativity and from Newton's laws of motion with a single undetermined parameter, which is found from Faraday's and Ampère's experimental work and from Maxwell's own introduction of the displacement current to be the -c(-2) term in the Lorentz transformations. The axiom of the constancy of the speed of light is quite unnecessary. The behaviour and the mechanism of the propagation of light are not at the foundations of special relativity.
A REGULARIZATION NEWTON METHOD FOR MIXED COMPLEMENTARITY PROBLEMS
王宜举; 周厚春; 王长钰
2004-01-01
In this paper, a regularization Newton method for mixed complementarity problem(MCP) based on the reformulation of MCP in [1] is proposed. Its global convergence is proved under the assumption that F is a Po-function. The main feature of our algorithm is that a priori of the existence of an accumulation point for convergence need not to be assumed.
Semismooth Newton method for quadratic programs with bound constraints
Daryina, A. N.; Izmailov, A. F.
2009-10-01
Convex quadratic programs with bound constraints are proposed to be solved by applying a semismooth Newton method to the corresponding variational inequality. Computational experiments demonstrate that, for strongly convex problems, this approach can be considerably more efficient than more traditional approaches.
Newton's Theorem of Revolving Orbits in General Relativity
Christian, Pierre
2016-01-01
Newton's theorem of revolving orbits states that one can multiply the angular speed of a Keplerian orbit by a factor $k$ by applying a radial inverse cubed force proportional to $(1-k^2)$. In this paper we derive two generalizations of this theorem in general relativity, valid for the motion of massive particles in any static, spherically symmetric metrics. The first generalization, which we named the "force" picture, generalizes Newton's radial inverse cubed force by a corresponding four-force. The second generalization, which we named the "metric" picture, instead modifies the metric of the system to produce the multiplication in angular speed. Further, we verify the Newtonian limits of both generalizations and demonstrate that there is no such generalization for rotating metrics.
State space Newton's method for topology optimization
Evgrafov, Anton
2014-01-01
We introduce a new algorithm for solving certain classes of topology optimization problems, which enjoys fast local convergence normally achieved by the full space methods while working in a smaller reduced space. The computational complexity of Newton’s direction finding subproblem in the algori......We introduce a new algorithm for solving certain classes of topology optimization problems, which enjoys fast local convergence normally achieved by the full space methods while working in a smaller reduced space. The computational complexity of Newton’s direction finding subproblem...
Spurious singularities in the generalized Newton variational method
Apagyi, B.; Levay, P. (Quantum Theory Group, Institute of Physics, Technical University of Budapest, H-1521 Budapest (Hungary)); Ladanyi, K. (Institute for Theoretical Physics, Roland Eoetvoes University, H-1088 Budapest (Hungary))
1991-12-01
The generalized Newton variational method is applied to the static-exchange approximation of the electron--hydrogen-atom scattering. Slater-type basis functions are employed to expand the amplitude density. Spurious singularities are encountered in both scattering processes. The width of the unphysical singularities is broader in the case of singlet scattering. Anomalous poles appear in narrow regions of the scale parameter and are in evident correlation with the zeros of the determinant of the free-particle Green's operator. As a by-product, simple least-squares extension of the generalized Newton variational method is developed in order to avoid spurious singularities and to recognize whether or not the convergence is of secondary nature.
Quasi-Newton Method for Optimal Blank Allowance Balancing
CHEN Manyi
2006-01-01
A balancing technique for casting or forging parts to be machined is presented in this paper. It allows an optimal part setup to make sure that no shortage of material (undercut) will occur during machining. Particularly in the heavy part industry, where the resulting casting size and shape may deviate from expectations, the balancing process discovers whether or not the design model is totally enclosed in the actual part to be machined. The alignment is an iterative process involving nonlinear constrained optimization, which forces data points to lie outside the nominal model under a specific order of priority. Newton methods for non-linear numerical minimization are rarely applied to this problem because of the high cost of computing. In this paper, Newton methods are applied to the balancing of blank part. The aforesaid algorithm is demonstrated in term of a marine propeller blade, and result shows that The Newton methods are more efficient and accurate than those implemented in past research and have distinct advantages compared to the registration methods widely used today.
Convergence analysis of a proximal Gauss-Newton method
Salzo, Saverio
2011-01-01
An extension of the Gauss-Newton algorithm is proposed to find local minimizers of penalized nonlinear least squares problems, under generalized Lipschitz assumptions. Convergence results of local type are obtained, as well as an estimate of the radius of the convergence ball. Some applications for solving constrained nonlinear equations are discussed and the numerical performance of the method is assessed on some significant test problems.
Fu Yuhua
2014-06-01
Full Text Available Neutrosophy is a new branch of philosophy, and "Quad-stage" (Four stages is the expansion of Hegel’s triad thesis, antithesis, synthesis of development. Applying Neutrosophy and "Quad-stage" method, the purposes of this paper are expanding Newton Mechanics and making it become New Newton Mechanics (NNW taking law of conservation of energy as unique source law. In this paper the examples show that in some cases other laws may be contradicted with the law of conservation of energy. The original Newton's three laws and the law of gravity, in principle can be derived by the law of conservation of energy. Through the example of free falling body, this paper derives the original Newton's second law by using the law of conservation of energy, and proves that there is not the contradiction between the original law of gravity and the law of conservation of energy; and through the example of a small ball rolls along the inclined plane (belonging to the problem cannot be solved by general relativity that a body is forced to move in flat space, derives improved Newton's second law and improved law of gravity by using law of conservation of energy. Whether or not other conservation laws (such as the law of conservation of momentum and the law of conservation of angular momentum can be utilized, should be tested by law of conservation of energy. When the original Newton's second law is not correct, then the laws of conservation of momentum and angular momentum are no longer correct; therefore the general forms of improved law of conservation of momentum and improved law of conservation of angular momentum are presented. In the cases that law of conservation of energy cannot be used effectively, New Newton Mechanics will not exclude that according to other theories or accurate experiments to derive the laws or formulas to solve some specific problems. For example, with the help of the result of general relativity, the improved Newton's formula of universal
On the Finite Convergence of Newton-type Methods for P0 Affine Variational Inequalities
Li Ping ZHANG; Wen Xun XING
2007-01-01
Based on the techniques used in non-smooth Newton methods and regularized smoothing Newton methods, a Newton-type algorithm is proposed for solving the P0 affine variational inequality problem. Under mild conditions, the algorithm can find an exact solution of the P0 affine variational inequality problem in finite steps. Preliminary numerical results indicate that the algorithm is promis-ing.
The global convergence of the non-quasi-Newton methods with non-monotone line search
无
2006-01-01
The non-quasi-Newton methods for unconstrained optimization was investigated. Non-monotone line search procedure is introduced, which is combined with the non-quasi-Newton family. Under the uniform convexity assumption on objective function, the global convergence of the non-quasi-Newton family was proved.Numerical experiments showed that the non-monotone line search was more effective.
A Two-Point Newton Method Suitable for Nonconvergent Cases and with Super-Quadratic Convergence
Ababu Teklemariam Tiruneh
2013-01-01
Full Text Available An iterative formula based on Newton’s method alone is presented for the iterative solutions of equations that ensures convergence in cases where the traditional Newton Method may fail to converge to the desired root. In addition, the method has super-quadratic convergence of order 2.414 (i.e., . Newton method is said to fail in certain cases leading to oscillation, divergence to increasingly large number, or offshooting away to another root further from the desired domain or offshooting to an invalid domain where the function may not be defined. In addition when the derivative at the iteration point is zero, Newton method stalls. In most of these cases, hybrids of several methods such as Newton, bisection, and secant methods are suggested as substitute methods and Newton method is essentially blended with other methods or altogether abandoned. This paper argues that a solution is still possible in most of these cases by the application of Newton method alone without resorting to other methods and with the same computational effort (two functional evaluations per iteration like the traditional Newton method. In addition, the proposed modified formula based on Newton method has better convergence characteristics than the traditional Newton method.
Silcowitz, Morten; Niebe, Sarah Maria; Erleben, Kenny
2009-01-01
contact response. In this paper, we present a new approach to contact force determination. We reformulate the contact force problem as a nonlinear root search problem, using a Fischer function. We solve this problem using a generalized Newton method. Our new Fischer - Newton method shows improved...... qualities for specific configurations where the most widespread alternative, the Projected Gauss-Seidel method, fails. Experiments show superior convergence properties of the exact Fischer - Newton method....
关于Newton-like-iterative方法新的收敛性定理%New convergence theorems for Newton-like-iterative methods
武敏
2010-01-01
用迭代法求解Newton-like法中的方程,T.J. Ypma提出Newton-like-iterative方法.在其早期的文章中,不精确牛顿法理论用来研究Newton-like-iterative方法的收敛性.与以往方法不同,今提出用不精确Newton-like法做相关的收敛性分析,所得定理更加简单,同时具有仿射不变性.%Newton-like-iterative methods proposed by T.J. Ypma are obtained by using an iterative method to solve Newton-like equations. In the early paper of Ypma, the theory of inexact Newton methods was applied to study the convergence of Newton-like-iterative methods. Unlike earlier results, new local convergence theorems for Newton-like-iterative methods by applying the theory of inexact Newton-like methods is proposed in this paper, which is seemed simpler and clearer. Moreover, the analysis is carried out in affine invariant terms.
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.
A Newton method for solving continuous multiple material minimum compliance problems
Stolpe, Mathias; Stegmann, Jan
2007-01-01
method, one or two linear saddle point systems are solved. These systems involve the Hessian of the objective function, which is both expensive to compute and completely dense. Therefore, the linear algebra is arranged such that the Hessian is not explicitly formed. The main concern is to solve......This paper presents an implementation of an active-set line-search Newton method intended for solving large-scale instances of a class of multiple material minimum compliance problems. The problem is modeled with a convex objective function and linear constraints. At each iteration of the Newton...... a sequence of closely related problems appearing as the continuous relaxations in a nonlinear branch and bound framework for solving discrete minimum compliance problems. A test-set consisting of eight discrete instances originating from the design of laminated composite structures is presented...
Parallel full-waveform inversion in the frequency domain by the Gauss-Newton method
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.
Quasi-Newton methods for implicit black-box FSI coupling
Bogaers, Alfred EJ
2014-09-01
Full Text Available In this paper we introduce a new multi-vector update quasi-Newton (MVQN) method for implicit coupling of partitioned, transient FSI solvers. The new quasi-Newton method facilitates the use of 'black-box' field solvers and under certain circumstances...
A preconditioned inexact newton method for nonlinear sparse electromagnetic imaging
Desmal, Abdulla
2015-03-01
A nonlinear inversion scheme for the electromagnetic microwave imaging of domains with sparse content is proposed. Scattering equations are constructed using a contrast-source (CS) formulation. The proposed method uses an inexact Newton (IN) scheme to tackle the nonlinearity of these equations. At every IN iteration, a system of equations, which involves the Frechet derivative (FD) matrix of the CS operator, is solved for the IN step. A sparsity constraint is enforced on the solution via thresholded Landweber iterations, and the convergence is significantly increased using a preconditioner that levels the FD matrix\\'s singular values associated with contrast and equivalent currents. To increase the accuracy, the weight of the regularization\\'s penalty term is reduced during the IN iterations consistently with the scheme\\'s quadratic convergence. At the end of each IN iteration, an additional thresholding, which removes small \\'ripples\\' that are produced by the IN step, is applied to maintain the solution\\'s sparsity. Numerical results demonstrate the applicability of the proposed method in recovering sparse and discontinuous dielectric profiles with high contrast values.
Solving Cocoa Pod Sigmoid Growth Model with Newton Raphson Method
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.
Sparse contrast-source inversion using linear-shrinkage-enhanced inexact Newton method
Desmal, Abdulla
2014-07-01
A contrast-source inversion scheme is proposed for microwave imaging of domains with sparse content. The scheme uses inexact Newton and linear shrinkage methods to account for the nonlinearity and ill-posedness of the electromagnetic inverse scattering problem, respectively. Thresholded shrinkage iterations are accelerated using a preconditioning technique. Additionally, during Newton iterations, the weight of the penalty term is reduced consistently with the quadratic convergence of the Newton method to increase accuracy and efficiency. Numerical results demonstrate the applicability of the proposed method.
A Newton method for solving continuous multiple material minimum compliance problems
Stolpe, M; Stegmann, Jan
This paper presents an implementation of an active-set line-search Newton method intended for solving large-scale instances of a class of multiple material minimum compliance problems. The problem is modeled with a convex objective function and linear constraints. At each iteration of the Newton....... Computational experiments with a branch and bound method indicate that the proposed Newton method can, on most instances in the test-set, take advantage of the available starting point information in an enumeration tree and resolve the relaxations after branching with few additional function evaluations...
A Study of BCI Signal Pattern Recognition by Using Quasi-Newton-SVM Method
YANG Chang-chun; MA Zheng-hua; SUN Yu-qiang; ZOU Ling
2006-01-01
The recognition of electroencephalogram (EEG) signals is the key of brain computer interface (BCI).Aimed at the problem that the recognition rate of EEG by using support vector machine (SVM) is low in BCI,based on the assumption that a well-defined physiological signal which also has a smooth form"hides" inside the noisy EEG signal,a Quasi-Newton-SVM recognition method based on Quasi-Newton method and SVM algorithm was presented.Firstly,the EEG signals were preprocessed by Quasi-Newton method and got the signals which were fit for SVM.Secondly,the preprocessed signals were classified by SVM method.The present simulation results indicated the Quasi-Newton-SVM approach improved the recognition rate compared with using SVM method; we also discussed the relationship between the artificial smooth signals and the classification errors.
NONLINEAR GALERKIN METHODS FOR SOLVING TWO DIMENSIONAL NEWTON-BOUSSINESQ EQUATIONS
GUOBOLING
1995-01-01
The nonlinear Galerkin methods for solving two-dimensional Newton-Boussinesq equations are proposed. The existence and uniqueness of global generalized solution of these equations,and the convergence of approximate solutions are also obtained.
Isaac Newton's scientific method turning data into evidence about gravity and cosmology
Harper, William L.
2014-01-01
Isaac Newton's Scientific Method examines Newton's argument for universal gravity and his application of it to resolve the problem of deciding between geocentric and heliocentric world systems by measuring masses of the sun and planets. William L. Harper suggests that Newton's inferences from phenomena realize an ideal of empirical success that is richer than prediction. Any theory that can achieve this rich sort of empirical success must not only be able to predict the phenomena it purports to explain, but also have those phenomena accurately measure the parameters which explain them. Harper explores the ways in which Newton's method aims to turn theoretical questions into ones which can be answered empirically by measurement from phenomena, and to establish that propositions inferred from phenomena are provisionally accepted as guides to further research. This methodology, guided by its rich ideal of empirical success, supports a conception of scientific progress that does not require construing it as progr...
On the Efficient Global Dynamics of Newton's Method for Complex Polynomials
Schleicher, Dierk
2011-01-01
We investigate Newton's method for complex polynomials of arbitrary degree $d$, normalized so that all their roots are in the unit disk. We specify an explicit universal set of starting points, consisting of $O(d\\log^2d)$ points and depending only on $d$, so that among them there are $d$ points that converge very quickly to the $d$ roots: we prove that the expected total number of Newton iterations required to find all $d$ roots with precision $\\eps$ is $O(d^3\\log^3d+d\\log|\\log\\eps|)$, which can be further improved to $O(d^2\\log^4d+d\\log|\\log\\eps|)$; in the worst case possibly with near-multiple roots, the complexity is $O(d^3\\log^2d(d+|\\log\\eps|))$. The arithmetic complexity for all these Newton iterations is the same as the number of Newton iterations, up to a factor of $\\log d$.
A TRULY GLOBALLY CONVERGENT FEASIBLE NEWTON-TYPE METHOD FOR MIXED COMPLEMENTARITY PROBLEMS
Deren Han
2004-01-01
Typical solution methods for solving mixed complementarity problems either generate feasible iterates but have to solve relatively complicated subproblems such as quadratic programs or linear complementarity problems, or (those methods) have relatively simple subproblems such as system of linear equations but possibly generate infeasible iterates.In this paper, we propose a new Newton-type method for solving monotone mixed complementarity problems, which ensures to generate feasible iterates, and only has to solve a system of well-conditioned linear equations with reduced dimension per iteration. Without any regularity assumption, we prove that the whole sequence of iterates converges to a solution of the problem (truly globally convergent). Furthermore, under suitable conditions,the local superlinear rate of convergence is also established.
A Smoothing Inexact Newton Method for Generalized Nonlinear Complementarity Problem
Meixia Li
2012-01-01
Full Text Available Based on the smoothing function of penalized Fischer-Burmeister NCP-function, we propose a new smoothing inexact Newton algorithm with non-monotone line search for solving the generalized nonlinear complementarity problem. We view the smoothing parameter as an independent variable. Under suitable conditions, we show that any accumulation point of the generated sequence is a solution of the generalized nonlinear complementarity problem. We also establish the local superlinear (quadratic convergence of the proposed algorithm under the BD-regular assumption. Preliminary numerical experiments indicate the feasibility and efficiency of the proposed algorithm.
A Newton type iterative method for heat-conduction inverse problems
HE Guo-qiang; MENG Ze-hong
2007-01-01
An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.
Einstein's equations from Einstein's inertial motion and Newton's law for relative acceleration
Schmid, Christoph
2016-01-01
We show that Einstein's $R^{\\hat{0} \\hat{0}}$ equation for nonrelativistic matter and strong gravitational fields is identical with Newton's equation for relative radial acceleration of neighbouring freefalling particles, spherically averaged. These laws are explicitely identical with primary observer's (1) space-time slicing by radial 4-geodesics, (2) radially parallel Local Ortho-Normal Bases, LONBs, (3) Riemann normal 3-coordinates. Hats on indices denote LONBs. General relativity follows from Newton's law of relative acceleration, Einstein's inertial motion, Lorentz covariance, and energy-momentum conservation combined with Bianchi identity. The gravitational field equation of Newton-Gauss and Einstein's $R^{\\hat{0} \\hat{0}}$ equation are identical and linear in gravitational field for an inertial primary observer.--- Einstein's equivalence between fictitious forces and gravitational forces is formulated as equivalence theorem in the equations of motion. With this, the gravitational field equation of 19th...
Improved Quasi-Newton method via PSB update for solving systems of nonlinear equations
Mamat, Mustafa; Dauda, M. K.; Waziri, M. Y.; Ahmad, Fadhilah; Mohamad, Fatma Susilawati
2016-10-01
The Newton method has some shortcomings which includes computation of the Jacobian matrix which may be difficult or even impossible to compute and solving the Newton system in every iteration. Also, the common setback with some quasi-Newton methods is that they need to compute and store an n × n matrix at each iteration, this is computationally costly for large scale problems. To overcome such drawbacks, an improved Method for solving systems of nonlinear equations via PSB (Powell-Symmetric-Broyden) update is proposed. In the proposed method, the approximate Jacobian inverse Hk of PSB is updated and its efficiency has improved thereby require low memory storage, hence the main aim of this paper. The preliminary numerical results show that the proposed method is practically efficient when applied on some benchmark problems.
Full-Newton step interior-point methods for conic optimization
Mansouri, H.
2008-01-01
In the theory of polynomial-time interior-point methods (IPMs) two important classes of methods are distinguished: small-update and large-update methods, respectively. Small-update IPMs have the best theoretical iteration bound and IPMs with full-Newton steps belong to this class of methods. Within
Full-Newton step interior-point methods for conic optimization
Mansouri, H.
2008-01-01
In the theory of polynomial-time interior-point methods (IPMs) two important classes of methods are distinguished: small-update and large-update methods, respectively. Small-update IPMs have the best theoretical iteration bound and IPMs with full-Newton steps belong to this class of methods. Within
CONVERGENCE OF NEWTON'S METHOD FOR A MINIMIZATION PROBLEM IN IMPULSE NOISE REMOVAL
Raymond H. Chan; Chung-wa Ho; Mila Nikolova
2004-01-01
Recently, two-phase schemes for removing salt-and-pepper and random-valued impulse noise are proposed in [6, 7]. The first phase uses decision-based median filters to locate those pixels which are likely to be corrupted by noise (noise candidates). In the second phase, these noise candidates are restored using a detail-preserving regularization method which allows edges and noise-free pixels to be preserved. As shown in [18], this phase is equivalent to solving a one-dimensional nonlinear equation for each noise candidate.One can solve these equations by using Newton's method. However, because of the edgepreserving term, the domain of convergence of Newton's method will be very narrow. In this paper, we determine the initial guesses for these equations such that Newton's method will always converge.
A smoothing Newton method for a type of inverse semi-definite quadratic programming problem
Xiao, Xiantao; Zhang, Liwei; Zhang, Jianzhong
2009-01-01
We consider an inverse problem arising from the semi-definite quadratic programming (SDQP) problem. We represent this problem as a cone-constrained minimization problem and its dual (denoted ISDQD) is a semismoothly differentiable (SC1) convex programming problem with fewer variables than the original one. The Karush-Kuhn-Tucker conditions of the dual problem (ISDQD) can be formulated as a system of semismooth equations which involves the projection onto the cone of positive semi-definite matrices. A smoothing Newton method is given for getting a Karush-Kuhn-Tucker point of ISDQD. The proposed method needs to compute the directional derivative of the smoothing projector at the corresponding point and to solve one linear system per iteration. The quadratic convergence of the smoothing Newton method is proved under a suitable condition. Numerical experiments are reported to show that the smoothing Newton method is very effective for solving this type of inverse quadratic programming problems.
Newton method for determining the optimal replenishment policy for EPQ model with present value
Wu Kuo-Jung Jeff
2008-01-01
Full Text Available This paper is a response for the paper of Dohi, Kaio and Osaki, that was published in RAIRO: Operations Research, 26, 1-14 (1992 for an EPQ model with present value. The purpose of this paper is threefold. First, the convex and increasing properties for the first derivative of the objective function are proved. Second, we apply the Newton method to find the optimal cycle time. Third, we provide some numerical examples to demonstrate that the Newton method is more efficient than the bisection method. .
A novel method of Newton iteration-based interval analysis for multidisciplinary systems
Wang, Lei; Xiong, Chuang; Wang, RuiXing; Wang, XiaoJun; Wu, Di
2017-09-01
A Newton iteration-based interval uncertainty analysis method (NI-IUAM) is proposed to analyze the propagating effect of interval uncertainty in multidisciplinary systems. NI-IUAM decomposes one multidisciplinary system into single disciplines and utilizes a Newton iteration equation to obtain the upper and lower bounds of coupled state variables at each iterative step. NI-IUAM only needs to determine the bounds of uncertain parameters and does not require specific distribution formats. In this way, NI-IUAM may greatly reduce the necessity for raw data. In addition, NI-IUAM can accelerate the convergence process as a result of the super-linear convergence of Newton iteration. The applicability of the proposed method is discussed, in particular that solutions obtained in each discipline must be compatible in multidisciplinary systems. The validity and efficiency of NI-IUAM is demonstrated by both numerical and engineering examples.
Chaos in Solving Polynomial Systems for Computational Kinematics by Newton-Raphson Method
无
2000-01-01
Problems in mechanism analysis and synthesis and robotics lead naturally to systemsof nonlinear equations. In this paper, an approach based on Newton Raphson method and theproperty of fractals is presented to obtaining all roots of equation. An example from planemechanism synthesis is given to demonstrate the idea of the method.
A Smooth Newton Method for Nonlinear Programming Problems with Inequality Constraints
Vasile Moraru
2012-02-01
Full Text Available The paper presents a reformulation of the Karush-Kuhn-Tucker (KKT system associated nonlinear programming problem into an equivalent system of smooth equations. Classical Newton method is applied to solve the system of equations. The superlinear convergence of the primal sequence, generated by proposed method, is proved. The preliminary numerical results with a problems test set are presented.
Harmonic Issues Assessment on PWM VSC-Based Controlled Microgrids using Newton Methods
Agundis-Tinajero, Gibran; Segundo-Ramirez, Juan; Peña-Gallardo, Rafael;
2017-01-01
This paper presents the application of Newton-based methods in the time-domain for the computation of the periodic steady state solutions of microgrids with multiple distributed generation units, harmonic stability and power quality analysis. Explicit representation of the commutation process...
Global Convergence of the Broyden's Class of Quasi-Newton Methods with Nonmonotone Linesearch
Da-chuan Xu
2003-01-01
In this paper, the Broyden class of quasi-Newton methods for unconstrained optimization is investigated. Non-monotone linesearch procedure is introduced, which is combined with the Broyden's class. Under the convexity assumption on objective function, the global convergence of the Broyden's class is proved.
CONVERGENCE OF NEWTON'S METHOD FOR SYSTEMS OF EQUATIONS WITH CONSTANT RANK DERIVATIVES
Xiubin Xu; Chong Li
2007-01-01
The convergence properties of Newton's method for systems of equations with constant rank derivatives are studied under the hypothesis that the derivatives satisfy some weak Lipschitz conditions. The unified convergence results, which include Kantorovich type theorems and Smale's point estimate theorems as special cases, are obtained.
From Newton to Einstein: the birth of Special Relativity
Ferraro, Rafael
2007-01-01
Physics was in crisis at the beginning of the twentieth century because the newborn Maxwell's electromagnetism defied mechanistic preconceptions. Albert Einstein understood that the solution to the crisis required an audacious reworking of the concepts of space and time. Special Relativity deeply modified our way of regarding space and time, in order to harmonize electromagnetism with the principle of relativity. As a consequence, lengths and elapsed times were stripped of the invariant character that classical Physics conferred them; in their place, the speed of light acquired that privileged status. Such revolutionary change forced Einstein to reformulate Newtonian mechanics, a step that led him to discover the mass-energy equivalence.
Expanding the Applicability of a Third Order Newton-Type Method Free of Bilinear Operators
Sergio Amat
2015-08-01
Full Text Available This paper is devoted to the semilocal convergence, using centered hypotheses, of a third order Newton-type method in a Banach space setting. The method is free of bilinear operators and then interesting for the solution of systems of equations. Without imposing any type of Fréchet differentiability on the operator, a variant using divided differences is also analyzed. A variant of the method using only divided differences is also presented.
Zhang, Zhenyue [Zhejiang Univ., Hangzhou (People' s Republic of China); Zha, Hongyuan [Pennsylvania State Univ., University Park, PA (United States); Simon, Horst [Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2006-07-31
In this paper, we developed numerical algorithms for computing sparse low-rank approximations of matrices, and we also provided a detailed error analysis of the proposed algorithms together with some numerical experiments. The low-rank approximations are constructed in a certain factored form with the degree of sparsity of the factors controlled by some user-specified parameters. In this paper, we cast the sparse low-rank approximation problem in the framework of penalized optimization problems. We discuss various approximation schemes for the penalized optimization problem which are more amenable to numerical computations. We also include some analysis to show the relations between the original optimization problem and the reduced one. We then develop a globally convergent discrete Newton-like iterative method for solving the approximate penalized optimization problems. We also compare the reconstruction errors of the sparse low-rank approximations computed by our new methods with those obtained using the methods in the earlier paper and several other existing methods for computing sparse low-rank approximations. Numerical examples show that the penalized methods are more robust and produce approximations with factors which have fewer columns and are sparser.
On Newton-Kantorovich Method for Solving the Nonlinear Operator Equation
Hameed Husam Hameed
2015-01-01
Full Text Available We develop the Newton-Kantorovich method to solve the system of 2×2 nonlinear Volterra integral equations where the unknown function is in logarithmic form. A new majorant function is introduced which leads to the increment of the convergence interval. The existence and uniqueness of approximate solution are proved and a numerical example is provided to show the validation of the method.
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.
APPLICATION OF NEWTON'S AND CHEBYSHEV'S METHODS TO PARALLEL FACTORIZATION OF POLYNOMIALS
Shi-ming Zheng
2001-01-01
In this paper it is shown in two different ways that one of the family of parallel iterations to determine all real quadratic factors of polynomials presented in [12] is Newton's method applied to the special equation (1.7) below. Furthermore, we apply Chebyshev's method to (1.7) and obtain a new parallel iteration for factorization of polynomials. Finally, some properties of the parallel iterations are discussed.
Improved FRFT-based method for estimating the physical parameters from Newton's rings
Wu, Jin-Min; Lu, Ming-Feng; Tao, Ran; Zhang, Feng; Li, Yang
2017-04-01
Newton's rings are often encountered in interferometry, and in analyzing them, we can estimate the physical parameters, such as curvature radius and the rings' center. The fractional Fourier transform (FRFT) is capable of estimating these physical parameters from the rings despite noise and obstacles, but there is still a small deviation between the estimated coordinates of the rings' center and the actual values. The least-squares fitting method is popularly used for its accuracy but it is easily affected by the initial values. Nevertheless, with the estimated results from the FRFT, it is easy to meet the requirements of initial values. In this paper, the proposed method combines the advantages of the fractional Fourier transform (FRFT) with the least-squares fitting method in analyzing Newton's rings fringe patterns. Its performance is assessed by analyzing simulated and actual Newton's rings images. The experimental results show that the proposed method is capable of estimating the parameters in the presence of noise and obstacles. Under the same conditions, the estimation results are better than those obtained with the original FRFT-based method, especially for the rings' center. Some applications are shown to illustrate that the improved FRFT-based method is an important technique for interferometric measurements.
SOLVING A CLASS OF INVERSE QP PROBLEMS BY A SMOOTHING NEWTON METHOD
Xiantao Xiao; Liwei Zhang
2009-01-01
We consider an inverse quadratic programming (IQP) problem in which the parameters in the objective function of a given quadratic programming (QP) problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. This problem can be formulated as a minimization problem with a positive semidefinite cone constraint and its dual (denoted IQD(A, b)) is a semismoothly differentiable (SC~1) convex program-ming problem with fewer variables than the original one. In this paper a smoothing New-ton method is used for getting a Karush-Kuhn-Tucker point of IQD(A, b). The proposed method needs to solve only one linear system per iteration and achieves quadratic conver-gence. Numerical experiments are reported to show that the smoothing Newton method is effective for solving this class of inverse quadratic programming problems.
Newton-Type Greedy Selection Methods for $\\ell_0$-Constrained Minimization.
Yuan, Xiao-Tong; Liu, Qingshan
2017-01-11
We introduce a family of Newton-type greedy selection methods for ℓ0-constrained minimization problems. The basic idea is to construct a quadratic function to approximate the original objective function around the current iterate and solve the constructed quadratic program over the cardinality constraint. The next iterate is then estimated via a line search operation between the current iterate and the solution of the sparse quadratic program. This iterative procedure can be interpreted as an extension of the constrained Newton methods from convex minimization to non-convex ℓ0-constrained minimization. We show that the proposed algorithms converge asymptotically and the rate of local convergence is superlinear up to certain estimation precision. Our methods compare favorably against several state-of-the-art alternatives when applied to sparse logistic regression and sparse support vector machines.
FPGA-based Acceleration of Davidon-Fletcher-Powell Quasi-Newton Optimization Method
刘强; 桑若愚; 张齐军
2016-01-01
Quasi-Newton methods are the most widely used methods to find local maxima and minima of func-tions in various engineering practices. However, they involve a large amount of matrix and vector operations, which are computationally intensive and require a long processing time. Recently, with the increasing density and arithme-tic cores, field programmable gate array (FPGA) has become an attractive alternative to the acceleration of scien-tific computation. This paper aims to accelerate Davidon-Fletcher-Powell quasi-Newton (DFP-QN) method by pro-posing a customized and pipelined hardware implementation on FPGAs. Experimental results demonstrate that compared with a software implementation, a speed-up of up to 17 times can be achieved by the proposed hardware implementation.
OPTIMAL MOTION PLANNING FOR A RIGID SPACECRAFT WITH TWO MOMENTUM WHEELS USING QUASI-NEWTON METHOD
Ge Xinsheng; Zhang Qizhi; Chen LiQun
2006-01-01
An optimal motion planning scheme based on the quasi-Newton method is proposed for a rigid spacecraft with two momentum wheels. A cost functional is introduced to incorporate the control energy, the final state errors and the constraints on states. The motion planning for determining control inputs to minimize the cost functional is formulated as a nonlinear optimal control problem. Using the control parametrization, one can transform the infinite dimensional optimal control problem to a finite dimensional one that is solved via the quasi-Newton methods for a feasible trajectory which satisfies the nonholonomic constraint. The optimal motion planning scheme was applied to a rigid spacecraft with two momentum wheels. The simulation results show the effectiveness of the proposed optimal motion planning scheme.
Mishra Vinod
2016-01-01
Full Text Available Numerical Laplace transform method is applied to approximate the solution of nonlinear (quadratic Riccati differential equations mingled with Adomian decomposition method. A new technique is proposed in this work by reintroducing the unknown function in Adomian polynomial with that of well known Newton-Raphson formula. The solutions obtained by the iterative algorithm are exhibited in an infinite series. The simplicity and efficacy of method is manifested with some examples in which comparisons are made among the exact solutions, ADM (Adomian decomposition method, HPM (Homotopy perturbation method, Taylor series method and the proposed scheme.
Semi-Smooth Newton Method for Solving 2D Contact Problems with Tresca and Coulomb Friction
Kristina Motyckova
2013-01-01
Full Text Available The contribution deals with contact problems for two elastic bodies with friction. After the description of the problem we present its discretization based on linear or bilinear finite elements. The semi--smooth Newton method is used to find the solution, from which we derive active sets algorithms. Finally, we arrive at the globally convergent dual implementation of the algorithms in terms of the Langrange multipliers for the Tresca problem. Numerical experiments conclude the paper.
The Smoothing Newton Method for Solving the Extended Linear Complementarity Problem
TANG Jia; MA Chang-feng
2012-01-01
The extended linear complementarity problem(denoted by ELCP) can be reformulated as the solution of a nonsmooth system of equations.By the symmetrically perturbed CHKS smoothing function,the ELCP is approximated by a family of parameterized smooth equations.A one-step smoothing Newton method is designed for solving the ELCP.The proposed algorithm is proved to be globally convergent under suitable assumptions.
Shulin Wu
2009-01-01
Full Text Available We propose a new idea to construct an effective algorithm to compute the minimal positive solution of the nonsymmetric algebraic Riccati equations arising from transport theory. For a class of these equations, an important feature is that the minimal positive solution can be obtained by computing the minimal positive solution of a couple of fixed-point equations with vector form. Based on the fixed-point vector equations, we introduce a new algorithm, namely, two-step relaxation Newton, derived by combining two different relaxation Newton methods to compute the minimal positive solution. The monotone convergence of the solution sequence generated by this new algorithm is established. Numerical results are given to show the advantages of the new algorithm for the nonsymmetric algebraic Riccati equations in vector form.
Modified Newton-Raphson GRAPE methods for optimal control of spin systems
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.
AN INEXACT LAGRANGE-NEWTON METHOD FOR STOCHASTIC QUADRATIC PROGRAMS WITH RECOURSE
ZhouChangyin; HeGuoping
2004-01-01
In this paper, two-stage stochastic quadratic programming problems with equality constraints are considered. By Monte Carlo simulation-based approximations of the objective function and its first (second)derivative,an inexact Lagrange-Newton type method is proposed.It is showed that this method is globally convergent with probability one. In particular, the convergence is local superlinear under an integral approximation error bound condition.Moreover, this method can be easily extended to solve stochastic quadratic programming problems with inequality constraints.
On the Reversibility of Newton-Raphson Root-Finding Method
Perumalla, Kalyan S [ORNL; Wright, John P [ORNL; Kuruganti, Phani Teja [ORNL
2008-07-01
Reversibility of a computational method is the ability to execute the method forward as well as backward. Reversible computational methods are generally useful in undoing incorrect computation in a speculative execution setting designed for efficient parallel processing. Here, reversibility is explored of a common component in scientific codes, namely, the Newton-Raphson root-finding method. A reverse method is proposed that is aimed at retracing the sequence of points that are visited by the forward method during forward iterations. When given the root, along with the number of iterations, of the forward method, this reverse method is aimed at backtracking along the reverse sequence of points to finally recover the original starting point of the forward method. The operation of this reverse method is illustrated on a few example functions, serving to highlight the method's strengths and shortcomings.
Mohd Arfian Ismail
2017-09-01
Full Text Available In this paper, an improve method of multi-objective optimization for biochemical system production is presented and discussed in detail. The optimization process of biochemical system production become hard and difficult when involved a large biochemical system that contain with many components. In addition, the multi-objective problem also need to be considered. Due to that, this study proposed and improve method that comprises with Newton method, differential evolution algorithm (DE and competitive co-evolutionary algorithm(ComCA. The aim of the proposed method is to maximize the production and simultaneously minimize the total amount of chemical concentrations involves. The operation of the proposed method starts with Newton method by dealing with biochemical system production as a nonlinear equations system. Then DE and ComCA are used to represent the variables in nonlinear equation system and tune the variables in order to find the best solution. The used of DE is to maximize the production while ComCA is to minimize the total amount of chemical concentrations involves. The effectiveness of the proposed method is evaluated using two benchmark biochemical systems and the experimental results show that the proposed method perform well compared to other works.
Laadhari, Aymen; Saramito, Pierre; Misbah, Chaouqi; Székely, Gábor
2017-08-01
This framework is concerned with the numerical modeling of the dynamics of individual biomembranes and capillary interfaces in a surrounding Newtonian fluid. A level set approach helps to follow the interface motion. Our method features the use of high order fully implicit time integration schemes that enable to overcome stability issues related to the explicit discretization of the highly non-linear bending force or capillary force. At each time step, the tangent systems are derived and the resulting nonlinear problems are solved by a Newton-Raphson method. Based on the signed distance assumption, several inexact Newton strategies are employed to solve the capillary and vesicle problems and guarantee the second-order convergence behavior. We address in detail the main features of the proposed method, and we report several experiments in the two-dimensional case with the aim of illustrating its accuracy and efficiency. Comparative investigations with respect to the fully explicit scheme depict the stabilizing effect of the new method, which allows to use significantly larger time step sizes.
Liu, Lulu
2013-01-01
The fully implicit approach is attractive in reservoir simulation for reasons of numerical stability and the avoidance of splitting errors when solving multiphase flow problems, but a large nonlinear system must be solved at each time step, so efficient and robust numerical methods are required to treat the nonlinearity. The Additive Schwarz Preconditioned Inexact Newton (ASPIN) framework, as an option for the outermost solver, successfully handles strong nonlinearities in computational fluid dynamics, but is barely explored for the highly nonlinear models of complex multiphase flow with capillarity, heterogeneity, and complex geometry. In this paper, the fully implicit ASPIN method is demonstrated for a finite volume discretization based on incompressible two-phase reservoir simulators in the presence of capillary forces and gravity. Numerical experiments show that the number of global nonlinear iterations is not only scalable with respect to the number of processors, but also significantly reduced compared with the standard inexact Newton method with a backtracking technique. Moreover, the ASPIN method, in contrast with the IMPES method, saves overall execution time because of the savings in timestep size.
Buried Object Detection by an Inexact Newton Method Applied to Nonlinear Inverse Scattering
Matteo Pastorino
2012-01-01
Full Text Available An approach to reconstruct buried objects is proposed. It is based on the integral equations of the electromagnetic inverse scattering problem, written in terms of the Green’s function for half-space geometries. The full nonlinearity of the problem is exploited in order to inspect strong scatterers. After discretization of the continuous model, the resulting equations are solved in a regularization sense by means of a two-step inexact Newton algorithm. The capabilities and limitations of the method are evaluated by means of some numerical simulations.
Derivation and Global Convergence for Memoryless Non-quasi-Newton Method%无记忆非拟Newton算法的导出和全局收敛性
焦宝聪; 于静静; 陈兰平
2009-01-01
In this paper, a new class of memoryless non-quasi-Newton method for solving un- constrained optimization problems is proposed, and the global convergence of this method with inexact line search is proved. Furthermore, we propose a hybrid method that mixes both the memoryless non-quasi-Newton method and the memoryless Perry-Shanno quasi-Newton method. The global convergence of this hybrid memoryless method is proved under mild assumptions. The initial results show that these new methods are efficient for the given test problems. Espe- cially the memoryless non-quasi-Newton method requires little storage and computation, so it is able to efficiently solve large scale optimization problems.
Bailey, Harry E.; Beam, Richard M.
1991-01-01
Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.
Exact Jacobians in an implicit Newton method for two-phase flow in porous media
Büsing, H.; Clauser, C.
2012-04-01
Geological storage of CO2 is one option for mitigating the effects of CO2 emissions on global warming. Since extensive on-site monitoring of the CO2 plume propagation is expensive, numerical simulations are an attractive alternative for gaining deeper insight in the dynamics of this system. We consider a model for two-phase flow in porous media for representing the injection stage of a CO2 sequestration scenario, when the plume propagation is dominated by advection. The porous medium filled by the two phases CO2 and brine is modelled as an initial-boundary-value problem consisting of two nonlinear, coupled partial differential equations, which are complemented by appropriate boundary and initial conditions. We present a new numerical approach to solve this fully coupled system using exact Jacobians. The method is based on the finite element, finite volume, box method [Huber & Helmig(2000)] for the space discretization and, since stability of the method is one of the main concerns, the fully implicit Euler method for the time discretization. A simple first order upwind method takes into account advective contributions. The resulting system of nonlinear algebraic equations is linearized by Newton's method. The required Jacobians can be obtained elegantly by automatic differentiation (AD) [Griewank & Walther(2008), Rall(1981)], a source code transformation giving exact derivatives of the discretized equations with respect to primary variables. The resulting system of linear equations is then solved by an iterative method (BiCGStab) with ILU0 preconditioning in every Newton step. We compare the forward AD differentiation mode to the standard finite difference method in terms of precision and performance. It turns out that AD performs favourable in both aspects. We also illustrate the advantages of exact Jacobians for two-phase flow in a sequestration scenario investigating the evolution of pressure and saturation.
On the speed of convergence of Newton's method for complex polynomials
Bilarev, Todor; Schleicher, Dierk
2012-01-01
We investigate Newton's method for complex polynomials of arbitrary degree $d$, normalized so that all their roots are in the unit disk. For each degree $d$, we give an explicit set $\\mathcal{S}_d$ of $3.33d\\log^2 d(1 + o(1))$ points with the following universal property: for every normalized polynomial of degree $d$ there are $d$ starting points in $\\mathcal{S}_d$ whose Newton iterations find all the roots. If the roots are uniformly and independently distributed, we show that the number of iterations for these $d$ starting points to reach all roots with precision $\\varepsilon$ is $O(d^2\\log^4 d + d\\log|\\log \\varepsilon|)$ (with probability $p_d$ tending to 1 as $d\\to\\infty$). This is an improvement of an earlier result in \\cite{D}, where the number of iterations is shown to be $O(d^4\\log^2 d + d^3\\log^2d|\\log \\varepsilon|)$ in the worst case (allowing multiple roots) and $O(d^3\\log^2 d(\\log d + \\log \\delta) + d\\log|\\log \\varepsilon|)$ for well-separated (so-called $\\delta$-separated) roots. Our result is al...
Computing the laser beam path in optical cavities: a geometric Newton's method based approach
Cuccato, Davide; Ortolan, Antonello; Beghi, Alessandro
2015-01-01
In the last decade, increasing attention has been drawn to high precision optical experiments, which push resolution and accuracy of the measured quantities beyond their current limits. This challenge requires to place optical elements (e.g. mirrors, lenses, etc.) and to steer light beams with sub-nanometer precision. Existing methods for beam direction computing in resonators, e.g. iterative ray tracing or generalized ray transfer matrices, are either computationally expensive or rely on overparametrized models of optical elements. By exploiting Fermat's principle, we develop a novel method to compute the steady-state beam configurations in resonant optical cavities formed by spherical mirrors, as a function of mirror positions and curvature radii. The proposed procedure is based on the geometric Newton method on matrix manifold, a tool with second order convergence rate that relies on a second order model of the cavity optical length. As we avoid coordinates to parametrize the beam position on mirror surfac...
Improved Full-Newton-Step Infeasible Interior-Point Method for Linear Complementarity Problems
Goran Lešaja
2016-04-01
Full Text Available We present an Infeasible Interior-Point Method for monotone Linear Complementarity Problem (LCP which is an improved version of the algorithm given in [13]. In the earlier version, each iteration consisted of one feasibility step and few centering steps. The improved version guarantees that after one feasibility step, the new iterate is feasible and close enough to the central path thanks to the much tighter proximity estimate which is based on the new lemma introduced in [18]. Thus, the centering steps are eliminated. Another advantage of this method is the use of full-Newton-steps, that is, no calculation of the step size is required. The preliminary implementation and numerical results demonstrate the advantage of the improved version of the method in comparison with the old one.
Finding optimal step of fuzzy Newton-Cotes integration rules by using the CESTAC method
Samad Noeiaghdam
2017-08-01
Full Text Available The aim of this work, is to evaluate the value of a fuzzy integral by applying the Newton-Cotes integration rules via a reliable scheme. In order to perform the numerical examples, the CADNA (Control of Accuracy and Debugging for Numerical Applications library and the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs method are applied based on the stochastic arithmetic. By using this method, the optimal number of points in the fuzzy numerical integration rules and the optimal approximate solution are obtained. Also, the accuracy of the fuzzy quadrature rules are discussed. An algorithm is given to illustrate the implementation of the method. In this case, the termination criterion is considered as the Hausdorff distance between two sequential results to be an informatical zero. Two sample fuzzy integrals are evaluated based on the proposed algorithm to show the importance and advantage of using the stochastic arithmetic in place of the floating-point arithmetic.
Shadid, J.N.; Tuminaro, R.S. [Sandia National Labs., Albuquerque, NM (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States). Dept. of Mathematics and Statistics
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.
Shadid, J.N.; Tuminaro, R.S. [Sandia National Labs., Albuquerque, NM (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States). Dept. of Mathematics and Statistics
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.
A Semismooth Newton Method for Nonlinear Parameter Identification Problems with Impulsive Noise
Clason, Christian
2012-01-01
This work is concerned with nonlinear parameter identification in partial differential equations subject to impulsive noise. To cope with the non-Gaussian nature of the noise, we consider a model with L 1 fitting. However, the nonsmoothness of the problem makes its efficient numerical solution challenging. By approximating this problem using a family of smoothed functionals, a semismooth Newton method becomes applicable. In particular, its superlinear convergence is proved under a second-order condition. The convergence of the solution to the approximating problem as the smoothing parameter goes to zero is shown. A strategy for adaptively selecting the regularization parameter based on a balancing principle is suggested. The efficiency of the method is illustrated on several benchmark inverse problems of recovering coefficients in elliptic differential equations, for which one- and two-dimensional numerical examples are presented. © by SIAM.
1979-08-01
theorem of Kantoravich [531 as given by Henrici [541, An additional discussion of the theorem and its application to the ! 1 I 29 Newton method may be...is a matrix, then n I1-11 - max . lb I (3.13) 1i n j1 bij We next cite the following lemma due to Banach ( Henrici [54], pp. 365). Lemma: Let B be a...details of this proof here; it may be found in Henrici 54], pp. 366. Let us determine how this theorem applies to the modified Newton method as compared
De-tong Zhu
2009-01-01
In this paper we extend and improve the classical affine scaling interior-point Newton method for solving nonlinear optimization subject to linear inequality constraints in the absence of the strict complementar-ity assumption. Introducing a computationally efficient technique and employing an identification function for the definition of the new affine scaling matrix, we propose and analyze a new affine scaling interior-point Newton method which improves the Coleman and Li affine scaling matrix in [2] for solving the linear inequality con-strained optimization. Local superlinear and quadratical convergence of the proposed algorithm is established under the strong second order sufficiency condition without assuming strict complementarity of the solution.
Load flow studies using Newton Raphson decouled method exploiting sparsity. Technical report
1980-10-01
The rapid growth of power systems to meet the ever increasing demand for energy has cast a great challenge upon the power system engineer. It devolves on the engineer to technically and economically analyse the various plans before him and assess their relative merits in order to ensure reliable and economical operations of power systems. This, in turn, calls for rigorous and accurate modelling of power systems and their analysis. As a first step, load flow studies form a vital part of system planning and operational studies. There is always a need to improve the technique of analysing the load flow problem and for its accurate and quick analysis. A computer program was developed in CPRI using Newton Raphson decoupled approach which may be of use to various electricity boards.
Superlinear/Quadratic One-step Smoothing Newton Method for P0-NCP
Li Ping ZHANG; Ji Ye HAN; Zheng Hai HUANG
2005-01-01
We propose a one-step smoothing Newton method for solving the non-linear complementarity problem with P0-function (P0-NCP) based on the smoothing symmetric perturbed Fisher function (for short, denoted as the SSPF-function). The proposed algorithm has to solve only one linear system of equations and performs only one line search per iteration. Without requiring any strict complementarity assumption at the P0-NCP solution, we show that the proposed algorithm converges globally and superlinearly under mild conditions. Furthermore, the algorithm has local quadratic convergence under suitable conditions. The main feature of our global convergence results is that we do not assume a priori the existence of an accumulation point. Compared to the previous literatures, our algorithm has stronger convergence results under weaker conditions.
Preconditioning strategies for nonlinear conjugate gradient methods, based on quasi-Newton updates
Andrea, Caliciotti; Giovanni, Fasano; Massimo, Roma
2016-10-01
This paper reports two proposals of possible preconditioners for the Nonlinear Conjugate Gradient (NCG) method, in large scale unconstrained optimization. On one hand, the common idea of our preconditioners is inspired to L-BFGS quasi-Newton updates, on the other hand we aim at explicitly approximating in some sense the inverse of the Hessian matrix. Since we deal with large scale optimization problems, we propose matrix-free approaches where the preconditioners are built using symmetric low-rank updating formulae. Our distinctive new contributions rely on using information on the objective function collected as by-product of the NCG, at previous iterations. Broadly speaking, our first approach exploits the secant equation, in order to impose interpolation conditions on the objective function. In the second proposal we adopt and ad hoc modified-secant approach, in order to possibly guarantee some additional theoretical properties.
Modeling quantum mechanical scattering with continuous analogue of the newton method
Algirdas Deveikis
2013-09-01
Full Text Available Computational modelling of potential and resonant scattering for short range and Coulomb potentials was investigated in this study. The resonant scattering problem is formulated with the short range potential composed of a spherically symmetric square well and spherically symmetric square barrier. An iteration scheme of a continuous analogue of the Newton method for continuous spectral problem with correct asymptotic in uncoupled partial waves has been developed. The nonlinear representation of the scattering problem for the normalized radial Schrödinger equation is solved numerically using the difference sweep technique. The second order accuracy scheme developed allow to find scattering phases and wave functions as well as investigate their numerical evolution. The scattering phases and wave functions dependence on the scattering problem parameters have been studied.
Rubæk, Tonny; Meaney, P. M.; Meincke, Peter;
2007-01-01
Breast-cancer screening using microwave imaging is emerging as a new promising technique as a supplement to X-ray mammography. To create tomographic images from microwave measurements, it is necessary to solve a nonlinear inversion problem, for which an algorithm based on the iterative Gauss-Newton...... method has been developed at Dartmouth College. This algorithm determines the update values at each iteration by solving the set of normal equations of the problem using the Tikhonov algorithm. In this paper, a new algorithm for determining the iteration update values in the Gauss-Newton algorithm...... algorithm is compared to the Gauss-Newton algorithm with Tikhonov regularization and is shown to reconstruct images of similar quality using fewer iterations....
Calibration of the galaxy cluster M_500-Y_X relation with XMM-Newton
Arnaud, M; Pratt, G W
2007-01-01
The quantity Y_ X, the product of the X-ray temperature T_ X and gas mass M_ g, has recently been proposed as a robust low-scatter mass indicator for galaxy clusters. Using precise measurements from XMM-Newton data of a sample of 10 relaxed nearby clusters, spanning a Y_ X range of 10^13 -10^15 M_sun keV, we investigate the M_500-Y_ X relation. The M_500 - Y_ X data exhibit a power law relation with slope alpha=0.548 \\pm 0.027, close to the self-similar value (3/5) and independent of the mass range considered. However, the normalisation is \\sim 20% below the prediction from numerical simulations including cooling and galaxy feedback. We discuss two effects that could contribute to the normalisation offset: an underestimate of the true mass due to the HE assumption used in X-ray mass estimates, and an underestimate of the hot gas mass fraction in the simulations. A comparison of the functional form and scatter of the relations between various observables and the mass suggest that Y_ X may indeed be a better ma...
Improved Power Flow Algorithm for VSC-HVDC System Based on High-Order Newton-Type Method
Yanfang Wei
2013-01-01
Full Text Available Voltage source converter (VSC based high-voltage direct-current (HVDC system is a new transmission technique, which has the most promising applications in the fields of power systems and power electronics. Considering the importance of power flow analysis of the VSC-HVDC system for its utilization and exploitation, the improved power flow algorithms for VSC-HVDC system based on third-order and sixth-order Newton-type method are presented. The steady power model of VSC-HVDC system is introduced firstly. Then the derivation solving formats of multivariable matrix for third-order and sixth-order Newton-type power flow method of VSC-HVDC system are given. The formats have the feature of third-order and sixth-order convergence based on Newton method. Further, based on the automatic differentiation technology and third-order Newton method, a new improved algorithm is given, which will help in improving the program development, computation efficiency, maintainability, and flexibility of the power flow. Simulations of AC/DC power systems in two-terminal, multi-terminal, and multi-infeed DC with VSC-HVDC are carried out for the modified IEEE bus systems, which show the effectiveness and practicality of the presented algorithms for VSC-HVDC system.
Matilainen, Kaarina; Mäntysaari, Esa A; Lidauer, Martin H; Strandén, Ismo; Thompson, Robin
2013-01-01
Estimation of variance components by Monte Carlo (MC) expectation maximization (EM) restricted maximum likelihood (REML) is computationally efficient for large data sets and complex linear mixed effects models. However, efficiency may be lost due to the need for a large number of iterations of the EM algorithm. To decrease the computing time we explored the use of faster converging Newton-type algorithms within MC REML implementations. The implemented algorithms were: MC Newton-Raphson (NR), where the information matrix was generated via sampling; MC average information(AI), where the information was computed as an average of observed and expected information; and MC Broyden's method, where the zero of the gradient was searched using a quasi-Newton-type algorithm. Performance of these algorithms was evaluated using simulated data. The final estimates were in good agreement with corresponding analytical ones. MC NR REML and MC AI REML enhanced convergence compared to MC EM REML and gave standard errors for the estimates as a by-product. MC NR REML required a larger number of MC samples, while each MC AI REML iteration demanded extra solving of mixed model equations by the number of parameters to be estimated. MC Broyden's method required the largest number of MC samples with our small data and did not give standard errors for the parameters directly. We studied the performance of three different convergence criteria for the MC AI REML algorithm. Our results indicate the importance of defining a suitable convergence criterion and critical value in order to obtain an efficient Newton-type method utilizing a MC algorithm. Overall, use of a MC algorithm with Newton-type methods proved feasible and the results encourage testing of these methods with different kinds of large-scale problem settings.
Kaarina Matilainen
Full Text Available Estimation of variance components by Monte Carlo (MC expectation maximization (EM restricted maximum likelihood (REML is computationally efficient for large data sets and complex linear mixed effects models. However, efficiency may be lost due to the need for a large number of iterations of the EM algorithm. To decrease the computing time we explored the use of faster converging Newton-type algorithms within MC REML implementations. The implemented algorithms were: MC Newton-Raphson (NR, where the information matrix was generated via sampling; MC average information(AI, where the information was computed as an average of observed and expected information; and MC Broyden's method, where the zero of the gradient was searched using a quasi-Newton-type algorithm. Performance of these algorithms was evaluated using simulated data. The final estimates were in good agreement with corresponding analytical ones. MC NR REML and MC AI REML enhanced convergence compared to MC EM REML and gave standard errors for the estimates as a by-product. MC NR REML required a larger number of MC samples, while each MC AI REML iteration demanded extra solving of mixed model equations by the number of parameters to be estimated. MC Broyden's method required the largest number of MC samples with our small data and did not give standard errors for the parameters directly. We studied the performance of three different convergence criteria for the MC AI REML algorithm. Our results indicate the importance of defining a suitable convergence criterion and critical value in order to obtain an efficient Newton-type method utilizing a MC algorithm. Overall, use of a MC algorithm with Newton-type methods proved feasible and the results encourage testing of these methods with different kinds of large-scale problem settings.
Regularized Newton Methods for X-ray Phase Contrast and General Imaging Problems
Maretzke, Simon; Krenkel, Martin; Salditt, Tim; Hohage, Thorsten
2015-01-01
Like many other advanced imaging methods, x-ray phase contrast imaging and tomography require mathematical inversion of the observed data to obtain real-space information. While an accurate forward model describing the generally nonlinear image formation from a given object to the observations is often available, explicit inversion formulas are typically not known. Moreover, the measured data might be insufficient for stable image reconstruction, in which case it has to be complemented by suitable a priori information. In this work, regularized Newton methods are presented as a general framework for the solution of such ill-posed nonlinear imaging problems. For a proof of principle, the approach is applied to x-ray phase contrast imaging in the near-field propagation regime. Simultaneous recovery of the phase- and amplitude from a single near-field diffraction pattern is demonstrated for the first time. The presented methods further permit all-at-once phase contrast tomography, i.e. simultaneous phase retriev...
"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.
Quantum Mechanics from Newton's Second Law and the Canonical Commutation Relation [X,P]=i
Palenik, Mark C
2014-01-01
Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian or Lagrangian formulations of mechanics. Here, we first derive the existing Heisenberg equations of motion from Newton's laws and the uncertainty principle using only the equations $F=\\frac{dP}{dt}$, $P=m\\frac{dV}{dt}$, and $\\left[X,P\\right]=i$. Then, a new...
Flexibility-based structural damage identiﬁcation using Gauss–Newton method
B Chen; S Nagarajaiah
2013-08-01
Structural damage will change the dynamic characteristics, including natural frequencies, modal shapes, damping ratios and modal ﬂexibility matrix of the structure. Modal ﬂexibility matrix is a function of natural frequencies and mode shapes and can be used for structural damage detection and health monitoring. In this paper, experimental modal ﬂexibility matrix is obtained from the ﬁrst few lower measured natural frequencies and incomplete modal shapes. The optimization problem is then constructed by minimizing Frobenius norm of the change of ﬂexibility matrix. Gauss–Newton method is used to solve the optimization problem, where the sensitivity of ﬂexibility matrix with respect to structural parameters is calculated iteratively by only using the ﬁrst few lower modes. The optimal solution corresponds to structural parameters which can be used to identify damage sites and extent. Numerical results show that ﬂexibility-based method can be successfully applied to identify the damage elements and is robust to measurement noise.
A Gauss-Newton method for the integration of spatial normal fields in shape Space
Balzer, Jonathan
2011-08-09
We address the task of adjusting a surface to a vector field of desired surface normals in space. The described method is entirely geometric in the sense, that it does not depend on a particular parametrization of the surface in question. It amounts to solving a nonlinear least-squares problem in shape space. Previously, the corresponding minimization has been performed by gradient descent, which suffers from slow convergence and susceptibility to local minima. Newton-type methods, although significantly more robust and efficient, have not been attempted as they require second-order Hadamard differentials. These are difficult to compute for the problem of interest and in general fail to be positive-definite symmetric. We propose a novel approximation of the shape Hessian, which is not only rigorously justified but also leads to excellent numerical performance of the actual optimization. Moreover, a remarkable connection to Sobolev flows is exposed. Three other established algorithms from image and geometry processing turn out to be special cases of ours. Our numerical implementation founds on a fast finite-elements formulation on the minimizing sequence of triangulated shapes. A series of examples from a wide range of different applications is discussed to underline flexibility and efficiency of the approach. © 2011 Springer Science+Business Media, LLC.
Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns
Pethiyagoda, Ravindra; Moroney, Timothy J; Back, Julian M
2014-01-01
The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface of the fluid. By reformulating the governing equations with a standard boundary-integral method, we derive a system of nonlinear algebraic equations that enforce a singular integro-differential equation at each midpoint on a two-dimensional mesh. Our contribution is to solve the system of equations with a Jacobian-free Newton-Krylov method together with a banded preconditioner that is carefully constructed with entries taken from the Jacobian of the linearised problem. Further, we are able to utilise graphics processing unit acceleration to significantly increase the grid refinement and decrease the run-time of our solutions in comparison to schemes that are presently employed in the literature. Our approach provides opportunities to explore the nonlinear features of three-...
A Jacobian-free Newton Krylov method for mortar-discretized thermomechanical contact problems
Hansen, Glen
2011-07-01
Multibody contact problems are common within the field of multiphysics simulation. Applications involving thermomechanical contact scenarios are also quite prevalent. Such problems can be challenging to solve due to the likelihood of thermal expansion affecting contact geometry which, in turn, can change the thermal behavior of the components being analyzed. This paper explores a simple model of a light water reactor nuclear fuel rod, which consists of cylindrical pellets of uranium dioxide (UO 2) fuel sealed within a Zircalloy cladding tube. The tube is initially filled with helium gas, which fills the gap between the pellets and cladding tube. The accurate modeling of heat transfer across the gap between fuel pellets and the protective cladding is essential to understanding fuel performance, including cladding stress and behavior under irradiated conditions, which are factors that affect the lifetime of the fuel. The thermomechanical contact approach developed here is based on the mortar finite element method, where Lagrange multipliers are used to enforce weak continuity constraints at participating interfaces. In this formulation, the heat equation couples to linear mechanics through a thermal expansion term. Lagrange multipliers are used to formulate the continuity constraints for both heat flux and interface traction at contact interfaces. The resulting system of nonlinear algebraic equations are cast in residual form for solution of the transient problem. A Jacobian-free Newton Krylov method is used to provide for fully-coupled solution of the coupled thermal contact and heat equations.
On the convergence of Newton-type methods under mild differentiability conditions
Argyros, Ioannis; Hilout, Saïd
2009-12-01
We introduce the new idea of recurrent functions to provide a new semilocal convergence analysis for Newton-type methods, under mild differentiability conditions. It turns out that our sufficient convergence conditions are weaker, and the error bounds are tighter than in earlier studies in some interesting cases (Chen, Ann Inst Stat Math 42:387-401, 1990; Chen, Numer Funct Anal Optim 10:37-48, 1989; Cianciaruso, Numer Funct Anal Optim 24:713-723, 2003; Cianciaruso, Nonlinear Funct Anal Appl 2009; Dennis 1971; Deuflhard 2004; Deuflhard, SIAM J Numer Anal 16:1-10, 1979; Gutiérrez, J Comput Appl Math 79:131-145, 1997; Hernández, J Optim Theory Appl 109:631-648, 2001; Hernández, J Comput Appl Math 115:245-254, 2000; Huang, J Comput Appl Math 47:211-217, 1993; Kantorovich 1982; Miel, Numer Math 33:391-396, 1979; Miel, Math Comput 34:185-202, 1980; Moret, Computing 33:65-73, 1984; Potra, Libertas Mathematica 5:71-84, 1985; Rheinboldt, SIAM J Numer Anal 5:42-63, 1968; Yamamoto, Numer Math 51: 545-557, 1987; Zabrejko, Numer Funct Anal Optim 9:671-684, 1987; Zinc̆ko 1963). Applications and numerical examples, involving a nonlinear integral equation of Chandrasekhar-type, and a differential equation are also provided in this study.
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…
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…
一类修正的阻尼牛顿法%A Modified Damped Newton Method
庞军彦; 李秦
2015-01-01
Based on the methods of Marquardt -Levenber and Goldstein -Price,the damped Newton method x(k+1) =x(k) -λk ["2 f(x(k))]-1 "f(x(k))is improved properly to propose a new algorithm which can avoid the singularity and non-positive definite-ness of two order derivative matrixes in the original algorithm.Thus the iteration can continue under the singular and non-positive defi-nite conditions of two order derivative matrixes.The convergence analysis and steps of the new algorithm are also given.Finally,the numerical tests are conducted.%在 Marquardt ！ Levenber 方法和 Goldstein ！ Price 方法的基础上对阻尼牛顿法 x（k＋1）＝x（k）－λk ["2 f（x（k））]－1"f（x（k））作了适当改进，得出了一种新的算法。与原来算法相比较，新算法避免了二阶导数矩阵的奇异性和非正定性，从而使迭代在二阶导数矩阵奇异和非正定的条件下也能进行。文章还给出了新算法的收敛性分析和算法步骤，最后给出了数值试验。
Chaitanya, T Sai; Krishna, V Sai; Anandh, B Shankar; Umesh, K S
2010-01-01
In an earlier work (Shankar kumar Jha, A Vyas, O S K S Sastri, Rajkumar Jain & K S Umesh, 'Determination of wavelength of laser light using Modified Newton's rings setup', Physics Education, vol. 22, no.3, 195-202(2005)) reported by our group, a version of Newton's rings experiment called Modified Newton's rings was proposed. The present work is an extension of this work. Here, a general formula for wavelength has been derived, applicable for a plane of observation at any distance. A relation between the focal length and the radius curvature is also derived for a plano-convex lens which is essentially used as a concave mirror. Tracker, a video analysis software, freely downloadable from the net, is employed to analyze the fringes captured using a CCD camera. Two beams which give rise to interference fringes in conventional Newton's rings and in the present setup are clearly distinguished.
Quantum mechanics from Newton's second law and the canonical commutation relation [X, P] = i
Palenik, Mark C.
2014-07-01
Despite the fact that it has been known since the time of Heisenberg that quantum operators obey a quantum version of Newton's laws, students are often told that derivations of quantum mechanics must necessarily follow from the Hamiltonian or Lagrangian formulations of mechanics. Here, we first derive the existing Heisenberg equations of motion from Newton's laws and the uncertainty principle using only the equations F=\\frac{dP}{dt}, P=m\\frac{dV}{dt}, and [X, P] = i. Then, a new expression for the propagator is derived that makes a connection between time evolution in quantum mechanics and the motion of a classical particle under Newton's laws. The propagator is solved for three cases where an exact solution is possible: (1) the free particle; (2) the harmonic oscillator; and (3) a constant force, or linear potential in the standard interpretation. We then show that for a general for a general force F(X), by Taylor expanding X(t) in time, we can use this methodology to reproduce the Feynman path integral formula for the propagator. Such a picture may be useful for students as they make the transition from classical to quantum mechanics and help solidify the equivalence of the Hamiltonian, Lagrangian, and Newtonian pictures of physics in their minds.
Reynolds, Daniel R.; Samtaney, Ravi; Tiedeman, Hilari C.
2012-01-01
Single-fluid resistive magnetohydrodynamics (MHD) is a fluid description of fusion plasmas which is often used to investigate macroscopic instabilities in tokamaks. In MHD modeling of tokamaks, it is often desirable to compute MHD phenomena to resistive time scales or a combination of resistive-Alfvén time scales, which can render explicit time stepping schemes computationally expensive. We present recent advancements in the development of preconditioners for fully nonlinearly implicit simulations of single-fluid resistive tokamak MHD. Our work focuses on simulations using a structured mesh mapped into a toroidal geometry with a shaped poloidal cross-section, and a finite-volume spatial discretization of the partial differential equation model. We discretize the temporal dimension using a fully implicit θ or the backwards differentiation formula method, and solve the resulting nonlinear algebraic system using a standard inexact Newton-Krylov approach, provided by the sundials library. The focus of this paper is on the construction and performance of various preconditioning approaches for accelerating the convergence of the iterative solver algorithms. Effective preconditioners require information about the Jacobian entries; however, analytical formulae for these Jacobian entries may be prohibitive to derive/implement without error. We therefore compute these entries using automatic differentiation with OpenAD. We then investigate a variety of preconditioning formulations inspired by standard solution approaches in modern MHD codes, in order to investigate their utility in a preconditioning context. We first describe the code modifications necessary for the use of the OpenAD tool and sundials solver library. We conclude with numerical results for each of our preconditioning approaches in the context of pellet-injection fueling of tokamak plasmas. Of these, our optimal approach results in a speedup of a factor of 3 compared with non-preconditioned implicit tests
Reynolds, Daniel R.
2012-01-01
Single-fluid resistive magnetohydrodynamics (MHD) is a fluid description of fusion plasmas which is often used to investigate macroscopic instabilities in tokamaks. In MHD modeling of tokamaks, it is often desirable to compute MHD phenomena to resistive time scales or a combination of resistive-Alfvén time scales, which can render explicit time stepping schemes computationally expensive. We present recent advancements in the development of preconditioners for fully nonlinearly implicit simulations of single-fluid resistive tokamak MHD. Our work focuses on simulations using a structured mesh mapped into a toroidal geometry with a shaped poloidal cross-section, and a finite-volume spatial discretization of the partial differential equation model. We discretize the temporal dimension using a fully implicit or the backwards differentiation formula method, and solve the resulting nonlinear algebraic system using a standard inexact Newton-Krylov approach, provided by the sundials library. The focus of this paper is on the construction and performance of various preconditioning approaches for accelerating the convergence of the iterative solver algorithms. Effective preconditioners require information about the Jacobian entries; however, analytical formulae for these Jacobian entries may be prohibitive to derive/implement without error. We therefore compute these entries using automatic differentiation with OpenAD. We then investigate a variety of preconditioning formulations inspired by standard solution approaches in modern MHD codes, in order to investigate their utility in a preconditioning context. We first describe the code modifications necessary for the use of the OpenAD tool and sundials solver library. We conclude with numerical results for each of our preconditioning approaches in the context of pellet-injection fueling of tokamak plasmas. Of these, our optimal approach results in a speedup of a factor of 3 compared with non-preconditioned implicit tests, with
NEWTON'S METHOD FOR ANISOTROPIC ANALYSIS OF ACM ELEMENT%ACM元各向异性分析的Newton方法
赵永成; 陈绍春
2011-01-01
In this paper we generalize the Newton's formula of Lagrange interpolation in one dimension to nonstandard Hermite interpolation in two dimension, and give Newton's formula for the interpolation polynomial of well-known ACM plate element. By this formula we give anisotropic interpolation error estimates of ACM element for 4-order and 2-order elliptic problems which open new analysis method for anisotropic finite elements.%本文将一维Lagrange插值多项式的Newton表达式推广到二维非标准的Hermite插值,给出著名板元-ACM元插值多项式的Newton表达式,由此给出ACM元对四阶和二阶椭圆问题的各向异性插值误差估计,为复杂单元的各向异性分析开辟了新的途径.
Novel Newton's learning algorithm of neural networks
Long Ning; Zhang Fengli
2006-01-01
Newton's learning algorithm of NN is presented and realized. In theory, the convergence rate of learning algorithm of NN based on Newton's method must be faster than BP's and other learning algorithms, because the gradient method is linearly convergent while Newton's method has second order convergence rate.The fast computing algorithm of Hesse matrix of the cost function of NN is proposed and it is the theory basis of the improvement of Newton's learning algorithm. Simulation results show that the convergence rate of Newton's learning algorithm is high and apparently faster than the traditional BP method's, and the robustness of Newton's learning algorithm is also better than BP method's.
Kastanya, Doddy Febrian
A Newton-BICGSTAB solver has been developed to reduce the CPU execution time of the FORMOSA-B boiling water reactor (BWR) core simulator. The new solver treats the strong non-linearities in the problem explicitly using the Newton's method, replacing the traditionally used nested iterative approach. Taking advantage of the higher convergence rate provided by the Newton's method, assuming that a good initial estimate of the unknowns is provided, and utilizing an efficient preconditioned BICGSTAB solver, we have developed a computationally efficient Newton-BICGSTAB solver to evaluate the three-dimensional, two-group neutron diffusion equations coupled with a two-phase flow model within a BWR core simulator. The robustness of the solver has been tested against numerous BWR core configurations and consistent results have been observed each time. The best exact Newton-BICGSTAB solver performance provides an overall speedup of 2.07 to the core simulator, with reference to the traditional approach, i.e. outer (fission-source)-inner (red/black line SOR). When solving the same problem using the traditional approach but with the BICGSTAB solver as the inner iteration solver [traditional (BICGSTAB)], we observed a speedup of 1.85. This means that the Newton-BICGSTAB solver provides an additional 12% increase in the overall speedup over the traditional (BICGSTAB) solver. However, one needs to note that, on average, the exact Newton-BICGSTAB solver provides an overall speedup of around 1.70; whereas, on average, the traditional (BICGSTAB) provides an overall speedup of around 1.60. An investigation on the feasibility of implementing an inexact Newton-BICGSTAB solver indicates that further reduction in the execution time can likely be obtained through this approach. This study shows that the inexact Newton-BICGSTAB solver can provide speedups of 1.73 to 2.10 with respect to the traditional solver.
基于信赖域Newton算法的ELM网络%ELM based on trust region Newton method
韩敏; 王新迎
2011-01-01
Considering the problems that the complexity of generalized inverse limits the learning speed of extreme machine learning(ELM), a novel ELM, called TRON-ELM, is proposed based on the trust region Newton method in which the trust region Newton method is used to derive the output weights.The proposed method takes the Newton equation of the cost funcion of ELM as an unconstrained optimization, and a conjugate gradient method is used to solve the equation, which avoids solving the inverse of the Hessian matrix, thus the operation speed is improved.Meanwhile, the existence of trust region guarantees the global convergence.The experimental results show the effectiveness of the proposed method.%针对极端学习机(ELM)网络伪逆输出权值计算方法的运算复杂度制约其训练速度问题,提出一种基于信赖域Newton算法的新型ELM网络(TRON-ELM),并采用信赖域Newton算法求解ELM网络的输出权值.该算法首先构造一个ELM网络代价函数的Newton方程,并将其作为一个无约束优化问题,采用共轭梯度法求解,避免了求代价函数Hessian矩阵逆的运算,提高了训练速度,信赖域条件的存在保证了算法的整体收敛性.仿真实验结果验证了所提出方法的有效性.
Engelman, Jonathan
Changing student conceptions in physics is a difficult process and has been a topic of research for many years. The purpose of this study was to understand what prompted students to change or not change their incorrect conceptions of Newtons Second or Third Laws in response to an intervention, Interactive Video Vignettes (IVVs), designed to overcome them. This study is based on prior research reported in the literature which has found that a curricular framework of elicit, confront, resolve, and reflect (ECRR) is important for changing student conceptions (McDermott, 2001). This framework includes four essential parts such that during an instructional event student conceptions should be elicited, incorrect conceptions confronted, these conflicts resolved, and then students should be prompted to reflect on their learning. Twenty-two undergraduate student participants who completed either or both IVVs were studied to determine whether or not they experienced components of the ECRR framework at multiple points within the IVVs. A fully integrated, mixed methods design was used to address the study purpose. Both quantitative and qualitative data were collected iteratively for each participant. Successive data collections were informed by previous data collections. All data were analyzed concurrently. The quantitative strand included a pre/post test that participants took before and after completing a given IVV and was used to measure the effect of each IVV on learning. The qualitative strand included video of each participant completing the IVV as well as an audio-recorded video elicitation interview after the post-test. The qualitative data collection was designed to describe student experiences with each IVV as well as to observe how the ECRR framework was experienced. Collecting and analyzing data using this mixed methods approach helped develop a more complete understanding of how student conceptions of Newtons Second and Third Laws changed through completion of
Li, Jiang-Tao; Miceli, Marco; Vink, Jacco; Bocchino, Fabrizio
2015-01-01
Based on our newly developed methods and the XMM-Newton large program of SN1006, we extract and analyze the spectra from 3596 tessellated regions of this SNR each with 0.3-8 keV counts $>10^4$. For the first time, we map out multiple physical parameters, such as the temperature ($kT$), electron density ($n_e$), ionization parameter ($n_et$), ionization age ($t_{ion}$), metal abundances, as well as the radio-to-X-ray slope ($\\alpha$) and cutoff frequency ($\
Yang, Haijian
2016-12-10
Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.
Yang, Haijian; Sun, Shuyu; Yang, Chao
2017-03-01
Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.
Lee, Yoon Hee; Cho, Nam Zin [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)
2010-05-15
Nowadays lattice physics codes tend to utilize a detailed burnup chain including short-lived nuclides in order to perform more accurate burnup calculations. But, since production codes, for example, ORIGEN2, take account of nuclides which have relatively long half-life, it is inappropriate for such detailed burnup chain calculation. To enhance that drawback, many matrix exponential calculation methods have been developed. Recently, a Krylov subspace method with the PADE approximation was used. In this paper, a Krylov subspace method based on spectral decomposition property of the matrix function theory with the Newton divided difference (NDD) is introduced. It is tested with a sample problem and compared with simple Taylor expansion method
SKRYN: A fast semismooth-Krylov-Newton method for controlling Ising spin systems
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.
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)
Lin Shao
2016-01-01
Full Text Available Due to large numbers of antennas and users, matrix inversion is complicated in linear precoding techniques for massive MIMO systems. Several approximated matrix inversion methods, including the Neumann series, have been proposed to reduce the complexity. However, the Neumann series does not converge fast enough. In this paper, to speed up convergence, a new joint Newton iteration and Neumann series method is proposed, with the first iteration result of Newton iteration method being employed to reconstruct the Neumann series. Then, a high probability convergence condition is established, which can offer useful guidelines for practical massive MIMO systems. Finally, simulation examples are given to demonstrate that the new joint Newton iteration and Neumann series method has a faster convergence rate compared to the previous Neumann series, with almost no increase in complexity when the iteration number is greater than or equal to 2.
A Modified Quasi- Newton Method for Nonlinear Least Squares Problems%非线性最小二乘问题的修正拟牛顿法
吴淦洲
2011-01-01
A modified quasi - Newton method for nonlinear least squares problems is proposed. By using non - monotone line search technique and structured quasi - Newton method, we establish a modified quasi - Newton method for nonlinear least squares problems, and the global convergence of the algorithm is proved.%给出了求解非线性最小二乘的修正拟牛顿方法。该方法结合了非单调搜索技术和结构化拟牛顿法的思想，提出了一种新的求解非线性最小二乘的修正拟牛顿法，并证明了该方法的全局收敛性。
Zhang, Y.-Y.; Finoguenov, A.; Boehringer, H.; Kneib, J.-P.; Smith, G. P.; Czoske, O.; Soucail, G.
2007-01-01
We present the X-ray properties and scaling relations of a flux-limited morphology-unbiased sample of 12 X-ray luminous galaxy clusters at redshift around 0.2 based on XMM-Newton observations. The scaled radial profiles are characterized by a self-similar behavior at radii outside the cluster cores
Nunan, E.
1973-01-01
Presents a brief biography of Sir Isaac Newton, lists contemporary scientists and scientific developments and discusses Newton's optical research and conceptual position concerning the nature of light. (JR)
Yang, Zhongming; Wang, Kailiang; Cheng, Jinlong; Gao, Zhishan; Yuan, Qun
2016-06-10
We have proposed a virtual quadratic Newton rings phase-shifting moiré-fringes measurement method in a nonnull interferometer to measure the large radius of curvature for a spherical surface. In a quadratic polar coordinate system, linear carrier testing Newton rings interferogram and virtual Newton rings interferogram form the moiré fringes. It is possible to retrieve the wavefront difference data between the testing and standard spherical surface from the moiré fringes after low-pass filtering. Based on the wavefront difference data, we deduced a precise formula to calculate the radius of curvature in the quadratic polar coordinate system. We calculated the retrace error in the nonnull interferometer using the multi-configuration model of the nonnull interferometric system in ZEMAX. Our experimental results indicate that the measurement accuracy is better than 0.18% for a spherical mirror with a radius of curvature of 41,400 mm.
Rethinking Newton's $\\textit{Principia}$
Saunders, Simon
2016-01-01
It is widely accepted that the notion of an inertial frame is central to Newtonian mechanics and that the correct space-time structure underlying $\\text{Newton's}$ methods in $\\textit{Principia}$ is neo-Newtonian or Galilean space-time. I argue to the contrary that inertial frames are not needed in $\\text{Newton's}$ theory of motion, and that the right space-time structure for $\\text{Newton's}$ $\\textit{Principia}$ requires the notion of parallelism of spatial directions at different times and nothing more.
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
2006-01-01
Full Text Available The dynamics of complex cubic polynomials have been studied extensively in the recent years. The main interest in this work is to focus on the Julia sets in the dynamical plane, and then is consecrated to the study of several topics in more detail. Newton's method is considered since it is the main tool for finding solutions to equations, which leads to some fantastic images when it is applied to complex functions and gives rise to a chaotic sequence.
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
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.
Why do we Still Believe in Newton's Law ? Facts, Myths and Methods in Gravitational Physics
Unzicker, A
2007-01-01
An overview of the experimental and observational status in gravitational physics is given, both for the known tests of general relativity and Newtonian gravity, but also for the increasing number of results where these theories run into problems, such as for dark matter, dark energy, and the Pioneer and flyby anomalies. It is argued that (1) scientific theories should be tested (2) current theories of gravity are poorly tested in the weak-acceleration regime (3) the measurements suggest that the anomalous phenomena have a common origin (4) it is useful to consider the present situation under a historical perspective and (5) it could well be that we still do not understand gravity. Proposals for improving the current use of scientific methods are given. `We do not know anything - this is the first. Therefore, we should be very modest - this is the second. Not to claim that we do know when we do not - this is the third. That's the kind of attitude I'd like to popularize. There is little hope for success.' (Kar...
Steward, David R.
2016-11-01
Recharge from surface to groundwater is an important component of the hydrological cycle, yet its rate is difficult to quantify. Percolation through two-dimensional circular inhomogeneities in the vadose zone is studied where one soil type is embedded within a uniform background, and nonlinear interface conditions in the quasilinear formulation are solved using Newton's method with the Analytic Element Method. This numerical laboratory identifies detectable variations in pathline and pressure head distributions that manifest due to a shift in recharge rate through in a heterogeneous media. Pathlines either diverge about or converge through coarser and finer grained materials with inverse patterns forming across lower and upper elevations; however, pathline geometry is not significantly altered by recharge. Analysis of pressure head in lower regions near groundwater identifies a new phenomenon: its distribution is not significantly impacted by an inhomogeneity soil type, nor by its placement nor by recharge rate. Another revelation is that pressure head for coarser grained inhomogeneities in upper regions is completely controlled by geometry and conductivity contrasts; a shift in recharge generates a difference Δp that becomes an additive constant with the same value throughout this region. In contrast, shifts in recharge for finer grained inhomogeneities reveal patterns with abrupt variations across their interfaces. Consequently, measurements aimed at detecting shifts in recharge in a heterogeneous vadose zone by deciphering the corresponding patterns of change in pressure head should focus on finer grained inclusions well above a groundwater table.
The Jacobi-Davidson method for eigenvalue problems as an accelerated inexact Newton scheme
Sleijpen, G.L.G.; Vorst, H.A. van der
1995-01-01
We discuss a new method for the iterative computation of a portion of the spectrum of a large sparse matrix. The matrix may be complex and non-normal. The method also delivers the Schur vectors associated with the computed eigenvalues. The eigenvectors can easily be computed from the Schur vectors,
The Jacobi-Davidson method for eigenvalue problems as an accelerated inexact Newton scheme
Sleijpen, G.L.G.; Vorst, H.A. van der
2001-01-01
We discuss a new method for the iterative computation of a portion of the spectrum of a large sparse matrix. The matrix may be complex and non-normal. The method also delivers the Schur vectors associated with the computed eigenvalues. The eigenvectors can easily be computed from the Schur vectors,
Newton's method as applied to the Riemann problem for media with general equations of state
Moiseev, N. Ya.; Mukhamadieva, T. A.
2008-06-01
An approach based on Newton’s method is proposed for solving the Riemann problem for media with normal equations of state. The Riemann integrals are evaluated using a cubic approximation of an isentropic curve that is superior to the Simpson method in terms of accuracy, convergence rate, and efficiency. The potentials of the approach are demonstrated by solving problems for media obeying the Mie-Grüneisen equation of state. The algebraic equation of the isentropic curve and some exact solutions for configurations with rarefaction waves are explicitly given.
A Newton-Picard collocation method for periodic solutions of delay differential equations
Verheyden, Koen; Lust, Kurt
This paper presents a collocation method with an iterative linear system solver to compute periodic solutions of a system of autonomous delay differential equations (DDEs). We exploit the equivalence of the linearized collocation system and the discretization of the linearized periodic boundary
Gustavo Fernández-Torres
2015-01-01
Full Text Available A geometric modification to the Newton-Secant method to obtain the root of a nonlinear equation is described and analyzed. With the same number of evaluations, the modified method converges faster than Newton’s method and the convergence order of the new method is 1+2≈2.4142. The numerical examples and the dynamical analysis show that the new method is robust and converges to the root in many cases where Newton’s method and other recently published methods fail.
A Newton--Galerkin Method for Fluid Flow Exhibiting Uncertain Periodic Dynamics
Schick, M.
2014-01-01
The determination of stable limit-cycles plays an important role in quantifying the characteristics of dynamical systems. In practice, exact knowledge of model parameters is rarely available leading to parameter uncertainties, which can be modeled as an input of random variables. This has the effect that the limit-cycles become stochastic themselves, resulting in almost surely time-periodic solutions with a stochastic period. In this paper we introduce a novel numerical method for the computation of stable stochastic limit-cycles based on the spectral stochastic finite element method using polynomial chaos (PC). We are able to overcome the difficulties of PC regarding its well-known convergence breakdown for long term integration. To this end, we introduce a stochastic time scaling which treats the stochastic period as an additional random variable and controls the phase-drift of the stochastic trajectories, keeping the necessary PC order low. Based on the rescaled governing equations, we aim at determining an initial condition and a period such that the trajectories close after completion of one stochastic cycle. Furthermore, we verify the numerical method by computation of a vortex shedding of a flow around a circular domain with stochastic inflow boundary conditions as a benchmark problem. The results are verified by comparison to purely deterministic reference problems and demonstrate high accuracy up to machine precision in capturing the stochastic variations of the limit-cycle.
A Newton-Raphson Method Approach to Adjusting Multi-Source Solar Simulators
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.
The XMM-Newton Serendipitous Survey. VI. The Second XMM-Newton Serendipitous Source Catalogue
Watson, M G; Fyfe, D; Page, C G; Lamer, G; Mateos, S; Pye, J; Sakano, M; Rosen, S; Ballet, J; Barcons, X; Barret, D; Boller, T; Brunner, H; Brusa, M; Caccianiga, A; Carrera, F J; Ceballos, M; Della Ceca, R; Denby, M; Denkinson, G; Dupuy, S; Farrell, S; Fraschetti, F; Freyberg, M J; Guillout, P; Hambaryan, V; MacCacaro, T; Mathiesen, B; McMahon, R; Michel, L; Motch, C; Osborne, J P; Page, M; Pakull, M W; Pietsch, W; Saxton, R; Schwope, A; Severgnini, P; Simpson, M; Sironi, G; Stewart, G; Stewart, I M; Stobbart, A-M; Tedds, J; Warwick, R; Webb, N; West, R; Worrall, D; Yuan, W
2008-01-01
Aims: Pointed observations with XMM-Newton provide the basis for creating catalogues of X-ray sources detected serendipitously in each field. This paper describes the creation and characteristics of the 2XMM catalogue. Methods: The 2XMM catalogue has been compiled from a new processing of the XMM-Newton EPIC camera data. The main features of the processing pipeline are described in detail. Results: The catalogue, the largest ever made at X-ray wavelengths, contains 246,897 detections drawn from 3491 public XMM-Newton observations over a 7-year interval, which relate to 191,870 unique sources. The catalogue fields cover a sky area of more than 500 sq.deg. The non-overlapping sky area is ~360 sq.deg. (~1% of the sky) as many regions of the sky are observed more than once by XMM-Newton. The catalogue probes a large sky area at the flux limit where the bulk of the objects that contribute to the X-ray background lie and provides a major resource for generating large, well-defined X-ray selected source samples, stu...
Newton On Absolute Space A Commentary
Adewole, A I A
2001-01-01
Newton seems to have stated a quantitative relationship between the position of a body in relative space and the position of the body in absolute space in the first scholium of his Principia. We show that if this suspected relationship is assumed to hold, it will dispel many errors and misrepresentations that have befallen Newton's ideas on absolute space.
Calder, Lucy
2007-01-01
Dark Energy is currently one of the biggest mysteries in science. In this article the origin of the concept is traced as far back as Newton and Hooke in the seventeenth century. Newton considered, along with the inverse square law, a force of attraction that varies linearly with distance. A direct link can be made between this term and Einstein's cosmological constant, Lambda, and this leads to a possible relation between Lambda and the total mass of the universe. Mach's influence on Einstein is discussed and the convoluted history of Lambda throughout the last ninety years is coherently presented.
Modified two-grid method for solving coupled Navier-Stokes/Darcy model based on Newton iteration
SHEN Yu-jing; HAN Dan-fu; SHAO Xin-ping
2015-01-01
A new decoupled two-gird algorithm with the Newton iteration is proposed for solving the coupled Navier-Stokes/Darcy model which describes a fluid flow filtrating through porous media. Moreover the error estimate is given, which shows that the same order of accuracy can be achieved as solving the system directly in the fine mesh when h=H2. Both theoretical analysis and numerical experiments illustrate the eﬃ ciency of the algorithm for solving the coupled problem.
Connor, Thomas; Sun, Ming; Hoekstra, Henk; Mahdavi, Andisheh; Conselice, Christopher J; McNamara, Brian
2014-01-01
We present new X-ray temperatures and improved X-ray luminosity estimates for 15 new and archival XMM-Newton observations of galaxy clusters at intermediate redshift with mass and luminosities near the galaxy group/cluster division (M2500 < $2.4\\times 10^{14} h_{70}^{-1} M_\\odot$, L < $2\\times 10^{44}$ erg $s^{-1}$, 0.3< z < 0.6). These clusters have weak-lensing mass measurements based on Hubble Space Telescope observations of clusters representative of an X-ray selected sample (the ROSAT 160SD survey). The angular resolution of XMM-Newton allows us to disentangle the emission of these galaxy clusters from nearby point sources, which significantly contaminated previous X-ray luminosity estimates for six of the fifteen clusters. We extend cluster scaling relations between X-ray luminosity, temperature, and weak-lensing mass for low-mass, X-ray-selected clusters out to redshift $\\approx$0.45. These relations are important for cosmology and the astrophysics of feedback in galaxy groups and clusters....
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.
Programming for the Newton software development with NewtonScript
McKeehan, Julie
1994-01-01
Programming for the Newton: Software Development with NewtonScript focuses on the processes, approaches, operations, and principles involved in software development with NewtonScript.The publication first elaborates on Newton application design, views on the Newton, and protos. Discussions focus on system protos, creating and using user protos, linking and naming templates, creating the views of WaiterHelper, Newton application designs, and life cycle of an application. The text then elaborates on the fundamentals of NewtonScript, inheritance in NewtonScript, and view system and messages. Topi
Experiments with "Newton's Cradle."
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)
A modified global Newton solver for viscous-plastic sea ice models
Mehlmann, C.; Richter, T.
2017-08-01
We present and analyze a modified Newton solver, the so called operator-related damped Jacobian method, with a line search globalization for the solution of the strongly nonlinear momentum equation in a viscous-plastic (VP) sea ice model.Due to large variations in the viscosities, the resulting nonlinear problem is very difficult to solve. The development of fast, robust and converging solvers is subject to present research. There are mainly three approaches for solving the nonlinear momentum equation of the VP model, a fixed-point method denoted as Picard solver, an inexact Newton method and a subcycling procedure based on an elastic-viscous-plastic model approximation. All methods tend to have problems on fine meshes by sharp structures in the solution. Convergence rates deteriorate such that either too many iterations are required to reach sufficient accuracy or convergence is not obtained at all.To improve robustness globalization and acceleration approaches, which increase the area of fast convergence, are needed. We develop an implicit scheme with improved convergence properties by combining an inexact Newton method with a Picard solver. We derive the full Jacobian of the viscous-plastic sea ice momentum equation and show that the Jacobian is a positive definite matrix, guaranteeing global convergence of a properly damped Newton iteration. We compare our modified Newton solver with line search damping to an inexact Newton method with established globalization and acceleration techniques. We present a test case that shows improved robustness of our new approach, in particular on fine meshes.
Quapp, Wolfgang; Kraka, Elfi; Cremer, Dieter
2007-11-08
A method for finding a transition state (TS) between a reactant minimum and a quasi-flat, high dissociation plateau on the potential energy surface is described. The method is based on the search of a growing string (GS) along reaction pathways defined by different Newton trajectories (NT). Searches with the GS-NT method always make it possible to identify the TS region because monotonically increasing NTs cross at the TS or, if not monotonically increasing, possess turning points that are located in the TS region. The GS-NT method is applied to quasi-barrierless and truly barrierless chemical reactions. Examples are the dissociation of methylenecyclopropene to acetylene and vinylidene, for which a small barrier far out in the exit channel is found, and the cycloaddition of singlet methylene and ethene, which is barrierless for a broad reaction channel with Cs-symmetry reminiscent of a mountain cirque formed by a glacier.
Isaac Newton's sinister heraldry
Jenkins, Alejandro
2013-01-01
After Isaac Newton was knighted by Queen Anne in 1705 he adopted an unusual coat of arms: a pair of human tibiae crossed on a black background, like a pirate flag without the skull. After some general reflections on Newton's monumental scientific achievements and on his rather enigmatic life, we investigate the story behind his coat of arms. We also discuss how that simple heraldic design illustrates the concept of chirality, which would later play an important role in the philosophical arguments about Newton's conception of space, as well as in the development of modern chemistry and particle physics.
May, Andrew
2015-01-01
Isaac Newton had an extraordinary idea. He believed the physical universe and everything in it could be described in exact detail using mathematical relationships. He formulated a law of gravity that explained why objects fall downwards, how the moon causes the tides, and why planets and comets orbit the sun. While Newton's work has been added to over the years, his basic approach remains at the heart of the scientific worldview. Yet Newton's own had little in common with that of a modern scientist. He believed the universe was created to a precise and rational design - a design that was fully
Asgharzadeh, Hafez; Borazjani, Iman
2017-02-01
The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for non-linear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form a preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the
Zinoviev, Yury M
2012-01-01
The equations of the relativistic causal Newton gravity law for the planets of the solar system are studied in the approximation when the Sun rests at the coordinates origin and the planets do not iteract between each other.
Hall, Alfred Rupert
1982-01-01
The near century (1630–1720) that separates the important astronomical findings of Galileo Galilei (1564–1642) and the vastly influential mathematical work of Sir Isaac Newton (1642–1727) represents a pivotal stage of transition in the history of science. Tracing the revolution in physics initiated by Galileo and culminating in Newton's achievements, this book surveys the work of Huygens, Leeuwenhoek, Boyle, Descartes, and others. 35 illustrations.
Bretaudeau, F.; Metivier, L.; Brossier, R.; Virieux, J.
2013-12-01
Traveltime tomography algorithms generally use ray tracing. The use of rays in tomography may not be suitable for handling very large datasets and perform tomography in very complex media. Traveltime maps can be computed through finite-difference approach (FD) and avoid complex ray-tracing algorithm for the forward modeling (Vidale 1998, Zhao 2004). However, rays back-traced from receiver to source following the gradient of traveltime are still used to compute the Fréchet derivatives. As a consequence, the sensitivity information computed using back-traced rays is not numerically consistent with the FD modeling used (the derivatives are only a rough approximation of the true derivatives of the forward modeling). Leung & Quian (2006) proposed a new approach that avoid ray tracing where the gradient of the misfit function is computed using the adjoint-state method. An adjoint-state variable is thus computed simultaneously for all receivers using a numerical method consistent with the forward modeling, and for the computational cost of one forward modeling. However, in their formulation, the receivers have to be located at the boundary of the investigated model, and the optimization approach is limited to simple gradient-based method (i.e. steepest descent, conjugate gradient) as only the gradient is computed. However, the Hessian operator has an important role in gradient-based reconstruction methods, providing the necessary information to rescale the gradient, correct for illumination deficit and remove artifacts. Leung & Quian (2006) uses LBFGS, a quasi-Newton method that provides an improved estimation of the influence of the inverse Hessian. Lelievre et al. (2011) also proposed a tomography approach in which the Fréchet derivatives are computed directly during the forward modeling using explicit symbolic differentiation of the modeling equations, resulting in a consistent Gauss-Newton inversion. We are interested here in the use of a new optimization approach
Ducheyne, Steffen
2017-03-29
In this paper I will probe into Herman Boerhaave's (1668-1738) appropriation of Isaac Newton's natural philosophy. It will be shown that Newton's work served multiple purposes in Boerhaave's oeuvre, for he appropriated Newton's work differently in different contexts and in different episodes in his career. Three important episodes in, and contexts of, Boerhaave's appropriation of Newton's natural philosophical ideas and methods will be considered: 1710-11, the time of his often neglected lectures on the place of physics in medicine; 1715, when he delivered his most famous rectorial address; and, finally, 1731/2, in publishing his Elementa chemiae. Along the way, I will spell out the implications of Boerhaave's case for our understanding of the reception, or use, of Newton's ideas more generally.
Zeng Ming
2013-09-01
Full Text Available Under the market environment of low carbon, whether renewable energy can obtain the power for sustainable development, promote the goal of the whole society and make money for investors depends on the rational optimization of power investment capacity and achieving power generation resources coordinated scheduling. This study constructs an expansion model of the generation capacity investment taking oligopoly, policy tools, carbon emissions trading right and green certificate system into account and uses the case analysis of the impact of ETS mechanism and the Tradable Green Certificate mechanism on power generation enterprises investment capacity with Newton KKT interior-point method. This study can also provide a strong decision basis for policy making.
NITSOL: A Newton iterative solver for nonlinear systems
Pernice, M. [Univ. of Utah, Salt Lake City, UT (United States); Walker, H.F. [Utah State Univ., Logan, UT (United States)
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.
张华; 焦宝聪
2007-01-01
针对无约束优化问题,将Goldstein非精确线搜索技术引入伪Newton-B族算法.在假设目标函数f(x)二阶连续可微有下界,水平集L={x|f(x)≤f(x(1))]有界的条件下,证明该算法对一般目标函数的全局收敛性,得到一个条件更弱的结论.
González S., Fabio
2015-01-01
La labor de Newton en el campo de la física, una de las piedras angulares en que se fundamenta esta ciencia, se caracteriza por el hecho de que a partir de unos enunciados básicos explica los diversos fenómenos que estudia la mecánica. Entre las grandes contribuciones de Newton se pueden citar: el descubrimiento de la ley de la gravitación universal, el enunciado de las leyes del movimiento, el teorema del binomio, la formulación básica del cálculo diferencial e integral, así-como algunos tra...
Turning around Newton's Second Law
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.
Gauss-Newton Method Full Waveform Inversion Based on GPU Acceleration%基于GPU加速的高斯牛顿法全波形反演
邓哲; 黄慧明; 杨艳
2016-01-01
The Gauss-Newton method for seismic full waveform inversion is extensive computational and time-consuming. The fast parallel platform of CUDA is applied to speed up the program on graphics processing unit (GPU). The time consuming parts of Gauss-Newton method full waveform inversion are waveform forward modeling and matrix multiplication, and they all meet the requirements of parallelism in the algorithm. For the acceleration of the wave forward modeling, we study and implement the finite-difference time-domain (FDTD) method based on CUDA platform; and for matrix multiplication, CUBLAS library with strong ability of calculation is directly used. Implementing the code of different model size on Personal Computer (PC) with GTX650ti GPU to test the speedups, the test shows that the GPU-based code is 10-30 times faster than the CPU-based code and it will perform faster when the model size is bigger. Numerical test of the Overthrust velocity model indicates the time cost is never a question to Guass-Newton method full waveform inversion.%针对高斯牛顿法地震全波形反演计算量大、计算速度慢的问题，采用图形处理器(GPU)对其加速。高斯牛顿法全波形反演耗时主要集中在波形正演模拟和矩阵乘法计算两个方面，而波形正演算法和矩阵乘法计算在算法特性上都满足并行性的要求。对于波形正演模拟的加速，研究并实现了基于CUDA平台的时域有限差分（FDTD）正演算法。对于矩阵乘法的加速，直接使用计算能力很强的CUB⁃LAS库来完成计算。在台式PC上对不同模型大小的反演区域做合成数据反演，所用显卡型号为GTX650ti，程序速度提升10~30倍，且随着模型增大，程序的加速比将进一步提高。二维Overthrust截取模型反演算例表明时间成本已经不再是影响高斯牛顿法全波形反演发展的主要问题。
On Hypherpes corallirostris Newton
Schlegel, H.
1879-01-01
This species was established after a single specimen without indication of the sex. See Newton in Proc. Zol. Soc. London, 1863, p. 85, pl. 13. Crossley collected two other specimens (Sharpe, ibid. 1871, p. 318), and Hartlaub, Vögel Madagascars, 1877, p. 105, mentions a few other specimens existing
Voltaire-Newton... Renversant!
2004-01-01
The encounter, even improbable, between François Marie Arouet, said Voltaire, and Isaac Newton could occur only in Pays de Gex, near his city... It's indeed right above of the accelerator, in Saint-Genis, that the meeting between this two "monsters" of the 18e century took place
2008-01-01
Isaac Newton, besides being the founder of modern physics, was also master of Britain's mint. That is a precedent which many British physicists must surely wish had become traditional. At the moment, money for physics is in short supply in Britain.
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.
求解P0-NCP的-步光滑牛顿法%One-step Smoothing Newton Method for Solving Complementarity Problem with Po- NCP
张丽娜; 谢亚君; 马昌凤
2011-01-01
A nonlinear complementarity problem (denoted by ( NCP(F) ) ) can be reformulated as a nonsmooth equation.Based on a new smoothing function, the problem is approximated by a new smooth equation.The authors present a one-step smoothing Newton method for solving complementarity problem with P0- function.The algorithm is proved to be convergent globally.Some numerical resnlts show that this method is effective.%在将非线性互补问题转化为求解非光滑方程组的基础上,利用一个新的光滑NCP函数,构造新的价值函数,建立了求解P0函数的一步光滑牛顿法.在一定的条件下,证明了该算法的全局收敛性.数值实验表明该算法是有效的.
Transient Newton rings in dielectrics upon fs laser ablation
Garcia-Lechuga, Mario; Hernandez-Rueda, Javier; Solis, Javier
2014-01-01
We report the appearance of transient Newton rings in dielectrics (sapphire and lead-oxide glass) during ablation with single fs laser pulses. Employing femtosecond microscopy with 800 nm excitation and 400 nm illumination, we observe a characteristic ring pattern that dynamically changes for increasing delay times between pump and probe pulse. Such transient Newton rings have been previously observed in metals and semiconductors at fluences above the ablation threshold and were related to optical interference of the probe beam reflected at the front surface of the ablating layer and at the interface of the non-ablating substrate. Yet, it had been generally assumed that this phenomenon cannot be (and has not been) observed in dielectrics due to the different ablation mechanism and optical properties of dielectrics. The fact that we are able to observe them has important consequences for the comprehension of the ablation mechanisms in dielectrics and provides a new method for investigating these mechanisms in ...
Maris, Virginie
An existing 3-D magnetotelluric (MT) inversion program written for a single processor personal computer (PC) has been modified and parallelized using OpenMP, in order to run the program efficiently on a multicore workstation. The program uses the Gauss-Newton inversion algorithm based on a staggered-grid finite-difference forward problem, requiring explicit calculation of the Frechet derivatives. The most time-consuming tasks are calculating the derivatives and determining the model parameters at each iteration. Forward modeling and derivative calculations are parallelized by assigning the calculations for each frequency to separate threads, which execute concurrently. Model parameters are obtained by factoring the Hessian using the LDLT method, implemented using a block-cyclic algorithm and compact storage. MT data from 102 tensor stations over the East Flank of the Coso Geothermal Field, California are inverted. Less than three days are required to invert the dataset for ˜ 55,000 inversion parameters on a 2.66 GHz 8-CPU PC with 16 GB of RAM. Inversion results, recovered from a halfspace rather than initial 2-D inversions, qualitatively resemble models from massively parallel 3-D inversion by other researchers and overall, exhibit an improved fit. A steeply west-dipping conductor under the western East Flank is tentatively correlated with a zone of high-temperature ionic fluids based on known well production and lost circulation intervals. Beneath the Main Field, vertical and north-trending shallow conductors are correlated with geothermal producing intervals as well.
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.
The history of Newton's apple tree
Keesing, R. G.
1998-05-01
This article contains a brief introduction to Newton's early life to put into context the subsequent events in this narrative. It is followed by a summary of accounts of Newton's famous story of his discovery of universal gravitation which was occasioned by the fall of an apple in the year 1665/6. Evidence of Newton's friendship with a prosperous Yorkshire family who planted an apple tree arbour in the early years of the eighteenth century to celebrate his discovery is presented. A considerable amount of new and unpublished pictorial and documentary material is included relating to a particular apple tree which grew in the garden of Woolsthorpe Manor (Newton's birthplace) and which blew down in a storm before the year 1816. Evidence is then presented which describes how this tree was chosen to be the focus of Newton's account. Details of the propagation of the apple tree growing in the garden at Woolsthorpe in the early part of the last century are then discussed, and the results of a dendrochronological study of two of these trees is presented. It is then pointed out that there is considerable evidence to show that the apple tree presently growing at Woolsthorpe and known as 'Newton's apple tree' is in fact the same specimen which was identified in the middle of the eighteenth century and which may now be 350 years old. In conclusion early results from a radiocarbon dating study being carried out at the University of Oxford on core samples from the Woolsthorpe tree lend support to the contention that the present tree is one and the same as that identified as Newton's apple tree more than 200 years ago. Very recently genetic fingerprinting techniques have been used in an attempt to identify from which sources the various 'Newton apple trees' planted throughout the world originate. The tentative result of this work suggests that there are two separate varieties of apple tree in existence which have been accepted as 'the tree'. One may conclude that at least some of
Verlet, Loup
1993-01-01
En 1936, une vente publique ramena au jour le contenu d'une malle où Newton avait enfermé ses manuscrits. Ô surprise, les travaux du savant y voisinaient avec les spéculations de l'exégète et de l'alchimiste. Ce n'est pas seulement la face cachée d'un exceptionnel génie scientifique qui nous était ainsi révélée, mais, au-delà du mystère d'un homme, le secret partage qui gouverne notre univers, comme le montre cette lecture originale de la naissance de la physique moderne.Dans quel monde suis-je tombé ? Pourquoi les choses sont-elles ainsi ? Comment faire avec ? Questions lancinantes de l'enfant quand la mère fait défaut, du chercheur face à la nature qui se dérobe. La réponse, Newton sait où la trouver : Dieu le Père, à jamais insaisissable, est présent «partout et toujours», Il se révèle par la bouche des prophètes, se devine dans les arcanes de l'alchimie, se manifeste par les lois admirables qui règlent le cours ordinaire des choses. Ses écrits de l'ombre l'attestent, Newton ...
Isaac Newton and the astronomical refraction.
Lehn, Waldemar H
2008-12-01
In a short interval toward the end of 1694, Isaac Newton developed two mathematical models for the theory of the astronomical refraction and calculated two refraction tables, but did not publish his theory. Much effort has been expended, starting with Biot in 1836, in the attempt to identify the methods and equations that Newton used. In contrast to previous work, a closed form solution is identified for the refraction integral that reproduces the table for his first model (in which density decays linearly with elevation). The parameters of his second model, which includes the exponential variation of pressure in an isothermal atmosphere, have also been identified by reproducing his results. The implication is clear that in each case Newton had derived exactly the correct equations for the astronomical refraction; furthermore, he was the first to do so.
Eigenvalue Decomposition-Based Modified Newton Algorithm
Wen-jun Wang
2013-01-01
Full Text Available When the Hessian matrix is not positive, the Newton direction may not be the descending direction. A new method named eigenvalue decomposition-based modified Newton algorithm is presented, which first takes the eigenvalue decomposition of the Hessian matrix, then replaces the negative eigenvalues with their absolute values, and finally reconstructs the Hessian matrix and modifies the searching direction. The new searching direction is always the descending direction. The convergence of the algorithm is proven and the conclusion on convergence rate is presented qualitatively. Finally, a numerical experiment is given for comparing the convergence domains of the modified algorithm and the classical algorithm.
2010-05-01
number of papers have reported new methods to prove classic results. For example, Borobia and Canto [5] proved Sinkhorn’s early result on scaling positive...Bloemen Waanders, editors. Large- Scale PDE-Constrained Optimization. Springer, 2003. [5] A. Borobia and R. Canto . Matrix scaling: A geometric proof of
Mahdavi, Andisheh [Department of Physics and Astronomy, San Francisco State University, San Francisco, CA 94131 (United States); Hoekstra, Henk [Leiden Observatory, Leiden University, Niels Bohrweg 2, NL-2333 CA Leiden (Netherlands); Babul, Arif; Bildfell, Chris [Department of Physics and Astronomy, University of Victoria, Victoria, BC V8W 3P6 (Canada); Jeltema, Tesla [Santa Cruz Institute for Particle Physics, UC Santa Cruz, 1156 High Street, Santa Cruz, CA 95064 (United States); Henry, J. Patrick [Institute for Astronomy, 2680 Woodlawn Drive, Honolulu, HI 96822 (United States)
2013-04-20
We present a study of multiwavelength X-ray and weak lensing scaling relations for a sample of 50 clusters of galaxies. Our analysis combines Chandra and XMM-Newton data using an energy-dependent cross-calibration. After considering a number of scaling relations, we find that gas mass is the most robust estimator of weak lensing mass, yielding 15% {+-} 6% intrinsic scatter at r{sub 500}{sup WL} (the pseudo-pressure Y{sub X} yields a consistent scatter of 22% {+-} 5%). The scatter does not change when measured within a fixed physical radius of 1 Mpc. Clusters with small brightest cluster galaxy (BCG) to X-ray peak offsets constitute a very regular population whose members have the same gas mass fractions and whose even smaller (<10%) deviations from regularity can be ascribed to line of sight geometrical effects alone. Cool-core clusters, while a somewhat different population, also show the same (<10%) scatter in the gas mass-lensing mass relation. There is a good correlation and a hint of bimodality in the plane defined by BCG offset and central entropy (or central cooling time). The pseudo-pressure Y{sub X} does not discriminate between the more relaxed and less relaxed populations, making it perhaps the more even-handed mass proxy for surveys. Overall, hydrostatic masses underestimate weak lensing masses by 10% on the average at r{sub 500}{sup WL}; but cool-core clusters are consistent with no bias, while non-cool-core clusters have a large and constant 15%-20% bias between r{sub 2500}{sup WL} and r{sub 500}{sup WL}, in agreement with N-body simulations incorporating unthermalized gas. For non-cool-core clusters, the bias correlates well with BCG ellipticity. We also examine centroid shift variance and power ratios to quantify substructure; these quantities do not correlate with residuals in the scaling relations. Individual clusters have for the most part forgotten the source of their departures from self-similarity.
Newton's Law: Not so Simple after All
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…
BLOCK BASED NEWTON-LIKE BLENDING INTERPOLATION
Qian-jin Zhao; Jie-qing Tan
2006-01-01
Newton's polynomial interpolation may be the favourite linear interpolation in the sense that it is built up by means of the divided differences which can be calculated recursively and produce useful intermediate results. However Newton interpolation is in fact point based interpolation since a new interpolating polynomial with one more degree is obtained by adding a new support point into the current set of support points once at a time. In this paper we extend the point based interpolation to the block based interpolation. Inspired by the idea of the modern architectural design, we first divide the original set of support points into some subsets (blocks), then construct each block by using whatever interpolation means, linear or rational and finally assemble these blocks by Newton's method to shape the whole interpolation scheme. Clearly our method offers many flexible interpolation schemes for choices which include the classical Newton's polynomial interpolation as its special case. A bivariate analogy is also discussed and numerical examples are given to show the effectiveness of our method.
Westfall, Richard S
1994-01-01
Le plus célèbre des savants, Isaac Newton, est aussi celui qui a le plus de biographes. Avant même sa mort, en 1727, l'un d'eux publiait un récit de la vie du grand homme. Richard Westfall, universitaire américain, est aujourd'hui le meilleur connaisseur d'un personnage en tout point extraordinaire, dont Aldous Huxley disait : « En tant qu'homme, c'est un fiasco ; en tant que monstre, il est superbe ! » Découvrant à 24 ans la loi de la gravitation universelle, établissant peu après les lois de l'optique tout en poursuivant des études alchimiques et théologiques, cet homme capable de rester des jours entiers sans manger ni dormir, absorbé par les énigmes du savoir, connaît une grave dépression dont il réchappe de justesse... pour se consacrer à l'économie de son pays : il devient directeur de la Monnaie de Londres, organisant une impitoyable chasse aux faux-monnayeurs ! L'image d'Épinal de Newton regardant une pomme tomber sort enrichie et complexifiée de ce livre fruit d'une vie de reche...
Isaac Newton: Man, Myth, and Mathematics.
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)
Edme Mariotte and Newton's Cradle
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…
Newton's Cradle in Physics Education
Gauld, Colin F.
2006-01-01
Newton's Cradle is a series of bifilar pendulums used in physics classrooms to demonstrate the role of the principles of conservation of momentum and kinetic energy in elastic collisions. The paper reviews the way in which textbooks use Newton's Cradle and points out the unsatisfactory nature of these treatments in almost all cases. The literature…
Edme Mariotte and Newton's Cradle
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…
周长银; 贺国平
2004-01-01
In this paper, two-stage stochastic quadratic programming problems with equality constraints are considered.By Monte Carlo simulation-based approximations of the objective function and its first(second)derivative,an inexact Lagrange-Newton type method is proposed.It is showed that this method is globally convergent with probability one.In particular, the convergence is local superlinear under an integral approximation error bound condition.Moreover, this method can be easily extended to solve stochastic quadratic programming problems with inequality constraints.
Field-Split Preconditioned Inexact Newton Algorithms
Liu, Lulu
2015-06-02
The multiplicative Schwarz preconditioned inexact Newton (MSPIN) algorithm is presented as a complement to additive Schwarz preconditioned inexact Newton (ASPIN). At an algebraic level, ASPIN and MSPIN are variants of the same strategy to improve the convergence of systems with unbalanced nonlinearities; however, they have natural complementarity in practice. MSPIN is naturally based on partitioning of degrees of freedom in a nonlinear PDE system by field type rather than by subdomain, where a modest factor of concurrency can be sacrificed for physically motivated convergence robustness. ASPIN, originally introduced for decompositions into subdomains, is natural for high concurrency and reduction of global synchronization. We consider both types of inexact Newton algorithms in the field-split context, and we augment the classical convergence theory of ASPIN for the multiplicative case. Numerical experiments show that MSPIN can be significantly more robust than Newton methods based on global linearizations, and that MSPIN can be more robust than ASPIN and maintain fast convergence even for challenging problems, such as high Reynolds number Navier--Stokes equations.
Nanowires:inter-connection between newton mechanics and quantum mechanics
无
2007-01-01
Nanowires have been proved to be excellent candidates for future nanodevices for their advantages of being the smallest charge carrier,enabling abundant choice of materials,and related size,surface and quantum effects.Nanowires thus play important role to understand the physical phenomena between macro-scale Newton world and the micro-scale quantum mechanical world. Our group is among the few pioneers in early 1998's in developing methods for synthesis of silicon nanowires,and extending the nanowire synt...
E. A. Venter
1964-03-01
Full Text Available Die geweldige oplewing van die Christelike wetenskaps- gedagte in ons geeslose tyd, is ongetwyfeld ’n haas onverklaar- bare verskynsel. Dwarsdeur die eeue het Christene ook wetenskap beoefen saam met ongelowiges, maar dit was eers in ons leeftyd dat die principia van die Christelike religie ook vrugbaar gemaak is vir die wetenskapsbeoefening. In hierdie verband sal die name van Dooyeweerd, Vollenhoven, Stoker e.a. steeds met eer vermeld word. Natuurlik het belydende Christene ook voorheen wel deeglik saamgewerk aan die gebou van die wetenskap. Die intieme verband tussen religie, wysbegeerte en wetenskaps beoefening is toe egter nog nie suiwer ingesien nie. Uit hier die tydperk dateer die arbeid van sir Isaac Newton.
Spectral Methods for Numerical Relativity
Grandclément, Philippe
2007-01-01
Equations arising in General Relativity are usually to complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled, partial differential, equations. Amongst the possible choices, this paper focuses on a class called spectral methods where, typically, the various functions are expanded onto sets of orthogonal polynomials or functions. A theoretical introduction on spectral expansion is first given and a particular emphasize is put on the fast convergence of the spectral approximation. We present then different approaches to solve partial differential equations, first limiting ourselves to the one-dimensional case, with one or several domains. Generalization to more dimensions is then discussed. In particular, the case of time evolutions is carefully studied and the stability of such evolutions investigated. One then turns to results obtained by various groups in the field of General Relativity by means of spectral methods. First, works which do not involve explicit t...
PEOPLE IN PHYSICS: Newton's apple
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.
Spectral Methods for Numerical Relativity
Grandclément Philippe
2009-01-01
Full Text Available Equations arising in general relativity are usually too complicated to be solved analytically and one must rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses on a class called spectral methods in which, typically, the various functions are expanded in sets of orthogonal polynomials or functions. First, a theoretical introduction of spectral expansion is given with a particular emphasis on the fast convergence of the spectral approximation. We then present different approaches to solving partial differential equations, first limiting ourselves to the one-dimensional case, with one or more domains. Generalization to more dimensions is then discussed. In particular, the case of time evolutions is carefully studied and the stability of such evolutions investigated. We then present results obtained by various groups in the field of general relativity by means of spectral methods. Work, which does not involve explicit time-evolutions, is discussed, going from rapidly-rotating strange stars to the computation of black-hole–binary initial data. Finally, the evolution of various systems of astrophysical interest are presented, from supernovae core collapse to black-hole–binary mergers.
Introducing Newton and classical physics
Rankin, William
2002-01-01
The rainbow, the moon, a spinning top, a comet, the ebb and flood of the oceans ...a falling apple. There is only one universe and it fell to Isaac Newton to discover its secrets. Newton was arguably the greatest scientific genius of all time, and yet he remains a mysterious figure. Written and illustrated by William Rankin, "Introducting Newton and Classical Physics" explains the extraordinary ideas of a man who sifted through the accumulated knowledge of centuries, tossed out mistaken beliefs, and single-handedly made enormous advances in mathematics, mechanics and optics. By the age of 25, entirely self-taught, he had sketched out a system of the world. Einstein's theories are unthinkable without Newton's founding system. He was also a secret heretic, a mystic and an alchemist, the man of whom Edmund Halley said "Nearer to the gods may no man approach!". This is an ideal companion volume to "Introducing Einstein".
[Malthus's Essay and Newton's Principia].
Nakanishi, Y
1989-05-01
The author examines a natural scientific approach to demography using the example of Malthus's "Essay on the Principle of Population." The work is analyzed and compared to Newton's "Philosophiae Naturalis Principia Mathematica."
XMM-Newton publication statistics
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
A tour about Isaac Newton's life
Sparavigna, A C
2012-01-01
Here we propose a tour about the life of Isaac Newton, using a georeferenced method, based on the free satellite maps. Our tour is modelled on the time-line of the great scientist's life, as an ancient "itinerarium" was modelled on the Roman roads, providing a listing of places and intervening distances, sometimes with short description or symbols concerning the places. KML language and Google Earth, with its Street View and 3D images are powerful tools to create this virtual tour.
Conformal methods in general relativity
Valiente Kroon, Juan A
2016-01-01
This book offers a systematic exposition of conformal methods and how they can be used to study the global properties of solutions to the equations of Einstein's theory of gravity. It shows that combining these ideas with differential geometry can elucidate the existence and stability of the basic solutions of the theory. Introducing the differential geometric, spinorial and PDE background required to gain a deep understanding of conformal methods, this text provides an accessible account of key results in mathematical relativity over the last thirty years, including the stability of de Sitter and Minkowski spacetimes. For graduate students and researchers, this self-contained account includes useful visual models to help the reader grasp abstract concepts and a list of further reading, making this the perfect reference companion on the topic.
Numerical relativity and spectral methods
Grandclement, P.
2016-12-01
The term numerical relativity denotes the various techniques that aim at solving Einstein's equations using computers. Those computations can be divided into two families: temporal evolutions on the one hand and stationary or periodic solutions on the other one. After a brief presentation of those two classes of problems, I will introduce a numerical tool designed to solve Einstein's equations: the KADATH library. It is based on the the use of spectral methods that can reach high accuracy with moderate computational resources. I will present some applications about quasicircular orbits of black holes and boson star configurations.
XMM-Newton Publication Statistics
Ness, J -U; Valencic, L A; Smith, R; Loiseau, N; Salama, A; Ehle, M; Schartel, N
2013-01-01
We assessed the scientific productivity and data usage statistics of XMM-Newton by examining 3272 refereed papers published until the end of 2012 that directly use XMM-Newton data. The SAO/NASA Astrophysics Data System (ADS) was accessed for information on each paper including the number of citations. For each paper, the XMM-Newton observation identifiers and instruments were determined and used extract detailed information from the XMM-Newton archive on the parameters of the observations. The information obtained from these sources was then combined to allow the scientific productivity of the mission to be assessed. Since three years after the launch, about 300 refereed papers per year were published that directly use XMM-Newton data. After more than 13 years in operation, this rate shows no decline. Since 2002, around 100 scientists per year have become lead authors for the first time. Each refereed XMM-Newton paper receives around four citations per year in the first few years with a long-term citation rat...
XMM Newton Observations of Toothbrush Cluster
Kara, Sinancan; Nihal Ercan, Enise; De Plaa, Jelle; Mernier, Francois
2016-07-01
Galaxy clusters are the largest gravitationally-bound objects in the universe. The member galaxies are embedded in a hot X-ray emitting Intra-Cluster Medium (ICM) that has been enriched over time with metals produced by supernovae. In this presentation we show new results from XMM-Newton regarding the merging cluster 1RXSJ0603.3+4213. This cluster, also known as the Toothbrush cluster, shows a large toothbrush-shaped radio relic associated with a merger shock North of the cluster core. We show the distribution and the abundances of the metals in this merging cluster in relation to the merger shock. The results are derived from spatially resolved X-ray spectra from the EPIC instrument aboard XMM-Newton.
The Unknown Detective Career of Isaac Newton
Levenson, Thomas (MIT)
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.
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.
Groping Toward Linear Regression Analysis: Newton's Analysis of Hipparchus' Equinox Observations
Belenkiy, Ari
2008-01-01
In 1700, Newton, in designing a new universal calendar contained in the manuscripts known as Yahuda MS 24 from Jewish National and University Library at Jerusalem and analyzed in our recent article in Notes & Records Royal Society (59 (3), Sept 2005, pp. 223-54), attempted to compute the length of the tropical year using the ancient equinox observations reported by a famous Greek astronomer Hipparchus of Rhodes, ten in number. Though Newton had a very thin sample of data, he obtained a tropical year only a few seconds longer than the correct length. The reason lies in Newton's application of a technique similar to modern regression analysis. Actually he wrote down the first of the two so-called "normal equations" known from the Ordinary Least Squares method. Newton also had a vague understanding of qualitative variables. This paper concludes by discussing open historico-astronomical problems related to the inclination of the Earth's axis of rotation. In particular, ignorance about the long-range variation...
Alquimia: Isaac Newton revisitado Alchemy: Isaac Newton Revisited
Reginaldo Carmello Corrêa de Moraes
1997-01-01
Full Text Available Nota sobre publicações recentes que revelam aspectos pouco conhecidos da biblioteca de Newton - os numerosos textos religiosos, místicos e herméticos. Os biógrafos de Newton resistiram muito até admitir que os escritos esotéricos fossem genuíno interesse do sábio e que tivessem importância para entender sua trajetória intelectual. As publicações aqui indicadas afirmam o contrário, seguindo trilha aberta por ensaio pioneiro de J. M. Keynes (1946.A note on recent books about an unexplored side of Newtons library: religious, mystical and hermetic texts. Newton's biographers had resisted so much to believe that esoteric writings were in Newtons field of interest. Even if they recognized that, they didn't believe those strange works were important elements to understand his intellectual trajectory. The studies we mention here are saying just the opposite thing, exploring the way opened by the pioneer essay of J. M. Keynes (1946.
Astronomical arguments in Newton's Chronology
Naze, Yael
2012-01-01
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.
赵东东; 张钱江; 戴世坤; 陈龙伟; 李昆
2015-01-01
从二维线源问题出发，对二维直流电阻率法高效、高精度正反演方法进行研究。在正演数值模拟中，引入直接解法求解器求解线性方程组，既保证了起伏地形条件下有限元法正演数值模拟的计算精度和计算效率，又为反演算法中“拟正演”快速回代求解提供了条件。结合高效、高精度的正演算法，采用高斯牛顿法对电阻率进行反演成像。在弱非均匀介质前提下，基于近似海森矩阵主对角线元素严格占优的特点，采用舍弃海森矩阵非对角线元素的策略，提高整个反演计算的效率。最后，利用合成数据对反演算法的有效性进行检验。结果表明：给出的反演算法稳定、快速，结合偶极−偶极装置和三极装置，能有效地反演出异常体的形状、大小和位置。%Fast and high-precision inversion method for two-dimensional line source problem was studied. In the forward numerical simulation, linear equations solver was applied for direct solution, which not only improved the precision and the speed of numerical simulation of finite element method in the case of rugged topography, but also provided conditions for the “quasi forward” fast back substitution solution in the inversion algorithm. Combined with high efficient simulation method, Gauss-Newton method was adopted for inversion of resistivity. In the case of low inhomogeneity, the main diagonal elements of the approximated Hessen matrix possessed priority than others. Based on this, non-diagonal elements were deleted when Gauss-Newton iterative equations were solved. The whole process of inversion was made more efficient by this scheme. Finally, synthetic data were used to test the validity of the presented inversion method. The results show that the inversion method is stable and fast. Combine with dipole-dipole and pole-dipole arrays, the shape, size and the location of the anomalous body can be reflected
Resolving galaxy cluster gas properties at z ∼ 1 with XMM-Newton and Chandra
Bartalucci, I.; Arnaud, M.; Pratt, G. W.; Démoclès, J.; van der Burg, R. F. J.; Mazzotta, P.
2017-02-01
Massive, high-redshift, galaxy clusters are useful laboratories to test cosmological models and to probe structure formation and evolution, but observations are challenging due to cosmological dimming and angular distance effects. Here we present a pilot X-ray study of the five most massive (M500 > 5 × 1014M⊙), distant (z 1), clusters detected via the Sunyaev-Zel'Dovich effect. We optimally combine XMM-Newton and Chandra X-ray observations by leveraging the throughput of XMM-Newton to obtain spatially-resolved spectroscopy, and the spatial resolution of Chandra to probe the bright inner parts and to detect embedded point sources. Capitalising on the excellent agreement in flux-related measurements, we present a new method to derive the density profiles, which are constrained in the centre by Chandra and in the outskirts by XMM-Newton. We show that the Chandra-XMM-Newton combination is fundamental for morphological analysis at these redshifts, the Chandra resolution being required to remove point source contamination, and the XMM-Newton sensitivity allowing higher significance detection of faint substructures. Measuring the morphology using images from both instruments, we found that the sample is dominated by dynamically disturbed objects. We use the combined Chandra-XMM-Newton density profiles and spatially-resolved temperature profiles to investigate thermodynamic quantities including entropy and pressure. From comparison of the scaled profiles with the local REXCESS sample, we find no significant departure from standard self-similar evolution, within the dispersion, at any radius, except for the entropy beyond 0.7 R500. The baryon mass fraction tends towards the cosmic value, with a weaker dependence on mass than that observed in the local Universe. We make a comparison with the predictions from numerical simulations. The present pilot study demonstrates the utility and feasibility of spatially-resolved analysis of individual objects at high-redshift through
Newton's apple Isaac Newton and the English scientific renaissance
Aughton, Peter
2003-01-01
In the aftermath of the English Civil War, the Restoration overturned England's medieval outlook and a new way of looking at the world allowed the genius of Isaac Newton (b. 1642) and his contemporaries to flourish. Newton had a long and eventful life apart from his scentific discoveries. He was born at the beginnings of the Civil War, his studies were disrupted by the twin disasters of the Great Plague and the Fire of London; a brilliant and enigmatic genius, Newton dabbled in alchemy, wrote over a million words on the Bible, quarrelled with his contemporaries and spent his last years as Master of the Royal Mint as well as President of the Royal Society. This book sets Newton's life and work against this dramatic intellectual rebirth; among his friends and contemporaries were Samuel Pepys, the colourful diarist, John Evelyn, the eccentric antiquarian, the astronomers Edmund Halley and John Flamsteed, and Christopher Wren, the greatest architect of his age. They were all instrumental in the founding of the Ro...
侯蕊
2015-01-01
In view of the traditional destructive method for measuring the refractive index of spectacle lenses, a non-destructive method was proposed by measuring the lens’ transmittance and fitting the curve by Gauss-Newton iterative method. The experimental results showed that the non-destructive method could measure the refractive index quickly, and the relative error was less than±1%, and the measurement accuracy could basically met the judgement of the lens refractive index.%针对传统测量眼镜镜片折射率的有损方法，提出通过测量眼镜镜片透射比，采用高斯牛顿迭代法拟合透射比曲线来无损检测眼镜镜片基底折射率。实验结果表明，此无损检测方法可快速检测镜片折射率，测量相对误差不超过±1%，基本满足对镜片折射率区间的判定。
MODIFIED NEWTON'S ALGORITHM FOR COMPUTING THE GROUP INVERSES OF SINGULAR TOEPLITZ MATRICES
Jian-feng Cai; Michael K.Ng; Yi-min Wei
2006-01-01
Newton's iteration is modified for the computation of the group inverses of singular Toeplitz matrices. At each iteration,the iteration matrix is approximated by a matrix with a low displacement rank. Because of the displacement structure of the iteration matrix,the matrix-vector multiplication involved in Newton's iteration can be done efficiently. We show that the convergence of the modified Newton iteration is still very fast. Numerical results are presented to demonstrate the fast convergence of the proposed method.
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.
Black Hole Results from XMM-Newton
Norbert Schartel
2014-12-01
Full Text Available XMM-Newton is one of the most successful science missions of the European Space Agency. Since 2003 every year about 300 articles are published in refereed journals making directly use of XMM-Newton data. All XMM-Newton calls for observing proposals are highly oversubscribed by factors of six and more. In the following some scientic highlights of XMM-Newton observations of black holes are summarized.
Newton's Law of Cooling Revisited
Vollmer, M.
2009-01-01
The cooling of objects is often described by a law, attributed to Newton, which states that the temperature difference of a cooling body with respect to the surroundings decreases exponentially with time. Such behaviour has been observed for many laboratory experiments, which led to a wide acceptance of this approach. However, the heat transfer…
POEMS in Newton's Aerodynamic Frustum
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…
Atomism from Newton to Dalton.
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)
POEMS in Newton's Aerodynamic Frustum
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…
Six roads from Newton great discoveries in physics
Speyer, Edward
1994-01-01
Why is time relative to the observer? Can an atomic particle exist in two places at once? Is light a wave, a particle, or both? Six Roads from Newton is a lively tour through six monumental developments in physics since Newton: wave theory, field theory, statistical physics, special relativity, quantum theory, and general relativity. Together these crucial discoveries formed the basis of the modern revolution in physics, shattering Newton's view of the universe, and leading the way to the mind-boggling and fascinating questions at the cutting edge of physics today. With real-world examples that bring physics vividly to life, Edward Speyer explains each theoretical development, in-troducing the leading figures, their famous experiments, and a number of delightfully perplexing problems that have challenged physicists along the way--from the Paradox of the Three Polarizers to Maxwell's Demon and the infamous case of Schrodinger's Cat.
Accelerating Inexact Newton Schemes for Large Systems of Nonlinear Equations
Fokkema, D.R.; Sleijpen, G.L.G.; Vorst, H.A. van der
1998-01-01
Classical iteration methods for linear systems, such as Jacobi iteration, can be accelerated considerably by Krylov subspace methods like GMRES. In this paper, we describe how inexact Newton methods for nonlinear problems can be accelerated in a similar way and how this leads to a general framework
Gutierrez, V.; Roeorp, R.; Carsi, M.; Ruano, O. A.
2013-07-01
A new numerical algorithm has been developed, based on Newton's method, for optimizing the parameters of a new strain dependent constitutive equation, based on the Garofalo equation. The adjustment is direct, with second order algorithms, for an equation derived from that of Garofalo with a nonlinear objective function. This new optimization algorithm has been applied to creep data of two magnesium alloys AZ80 and AZ61, having an unusual plastic behavior. A certain pseudo-stationary exists in the curves studied, in the sense that the usual deformation states are not manifested in an obvious way. The parameters of the new constitutive equation, dependent on strain, have been determined for these alloys. For analyzing the precision of the parameters and the accuracy of modeling of the stress-strain curves, a statistical treatment has been applied which allows assessing the quality of the constitutive equation proposed and the consistency of these parameters. Stress-strain curves have been compared with the modeling results, reaching a good agreement between the experimental data and the resulting modeling. (Author)
Student conception and perception of Newton's law
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.
Classical mechanics from Newton to Einstein : a modern introduction
McCall, Martin
2011-01-01
This new edition of Classical Mechanics, aimed at undergraduate physics and engineering students, presents in a user-friendly style an authoritative approach to the complementary subjects of classical mechanics and relativity. The text starts with a careful look at Newton's Laws, before applying them in one dimension to oscillations and collisions. More advanced applications - including gravitational orbits and rigid body dynamics - are discussed after the limitations of Newton's inertial frames have been highlighted through an exposition of Einstein's Special Relativity. Examples gi
Deep XMM-Newton observation of the η Chamaleontis cluster
López-Santiago, J.; Albacete Colombo, J. F.; López-García, M. A.
2010-12-01
Context. The members of the η Chamaleontis cluster are in an evolutionary stage in which disks are rapidly evolving. It also exhibits some peculiarities, such as the large fraction of binaries and accretion disks, probably related to the cluster formation process. Its proximity makes this stellar group an ideal target for studying the relation between X-ray emission and those stellar parameters. Aims: Our main objective is to determine the general X-ray properties of the cluster members in terms of coronal temperature, column density, emission measure, X-ray luminosity, and variability. We also aim to establish the relation between the X-ray luminosity of these stars and other stellar parameters, such as effective temperature, binarity, and the presence of accretion disks. Finally, a study of flare energies in each flare event detected during the observations and their relation with some stellar parameters is also performed. Methods: We used proprietary data from a deep XMM-Newton EPIC observation targeting the core of the η Chamaleontis cluster. Specific software for the reduction of XMM-Newton data was used to analyze our observation. To detect sources in the composed EPIC pn+mos image, we used the wavelet-based code PWDetect. General coronal properties were derived from plasma model fitting. X-ray light curves in the 0.3-8.0 keV energy range were generated for each star. Results: We determine both the coronal properties and variability of the η Chamaleontis members in the XMM-Newton EPIC field-of-view. A total of six flare-like events are clearly detected in five different stars. For them, we derived coronal properties during the flare events and pseudo-quiescent state separately. In our observations, stars that experienced a flare event have higher X-ray luminosities in the pseudo-quiescent state than cluster members of similar spectral type that exhibit no evidence of flaring independently of whether they have an accretion disk or not. Observed flare
Nesseris, Savvas; Davis, Tamara; Parkinson, David
2011-01-01
We constrain the evolution of Newton's constant using the growth rate of large-scale structure measured by the WiggleZ Dark Energy Survey in the redshift range $0.1 < z < 0.9$. We use this data in two ways. Firstly we constrain the matter density of the Universe, $\\Omega_m$ (assuming General Relativity), and use this to construct a diagnostic to detect the presence of an evolving Newton's constant. Secondly we directly measure the evolution of Newton's constant, $G_{eff}$, that appears in Modified Gravity theories, without assuming General Relativity to be true. The novelty of these approaches are that, contrary to other methods, they do not require knowledge of the expansion history of the Universe, $H(z)$, making them model independent tests. Our constraints for the second derivative of Newton's constant at the present day, assuming it is slowly evolving as suggested by Big Bang Nucleosynthesis constraints, using the WiggleZ data is $\\ddotGeff(t_0)=-1.19\\pm 0.95\\cdot 10^{-20}h^2 yr^{-2}$, where $h$ is...
Hooke, orbital motion, and Newton's Principia
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.
Newton's Principia: Myth and Reality
Smith, George
2016-03-01
Myths about Newton's Principia abound. Some of them, such as the myth that the whole book was initially developed using the calculus and then transformed into a geometric mathematics, stem from remarks he made during the priority controversy with Leibniz over the calculus. Some of the most persistent, and misleading, arose from failures to read the book with care. Among the latter are the myth that he devised his theory of gravity in order to explain the already established ``laws'' of Kepler, and that in doing so he took himself to be establishing that Keplerian motion is ``absolute,'' if not with respect to ``absolute space,'' then at least with respect to the fixed stars taken as what came later to be known as an inertial frame. The talk will replace these two myths with the reality of what Newton took himself to have established.
The Reception of Newton's Principia
Nauenberg, Michael
2015-01-01
Newton's Principia, when it appeared in 1687, was received with the greatest admiration, not only by the foremost mathematicians and astronomers in Europe, but also by philosophers like Voltaire and Locke and by members of the educated public. In this account I describe some of the controversies that it provoked, and the impact it had during the next century on the development of celestial mechanics, and the theory of gravitation.
The XMM-Newton serendipitous survey. VII. The third XMM-Newton serendipitous source catalogue
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
The Riemann hypothesis illuminated by the Newton flow of ζ
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.
Exotic Newton-Hooke group, noncommutative plane and superconformal symmetry
Alvarez, Pedro D
2009-01-01
In this thesis we have studied some systems with exotic symmetries, which are a peculiarity in 2+1 space-time dimensions. Coded in the exotic structure appears noncommutative coordinates and a phases structure. This kind of systems has attracted attention from different areas of physics independently. Among them we can mention: theory of ray representations of Lie groups, anyons physics, some condensed matter systems, for instance the quantum Hall effect, planar gauge and gravitation theories, noncommutative field theory, noncommutative geometry and noncommutative quantum mechanics. We will focus our study in some topics on exotic nonrelativistic symmetries, such as the exotic Newton-Hooke group, the relation between the systems of exotic Newton-Hooke and the noncommutative Landau problem and the symmetries of noncommutative Landau problem, its conformal and supersymmetric extensions. The exotic Newton-Hooke group correspond to the nonrelativistic limit of the de Sitter groups, and has as a particular case (f...
Preconditioned Inexact Newton for Nonlinear Sparse Electromagnetic Imaging
Desmal, Abdulla
2014-05-04
Newton-type algorithms have been extensively studied in nonlinear microwave imaging due to their quadratic convergence rate and ability to recover images with high contrast values. In the past, Newton methods have been implemented in conjunction with smoothness promoting optimization/regularization schemes. However, this type of regularization schemes are known to perform poorly when applied in imagining domains with sparse content or sharp variations. In this work, an inexact Newton algorithm is formulated and implemented in conjunction with a linear sparse optimization scheme. A novel preconditioning technique is proposed to increase the convergence rate of the optimization problem. Numerical results demonstrate that the proposed framework produces sharper and more accurate images when applied in sparse/sparsified domains.
Preconditioned Inexact Newton for Nonlinear Sparse Electromagnetic Imaging
Desmal, Abdulla
2014-01-06
Newton-type algorithms have been extensively studied in nonlinear microwave imaging due to their quadratic convergence rate and ability to recover images with high contrast values. In the past, Newton methods have been implemented in conjunction with smoothness promoting optimization/regularization schemes. However, this type of regularization schemes are known to perform poorly when applied in imagining domains with sparse content or sharp variations. In this work, an inexact Newton algorithm is formulated and implemented in conjunction with a linear sparse optimization scheme. A novel preconditioning technique is proposed to increase the convergence rate of the optimization problem. Numerical results demonstrate that the proposed framework produces sharper and more accurate images when applied in sparse/sparsified domains.
Demonstrating Kinematics and Newton's Laws in a Jump
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…
Visualizing and Understanding the Components of Lagrange and Newton Interpolation
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.
Conformal Newton-Hooke algebras, Niederer's transformation and Pais-Uhlenbeck oscillator
Andrzejewski, K
2014-01-01
Dynamical systems invariant under the action of the l-conformal Newton-Hooke algebras are constructed by the method of nonlinear realizations. The relevant first order Lagrangians together with the corresponding Hamiltonians are found. The relation to the Galajinsky and Masterov [Phys. Lett. B 723 (2013) 190] approach as well as the higher derivatives formulation is discussed. The generalized Niederer's transformation are presented which relate the systems under consideration to those invariant under the action of the l-conformal Galilei algebra [Nucl. Phys. B 876 (2013) 309]. As a nice application of these results an analogue of Niederer's transformation, on the Hamiltonian level, for the Pais-Uhlenbeck oscillator is constructed.
Paty,Michel
1995-01-01
Repris dans Encyclopaedia Universalis, Dictionnaire des Philosophes, Encyclopaedia Universalis/ Albin Michel, Paris, 1998, p.1111-1118 ; repris dans Encyclopaedia Universalis, Dictionnaire de l'Astronomie, Encyclopaedia Universalis/ Albin Michel, Paris, 1999, p.642-650; L'article sur Isaac Newton (1642-1727) se décompose ainsi :Introduction1- Biographie2- 1676 : l'annus mirabilis3- L'oeuvre mathématique et le calcul des fluxions4- L'optique5- La gravitation universelle et les Principia6- La p...
Glendinning, Paul
2011-12-01
Newton's cradle for two balls with Hertzian interactions is considered as a hybrid system, and this makes it possible to derive return maps for the motion between collisions in an exact form despite the fact that the three-halves interaction law cannot be solved in closed form. The return maps depend on a constant whose value can only be determined numerically, but solutions can be written down explicitly in terms of this parameter, and we compare this with the results of simulations. The results are in fact independent of the details of the interaction potential.
The Schr\\"odinger-Newton equations beyond Newton
Manfredi, Giovanni
2014-01-01
The scope of this paper is twofold. First, we derive rigorously a low-velocity and Galilei-covariant limit of the gravitoelectromagnetic (GEM) equations. Subsequently, these reduced GEM equations are coupled to the Schr\\"odinger equation with gravitoelectric and gravitomagnetic potentials. The resulting extended Schr\\"odinger-Newton equations constitute a minimal model where the three fundamental constants of nature ($G$, $\\hbar$, and $c$) appear naturally. We show that the relativistic correction coming from the gravitomagnetic potential scales as the ratio of the mass of the system to the Planck mass, and that it reinforces the standard Newtonian (gravitoelectric) attraction. The theory is further generalized to many particles through a Wigner function approach.
Happy Balls, Unhappy Balls, and Newton's Cradle
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).
A new Newton's law of cooling?
Kleiber, M
1972-12-22
Several physiologists confuse Fourier's law of animal heat flow with Newton's law of cooling. A critique of this error in 1932 remained ineffective. In 1969 Molnar tested Newton's cooling law. In 1971 Strunk found Newtonian cooling unrealistic for animals. Unfortunately, he called the Fourier formulation of animal heat flow, requiring post-Newtonian observations, a "contemporary Newtonian law of cooling."
3, 2, 1 ... Discovering Newton's Laws
Lutz, Joe; Sylvester, Kevin; Oliver, Keith; Herrington, Deborah
2017-01-01
"For every action there is an equal and opposite reaction." "Except when a bug hits your car window, the car must exert more force on the bug because Newton's laws only apply in the physics classroom, right?" Students in our classrooms were able to pick out definitions as well as examples of Newton's three laws; they could…
Happy Balls, Unhappy Balls, and Newton's Cradle
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).
Methods of modelling relative growth rate
Arne Pommerening; Anders Muszta
2015-01-01
Background:Analysing and modelling plant growth is an important interdisciplinary field of plant science. The use of relative growth rates, involving the analysis of plant growth relative to plant size, has more or less independently emerged in different research groups and at different times and has provided powerful tools for assessing the growth performance and growth efficiency of plants and plant populations. In this paper, we explore how these isolated methods can be combined to form a consistent methodology for modelling relative growth rates. Methods:We review and combine existing methods of analysing and modelling relative growth rates and apply a combination of methods to Sitka spruce (Picea sitchensis (Bong.) Carr.) stem-analysis data from North Wales (UK) and British Douglas fir (Pseudotsuga menziesi (Mirb.) Franco) yield table data. Results:The results indicate that, by combining the approaches of different plant-growth analysis laboratories and using them simultaneously, we can advance and standardise the concept of relative plant growth. Particularly the growth multiplier plays an important role in modelling relative growth rates. Another useful technique has been the recent introduction of size-standardised relative growth rates. Conclusions:Modelling relative growth rates mainly serves two purposes, 1) an improved analysis of growth performance and efficiency and 2) the prediction of future or past growth rates. This makes the concept of relative growth ideally suited to growth reconstruction as required in dendrochronology, climate change and forest decline research and for interdisciplinary research projects beyond the realm of plant science.
Methods of modelling relative growth rate
Arne Pommerening
2015-03-01
Full Text Available Background Analysing and modelling plant growth is an important interdisciplinary field of plant science. The use of relative growth rates, involving the analysis of plant growth relative to plant size, has more or less independently emerged in different research groups and at different times and has provided powerful tools for assessing the growth performance and growth efficiency of plants and plant populations. In this paper, we explore how these isolated methods can be combined to form a consistent methodology for modelling relative growth rates. Methods We review and combine existing methods of analysing and modelling relative growth rates and apply a combination of methods to Sitka spruce (Picea sitchensis (Bong. Carr. stem-analysis data from North Wales (UK and British Douglas fir (Pseudotsuga menziesii (Mirb. Franco yield table data. Results The results indicate that, by combining the approaches of different plant-growth analysis laboratories and using them simultaneously, we can advance and standardise the concept of relative plant growth. Particularly the growth multiplier plays an important role in modelling relative growth rates. Another useful technique has been the recent introduction of size-standardised relative growth rates. Conclusions Modelling relative growth rates mainly serves two purposes, 1 an improved analysis of growth performance and efficiency and 2 the prediction of future or past growth rates. This makes the concept of relative growth ideally suited to growth reconstruction as required in dendrochronology, climate change and forest decline research and for interdisciplinary research projects beyond the realm of plant science.
2010-07-01
... Company G Appendix G to Part 60 Protection of Environment ENVIRONMENTAL PROTECTION AGENCY (CONTINUED) AIR PROGRAMS (CONTINUED) STANDARDS OF PERFORMANCE FOR NEW STATIONARY SOURCES (CONTINUED) Pt. 60, App. G Appendix G to Part 60—Provisions for an Alternative Method of Demonstrating Compliance With 40 CFR...
Lawton, Wayne M
2011-01-01
We model the time evolution of a Bose-Einstein condensate, subject to a special periodically excited optical lattice, by a unitary quantum operator U on a Hilbert space H. If a certain parameter alpha = p/q, where p and q are coprime positive integers, then H = L^2(R/Z,C^q) and U is represented by a q x q matrix-valued function M on R/Z that acts pointwise on functions in H. The dynamics of the quantum system is described by the eigenvalues of M. Numerical computations show that the characteristic polynomial det(zI - M(t)) = Prod_j=1^q (z - lambda_j(t)) where each lambda_j is a real analytic functions that has period 1/q. We discuss this phenomena using Newton's Theorem, published in Geometria analytica in 1660, and modern concepts from analytic geometry.
蔡珣; 陈智; Kanishka T yagi; 于宽3; 李子强; 朱波
2015-01-01
提出了一种混合加权距离测量（weighted distance measure ，weighted DM ）参数的构建和训练RBF（radial basis function）神经网络的两步批处理算法。该算法在引进了 DM 系数参数的基础上，采用Newton 法分别对径向基函数的覆盖参数、均值向量参数、加权距离测度系数以及输出权值进行了优化，并在优化过程中利用 OLS（orthogonal least squares）法来求解 New ton 法的方程组。通过实验数据，不仅分析了 New ton 法优化的各个参数向量对 RBF 网络训练的影响，而且比较了混合优化加权 DM 与RLS‐RBF（recursive least square RBF neural network）网络训练算法的收敛性和计算成本。所得到的结论表明整合了优化参数的加权 DM‐RBF 网络训练算法收敛速度比 RLS‐RBF 网络训练算法更快，而且具有比 LM‐RBF （Levenberg‐Marquardt RBF ）训练算法更小的计算成本，从而说明 OLS 求解的Newton 法对优化 RBF 网络参数具有重要应用价值。%A hybrid two‐step second‐order batch approach is presented for constructing and training radial basis function (RBF) neural networks .Unlike other RBF neural network learning algorithms , the proposed paradigm uses New ton’s method to train each set of network parameters ,i .e .spread parameters ,mean vector parameters and weighted distance measure (DM ) coefficients and output weights parameters .For efficiently calculating the second‐order equations of New ton’s method ,all the optimal parameters are found out using orthogonal least squares (OLS ) with the multiply optimal learning factors(MOLFs) for training mean vector parameters .The simulation results of the proposed hybrid training algorithm on a real dataset are compared with those of the recursive least square based RBF(RLS‐RBF) and Levenberg‐Marquardt method based RBF(LM‐RBF) training algorithms .Also , the analysis of the training performance for optimization of each
QUAD METHOD FOR IDENTIFYING RELATIVELY STABLE STATIONS
HuangLiren
2003-01-01
The QUAD(Quasi-Accurate Detection of gross errors) method which is originally developed to detect gross errors in the geodetic data is extended and used to select and indentify relatively stable stations. The formulas and algorithm are described in detail. Some problems that should be noticed in the use of this method are discussed. Finally, this method is applied to some data observed in North China as an example.
QUAD METHOD FOR IDENTIFYING RELATIVELY STABLE STATIONS
Huang Liren
2003-01-01
The QUAD(Quasi-Accurate Detection of gross errors) method which is originally developed to detect gross errors in the geodetic data is extended and used to select and identify relatively stable stations. The formulas and algorithm are described in detail. Some problems that should be noticed in the use of this method are discussed. Finally, this method is applied to some data observed in North China as an example.
Illustrating Newton's Second Law with the Automobile Coast-Down Test.
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)
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.
熊兴隆; 蒋立辉; 冯帅; 庄子波; 赵俊媛
2012-01-01
在用激光雷达方程反演大气消光系数时,大气消先系数边界值对反演精度影响较大,而在低层大气中该值较难确定.文中提出了一种基于改进牛顿法的大气消光系数边界值确定方法,其核心思想是,把确定大气消光系数边界值的问题转化为求非线性方程的数值解.首先,根据大气消光系数边界值与激光雷达回波信号功率以及大气光学厚度之间的关系,假设大气消光系数边界值为x,构建一个非线性方程.其次,采用改进的牛顿法求非线性方程的数值解,得到大气消光系数边界值.使用香港天文台装置在香港国际机场的多普勒激光雷达回波信号数据,对该方法的可行性和可靠性进行了验证.结果表明:利用该方法确定边界值,可以较为准确地反演出低层大气消光系数.该方法收敛速度快,迭代次数少,并且不需要计算导数值,极大地减少了运算量,具有较强的实际应用价值.%When using lidar equation to inverse the extinction coefficient of atmosphere, its boundary value has a great influence on the inversion precision, however, it is hard to be determined in the lower atmosphere. A method was proposed to determine the boundary value of the extinction coefficient of atmosphere based on improved Newton; the core idea was to transform the problem of determining boundary value of the extinction coefficient of atmosphere to get numerical solution of the nonlinear equation. First of all, according to the relationship between the boundary value of extinction coefficient of atmosphere and the power of laser radar echo as well as optical thickness of atmosphere, it was supposed the boundary value of the extinction coefficient of atmosphere was x, a nonlinear equation could be constructed. Secondly, by using the improved Newton method to get the numerical solution of the nonlinear equation, the boundary value of the extinction coefficient of atmosphere can be got. By means of
A Line Search Multilevel Truncated Newton Algorithm for Computing the Optical Flow
Lluís Garrido
2015-06-01
Full Text Available We describe the implementation details and give the experimental results of three optimization algorithms for dense optical flow computation. In particular, using a line search strategy, we evaluate the performance of the unilevel truncated Newton method (LSTN, a multiresolution truncated Newton (MR/LSTN and a full multigrid truncated Newton (FMG/LSTN. We use three image sequences and four models of optical flow for performance evaluation. The FMG/LSTN algorithm is shown to lead to better optical flow estimation with less computational work than both the LSTN and MR/LSTN algorithms.
CONVERGENCE OF THE CRANK-NICOLSON/NEWTON SCHEME FOR NONLINEAR PARABOLIC PROBLEM
Xinlong FENG; Yinnian HE
2016-01-01
In this paper, the Crank-Nicolson/Newton scheme for solving numerically second-order nonlinear parabolic problem is proposed. The standard Galerkin finite element method based on P2 conforming elements is used to the spatial discretization of the problem and the Crank-Nicolson/Newton scheme is applied to the time discretization of the resulted finite element equations. Moreover, assuming the appropriate regularity of the exact solution and the finite element solution, we obtain optimal error estimates of the fully discrete Crank-Nicolson/Newton scheme of nonlinear parabolic problem. Finally, numerical experiments are presented to show the effcient performance of the proposed scheme.
Why Goethe rejected Newton's theory of light.
Treisman, M
1996-01-01
Observations that he himself had made persuaded Goethe to reject Newton's theory of light and to put forward an alternative theory of the colour phenomena seen with a prism. Duck has argued that Goethe's attack on Newton's theory rested on valid experimental observations that appeared to present a difficulty for Newton's theory but to support his own views on colour. Duck has also proposed that these observations may be accounted for as an instance of the Bezold-Brücke phenomenon. It is argued here that this explanation is invalid and that two other features of colour processing can explain Goethe's observations.
Centrifugal separator devices, systems and related methods
Meikrantz, David H.; Law, Jack D.; Garn, Troy G.; Todd, Terry A.; Macaluso, Lawrence L.
2012-03-20
Centrifugal separator devices, systems and related methods are described. More particularly, fluid transfer connections for a centrifugal separator system having support assemblies with a movable member coupled to a connection tube and coupled to a fixed member, such that the movable member is constrained to movement along a fixed path relative to the fixed member are described. Also, centrifugal separator systems including such fluid transfer connections are described. Additionally, methods of installing, removing and/or replacing centrifugal separators from centrifugal separator systems are described.
Stabilized Quasi-Newton Optimization of Noisy Potential Energy Surfaces
Schaefer, Bastian; Roy, Shantanu; Goedecker, Stefan
2014-01-01
Optimizations of atomic positions belong to the most commonly performed tasks in electronic structure calculations. Many simulations like global minimum searches or characterizations of chemical reactions require performing hundreds or thousands of minimizations or saddle computations. To automatize these tasks, optimization algorithms must not only be efficient, but also very reliable. Unfortunately computational noise in forces and energies is inherent to electronic structure codes. This computational noise poses a sever problem to the stability of efficient optimization methods like the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. We here present a technique that allows obtaining significant curvature information of noisy potential energy surfaces. We use this technique to construct both, a stabilized quasi-Newton minimization method and a stabilized quasi-Newton saddle finding approach. We demonstrate with the help of benchmarks that both the minimizer and the saddle finding approach are sup...
A Newton Algorithm for Multivariate Total Least Squares Problems
WANG Leyang
2016-04-01
Full Text Available In order to improve calculation efficiency of parameter estimation, an algorithm for multivariate weighted total least squares adjustment based on Newton method is derived. The relationship between the solution of this algorithm and that of multivariate weighted total least squares adjustment based on Lagrange multipliers method is analyzed. According to propagation of cofactor, 16 computational formulae of cofactor matrices of multivariate total least squares adjustment are also listed. The new algorithm could solve adjustment problems containing correlation between observation matrix and coefficient matrix. And it can also deal with their stochastic elements and deterministic elements with only one cofactor matrix. The results illustrate that the Newton algorithm for multivariate total least squares problems could be practiced and have higher convergence rate.
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)
Discovery Science: Newton All around You.
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)
Newton and the American Political Tradition
Arons, A. B.
1975-01-01
Traces the historical sequence that establishes a clear line of connection from Newton and Locke through the philosophy of the Enlightenment and the evolution of deism to the American political tradition. (Author/GS)
Gauld, Colin F.
2010-01-01
Newton's experiments into the resistance which fluids offer to moving bodies provide some insight into the way he related theory and experiment. His theory demonstrates a way of thought typical of 17th century physics and his experiments are simple enough to be replicated by present day students. Newton's investigations using pendulums were…
Newton-Leibniz公式的推广%Popularization of the Formula Newton-Leibniz
胡洪萍
2002-01-01
研究了 Newton-Leibniz公式,对传统Newton-Leibniz公式中被积函数f(x)和原函数F(x)的条件进行了减弱,推广完善了传统的Newton-Leibniz公式,新公式使用范围更广,使用价值更大.文中还给出了事例,说明了推广的Newton-Leibniz公式在实践中的应用.
Newton's Law of Universal Gravitation and Hume's Conception of Causality
Slavov, Matias
2013-01-01
This article investigates the relationship between Hume’s causal philosophy and Newton’s philosophy of nature. I claim that Newton’s experimentalist methodology in gravity research is an important background for understanding Hume’s conception of causality: Hume sees the relation of cause and effect as not being founded on a priori reasoning, similar to the way that Newton criticized non-empirical hypotheses about the properties of gravity. However, according to Hume’s criteria of...
Traveling and Standing Waves in Coupled Pendula and Newton's Cradle
García-Azpeitia, Carlos
2016-12-01
The existence of traveling and standing waves is investigated for chains of coupled pendula with periodic boundary conditions. The results are proven by applying topological methods to subspaces of symmetric solutions. The main advantage of this approach comes from the fact that only properties of the linearized forces are required. This allows to cover a wide range of models such as Newton's cradle, the Fermi-Pasta-Ulam lattice, and the Toda lattice.
Centrifugal separators and related devices and methods
Meikrantz, David H.; Law, Jack D.; Garn, Troy G.; Macaluso, Lawrence L.; Todd, Terry A.
2012-03-06
Centrifugal separators and related methods and devices are described. More particularly, centrifugal separators comprising a first fluid supply fitting configured to deliver fluid into a longitudinal fluid passage of a rotor shaft and a second fluid supply fitting sized and configured to sealingly couple with the first fluid supply fitting are described. Also, centrifugal separator systems comprising a manifold having a drain fitting and a cleaning fluid supply fitting are described, wherein the manifold is coupled to a movable member of a support assembly. Additionally, methods of cleaning centrifugal separators are described.
Newton law in covariant unimodular $F(R)$ gravity
Nojiri, S; Oikonomou, V K
2016-01-01
We propose a covariant ghost-free unimodular $F(R)$ gravity theory, which contains a three-form field and study its structure using the analogy of the proposed theory with a quantum system which describes a charged particle in uniform magnetic field. Newton's law in non-covariant unimodular $F(R)$ gravity as well as in unimodular Einstein gravity is derived and it is shown to be just the same as in General Relativity. The derivation of Newton's law in covariant unimodular $F(R)$ gravity shows that it is modified precisely in the same way as in the ordinary $F(R)$ theory. We also demonstrate that the cosmology of a Friedmann-Robertson-Walker background, is equivalent in the non-covariant and covariant formulations of unimodular $F(R)$ theory.
Newton's gift how Sir Isaac Newton unlocked the system of the world
Berlinski, David
2000-01-01
Sir Isaac Newton, creator of the first and perhaps most important scientific theory, is a giant of the scientific era. Despite this, he has remained inaccessible to most modern readers, indisputably great but undeniably remote. In this witty, engaging, and often moving examination of Newton's life, David Berlinski recovers the man behind the mathematical breakthroughs. The story carries the reader from Newton's unremarkable childhood to his awkward undergraduate days at Cambridge through the astonishing year in which, working alone, he laid the foundation for his system of the world, his Principia Mathematica, and to the subsequent monumental feuds that poisoned his soul and wearied his supporters. An edifying appreciation of Newton's greatest accomplishment, Newton's Gift is also a touching celebration of a transcendent man.
The XMM-Newton Survey of the Small Magellanic Cloud
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.
3, 2, 1 … Discovering Newton's Laws
Lutz, Joe; Sylvester, Kevin; Oliver, Keith; Herrington, Deborah
2017-03-01
"For every action there is an equal and opposite reaction." "Except when a bug hits your car window, the car must exert more force on the bug because Newton's laws only apply in the physics classroom, right?" Students in our classrooms were able to pick out definitions as well as examples of Newton's three laws; they could recite the laws and even solve for force, mass, and acceleration. However, when given "real world" questions, they would quickly revert to naive explanations. This frustration led to an examination of our approach to teaching Newton's laws. Like many, we taught Newton's laws in their numerical order—first, second, and then third. Students read about the laws, copied definitions, and became proficient with vocabulary before they applied the laws in a lab setting. This paper discusses how we transformed our teaching of Newton's laws by flipping the order (3, 2, 1) and putting the activity before concept, as well as how these changes affected student outcomes.
Disformal transformation in Newton-Cartan geometry
Huang, Peng [Zhejiang Chinese Medical University, Department of Information, Hangzhou (China); Sun Yat-Sen University, School of Physics and Astronomy, Guangzhou (China); Yuan, Fang-Fang [Nankai University, School of Physics, Tianjin (China)
2016-08-15
Newton-Cartan geometry has played a central role in recent discussions of the non-relativistic holography and condensed matter systems. Although the conformal transformation in non-relativistic holography can easily be rephrased in terms of Newton-Cartan geometry, we show that it requires a nontrivial procedure to arrive at the consistent form of anisotropic disformal transformation in this geometry. Furthermore, as an application of the newly obtained transformation, we use it to induce a geometric structure which may be seen as a particular non-relativistic version of the Weyl integrable geometry. (orig.)
Newton and the origin of civilization
Buchwald, Jed Z
2012-01-01
Isaac Newton's Chronology of Ancient Kingdoms Amended, published in 1728, one year after the great man's death, unleashed a storm of controversy. And for good reason. The book presents a drastically revised timeline for ancient civilizations, contracting Greek history by five hundred years and Egypt's by a millennium. Newton and the Origin of Civilization tells the story of how one of the most celebrated figures in the history of mathematics, optics, and mechanics came to apply his unique ways of thinking to problems of history, theology, and mythology, and of how his radical ideas produced an
XMM-Newton Mobile Web Application
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.
许万银
2005-01-01
给出了计算定积分的Newton-Leibniz公式的推广：把f（x）在[a，b]上连续减弱为f（x）在[a，b]上可积，把F’（s）=f（x）在[a，b]上成立减弱为在[a，b]上除有限个点外成立F’（x）=f（x）．同时建立了计算广义积分与二重积分的Newton-Leibniz公式．
Newton-Leibniz公式的推广%Generalization of Newton - leibniz
王雄瑞
2003-01-01
Newton-Leibniz公式是中十分重要的公式,但其应用是有一定条件的.在实际问题的解决过程中,常常遇到不全满足Newton-Lebniz公式的条件的问题,从而使得公式失效.本文通过对这一情况的讨论,将Newton-Leibniz公式推广,扩大其适用范围.
Newton's Metaphysics of Space as God's Emanative Effect
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.
Magnetic Levitation and Newton's Third Law
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…
Bernoulli and Newton in Fluid Mechanics
Smith, Norman F.
1972-01-01
Bernoulli's theorem can be better understood with the aid of Newton's laws and the law of conservation of energy. Application of this theorem should involve only cases dealing with an interchange of velocity and pressure within a fluid under isentropic conditions. (DF)
Newton's First Law: A Learning Cycle Approach
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
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…
Magnetic Levitation and Newton's Third Law
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…
Sonic Beam Model of Newton's Cradle
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…
Bernoulli and Newton in Fluid Mechanics
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)
British physics Newton's law of funding
2007-01-01
In Britain, fundamental physics is in a pickle ISAAC NEWTON, besides being the founder of modern physics, was also master of Britain's mint. That is a precedent which many British physicists must surely wish had become traditional. At the moment, money for physics is in short supply in Britain.
BLOCK BASED NEWTON-LIKE BLENDING OSCULATORY RATIONAL INTERPOLATION
Shuo Tang; Le Zou; Chensheng Li
2010-01-01
With Newton's interpolating formula,we construct a kind of block based Newton-like blending osculatory interpolation.The interpolation provides us many flexible interpolation schemes for choices which include the expansive Newton's polynomial interpolation as its special case.A bivariate analogy is also discussed and numerical examples are given to show the effectiveness of the interpolation.
27 CFR 9.152 - Malibu-Newton Canyon.
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...
Constructs and Attributes in Test Validity: Reflections on Newton's Account
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…
Newton’s method an updated approach of Kantorovich’s theory
Ezquerro Fernández, José Antonio
2017-01-01
This book shows the importance of studying semilocal convergence in iterative methods through Newton's method and addresses the most important aspects of the Kantorovich's theory including implicated studies. Kantorovich's theory for Newton's method used techniques of functional analysis to prove the semilocal convergence of the method by means of the well-known majorant principle. To gain a deeper understanding of these techniques the authors return to the beginning and present a deep-detailed approach of Kantorovich's theory for Newton's method, where they include old results, for a historical perspective and for comparisons with new results, refine old results, and prove their most relevant results, where alternative approaches leading to new sufficient semilocal convergence criteria for Newton's method are given. The book contains many numerical examples involving nonlinear integral equations, two boundary value problems and systems of nonlinear equations related to numerous physical phenomena. The book i...
Newton flow of the Riemann zeta function: separatrices control the appearance of zeros
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.
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.
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.
A Switching Algorithm Based on Modified Quasi-Newton Equation
Yueting Yang; Chengxian Xu
2006-01-01
In this paper, a switching method for unconstrained minimization is proposed.The method is based on the modified BFGS method and the modified SR1 method. The eigenvalues and condition numbers of both the modified updates are evaluated and used in the switching rule. When the condition number of the modified SR1 update is superior to the modified BFGS update, the step in the proposed quasi-Newton method is the modified SR1 step. Otherwise the step is the modified BFGS step. The efficiency of the proposed method is tested by numerical experiments on small, medium and large scale optimization.The numerical results are reported and analyzed to show the superiority of the proposed method.
Active set truncated-Newton algorithm for simultaneous optimization of distillation column
LIANG Xi-ming
2005-01-01
An active set truncated-Newton algorithm (ASTNA) is proposed to solve the large-scale bound constrained sub-problems. The global convergence of the algorithm is obtained and two groups of numerical experiments are made for the various large-scale problems of varying size. The comparison results between ASTNA and the subspace limited memory quasi-Newton algorithm and between the modified augmented Lagrange multiplier methods combined with ASTNA and the modified barrier function method show the stability and effectiveness of ASTNA for simultaneous optimization of distillation column.
Quasi-Newton-type optimized iterative learning control for discrete linear time invariant systems
Yan GENG; Xiaoe RUAN
2015-01-01
In this paper, a quasi-Newton-type optimized iterative learning control (ILC) algorithm is investigated for a class of discrete linear time-invariant systems. The proposed learning algorithm is to update the learning gain matrix by a quasi-Newton-type matrix instead of the inversion of the plant. By means of the mathematical inductive method, the monotone convergence of the proposed algorithm is analyzed, which shows that the tracking error monotonously converges to zero after a finite number of iterations. Compared with the existing optimized ILC algorithms, due to the superlinear convergence of quasi-Newton method, the proposed learning law operates with a faster convergent rate and is robust to the ill-condition of the system model, and thus owns a wide range of applications. Numerical simulations demonstrate the validity and effectiveness.
Plants with useful traits and related methods
Mackenzie, Sally Ann; De la Rosa Santamaria, Roberto
2017-07-18
The present invention provides methods for obtaining plants that exhibit useful traits by transient suppression of the MSH1 gene of the plants. Methods for identifying genetic loci that provide for useful traits in plants and plants produced with those loci are also provided. In addition, plants that exhibit the useful traits, parts of the plants including seeds, and products of the plants are provided as well as methods of using the plants.
Plants with useful traits and related methods
Mackenzie, Sally Ann; De la Rosa Santamaria, Roberto
2016-10-25
The present invention provides methods for obtaining plants that exhibit useful traits by transient suppression of the MSH1 gene of the plants. Methods for identifying genetic loci that provide for useful traits in plants and plants produced with those loci are also provided. In addition, plants that exhibit the useful traits, parts of the plants including seeds, and products of the plants are provided as well as methods of using the plants.
Plants with useful traits and related methods
Mackenzie, Sally Ann; De la Rosa Santamaria, Roberto
2016-10-25
The present invention provides methods for obtaining plants that exhibit useful traits by transient suppression of the MSH1 gene of the plants. Methods for identifying genetic loci that provide for useful traits in plants and plants produced with those loci are also provided. In addition, plants that exhibit the useful traits, parts of the plants including seeds, and products of the plants are provided as well as methods of using the plants.
Relating Actor Analysis Methods to Policy Problems
Van der Lei, T.E.
2009-01-01
For a policy analyst the policy problem is the starting point for the policy analysis process. During this process the policy analyst structures the policy problem and makes a choice for an appropriate set of methods or techniques to analyze the problem (Goeller 1984). The methods of the policy anal
Newtons Principia Mathematica Philosophia und Plancks Elementarkonstanten
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.
One dimensional Newton's equation with variable mass
Mazharimousavi, S Habib
2013-01-01
We revisit Newton's equation of motion in one dimension when the moving particle has a variable mass m(x,t) depending both on position (x) and time (t). Geometrically the mass function is identified with one of the metric function in a 1+1-dimensional spacetime. As a reflection of the equivalence principle geodesics equation gives the Newton's law of motion leaving the right hand side to be supplemented by the external forces. The resulting equation involves the speed of light so that our equation of motion addresses a wider scope than the customary classical mechanics. In the limit of infinite light speed which amounts to instantaneous interaction we recover the classical results.
High-temperature thermocouples and related methods
Rempe, Joy L.; Knudson, Darrell L.; Condie, Keith G.; Wilkins, S. Curt
2011-01-18
A high-temperature thermocouple and methods for fabricating a thermocouple capable of long-term operation in high-temperature, hostile environments without significant signal degradation or shortened thermocouple lifetime due to heat induced brittleness.
Microorganism genomics, compositions and methods related thereto
Handelsman, Jo; Goodman, Robert M.; Rondon, Michelle R.
2001-01-01
The present invention provides methods and compositions for accessing, in a generally unbaised manner, a diverse genetic pool for genes involved in biosynthetic pathways. The invention also provides compounds which can be identified by cloning biosynthetic pathways.
Newton's Second Law in a Noncommutative Space
Romero, J M; Vergara, J D; Romero, Juan M.
2003-01-01
In this work we show that corrections to the Newton's second law appears if we assume that the phase space has a symplectic structure consistent with the rules of commutation of noncommutative quantum mechanis. In the central field case we find that the correction term breaks the rotational symmetry. In particular, for the Kepler problem, this term takes the form of a Coriolis force produced by the weak gravitational field far from a rotating massive object.
Fast Newton active appearance models
Kossaifi, Jean; Tzimiropoulos, Georgios; Pantic, Maja
2014-01-01
Active Appearance Models (AAMs) are statistical models of shape and appearance widely used in computer vision to detect landmarks on objects like faces. Fitting an AAM to a new image can be formulated as a non-linear least-squares problem which is typically solved using iterative methods. Owing to i
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.
Fully ceramic nuclear fuel and related methods
Venneri, Francesco; Katoh, Yutai; Snead, Lance Lewis
2016-03-29
Various embodiments of a nuclear fuel for use in various types of nuclear reactors and/or waste disposal systems are disclosed. One exemplary embodiment of a nuclear fuel may include a fuel element having a plurality of tristructural-isotropic fuel particles embedded in a silicon carbide matrix. An exemplary method of manufacturing a nuclear fuel is also disclosed. The method may include providing a plurality of tristructural-isotropic fuel particles, mixing the plurality of tristructural-isotropic fuel particles with silicon carbide powder to form a precursor mixture, and compacting the precursor mixture at a predetermined pressure and temperature.
Analysis of XMM-Newton Data from Extended Sources and the Diffuse X-Ray Background
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).
Has ESA's XMM-Newton cast doubt over dark energy?
2003-12-01
Galaxy cluster RXJ0847 hi-res Size hi-res: 100k Galaxy cluster RXJ0847 The fuzzy object at the centre of the frame is one of the galaxy clusters observed by XMM-Newton in its investigation of the distant Universe. The cluster, designated RXJ0847.2+3449, is about 7 000 million light years away, so we see it here as it was 7 000 million years ago, when the Universe was only about half of its present age. This cluster is made up of several dozen galaxies. Observations of eight distant clusters of galaxies, the furthest of which is around 10 thousand million light years away, were studied by an international group of astronomers led by David Lumb of ESA's Space Research and Technology Centre (ESTEC) in the Netherlands. They compared these clusters to those found in the nearby Universe. This study was conducted as part of the larger XMM-Newton Omega Project, which investigates the density of matter in the Universe under the lead of Jim Bartlett of the College de France. Clusters of galaxies are prodigious emitters of X-rays because they contain a large quantity of high-temperature gas. This gas surrounds galaxies in the same way as steam surrounds people in a sauna. By measuring the quantity and energy of X-rays from a cluster, astronomers can work out both the temperature of the cluster gas and also the mass of the cluster. Theoretically, in a Universe where the density of matter is high, clusters of galaxies would continue to grow with time and so, on average, should contain more mass now than in the past. Most astronomers believe that we live in a low-density Universe in which a mysterious substance known as 'dark energy' accounts for 70% of the content of the cosmos and, therefore, pervades everything. In this scenario, clusters of galaxies should stop growing early in the history of the Universe and look virtually indistinguishable from those of today. In a paper soon to be published by the European journal Astronomy and Astrophysics, astronomers from the XMM-Newton
Chemical detection system and related methods
Caffrey, Augustine J.; Chichester, David L.; Egger, Ann E.; Krebs, Kenneth M.; Seabury, Edward H.; Van Siclen, Clinton D.; Wharton, C. Jayson; Zabriskie, John M.
2017-06-27
A chemical detection system includes a frame, an emitter coupled to the frame, and a detector coupled to the frame proximate the emitter. The system also includes a shielding system coupled to the frame and positioned at least partially between the emitter and the detector, wherein the frame positions a sensing surface of the detector in a direction substantially parallel to a plane extending along a front portion of the frame. A method of analyzing composition of a suspect object includes directing neutrons at the object, detecting gamma rays emitted from the object, and communicating spectrometer information regarding the gamma rays. The method also includes presenting a GUI to a user with a dynamic status of an ongoing neutron spectroscopy process. The dynamic status includes a present confidence for a plurality of compounds being present in the suspect object responsive to changes in the spectrometer information during the ongoing process.
Methods of decontaminating surfaces and related compositions
Demmer, Ricky L.; Crosby, Daniel; Norton, Christopher J.
2016-11-22
A composition of matter includes water, at least one acid, at least one surfactant, at least one fluoride salt, and ammonium nitrate. A method of decontaminating a surface includes exposing a surface to such a composition and removing the composition from the surface. Other compositions of matter include water, a fatty alcohol ether sulfate, nitrilotriacetic acid, at least one of hydrochloric acid and nitric acid, sodium fluoride, potassium fluoride, ammonium nitrate, and gelatin.
The XMM-Newton serendipitous ultraviolet source survey catalogue
Page, M J; Talavera, A; Still, M; Rosen, S R; Yershov, V N; Ziaeepour, H; Mason, K O; Cropper, M S; Breeveld, A A; Loiseau, N; Mignani, R; Smith, A; Murdin, P
2012-01-01
The XMM-Newton Serendipitous Ultraviolet Source Survey (XMM-SUSS) is a catalogue of ultraviolet (UV) sources detected serendipitously by the Optical Monitor (XMM-OM) on-board the XMM-Newton observatory. The catalogue contains ultraviolet-detected sources collected from 2,417 XMM-OM observations in 1-6 broad band UV and optical filters, made between 24 February 2000 and 29 March 2007. The primary contents of the catalogue are source positions, magnitudes and fluxes in 1 to 6 passbands, and these are accompanied by profile diagnostics and variability statistics. The XMM-SUSS is populated by 753,578 UV source detections above a 3 sigma signal-to-noise threshold limit which relate to 624,049 unique objects. Taking account of substantial overlaps between observations, the net sky area covered is 29-54 square degrees, depending on UV filter. The magnitude distributions peak at 20.2, 20.9 and 21.2 in UVW2, UVM2 and UVW1 respectively. More than 10 per cent of sources have been visited more than once using the same fi...
Polar Satcom System and Related Method
Mitchell, James P. (Inventor)
2016-01-01
A system and method for communication relay via a repeater platform satellite vehicle to a near surface station in the Polar Region is disclosed. A preferred embodiment receives a plurality of positioning and content data from a plurality of constellations of Geosynchronous Equatorial Orbit (GEO) Satellite Vehicles (SAT). Additionally, the system receives a plurality of position, time and altitude data from constellations of available repeater platform (RP) SATs. The system receives a request for content from a near surface station located in an area lacking adequate line-of-sight to the GEO based signal. The system aligns antenna elements onboard the desired RP SATs to amplify and relay the GEO based signal toward the near surface station and vice versa. Additionally, the system commands directional antenna elements onboard the station to send and receive the relayed signal making the GEO based content available to the near surface station.
Energy harvesting devices, systems, and related methods
Kotter, Dale K.
2016-10-18
Energy harvesting devices include a substrate and a plurality of resonance elements coupled to the substrate. Each resonance element is configured to collect energy in the visible and infrared light spectra and to reradiate energy having a wavelength in the range of about 0.8 .mu.m to about 0.9 .mu.m. The resonance elements are arranged in groups of two or more resonance elements. Systems for harvesting electromagnetic radiation include a substrate, a plurality of resonance elements including a conductive material carried by the substrate, and a photovoltaic material coupled to the substrate and to at least one resonance element. The resonance elements are arranged in groups, such as in a dipole, a tripole, or a bowtie configuration. Methods for forming an energy harvesting device include forming groups of two or more discrete resonance elements in a substrate and coupling a photovoltaic material to the groups of discrete resonance elements.
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.
Guidelines for Interactive Reliability-Based Structural Optimization using Quasi-Newton Algorithms
Pedersen, C.; Thoft-Christensen, Palle
Guidelines for interactive reliability-based structural optimization problems are outlined in terms of modifications of standard quasi-Newton algorithms. The proposed modifications minimize the condition number of the approximate Hessian matrix in each iteration, restrict the relative and absolute...
Experimentally Building a Qualitative Understanding of Newton's Second Law
Gates, Joshua
2014-01-01
Newton's second law is one of the cornerstones of the introductory physics curriculum, but it can still trouble a large number of students well after its introduction, hobbling their ability to apply the concept to problem solving and to related concepts, such as momentum, circular motion, and orbits. While there are several possibilities for…
Student Teachers' Levels of Understanding and Model of Understanding about Newton's Laws of Motion
Saglam-Arslan, Aysegul; Devecioglu, Yasemin
2010-01-01
This study was conducted to determine the level of student teachers' understandings of Newton's laws of motion and relating these levels to identify student teachers' models of understanding. An achievement test composed of two parts comprising 12 open ended questions was constructed and given to 45 pre-service classroom teachers. The first part…
The Effect of Group Work on Misconceptions of 9th Grade Students about Newton's Laws
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…
The qualitative behaviour of Newton flows for Weierstrass’ ℘-functions
Helminck, G.F.; Kamphof, F.H.; Streng, M.; Twilt, F.
2002-01-01
We study the continuous, desingularized Newton method for Weierstrass' ℘-functions. This leads to a family of autonomous differential equations in the plane, which depends on two complex parameters ω 1 and ω 2. For the associated flows there are, up to conjugacy, precisely three possibilities. These
Cudeck, Robert; And Others
1993-01-01
An implementation of the Gauss-Newton algorithm for the analysis of covariance structure that is specifically adapted for high-level computer languages is reviewed. This simple method for estimating structural equation models is useful for a variety of standard models, as is illustrated. (SLD)
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…
Newton's law in braneworlds with an infinite extra dimension
Ito, M
2002-01-01
We study the behavior of the four$-$dimensional Newton's law in warped braneworlds. The setup considered here is a $(3+n)$-brane embedded in $(5+n)$ dimensions, where $n$ extra dimensions are compactified and a dimension is infinite. We show that the wave function of gravity is described in terms of the Bessel functions of $(2+n/2)$-order and that estimate the correction to Newton's law. In particular, the Newton's law for $n=1$ can be exactly obtained.
Geodesics and Newton's Law in Brane Backgrounds
Mück, W; Volovich, I V
2000-01-01
In brane world models our universe is considered as a brane imbedded into ahigher dimensional space. We discuss the behaviour of geodesics in theRandall-Sundrum background and point out that free massive particles cannotmove along the brane only. The brane is repulsive, and matter will be expelledfrom the brane into the extra dimension. This is rather undesirable, and hencewe study an alternative model with a non-compact extra dimension, but with anattractive brane embedded into the higher dimensional space. We study thelinearized gravity equations and show that Newton's gravitational law is validon the brane also in the alternative background.
High degree interpolation polynomial in Newton form
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
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
Newton's laws through a science adventure
Šuštar, Sara
2013-01-01
The main purpose of my diploma thesis is to create a scientific adventure based on the Newton's laws. My aim has been to introduce this topic to the kids in elementary school as well as the general public. That is why the adventure will take place in the House of Experiments. The first part is dedicated to theory and various experiments, which lead to deeper understanding of the laws. I implemented experiments on rollerblades, such as free movement, movement with the help of springs which wer...
The XMM-Newton serendipitous survey. VII. The third XMM-Newton serendipitous source catalogue
Rosen, S R; 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; Law-Green, D; Lamer, G; Lin, D; Martino, R; Michel, L; Motch, C; Gomez-Moran, A Nebot; 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
2015-01-01
Thanks to the large collecting area (3 x ~1500 cm$^2$ 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 hundreds of X-ray sources, most of which are newly discovered. 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, with better signal-to-noise. Further, almost 50% more observations are in the public domain compared to 2XMMi-DR3, allowing the XMM-Newton Survey Science Centre (XMM-SSC) to produce a much larger and better quality X-ray source catalogue. The XMM-SSC has developed a pipeline to reduce the XMM-Newton data automatically and using improved calibration a new catalogue ve...
Newton's Telescope in Print: the Role of Images in the Reception of Newton's Instrument
Dupré, Sven
2008-01-01
While Newton tried to make his telescope into a proof of the supremacy of his theory of colours over older theories, his instrument was welcomed as a way to shorten telescopes, not as a way to solve the problem of chromatic aberration. This paper argues that the image published together with the rep
The Newton papers the strange and true odyssey of Isaac Newton's manuscripts
Dry, Sarah
2014-01-01
When Isaac Newton died at 85 without a will on March 20, 1727, he left a mass of disorganized papers-upwards of 8 million words-that presented an immediate challenge to his heirs. Most of these writings, on subjects ranging from secret alchemical formulas to impassioned rejections of the Holy Trinity to notes and calculations on his core discoveries in calculus, universal gravitation, and optics, were summarily dismissed by his heirs as "not fit to be printed." Rabidly heretical, alchemically obsessed, and possibly even mad, the Newton presented in these papers threatened to undermine not just his personal reputation but the status of science itself. As a result, the private papers of the world's greatest scientist remained hidden to all but a select few for over two hundred years. In The Newton Papers, Sarah Dry divulges the story of how this secret archive finally came to light-and the complex and contradictory man it revealed. Covering a broad swath of history, Dry explores who controlled Newton's legacy, ...
Stirring Astronomy into Theology: Sir Isaac Newton on the Date of the Passion of Christ
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
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
Francesco Fiorentino
2015-11-01
Full Text Available This contribution investigates a hidden and surely singular – but far from marginal – aspect of the Scientific Revolution of the 17th century, in other words the interpretation of the Holy Scriptures. First of all, this work analyzes the situation immediately before the advent of the fathers of the 17th Century Scientific Revolution like Galileo Galilei and Isaac Newton, starting from the Council of Trent. This reconstruction aims to throw light on the particular way that Galileo and Newton intended to approach the interpretation of the Holy Scriptures with respect to the main tendencies of the Catholic Reformation of biblical hermeneutics. Their way is important both in itself and in relation to the Scientific Revolution. In itself because Galileo and Newton elaborate original theories that are not entirely in agreement with the predominant views and that are decidedly no less interesting than their pure scientific theories. In relation to the Scientific Revolution because the interpretation of the Holy Scriptures is addressed in an original fashion by both Galileo and Newton, also with the intent of facilitating the spread and approval of their own scientific theories in their respective socio-cultural environments. The primacy of nature is not manifested only in contrast to and outside the book of Scriptures, but conditions the Book of Scriptures, locating it within a precise cultural perspective and religious sense that are by no means contrary to Galileo and Newton’s views.
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.
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
Consequences That Cannot Be Avoided: A Response to Paul Newton
Bennett, Randy Elliot
2012-01-01
This article presents the author's response to Paul E. Newton's paper titled "Clarifying the Consensus Definition of Validity" ("Measurement: Interdisciplinary Research and Perspectives," 2012). Newton's paper offers an interesting and constructive discussion about how people think about validity. In this reaction, the author comments on some of…
On the Shoulders of Sir Isaac Newton and Arthur Storer
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…
Can Newton's Third Law Be "Derived" from the Second?
Gangopadhyaya, Asim; Harrington, James
2017-01-01
Newton's laws have engendered much discussion over several centuries. Today, the internet is awash with a plethora of information on this topic. We find many references to Newton's laws, often discussions of various types of misunderstandings and ways to explain them. Here we present an intriguing example that shows an assumption hidden in…
Newton's Path to Universal Gravitation: The Role of the Pendulum
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…
Newton's First Law: Text, Translations, Interpretations and Physics Education.
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…
Newton's laws of motion in form of Riccati equation
Nowakowski, M
2002-01-01
We discuss two applications of Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential V(r)=k r^{\\epsilon}. For zero total energy we show that the equation of motion can be cast in the Riccati form. We briefly show here an analogy to barotropic Friedmann-Robertson-Lemaitre cosmology where the expansion of the universe can be also shown to obey a Riccati equation. A second application in classical mechanics, where again the Riccati equation appears naturally, are problems involving quadratic friction. We use methods reminiscent to nonrelativistic supersymmetry to generalize and solve such problems
Cross-Calibration of the XMM-Newton EPIC pn & MOS On-Axis Effective Areas Using 2XMM Sources
Read, A M; Sembay, S
2014-01-01
We aim to examine the relative cross-calibration accuracy of the on-axis effective areas of the XMM-Newton EPIC pn and MOS instruments. Spectra from a sample of 46 bright, high-count, non-piled-up isolated on-axis point sources are stacked together, and model residuals are examined to characterize the EPIC MOS-to-pn inter-calibration. The MOS1-to-pn and MOS2-to-pn results are broadly very similar. The cameras show the closest agreement below 1 keV, with MOS excesses over pn of 0-2% (MOS1/pn) and 0-3% (MOS2/pn). Above 3 keV, the MOS/pn ratio is consistent with energy-independent (or only mildly increasing) excesses of 7-8% (MOS1/pn) and 5-8% (MOS2/pn). In addition, between 1-2 keV there is a `silicon bump' - an enhancement at a level of 2-4% (MOS1/pn) and 3-5% (MOS2/pn). Tests suggest that the methods employed here are stable and robust. The results presented here provide the most accurate cross-calibration of the effective areas of the XMM-Newton EPIC pn and MOS instruments to date. They suggest areas of furt...
Moranchel y Rodriguez, M. [IPN, ESFM, Departamento de Ingenieria Nuclear, 07738 Mexico D.F. (Mexico)]. e-mail: mmoranchel@ipn.mx
2008-07-01
The central problem of the dosimetry of the ionizing radiations is the determination of the dissipated energy by unit of mass of irradiated material. This energy usually is inferred of ionization measures in a small cavity of air housed inside the material medium. The Bragg-Gray cavity theory was the first one in estimating the dissipated energy through the ionizations that the primary electrons cause in the cavity. The primary electrons are generated by photoelectric effect, pair production and by Compton dispersion of the photon beams that initially impact on the material. However, in a more realist approach the existence of secondary electrons due to the electron-electron interaction it will be considered. The Spencer-Attix cavity theory considers to the secondary electrons as responsible part for the energy deposited in the means, for that a total spectral fluence of electrons (primary and secondary) it appears in this theory. Few electrons spectra have been published, mainly, those that include the contribution of secondary electrons ({delta} rays). Leaving of the ideas of Spencer-Attix, in this work an approach method to determine the rate of electron spectral fluences (total regarding primary) for a wide variety of material Z, and energy sources T{sub 0} is presented. The method for materials used by Spencer-Attix is applied, it is proven its reliability and it is applied to the water like absorber medium by its importance in the clinical dosimetry. (Author)
Finding Rare AGN: XMM-Newton and Chandra Observations of SDSS Stripe 82
LaMassa, Stephanie M; Cappelluti, Nico; Civano, Francesca; Ranalli, Piero; Glikman, Eilat; Treister, Ezequiel; Richards, Gordon; Ballantyne, David; Stern, Daniel; Comastri, Andrea; Cardamone, Carie; Schawinski, Kevin; Boehringer, Hans; Chon, Gayoung; Murray, Stephen S; Green, Paul; Nandra, Kirpal
2013-01-01
We have analyzed the {\\it XMM-Newton} and {\\it Chandra} data overlapping $\\sim$16.5 deg$^2$ of Sloan Digital Sky Survey Stripe 82, including $\\sim$4.6 deg$^2$ of proprietary {\\it XMM-Newton} data that we present here. In total, 3362 unique X-ray sources are detected at high significance. We derive the {\\it XMM-Newton} number counts and compare them with our previously reported {\\it Chandra} Log$N$-Log$S$ relations and other X-ray surveys. The Stripe 82 X-ray source lists have been matched to multi-wavelength catalogs using a maximum likelihood estimator algorithm. We discovered the highest redshift ($z=5.86$) quasar yet identified in an X-ray survey. We find 2.5 times more high luminosity (L$_x \\geq 10^{45}$ erg s$^{-1}$) AGN than the smaller area {\\it Chandra} and {\\it XMM-Newton} survey of COSMOS and 1.3 times as many identified by XBo\\"otes. Comparing the high luminosity AGN we have identified with those predicted by population synthesis models, our results suggest that this AGN population is a more import...
L. M. Kimball
2002-01-01
Full Text Available This paper presents an interior point algorithm to solve the multiperiod hydrothermal economic dispatch (HTED. The multiperiod HTED is a large scale nonlinear programming problem. Various optimization methods have been applied to the multiperiod HTED, but most neglect important network characteristics or require decomposition into thermal and hydro subproblems. The algorithm described here exploits the special bordered block diagonal structure and sparsity of the Newton system for the first order necessary conditions to result in a fast efficient algorithm that can account for all network aspects. Applying this new algorithm challenges a conventional method for the use of available hydro resources known as the peak shaving heuristic.
Newton`s iteration for inversion of Cauchy-like and other structured matrices
Pan, V.Y. [Lehman College, Bronx, NY (United States); Zheng, Ailong; Huang, Xiaohan; Dias, O. [CUNY, New York, NY (United States)
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.
Stokes's cradle: Newton's cradle with liquid coating.
Donahue, C M; Hrenya, C M; Davis, R H
2010-07-16
Granular flows involving liquid-coated solids are ubiquitous in nature (pollen capture, avalanches) and industry (filtration, pharmaceutical mixing). In this Letter, three-body collisions between liquid-coated spheres are investigated experimentally using a "Stokes's cradle," which resembles the popular desktop toy Newton's cradle (NC). Surprisingly, previous work shows that every possible outcome was observed in the Stokes's cradle except the traditional NC outcome. Here, we experimentally achieve NC via guidance from a theory, which revealed that controlling the liquid-bridge volume connecting two target particles is the key in attaining the NC outcome. These three-body experiments also provide direct evidence that the fluid resistance upon rebound cannot be completely neglected due to presumed cavitation; this resistance also influences two-body systems yet cannot be isolated experimentally in such systems.
Photometric redshifts with Quasi Newton Algorithm (MLPQNA). Results in the PHAT1 contest
Cavuoti, Stefano; Longo, Giuseppe; Mercurio, Amata
2012-01-01
Context. Since the advent of modern multiband digital sky surveys, photometric redshifts (photo-z's) have become relevant if not crucial to many fields of observational cosmology, from the characterization of cosmic structures, to weak and strong lensing. Aims. We describe an application to an astrophysical context, namely the evaluation of photometric redshifts, of MLPQNA, a machine learning method based on Quasi Newton Algorithm. Methods. Empirical methods for photo-z's evaluation are based on the interpolation of a priori knowledge (spectroscopic redshifts or SED templates) and represent an ideal test ground for neural networks based methods. The MultiLayer Perceptron with Quasi Newton learning rule (MLPQNA) described here is a computing effective implementation of Neural Networks and is offered to the community through the DAMEWARE (DAta Mining & Exploration Web Application REsource) infrastructure. Results. The PHAT contest (Hildebrandt et al. 2010) provides a standard dataset to test old and new met...
Goethe's Exposure of Newton's theory a polemic on Newton's theory of light and colour
Goethe, Johann Wolfgang von
2016-01-01
Johann Wolfgang von Goethe, although best known for his literary work, was also a keen and outspoken natural scientist. In the second polemic part of Zur Farbenlehre (Theory of Colours), for example, Goethe attacked Isaac Newton's ground-breaking revelation that light is heterogeneous and not immutable, as was previously thought.This polemic was unanimously rejected by the physicists of the day, and has often been omitted from compendia of Goethe's works. Indeed, although Goethe repeated all of Newton's key experiments, he was never able to achieve the same results. Many reasons have been proposed for this, ranging from the psychological — such as a blind hatred of Newtonism, self-deceit and paranoid psychosis — to accusations of incapability — Goethe simply did not understand the experiments. Yet Goethe was never to be dissuaded from this passionate conviction.This translation of Goethe's second polemic, published for the first time in English, makes it clear that Goethe did understand the thrust of Ne...
刘庭磊; 王韶; 张知; 朱姜峰
2015-01-01
In order to calculate the theoretical line loss of low-voltage distribution transformer district and improve the line loss management level by using automatic meter reading system, a Newton-Raphson method to calculate the theoretical line loss of low-voltage distribution transformer district by adopting the load electrical energy is proposed. On the basis of the equivalent resistance method and the electrical energy acquired from the watt-hour meters of customers, the mathematical model of regarding theoretical line loss of transformer district as a variable is created. The model introduces relationship between load shape coefficients and the average load current, and the line loss modified coefficient of unbalanced three-phase load. The procedure of the Newton-Raphson method to solve the model is presented. Case analyses show that the proposed method can not only calculate the theoretical line loss of low-voltage distribution transformer district, but also provide the information to identify unknown line loss.%为计算低压配电台区理论线损和利用远程自动抄表系统提高管理线损水平,提出一种采用负荷电量计算低压配电台区理论线损的牛拉法.该方法基于等值电阻法和用户电能表实抄电量,通过引入线路负荷曲线形状系数与平均负荷电流的关系和三相负荷不平衡线损修正系数建立以台区理论线损为变量的数学模型.给出了运用牛拉法求解该模型的实现过程.算例分析表明,提出的方法不仅能够计算低压配电台区的理论线损,而且能够为识别不明线损提供信息.
Newton—Like Iteration Method for Solving Algebraic Equations
JihuanHE
1998-01-01
In this paper,a Newton-like iteration method is proposed to solve an approximate solution of an algebraic equation.The iteration formula obtained by homotopy perturbation method contains the well-known Newton iteration formulain logic.
Dark Matter, the Correction to Newton's Law in a Disk
Heymann, Yuri
2016-09-01
The dark matter problem in the context of spiral galaxies refers to the discrepancy between the galactic mass estimated from luminosity measurements of galaxies with a given mass-to-luminosity ratio and the galactic mass measured from the rotational speed of stars using the Newton's law. Newton's law fails when applied to a star in a spiral galaxy. The problem stems from the fact that Newton's law is applicable to masses represented as points by their barycenter. As spiral galaxies have shapes similar to a disk, we shall correct Newton's law accordingly. We found that the Newton's force exerted by the interior mass of a disk on an adjacent mass shall be multiplied by the coefficient ηdisk estimated to be 7.44±0.83 at a 99% confidence level. The corrective coefficient for the gravitational force exerted by a homogeneous sphere at it's surface is 1.00±0.01 at a 99% confidence level, meaning that Newton's law is not modified for a spherical geometry. This result was proven a long time ago by Newton in the shell theorem.
Newton-Krylov-Schwarz algorithms for the 2D full potential equation
Cai, Xiao-Chuan [Univ. of Colorado, Boulder, CO (United States); Gropp, W.D. [Argonne National Lab., IL (United States); Keyes, D.E. [Old Dominion Univ. Norfolk, VA (United States)] [and others
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.
Yuan, Xiao-Tong; Yan, Shuicheng
2012-04-01
We investigate Newton-type optimization methods for solving piecewise linear systems (PLSs) with nondegenerate coefficient matrix. Such systems arise, for example, from the numerical solution of linear complementarity problem, which is useful to model several learning and optimization problems. In this letter, we propose an effective damped Newton method, PLS-DN, to find the exact (up to machine precision) solution of nondegenerate PLSs. PLS-DN exhibits provable semiiterative property, that is, the algorithm converges globally to the exact solution in a finite number of iterations. The rate of convergence is shown to be at least linear before termination. We emphasize the applications of our method in modeling, from a novel perspective of PLSs, some statistical learning problems such as box-constrained least squares, elitist Lasso (Kowalski & Torreesani, 2008), and support vector machines (Cortes & Vapnik, 1995). Numerical results on synthetic and benchmark data sets are presented to demonstrate the effectiveness and efficiency of PLS-DN on these problems.
Catch a falling apple: Isaac Newton and myths of genius.
Fara, P
1999-01-01
Newton has become a legendary figure belonging to the distant past rather than a historical person who lived at a specific time. Historians and scientists have constantly reinterpreted many anecdotal tales describing Newton's achievements and behaviour, but the most famous concerns the falling apple in his country garden. Newton's apple conjures up multiple allegorical resonances, and examining its historical accuracy is less important than uncovering the mythical truths embedded within this symbol. Because interest groups fashion different collective versions of the past, analysing mythical tales can reveal fundamental yet conflicting attitudes towards science and its practices.
陈国庆; 曹兵
2002-01-01
A new NCP-function for the box constrained variational inequality VI([a, b], F) is proposed and its properties are investigated. Using this NCP-function the box constrained variational inequality is reformulated as a system of semismooth equations whose merit function is differentiable every where. For the Po-function F,any stationary point of the merit function solves the VI([a, b],F). The related Newton-type method is proposed. For continuously differentiable and monotone function F, the generalized Newton equation involved in the method is always a uniquely solvable system of linear equations and affords a direction of sufficient decrease for the merit function. Under the condition of BD-regular solution, the algorithm is globally convergent and has a superlinear or possibly quadratic rate of convergence. The numerical results suggest that the algorithm is robust and efficient.
Water Rockets. Get Funny With Newton's Laws
Manuel Roca Vicent
2017-01-01
Full Text Available The study of the movement of the rocket has been used for decades to encourage students in the study of physics. This system has an undeniable interest to introduce concepts such as properties of gases, laws of Newton, exchange between different types of energy and its conservation or fluid mechanics. Our works has been to build and launch these rockets in different educational levels and in each of these ones have introduced the part of Physics more suited to the knowledge of our students. The aim of the learning experience is to launch the rocket as far as possible and learn to predict the travelled distance, using Newton's laws and fluid mechanics. After experimentation we demonstrated to be able to control the parameters that improve the performance of our rocket, such as the fill factor, the volume and mass of the empty bottle, liquid density, launch angle, pressure prior air release. In addition, it is a fun experience can be attached to all levels of education in primary and high school.
Tornadogenesis Versus Newton's Third Law of Motion
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
Claudio Estatico
2013-01-01
Full Text Available A microwave imaging method previously developed for tomographic inspection of dielectric targets is extended to three-dimensional objects. The approach is based on the full vector equations of the electromagnetic inverse scattering problem. The ill-posedness of the problem is faced by the application of an inexact-Newton method. Preliminary reconstruction results are reported.
Parcels and Land Ownership, Published in 2011, Newton County Government.
NSGIC GIS Inventory (aka Ramona) — This Parcels and Land Ownership dataset as of 2011. The extent of these data is generally Newton County, IN. This metadata was auto-generated through the Ramona GIS...
A Modification of the Newton's Cooling Law and Mpemba Effect
Pankovic, Vladan
2010-01-01
In this work we suggest a simple modification of the Newton's cooling law that can model Mpemba effect. We introduce, in the usual Newton's law, i.e. linear differential equation, an additional term proportional to the quadrate of the geometrical average value of the initial and latter difference between liquid and cooling thermostat (environment) temperature. It, after simple transformations, yields usual Newton's linear differential equation but with modified cooling parameter. This modified cooling parameter represents sum of the usual cooling parameter and an additional term directly proportional to the difference between initial temperature of the liquid and cooling thermostat temperature. Corresponding solution of the modified Newton's cooling equation, i.e. temperature decrease during time, has an additional exponential term with negative argument proportional to mentioned difference between initial temperature of the liquid and temperature of the cooling thermostat. (It can be observed that appearance...
Emilie du Châtelet between Leibniz and Newton
Hagengruber, Ruth
2012-01-01
This book describes Emilie du Chatelet known as "Emilia Newtonmania", and her innovative and outstanding position within the controversy between Newton and Leibniz, one of the fundamental scientific discourses of her time.
"Yugoslavia" Branch of the International Astronomical Institute "Isaac Newton"
Dimitrijević, Milan S.; Popović, Luka Č.; Simić, Zoran; Jovanović, Predrag; Milovanović, Nenad; Bon, Edi
2005-10-01
Isaac Newton Institute of Chile in Eastern Europe and Eurasia and its president and founder Gonzalo Alcaino Barros have been presented as well as the foundation and activities of its "Yugoslavia" branch.
An adaptation of Krylov subspace methods to path following
Walker, H.F. [Utah State Univ., Logan, UT (United States)
1996-12-31
Krylov subspace methods at present constitute a very well known and highly developed class of iterative linear algebra methods. These have been effectively applied to nonlinear system solving through Newton-Krylov methods, in which Krylov subspace methods are used to solve the linear systems that characterize steps of Newton`s method (the Newton equations). Here, we will discuss the application of Krylov subspace methods to path following problems, in which the object is to track a solution curve as a parameter varies. Path following methods are typically of predictor-corrector form, in which a point near the solution curve is {open_quotes}predicted{close_quotes} by some easy but relatively inaccurate means, and then a series of Newton-like corrector iterations is used to return approximately to the curve. The analogue of the Newton equation is underdetermined, and an additional linear condition must be specified to determine corrector steps uniquely. This is typically done by requiring that the steps be orthogonal to an approximate tangent direction. Augmenting the under-determined system with this orthogonality condition in a straightforward way typically works well if direct linear algebra methods are used, but Krylov subspace methods are often ineffective with this approach. We will discuss recent work in which this orthogonality condition is imposed directly as a constraint on the corrector steps in a certain way. The means of doing this preserves problem conditioning, allows the use of preconditioners constructed for the fixed-parameter case, and has certain other advantages. Experiments on standard PDE continuation test problems indicate that this approach is effective.
Motion Equation of Vorticity for Newton Fluid
Jianhua, X
2005-01-01
The vorticity plays an important role in aerodynamics and rotational flow. Usually, they are studied with modified Navier-Stokes equation. This research will deduce the motion equation of vorticity from Navier-Stokes equation. To this propose, the velocity gradient field is decomposed as the stack of non-rotation field and pure-rotation field. By introducing the Chen S+R decomposition, the rotational flow is redefined. For elastic fluid, the research shows that for Newton fluid, the local average rotation always produces an additional pressure on the rotation plane. This item is deterministic rather than stochastic (as Reynolds stress) or adjustable. For non-elastic fluid, such as air, the research shows that the rotation will produce an additional stress along the rotation axis direction, that is on the normal direction of rotation plane. This result can be used to explain the lift force connected with vortex. The main purpose of this research is to supply a solvable mathematical model for the calculation of...
XMM-Newton and Broad Iron Lines
Fabian, A C
2007-01-01
Iron line emission is common in the X-ray spectra of accreting black holes. When the line emission is broad or variable then it is likely to originate from close to the black hole. X-ray irradiation of the accretion flow by the power-law X-ray continuum produces the X-ray 'reflection' spectrum which includes the iron line. The shape and variability of the iron lines and reflection can be used as a diagnostic of the radius, velocity and nature of the flow. The inner radius of the dense flow corresponds to the innermost stable circular orbit and thus can be used to determine the spin of the black hole. Studies of broad iron lines and reflection spectra offer much promise for understanding how the inner parts of accretion flows (and outflows) around black holes operate. There remains great potential for XMM-Newton to continue to make significant progress in this work. The need for high quality spectra and thus for long exposure times is paramount.
Insect Flight: From Newton's Law to Neurons
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.
Arakelian 564: An XMM-Newton view
Vignali, C; Boller, T; Fabian, A C; Vaughan, S; Boller, Th.
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 (kT~140-150 eV) plus a steep power law (Gamma~2.50-2.55). No significant spectral changes are observed between the two observations, although the X-ray flux in the second observation is ~40-50 per cent lower. In both observations we detect a significant absorption edge at a rest-frame energy of ~0.73 keV, corresponding to OVII. 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 parameterisation 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...
Fan, Hong-yi; Lu, Hai-liang; Fan, Yue
2006-02-01
Newton-Leibniz integration rule only applies to commuting functions of continuum variables, while operators made of Dirac's symbols (ket versus bra, e.g., | q>mechanics are usually not commutative. Therefore, integrations over the operators of type |>mathematical gap between classical mechanics and quantum mechanics, and further reveals the beauty and elegance of Dirac's symbolic method and transformation theory. Various applications of the IWOP technique, including constructing the entangled state representations and their applications, are presented.
Newton-Cartan, Galileo-Maxwell and Kaluza-Klein
Bleeken, Dieter Van den
2015-01-01
We study Kaluza-Klein reduction in Newton-Cartan gravity. In particular we show that dimensional reduction and the nonrelativistic limit commute. The resulting theory contains Galilean electromagnetism and a nonrelativistic scalar. It provides the first example of back-reacted couplings of scalar and vector matter to Newton-Cartan gravity. This back-reaction is interesting as it sources the spatial Ricci curvature, providing an example where nonrelativistic gravity is more than just a Newtonian potential.
What are the Hidden Quantum Processes Behind Newton's Laws?
Ostoma, Tom; Trushyk, Mike
1999-01-01
We investigate the hidden quantum processes that are responsible for Newton's laws of motion and Newton's universal law of gravity. We apply Electro-Magnetic Quantum Gravity or EMQG to investigate Newtonian classical physics. EQMG is a quantum gravity theory that is manifestly compatible with Cellular Automata (CA) theory, a new paradigm for physical reality. EMQG is also based on a theory of inertia proposed by R. Haisch, A. Rueda, and H. Puthoff, which we modified and called Quantum Inertia...
Newton-Cartan, Galileo-Maxwell and Kaluza-Klein
Van den Bleeken, Dieter; Yunus, Çağin
2016-07-01
We study Kaluza-Klein reduction in Newton-Cartan gravity. In particular we show that dimensional reduction and the nonrelativistic limit commute. The resulting theory contains Galilean electromagnetism and a nonrelativistic scalar. It provides the first example of back-reacted couplings of scalar and vector matter to Newton-Cartan gravity. This back-reaction is interesting as it sources the spatial Ricci curvature, providing an example where nonrelativistic gravity is more than just a Newtonian potential.
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.
A Frisch-Newton Algorithm for Sparse Quantile Regression
Roger Koenker; Pin Ng
2005-01-01
Recent experience has shown that interior-point methods using a log barrier approach are far superior to classical simplex methods for computing solutions to large parametric quantile regression problems.In many large empirical applications, the design matrix has a very sparse structure. A typical example is the classical fixed-effect model for panel data where the parametric dimension of the model can be quite large, but the number of non-zero elements is quite small. Adopting recent developments in sparse linear algebra we introduce a modified version of the Frisch-Newton algorithm for quantile regression described in Portnoy and Koenker[28].The new algorithm substantially reduces the storage (memory) requirements and increases computational speed.The modified algorithm also facilitates the development of nonparametric quantile regression methods. The pseudo design matrices employed in nonparametric quantile regression smoothing are inherently sparse in both the fidelity and roughness penalty components. Exploiting the sparse structure of these problems opens up a whole range of new possibilities for multivariate smoothing on large data sets via ANOVA-type decomposition and partial linear models.
Quasi-Newton Exploration of Implicitly Constrained Manifolds
Tang, Chengcheng
2011-08-01
A family of methods for the efficient update of second order approximations of a constraint manifold is proposed in this thesis. The concept of such a constraint manifold corresponds to an abstract space prescribed by implicit nonlinear constraints, which can be a set of objects satisfying certain desired properties. This concept has a variety of applications, and it has been successfully introduced to fabrication-aware architectural design as a shape space consisting of all the implementable designs. The local approximation of such a manifold can be first order, in the tangent space, or second order, in the osculating surface, with higher precision. For a nonlinearly constrained manifold with rather high dimension and codimension, the computation of second order approximants (osculants) is time consuming. In this thesis, a type of so-called quasi-Newton manifold exploration methods which approximate the new osculants by updating the ones of a neighbor point by 1st-order information is introduced. The procedures are discussed in detail and the examples implemented to visually verify the methods are illustrated.
Newton law in covariant unimodular F(R) gravity
Nojiri, S.; Odintsov, S. D.; Oikonomou, V. K.
2016-09-01
We investigate the Newton law in the unimodular F(R) gravity. In the standard F(R) gravity, due to the extra scalar mode, there often appear the large corrections to the Newton law and such models are excluded by the experiments and/or the observations. In the unimodular F(R) gravity, however, the extra scalar mode become not to be dynamical due to the unimodular constraint and there is not any correction to the Newton law. Even in the unimodular Einstein gravity, the Newton law is reproduced but the mechanism is a little bit different from that in the unimodular F(R) gravity. We also investigate the unimodular F(R) gravity in the covariant formulation. In the covariant formulation, we include the three-form field. We show that the three-form field could not have any unwanted property, like ghost nor correction to the Newton law. In the covariant formulation, however, the above extra scalar mode becomes dynamical and could give a correction to the Newton law. We also show that there are no difference in the Friedmann-Robertson-Walker (FRW) dynamics in the non-covariant and covariant formulation.
Outdoor relative radiometric calibration method using gray scale targets
DUAN; YiNi; YAN; Lei; YANG; Bin; JING; Xin; CHEN; Wei
2013-01-01
The radiometric calibration of remote sensors is a basis and prerequisite of information quantification in remote sensing. This paper proposes a method for outdoor relative radiometric calibration using gray scale targets. In this method, the idea of two substitutions is adopted. Sunlight is used to replace the integrating sphere light source, and gray scale targets are used to re-place the diffuser. In this way, images at different radiance levels obtained outdoors can calculate the relative radiometric cali-bration coefficients using the least square method. The characteristics of this method are as follows. Firstly, compared with la-boratory calibration, it greatly reduces the complexity of the calibration method and the test cost. Secondly, compared with the existing outdoor relative radiometric calibration of a single radiance level, it uses test images of different radiance levels to re-duce errors. Thirdly, it is easy to operate with fewer environmental requirements, has obvious advantages in the rapid calibra-tion of airborne remote sensors before or after flight and is practical in engineering. This paper theoretically and experimental-ly proves the feasibility of this method. Calibration experiments were conducted on the wide-view multispectral imager (WVMI) using this method, and the precision of this method was evaluated by analyzing the corrected images of large uniform targets on ground. The experiment results have demonstrated that the new method is effective and its precision meets the re-quirement of the absolute radiometric calibration.
Koutroumpa, Dimitra; Smith, Randall K.; Edgar, Richard J.; Kuntz, Kip D.; Plucinsky, Paul P.; Snowden, Steven L.
2010-01-01
We present the first analysis of an XMM-Newton observation of the nearby molecular cloud MBM 12. We find that in the direction of MBM 12 the total O VII (0.57 keV) triplet emission is 1.8(+0.5/-0.6) photons/sq cm/s/sr (or Line Units - LU) while for the O VIII (0.65 keV) line emission we find a 3(sigma) upper limit of Newton observations. This comparison provides new constraints on the relative heliospheric and Local Bubble contributions to the local diffuse X-ray background. The heliospheric SWCX model predicts 0.82 LU for O VII, which accounts for approx. 46+/-15% of the observed value, and 0.33 LU for the O VIII line emission consistent with the XMM-Newton observed value. We discuss our results in combination with previous observations of the MBM 12 with CHANDRA and Suzaku.
何超; 刘西林; 李佳珍
2012-01-01
This paper is aimed to solve the maximum eigenvalue of high order matrix and its corresponding eigenvector through the method which transfers the equations into a higher order nonlinear equations. At the same time, this paper puts forward the Quasi-Newton method which can solve the maximum eigenvalue and its corresponding eigenvector, the rearranging formula and algorithm of Broyden methods are given to solve the maximum eigenvalue and the corresponding eigenvector; the rearranging formula and algorithm of BFS methods; the rearranging formula and algorithm of DFP methods. The judgment matrix of analytic hierarchy process is used as an example. The results show that the idea is feasible and the convergence speed is higher.%将求解高阶矩阵的最大特征值及其对应的特征向量问题转化为高阶非线性方程组的求解问题.在此基础上,提出了求解矩阵最大特征值及其对应特征向量的拟Newton法,给出求解矩阵最大特征值及其单位化向量重新整理后的Broyden方法公式、BFS方法公式、DFP方法公式及其对应的Broyden算法,BFS算法,DFP算法.以层次分析法中高阶判断矩阵为例验证了该方法的可行性,说明了该方法相对收敛速度快的优势.
胡先磊
2011-01-01
为计算斜交的平行式墩台布置桥梁设计中直线与缓和曲线交点桩号,采用牛顿迭代法进行求解.该方法具有趋近次数少、精度满足要求的特点.经实际论证,该方法为近似求解弯斜坡桥直线与缓和曲线交点桩号较好的方法之一.%Skew bridge pier and abutment adopt parallel's axis layout,in order to describe the easement curve and straight line intersection point's mileage. This paper describes Newton-Raphson method to solve this problem, approaching number of times is not too much, and the required precision is very good. The results show that its one of good metlods to describe the easement curve and straight line intersection point's mileage of the skew curved and ramp bridge.
Entropic corrected Newton's law of gravitation and the loop quantum black hole gravitational atom
Aragão, R. G. L.; Silva, C. A. S.
2016-07-01
One proposal by Verlinde is that gravity is not a fundamental, but an entropic force (Verlinde in JHEP 1104:029, 2011. arXiv:hep-th/1001.0785). Based on this new interpretation of the gravity, Verlinde has provide us with a way to derive the Newton's law of gravitation from the Bekenstein-Hawking entropy-area formula. On the other hand, since it has been demonstrated that this formula is susceptible to quantum gravity corrections, one may hope that such corrections could be inherited by Newton's law. In this sense, the entropic interpretation of Newton's law could be a prolific way in order to get verifiable or falsifiable quantum corrections to ordinary gravity in an observationally accessible regimes. On the other hand, loop quantum gravity is a theory that provide a scheme to approach the quantum properties of spacetime. From this theory, emerges a quantum corrected semiclassical black hole solution called loop quantum black hole or self-dual black hole. Among the interesting features of loop quantum black holes, is the fact that they give rise to a modified entropy-area relation where quantum gravity corrections are present. In this work, we obtain a quantum corrected Newton's law from the entropy-area relation given by loop quantum black holes by using the nonrelativistic Verlinde's approach. Moreover, in order to relate our results with the recent experimental activity, we consider the quantum mechanical properties of a huge gravitational atom consisting in a light neutral elementary particle in the presence of a loop quantum black hole.
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.
The RNA Newton polytope and learnability of energy parameters.
Forouzmand, Elmirasadat; Chitsaz, Hamidreza
2013-07-01
Computational RNA structure prediction is a mature important problem that has received a new wave of attention with the discovery of regulatory non-coding RNAs and the advent of high-throughput transcriptome sequencing. Despite nearly two score years of research on RNA secondary structure and RNA-RNA interaction prediction, the accuracy of the state-of-the-art algorithms are still far from satisfactory. So far, researchers have proposed increasingly complex energy models and improved parameter estimation methods, experimental and/or computational, in anticipation of endowing their methods with enough power to solve the problem. The output has disappointingly been only modest improvements, not matching the expectations. Even recent massively featured machine learning approaches were not able to break the barrier. Why is that? The first step toward high-accuracy structure prediction is to pick an energy model that is inherently capable of predicting each and every one of known structures to date. In this article, we introduce the notion of learnability of the parameters of an energy model as a measure of such an inherent capability. We say that the parameters of an energy model are learnable iff there exists at least one set of such parameters that renders every known RNA structure to date the minimum free energy structure. We derive a necessary condition for the learnability and give a dynamic programming algorithm to assess it. Our algorithm computes the convex hull of the feature vectors of all feasible structures in the ensemble of a given input sequence. Interestingly, that convex hull coincides with the Newton polytope of the partition function as a polynomial in energy parameters. To the best of our knowledge, this is the first approach toward computing the RNA Newton polytope and a systematic assessment of the inherent capabilities of an energy model. The worst case complexity of our algorithm is exponential in the number of features. However, dimensionality
Implementation of Newton-Rapshon iterations for parallel staggered-grid geodynamic models
Popov, A. A.; Kaus, B. J. P.
2012-04-01
Staggered-grid finite differences discretization has a good potential for solving highly heterogeneous geodynamic models on parallel computers (e.g. Tackey, 2008; Gerya &Yuen, 2007). They are inherently stable, computationally inexpensive and relatively easy to implement. However, currently used staggered-grid geodynamic codes employ almost exclusively the sub-optimal Picard linearization scheme to deal with nonlinearities. It was shown that Newton-Rapshon linearization can lead to substantial improvements of the solution quality in geodynamic problems, simultaneously with reduction of computer time (e.g. Popov & Sobolev, 2008). This work is aimed at implementation of the Newton-Rapshon linearization in the parallel geodynamic code LaMEM together with staggered-grid discretization and viso-(elasto)-plastic rock rheologies. We present the expressions for the approximate Jacobian matrix, and give detailed comparisons with the currently employed Picard linearization scheme, in terms of solution quality and number of iterations.
Calibration and in orbit performance of the reflection grating spectrometer onboard XMM-Newton
de Vries, C P; Gabriel, C; Gonzalez-Riestra, R; Ibarra, A; Kaastra, J S; Pollock, A M T; Raassen, A J J; Paerels, F B S
2014-01-01
Context: XMM-Newton was launched on 10 December 1999 and has been operational since early 2000. One of the instruments onboard XMM-Newton is the reflection grating spectrometer (RGS). Two identical RGS instruments are available, with each RGS combining a reflection grating assembly (RGA) and a camera with CCDs to record the spectra. Aims: We describe the calibration and in-orbit performance of the RGS instrument. By combining the preflight calibration with appropriate inflight calibration data including the changes in detector performance over time, we aim at profound knowledge about the accuracy in the calibration. This will be crucial for any correct scientific interpretation of spectral features for a wide variety of objects. Methods: Ground calibrations alone are not able to fully characterize the instrument. Dedicated inflight measurements and constant monitoring are essential for a full understanding of the instrument and the variations of the instrument response over time. Physical models of the instru...
Hot stars observed by XMM-Newton. I. The catalog and the properties of OB stars
Nazé, Y.
2009-11-01
Aims: Following the advent of increasingly sensitive X-ray observatories, deep observations of early-type stars became possible. However, the results for only a few objects or clusters have until now been reported and there has been no large survey comparable to that based upon the ROSAT All-Sky Survey (RASS). Methods: A limited survey of X-ray sources, consisting of all public XMM-Newton observations (2XMMi) and slew survey data (XMMSL1), is now available. The X-ray counterparts to hot, massive stars have been searched for in these catalogs. Results: About 300 OB stars were detected with XMM-Newton. Half of them were bright enough for a spectral analysis to be possible, and we make available the detailed spectral properties that were derived. The X-ray spectra of O stars are represented well by low (FNRS. Visiting astronomer, UNAM-Morelos (Mexico).
Graviton KK resonant mode in the correction of the Newton's law from 6D braneworlds
Araujo, J C B; Dantas, D M; Almeida, C A S
2016-01-01
In this work, we derive an expression for the correction in the Newton's law of gravitation due to the gravitational Kaluza-Klein states in a general thick string-like braneworld scenario in six dimensions. In order to analyze corrections to Newton's law we study the gravity fluctuations in a 3-brane placed in a transverse resolved conifold and use suitable numerical methods to attain the massive spectrum and the corresponding eigenfunctions. Such braneworld model has a resolution parameter which removes the conical singularity. The correction has an exponentially suppressed mass term and depends on the values of the eigenfunctions and warp factors computed at the core peak of the brane. The spectrum is real and monotonically increased, as desired. However, the resolution parameter must assume moderate values to have physically acceptable states. Moreover, the trapped massless mode regains the 4D gravity and it is displaced from the origin, sharing similar profile with the energy density of brane for small va...
Cari, C.; Suparmi, A.; Handhika, J.
2016-11-01
The purpose of this study was to describe of preconceptions and anxieties students in solving the representation concepts in newton laws and it's application. This research was conducted for junior undergraduate student's in physics department (36 Students) and physics education (31 Students). The method used in this study is a qualitative descriptive. The data was collection using test for multirepresentation concept, questionnaires for anxiety, and interviews. Based on the analysis it can be concluded that (1) the higher is anxiety, the higher is unconsistency (67,16%), (2) the higher is anxiety, the higher is consistency but wrong answer (29,85%), (3) the lower is anxiety, the higher is consistency of right answer (2,98%). Mostly students have understood fewer physics concept in newtons laws.
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.
Why are Newton's laws laws and why is this question of importance in astrophysics?
Jennison, R. C.
Newton's law of gravitation has been well researched and one may now associate the cause with the geometry of space. Newton's third law is a general law not confined to inertial forces -any physically measurable force appears to require a physically measurable reaction in order that it may exist as a real observable quantity. Newton's first and second laws are in a different category for they are associated with relative motion and the physical reason for this has been an enigma since the publication of Principia Mathematica. Is the phenomenon associated with these two laws caused by the influence of the distance masses of the universe on point-like test masses, as Mach suggested but did not prove, or is it associated with a fundamental internal property of trapped energy within physically finite test masses, befitting to the principle of relativity, as has been proposed in the last decade? The resolution of this problem has profound implications for the identification of hidden matter in the Universe and for the cosmological modelling of the Universe as a whole.
Consistent linguistic fuzzy preference relations method with ranking fuzzy numbers
Ridzuan, Siti Amnah Mohd; Mohamad, Daud; Kamis, Nor Hanimah
2014-12-01
Multi-Criteria Decision Making (MCDM) methods have been developed to help decision makers in selecting the best criteria or alternatives from the options given. One of the well known methods in MCDM is the Consistent Fuzzy Preference Relation (CFPR) method, essentially utilizes a pairwise comparison approach. This method was later improved to cater subjectivity in the data by using fuzzy set, known as the Consistent Linguistic Fuzzy Preference Relations (CLFPR). The CLFPR method uses the additive transitivity property in the evaluation of pairwise comparison matrices. However, the calculation involved is lengthy and cumbersome. To overcome this problem, a method of defuzzification was introduced by researchers. Nevertheless, the defuzzification process has a major setback where some information may lose due to the simplification process. In this paper, we propose a method of CLFPR that preserves the fuzzy numbers form throughout the process. In obtaining the desired ordering result, a method of ranking fuzzy numbers is utilized in the procedure. This improved procedure for CLFPR is implemented to a case study to verify its effectiveness. This method is useful for solving decision making problems and can be applied to many areas of applications.
Rewaria S
2013-05-01
Full Text Available A new simple, accurate, precise and reproducible Ion chromatography method has been developed forthe estimation of Methane sulfonic acid in Busulfan injectable dosage. The method which is developedis also validated in complete compliance with the current regulatory guidelines by using well developedanalytical method validation techniques and tools which comprises with the analytical method validationparameters like Linearity, LOD and LOQ determination, Accuracy, Method precision, Specificity,System suitability, Robustness, Ruggedness etc. by adopting the current method the linearity obtained isnear to 0.999 and thus this shows that the method is capable to give a good detector response, therecovery calculated was within the range of 85% to 115% of the specification limits.
Walton, D. J.; Risaliti, G.; Harrison, F. A.;
2014-01-01
We present a spectral analysis of four coordinated NuSTAR+XMM-Newton observations of the Seyfert galaxy NGC 1365. These exhibit an extreme level of spectral variability, which is primarily due to variable line-of-sight absorption, revealing relatively unobscured states in this source for the firs...
Resolving galaxy cluster gas properties at z~1 with XMM-Newton and Chandra
Bartalucci, I; Pratt, G W; Démoclès, J; van der Burg, R F J; Mazzotta, P
2016-01-01
We present a pilot X-ray study of the five most massive ($M_{500}>5 \\times 10^{14} M_{\\odot}$), distant (z~1), galaxy clusters detected via the Sunyaev-Zeldovich effect. We optimally combine XMM-Newton and Chandra X-ray observations by leveraging the throughput of XMM to obtain spatially-resolved spectroscopy, and the spatial resolution of Chandra to probe the bright inner parts and to detect embedded point sources. Capitalising on the excellent agreement in flux-related measurements, we present a new method to derive the density profiles, constrained in the centre by Chandra and in the outskirts by XMM. We show that the Chandra-XMM combination is fundamental for morphological analysis at these redshifts, the Chandra resolution being required to remove point source contamination, and the XMM sensitivity allowing higher significance detection of faint substructures. The sample is dominated by dynamically disturbed objects. We use the combined Chandra-XMM density profiles and spatially-resolved temperature prof...
Extensive X-ray variability studies of NGC 7314 using long XMM-Newton observations
Emmanoulopoulos, D; Vaughan, S; Papadakis, I E
2016-01-01
We present a detailed X-ray variability study of the low mass Active Galactic Nuclei (AGN) NGC 7314 using the two newly obtained XMM-Newton observations ($140$ and $130$ ks), together with two archival data sets of shorter duration ($45$ and $84$ ks). The relationship between the X-ray variability characteristics and other physical source properties (such as the black hole mass) are still relatively poorly defined, especially for low-mass AGN. We perform a new, fully analytical, power spectral density (PSD) model analysis method, which will be described in detail in a forthcoming paper, that takes into consideration the spectral distortions, caused by red-noise leak. We find that the PSD in the $0.5-10$ keV energy range, can be represented by a bending power-law with a bend around $6.7\\times10^{-5}$ Hz, having a slope of $0.51$ and $1.99$ below and above the bend, respectively. Adding our bend time-scale estimate, to an already published ensemble of estimates from several AGN, supports the idea that the bend ...
Rotarius, Timothy; Wan, Thomas T H; Liberman, Aaron
2007-01-01
Research plays a critical role throughout virtually every conduit of the health services industry. The key terms of research, public relations, and organizational interests are discussed. Combining public relations as a strategic methodology with the organizational concern as a factor, a typology of four different research methods emerges. These four health marketing research methods are: investigative, strategic, informative, and verification. The implications of these distinct and contrasting research methods are examined.
On the origin of two unidentified radio/X-ray sources discovered with XMM-Newton
García, Federico; Combi, Jorge A.; Medina, María C.; Romero, Gustavo E.
2015-12-01
Aims: We aim at clarifying the nature of the emission of two spatially related unidentified X-ray sources detected with XMM-Newton telescope at intermediate-low Galactic latitude Methods: We use the imaging and spectral capabilities of XMM-Newton to study the X-ray properties of these two sources. In addition, we complement our study with radio data obtained at different frequencies to analyze a possible physical association between the sources. Results: Observations reveal a point-like source aligned with elongated diffuse emission. The X-ray spectra of these sources is best-fitted by an absorbed power law with photon index Γ ~ 1.7 for the point-like source and ~2.0 for the extended source. Both sources show nonthermal radio-continuum counterparts that might indicate a physical association. In addition, from the available data, we did not detect variability on the point-like source in several timescales. Two possible scenarios are analyzed: one Galactic and one extra-Galactic. First, based on HI line absorption, assuming a Galactic origin, we infer a distance upper bound of ≲2 kpc, which poses a constraint on the height over the Galactic plane of ≲200 pc and on the linear size of the system of ≲2.3 pc. In this case, the X-ray luminosities are ≳1032 erg s-1 and ≳7.5 × 1032 erg s-1, for the point-like and extended sources, respectively. Second, an extra-Galactic nature is discussed, where the point-like source might be the core of a radio galaxy and the extended source its lobe. In this case, we compare derived fluxes, spectral indices, and spatial correlation with those typical from the radio galaxy population, showing the feasibility of this alternative astrophysical scenario. Conclusions: From the available observational evidence, we suggest that the most promising scenario to explain the nature of these sources is a system consisting of a one-sided radio galaxy, where the point-like source is an active galactic nucleus and the extended source
The XMM-Newton Extended Survey of the Taurus Molecular Cloud (XEST)
Guedel, M.; Briggs, K. R.; Arzner, K.; Audard, M.; Bouvier, J.; Feigelson, E. D.; Franciosini, E.; Glauser, A.; Grosso, N.; Micela, G.; Monin, J.-L.; Montmerle, T.; Padgett, D. L.; Palla, F.; Pillitteri, I.; Rebull, L.; Scelsi, L.; Silva, B.; Skinner, S. L.; Stelzer, B.; Telleschi, A.
2007-01-01
The Taurus Molecular Cloud (TMC) is the nearest large star-forming region, prototypical for the distributed mode of low-mass star formation. Pre-main sequence stars are luminous X-ray sources, probably mostly owing to magnetic energy release. Aims. The XMM-Newton Extended Survey of the Taurus Molecular Cloud (EST) presented in this paper surveys the most populated =5 square degrees of the TMC, using the XMM-Newton X-ray observatory to study the thermal structure, variability, and long-term evolution of hot plasma, to investigate the magnetic dynamo, and to search for new potential members of the association. Many targets are also studied in the optical, and high-resolution X-ray grating spectroscopy has been obtained for selected bright sources. Methods. The X-ray spectra have been coherently analyzed with two different thermal models (2-component thermal model, and a continuous emission measure distribution model). We present overall correlations with fundamental stellar parameters that were derived from the previous literature. A few detections from Chandra observations have been added. Results. The present overview paper introduces the project and provides the basic results from the X-ray analysis of all sources detected in the XEST survey. Comprehensive tables summarize the stellar properties of all targets surveyed. The survey goes deeper than previous X-ray surveys of Taurus by about an order of magnitude and for the first time systematically accesses very faint and strongly absorbed TMC objects. We find a detection rate of 85% and 98% for classical and weak-line T Tau stars (CTTS resp. WTTS), and identify about half of the surveyed protostars and brown dwarfs. Overall, 136 out of 169 surveyed stellar systems are detected. We describe an X-ray luminosity vs. mass correlation, discuss the distribution of X-ray-to-bolometric luminosity ratios, and show evidence for lower X-ray luminosities in CTTS compared to WTTS. Detailed analysis (e.g., variability, rotation
Sample Selected Averaging Method for Analyzing the Event Related Potential
Taguchi, Akira; Ono, Youhei; Kimura, Tomoaki
The event related potential (ERP) is often measured through the oddball task. On the oddball task, subjects are given “rare stimulus” and “frequent stimulus”. Measured ERPs were analyzed by the averaging technique. In the results, amplitude of the ERP P300 becomes large when the “rare stimulus” is given. However, measured ERPs are included samples without an original feature of ERP. Thus, it is necessary to reject unsuitable measured ERPs when using the averaging technique. In this paper, we propose the rejection method for unsuitable measured ERPs for the averaging technique. Moreover, we combine the proposed method and Woody's adaptive filter method.
XMM-Newton observations of Sagittarius A East
Sakano, M; Decourchelle, A; Predehl, P; Sakano, Masaaki; Warwick, Robert S.; Decourchelle, Anne; Predehl, Peter
2003-01-01
We present an analysis of a recent XMM-Newton observation of Sgr A East, a supernova remnant located close to the Galactic Centre. Very high quality X-ray spectra reveal many emission lines from highly ionized atoms consistent with a multi-temperature thin thermal plasma in ionization equilibrium. We use a two-temperature model to fit the spectra and derive temperatures of 1 keV and 4 keV. There is significant concentration of iron towards the centre of the X-ray source such that the iron abundance varies from ~4 times solar in the core down to ~0.5 solar in the outer regions, which contrasts with the rather uniform distribution of other metals such as sulfur, argon and calcium, which have abundances in the range 1--3. The derived total energy, mass, and the abundance pattern are consistent with a single supernova event, either of type-Ia or type-II origin, involving a relatively low-mass progenitor star. A weak 6.4-keV neutral iron fluorescence line is also detected, the illumination source most likely being...
XMM-Newton EPIC observations of Her X-1
Ramsay, G; Jiménez-Garate, M A; Den Herder, J W A; Hailey, C J; Ramsay, Gavin; Zane, Silvia; Jimenez-Garate, Mario; Herder, Jan-Willem den
2002-01-01
We present spin-resolved X-ray data of the neutron star binary Her X-1 taken using the EPIC detectors on XMM-Newton. The data were taken at three distinct epochs through the 35 day precession period. The energy dependent light curves of this source vary significantly from epoch to epoch. It is known that the relative phasing of the soft (2 keV) X-rays varies. Here, we find that the phase shift between the soft and hard bands during the main-on state is considerably different from that observed in the past. Further, it continues to change significantly during the other two observations. This suggests that we are observing, for the first time, a it substantial and continuous variation in the tilt of the disk, as it is expected if the accretion disk is precessing in the system. Analysis of the spin resolved data confirms that the equivalent width variation of the fluorescence Fe K line at \\~6.4 keV follows that of the soft X-ray emission in the main-on state, thus suggesting a common origin for Fe K line and the...
A numerical study of the Schroedinger-Newton equations
Harrison, R I
2001-01-01
and added perturbations oscillate at frequencies determined by the linear perturbation theory. The higher states are shown to be unstable, emitting scatter and leaving a rescaled ground state. The rate at which they decay is controlled by the complex eigenvalues of the linear perturbation. Next we consider adding another dimension in two different ways: by considering the axisymmetric case and the 2-D equations. The stationary solutions are found. We modify the evolution method and find that the higher states are unstable. In 2-D case we consider rigidly rotating solutions and show they exist and are unstable. The Schroedinger-Newton (S-N) equations were proposed by Penrose [18] as a model for gravitational collapse of the wave-function. The potential in the Schroedinger equation is the gravity due to the density of vertical bar psi vertical bar sup 2 , where psi is the wave-function. As with normal Quantum Mechanics the probability, momentum and angular momentum are conserved. We first consider the spherical...
Newton-Krylov-BDDC solvers for nonlinear cardiac mechanics
Pavarino, L.F.
2015-07-18
The aim of this work is to design and study a Balancing Domain Decomposition by Constraints (BDDC) solver for the nonlinear elasticity system modeling the mechanical deformation of cardiac tissue. The contraction–relaxation process in the myocardium is induced by the generation and spread of the bioelectrical excitation throughout the tissue and it is mathematically described by the coupling of cardiac electro-mechanical models consisting of systems of partial and ordinary differential equations. In this study, the discretization of the electro-mechanical models is performed by Q1 finite elements in space and semi-implicit finite difference schemes in time, leading to the solution of a large-scale linear system for the bioelectrical potentials and a nonlinear system for the mechanical deformation at each time step of the simulation. The parallel mechanical solver proposed in this paper consists in solving the nonlinear system with a Newton-Krylov-BDDC method, based on the parallel solution of local mechanical problems and a coarse problem for the so-called primal unknowns. Three-dimensional parallel numerical tests on different machines show that the proposed parallel solver is scalable in the number of subdomains, quasi-optimal in the ratio of subdomain to mesh sizes, and robust with respect to tissue anisotropy.
Statistical evaluation of the flux cross-calibration of the XMM-Newton EPIC cameras
Mateos, S; Read, A M; Sembay, S
2009-01-01
The second XMM-Newton serendipitous source catalogue, 2XMM, provides the ideal data base for performing a statistical evaluation of the flux cross-calibration of the XMM-Newton European Photon Imaging Cameras (EPIC). We aim to evaluate the status of the relative flux calibration of the EPIC cameras on board XMM-Newton (MOS1, MOS2, and pn) and investigate the dependence of the calibration on energy, position in the field of view of the X-ray detectors, and lifetime of the mission. We compiled the distribution of flux percentage differences for large samples of 'good quality' objects detected with at least two of the EPIC cameras. The mean offset of the fluxes and dispersion of the distributions was then found by Gaussian fitting. Count rate to flux conversion was performed with a fixed spectral model. The impact on the results of varying this model was investigated. Excellent agreement was found between the two EPIC MOS cameras to better than 4% from 0.2 keV to 12.0 keV. MOS cameras register 7-9% higher flux t...
Entropic corrected Newton's law of gravitation and the Loop Quantum Black Hole gravitational atom
Aragão, R G L
2016-01-01
One proposal by Verlinde \\cite{Verlinde:2010hp} is that gravity is not a fundamental, but an entropic force. In this way, Verlinde has provide us with a way to derive the Newton's law of gravitation from the Bekenstein-Hawking entropy-area formula. On the other hand, since it has been demonstrated that this formula is susceptible to quantum gravity corrections, one may hope that these corrections could be inherited by the Newton's law. In this way, the entropic interpretation of Newton's law could be a prolific way in order to get verifiable or falsifiable quantum corrections to ordinary gravity in an observationally accessible regimes. Loop quantum gravity is a theory that provide a way to approach the quantum properties of spacetime. From this theory, emerges a quantum corrected semiclassical black hole solution called loop quantum black holes or self-dual black holes. Among the interesting features of loop quantum black holes is the fact that they give rise to a modified entropy-area relation where quantum...
Object relations and real life relationships: a cross method assessment.
Handelzalts, Jonathan E; Fisher, Shimrit; Naot, Rachel
2014-04-01
This study examines the relationship between the psychoanalytic concept of object relations and real life behavior of being in an intimate relationship among heterosexual women. In a multi-method approach we used two different measures; the self-report Bell Object Relations and Reality Testing Inventory (BORRTI; Bell, Billington & Becker, 1986) and the performance based Thematic Apperception Test (TAT) Social Cognition & Object Relations Scale- Global Rating Method SCORS-G (Westen, 1995) to measure the object relations of 60 women. The Alienation subscale of the BORRTI and understanding of social causality subscale of the SCORS-G explained 34.8% of variance of the intimate relationship variable. Thus, women involved in a romantic relationship reported lower rates of alienation on the BORRTI and produced TAT narratives that were more adaptive with regard to understanding of social causality as measured by the SCORS-G than those not currently in a relationship. Results are discussed with reference to the relationship between object relations and real life measures of healthy individuals and in light of the need for a multi-method approach of assessment.
A graphic method for identification of novel glioma related genes.
Gao, Yu-Fei; Shu, Yang; Yang, Lei; He, Yi-Chun; Li, Li-Peng; Huang, GuaHua; Li, Hai-Peng; Jiang, Yang
2014-01-01
Glioma, as the most common and lethal intracranial tumor, is a serious disease that causes many deaths every year. Good comprehension of the mechanism underlying this disease is very helpful to design effective treatments. However, up to now, the knowledge of this disease is still limited. It is an important step to understand the mechanism underlying this disease by uncovering its related genes. In this study, a graphic method was proposed to identify novel glioma related genes based on known glioma related genes. A weighted graph was constructed according to the protein-protein interaction information retrieved from STRING and the well-known shortest path algorithm was employed to discover novel genes. The following analysis suggests that some of them are related to the biological process of glioma, proving that our method was effective in identifying novel glioma related genes. We hope that the proposed method would be applied to study other diseases and provide useful information to medical workers, thereby designing effective treatments of different diseases.
A Graphic Method for Identification of Novel Glioma Related Genes
Yu-Fei Gao
2014-01-01
Full Text Available Glioma, as the most common and lethal intracranial tumor, is a serious disease that causes many deaths every year. Good comprehension of the mechanism underlying this disease is very helpful to design effective treatments. However, up to now, the knowledge of this disease is still limited. It is an important step to understand the mechanism underlying this disease by uncovering its related genes. In this study, a graphic method was proposed to identify novel glioma related genes based on known glioma related genes. A weighted graph was constructed according to the protein-protein interaction information retrieved from STRING and the well-known shortest path algorithm was employed to discover novel genes. The following analysis suggests that some of them are related to the biological process of glioma, proving that our method was effective in identifying novel glioma related genes. We hope that the proposed method would be applied to study other diseases and provide useful information to medical workers, thereby designing effective treatments of different diseases.
Students’ misconceptions about Newton's second law in outer space
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.
Rompe, R.; Thiessen, P. A.; Treder, H.-J.
and Abilities of Theoretical PhysicsThe Newtonean principles and - derived from them - the congnition of the exixtence of elementary constants according to Planck, Einstein and Bohr increasingly prove to be a strong base not only of physics and its apllication in technology but also of each kind of exact sciences in the broadest sense of the word.Since Newton the clarification of concepts with regard so their physical takes place in close connection with the development of mathematical methods. This combination proves to be further productive and ensures the progress of physics an of the exact sciences.Most likely all problems which may be of importance in the realm of life can be treated successfully - adequate expenditure taken for granted - with the existing fund of knowledge and methods.The connection between law and accident resting on reality proves to be a relation of complementarity (there is no absolute accident). This becomes evident in all branches in all branches of physics, not only in thermodynamics and quantum physics, and can be treated already on the level of the Newtonean principles and elementary constants.Theoretical physics as initiated by newton was designed to comprise all parts of nature. About that there is no contrast between classical physics and quantum physics. It is only a matter of differentiation with regard to the different physical contents and the appropriate mathematical methods, dependent of course on the choice problems.Theoretical physics represents a generally available concentration of the reliable knowledge of physics, which is at
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.
Methods and systems relating to an augmented virtuality environment
Nielsen, Curtis W; Anderson, Matthew O; McKay, Mark D; Wadsworth, Derek C; Boyce, Jodie R; Hruska, Ryan C; Koudelka, John A; Whetten, Jonathan; Bruemmer, David J
2014-05-20
Systems and methods relating to an augmented virtuality system are disclosed. A method of operating an augmented virtuality system may comprise displaying imagery of a real-world environment in an operating picture. The method may further include displaying a plurality of virtual icons in the operating picture representing at least some assets of a plurality of assets positioned in the real-world environment. Additionally, the method may include displaying at least one virtual item in the operating picture representing data sensed by one or more of the assets of the plurality of assets and remotely controlling at least one asset of the plurality of assets by interacting with a virtual icon associated with the at least one asset.
Galerkin projection methods for solving multiple related linear systems
Chan, T.F.; Ng, M.; Wan, W.L.
1996-12-31
We consider using Galerkin projection methods for solving multiple related linear systems A{sup (i)}x{sup (i)} = b{sup (i)} for 1 {le} i {le} s, where A{sup (i)} and b{sup (i)} are different in general. We start with the special case where A{sup (i)} = A and A is symmetric positive definite. The method generates a Krylov subspace from a set of direction vectors obtained by solving one of the systems, called the seed system, by the CG method and then projects the residuals of other systems orthogonally onto the generated Krylov subspace to get the approximate solutions. The whole process is repeated with another unsolved system as a seed until all the systems are solved. We observe in practice a super-convergence behaviour of the CG process of the seed system when compared with the usual CG process. We also observe that only a small number of restarts is required to solve all the systems if the right-hand sides are close to each other. These two features together make the method particularly effective. In this talk, we give theoretical proof to justify these observations. Furthermore, we combine the advantages of this method and the block CG method and propose a block extension of this single seed method. The above procedure can actually be modified for solving multiple linear systems A{sup (i)}x{sup (i)} = b{sup (i)}, where A{sup (i)} are now different. We can also extend the previous analytical results to this more general case. Applications of this method to multiple related linear systems arising from image restoration and recursive least squares computations are considered as examples.
A Relation-Based Modeling Method for Workshop Reconfiguration
LI Pan-jing; QIN Xian-sheng; WANG Ke-qin; LI Min
2004-01-01
To respond to the changes in the market rapidly, the workshop has become an ever-changing dynamic environment in regard to personnel change and organization alternation, etc. Therefore it is necessary to reconfigure the workshop system. In this paper, we present the point of view that the closer the relations are among elements in the system, the closer they should be connected with each other when they are integrated in designing and structural modeling of the workshop system. At first, this paper discusses the relationship among elements in the workshop system and events describing the relationship, and provides a technical overview of the expression, definition and classification of relationship. This paper focuses on the steps and algorithm to evaluate the degree of closeness of relations among elements in systems, and emphasizes the modeling methods for workshop reconfiguration by use of a fuzzy cluster. In light of the above steps and methods, types and contents of basic relationships among elements should be determined, and a standard relation tree should be set up. Then, correlation coefficients are calculated by the standard relation tree, and a fuzzy relation matrix is built up. After that, the structure modeling of the workshop equipment system can be completed through a fuzzy cluster. The paper eads with an application of a FMS ( Flexible Manufactuing System) function system modeling. Results of the modeling and calculations are presented.
Bohlin transformation: the hidden symmetry that connects Hooke to Newton
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.
Newton slopes for Artin-Schreier-Witt towers
Davis, Christopher James; Wan, Daqing; Xiao, Liang
2016-01-01
We fix a monic polynomial f(x)∈Fq[x] over a finite field and consider the Artin-Schreier-Witt tower defined by f(x); this is a tower of curves ⋯→Cm→Cm−1→⋯→C0=A1, with total Galois group Zp. We study the Newton slopes of zeta functions of this tower of curves. This reduces to the study of the Newton...... slopes of L-functions associated to characters of the Galois group of this tower. We prove that, when the conductor of the character is large enough, the Newton slopes of the L-function form arithmetic progressions which are independent of the conductor of the character. As a corollary, we obtain...
Non-relativistic twistor theory and Newton--Cartan geometry
Dunajski, Maciej
2015-01-01
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 ${\\mathcal O}\\oplus{\\mathcal O}(2)$. 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.
Newton da Costa and the school of Curitiba
Artibano Micali
2011-06-01
Full Text Available This paper intends to report on the beginning of the publications of Newton da Costa outside Brazil. Two mathematicians played an important role in this beginning: Marcel Guillaume from the University of Clermont-Ferrand and Paul Dedecker from the Universities of Lille and Liège. At the same time we recall the role played by Newton da Costa and Jayme Machado Cardoso in the development of what we call here the School of Curitiba [Escola de Curitiba]. Paraconsistent logic was initiated in this school under the influence of Newton da Costa. As another contribution of this school we mention the development of the theory of quasigroups; Jayme Machado Cardoso's name has been given, by Sade, to some particular objects which are now called Cardoso quasigroups.
Cartan's Equivalence Method and Null coframes in General Relativity
Gallo, E; Kozameh, C; Gallo, Emanuel; Iriondo, Mirta; Kozameh, Carlos
2004-01-01
Using Cartan's equivalence method for point transformations we obtain from first principles the conformal geometry associated with third order ODEs and a special class of PDEs in two dimensions. We explicitly construct the null tetrads of a family of Lorentzian metrics, the conformal group in three and four dimensions and the so called normal metric connection. A special feature of this connection is that the non vanishing components of its torsion depend on one relative invariant, the (generalized) W\\"unschmann Invariant. We show that the above mentioned construction naturally contains the Null Surface Formulation of General Relativity.
Improvement of the relative entropy based protein folding method
无
2009-01-01
The "relative entropy" has been used as a minimization function to predict the tertiary structure of a protein backbone, and good results have been obtained. However, in our previous work, the ensemble average of the contact potential was estimated by an approximate calculation. In order to improve the theoretical integrity of the relative-entropy-based method, a new theoretical calculation method of the ensemble average of the contact potential was presented in this work, which is based on the thermodynamic perturbation theory. Tests of the improved algorithm were performed on twelve small proteins. The root mean square deviations of the predicted versus the native structures from Protein Data Bank range from 0.40 to 0.60 nm. Compared with the previous approximate values, the average prediction accuracy is improved by 0.04 nm.
Improvement of the relative entropy based protein folding method
QI LiSheng; SU JiGuo; CHEN WeiZu; WANG CunXin
2009-01-01
The "relative entropy" has been used as a minimization function to predict the tertiary structure of a protein backbone, and good results have been obtained. However, in our previous work, the ensemble average of the contact potential was estimated by an approximate calculation. In order to improve the theoretical integrity of the relative-entropy-based method, a new theoretical calculation method of the ensemble average of the contact potential was presented in this work, which is based on the thermodynamic perturbation theory. Testa of the improved algorithm were performed on twelve small proteins. The root mean square deviations of the predicted versus the native structures from Protein Data Bank range from 0.40 to 0.60 nm. Compared with the previous approximate values, the average prediction accuracy is improved by 0.04 nm.
RELATIVE CAMERA POSE ESTIMATION METHOD USING OPTIMIZATION ON THE MANIFOLD
C. Cheng
2017-05-01
Full Text Available To solve the problem of relative camera pose estimation, a method using optimization with respect to the manifold is proposed. Firstly from maximum-a-posteriori (MAP model to nonlinear least squares (NLS model, the general state estimation model using optimization is derived. Then the camera pose estimation model is applied to the general state estimation model, while the parameterization of rigid body transformation is represented by Lie group/algebra. The jacobian of point-pose model with respect to Lie group/algebra is derived in detail and thus the optimization model of rigid body transformation is established. Experimental results show that compared with the original algorithms, the approaches with optimization can obtain higher accuracy both in rotation and translation, while avoiding the singularity of Euler angle parameterization of rotation. Thus the proposed method can estimate relative camera pose with high accuracy and robustness.
An extension of relational methods in mortality estimations
2001-06-01
Full Text Available Actuaries and demographers have a long tradition of utilising collateral data to improve mortality estimates. Three main approaches have been used to accomplish the improvement- mortality laws, model life tables, and relational methods. The present paper introduces a regression model that incorporates all of the beneficial principles from each of these approaches. The model is demonstrated on mortality data pertaining to various groups of life insured people in Sweden.
Newton-Cartan supergravity with torsion and Schroedinger supergravity
Bergshoeff, Eric; Zojer, Thomas
2015-01-01
We derive a torsionfull version of three-dimensional N=2 Newton-Cartan supergravity using a non-relativistic notion of the superconformal tensor calculus. The "superconformal" theory that we start with is Schroedinger supergravity which we obtain by gauging the Schroedinger superalgebra. We present two non-relativistic N=2 matter multiplets that can be used as compensators in the superconformal calculus. They lead to two different off-shell formulations which, in analogy with the relativistic case, we call "old minimal" and "new minimal" Newton-Cartan supergravity. We find similarities but also point out some differences with respect to the relativistic case.
The XMM-Newton SSC Survey of the Galactic Plane
Motch, C; Carrera, F; Guillout, P; Hands, A; Hassal, B J M; Herent, O; Lamer, G; Schwope, A; Szokoly, G; Warwick, R; Watson, M; Webb, N; Wheatley, P
2002-01-01
The XMM-Newton Survey Science Center is currently conducting an optical identification programme of serendipitous EPIC sources at low galactic latitudes. The aim of this study is to quantify the various populations contributing to the overall X-ray emission of the Galaxy and elaborate identification rules that can be later applied to the bulk of the low galactic latitude EPIC detections. We report here on preliminary results from an optical campaign performed in two very low b XMM-Newton fields and discuss the contributions of the various X-ray populations. This paper is presented on behalf of the Survey Science Center and of the AXIS collaboration.
DE NEWTON A EINSTEIN: A DEBATE EL DESTINO DEL UNIVERSO
ROGELIO PARREIRA
2010-01-01
Full Text Available En este artículo se describe la historia del pensamiento científico en términos de las teorías de la inercia, el espacio absoluto, la relatividad y la gravitación; de cómo Newton utilizó el trabajo de los primeros investigadores en sus teorías, y Einstein las teorías de Newton en la suya, para tratar de explicar el destino del universo. Es la descripción de un proceso revolucionario del conocimiento científico, y sus aportes al desarrollo de muchos otros campos del saber
Torsional Newton-Cartan geometry from Galilean gauge theory
Banerjee, Rabin
2016-01-01
Using the recently advanced Galilean gauge theory we give a comprehensive construction of torsional Newton Cartan geometry. A complete (implicit) expression of the torsion tensor for the Newton Cartan spacetime is provided. The implicit expression containing torsion is similar to contorsion tensor in Riemann - Cartan space time and it contains an arbitrary shift. This is similar to the shift given by Dautcourt's formula for the symmetric part of the connection. These findings are new in the literature. The well known result for the temporal part of torsion is reproduced from our expression.
Methods of prescribing relative exercise intensity: physiological and practical considerations.
Mann, Theresa; Lamberts, Robert Patrick; Lambert, Michael Ian
2013-07-01
Exercise prescribed according to relative intensity is a routine feature in the exercise science literature and is intended to produce an approximately equivalent exercise stress in individuals with different absolute exercise capacities. The traditional approach has been to prescribe exercise intensity as a percentage of maximal oxygen uptake (VO2max) or maximum heart rate (HRmax) and these methods remain common in the literature. However, exercise intensity prescribed at a %VO2max or %HRmax does not necessarily place individuals at an equivalent intensity above resting levels. Furthermore, some individuals may be above and others below metabolic thresholds such as the aerobic threshold (AerT) or anaerobic threshold (AnT) at the same %VO2max or %HRmax. For these reasons, some authors have recommended that exercise intensity be prescribed relative to oxygen consumption reserve (VO2R), heart rate reserve (HRR), the AerT, or the AnT rather than relative to VO2max or HRmax. The aim of this review was to compare the physiological and practical implications of using each of these methods of relative exercise intensity prescription for research trials or training sessions. It is well established that an exercise bout at a fixed %VO2max or %HRmax may produce interindividual variation in blood lactate accumulation and a similar effect has been shown when relating exercise intensity to VO2R or HRR. Although individual variation in other markers of metabolic stress have seldom been reported, it is assumed that these responses would be similarly heterogeneous at a %VO2max, %HRmax, %VO2R, or %HRR of moderate-to-high intensity. In contrast, exercise prescribed relative to the AerT or AnT would be expected to produce less individual variation in metabolic responses and less individual variation in time to exhaustion at a constant exercise intensity. Furthermore, it would be expected that training prescribed relative to the AerT or AnT would provide a more homogenous training
Methods for Dissecting Motivation and Related Psychological Processes in Rodents.
Ward, Ryan D
2016-01-01
Motivational impairments are increasingly recognized as being critical to functional deficits and decreased quality of life in patients diagnosed with psychiatric disease. Accordingly, much preclinical research has focused on identifying psychological and neurobiological processes which underlie motivation . Inferring motivation from changes in overt behavioural responding in animal models, however, is complicated, and care must be taken to ensure that the observed change is accurately characterized as a change in motivation , and not due to some other, task-related process. This chapter discusses current methods for assessing motivation and related psychological processes in rodents. Using an example from work characterizing the motivational impairments in an animal model of the negative symptoms of schizophrenia, we highlight the importance of careful and rigorous experimental dissection of motivation and the related psychological processes when characterizing motivational deficits in rodent models . We suggest that such work is critical to the successful translation of preclinical findings to therapeutic benefits for patients.
Event horizons in numerical relativity; 1, methods and tests
Libson, J; Seidel, E; Suen, W M; Walker, P; Libson, Joseph; Masso, Joan; Seidel, Edward; Suen, Wai Mo; Walker, Paul
1996-01-01
This is the first paper in a series on event horizons in numerical relativity. In this paper we present methods for obtaining the location of an event horizon in a numerically generated spacetime. The location of an event horizon is determined based on two key ideas: (1) integrating backward in time, and (2) integrating the whole horizon surface. The accuracy and efficiency of the methods are examined with various sample spacetimes, including both analytic (Schwarzschild and Kerr) and numerically generated black holes. The numerically evolved spacetimes contain highly distorted black holes, rotating black holes, and colliding black holes. In all cases studied, our methods can find event horizons to within a very small fraction of a grid zone.
Fara, Patricia
2015-04-13
Isaac Newton's reputation was initially established by his 1672 paper on the refraction of light through a prism; this is now seen as a ground-breaking account and the foundation of modern optics. In it, he claimed to refute Cartesian ideas of light modification by definitively demonstrating that the refrangibility of a ray is linked to its colour, hence arguing that colour is an intrinsic property of light and does not arise from passing through a medium. Newton's later significance as a world-famous scientific genius and the apparent confirmation of his experimental results have tended to obscure the realities of his reception at the time. This paper explores the rhetorical strategies Newton deployed to convince his audience that his conclusions were certain and unchallengeable. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.
Bellon, Richard
2014-01-01
For Victorian men of science, the scientific revolution of the seventeenth century represented a moral awakening. Great theoretical triumphs of inductive science flowed directly from a philosophical spirit that embraced the virtues of self-discipline, courage, patience and humility. Isaac Newton exemplified this union of moral and intellectual excellence. This, at least, was the story crafted by scientific leaders like David Brewster, Thomas Chalmers, John Herschel, Adam Sedgwick and William Whewell. Not everyone accepted this reading of history. Evangelicals who decried the 'materialism' of mainstream science assigned a different meaning to Newton's legacy on behalf of their 'scriptural' alternative. High-church critics of science like John Henry Newman, on the other hand, denied that Newton's secular achievements carried any moral significance at all. These debates over Newtonian standards of philosophical behavior had a decisive influence on Charles Darwin as he developed his theory of evolution by natural selection. Copyright © 2014 Elsevier Ltd. All rights reserved.
Faller, Sven
2008-06-01
In this paper we consider general relativity and its combination with scalar quantum electrodynamics (QED) as an effective quantum field theory at energies well below the Planck scale. This enables us to compute the one-loop quantum corrections to the Newton and Coulomb potentials induced by the combination of graviton and photon fluctuations. We derive the relevant Feynman rules and compute the nonanalytical contributions to the one-loop scattering matrix for charged scalars in the nonrelativistic limit. In particular, we derive the post-Newtonian corrections of order Gm/c2r from general relativity and the genuine quantum corrections of order Gℏ/c3r2.
Poruba Z.
2009-06-01
Full Text Available For the numerical solution of elasto-plastic problems with use of Newton-Raphson method in global equilibrium equation it is necessary to determine the tangent modulus in each integration point. To reach the parabolic convergence of Newton-Raphson method it is convenient to use so called algorithmic tangent modulus which is consistent with used integration scheme. For more simple models for example Chaboche combined hardening model it is possible to determine it in analytical way. In case of more robust macroscopic models it is in many cases necessary to use the approximation approach. This possibility is presented in this contribution for radial return method on Chaboche model. An example solved in software Ansys corresponds to line contact problem with assumption of Coulomb's friction. The study shows at the end that the number of iteration of N-R method is higher in case of continuum tangent modulus and many times higher with use of modified N-R method, initial stiffness method.
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(4) model and atomic clusters.
Communication: Newton homotopies for sampling stationary points of potential energy landscapes
Mehta, Dhagash, E-mail: dmehta@nd.edu [Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, Indiana 46556 (United States); University Chemical Laboratory, The University of Cambridge, Cambridge CB2 1EW (United Kingdom); Chen, Tianran, E-mail: chentia1@msu.edu [Department of Mathematics, Michigan State University, East Lansing, Michigan 48823 (United States); Hauenstein, Jonathan D., E-mail: hauenstein@nd.edu [Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, Indiana 46556 (United States); Wales, David J., E-mail: dw34@cam.ac.uk [University Chemical Laboratory, The University of Cambridge, Cambridge CB2 1EW (United Kingdom)
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.
Generación de fractales a partir del método de Newton
María José Marín
2013-06-01
Full Text Available A large number of fractals known, as Julia fractals and Mandelbrot, can be generated from an iterative method. In this paper we present a virtual laboratory developed as a Graphical User Interface (GUI of Matlab that allows us to study and visualize in real time the relationship between Newton iterative methods of two variables and the generation of fractals. The main objective is to allow Technical School students in Numerical Computation subjects to acquire the skills to generate fractals and interpret their plots in terms of the convergence or divergence speed of the sequence of iterated.
Newton Methods for Large Scale Problems in Machine Learning
Hansen, Samantha Leigh
2014-01-01
The focus of this thesis is on practical ways of designing optimization algorithms for minimizing large-scale nonlinear functions with applications in machine learning. Chapter 1 introduces the overarching ideas in the thesis. Chapters 2 and 3 are geared towards supervised machine learning applications that involve minimizing a sum of loss…
A stochastic quasi Newton method for molecular simulations
Chau, Chun Dong
2010-01-01
In this thesis the Langevin equation with a space-dependent alternative mobility matrix has been considered. Simulations of a complex molecular system with many different length and time scales based on the fundamental equations of motion take a very long simulation time before capturing the functio
Coupling of partitioned physics codes with quasi-Newton methods
Haelterman, R
2017-03-01
Full Text Available Many physics problems can only be studied by coupling various numerical codes, each modeling a subaspect of the physics problem that is addressed. Often, each of these codes needs to be considered as a black box, either because the codes were...
Newton-Krylov Methods in Power Flow and Contingency Analysis
Idema, R.
2012-01-01
A power system is a system that provides for the generation, transmission, and distribution of electrical energy. Power systems are considered to be the largest and most complex man-made systems. As electrical energy is vital to our society, power systems have to satisfy the highest security and re
Newton Methods for Large Scale Problems in Machine Learning
Hansen, Samantha Leigh
2014-01-01
The focus of this thesis is on practical ways of designing optimization algorithms for minimizing large-scale nonlinear functions with applications in machine learning. Chapter 1 introduces the overarching ideas in the thesis. Chapters 2 and 3 are geared towards supervised machine learning applications that involve minimizing a sum of loss…
Moving grids for magnetic reconnection via Newton-Krylov methods
Yuan, Xuefei
2011-01-01
This paper presents a set of computationally efficient, adaptive grids for magnetic reconnection phenomenon where the current density can develop large gradients in the reconnection region. Four-field extended MagnetoHydroDynamics (MHD) equations with hyperviscosity terms are transformed so that the curvilinear coordinates replace the Cartesian coordinates as the independent variables, and moving grids\\' velocities are also considered in this transformed system as a part of interpolating the physical solutions from the old grid to the new grid as time advances. The curvilinear coordinates derived from the current density through the Monge-Kantorovich (MK) optimization approach help to reduce the resolution requirements during the computation. © 2010 Elsevier B.V. All rights reserved.
Study of quantum correlation swapping with relative entropy methods
Xie, Chuanmei; Liu, Yimin; Chen, Jianlan; Zhang, Zhanjun
2016-02-01
To generate long-distance shared quantum correlations (QCs) for information processing in future quantum networks, recently we proposed the concept of QC repeater and its kernel technique named QC swapping. Besides, we extensively studied the QC swapping between two simple QC resources (i.e., a pair of Werner states) with four different methods to quantify QCs (Xie et al. in Quantum Inf Process 14:653-679, 2015). In this paper, we continue to treat the same issue by employing other three different methods associated with relative entropies, i.e., the MPSVW method (Modi et al. in Phys Rev Lett 104:080501, 2010), the Zhang method (arXiv:1011.4333 [quant-ph]) and the RS method (Rulli and Sarandy in Phys Rev A 84:042109, 2011). We first derive analytic expressions of all QCs which occur during the swapping process and then reveal their properties about monotonicity and threshold. Importantly, we find that a long-distance shared QC can be generated from two short-distance ones via QC swapping indeed. In addition, we simply compare our present results with our previous ones.
A Method of Precision Testing Relative Relation of Space Points and Its Application
田林亚; 李鹏; 夏开旺
2003-01-01
In response to the high requirements of industrial precision test, presenting a method of testing relative relation of space points was studied. The spatial-coordinate testing system was established by using high precision theodolites and horizontal staff. The related test was conducted with the use of the space intersection and the precision was evaluated based on the error of baseline. In the practical application of radar-development base, the relative relation of space points was implemented by using electronic theodolite and horizontal staff, which can be easily operated. Furthermore, it can be conveniently used to test small areas where the instruments are difficult to be installed and for high industrial requirements of precision test. The test results can fully meet the strict industrial requirements.
Newton's Laws, Euler's Laws and the Speed of Light
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…
Assessment and Learning of Qualitative Physics in Newton's Playground
Shute, Valerie J.; Ventura, Matthew; Kim, Yoon Jeon
2013-01-01
Digital games are very popular in modern culture. The authors are examining ways to leverage these engaging environments to assess and support student competencies. The authors examine gameplay and learning using a physics game they developed called Newton's Playground. The sample consisted of 167 eighth- and ninth-grade students who played…
Newton's Radii, Maupertuis' Arc Length, and Voltaire's Giant
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…
Gamow on Newton: Another Look at Centripetal Acceleration
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…
Can Newton's Third Law Be "Derived" from the Second?
Gangopadhyaya, Asim; Harrington, James
2017-04-01
Newton's laws have engendered much discussion over several centuries. Today, the internet is awash with a plethora of information on this topic. We find many references to Newton's laws, often discussions of various types of misunderstandings and ways to explain them. Here we present an intriguing example that shows an assumption hidden in Newton's third law that is often overlooked. As is well known, the first law defines an inertial frame of reference and the second law determines the acceleration of a particle in such a frame due to an external force. The third law describes forces exerted on each other in a two-particle system, and allows us to extend the second law to a system of particles. Students are often taught that the three laws are independent. Here we present an example that challenges this assumption. At first glance, it seems to show that, at least for a special case, the third law follows from the second law. However, a careful examination of the assumptions demonstrates that is not quite the case. Ultimately, the example does illustrate the significance of the concept of mass in linking Newton's dynamical principles.
Smoothing Newton Algorithm for Solving Generalized Complementarity Problem
刘晓红; 倪铁
2010-01-01
The generalized complementarity problem includes the well-known nonlinear complementarity problem and linear complementarity problem as special cases.In this paper, based on a class of smoothing functions, a smoothing Newton-type algorithm is proposed for solving the generalized complementarity problem.Under suitable assumptions, the proposed algorithm is well-defined and global convergent.
Newton Algorithms for Analytic Rotation: An Implicit Function Approach
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…
Torsional Newton-Cartan geometry and the Schrodinger algebra
Bergshoeff, Eric A.; Hartong, Jelle; Rosseel, Jan
2015-01-01
We show that by gauging the Schrodinger algebra with critical exponent z and imposing suitable curvature constraints, that make diffeomorphisms equivalent to time and space translations, one obtains a geometric structure known as (twistless) torsional Newton-Cartan geometry (TTNC). This is a version
Newton-Cartan supergravity with torsion and Schrodinger supergravity
Bergshoeff, Eric; Rosseel, Jan; Zojer, Thomas
2015-01-01
We derive a torsionfull version of three-dimensional N - 2 Newton-Cartan supergravity using a non-relativistic notion of the superconformal tensor calculus. The "superconformal" theory that we start with is Schrodinger supergravity which we obtain by gauging the Schrodinger superalgebra. We present
Newton's Radii, Maupertuis' Arc Length, and Voltaire's Giant
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…
Heat kernel for Newton-Cartan trace anomalies
Auzzi, Roberto [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via Musei 41, Brescia, 25121 (Italy); INFN Sezione di Perugia, Via A. Pascoli, Perugia, 06123 (Italy); Nardelli, Giuseppe [Dipartimento di Matematica e Fisica, Università Cattolica del Sacro Cuore, Via Musei 41, Brescia, 25121 (Italy); TIFPA - INFN, Università di Trento,c/o Dipartimento di Fisica, Povo, TN, 38123 (Italy)
2016-07-11
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.
Newton's Laws, Euler's Laws and the Speed of Light
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…
Newton Algorithms for Analytic Rotation: An Implicit Function Approach
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…
Medium-resolution isaac newton telescope library of empirical spectra
Sanchez-Blazquez, P.; Peletier, R. F.; Jimenez-Vicente, J.; Cardiel, N.; Cenarro, A. J.; Falcon-Barroso, J.; Gorgas, J.; Selam, S.; Vazdekis, A.
2006-01-01
A new stellar library developed for stellar population synthesis modelling is presented. The library consists of 985 stars spanning a large range in atmospheric parameters. The spectra were obtained at the 2.5-m Isaac Newton Telescope and cover the range lambda lambda 3525-7500 angstrom at 2.3 angst
Dramatic (and Simple!) Demonstration of Newton's Third Law
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…
A Magnetic Set-Up to Help Teach Newton's Laws
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…
Proving Newton Right or Wrong with Blur Photography
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.)
Smoothing Newton Algorithm for Linear Programming over Symmetric Cones
LIU Xiaohong; NI Tie
2009-01-01
By using the theory of Euclidean Jordan algebras,based on a new class of smoothing functions,the QiSun-Zhou's smoothing Newton algorithm is extended to solve linear programming over symmetric cones (SCLP).The algorithm is globally convergent under suitable assumptions.
Massless QFT and the Newton-Wigner Operator
Much, Albert
2016-01-01
In this work, the second-quantized version of the spatial-coordinate operator, known as the Newton-Wigner-Pryce operator, is explicitly given w.r.t. the massless scalar field. Moreover, transformations of the conformal group are calculated on eigenfunctions of this operator in order to investigate the covariance group w.r.t. probability amplitudes of localizing particles.
Third-Order Family of Methods in Banach Spaces
2011-01-24
methods , the latest of which is free of second derivative and it is of third order. In this paper, we use an idea of Kou and Li [Appl. Math . Comp. 187...modified Newton method in Banach space, Appl. Math . Comput. 175 (2006), 1515–1524. [5] L. B. Rall, Computational Solution of Nonlinear Operator...like method in Banach spaces, J. Comp. Appl. Math . 206 (2007), 873–887. [8] V. Candella, A. Marquina, Recurrence relations for rational cubic methods
Theoretical and applied aerodynamics and related numerical methods
Chattot, J J
2015-01-01
This book covers classical and modern aerodynamics, theories and related numerical methods, for senior and first-year graduate engineering students, including: -The classical potential (incompressible) flow theories for low speed aerodynamics of thin airfoils and high and low aspect ratio wings. - The linearized theories for compressible subsonic and supersonic aerodynamics. - The nonlinear transonic small disturbance potential flow theory, including supercritical wing sections, the extended transonic area rule with lift effect, transonic lifting line and swept or oblique wings to minimize wave drag. Unsteady flow is also briefly discussed. Numerical simulations based on relaxation mixed-finite difference methods are presented and explained. - Boundary layer theory for all Mach number regimes and viscous/inviscid interaction procedures used in practical aerodynamics calculations. There are also four chapters covering special topics, including wind turbines and propellers, airplane design, flow analogies and h...
Improvement of CCME WQI using grey relational method
Yan, Feng; Qiao, Danying; Qian, Bao; Ma, Lin; Xing, Xigang; Zhang, You; Wang, Xiaogang
2016-12-01
The conventional CCME WQI ignores the uncertainties in aquatic environment, which may lead to biases and abrupt changes in evaluation results. To overcome this shortcoming, this study improves the calculation of CCME WQI using trapezoid grey relational degree method, a model dealing with uncertainties introduced by incomplete information. Compared with the conventional CCME WQI, the grey CCME WQI has a stricter calculation method in synthetic evaluation and a better capacity in water quality warning. The water quality of New Tongyang Canal is evaluated and the result shows that its environment deteriorates with the increasing rainfall and improves with the decreasing precipitation. To decrease its environmental risk, it is suggested to reduce the nutrients in agricultural runoff and the oxygen-consuming pollutants in urban runoff in the rainy season.
Permittivity and permeability measurements methods for particle accelerator related materials
Vollinger, C; Jensen, E
2014-01-01
For the special requirements related to particle accelerators, knowledge of the different material parameters of dielectrics and other materials are needed in order to carry out simulations during the design process of accelerator components. This includes also properties of magnetically biased ferrites of which usually little information is available about material characteristics, especially in magnetic bias fields. Several methods of measurement are discussed and compared of which some require delicate sample preparation whereas others can work with unmodified material shapes that makes those methods also suited for acceptance checks on incoming materials delivered by industry. Applications include characterization of different materials, as absorbers in which dielectric losses play an increasing role, as well as low frequency measurements on ferrites that are used for tunable cavities. We present results obtained from both broadband and resonant measurements on different materials determined in the same s...
Fourier analysis for discontinuous Galerkin and related methods
ZHANG MengPing; SHU Chi-Wang
2009-01-01
In this paper we review a series of recent work on using a Fourier analysis technique to study the sta-bility and error estimates for the discontinuous Galerkin method and other related schemes. The ad-vantage of this approach is that it can reveal instability of certain "bad"' schemes; it can verify stability for certain good schemes which are not easily amendable to standard finite element stability analysis techniques; it can provide quantitative error comparisons among different schemes; and it can be used to study superconvergence and time evolution of errors for the discontinuous Galerkin method. We will briefly describe this Fourier analysis technique, summarize its usage in stability and error estimates for various schemes, and indicate the advantages and disadvantages of this technique in comparison with other finite element techniques.
Approximation method to compute domain related integrals in structural studies
Oanta, E.; Panait, C.; Raicu, A.; Barhalescu, M.; Axinte, T.
2015-11-01
Various engineering calculi use integral calculus in theoretical models, i.e. analytical and numerical models. For usual problems, integrals have mathematical exact solutions. If the domain of integration is complicated, there may be used several methods to calculate the integral. The first idea is to divide the domain in smaller sub-domains for which there are direct calculus relations, i.e. in strength of materials the bending moment may be computed in some discrete points using the graphical integration of the shear force diagram, which usually has a simple shape. Another example is in mathematics, where the surface of a subgraph may be approximated by a set of rectangles or trapezoids used to calculate the definite integral. The goal of the work is to introduce our studies about the calculus of the integrals in the transverse section domains, computer aided solutions and a generalizing method. The aim of our research is to create general computer based methods to execute the calculi in structural studies. Thus, we define a Boolean algebra which operates with ‘simple’ shape domains. This algebraic standpoint uses addition and subtraction, conditioned by the sign of every ‘simple’ shape (-1 for the shapes to be subtracted). By ‘simple’ shape or ‘basic’ shape we define either shapes for which there are direct calculus relations, or domains for which their frontiers are approximated by known functions and the according calculus is carried out using an algorithm. The ‘basic’ shapes are linked to the calculus of the most significant stresses in the section, refined aspect which needs special attention. Starting from this idea, in the libraries of ‘basic’ shapes, there were included rectangles, ellipses and domains whose frontiers are approximated by spline functions. The domain triangularization methods suggested that another ‘basic’ shape to be considered is the triangle. The subsequent phase was to deduce the exact relations for the
Problems with the Newton-Schrödinger equations
Anastopoulos, C.; Hu, B. L.
2014-08-01
We examine the origin of the Newton-Schrödinger equations (NSEs) that play an important role in alternative quantum theories (AQT), macroscopic quantum mechanics and gravity-induced decoherence. We show that NSEs for individual particles do not follow from general relativity (GR) plus quantum field theory (QFT). Contrary to what is commonly assumed, the NSEs are not the weak-field (WF), non-relativistic (NR) limit of the semi-classical Einstein equation (SCE) (this nomenclature is preferred over the ‘Moller-Rosenfeld equation’) based on GR+QFT. The wave-function in the NSEs makes sense only as that for a mean field describing a system of N particles as N\\to \\infty , not that of a single or finite many particles. From GR+QFT the gravitational self-interaction leads to mass renormalization, not to a non-linear term in the evolution equations of some AQTs. The WF-NR limit of the gravitational interaction in GR+QFT involves no dynamics. To see the contrast, we give a derivation of the equation (i) governing the many-body wave function from GR+QFT and (ii) for the non-relativistic limit of quantum electrodynamics. They have the same structure, being linear, and very different from NSEs. Adding to this our earlier consideration that for gravitational decoherence the master equations based on GR+QFT lead to decoherence in the energy basis and not in the position basis, despite some AQTs desiring it for the ‘collapse of the wave function’, we conclude that the origins and consequences of NSEs are very different, and should be clearly demarcated from those of the SCE equation, the only legitimate representative of semiclassical gravity, based on GR+QFT.
Chandra and XMM–Newton Observations of H2O Maser Galaxy Mrk 348
J. Wang; J. S. Zhang; Q. Guo
2014-09-01
For H2O megamaser galaxy Mrk 348, Chandra and XMM–Newton data are analysed. The nuclear fitting results of XMM–Newton data suggest the possible existence of a heavily obscured AGN. But the nuclear spectrum extracted from Chandra cannot be well-fitted by the best fitting model for XMM–Newton. Further optimal fitting and discussions are needed.
How Two Differing Portraits of Newton Can Teach Us about the Cultural Context of Science
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.
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
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…
Distributed AC power flow method for AC and AC-DC hybrid ...
DR OKE
Hence the distribution power flow models to be developed were supposed to include both mesh and DG modeling (Sedghi ... Newton-Raphson based power flow methods, namely Newton ... Equation (1) is the mathematical realization of this ...
Huo Hua; Liu Junqiang; Feng Boqin
2006-01-01
A language model for information retrieval is built by using a query language model to generate queries and a document language model to generate documents. The documents are ranked according to the relative entropies of estimated document language models with respect to the estimated query language model. Two popular and relatively efficient smoothing methods, the JelinekMercer method and the absolute discounting method, are used to smooth the document language model in estimation of the document language. A combined model composed of the feedback document language model and the collection language model is used to estimate the query model. A performacne comparison between the new retrieval method and the existing method with feedback is made,and the retrieval performances of the proposed method with the two different smoothing techniques are evaluated on three Text Retrieval Conference (TREC) data sets. Experimental results show that the method is effective and performs better than the basic language modeling approach; moreover, the method using the Jelinek-Mercer technique performs better than that using the absolute discounting technique, and the perfomance is sensitive to the smoothing paramters.
XMM-Newton Education and Public Outreach Program
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.
Gabriel, Carlos; Guainazzi, Matteo; Metcalfe, Leo
2006-12-01
XMM-Newton is a major X-ray observatory of the European Space Agency (ESA). Its observing time is open to astronomers from the whole scientific community on a peer reviewed competitive basis. The Science Operations Centre, located at ESA’s premises in Villafranca del Castillo, Spain, is responsible for the instrument operations, as well as for all the tasks related to facilitating the scientific exploitation of the data which the mission has been producing since its launch in December 1999. Among them, one may list: distribution of scientific data in different formats, from raw telemetry, up to processed and calibrated high-level science products, such as images, spectra, source lists, etc; development and distribution of dedicated science analysis software, as well as of continuously updated instrument calibration; regular organisation of training workshops (free of cost), for potential users of XMM-Newton data, where the procedures and techniques to successfully reduce and analyze XMM-Newton data are introduced; access to the data through state-of-the-art, in-house-developed archival facilities, either through the Internet or via CD-ROM; continuously updated documentation on all aspects of spacecraft and instrument operations, data reduction and analysis; maintenance of a comprehensive set of project web pages; a competent and responsive HelpDesk, providing dedicated support to individual XMM-Newton users. Everyone can be an XMM-Newton observer. So far, astronomers from 36 countries submitted observing programs. Public data can be accessed by every scientist in the world through the XMM-Newton Science Archive (XSA). Despite all these efforts, one can’t help noticing an asymmetric level of scientific exploitation in the realm of X-ray astronomy between developing and developed countries. The latter have traditionally enjoyed the comparative advantage of deeper know-how, deriving from direct experience in hardware and mission development. The XMM-Newton Science
Method of Numerical Modeling for Constitutive Relations of Clay
无
2006-01-01
In order to study the method of numerical modeling for constitutive relations of clay, on the basis of the principle of interaction between plastic volumetric strain and plastic generalized shear strain, the two constitutive functionals that include the function of stress path were used as the basic framework of the constitutive model, which are able to demonstrate the dependence of stress path.The two partial differential cross terms appear in the expression of stress-strain increment relation, which are used to demonstrate the interaction between plastic volumetric strain and plastic generalized shear strain.The elasoplastic constitutive models of clay under two kinds of stress paths, CTC and TC, have been constructed using the triaxial test results.The three basic characteristics of deformation of soils, pressure sensitivity, dilatancy, and dependence of stress path, are well explained using these two models.Using visualization, the three-dimensional surfaces of shear and volume strains in the whole stress field under stress paths of CTC and TC are given.In addition, the two families of shear and volumetric yield loci under CTC and TC paths are plotted respectively.By comparing the results of deformation under these two stress paths, it has been found that, there are obvious differences in the strain peaks, the shapes of strain surfaces, and the trends of variation of volumetric yield loci, however both families of shear yield loci are similar.These results demonstrate that the influences of stress path on the constitutive relations of clay are considerably large and not negligible.The numerical modeling method that can sufficiently reflect the dependence of stress path is superior to the traditional one.
THE NEWTON-LEIBNIZ FORMULA WITH LOWERING CONDITIONS%弱化条件的Newton-Leibniz公式
杨家兴
2001-01-01
鉴于定积分基本公式要求的条件较强，从定积分基本公式——Newton-Leibniz公式出发，首先在弱化其条件的基础上得到一个预备定理并予以证明。然后将预备定理的条件进一步削弱，得到定理弱化条件的Newton-Leibniz公式并予以证明。同时，对上述预备定理及定理中的情况分别举例说明，从而使得定积分基本公式的适用范围更加广泛。%Compared with the strong conditions,a prepared theorem under lowering conditions beginning from the Newtom-Leibniz formula was obtained.Then the further weaken conditions of the prepared theorem and the theorem Newton-Leibniz formula with lowering conditions proved.At the same time,examples to illustrate them and the wider scope of application of the Newton-Leibniz formula were given.
Evolution of the Schr\\"odinger--Newton system for a self--gravitating scalar field
Guzman, F S
2004-01-01
Using numerical techniques, we study the collapse of a scalar field configuration in the Newtonian limit of the spherically symmetric Einstein--Klein--Gordon (EKG) system, which results in the so called Schr\\"odinger--Newton (SN) set of equations. We present the numerical code developed to evolve the SN system and topics related, like equilibrium configurations and boundary conditions. Also, we analyze the evolution of different initial configurations and the physical quantities associated to them. In particular, we readdress the issue of the gravitational cooling mechanism for Newtonian systems and find that all systems settle down onto a 0--node equilibrium configuration.
Planck early results. IX. XMM-Newton follow-up for validation of Planck cluster candidates
Bucher, M.; Delabrouille, J.; Giraud-Héraud, Y.;
2011-01-01
to observe a sample of S/N > 5 candidates. The sensitivity and spatial resolution of XMM-Newton allows unambiguous discrimination between clusters and false candidates. The 4 false candidates have S/N = 4.1. A total of 21 candidates are confirmed as extended X-ray sources. Seventeen are single clusters...... suggest that Planck may have started to reveal a non-negligible population of massive dynamically perturbed objects that is under-represented in X-ray surveys. However, despite their particular properties, these new clusters appear to follow the Y500-YX relation established for X-ray selected objects...
Evaluation of fuzzy relation method for medical decision support.
Wagholikar, Kavishwar; Mangrulkar, Sanjeev; Deshpande, Ashok; Sundararajan, Vijayraghavan
2012-02-01
The potential of computer based tools to assist physicians in medical decision making, was envisaged five decades ago. Apart from factors like usability, integration with work-flow and natural language processing, lack of decision accuracy of the tools has hindered their utility. Hence, research to develop accurate algorithms for medical decision support tools, is required. Pioneering research in last two decades, has demonstrated the utility of fuzzy set theory for medical domain. Recently, Wagholikar and Deshpande proposed a fuzzy relation based method (FR) for medical diagnosis. In their case studies for heart and infectious diseases, the FR method was found to be better than naive bayes (NB). However, the datasets in their studies were small and included only categorical symptoms. Hence, more evaluative studies are required for drawing general conclusions. In the present paper, we compare the classification performance of FR with NB, for a variety of medical datasets. Our results indicate that the FR method is useful for classification problems in the medical domain, and that FR is marginally better than NB. However, the performance of FR is significantly better for datasets having high proportion of unknown attribute values. Such datasets occur in problems involving linguistic information, where FR can be particularly useful. Our empirical study will benefit medical researchers in the choice of algorithms for decision support tools.
Hierarchical robot control structure and Newton's divided difference approach to robot path planning
无
2001-01-01
A hierarchical robot control is proposed for robot soccer system. The Newton' s divided difference is utilized in robot path planning. This paper describes the problems encoutered, software design considerations, vision algorithm and controls of individual robots. The solutions.to the problems implemented are simple and di rect. It is observed that many of the ideas and solutions can be evolved based on simple theories and concepts. This paper focuses on software structure of multi-agent controls, vision algorithm and simple path planning method.
Smoothing Newton Algorithm for Nonlinear Complementarity Problem with a P* Function
无
2007-01-01
By using a smoothing function, the P* nonlinear complementarity problem (P* NCP) can be reformulated as a parameterized smooth equation. A Newton method is proposed to solve this equation. The iteration sequence generated by the proposed algorithm is bounded and this algorithm is proved to be globally convergent under an assumption that the P* NCP has a nonempty solution set. This assumption is weaker than the ones used in most existing smoothing algorithms. In particular, the solution obtained by the proposed algorithm is shown to be a maximally complementary solution of the P* NCP without any additional assumption.
Measurement of Newton's Constant Using a Torsion Balance with Angular Acceleration Feedback
Gundlach, J H; Gundlach, Jens H.; Merkowitz, Stephen M.
2000-01-01
We measured Newton's gravitational constant G using a new torsion balance method. Our technique greatly reduces several sources of uncertainty compared to previous measurements: (1) it is insensitive to anelastic torsion fiber properties; (2) a flat plate pendulum minimizes the sensitivity due to the pendulum density distribution; (3) continuous attractor rotation reduces background noise. We obtain G = (6.674215 +- 0.000092)x10^-11 m^3kg^-1s^-2; the Earth's mass is, therefore, M = (5.972245 +- 0.000082)x10^24 kg and the Sun's mass is M = (1.988435 +- 0.000027)x10^30kg.
Newton's laws of motion in the form of a Riccati equation.
Nowakowski, Marek; Rosu, Haret C
2002-04-01
We discuss two applications of a Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential V(r)=kr(epsilon). For zero total energy we show that the equation of motion can be cast in the Riccati form. We briefly show here an analogy to barotropic Friedmann-Robertson-Lemaitre cosmology where the expansion of the universe can be also shown to obey a Riccati equation. A second application in classical mechanics, where again the Riccati equation appears naturally, are problems involving quadratic friction. We use methods reminiscent to nonrelativistic supersymmetry to generalize and solve such problems.