Semismooth Newton method for gradient constrained minimization problem

NASA Astrophysics Data System (ADS)

Anyyeva, Serbiniyaz; Kunisch, Karl

2012-08-01

In this paper we treat a gradient constrained minimization problem, particular case of which is the elasto-plastic torsion problem. In order to get the numerical approximation to the solution we have developed an algorithm in an infinite dimensional space framework using the concept of the generalized (Newton) differentiation. Regularization was done in order to approximate the problem with the unconstrained minimization problem and to make the pointwise maximum function Newton differentiable. Using semismooth Newton method, continuation method was developed in function space. For the numerical implementation the variational equations at Newton steps are discretized using finite elements method.

Robust large-scale parallel nonlinear solvers for simulations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bader, Brett William; Pawlowski, Roger Patrick; Kolda, Tamara Gibson

2005-11-01

This report documents research to develop robust and efficient solution techniques for solving large-scale systems of nonlinear equations. The most widely used method for solving systems of nonlinear equations is Newton's method. While much research has been devoted to augmenting Newton-based solvers (usually with globalization techniques), little has been devoted to exploring the application of different models. Our research has been directed at evaluating techniques using different models than Newton's method: a lower order model, Broyden's method, and a higher order model, the tensor method. We have developed large-scale versions of each of these models and have demonstrated their usemore » in important applications at Sandia. Broyden's method replaces the Jacobian with an approximation, allowing codes that cannot evaluate a Jacobian or have an inaccurate Jacobian to converge to a solution. Limited-memory methods, which have been successful in optimization, allow us to extend this approach to large-scale problems. We compare the robustness and efficiency of Newton's method, modified Newton's method, Jacobian-free Newton-Krylov method, and our limited-memory Broyden method. Comparisons are carried out for large-scale applications of fluid flow simulations and electronic circuit simulations. Results show that, in cases where the Jacobian was inaccurate or could not be computed, Broyden's method converged in some cases where Newton's method failed to converge. We identify conditions where Broyden's method can be more efficient than Newton's method. We also present modifications to a large-scale tensor method, originally proposed by Bouaricha, for greater efficiency, better robustness, and wider applicability. Tensor methods are an alternative to Newton-based methods and are based on computing a step based on a local quadratic model rather than a linear model. The advantage of Bouaricha's method is that it can use any existing linear solver, which makes it simple to write and easily portable. However, the method usually takes twice as long to solve as Newton-GMRES on general problems because it solves two linear systems at each iteration. In this paper, we discuss modifications to Bouaricha's method for a practical implementation, including a special globalization technique and other modifications for greater efficiency. We present numerical results showing computational advantages over Newton-GMRES on some realistic problems. We further discuss a new approach for dealing with singular (or ill-conditioned) matrices. In particular, we modify an algorithm for identifying a turning point so that an increasingly ill-conditioned Jacobian does not prevent convergence.« less

Globally convergent techniques in nonlinear Newton-Krylov

NASA Technical Reports Server (NTRS)

Brown, Peter N.; Saad, Youcef

1989-01-01

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

How concept images affect students' interpretations of Newton's method

NASA Astrophysics Data System (ADS)

Engelke Infante, Nicole; Murphy, Kristen; Glenn, Celeste; Sealey, Vicki

2018-07-01

Knowing when students have the prerequisite knowledge to be able to read and understand a mathematical text is a perennial concern for instructors. Using text describing Newton's method and Vinner's notion of concept image, we exemplify how prerequisite knowledge influences understanding. Through clinical interviews with first-semester calculus students, we determined how evoked concept images of tangent lines and roots contributed to students' interpretation and application of Newton's method. Results show that some students' concept images of root and tangent line developed throughout the interview process, and most students were able to adequately interpret the text on Newton's method. However, students with insufficient concept images of tangent line and students who were unwilling or unable to modify their concept images of tangent line after reading the text were not successful in interpreting Newton's method.

Newton-Krylov-Schwarz: An implicit solver for CFD

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

Parallel block schemes for large scale least squares computations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Golub, G.H.; Plemmons, R.J.; Sameh, A.

1986-04-01

Large scale least squares computations arise in a variety of scientific and engineering problems, including geodetic adjustments and surveys, medical image analysis, molecular structures, partial differential equations and substructuring methods in structural engineering. In each of these problems, matrices often arise which possess a block structure which reflects the local connection nature of the underlying physical problem. For example, such super-large nonlinear least squares computations arise in geodesy. Here the coordinates of positions are calculated by iteratively solving overdetermined systems of nonlinear equations by the Gauss-Newton method. The US National Geodetic Survey will complete this year (1986) the readjustment ofmore » the North American Datum, a problem which involves over 540 thousand unknowns and over 6.5 million observations (equations). The observation matrix for these least squares computations has a block angular form with 161 diagnonal blocks, each containing 3 to 4 thousand unknowns. In this paper parallel schemes are suggested for the orthogonal factorization of matrices in block angular form and for the associated backsubstitution phase of the least squares computations. In addition, a parallel scheme for the calculation of certain elements of the covariance matrix for such problems is described. It is shown that these algorithms are ideally suited for multiprocessors with three levels of parallelism such as the Cedar system at the University of Illinois. 20 refs., 7 figs.« less

Synthetic Division and Matrix Factorization

ERIC Educational Resources Information Center

Barabe, Samuel; Dubeau, Franc

2007-01-01

Synthetic division is viewed as a change of basis for polynomials written under the Newton form. Then, the transition matrices obtained from a sequence of changes of basis are used to factorize the inverse of a bidiagonal matrix or a block bidiagonal matrix.

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

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

NASA Technical Reports Server (NTRS)

Thurston, G. A.

1980-01-01

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

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

NASA Technical Reports Server (NTRS)

Bailey, Harry E.; Beam, Richard M.

1991-01-01

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

Reading the Principia

NASA Astrophysics Data System (ADS)

Guicciardini, Niccoló

2003-10-01

1. Purpose of this book; Part I. Newton's Methods: 2. Newton's methods of series and fluxions; 3. The mathematical methods of the Principia; Part II. Three Readers: 4. Newton: between tradition and innovation; 5. Huygens: the Principia and proportion theory; 6. Leibniz: not equivalent in practice; Part III. Two Schools: 7. Britain: in the wake of the Principia; 8. Basel: challenging the Principia; 9. Conclusion: Newtonians, Leibnizians and Eulerians; References.

Scalable parallel elastic-plastic finite element analysis using a quasi-Newton method with a balancing domain decomposition preconditioner

NASA Astrophysics Data System (ADS)

Yusa, Yasunori; Okada, Hiroshi; Yamada, Tomonori; Yoshimura, Shinobu

2018-04-01

A domain decomposition method for large-scale elastic-plastic problems is proposed. The proposed method is based on a quasi-Newton method in conjunction with a balancing domain decomposition preconditioner. The use of a quasi-Newton method overcomes two problems associated with the conventional domain decomposition method based on the Newton-Raphson method: (1) avoidance of a double-loop iteration algorithm, which generally has large computational complexity, and (2) consideration of the local concentration of nonlinear deformation, which is observed in elastic-plastic problems with stress concentration. Moreover, the application of a balancing domain decomposition preconditioner ensures scalability. Using the conventional and proposed domain decomposition methods, several numerical tests, including weak scaling tests, were performed. The convergence performance of the proposed method is comparable to that of the conventional method. In particular, in elastic-plastic analysis, the proposed method exhibits better convergence performance than the conventional method.

Performance of Nonlinear Finite-Difference Poisson-Boltzmann Solvers

PubMed Central

Cai, Qin; Hsieh, Meng-Juei; Wang, Jun; Luo, Ray

2014-01-01

We implemented and optimized seven finite-difference solvers for the full nonlinear Poisson-Boltzmann equation in biomolecular applications, including four relaxation methods, one conjugate gradient method, and two inexact Newton methods. The performance of the seven solvers was extensively evaluated with a large number of nucleic acids and proteins. Worth noting is the inexact Newton method in our analysis. We investigated the role of linear solvers in its performance by incorporating the incomplete Cholesky conjugate gradient and the geometric multigrid into its inner linear loop. We tailored and optimized both linear solvers for faster convergence rate. In addition, we explored strategies to optimize the successive over-relaxation method to reduce its convergence failures without too much sacrifice in its convergence rate. Specifically we attempted to adaptively change the relaxation parameter and to utilize the damping strategy from the inexact Newton method to improve the successive over-relaxation method. Our analysis shows that the nonlinear methods accompanied with a functional-assisted strategy, such as the conjugate gradient method and the inexact Newton method, can guarantee convergence in the tested molecules. Especially the inexact Newton method exhibits impressive performance when it is combined with highly efficient linear solvers that are tailored for its special requirement. PMID:24723843

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

NASA Astrophysics Data System (ADS)

Argyros, Ioannis K.

2009-06-01

We provide a semilocal convergence analysis for a certain class of Newton-like methods considered also in [I.K. Argyros, A unifying local-semilocal convergence analysis and applications for two-point Newton-like methods in Banach space, J. Math. Anal. Appl. 298 (2004) 374-397; I.K. Argyros, Computational theory of iterative methods, in: C.K. Chui, L. Wuytack (Eds.), Series: Studies in Computational Mathematics, vol. 15, Elsevier Publ. Co, New York, USA, 2007; J.E. Dennis, Toward a unified convergence theory for Newton-like methods, in: L.B. Rall (Ed.), Nonlinear Functional Analysis and Applications, Academic Press, New York, 1971], in order to approximate a locally unique solution of an equation in a Banach space. Using a combination of Lipschitz and center-Lipschitz conditions, instead of only Lipschitz conditions [F.A. Potra, Sharp error bounds for a class of Newton-like methods, Libertas Math. 5 (1985) 71-84], we provide an analysis with the following advantages over the work in [F.A. Potra, Sharp error bounds for a class of Newton-like methods, Libertas Math. 5 (1985) 71-84] which improved the works in [W.E. Bosarge, P.L. Falb, A multipoint method of third order, J. Optimiz. Theory Appl. 4 (1969) 156-166; W.E. Bosarge, P.L. Falb, Infinite dimensional multipoint methods and the solution of two point boundary value problems, Numer. Math. 14 (1970) 264-286; J.E. Dennis, On the Kantorovich hypothesis for Newton's method, SIAM J. Numer. Anal. 6 (3) (1969) 493-507; J.E. Dennis, Toward a unified convergence theory for Newton-like methods, in: L.B. Rall (Ed.), Nonlinear Functional Analysis and Applications, Academic Press, New York, 1971; H.J. Kornstaedt, Ein allgemeiner Konvergenzstaz fü r verschä rfte Newton-Verfahrem, in: ISNM, vol. 28, Birkhaü ser Verlag, Basel and Stuttgart, 1975, pp. 53-69; P. Laasonen, Ein überquadratisch konvergenter iterativer algorithmus, Ann. Acad. Sci. Fenn. Ser I 450 (1969) 1-10; F.A. Potra, On a modified secant method, L'analyse numérique et la theorie de l'approximation 8 (2) (1979) 203-214; F.A. Potra, An application of the induction method of V. Pták to the study of Regula Falsi, Aplikace Matematiky 26 (1981) 111-120; F.A. Potra, On the convergence of a class of Newton-like methods, in: Iterative Solution of Nonlinear Systems of Equations, in: Lecture Notes in Mathematics, vol. 953, Springer-Verlag, New York, 1982; F.A. Potra, V. Pták, Nondiscrete induction and double step secant method, Math. Scand. 46 (1980) 236-250; F.A. Potra, V. Pták, On a class of modified Newton processes, Numer. Funct. Anal. Optim. 2 (1) (1980) 107-120; F.A. Potra, Sharp error bounds for a class of Newton-like methods, Libertas Math. 5 (1985) 71-84; J.W. Schmidt, Untere Fehlerschranken für Regula-Falsi Verfahren, Period. Math. Hungar. 9 (3) (1978) 241-247; J.W. Schmidt, H. Schwetlick, Ableitungsfreie Verfhren mit höherer Konvergenzgeschwindifkeit, Computing 3 (1968) 215-226; J.F. Traub, Iterative Methods for the Solution of Equations, Prentice Hall, Englewood Cliffs, New Jersey, 1964; M.A. Wolfe, Extended iterative methods for the solution of operator equations, Numer. Math. 31 (1978) 153-174]: larger convergence domain and weaker sufficient convergence conditions. Numerical examples further validating the results are also provided.

What can numerical computation do for the history of science? (a study of an orbit drawn by Newton in a letter to Hooke)

NASA Astrophysics Data System (ADS)

Cardozo Dias, Penha Maria; Stuchi, T. J.

2013-11-01

In a letter to Robert Hooke, Isaac Newton drew the orbit of a mass moving under a constant attracting central force. The drawing of the orbit may indicate how and when Newton developed dynamic categories. Some historians claim that Newton used a method contrived by Hooke; others that he used some method of curvature. We prove that Hooke’s method is a second-order symplectic area-preserving algorithm, and the method of curvature is a first-order algorithm without special features; then we integrate the Hamiltonian equations. Integration by the method of curvature can also be done, exploring the geometric properties of curves. We compare three methods: Hooke’s method, the method of curvature and a first-order method. A fourth-order algorithm sets a standard of comparison. We analyze which of these methods best explains Newton’s drawing.

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

USGS Publications Warehouse

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

1992-01-01

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

Program for Calculating the Cubic and Fifth Roots of a Number of Newton's Method (610 IBM Electronic Computer); PROGRAMMA PER IL CALCOLO DELLE RADICI TERZA E QUINTA DI UN NUMERO, COL METODO DI NEWTON (CALCOLATORE ELETTRONICO IBM 610)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Giucci, D.

1963-01-01

A program was devised for calculating the cubic and fifth roots of a number of Newton's method using the 610 IBM electronic computer. For convenience a program was added for obtaining n/sup th/ roots by the logarithmic method. (auth)

A New Newton-Like Iterative Method for Roots of Analytic Functions

ERIC Educational Resources Information Center

Otolorin, Olayiwola

2005-01-01

A new Newton-like iterative formula for the solution of non-linear equations is proposed. To derive the formula, the convergence criteria of the one-parameter iteration formula, and also the quasilinearization in the derivation of Newton's formula are reviewed. The result is a new formula which eliminates the limitations of other methods. There is…

Multivariable frequency domain identification via 2-norm minimization

NASA Technical Reports Server (NTRS)

Bayard, David S.

1992-01-01

The author develops a computational approach to multivariable frequency domain identification, based on 2-norm minimization. In particular, a Gauss-Newton (GN) iteration is developed to minimize the 2-norm of the error between frequency domain data and a matrix fraction transfer function estimate. To improve the global performance of the optimization algorithm, the GN iteration is initialized using the solution to a particular sequentially reweighted least squares problem, denoted as the SK iteration. The least squares problems which arise from both the SK and GN iterations are shown to involve sparse matrices with identical block structure. A sparse matrix QR factorization method is developed to exploit the special block structure, and to efficiently compute the least squares solution. A numerical example involving the identification of a multiple-input multiple-output (MIMO) plant having 286 unknown parameters is given to illustrate the effectiveness of the algorithm.

A Block Preconditioned Conjugate Gradient-type Iterative Solver for Linear Systems in Thermal Reservoir Simulation

NASA Astrophysics Data System (ADS)

Betté, Srinivas; Diaz, Julio C.; Jines, William R.; Steihaug, Trond

1986-11-01

A preconditioned residual-norm-reducing iterative solver is described. Based on a truncated form of the generalized-conjugate-gradient method for nonsymmetric systems of linear equations, the iterative scheme is very effective for linear systems generated in reservoir simulation of thermal oil recovery processes. As a consequence of employing an adaptive implicit finite-difference scheme to solve the model equations, the number of variables per cell-block varies dynamically over the grid. The data structure allows for 5- and 9-point operators in the areal model, 5-point in the cross-sectional model, and 7- and 11-point operators in the three-dimensional model. Block-diagonal-scaling of the linear system, done prior to iteration, is found to have a significant effect on the rate of convergence. Block-incomplete-LU-decomposition (BILU) and block-symmetric-Gauss-Seidel (BSGS) methods, which result in no fill-in, are used as preconditioning procedures. A full factorization is done on the well terms, and the cells are ordered in a manner which minimizes the fill-in in the well-column due to this factorization. The convergence criterion for the linear (inner) iteration is linked to that of the nonlinear (Newton) iteration, thereby enhancing the efficiency of the computation. The algorithm, with both BILU and BSGS preconditioners, is evaluated in the context of a variety of thermal simulation problems. The solver is robust and can be used with little or no user intervention.

Rate of convergence of k-step Newton estimators to efficient likelihood estimators

Treesearch

Steve Verrill

2007-01-01

We make use of Cramer conditions together with the well-known local quadratic convergence of Newton?s method to establish the asymptotic closeness of k-step Newton estimators to efficient likelihood estimators. In Verrill and Johnson [2007. Confidence bounds and hypothesis tests for normal distribution coefficients of variation. USDA Forest Products Laboratory Research...

Improved Quasi-Newton method via PSB update for solving systems of nonlinear equations

NASA Astrophysics Data System (ADS)

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.

Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Paul T.; Shadid, John N.; Sala, Marzio

In this study results are presented for the large-scale parallel performance of an algebraic multilevel preconditioner for solution of the drift-diffusion model for semiconductor devices. The preconditioner is the key numerical procedure determining the robustness, efficiency and scalability of the fully-coupled Newton-Krylov based, nonlinear solution method that is employed for this system of equations. The coupled system is comprised of a source term dominated Poisson equation for the electric potential, and two convection-diffusion-reaction type equations for the electron and hole concentration. The governing PDEs are discretized in space by a stabilized finite element method. Solution of the discrete system ismore » obtained through a fully-implicit time integrator, a fully-coupled Newton-based nonlinear solver, and a restarted GMRES Krylov linear system solver. The algebraic multilevel preconditioner is based on an aggressive coarsening graph partitioning of the nonzero block structure of the Jacobian matrix. Representative performance results are presented for various choices of multigrid V-cycles and W-cycles and parameter variations for smoothers based on incomplete factorizations. Parallel scalability results are presented for solution of up to 10{sup 8} unknowns on 4096 processors of a Cray XT3/4 and an IBM POWER eServer system.« less

Progress on a generalized coordinates tensor product finite element 3DPNS algorithm for subsonic

NASA Technical Reports Server (NTRS)

Baker, A. J.; Orzechowski, J. A.

1983-01-01

A generalized coordinates form of the penalty finite element algorithm for the 3-dimensional parabolic Navier-Stokes equations for turbulent subsonic flows was derived. This algorithm formulation requires only three distinct hypermatrices and is applicable using any boundary fitted coordinate transformation procedure. The tensor matrix product approximation to the Jacobian of the Newton linear algebra matrix statement was also derived. Tne Newton algorithm was restructured to replace large sparse matrix solution procedures with grid sweeping using alpha-block tridiagonal matrices, where alpha equals the number of dependent variables. Numerical experiments were conducted and the resultant data gives guidance on potentially preferred tensor product constructions for the penalty finite element 3DPNS algorithm.

An improved Newton iteration for the generalized inverse of a matrix, with applications

NASA Technical Reports Server (NTRS)

Pan, Victor; Schreiber, Robert

1990-01-01

The purpose here is to clarify and illustrate the potential for the use of variants of Newton's method of solving problems of practical interest on highly personal computers. The authors show how to accelerate the method substantially and how to modify it successfully to cope with ill-conditioned matrices. The authors conclude that Newton's method can be of value for some interesting computations, especially in parallel and other computing environments in which matrix products are especially easy to work with.

Convergence of Newton's method for a single real equation

NASA Technical Reports Server (NTRS)

Campbell, C. W.

1985-01-01

Newton's method for finding the zeroes of a single real function is investigated in some detail. Convergence is generally checked using the Contraction Mapping Theorem which yields sufficient but not necessary conditions for convergence of the general single point iteration method. The resulting convergence intervals are frequently considerably smaller than actual convergence zones. For a specific single point iteration method, such as Newton's method, better estimates of regions of convergence should be possible. A technique is described which, under certain conditions (frequently satisfied by well behaved functions) gives much larger zones where convergence is guaranteed.

A comparison of several methods of solving nonlinear regression groundwater flow problems

USGS Publications Warehouse

Cooley, Richard L.

1985-01-01

Computational efficiency and computer memory requirements for four methods of minimizing functions were compared for four test nonlinear-regression steady state groundwater flow problems. The fastest methods were the Marquardt and quasi-linearization methods, which required almost identical computer times and numbers of iterations; the next fastest was the quasi-Newton method, and last was the Fletcher-Reeves method, which did not converge in 100 iterations for two of the problems. The fastest method per iteration was the Fletcher-Reeves method, and this was followed closely by the quasi-Newton method. The Marquardt and quasi-linearization methods were slower. For all four methods the speed per iteration was directly related to the number of parameters in the model. However, this effect was much more pronounced for the Marquardt and quasi-linearization methods than for the other two. Hence the quasi-Newton (and perhaps Fletcher-Reeves) method might be more efficient than either the Marquardt or quasi-linearization methods if the number of parameters in a particular model were large, although this remains to be proven. The Marquardt method required somewhat less central memory than the quasi-linearization metilod for three of the four problems. For all four problems the quasi-Newton method required roughly two thirds to three quarters of the memory required by the Marquardt method, and the Fletcher-Reeves method required slightly less memory than the quasi-Newton method. Memory requirements were not excessive for any of the four methods.

How Fast Does a Building Fall?

ERIC Educational Resources Information Center

Denny, Mark

2010-01-01

In this paper, the time required for a tower block to collapse is calculated. The tower collapses progressively, with one floor falling onto the floor below, causing it to fall. The rate of collapse is found to be not much slower than freefall. The calculation is an engaging and relevant application of Newton's laws, suitable for undergraduate…

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

PubMed

Schilt, Cornelis J

2016-01-01

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

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

NASA Technical Reports Server (NTRS)

Thurston, Gaylen A.

1989-01-01

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

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

PubMed Central

Kuehn, Daniel

2013-01-01

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

High-order Newton-penalty algorithms

NASA Astrophysics Data System (ADS)

Dussault, Jean-Pierre

2005-10-01

Recent efforts in differentiable non-linear programming have been focused on interior point methods, akin to penalty and barrier algorithms. In this paper, we address the classical equality constrained program solved using the simple quadratic loss penalty function/algorithm. The suggestion to use extrapolations to track the differentiable trajectory associated with penalized subproblems goes back to the classic monograph of Fiacco & McCormick. This idea was further developed by Gould who obtained a two-steps quadratically convergent algorithm using prediction steps and Newton correction. Dussault interpreted the prediction step as a combined extrapolation with respect to the penalty parameter and the residual of the first order optimality conditions. Extrapolation with respect to the residual coincides with a Newton step.We explore here higher-order extrapolations, thus higher-order Newton-like methods. We first consider high-order variants of the Newton-Raphson method applied to non-linear systems of equations. Next, we obtain improved asymptotic convergence results for the quadratic loss penalty algorithm by using high-order extrapolation steps.

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

NASA Technical Reports Server (NTRS)

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

1976-01-01

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

Designing stellarator coils by a modified Newton method using FOCUS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhu, Caoxiang; Hudson, Stuart R.; Song, Yuntao

To find the optimal coils for stellarators, nonlinear optimization algorithms are applied in existing coil design codes. However, none of these codes have used the information from the second-order derivatives. In this paper, we present a modified Newton method in the recently developed code FOCUS. The Hessian matrix is calculated with analytically derived equations. Its inverse is approximated by a modified Cholesky factorization and applied in the iterative scheme of a classical Newton method. Using this method, FOCUS is able to recover the W7-X modular coils starting from a simple initial guess. Results demonstrate significant advantages.

Designing stellarator coils by a modified Newton method using FOCUS

NASA Astrophysics Data System (ADS)

Zhu, Caoxiang; Hudson, Stuart R.; Song, Yuntao; Wan, Yuanxi

2018-06-01

To find the optimal coils for stellarators, nonlinear optimization algorithms are applied in existing coil design codes. However, none of these codes have used the information from the second-order derivatives. In this paper, we present a modified Newton method in the recently developed code FOCUS. The Hessian matrix is calculated with analytically derived equations. Its inverse is approximated by a modified Cholesky factorization and applied in the iterative scheme of a classical Newton method. Using this method, FOCUS is able to recover the W7-X modular coils starting from a simple initial guess. Results demonstrate significant advantages.

Designing stellarator coils by a modified Newton method using FOCUS

DOE PAGES

Zhu, Caoxiang; Hudson, Stuart R.; Song, Yuntao; ...

2018-03-22

To find the optimal coils for stellarators, nonlinear optimization algorithms are applied in existing coil design codes. However, none of these codes have used the information from the second-order derivatives. In this paper, we present a modified Newton method in the recently developed code FOCUS. The Hessian matrix is calculated with analytically derived equations. Its inverse is approximated by a modified Cholesky factorization and applied in the iterative scheme of a classical Newton method. Using this method, FOCUS is able to recover the W7-X modular coils starting from a simple initial guess. Results demonstrate significant advantages.

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

NASA Astrophysics Data System (ADS)

Tang, Peipei; Wang, Chengjing; Dai, Xiaoxia

2016-04-01

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

Krylov Deferred Correction Accelerated Method of Lines Transpose for Parabolic Problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jia, Jun; Jingfang, Huang

2008-01-01

In this paper, a new class of numerical methods for the accurate and efficient solutions of parabolic partial differential equations is presented. Unlike traditional method of lines (MoL), the new {\\bf \\it Krylov deferred correction (KDC) accelerated method of lines transpose (MoL^T)} first discretizes the temporal direction using Gaussian type nodes and spectral integration, and symbolically applies low-order time marching schemes to form a preconditioned elliptic system, which is then solved iteratively using Newton-Krylov techniques such as Newton-GMRES or Newton-BiCGStab method. Each function evaluation in the Newton-Krylov method is simply one low-order time-stepping approximation of the error by solving amore » decoupled system using available fast elliptic equation solvers. Preliminary numerical experiments show that the KDC accelerated MoL^T technique is unconditionally stable, can be spectrally accurate in both temporal and spatial directions, and allows optimal time-step sizes in long-time simulations.« less

A Practical, Robust and Fast Method for Location Localization in Range-Based Systems.

PubMed

Huang, Shiping; Wu, Zhifeng; Misra, Anil

2017-12-11

Location localization technology is used in a number of industrial and civil applications. Real time location localization accuracy is highly dependent on the quality of the distance measurements and efficiency of solving the localization equations. In this paper, we provide a novel approach to solve the nonlinear localization equations efficiently and simultaneously eliminate the bad measurement data in range-based systems. A geometric intersection model was developed to narrow the target search area, where Newton's Method and the Direct Search Method are used to search for the unknown position. Not only does the geometric intersection model offer a small bounded search domain for Newton's Method and the Direct Search Method, but also it can self-correct bad measurement data. The Direct Search Method is useful for the coarse localization or small target search domain, while the Newton's Method can be used for accurate localization. For accurate localization, by utilizing the proposed Modified Newton's Method (MNM), challenges of avoiding the local extrema, singularities, and initial value choice are addressed. The applicability and robustness of the developed method has been demonstrated by experiments with an indoor system.

A Newton method for the magnetohydrodynamic equilibrium equations

NASA Astrophysics Data System (ADS)

Oliver, Hilary James

We have developed and implemented a (J, B) space Newton method to solve the full nonlinear three dimensional magnetohydrodynamic equilibrium equations in toroidal geometry. Various cases have been run successfully, demonstrating significant improvement over Picard iteration, including a 3D stellarator equilibrium at β = 2%. The algorithm first solves the equilibrium force balance equation for the current density J, given a guess for the magnetic field B. This step is taken from the Picard-iterative PIES 3D equilibrium code. Next, we apply Newton's method to Ampere's Law by expansion of the functional J(B), which is defined by the first step. An analytic calculation in magnetic coordinates, of how the Pfirsch-Schlüter currents vary in the plasma in response to a small change in the magnetic field, yields the Newton gradient term (analogous to ∇f . δx in Newton's method for f(x) = 0). The algorithm is computationally feasible because we do this analytically, and because the gradient term is flux surface local when expressed in terms of a vector potential in an Ar=0 gauge. The equations are discretized by a hybrid spectral/offset grid finite difference technique, and leading order radial dependence is factored from Fourier coefficients to improve finite- difference accuracy near the polar-like origin. After calculating the Newton gradient term we transfer the equation from the magnetic grid to a fixed background grid, which greatly improves the code's performance.

Application of Four-Point Newton-EGSOR iteration for the numerical solution of 2D Porous Medium Equations

NASA Astrophysics Data System (ADS)

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

2017-09-01

Partial differential equations that are used in describing the nonlinear heat and mass transfer phenomena are difficult to be solved. For the case where the exact solution is difficult to be obtained, it is necessary to use a numerical procedure such as the finite difference method to solve a particular partial differential equation. In term of numerical procedure, a particular method can be considered as an efficient method if the method can give an approximate solution within the specified error with the least computational complexity. Throughout this paper, the two-dimensional Porous Medium Equation (2D PME) is discretized by using the implicit finite difference scheme to construct the corresponding approximation equation. Then this approximation equation yields a large-sized and sparse nonlinear system. By using the Newton method to linearize the nonlinear system, this paper deals with the application of the Four-Point Newton-EGSOR (4NEGSOR) iterative method for solving the 2D PMEs. In addition to that, the efficiency of the 4NEGSOR iterative method is studied by solving three examples of the problems. Based on the comparative analysis, the Newton-Gauss-Seidel (NGS) and the Newton-SOR (NSOR) iterative methods are also considered. The numerical findings show that the 4NEGSOR method is superior to the NGS and the NSOR methods in terms of the number of iterations to get the converged solutions, the time of computation and the maximum absolute errors produced by the methods.

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

Representation of deformable motion for compression of dynamic cardiac image data

NASA Astrophysics Data System (ADS)

Weinlich, Andreas; Amon, Peter; Hutter, Andreas; Kaup, André

2012-02-01

We present a new approach for efficient estimation and storage of tissue deformation in dynamic medical image data like 3-D+t computed tomography reconstructions of human heart acquisitions. Tissue deformation between two points in time can be described by means of a displacement vector field indicating for each voxel of a slice, from which position in the previous slice at a fixed position in the third dimension it has moved to this position. Our deformation model represents the motion in a compact manner using a down-sampled potential function of the displacement vector field. This function is obtained by a Gauss-Newton minimization of the estimation error image, i. e., the difference between the current and the deformed previous slice. For lossless or lossy compression of volume slices, the potential function and the error image can afterwards be coded separately. By assuming deformations instead of translational motion, a subsequent coding algorithm using this method will achieve better compression ratios for medical volume data than with conventional block-based motion compensation known from video coding. Due to the smooth prediction without block artifacts, particularly whole-image transforms like wavelet decomposition as well as intra-slice prediction methods can benefit from this approach. We show that with discrete cosine as well as with Karhunen-Lo`eve transform the method can achieve a better energy compaction of the error image than block-based motion compensation while reaching approximately the same prediction error energy.

Design and modeling of a hydraulically amplified magnetostrictive actuator for automotive engine mounts

NASA Astrophysics Data System (ADS)

Chakrabarti, Suryarghya; Dapino, Marcelo J.

2009-03-01

A bidirectional magnetostrictive actuator with millimeter stroke and a blocked force of few tens of Newtons has been developed based on a Terfenol-D driver and a simple hydraulic magnification stage. The actuator is compared with an electrodynamic actuator used in active powertrain mounts in terms of electrical power consumption, frequency bandwidth, and spectral content of the response. The measurements show that the actuator has a flat free-displacement and blocked-force response up to 200 Hz, suggesting a significantly broader frequency bandwidth than commercial electromagnetic actuators while drawing comparable amounts of power.

Limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method for the parameter estimation on geographically weighted ordinal logistic regression model (GWOLR)

NASA Astrophysics Data System (ADS)

Saputro, Dewi Retno Sari; Widyaningsih, Purnami

2017-08-01

In general, the parameter estimation of GWOLR model uses maximum likelihood method, but it constructs a system of nonlinear equations, making it difficult to find the solution. Therefore, an approximate solution is needed. There are two popular numerical methods: the methods of Newton and Quasi-Newton (QN). Newton's method requires large-scale time in executing the computation program since it contains Jacobian matrix (derivative). QN method overcomes the drawback of Newton's method by substituting derivative computation into a function of direct computation. The QN method uses Hessian matrix approach which contains Davidon-Fletcher-Powell (DFP) formula. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is categorized as the QN method which has the DFP formula attribute of having positive definite Hessian matrix. The BFGS method requires large memory in executing the program so another algorithm to decrease memory usage is needed, namely Low Memory BFGS (LBFGS). The purpose of this research is to compute the efficiency of the LBFGS method in the iterative and recursive computation of Hessian matrix and its inverse for the GWOLR parameter estimation. In reference to the research findings, we found out that the BFGS and LBFGS methods have arithmetic operation schemes, including O(n2) and O(nm).

MODFLOW-NWT, A Newton formulation for MODFLOW-2005

USGS Publications Warehouse

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

2011-01-01

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

Global convergence of inexact Newton methods for transonic flow

NASA Technical Reports Server (NTRS)

Young, David P.; Melvin, Robin G.; Bieterman, Michael B.; Johnson, Forrester T.; Samant, Satish S.

1990-01-01

In computational fluid dynamics, nonlinear differential equations are essential to represent important effects such as shock waves in transonic flow. Discretized versions of these nonlinear equations are solved using iterative methods. In this paper an inexact Newton method using the GMRES algorithm of Saad and Schultz is examined in the context of the full potential equation of aerodynamics. In this setting, reliable and efficient convergence of Newton methods is difficult to achieve. A poor initial solution guess often leads to divergence or very slow convergence. This paper examines several possible solutions to these problems, including a standard local damping strategy for Newton's method and two continuation methods, one of which utilizes interpolation from a coarse grid solution to obtain the initial guess on a finer grid. It is shown that the continuation methods can be used to augment the local damping strategy to achieve convergence for difficult transonic flow problems. These include simple wings with shock waves as well as problems involving engine power effects. These latter cases are modeled using the assumption that each exhaust plume is isentropic but has a different total pressure and/or temperature than the freestream.

What can Numerical Computation do for the History of Science? (Study of an Orbit Drawn by Newton on a Letter to Hooke)

NASA Astrophysics Data System (ADS)

Stuchi, Teresa; Cardozo Dias, P.

2013-05-01

Abstract (2,250 Maximum Characters): On a letter to Robert Hooke, Isaac Newton drew the orbit of a mass moving under a constant attracting central force. How he drew the orbit may indicate how and when he developed dynamic categories. Some historians claim that Newton used a method contrived by Hooke; others that he used some method of curvature. We prove geometrically: 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 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.

Approximate tensor-product preconditioners for very high order discontinuous Galerkin methods

NASA Astrophysics Data System (ADS)

Pazner, Will; Persson, Per-Olof

2018-02-01

In this paper, we develop a new tensor-product based preconditioner for discontinuous Galerkin methods with polynomial degrees higher than those typically employed. This preconditioner uses an automatic, purely algebraic method to approximate the exact block Jacobi preconditioner by Kronecker products of several small, one-dimensional matrices. Traditional matrix-based preconditioners require O (p2d) storage and O (p3d) computational work, where p is the degree of basis polynomials used, and d is the spatial dimension. Our SVD-based tensor-product preconditioner requires O (p d + 1) storage, O (p d + 1) work in two spatial dimensions, and O (p d + 2) work in three spatial dimensions. Combined with a matrix-free Newton-Krylov solver, these preconditioners allow for the solution of DG systems in linear time in p per degree of freedom in 2D, and reduce the computational complexity from O (p9) to O (p5) in 3D. Numerical results are shown in 2D and 3D for the advection, Euler, and Navier-Stokes equations, using polynomials of degree up to p = 30. For many test cases, the preconditioner results in similar iteration counts when compared with the exact block Jacobi preconditioner, and performance is significantly improved for high polynomial degrees p.

Teaching the Calculus

ERIC Educational Resources Information Center

Sauerheber, Richard D.

2012-01-01

Methods of teaching the Calculus are presented in honour of Sir Isaac Newton, by discussing an extension of his original proofs and discoveries. The methods, requested by Newton to be used that reflect the historical sequence of the discovered Fundamental Theorems, allow first-time students to grasp quickly the basics of the Calculus from its…

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

PubMed

Leszczynski, Henryk; Wrzosek, Monika

2017-02-01

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

Low cost and efficient kurtosis-based deflationary ICA method: application to MRS sources separation problem.

PubMed

Saleh, M; Karfoul, A; Kachenoura, A; Senhadji, L; Albera, L

2016-08-01

Improving the execution time and the numerical complexity of the well-known kurtosis-based maximization method, the RobustICA, is investigated in this paper. A Newton-based scheme is proposed and compared to the conventional RobustICA method. A new implementation using the nonlinear Conjugate Gradient one is investigated also. Regarding the Newton approach, an exact computation of the Hessian of the considered cost function is provided. The proposed approaches and the considered implementations inherit the global plane search of the initial RobustICA method for which a better convergence speed for a given direction is still guaranteed. Numerical results on Magnetic Resonance Spectroscopy (MRS) source separation show the efficiency of the proposed approaches notably the quasi-Newton one using the BFGS method.

Toward Directly-Deposited Optical Blocking Filters for High-performance, Back-illuminated Imaging X-ray Detectors

NASA Astrophysics Data System (ADS)

Bautz, Mark W.; Kissel, S. E.; Ryu, K.; Suntharalingam, V.

2014-01-01

Silicon X-ray detectors require optical blocking filters to prevent out-of-band (UV, visible and near-IR) radiation from corrupting the X-ray signal. Traditionally, blocking filters have been deposited on thin, free-standing membranes suspended over the detector. Free-standing filters are fragile, however, and in past instruments have required heavy and complex vacuum housings to protect them from acoustic loads during ground operations and launch. A directly-deposited blocking filter greatly simplifies the instrument and in principle permits better soft X-ray detection efficiency than a traditional free-standing filter. Directly-deposited filters have flown in previous generation instruments (e.g. the XMM/Newton Reflection Grating Spectrometer) but none has yet been demonstrated on a modern, high-performance back-illuminated X-ray CCD. We report here on the status of our NASA-funded Strategic Astrophysics Technology program to demonstrate such filters.

Calibration of gravitational radiation antenna by dynamic Newton field

NASA Astrophysics Data System (ADS)

Suzuki, T.; Tsubono, K.; Kuroda, K.; Hirakawa, H.

1981-07-01

A method is presented of calibrating antennas for gravitational radiation. The method, which used the dynamic Newton field of a rotating body, is suitable in experiments for frequencies up to several hundred hertz. What is more, the method requires no hardware inside the vacuum chamber of the antenna and is particularly convenient for calibration of low-temperature antenna systems.

Respiratory Toxicology: 1981

DTIC Science & Technology

1981-08-01

AFAMRL-TR-81-81 D /a , 𔄁 RESPIRATORY TOXICOLOGY Annual Technical Report: 1981 P. E. NEWTON, Ph.D. UNIVERSITY OF CALIFORNIA, IRVINE OVERLOOK BRANCH...OF REPORT & PERIOD COVERED RESPIRATORY TOXICOLOGY: 1981 Annual Technical June 1980 through May 198 Ś. PERFORMING ORG. REPORT NUMBER 7. AUTHOR(s) 8...ABSTRACT (Continue on reverse side if necessary and Identify by block number) The Respiratory Toxicology research programs conducted at the Toxic Hazards

Fully implicit adaptive mesh refinement solver for 2D MHD

NASA Astrophysics Data System (ADS)

Philip, B.; Chacon, L.; Pernice, M.

2008-11-01

Application of implicit adaptive mesh refinement (AMR) to simulate resistive magnetohydrodynamics is described. Solving this challenging multi-scale, multi-physics problem can improve understanding of reconnection in magnetically-confined plasmas. AMR is employed to resolve extremely thin current sheets, essential for an accurate macroscopic description. Implicit time stepping allows us to accurately follow the dynamical time scale of the developing magnetic field, without being restricted by fast Alfven time scales. At each time step, the large-scale system of nonlinear equations is solved by a Jacobian-free Newton-Krylov method together with a physics-based preconditioner. Each block within the preconditioner is solved optimally using the Fast Adaptive Composite grid method, which can be considered as a multiplicative Schwarz method on AMR grids. We will demonstrate the excellent accuracy and efficiency properties of the method with several challenging reduced MHD applications, including tearing, island coalescence, and tilt instabilities. B. Philip, L. Chac'on, M. Pernice, J. Comput. Phys., in press (2008)

Convergence and Applications of a Gossip-Based Gauss-Newton Algorithm

NASA Astrophysics Data System (ADS)

Li, Xiao; Scaglione, Anna

2013-11-01

The Gauss-Newton algorithm is a popular and efficient centralized method for solving non-linear least squares problems. In this paper, we propose a multi-agent distributed version of this algorithm, named Gossip-based Gauss-Newton (GGN) algorithm, which can be applied in general problems with non-convex objectives. Furthermore, we analyze and present sufficient conditions for its convergence and show numerically that the GGN algorithm achieves performance comparable to the centralized algorithm, with graceful degradation in case of network failures. More importantly, the GGN algorithm provides significant performance gains compared to other distributed first order methods.

The Use of Kruskal-Newton Diagrams for Differential Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

T. Fishaleck and R.B. White

2008-02-19

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

The Adams formulas for numerical integration of differential equations from 1st to 20th order

NASA Technical Reports Server (NTRS)

Kirkpatrick, J. C.

1976-01-01

The Adams Bashforth predictor coefficients and the Adams Moulton corrector coefficients for the integration of differential equations are presented for methods of 1st to 20th order. The order of the method as presented refers to the highest order difference formula used in Newton's backward difference interpolation formula, on which the Adams method is based. The Adams method is a polynomial approximation method derived from Newton's backward difference interpolation formula. The Newton formula is derived and expanded to 20th order. The Adams predictor and corrector formulas are derived and expressed in terms of differences of the derivatives, as well as in terms of the derivatives themselves. All coefficients are given to 18 significant digits. For the difference formula only, the ratio coefficients are given to 10th order.

Hybrid DFP-CG method for solving unconstrained optimization problems

NASA Astrophysics Data System (ADS)

Osman, Wan Farah Hanan Wan; Asrul Hery Ibrahim, Mohd; Mamat, Mustafa

2017-09-01

The conjugate gradient (CG) method and quasi-Newton method are both well known method for solving unconstrained optimization method. In this paper, we proposed a new method by combining the search direction between conjugate gradient method and quasi-Newton method based on BFGS-CG method developed by Ibrahim et al. The Davidon-Fletcher-Powell (DFP) update formula is used as an approximation of Hessian for this new hybrid algorithm. Numerical result showed that the new algorithm perform well than the ordinary DFP method and proven to posses both sufficient descent and global convergence properties.

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

NASA Technical Reports Server (NTRS)

Scott, James R.; Chang, Sin-Chung

1993-01-01

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hiebert, Ray; Hiebert, Roselyn

This brief booklet gives a snapshot view of 25 men, each of whom contributed an important building block to the foundations of atomic science. The 25 men are: Anaxagoras; Archimedes; Avogadro, Amedeo; Berthollet, Claude Louis; Berzelius, Jons Jakob; Boyle, Robert; Bruno, Giordano; Copernicus; Dalton, John; Davy, Humphry; Democritus; Descartes, Rene; Empedocles; Fpicurus; Franklin, Benjamin; Galilei, Galileo; Gassendi, Pierre; Gay-Lussac, Joseph Louis; Lavoisier, Antoine; Leucippus; Lucretius; Newton, Isaac; Proust, Joseph Louis; Pythagoras; and Wollaston, William Hyde.

An actuator extension transformation for a motion simulator and an inverse transformation applying Newton-Raphson's method

NASA Technical Reports Server (NTRS)

Dieudonne, J. E.

1972-01-01

A set of equations which transform position and angular orientation of the centroid of the payload platform of a six-degree-of-freedom motion simulator into extensions of the simulator's actuators has been derived and is based on a geometrical representation of the system. An iterative scheme, Newton-Raphson's method, has been successfully used in a real time environment in the calculation of the position and angular orientation of the centroid of the payload platform when the magnitude of the actuator extensions is known. Sufficient accuracy is obtained by using only one Newton-Raphson iteration per integration step of the real time environment.

Newton-like methods for Navier-Stokes solution

NASA Astrophysics Data System (ADS)

Qin, N.; Xu, X.; Richards, B. E.

1992-12-01

The paper reports on Newton-like methods called SFDN-alpha-GMRES and SQN-alpha-GMRES methods that have been devised and proven as powerful schemes for large nonlinear problems typical of viscous compressible Navier-Stokes solutions. They can be applied using a partially converged solution from a conventional explicit or approximate implicit method. Developments have included the efficient parallelization of the schemes on a distributed memory parallel computer. The methods are illustrated using a RISC workstation and a transputer parallel system respectively to solve a hypersonic vortical flow.

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

ERIC Educational Resources Information Center

Bryan, Ronald A.; And Others

1988-01-01

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

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

2013-12-01

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

A multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Jameson, Antony

1986-01-01

A new efficient relaxation scheme in conjunction with a multigrid method is developed for the Euler equations. The LU SSOR scheme is based on a central difference scheme and does not need flux splitting for Newton iteration. Application to transonic flow shows that the new method surpasses the performance of the LU implicit scheme.

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

PubMed

Kossaifi, Jean; Tzimiropoulos, Yorgos; Pantic, Maja

2016-12-21

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

A new Newton-like method for solving nonlinear equations.

PubMed

Saheya, B; Chen, Guo-Qing; Sui, Yun-Kang; Wu, Cai-Ying

2016-01-01

This paper presents an iterative scheme for solving nonline ar equations. We establish a new rational approximation model with linear numerator and denominator which has generalizes the local linear model. We then employ the new approximation for nonlinear equations and propose an improved Newton's method to solve it. The new method revises the Jacobian matrix by a rank one matrix each iteration and obtains the quadratic convergence property. The numerical performance and comparison show that the proposed method is efficient.

Sixteen years of X-ray monitoring of Sagittarius A*: Evidence for a decay of the faint flaring rate from 2013 August, 13 months before a rise in the bright flaring rate

NASA Astrophysics Data System (ADS)

Mossoux, Enmanuelle; Grosso, Nicolas

2017-08-01

Context. X-ray flaring activity from the closest supermassive black hole Sagittarius A* (Sgr A*) located at the center of our Galaxy has been observed since 2000 October 26 thanks to the current generation of X-ray facilities. In a study of X-ray flaring activity from Sgr A* using Chandra and XMM-Newton public observations from 1999 to 2014 and Swift monitoring in 2014, it was argued that the "bright and very bright" flaring rate has increased from 2014 August 31. Aims: As a result of additional observations performed in 2015 with Chandra, XMM-Newton, and Swift (total exposure of 482 ks), we seek to test the significance and persistence of this increase of flaring rate and to determine the threshold of unabsorbed flare flux or fluence leading to any change of flaring rate. Methods: We reprocessed the Chandra, XMM-Newton, and Swift data from 1999 to 2015 November 2. From these data, we detected the X-ray flares via our two-step Bayesian blocks algorithm with a prior on the number of change points properly calibrated for each observation. We improved the Swift data analysis by correcting the effects of the target variable position on the detector and we detected the X-ray flares with a 3σ threshold on the binned light curves. The mean unabsorbed fluxes of the 107 detected flares were consistently computed from the extracted spectra and the corresponding calibration files, assuming the same spectral parameters. We constructed the observed distribution of flare fluxes and durations from the XMM-Newton and Chandra detections. We corrected this observed distribution from the detection biases to estimate the intrinsic distribution of flare fluxes and durations. From this intrinsic distribution, we determined the average flare detection efficiency for each XMM-Newton, Chandra, and Swift observation. We finally applied the Bayesian blocks algorithm on the arrival times of the flares corrected from the corresponding efficiency. Results: We confirm a constant overall flaring rate from 1999 to 2015 and a rise in the flaring rate by a factor of three for the most luminous and most energetic flares from 2014 August 31, I.e., about four months after the pericenter passage of the Dusty S-cluster Object (DSO)/G2 close to Sgr A*. In addition, we identify a decay of the flaring rate for the less luminous and less energetic flares from 2013 August and November, respectively, I.e., about 10 and 7 months before the pericenter passage of the DSO/G2 and 13 and 10 months before the rise in the bright flaring rate. Conclusions: The decay of the faint flaring rate is difficult to explain in terms of the tidal disruption of a dusty cloud since it occurred well before the pericenter passage of the DSO/G2, whose stellar nature is now well established. Moreover, a mass transfer from the DSO/G2 to Sgr A* is not required to produce the rise in the bright flaring rate since the energy saved by the decay of the number of faint flares during a long period of time may be later released by several bright flares during a shorter period of time.

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

PubMed

Janiak, Andrew

2015-06-01

In the Scholium to the Definitions in Principia mathematica, Newton departs from his main task of discussing space, time and motion by suddenly mentioning the proper method for interpreting Scripture. This is surprising, and it has long been ignored by scholars. In this paper, I argue that the Scripture passage in the Scholium is actually far from incidental: it reflects Newton's substantive concern, one evident in correspondence and manuscripts from the 1680s, that any general understanding of space, time and motion must enable readers to recognize the veracity of Biblical claims about natural phenomena, including the motion of the earth. This substantive concern sheds new light on an aspect of Newton's project in the Scholium. It also underscores Newton's originality in dealing with the famous problem of reconciling theological and philosophical conceptions of nature in the seventeenth century. Copyright © 2015 Elsevier Ltd. All rights reserved.

Large radius of curvature measurement based on virtual quadratic Newton rings phase-shifting moiré-fringes measurement method in a nonnull interferometer.

PubMed

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.

3D CSEM data inversion using Newton and Halley class methods

NASA Astrophysics Data System (ADS)

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

2016-05-01

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

Parallel Newton-Krylov-Schwarz algorithms for the transonic full potential equation

NASA Technical Reports Server (NTRS)

Cai, Xiao-Chuan; Gropp, William D.; Keyes, David E.; Melvin, Robin G.; Young, David P.

1996-01-01

We study parallel two-level overlapping Schwarz algorithms for solving nonlinear finite element problems, in particular, for the full potential equation of aerodynamics discretized in two dimensions with bilinear elements. The overall algorithm, Newton-Krylov-Schwarz (NKS), employs an inexact finite-difference Newton method and a Krylov space iterative method, with a two-level overlapping Schwarz method as a preconditioner. We demonstrate that NKS, combined with a density upwinding continuation strategy for problems with weak shocks, is robust and, economical for this class of mixed elliptic-hyperbolic nonlinear partial differential equations, with proper specification of several parameters. We study upwinding parameters, inner convergence tolerance, coarse grid density, subdomain overlap, and the level of fill-in in the incomplete factorization, and report their effect on numerical convergence rate, overall execution time, and parallel efficiency on a distributed-memory parallel computer.

A different approach to estimate nonlinear regression model using numerical methods

NASA Astrophysics Data System (ADS)

Mahaboob, B.; Venkateswarlu, B.; Mokeshrayalu, G.; Balasiddamuni, P.

2017-11-01

This research paper concerns with the computational methods namely the Gauss-Newton method, Gradient algorithm methods (Newton-Raphson method, Steepest Descent or Steepest Ascent algorithm method, the Method of Scoring, the Method of Quadratic Hill-Climbing) based on numerical analysis to estimate parameters of nonlinear regression model in a very different way. Principles of matrix calculus have been used to discuss the Gradient-Algorithm methods. Yonathan Bard [1] discussed a comparison of gradient methods for the solution of nonlinear parameter estimation problems. However this article discusses an analytical approach to the gradient algorithm methods in a different way. This paper describes a new iterative technique namely Gauss-Newton method which differs from the iterative technique proposed by Gorden K. Smyth [2]. Hans Georg Bock et.al [10] proposed numerical methods for parameter estimation in DAE’s (Differential algebraic equation). Isabel Reis Dos Santos et al [11], Introduced weighted least squares procedure for estimating the unknown parameters of a nonlinear regression metamodel. For large-scale non smooth convex minimization the Hager and Zhang (HZ) conjugate gradient Method and the modified HZ (MHZ) method were presented by Gonglin Yuan et al [12].

WARP3D-Release 10.8: Dynamic Nonlinear Analysis of Solids using a Preconditioned Conjugate Gradient Software Architecture

NASA Technical Reports Server (NTRS)

Koppenhoefer, Kyle C.; Gullerud, Arne S.; Ruggieri, Claudio; Dodds, Robert H., Jr.; Healy, Brian E.

1998-01-01

This report describes theoretical background material and commands necessary to use the WARP3D finite element code. WARP3D is under continuing development as a research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads. Specific features in the code oriented toward the investigation of ductile fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, face loading), an element extinction facility to model crack growth, nonlinear material models including viscoplastic effects, and the Gurson-Tver-gaard dilatant plasticity model for void growth. The nonlinear, dynamic equilibrium equations are solved using an incremental-iterative, implicit formulation with full Newton iterations to eliminate residual nodal forces. The history integration of the nonlinear equations of motion is accomplished with Newmarks Beta method. A central feature of WARP3D involves the use of a linear-preconditioned conjugate gradient (LPCG) solver implemented in an element-by-element format to replace a conventional direct linear equation solver. This software architecture dramatically reduces both the memory requirements and CPU time for very large, nonlinear solid models since formation of the assembled (dynamic) stiffness matrix is avoided. Analyses thus exhibit the numerical stability for large time (load) steps provided by the implicit formulation coupled with the low memory requirements characteristic of an explicit code. In addition to the much lower memory requirements of the LPCG solver, the CPU time required for solution of the linear equations during each Newton iteration is generally one-half or less of the CPU time required for a traditional direct solver. All other computational aspects of the code (element stiffnesses, element strains, stress updating, element internal forces) are implemented in the element-by- element, blocked architecture. This greatly improves vectorization of the code on uni-processor hardware and enables straightforward parallel-vector processing of element blocks on multi-processor hardware.

Quasi-Newton parallel geometry optimization methods

NASA Astrophysics Data System (ADS)

Burger, Steven K.; Ayers, Paul W.

2010-07-01

Algorithms for parallel unconstrained minimization of molecular systems are examined. The overall framework of minimization is the same except for the choice of directions for updating the quasi-Newton Hessian. Ideally these directions are chosen so the updated Hessian gives steps that are same as using the Newton method. Three approaches to determine the directions for updating are presented: the straightforward approach of simply cycling through the Cartesian unit vectors (finite difference), a concurrent set of minimizations, and the Lanczos method. We show the importance of using preconditioning and a multiple secant update in these approaches. For the Lanczos algorithm, an initial set of directions is required to start the method, and a number of possibilities are explored. To test the methods we used the standard 50-dimensional analytic Rosenbrock function. Results are also reported for the histidine dipeptide, the isoleucine tripeptide, and cyclic adenosine monophosphate. All of these systems show a significant speed-up with the number of processors up to about eight processors.

Multilevel Iterative Methods in Nonlinear Computational Plasma Physics

NASA Astrophysics Data System (ADS)

Knoll, D. A.; Finn, J. M.

1997-11-01

Many applications in computational plasma physics involve the implicit numerical solution of coupled systems of nonlinear partial differential equations or integro-differential equations. Such problems arise in MHD, systems of Vlasov-Fokker-Planck equations, edge plasma fluid equations. We have been developing matrix-free Newton-Krylov algorithms for such problems and have applied these algorithms to the edge plasma fluid equations [1,2] and to the Vlasov-Fokker-Planck equation [3]. Recently we have found that with increasing grid refinement, the number of Krylov iterations required per Newton iteration has grown unmanageable [4]. This has led us to the study of multigrid methods as a means of preconditioning matrix-free Newton-Krylov methods. In this poster we will give details of the general multigrid preconditioned Newton-Krylov algorithm, as well as algorithm performance details on problems of interest in the areas of magnetohydrodynamics and edge plasma physics. Work supported by US DoE 1. Knoll and McHugh, J. Comput. Phys., 116, pg. 281 (1995) 2. Knoll and McHugh, Comput. Phys. Comm., 88, pg. 141 (1995) 3. Mousseau and Knoll, J. Comput. Phys. (1997) (to appear) 4. Knoll and McHugh, SIAM J. Sci. Comput. 19, (1998) (to appear)

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

NASA Technical Reports Server (NTRS)

Snowden, Steven

2011-01-01

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

Rule-governed Approaches to Physics--Newton's Third Law.

ERIC Educational Resources Information Center

Maloney, David P.

1984-01-01

Describes an approach to assessing the use of rules in solving problems related to Newton's third law of motion. Discusses the problems used, method of questioning, scoring of problem sets, and a general overview of the use of the technique in aiding the teacher in dealing with student's conceptual levels. (JM)

Numerical Solution of the Gyrokinetic Poisson Equation in TEMPEST

NASA Astrophysics Data System (ADS)

Dorr, Milo; Cohen, Bruce; Cohen, Ronald; Dimits, Andris; Hittinger, Jeffrey; Kerbel, Gary; Nevins, William; Rognlien, Thomas; Umansky, Maxim; Xiong, Andrew; Xu, Xueqiao

2006-10-01

The gyrokinetic Poisson (GKP) model in the TEMPEST continuum gyrokinetic edge plasma code yields the electrostatic potential due to the charge density of electrons and an arbitrary number of ion species including the effects of gyroaveraging in the limit kρ1. The TEMPEST equations are integrated as a differential algebraic system involving a nonlinear system solve via Newton-Krylov iteration. The GKP preconditioner block is inverted using a multigrid preconditioned conjugate gradient (CG) algorithm. Electrons are treated as kinetic or adiabatic. The Boltzmann relation in the adiabatic option employs flux surface averaging to maintain neutrality within field lines and is solved self-consistently with the GKP equation. A decomposition procedure circumvents the near singularity of the GKP Jacobian block that otherwise degrades CG convergence.

The Application of Simulation Method in Isothermal Elastic Natural Gas Pipeline

NASA Astrophysics Data System (ADS)

Xing, Chunlei; Guan, Shiming; Zhao, Yue; Cao, Jinggang; Chu, Yanji

2018-02-01

This Elastic pipeline mathematic model is of crucial importance in natural gas pipeline simulation because of its compliance with the practical industrial cases. The numerical model of elastic pipeline will bring non-linear complexity to the discretized equations. Hence the Newton-Raphson method cannot achieve fast convergence in this kind of problems. Therefore A new Newton Based method with Powell-Wolfe Condition to simulate the Isothermal elastic pipeline flow is presented. The results obtained by the new method aregiven based on the defined boundary conditions. It is shown that the method converges in all cases and reduces significant computational cost.

Isaac Newton and the astronomical refraction.

PubMed

Lehn, Waldemar H

2008-12-01

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

Computational aspects of helicopter trim analysis and damping levels from Floquet theory

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

["Anything goes"?: the implicit dialogue between Paul Feyerabend and two Brazilian researchers, Maurício da Rocha e Silva and Newton Freire-Maia].

PubMed

Bastos, Francisco Inácio

2010-03-01

The philosopher Paul Feyerabend and Brazilian scientists Maurício da Rocha e Silva and Newton Freire-Maia were contemporaries and lived surrounded by the fundamental dilemnas of science. The anarchist proposal of Feyerabend, then embryonic, was formulated in parallel by Rocha e Silva in his criticism of the scientific method. Two decades later, Feyerabend's ideas seemed implicitly to stimulate Newton Freire-Maia in his reflections on science. The web of interrelationships in the ideas of these three men - who never interacted - touches on central issues for Brazilian science from 1960 to 1980, a period in which the latter is consolidated in a dialogue with the nascent reflection on science and the scientific method in Brazil.

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

NASA Astrophysics Data System (ADS)

Goodwin, D. L.; Kuprov, Ilya

2016-05-01

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

Visualizing and Understanding the Components of Lagrange and Newton Interpolation

ERIC Educational Resources Information Center

Yang, Yajun; Gordon, Sheldon P.

2016-01-01

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

Exploratory Development of an Electrically Rechargeable Lithium Battery.

DTIC Science & Technology

1980-10-01

RECHARGEABLE LITHIUM BATTERY O K. M. Abraham GtJ. L. Goldman ~M. D. Dempsey MCG. L. Holleck EIC Laboratories, Inc. " - 55 Chapel Street Newton, MA 02158 October...COVERED (, Epl.oratory Development of an Electrically 7 9FINAL REPORT- 7-2-79 to 7-1-80 Rechargeable Lithium Battery * .. PFORMIN ORO. RE RT NUMBER 7...Bloek 20, Il diiItrent hurm Reprt) I. SUPPLEMENTARY NOTES IS. KEY WORDS (Continue n Mrverse side It necesary and identify by block number) Vanadium

Interior point techniques for LP and NLP

DOE Office of Scientific and Technical Information (OSTI.GOV)

Evtushenko, Y.

By using surjective mapping the initial constrained optimization problem is transformed to a problem in a new space with only equality constraints. For the numerical solution of the latter problem we use the generalized gradient-projection method and Newton`s method. After inverse transformation to the initial space we obtain the family of numerical methods for solving optimization problems with equality and inequality constraints. In the linear programming case after some simplification we obtain Dikin`s algorithm, affine scaling algorithm and generalized primal dual interior point linear programming algorithm.

Density reconstruction in multiparameter elastic full-waveform inversion

NASA Astrophysics Data System (ADS)

Sun, Min'ao; Yang, Jizhong; Dong, Liangguo; Liu, Yuzhu; Huang, Chao

2017-12-01

Elastic full-waveform inversion (EFWI) is a quantitative data fitting procedure that recovers multiple subsurface parameters from multicomponent seismic data. As density is involved in addition to P- and S-wave velocities, the multiparameter EFWI suffers from more serious tradeoffs. In addition, compared with P- and S-wave velocities, the misfit function is less sensitive to density perturbation. Thus, a robust density reconstruction remains a difficult problem in multiparameter EFWI. In this paper, we develop an improved scattering-integral-based truncated Gauss-Newton method to simultaneously recover P- and S-wave velocities and density in EFWI. In this method, the inverse Gauss-Newton Hessian has been estimated by iteratively solving the Gauss-Newton equation with a matrix-free conjugate gradient algorithm. Therefore, it is able to properly handle the parameter tradeoffs. To give a detailed illustration of the tradeoffs between P- and S-wave velocities and density in EFWI, wavefield-separated sensitivity kernels and the Gauss-Newton Hessian are numerically computed, and their distribution characteristics are analyzed. Numerical experiments on a canonical inclusion model and a modified SEG/EAGE Overthrust model have demonstrated that the proposed method can effectively mitigate the tradeoff effects, and improve multiparameter gradients. Thus, a high convergence rate and an accurate density reconstruction can be achieved.

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

NASA Astrophysics Data System (ADS)

Yang, Haijian; Sun, Shuyu; Yang, Chao

2017-03-01

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

Decentralized Quasi-Newton Methods

NASA Astrophysics Data System (ADS)

Eisen, Mark; Mokhtari, Aryan; Ribeiro, Alejandro

2017-05-01

We introduce the decentralized Broyden-Fletcher-Goldfarb-Shanno (D-BFGS) method as a variation of the BFGS quasi-Newton method for solving decentralized optimization problems. The D-BFGS method is of interest in problems that are not well conditioned, making first order decentralized methods ineffective, and in which second order information is not readily available, making second order decentralized methods impossible. D-BFGS is a fully distributed algorithm in which nodes approximate curvature information of themselves and their neighbors through the satisfaction of a secant condition. We additionally provide a formulation of the algorithm in asynchronous settings. Convergence of D-BFGS is established formally in both the synchronous and asynchronous settings and strong performance advantages relative to first order methods are shown numerically.

Robust iterative method for nonlinear Helmholtz equation

NASA Astrophysics Data System (ADS)

Yuan, Lijun; Lu, Ya Yan

2017-08-01

A new iterative method is developed for solving the two-dimensional nonlinear Helmholtz equation which governs polarized light in media with the optical Kerr nonlinearity. In the strongly nonlinear regime, the nonlinear Helmholtz equation could have multiple solutions related to phenomena such as optical bistability and symmetry breaking. The new method exhibits a much more robust convergence behavior than existing iterative methods, such as frozen-nonlinearity iteration, Newton's method and damped Newton's method, and it can be used to find solutions when good initial guesses are unavailable. Numerical results are presented for the scattering of light by a nonlinear circular cylinder based on the exact nonlocal boundary condition and a pseudospectral method in the polar coordinate system.

Implementation of Kane's Method for a Spacecraft Composed of Multiple Rigid Bodies

NASA Technical Reports Server (NTRS)

Stoneking, Eric T.

2013-01-01

Equations of motion are derived for a general spacecraft composed of rigid bodies connected via rotary (spherical or gimballed) joints in a tree topology. Several supporting concepts are developed in depth. Basis dyads aid in the transition from basis-free vector equations to component-wise equations. Joint partials allow abstraction of 1-DOF, 2-DOF, 3-DOF gimballed and spherical rotational joints to a common notation. The basic building block consisting of an "inner" body and an "outer" body connected by a joint enables efficient organization of arbitrary tree structures. Kane's equation is recast in a form which facilitates systematic assembly of large systems of equations, and exposes a relationship of Kane's equation to Newton and Euler's equations which is obscured by the usual presentation. The resulting system of dynamic equations is of minimum dimension, and is suitable for numerical solution by computer. Implementation is ·discussed, and illustrative simulation results are presented.

Strategies for the coupling of global and local crystal growth models

NASA Astrophysics Data System (ADS)

Derby, Jeffrey J.; Lun, Lisa; Yeckel, Andrew

2007-05-01

The modular coupling of existing numerical codes to model crystal growth processes will provide for maximum effectiveness, capability, and flexibility. However, significant challenges are posed to make these coupled models mathematically self-consistent and algorithmically robust. This paper presents sample results from a coupling of the CrysVUn code, used here to compute furnace-scale heat transfer, and Cats2D, used to calculate melt fluid dynamics and phase-change phenomena, to form a global model for a Bridgman crystal growth system. However, the strategy used to implement the CrysVUn-Cats2D coupling is unreliable and inefficient. The implementation of under-relaxation within a block Gauss-Seidel iteration is shown to be ineffective for improving the coupling performance in a model one-dimensional problem representative of a melt crystal growth model. Ideas to overcome current convergence limitations using approximations to a full Newton iteration method are discussed.

Adaptive Beam Loading Compensation in Room Temperature Bunching Cavities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Edelen, J. P.; Chase, B. E.; Cullerton, E.

In this paper we present the design, simulation, and proof of principle results of an optimization based adaptive feedforward algorithm for beam-loading compensation in a high impedance room temperature cavity. We begin with an overview of prior developments in beam loading compensation. Then we discuss different techniques for adaptive beam loading compensation and why the use of Newton?s Method is of interest for this application. This is followed by simulation and initial experimental results of this method.

On structure-exploiting trust-region regularized nonlinear least squares algorithms for neural-network learning.

PubMed

Mizutani, Eiji; Demmel, James W

2003-01-01

This paper briefly introduces our numerical linear algebra approaches for solving structured nonlinear least squares problems arising from 'multiple-output' neural-network (NN) models. Our algorithms feature trust-region regularization, and exploit sparsity of either the 'block-angular' residual Jacobian matrix or the 'block-arrow' Gauss-Newton Hessian (or Fisher information matrix in statistical sense) depending on problem scale so as to render a large class of NN-learning algorithms 'efficient' in both memory and operation costs. Using a relatively large real-world nonlinear regression application, we shall explain algorithmic strengths and weaknesses, analyzing simulation results obtained by both direct and iterative trust-region algorithms with two distinct NN models: 'multilayer perceptrons' (MLP) and 'complementary mixtures of MLP-experts' (or neuro-fuzzy modular networks).

Recovering galaxy cluster gas density profiles with XMM-Newton and Chandra

NASA Astrophysics Data System (ADS)

Bartalucci, I.; Arnaud, M.; Pratt, G. W.; Vikhlinin, A.; Pointecouteau, E.; Forman, W. R.; Jones, C.; Mazzotta, P.; Andrade-Santos, F.

2017-12-01

We examined the reconstruction of galaxy cluster radial density profiles obtained from Chandra and XMM-Newton X-ray observations, using high quality data for a sample of twelve objects covering a range of morphologies and redshifts. By comparing the results obtained from the two observatories and by varying key aspects of the analysis procedure, we examined the impact of instrumental effects and of differences in the methodology used in the recovery of the density profiles. We find that the final density profile shape is particularly robust. We adapted the photon weighting vignetting correction method developed for XMM-Newton for use with Chandra data, and confirm that the resulting Chandra profiles are consistent with those corrected a posteriori for vignetting effects. Profiles obtained from direct deprojection and those derived using parametric models are consistent at the 1% level. At radii larger than 6″, the agreement between Chandra and XMM-Newton is better than 1%, confirming an excellent understanding of the XMM-Newton PSF. Furthermore, we find no significant energy dependence. The impact of the well-known offset between Chandra and XMM-Newton gas temperature determinations on the density profiles is found to be negligible. However, we find an overall normalisation offset in density profiles of the order of 2.5%, which is linked to absolute flux cross-calibration issues. As a final result, the weighted ratios of Chandra to XMM-Newton gas masses computed at R2500 and R500 are r = 1.03 ± 0.01 and r = 1.03 ± 0.03, respectively. Our study confirms that the radial density profiles are robustly recovered, and that any differences between Chandra and XMM-Newton can be constrained to the 2.5% level, regardless of the exact data analysis details. These encouraging results open the way for the true combination of X-ray observations of galaxy clusters, fully leveraging the high resolution of Chandra and the high throughput of XMM-Newton.

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

NASA Technical Reports Server (NTRS)

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

2007-01-01

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

Some modifications of Newton's method for the determination of the steady-state response of nonlinear oscillatory circuits

NASA Astrophysics Data System (ADS)

Grosz, F. B., Jr.; Trick, T. N.

1982-07-01

It is proposed that nondominant states should be eliminated from the Newton algorithm in the steady-state analysis of nonlinear oscillatory systems. This technique not only improves convergence, but also reduces the size of the sensitivity matrix so that less computation is required for each iteration. One or more periods of integration should be performed after each periodic state estimation before the sensitivity computations are made for the next periodic state estimation. These extra periods of integration between Newton iterations are found to allow the fast states due to parasitic effects to settle, which enables the Newton algorithm to make a better prediction. In addition, the reliability of the algorithm is improved in high Q oscillator circuits by both local and global damping in which the amount of damping is proportional to the difference between the initial and final state values.

Alternative theoretical method for motion of a sand-filled funnel experiment

NASA Astrophysics Data System (ADS)

Byrd, David; White, Gary

2001-11-01

In "Motion of a Sand-Filled Funnel," Peter Sullivan and Anna McLoon described how to use numerical methods and a Microsoft Excel spreadsheet to predict the motion of a variant of Atwood's machine with variable mass. They wrote for noncalculus-based physics classes, but we solve the same problem using the methods of calculus. Our method highlights the less-familiar but more accurate version of Newton's second law, ∑F =dp/dt. This can help introductory physics students understand a broader definition of Newton's second law and enhance their calculus skills. It also teaches students how to solve a variable-mass problem.

Implicit Plasma Kinetic Simulation Using The Jacobian-Free Newton-Krylov Method

NASA Astrophysics Data System (ADS)

Taitano, William; Knoll, Dana; Chacon, Luis

2009-11-01

The use of fully implicit time integration methods in kinetic simulation is still area of algorithmic research. A brute-force approach to simultaneously including the field equations and the particle distribution function would result in an intractable linear algebra problem. A number of algorithms have been put forward which rely on an extrapolation in time. They can be thought of as linearly implicit methods or one-step Newton methods. However, issues related to time accuracy of these methods still remain. We are pursuing a route to implicit plasma kinetic simulation which eliminates extrapolation, eliminates phase-space from the linear algebra problem, and converges the entire nonlinear system within a time step. We accomplish all this using the Jacobian-Free Newton-Krylov algorithm. The original research along these lines considered particle methods to advance the distribution function [1]. In the current research we are advancing the Vlasov equations on a grid. Results will be presented which highlight algorithmic details for single species electrostatic problems and coupled ion-electron electrostatic problems. [4pt] [1] H. J. Kim, L. Chac'on, G. Lapenta, ``Fully implicit particle in cell algorithm,'' 47th Annual Meeting of the Division of Plasma Physics, Oct. 24-28, 2005, Denver, CO

An analysis of the convergence of Newton iterations for solving elliptic Kepler's equation

NASA Astrophysics Data System (ADS)

Elipe, A.; Montijano, J. I.; Rández, L.; Calvo, M.

2017-12-01

In this note a study of the convergence properties of some starters E_0 = E_0(e,M) in the eccentricity-mean anomaly variables for solving the elliptic Kepler's equation (KE) by Newton's method is presented. By using a Wang Xinghua's theorem (Xinghua in Math Comput 68(225):169-186, 1999) on best possible error bounds in the solution of nonlinear equations by Newton's method, we obtain for each starter E_0(e,M) a set of values (e,M) \\in [0, 1) × [0, π ] that lead to the q-convergence in the sense that Newton's sequence (E_n)_{n ≥ 0} generated from E_0 = E_0(e,M) is well defined, converges to the exact solution E^* = E^*(e,M) of KE and further \\vert E_n - E^* \\vert ≤ q^{2^n -1} \\vert E_0 - E^* \\vert holds for all n ≥ 0. This study completes in some sense the results derived by Avendaño et al. (Celest Mech Dyn Astron 119:27-44, 2014) by using Smale's α -test with q=1/2. Also since in KE the convergence rate of Newton's method tends to zero as e → 0, we show that the error estimates given in the Wang Xinghua's theorem for KE can also be used to determine sets of q-convergence with q = e^k \\widetilde{q} for all e \\in [0,1) and a fixed \\widetilde{q} ≤ 1. Some remarks on the use of this theorem to derive a priori estimates of the error \\vert E_n - E^* \\vert after n Kepler's iterations are given. Finally, a posteriori bounds of this error that can be used to a dynamical estimation of the error are also obtained.

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

ERIC Educational Resources Information Center

Kocakulah, Mustafa Sabri

2010-01-01

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

Moving mesh finite element simulation for phase-field modeling of brittle fracture and convergence of Newton's iteration

NASA Astrophysics Data System (ADS)

Zhang, Fei; Huang, Weizhang; Li, Xianping; Zhang, Shicheng

2018-03-01

A moving mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture. The moving mesh partial differential equation approach is employed to dynamically track crack propagation. Meanwhile, the decomposition of the strain tensor into tensile and compressive components is essential for the success of the phase-field modeling of brittle fracture but results in a non-smooth elastic energy and stronger nonlinearity in the governing equation. This makes the governing equation much more difficult to solve and, in particular, Newton's iteration often fails to converge. Three regularization methods are proposed to smooth out the decomposition of the strain tensor. Numerical examples of fracture propagation under quasi-static load demonstrate that all of the methods can effectively improve the convergence of Newton's iteration for relatively small values of the regularization parameter but without compromising the accuracy of the numerical solution. They also show that the moving mesh finite element method is able to adaptively concentrate the mesh elements around propagating cracks and handle multiple and complex crack systems.

Unstructured Finite Volume Computational Thermo-Fluid Dynamic Method for Multi-Disciplinary Analysis and Design Optimization

NASA Technical Reports Server (NTRS)

Majumdar, Alok; Schallhorn, Paul

1998-01-01

This paper describes a finite volume computational thermo-fluid dynamics method to solve for Navier-Stokes equations in conjunction with energy equation and thermodynamic equation of state in an unstructured coordinate system. The system of equations have been solved by a simultaneous Newton-Raphson method and compared with several benchmark solutions. Excellent agreements have been obtained in each case and the method has been found to be significantly faster than conventional Computational Fluid Dynamic(CFD) methods and therefore has the potential for implementation in Multi-Disciplinary analysis and design optimization in fluid and thermal systems. The paper also describes an algorithm of design optimization based on Newton-Raphson method which has been recently tested in a turbomachinery application.

Development of parallel algorithms for electrical power management in space applications

NASA Technical Reports Server (NTRS)

Berry, Frederick C.

1989-01-01

The application of parallel techniques for electrical power system analysis is discussed. The Newton-Raphson method of load flow analysis was used along with the decomposition-coordination technique to perform load flow analysis. The decomposition-coordination technique enables tasks to be performed in parallel by partitioning the electrical power system into independent local problems. Each independent local problem represents a portion of the total electrical power system on which a loan flow analysis can be performed. The load flow analysis is performed on these partitioned elements by using the Newton-Raphson load flow method. These independent local problems will produce results for voltage and power which can then be passed to the coordinator portion of the solution procedure. The coordinator problem uses the results of the local problems to determine if any correction is needed on the local problems. The coordinator problem is also solved by an iterative method much like the local problem. The iterative method for the coordination problem will also be the Newton-Raphson method. Therefore, each iteration at the coordination level will result in new values for the local problems. The local problems will have to be solved again along with the coordinator problem until some convergence conditions are met.

Quasi-Newton methods for parameter estimation in functional differential equations

NASA Technical Reports Server (NTRS)

Brewer, Dennis W.

1988-01-01

A state-space approach to parameter estimation in linear functional differential equations is developed using the theory of linear evolution equations. A locally convergent quasi-Newton type algorithm is applied to distributed systems with particular emphasis on parameters that induce unbounded perturbations of the state. The algorithm is computationally implemented on several functional differential equations, including coefficient and delay estimation in linear delay-differential equations.

Finite Volume Algorithms for Heat Conduction

DTIC Science & Technology

2010-05-01

scalar quantity). Although (3) is relatively easy to discretize by using finite differences , its form in generalized coordinates is not. Later, we...familiar with the finite difference method for discretizing differential equations. In fact, the Newton divided difference is the numerical analog for a...expression (8) for the average derivative matches the Newton divided difference formula, so for uniform one-dimensional meshes, the finite volume and

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

ERIC Educational Resources Information Center

Ergin, Serap

2016-01-01

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

Inverse problems with nonnegative and sparse solutions: algorithms and application to the phase retrieval problem

NASA Astrophysics Data System (ADS)

Quy Muoi, Pham; Nho Hào, Dinh; Sahoo, Sujit Kumar; Tang, Dongliang; Cong, Nguyen Huu; Dang, Cuong

2018-05-01

In this paper, we study a gradient-type method and a semismooth Newton method for minimization problems in regularizing inverse problems with nonnegative and sparse solutions. We propose a special penalty functional forcing the minimizers of regularized minimization problems to be nonnegative and sparse, and then we apply the proposed algorithms in a practical the problem. The strong convergence of the gradient-type method and the local superlinear convergence of the semismooth Newton method are proven. Then, we use these algorithms for the phase retrieval problem and illustrate their efficiency in numerical examples, particularly in the practical problem of optical imaging through scattering media where all the noises from experiment are presented.

Modelling Schumann resonances from ELF measurements using non-linear optimization methods

NASA Astrophysics Data System (ADS)

Castro, Francisco; Toledo-Redondo, Sergio; Fornieles, Jesús; Salinas, Alfonso; Portí, Jorge; Navarro, Enrique; Sierra, Pablo

2017-04-01

Schumann resonances (SR) can be found in planetary atmospheres, inside the cavity formed by the conducting surface of the planet and the lower ionosphere. They are a powerful tool to investigate both the electric processes that occur in the atmosphere and the characteristics of the surface and the lower ionosphere. In this study, the measurements are obtained in the ELF (Extremely Low Frequency) Juan Antonio Morente station located in the national park of Sierra Nevada. The three first modes, contained in the frequency band between 6 to 25 Hz, will be considered. For each time series recorded by the station, the amplitude spectrum was estimated by using Bartlett averaging. Then, the central frequencies and amplitudes of the SRs were obtained by fitting the spectrum with non-linear functions. In the poster, a study of nonlinear unconstrained optimization methods applied to the estimation of the Schumann Resonances will be presented. Non-linear fit, also known as optimization process, is the procedure followed in obtaining Schumann Resonances from the natural electromagnetic noise. The optimization methods that have been analysed are: Levenberg-Marquardt, Conjugate Gradient, Gradient, Newton and Quasi-Newton. The functions that the different methods fit to data are three lorentzian curves plus a straight line. Gaussian curves have also been considered. The conclusions of this study are outlined in the following paragraphs: i) Natural electromagnetic noise is better fitted using Lorentzian functions; ii) the measurement bandwidth can accelerate the convergence of the optimization method; iii) Gradient method has less convergence and has a highest mean squared error (MSE) between measurement and the fitted function, whereas Levenberg-Marquad, Gradient conjugate method and Cuasi-Newton method give similar results (Newton method presents higher MSE); v) There are differences in the MSE between the parameters that define the fit function, and an interval from 1% to 5% has been found.

P1 Nonconforming Finite Element Method for the Solution of Radiation Transport Problems

NASA Technical Reports Server (NTRS)

Kang, Kab S.

2002-01-01

The simulation of radiation transport in the optically thick flux-limited diffusion regime has been identified as one of the most time-consuming tasks within large simulation codes. Due to multimaterial complex geometry, the radiation transport system must often be solved on unstructured grids. In this paper, we investigate the behavior and the benefits of the unstructured P(sub 1) nonconforming finite element method, which has proven to be flexible and effective on related transport problems, in solving unsteady implicit nonlinear radiation diffusion problems using Newton and Picard linearization methods. Key words. nonconforrning finite elements, radiation transport, inexact Newton linearization, multigrid preconditioning

A numerical method to solve the 1D and the 2D reaction diffusion equation based on Bessel functions and Jacobian free Newton-Krylov subspace methods

NASA Astrophysics Data System (ADS)

Parand, K.; Nikarya, M.

2017-11-01

In this paper a novel method will be introduced to solve a nonlinear partial differential equation (PDE). In the proposed method, we use the spectral collocation method based on Bessel functions of the first kind and the Jacobian free Newton-generalized minimum residual (JFNGMRes) method with adaptive preconditioner. In this work a nonlinear PDE has been converted to a nonlinear system of algebraic equations using the collocation method based on Bessel functions without any linearization, discretization or getting the help of any other methods. Finally, by using JFNGMRes, the solution of the nonlinear algebraic system is achieved. To illustrate the reliability and efficiency of the proposed method, we solve some examples of the famous Fisher equation. We compare our results with other methods.

Mathematical and computational studies of equilibrium capillary free surfaces

NASA Technical Reports Server (NTRS)

Albright, N.; Chen, N. F.; Concus, P.; Finn, R.

1977-01-01

The results of several independent studies are presented. The general question is considered of whether a wetting liquid always rises higher in a small capillary tube than in a larger one, when both are dipped vertically into an infinite reservoir. An analytical investigation is initiated to determine the qualitative behavior of the family of solutions of the equilibrium capillary free-surface equation that correspond to rotationally symmetric pendent liquid drops and the relationship of these solutions to the singular solution, which corresponds to an infinite spike of liquid extending downward to infinity. The block successive overrelaxation-Newton method and the generalized conjugate gradient method are investigated for solving the capillary equation on a uniform square mesh in a square domain, including the case for which the solution is unbounded at the corners. Capillary surfaces are calculated on the ellipse, on a circle with reentrant notches, and on other irregularly shaped domains using JASON, a general purpose program for solving nonlinear elliptic equations on a nonuniform quadrilaterial mesh. Analytical estimates for the nonexistence of solutions of the equilibrium capillary free-surface equation on the ellipse in zero gravity are evaluated.

Statistical efficiency of adaptive algorithms.

PubMed

Widrow, Bernard; Kamenetsky, Max

2003-01-01

The statistical efficiency of a learning algorithm applied to the adaptation of a given set of variable weights is defined as the ratio of the quality of the converged solution to the amount of data used in training the weights. Statistical efficiency is computed by averaging over an ensemble of learning experiences. A high quality solution is very close to optimal, while a low quality solution corresponds to noisy weights and less than optimal performance. In this work, two gradient descent adaptive algorithms are compared, the LMS algorithm and the LMS/Newton algorithm. LMS is simple and practical, and is used in many applications worldwide. LMS/Newton is based on Newton's method and the LMS algorithm. LMS/Newton is optimal in the least squares sense. It maximizes the quality of its adaptive solution while minimizing the use of training data. Many least squares adaptive algorithms have been devised over the years, but no other least squares algorithm can give better performance, on average, than LMS/Newton. LMS is easily implemented, but LMS/Newton, although of great mathematical interest, cannot be implemented in most practical applications. Because of its optimality, LMS/Newton serves as a benchmark for all least squares adaptive algorithms. The performances of LMS and LMS/Newton are compared, and it is found that under many circumstances, both algorithms provide equal performance. For example, when both algorithms are tested with statistically nonstationary input signals, their average performances are equal. When adapting with stationary input signals and with random initial conditions, their respective learning times are on average equal. However, under worst-case initial conditions, the learning time of LMS can be much greater than that of LMS/Newton, and this is the principal disadvantage of the LMS algorithm. But the strong points of LMS are ease of implementation and optimal performance under important practical conditions. For these reasons, the LMS algorithm has enjoyed very widespread application. It is used in almost every modem for channel equalization and echo cancelling. Furthermore, it is related to the famous backpropagation algorithm used for training neural networks.

Evaluating the accuracy performance of Lucas-Kanade algorithm in the circumstance of PIV application

NASA Astrophysics Data System (ADS)

Pan, Chong; Xue, Dong; Xu, Yang; Wang, JinJun; Wei, RunJie

2015-10-01

Lucas-Kanade (LK) algorithm, usually used in optical flow filed, has recently received increasing attention from PIV community due to its advanced calculation efficiency by GPU acceleration. Although applications of this algorithm are continuously emerging, a systematic performance evaluation is still lacking. This forms the primary aim of the present work. Three warping schemes in the family of LK algorithm: forward/inverse/symmetric warping, are evaluated in a prototype flow of a hierarchy of multiple two-dimensional vortices. Second-order Newton descent is also considered here. The accuracy & efficiency of all these LK variants are investigated under a large domain of various influential parameters. It is found that the constant displacement constraint, which is a necessary building block for GPU acceleration, is the most critical issue in affecting LK algorithm's accuracy, which can be somehow ameliorated by using second-order Newton descent. Moreover, symmetric warping outbids the other two warping schemes in accuracy level, robustness to noise, convergence speed and tolerance to displacement gradient, and might be the first choice when applying LK algorithm to PIV measurement.

How College Students' Conceptions of Newton's Second and Third Laws Change through Watching Interactive Video Vignettes: A Mixed Methods Study

ERIC Educational Resources Information Center

Engelman, Jonathan

2016-01-01

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…

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

ERIC Educational Resources Information Center

Develaki, Maria

2012-01-01

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

Discrete-Time Zhang Neural Network for Online Time-Varying Nonlinear Optimization With Application to Manipulator Motion Generation.

PubMed

Jin, Long; Zhang, Yunong

2015-07-01

In this brief, a discrete-time Zhang neural network (DTZNN) model is first proposed, developed, and investigated for online time-varying nonlinear optimization (OTVNO). Then, Newton iteration is shown to be derived from the proposed DTZNN model. In addition, to eliminate the explicit matrix-inversion operation, the quasi-Newton Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is introduced, which can effectively approximate the inverse of Hessian matrix. A DTZNN-BFGS model is thus proposed and investigated for OTVNO, which is the combination of the DTZNN model and the quasi-Newton BFGS method. In addition, theoretical analyses show that, with step-size h=1 and/or with zero initial error, the maximal residual error of the DTZNN model has an O(τ(2)) pattern, whereas the maximal residual error of the Newton iteration has an O(τ) pattern, with τ denoting the sampling gap. Besides, when h ≠ 1 and h ∈ (0,2) , the maximal steady-state residual error of the DTZNN model has an O(τ(2)) pattern. Finally, an illustrative numerical experiment and an application example to manipulator motion generation are provided and analyzed to substantiate the efficacy of the proposed DTZNN and DTZNN-BFGS models for OTVNO.

Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD

NASA Technical Reports Server (NTRS)

Gropp, W. D.; Keyes, D. E.; McInnes, L. C.; Tidriri, M. D.

1998-01-01

Implicit solution methods are important in applications modeled by PDEs with disparate temporal and spatial scales. Because such applications require high resolution with reasonable turnaround, "routine" parallelization is essential. The pseudo-transient matrix-free Newton-Krylov-Schwarz (Psi-NKS) algorithmic framework is presented as an answer. We show that, for the classical problem of three-dimensional transonic Euler flow about an M6 wing, Psi-NKS can simultaneously deliver: globalized, asymptotically rapid convergence through adaptive pseudo- transient continuation and Newton's method-, reasonable parallelizability for an implicit method through deferred synchronization and favorable communication-to-computation scaling in the Krylov linear solver; and high per- processor performance through attention to distributed memory and cache locality, especially through the Schwarz preconditioner. Two discouraging features of Psi-NKS methods are their sensitivity to the coding of the underlying PDE discretization and the large number of parameters that must be selected to govern convergence. We therefore distill several recommendations from our experience and from our reading of the literature on various algorithmic components of Psi-NKS, and we describe a freely available, MPI-based portable parallel software implementation of the solver employed here.

A comparison between Gauss-Newton and Markov chain Monte Carlo basedmethods for inverting spectral induced polarization data for Cole-Coleparameters

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Jinsong; Kemna, Andreas; Hubbard, Susan S.

2008-05-15

We develop a Bayesian model to invert spectral induced polarization (SIP) data for Cole-Cole parameters using Markov chain Monte Carlo (MCMC) sampling methods. We compare the performance of the MCMC based stochastic method with an iterative Gauss-Newton based deterministic method for Cole-Cole parameter estimation through inversion of synthetic and laboratory SIP data. The Gauss-Newton based method can provide an optimal solution for given objective functions under constraints, but the obtained optimal solution generally depends on the choice of initial values and the estimated uncertainty information is often inaccurate or insufficient. In contrast, the MCMC based inversion method provides extensive globalmore » information on unknown parameters, such as the marginal probability distribution functions, from which we can obtain better estimates and tighter uncertainty bounds of the parameters than with the deterministic method. Additionally, the results obtained with the MCMC method are independent of the choice of initial values. Because the MCMC based method does not explicitly offer single optimal solution for given objective functions, the deterministic and stochastic methods can complement each other. For example, the stochastic method can first be used to obtain the means of the unknown parameters by starting from an arbitrary set of initial values and the deterministic method can then be initiated using the means as starting values to obtain the optimal estimates of the Cole-Cole parameters.« less

An Argument Against Augmenting the Lagrangean for Nonholonomic Systems

NASA Technical Reports Server (NTRS)

Roithmayr, Carlos M.; Hodges, Dewey H.

2009-01-01

Although it is known that correct dynamical equations of motion for a nonholonomic system cannot be obtained from a Lagrangean that has been augmented with a sum of the nonholonomic constraint equations weighted with multipliers, previous publications suggest otherwise. An example has been proposed in support of augmentation and purportedly demonstrates that an accepted method fails to produce correct equations of motion whereas augmentation leads to correct equations; this paper shows that in fact the opposite is true. The correct equations, previously discounted on the basis of a flawed application of the Newton-Euler method, are verified by using Kane's method and a new approach to determining the directions of constraint forces. A correct application of the Newton-Euler method reproduces valid equations.

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

NASA Astrophysics Data System (ADS)

García-Azpeitia, Carlos

2016-12-01

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

Recursive Newton-Euler formulation of manipulator dynamics

NASA Technical Reports Server (NTRS)

Nasser, M. G.

1989-01-01

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

Concerning an application of the method of least squares with a variable weight matrix

NASA Technical Reports Server (NTRS)

Sukhanov, A. A.

1979-01-01

An estimate of a state vector for a physical system when the weight matrix in the method of least squares is a function of this vector is considered. An iterative procedure is proposed for calculating the desired estimate. Conditions for the existence and uniqueness of the limit of this procedure are obtained, and a domain is found which contains the limit estimate. A second method for calculating the desired estimate which reduces to the solution of a system of algebraic equations is proposed. The question of applying Newton's method of tangents to solving the given system of algebraic equations is considered and conditions for the convergence of the modified Newton's method are obtained. Certain properties of the estimate obtained are presented together with an example.

A study of the parallel algorithm for large-scale DC simulation of nonlinear systems

NASA Astrophysics Data System (ADS)

Cortés Udave, Diego Ernesto; Ogrodzki, Jan; Gutiérrez de Anda, Miguel Angel

Newton-Raphson DC analysis of large-scale nonlinear circuits may be an extremely time consuming process even if sparse matrix techniques and bypassing of nonlinear models calculation are used. A slight decrease in the time required for this task may be enabled on multi-core, multithread computers if the calculation of the mathematical models for the nonlinear elements as well as the stamp management of the sparse matrix entries are managed through concurrent processes. This numerical complexity can be further reduced via the circuit decomposition and parallel solution of blocks taking as a departure point the BBD matrix structure. This block-parallel approach may give a considerable profit though it is strongly dependent on the system topology and, of course, on the processor type. This contribution presents the easy-parallelizable decomposition-based algorithm for DC simulation and provides a detailed study of its effectiveness.

Pectoral nerves I block is associated with a significant motor blockade with no dermatomal sensory changes: a prospective volunteer randomized-controlled double-blind study.

PubMed

Desroches, Jean; Belliveau, Marc; Bilodeau, Carole; Landry, Michel; Roy, Maxim; Beaulieu, Pierre

2018-03-29

The pectoral nerves (PECS) I block, first described in 2011 for surgery involving the pectoralis muscle, has principally been used for breast cancer surgery. No formal evaluation of its differential motor- and sensory-blocking abilities has been reported. We hypothesize that the PECS I block will produce a motor block of the pectoralis muscles with diminished upper limb adduction strength as measured with a handheld dynamometer. We conducted a PECS I block in a randomized placebo-controlled trial in six healthy subjects who received 0.4 mL·kg -1 of 0.9% saline (placebo) on one side and bupivacaine (0.25% with 1:400 000 epinephrine) on the other. We measured both upper limb adduction strength with a dynamometer and sensory skin levels over the thorax. The mean (standard deviation [SD]) adductor strength evaluated before the block was 119.4 (20.7) Newtons (N). After the PECS I block with bupivacaine, the mean (SD) strength of 54.2 (16.3) N was compared with 116.0 (30.4) N in the placebo group (difference in means 61.8 N; 95% confidence interval [CI], 27.8 to 95.8 N; P = 0.005), showing a 54.6% (95% CI, 43.6 to 65.6%) reduction in adductor strength. There was no difference in dermatomal skin sensory testing between the placebo and bupivacaine sides. This study shows that a PECS I block produces motor blockade as shown by reduced upper limb adductor strength without any overlying dermatomal sensory loss. www.clinicaltrials.gov (NCT03040167) 2 February 2017.

Stress measurement in thin films by geometrical optics

NASA Technical Reports Server (NTRS)

Rossnagel, S. M.; Gilstrap, P.; Rujkorakarn, R.

1982-01-01

A variation of Newton's rings experiment is proposed for measuring film stress. The procedure described, the geometrical optics method, is used to measure radii of curvature for a series of film depositions with Ta, Al, and Mo films. The method has a sensitivity of 1 x 10 to the 9th dyn/sq cm, corresponding to the practical radius limit of about 50 m, and a repeatability usually within five percent. For the purposes of comparison, radii are also measured by Newton's rings method and the Talysurf method; all results are found to be in general agreement. Measurement times are also compared: the geometrical optics method requires only 1/2-1 minute. It is concluded that the geometrical optics method provides an inexpensive, fast, and a reasonably correct technique with which to measure stresses in film.

Automated Calibration For Numerical Models Of Riverflow

NASA Astrophysics Data System (ADS)

Fernandez, Betsaida; Kopmann, Rebekka; Oladyshkin, Sergey

2017-04-01

Calibration of numerical models is fundamental since the beginning of all types of hydro system modeling, to approximate the parameters that can mimic the overall system behavior. Thus, an assessment of different deterministic and stochastic optimization methods is undertaken to compare their robustness, computational feasibility, and global search capacity. Also, the uncertainty of the most suitable methods is analyzed. These optimization methods minimize the objective function that comprises synthetic measurements and simulated data. Synthetic measurement data replace the observed data set to guarantee an existing parameter solution. The input data for the objective function derivate from a hydro-morphological dynamics numerical model which represents an 180-degree bend channel. The hydro- morphological numerical model shows a high level of ill-posedness in the mathematical problem. The minimization of the objective function by different candidate methods for optimization indicates a failure in some of the gradient-based methods as Newton Conjugated and BFGS. Others reveal partial convergence, such as Nelder-Mead, Polak und Ribieri, L-BFGS-B, Truncated Newton Conjugated, and Trust-Region Newton Conjugated Gradient. Further ones indicate parameter solutions that range outside the physical limits, such as Levenberg-Marquardt and LeastSquareRoot. Moreover, there is a significant computational demand for genetic optimization methods, such as Differential Evolution and Basin-Hopping, as well as for Brute Force methods. The Deterministic Sequential Least Square Programming and the scholastic Bayes Inference theory methods present the optimal optimization results. keywords: Automated calibration of hydro-morphological dynamic numerical model, Bayesian inference theory, deterministic optimization methods.

Method and system for training dynamic nonlinear adaptive filters which have embedded memory

NASA Technical Reports Server (NTRS)

Rabinowitz, Matthew (Inventor)

2002-01-01

Described herein is a method and system for training nonlinear adaptive filters (or neural networks) which have embedded memory. Such memory can arise in a multi-layer finite impulse response (FIR) architecture, or an infinite impulse response (IIR) architecture. We focus on filter architectures with separate linear dynamic components and static nonlinear components. Such filters can be structured so as to restrict their degrees of computational freedom based on a priori knowledge about the dynamic operation to be emulated. The method is detailed for an FIR architecture which consists of linear FIR filters together with nonlinear generalized single layer subnets. For the IIR case, we extend the methodology to a general nonlinear architecture which uses feedback. For these dynamic architectures, we describe how one can apply optimization techniques which make updates closer to the Newton direction than those of a steepest descent method, such as backpropagation. We detail a novel adaptive modified Gauss-Newton optimization technique, which uses an adaptive learning rate to determine both the magnitude and direction of update steps. For a wide range of adaptive filtering applications, the new training algorithm converges faster and to a smaller value of cost than both steepest-descent methods such as backpropagation-through-time, and standard quasi-Newton methods. We apply the algorithm to modeling the inverse of a nonlinear dynamic tracking system 5, as well as a nonlinear amplifier 6.

Instantaneous Impulses.

ERIC Educational Resources Information Center

Erlichson, Herman

2000-01-01

Describes an experiment that extends Newton's instantaneous-impulse method of orbital analysis to a graphical method of orbit determination. Discusses the experiment's usefulness for teaching both horizontal projectile motion and instantaneous impulse. (WRM)

Student's preconception and anxiety when they solve multi representation concepts in Newton laws and it's application

NASA Astrophysics Data System (ADS)

Cari, C.; Suparmi, A.; Handhika, J.

2016-11-01

The purpose of this study was to describe of preconceptions and anxieties students in solving the representation concepts in newton laws and it's application. This research was conducted for junior undergraduate student's in physics department (36 Students) and physics education (31 Students). The method used in this study is a qualitative descriptive. The data was collection using test for multirepresentation concept, questionnaires for anxiety, and interviews. Based on the analysis it can be concluded that (1) the higher is anxiety, the higher is unconsistency (67,16%), (2) the higher is anxiety, the higher is consistency but wrong answer (29,85%), (3) the lower is anxiety, the higher is consistency of right answer (2,98%). Mostly students have understood fewer physics concept in newtons laws.

Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructure

NASA Technical Reports Server (NTRS)

Tsiveriotis, K.; Brown, R. A.

1993-01-01

A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.

Resolving galaxy cluster gas properties at z ˜ 1 with XMM-Newton and Chandra

NASA Astrophysics Data System (ADS)

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

2017-02-01

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

Iterative procedures for space shuttle main engine performance models

NASA Technical Reports Server (NTRS)

Santi, L. Michael

1989-01-01

Performance models of the Space Shuttle Main Engine (SSME) contain iterative strategies for determining approximate solutions to nonlinear equations reflecting fundamental mass, energy, and pressure balances within engine flow systems. Both univariate and multivariate Newton-Raphson algorithms are employed in the current version of the engine Test Information Program (TIP). Computational efficiency and reliability of these procedures is examined. A modified trust region form of the multivariate Newton-Raphson method is implemented and shown to be superior for off nominal engine performance predictions. A heuristic form of Broyden's Rank One method is also tested and favorable results based on this algorithm are presented.

A Class of Prediction-Correction Methods for Time-Varying Convex Optimization

NASA Astrophysics Data System (ADS)

Simonetto, Andrea; Mokhtari, Aryan; Koppel, Alec; Leus, Geert; Ribeiro, Alejandro

2016-09-01

This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction steps, while sampling the problem data at a constant rate of $1/h$, where $h$ is the length of the sampling interval. The prediction step is derived by analyzing the iso-residual dynamics of the optimality conditions. The correction step adjusts for the distance between the current prediction and the optimizer at each time step, and consists either of one or multiple gradient steps or Newton steps, which respectively correspond to the gradient trajectory tracking (GTT) or Newton trajectory tracking (NTT) algorithms. Under suitable conditions, we establish that the asymptotic error incurred by both proposed methods behaves as $O(h^2)$, and in some cases as $O(h^4)$, which outperforms the state-of-the-art error bound of $O(h)$ for correction-only methods in the gradient-correction step. Moreover, when the characteristics of the objective function variation are not available, we propose approximate gradient and Newton tracking algorithms (AGT and ANT, respectively) that still attain these asymptotical error bounds. Numerical simulations demonstrate the practical utility of the proposed methods and that they improve upon existing techniques by several orders of magnitude.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Salinger, Andy; Evans, Katherine J; Lemieux, Jean-Francois

2011-01-01

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

Newton gauge cosmological perturbations for static spherically symmetric modifications of the de Sitter metric

NASA Astrophysics Data System (ADS)

Santa Vélez, Camilo; Enea Romano, Antonio

2018-05-01

Static coordinates can be convenient to solve the vacuum Einstein's equations in presence of spherical symmetry, but for cosmological applications comoving coordinates are more suitable to describe an expanding Universe, especially in the framework of cosmological perturbation theory (CPT). Using CPT we develop a method to transform static spherically symmetric (SSS) modifications of the de Sitter solution from static coordinates to the Newton gauge. We test the method with the Schwarzschild de Sitter (SDS) metric and then derive general expressions for the Bardeen's potentials for a class of SSS metrics obtained by adding to the de Sitter metric a term linear in the mass and proportional to a general function of the radius. Using the gauge invariance of the Bardeen's potentials we then obtain a gauge invariant definition of the turn around radius. We apply the method to an SSS solution of the Brans-Dicke theory, confirming the results obtained independently by solving the perturbation equations in the Newton gauge. The Bardeen's potentials are then derived for new SSS metrics involving logarithmic, power law and exponential modifications of the de Sitter metric. We also apply the method to SSS metrics which give flat rotation curves, computing the radial energy density profile in comoving coordinates in presence of a cosmological constant.

A Gauss-Newton full-waveform inversion in PML-truncated domains using scalar probing waves

NASA Astrophysics Data System (ADS)

Pakravan, Alireza; Kang, Jun Won; Newtson, Craig M.

2017-12-01

This study considers the characterization of subsurface shear wave velocity profiles in semi-infinite media using scalar waves. Using surficial responses caused by probing waves, a reconstruction of the material profile is sought using a Gauss-Newton full-waveform inversion method in a two-dimensional domain truncated by perfectly matched layer (PML) wave-absorbing boundaries. The PML is introduced to limit the semi-infinite extent of the half-space and to prevent reflections from the truncated boundaries. A hybrid unsplit-field PML is formulated in the inversion framework to enable more efficient wave simulations than with a fully mixed PML. The full-waveform inversion method is based on a constrained optimization framework that is implemented using Karush-Kuhn-Tucker (KKT) optimality conditions to minimize the objective functional augmented by PML-endowed wave equations via Lagrange multipliers. The KKT conditions consist of state, adjoint, and control problems, and are solved iteratively to update the shear wave velocity profile of the PML-truncated domain. Numerical examples show that the developed Gauss-Newton inversion method is accurate enough and more efficient than another inversion method. The algorithm's performance is demonstrated by the numerical examples including the case of noisy measurement responses and the case of reduced number of sources and receivers.

Analysis of the iteratively regularized Gauss-Newton method under a heuristic rule

NASA Astrophysics Data System (ADS)

Jin, Qinian; Wang, Wei

2018-03-01

The iteratively regularized Gauss-Newton method is one of the most prominent regularization methods for solving nonlinear ill-posed inverse problems when the data is corrupted by noise. In order to produce a useful approximate solution, this iterative method should be terminated properly. The existing a priori and a posteriori stopping rules require accurate information on the noise level, which may not be available or reliable in practical applications. In this paper we propose a heuristic selection rule for this regularization method, which requires no information on the noise level. By imposing certain conditions on the noise, we derive a posteriori error estimates on the approximate solutions under various source conditions. Furthermore, we establish a convergence result without using any source condition. Numerical results are presented to illustrate the performance of our heuristic selection rule.

Numerical methods for the design of gradient-index optical coatings.

PubMed

Anzengruber, Stephan W; Klann, Esther; Ramlau, Ronny; Tonova, Diana

2012-12-01

We formulate the problem of designing gradient-index optical coatings as the task of solving a system of operator equations. We use iterative numerical procedures known from the theory of inverse problems to solve it with respect to the coating refractive index profile and thickness. The mathematical derivations necessary for the application of the procedures are presented, and different numerical methods (Landweber, Newton, and Gauss-Newton methods, Tikhonov minimization with surrogate functionals) are implemented. Procedures for the transformation of the gradient coating designs into quasi-gradient ones (i.e., multilayer stacks of homogeneous layers with different refractive indices) are also developed. The design algorithms work with physically available coating materials that could be produced with the modern coating technologies.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Georget, Fabien, E-mail: fabieng@princeton.edu; Prévost, Jean H., E-mail: prevost@princeton.edu; Vanderbei, Robert J., E-mail: rvdb@princeton.edu

2015-02-15

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

ℓ1-Regularized full-waveform inversion with prior model information based on orthant-wise limited memory quasi-Newton method

NASA Astrophysics Data System (ADS)

Dai, Meng-Xue; Chen, Jing-Bo; Cao, Jian

2017-07-01

Full-waveform inversion (FWI) is an ill-posed optimization problem which is sensitive to noise and initial model. To alleviate the ill-posedness of the problem, regularization techniques are usually adopted. The ℓ1-norm penalty is a robust regularization method that preserves contrasts and edges. The Orthant-Wise Limited-Memory Quasi-Newton (OWL-QN) method extends the widely-used limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method to the ℓ1-regularized optimization problems and inherits the efficiency of L-BFGS. To take advantage of the ℓ1-regularized method and the prior model information obtained from sonic logs and geological information, we implement OWL-QN algorithm in ℓ1-regularized FWI with prior model information in this paper. Numerical experiments show that this method not only improve the inversion results but also has a strong anti-noise ability.

A Method for Approximating the Bivariate Normal Correlation Coefficient.

ERIC Educational Resources Information Center

Kirk, David B.

Improvements of the Gaussian quadrature in conjunction with the Newton-Raphson iteration technique (TM 000 789) are discussed as effective methods of calculating the bivariate normal correlation coefficient. (CK)

ESA's Integral discovers hidden black holes

NASA Astrophysics Data System (ADS)

2003-10-01

An artist's impression of the mechanisms in an interacting binar hi-res Size hi-res: 28 kb An artist's impression of the mechanisms in an interacting binary system An artist's impression of the mechanisms in an interacting binary system. The supermassive companion star (on the right-hand side) ejects a lot of gas in the form of 'stellar wind'. The compact black hole orbits the star and, due to its strong gravitational attraction, collects a lot of the gas. Some of it is funnelled and accelerated into a hot disc. This releases a large amount of energy in all spectral bands, from gamma rays through to visible and infrared. However, the remaining gas surrounding the black hole forms a thick cloud which blocks most of the radiation. Only the very energetic gamma rays can escape and be detected by Integral. XMM-Newton spacecraft hi-res Size hi-res: 254 kb Credits: ESA. Illustration by Ducros XMM-Newton spacecraft Detecting the Universe's hot spots. These are binary systems, probably including a black hole or a neutron star, embedded in a thick cocoon of cold gas. They have remained invisible so far to all other telescopes. Integral was launched one year ago to study the most energetic phenomena in the universe. Integral detected the first of these objects, called IGRJ16318-4848, on 29 January 2003. Although astronomers did not know its distance, they were sure it was in our Galaxy. Also, after some analysis, researchers concluded that the new object could be a binary system comprising a compact object, such as a neutron star or a black hole, and a very massive companion star. When gas from the companion star is accelerated and swallowed by the more compact object, energy is released at all wavelengths, from the gamma rays through to visible and infrared light. About 300 binary systems like those are known to exist in our galactic neighbourhood and IGRJ16318-4848 could simply have been one more. But something did not fit: why this particular object had not been discovered so far? Astronomers, who have been observing the object regularly, guess that it had remained invisible because there must be a very thick shell of obscuring material surrounding it. If that was the case, only the most energetic radiation from the object could get through the shell; less-energetic radiation would be blocked. That could explain why space telescopes that are sensitive only to low-energy radiation had overlooked the object, while Integral, specialised in detecting very energetic emissions, did see it. To test their theory, astronomers turned to ESA's XMM-Newton space observatory, which observes the sky in the X-ray wavelengths. As well as being sensitive to high-energy radiation, XMM-Newton is also able to check for the presence of obscuring material. Indeed, XMM-Newton detected this object last February, as well as the existence of a dense 'cocoon' of cold gas with a diameter of similar size to that of the Earth's orbit around the Sun. This obscuring material forming the cocoon is probably 'stellar wind', namely gas ejected by the supermassive companion star. Astronomers think that this gas may be accreted by the compact black hole, forming a dense shell around it. This obscuring cloud traps most of the energy produced inside it. The main author of these results, Roland Walter of the Integral Science Data Centre, Switzerland, explained: "Only photons with the highest energies [above 10 keV] could escape from that cocoon. IGR J16318-4848 has therefore not been detected by surveys performed at lower energies, nor by previous gamma-ray missions that were much less sensitive than Integral." The question now is to find out how many of these objects lurk in the Galaxy. XMM-Newton and Integral together are the perfect tools to do the job. They have already discovered two more new sources embedded in obscuring material. Future observations are planned. Christoph Winkler, ESA Project Scientist for Integral, said: "These early examples of using two complementary ESA high-energy missions, Integral and XMM-Newton, shows the potential for future discoveries in high-energy astrophysics." Notes to Editors: The paper explaining these results will be published in November in a special issue of Astronomy and Astrophysics dedicated to Integral, on the occasion of its first anniversary. Integral The International Gamma Ray Astrophysics Laboratory (Integral) is the first space observatory that can simultaneously observe celestial objects in gamma rays, X-rays and visible light. Integral was launched on a Russian Proton rocket on 17 October 2002 into a highly elliptical orbit around Earth. Its principal targets include regions of the galaxy where chemical elements are being produced and compact objects, such as black holes. XMM-Newton XMM-Newton can detect more X-ray sources than any previous satellite and is helping to solve many cosmic mysteries of the violent Universe, from black holes to the formation of galaxies. It was launched on 10 December 1999, using an Ariane-5 rocket from French Guiana. It is expected to return data for a decade. XMM-Newton's high-tech design uses over 170 wafer-thin cylindrical mirrors spread over three telescopes. Its orbit takes it almost a third of the way to the Moon, so that astronomers can enjoy long, uninterrupted views of celestial objects.

How College Students' Conceptions of Newton's Second and Third Laws Change Through Watching Interactive Video Vignettes: A Mixed Methods Study

NASA Astrophysics Data System (ADS)

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 IVVs and how the ECRR framework was experienced. In answering the research questions, two major conclusions were reached: (1) while the ECRR framework was experienced in both the Newtons 2nd Law and Newtons 3rd Law IVVs, these experiences were qualitatively different from each other and these differences help support the differences in gain scores on the post-tests for the participants; and (2) both IVVs were able to change certain misconceptions associated with either Newtons 2nd or 3rd laws more than others. Therefore, in researching student experiences while completing the Newtons 2nd Law and Newtons 3rd Law IVVs, I determined that a complete, sequential experience of the elicit, confront, resolve, reflect framework led to the greatest change in student conceptions. This dissertation adds to the field of physics education through finding the positive impact of the ECRR framework, as IVVs are still being created and disseminated. Physics educators and researchers interested in conceptual change can use these findings to provide evidence on what students think when interacting with videos designed to change their conceptions. Finally, this dissertation supports the conceptual change literature in that the full, sequential experience involving each component of the ECRR framework led to a change in student conceptions.

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

PubMed

Asgharzadeh, Hafez; Borazjani, Iman

2017-02-15

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42 - 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

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

NASA Astrophysics Data System (ADS)

Asgharzadeh, Hafez; Borazjani, Iman

2017-02-01

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for non-linear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form a preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42-74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal and full Jacobian, respectivley, when the stretching factor was increased. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

Dark Matter Search Using XMM-Newton Observations of Willman 1

NASA Technical Reports Server (NTRS)

Lowenstein, Michael; Kusenko, Alexander

2012-01-01

We report the results of a search for an emission line from radiatively decaying dark matter in the ultra-faint dwarf spheroidal galaxy Willman 1 based on analysis of spectra extracted from XMM-Newton X-ray Observatory data. The observation follows up our analysis of Chandra data of Willman 1that resulted in line flux upper limits over the Chandra bandpass and evidence of a 2.5 keY feature at a significance below the 99% confidence threshold used to define the limits. The higher effective area of the XMM-Newton detectors, combined with application of recently developing methods for extended-source analysis, allow us to derive improved constraints on the combination of mass and mixing angle of the sterile neutrino dark matter candidate. We do not confirm the Chandra evidence for a 2.5 keV emission line.

R programming for parameters estimation of geographically weighted ordinal logistic regression (GWOLR) model based on Newton Raphson

NASA Astrophysics Data System (ADS)

Zuhdi, Shaifudin; Saputro, Dewi Retno Sari

2017-03-01

GWOLR model used for represent relationship between dependent variable has categories and scale of category is ordinal with independent variable influenced the geographical location of the observation site. Parameters estimation of GWOLR model use maximum likelihood provide system of nonlinear equations and hard to be found the result in analytic resolution. By finishing it, it means determine the maximum completion, this thing associated with optimizing problem. The completion nonlinear system of equations optimize use numerical approximation, which one is Newton Raphson method. The purpose of this research is to make iteration algorithm Newton Raphson and program using R software to estimate GWOLR model. Based on the research obtained that program in R can be used to estimate the parameters of GWOLR model by forming a syntax program with command "while".

Isaac Newton: Eighteenth-century Perspectives

NASA Astrophysics Data System (ADS)

Hall, A. Rupert

1999-05-01

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

Simulation of fluid-structure interaction in micropumps by coupling of two commercial finite element programs

NASA Astrophysics Data System (ADS)

Klein, Andreas; Gerlach, Gerald

1998-09-01

This paper deals with the simulation of the fluid-structure interaction phenomena in micropumps. The proposed solution approach is based on external coupling of two different solvers, which are considered here as `black boxes'. Therefore, no specific intervention is necessary into the program code, and solvers can be exchanged arbitrarily. For the realization of the external iteration loop, two algorithms are considered: the relaxation-based Gauss-Seidel method and the computationally more extensive Newton method. It is demonstrated in terms of a simplified test case, that for rather weak coupling, the Gauss-Seidel method is sufficient. However, by simply changing the considered fluid from air to water, the two physical domains become strongly coupled, and the Gauss-Seidel method fails to converge in this case. The Newton iteration scheme must be used instead.

Development of iterative techniques for the solution of unsteady compressible viscous flows

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi N.; Hixon, Duane

1991-01-01

Efficient iterative solution methods are being developed for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. Thus, the extra work required by iterative schemes can also be designed to perform efficiently on current and future generation scalable, missively parallel machines. An obvious candidate for iteratively solving the system of coupled nonlinear algebraic equations arising in CFD applications is the Newton method. Newton's method was implemented in existing finite difference and finite volume methods. Depending on the complexity of the problem, the number of Newton iterations needed per step to solve the discretized system of equations can, however, vary dramatically from a few to several hundred. Another popular approach based on the classical conjugate gradient method, known as the GMRES (Generalized Minimum Residual) algorithm is investigated. The GMRES algorithm was used in the past by a number of researchers for solving steady viscous and inviscid flow problems with considerable success. Here, the suitability of this algorithm is investigated for solving the system of nonlinear equations that arise in unsteady Navier-Stokes solvers at each time step. Unlike the Newton method which attempts to drive the error in the solution at each and every node down to zero, the GMRES algorithm only seeks to minimize the L2 norm of the error. In the GMRES algorithm the changes in the flow properties from one time step to the next are assumed to be the sum of a set of orthogonal vectors. By choosing the number of vectors to a reasonably small value N (between 5 and 20) the work required for advancing the solution from one time step to the next may be kept to (N+1) times that of a noniterative scheme. Many of the operations required by the GMRES algorithm such as matrix-vector multiplies, matrix additions and subtractions can all be vectorized and parallelized efficiently.

Isaac Newton: Man, Myth, and Mathematics.

ERIC Educational Resources Information Center

Rickey, V. Frederick

1987-01-01

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

An analytical fuzzy-based approach to ?-gain optimal control of input-affine nonlinear systems using Newton-type algorithm

NASA Astrophysics Data System (ADS)

Milic, Vladimir; Kasac, Josip; Novakovic, Branko

2015-10-01

This paper is concerned with ?-gain optimisation of input-affine nonlinear systems controlled by analytic fuzzy logic system. Unlike the conventional fuzzy-based strategies, the non-conventional analytic fuzzy control method does not require an explicit fuzzy rule base. As the first contribution of this paper, we prove, by using the Stone-Weierstrass theorem, that the proposed fuzzy system without rule base is universal approximator. The second contribution of this paper is an algorithm for solving a finite-horizon minimax problem for ?-gain optimisation. The proposed algorithm consists of recursive chain rule for first- and second-order derivatives, Newton's method, multi-step Adams method and automatic differentiation. Finally, the results of this paper are evaluated on a second-order nonlinear system.

Projective-Dual Method for Solving Systems of Linear Equations with Nonnegative Variables

NASA Astrophysics Data System (ADS)

Ganin, B. V.; Golikov, A. I.; Evtushenko, Yu. G.

2018-02-01

In order to solve an underdetermined system of linear equations with nonnegative variables, the projection of a given point onto its solutions set is sought. The dual of this problem—the problem of unconstrained maximization of a piecewise-quadratic function—is solved by Newton's method. The problem of unconstrained optimization dual of the regularized problem of finding the projection onto the solution set of the system is considered. A connection of duality theory and Newton's method with some known algorithms of projecting onto a standard simplex is shown. On the example of taking into account the specifics of the constraints of the transport linear programming problem, the possibility to increase the efficiency of calculating the generalized Hessian matrix is demonstrated. Some examples of numerical calculations using MATLAB are presented.

Highly Accurate Analytical Approximate Solution to a Nonlinear Pseudo-Oscillator

NASA Astrophysics Data System (ADS)

Wu, Baisheng; Liu, Weijia; Lim, C. W.

2017-07-01

A second-order Newton method is presented to construct analytical approximate solutions to a nonlinear pseudo-oscillator in which the restoring force is inversely proportional to the dependent variable. The nonlinear equation is first expressed in a specific form, and it is then solved in two steps, a predictor and a corrector step. In each step, the harmonic balance method is used in an appropriate manner to obtain a set of linear algebraic equations. With only one simple second-order Newton iteration step, a short, explicit, and highly accurate analytical approximate solution can be derived. The approximate solutions are valid for all amplitudes of the pseudo-oscillator. Furthermore, the method incorporates second-order Taylor expansion in a natural way, and it is of significant faster convergence rate.

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

NASA Astrophysics Data System (ADS)

Belenkiy, Ari; Echagüe, Eduardo Vila

2007-08-01

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

The influence of implementation of interactive lecture demonstrations (ILD) conceptual change oriented toward the decreasing of the quantity students that misconception on the Newton's first law

NASA Astrophysics Data System (ADS)

Kurniawan, Yudi; Suhandi, Andi; Hasanah, Lilik

2016-02-01

This paper aims to know the influence of implementation of ILD conceptual change oriented (ILD-CC) toward the decreasing of the quantity of students that misconception on the Newton's First Law. The Newton's First Law misconceptions separated into five sub-misconceptions. This research is a quantitative research with one group pretest-posttest design. The samples of this research were 32 students on 9th grade of junior high school in Pandeglang, Banten, Indonesia. The diagnostic test is a multiple-choice form with three-tier test format. The result of this study found that there was decreasing of the quantity of students that misconception on the Newton's First Law. The largest percentage in the decreasing of the number of the students that misconception was on the Misconception 4 about 80, 77%. The Misconception 4 is "The cause of tendency of the body passenger that sat upright on the accelerated bus from motionless bus suddenly to backward be a backward force". For the future studies, it suggested to combine other methods to optimize the decreasing the number of students that misconception.

SPIDERS: selection of spectroscopic targets using AGN candidates detected in all-sky X-ray surveys

NASA Astrophysics Data System (ADS)

Dwelly, T.; Salvato, M.; Merloni, A.; Brusa, M.; Buchner, J.; Anderson, S. F.; Boller, Th.; Brandt, W. N.; Budavári, T.; Clerc, N.; Coffey, D.; Del Moro, A.; Georgakakis, A.; Green, P. J.; Jin, C.; Menzel, M.-L.; Myers, A. D.; Nandra, K.; Nichol, R. C.; Ridl, J.; Schwope, A. D.; Simm, T.

2017-07-01

SPIDERS (SPectroscopic IDentification of eROSITA Sources) is a Sloan Digital Sky Survey IV (SDSS-IV) survey running in parallel to the Extended Baryon Oscillation Spectroscopic Survey (eBOSS) cosmology project. SPIDERS will obtain optical spectroscopy for large numbers of X-ray-selected active galactic nuclei (AGN) and galaxy cluster members detected in wide-area eROSITA, XMM-Newton and ROSAT surveys. We describe the methods used to choose spectroscopic targets for two sub-programmes of SPIDERS X-ray selected AGN candidates detected in the ROSAT All Sky and the XMM-Newton Slew surveys. We have exploited a Bayesian cross-matching algorithm, guided by priors based on mid-IR colour-magnitude information from the Wide-field Infrared Survey Explorer survey, to select the most probable optical counterpart to each X-ray detection. We empirically demonstrate the high fidelity of our counterpart selection method using a reference sample of bright well-localized X-ray sources collated from XMM-Newton, Chandra and Swift-XRT serendipitous catalogues, and also by examining blank-sky locations. We describe the down-selection steps which resulted in the final set of SPIDERS-AGN targets put forward for spectroscopy within the eBOSS/TDSS/SPIDERS survey, and present catalogues of these targets. We also present catalogues of ˜12 000 ROSAT and ˜1500 XMM-Newton Slew survey sources that have existing optical spectroscopy from SDSS-DR12, including the results of our visual inspections. On completion of the SPIDERS programme, we expect to have collected homogeneous spectroscopic redshift information over a footprint of ˜7500 deg2 for >85 per cent of the ROSAT and XMM-Newton Slew survey sources having optical counterparts in the magnitude range 17 < r < 22.5, producing a large and highly complete sample of bright X-ray-selected AGN suitable for statistical studies of AGN evolution and clustering.

Lumbar segmental nerve blocks with local anesthetics, pain relief, and motor function: a prospective double-blind study between lidocaine and ropivacaine.

PubMed

Wolff, André P; Wilder Smith, Oliver H G; Crul, Ben J P; van de Heijden, Marc P; Groen, Gerbrand J

2004-08-01

Selective segmental nerve blocks with local anesthetics are applied for diagnostic purposes in patients with chronic back pain to determine the segmental level of the pain. We performed this study to establish myotomal motor effects after L4 spinal nerve blocks by lidocaine and ropivacaine and to evaluate the relationship with pain. Therefore, 20 patients, of which 19 finished the complete protocol, with chronic lumbosacral radicular pain without neurological deficits underwent segmental nerve blocks at L4 with both lidocaine and ropivacaine. Pain intensity scores (verbal numeric rating scale; VNRS) and the maximum voluntary muscle force (MVMF; using a dynamometer expressed in newtons) of the tibialis anterior and quadriceps femoris muscles were measured on the painful side and on the control side. The median VNRS decrease was 4.0 (P < 0.00001; Wilcoxon's signed rank test), without significant differences between ropivacaine and lidocaine (Mann-Whitney U-test). A difference in effect on MVMF was found for affected versus control side (P = 0.016; Tukey test). Multiple regression revealed a significant negative correlation for change in VNRS score versus change in median MVMF (Spearman R = -0.48: P = 0.00001). This study demonstrates that in patients with unilateral chronic low back pain radiating to the leg, pain reduction induced by local anesthetic segmental nerve (L4) block is associated with increased quadriceps femoris and tibialis anterior MVMF, without differences for lidocaine and ropivacaine.

Accelerated gradient based diffuse optical tomographic image reconstruction.

PubMed

Biswas, Samir Kumar; Rajan, K; Vasu, R M

2011-01-01

Fast reconstruction of interior optical parameter distribution using a new approach called Broyden-based model iterative image reconstruction (BMOBIIR) and adjoint Broyden-based MOBIIR (ABMOBIIR) of a tissue and a tissue mimicking phantom from boundary measurement data in diffuse optical tomography (DOT). DOT is a nonlinear and ill-posed inverse problem. Newton-based MOBIIR algorithm, which is generally used, requires repeated evaluation of the Jacobian which consumes bulk of the computation time for reconstruction. In this study, we propose a Broyden approach-based accelerated scheme for Jacobian computation and it is combined with conjugate gradient scheme (CGS) for fast reconstruction. The method makes explicit use of secant and adjoint information that can be obtained from forward solution of the diffusion equation. This approach reduces the computational time many fold by approximating the system Jacobian successively through low-rank updates. Simulation studies have been carried out with single as well as multiple inhomogeneities. Algorithms are validated using an experimental study carried out on a pork tissue with fat acting as an inhomogeneity. The results obtained through the proposed BMOBIIR and ABMOBIIR approaches are compared with those of Newton-based MOBIIR algorithm. The mean squared error and execution time are used as metrics for comparing the results of reconstruction. We have shown through experimental and simulation studies that Broyden-based MOBIIR and adjoint Broyden-based methods are capable of reconstructing single as well as multiple inhomogeneities in tissue and a tissue-mimicking phantom. Broyden MOBIIR and adjoint Broyden MOBIIR methods are computationally simple and they result in much faster implementations because they avoid direct evaluation of Jacobian. The image reconstructions have been carried out with different initial values using Newton, Broyden, and adjoint Broyden approaches. These algorithms work well when the initial guess is close to the true solution. However, when initial guess is far away from true solution, Newton-based MOBIIR gives better reconstructed images. The proposed methods are found to be stable with noisy measurement data.

Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order numerical schemes. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order numerical schemes only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order numerical schemes were employed. In this study, a second-order spatial discretization scheme that has been tested withmore » two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. Numerical verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization schemes. Finally, the drift-flux model, along with numerical methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).« less

Application of high-order numerical schemes and Newton-Krylov method to two-phase drift-flux model

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2017-08-07

This study concerns the application and solver robustness of the Newton-Krylov method in solving two-phase flow drift-flux model problems using high-order numerical schemes. In our previous studies, the Newton-Krylov method has been proven as a promising solver for two-phase flow drift-flux model problems. However, these studies were limited to use first-order numerical schemes only. Moreover, the previous approach to treating the drift-flux closure correlations was later revealed to cause deteriorated solver convergence performance, when the mesh was highly refined, and also when higher-order numerical schemes were employed. In this study, a second-order spatial discretization scheme that has been tested withmore » two-fluid two-phase flow model was extended to solve drift-flux model problems. In order to improve solver robustness, and therefore efficiency, a new approach was proposed to treating the mean drift velocity of the gas phase as a primary nonlinear variable to the equation system. With this new approach, significant improvement in solver robustness was achieved. With highly refined mesh, the proposed treatment along with the Newton-Krylov solver were extensively tested with two-phase flow problems that cover a wide range of thermal-hydraulics conditions. Satisfactory convergence performances were observed for all test cases. Numerical verification was then performed in the form of mesh convergence studies, from which expected orders of accuracy were obtained for both the first-order and the second-order spatial discretization schemes. Finally, the drift-flux model, along with numerical methods presented, were validated with three sets of flow boiling experiments that cover different flow channel geometries (round tube, rectangular tube, and rod bundle), and a wide range of test conditions (pressure, mass flux, wall heat flux, inlet subcooling and outlet void fraction).« less

Parallel computing techniques for rotorcraft aerodynamics

NASA Astrophysics Data System (ADS)

Ekici, Kivanc

The modification of unsteady three-dimensional Navier-Stokes codes for application on massively parallel and distributed computing environments is investigated. The Euler/Navier-Stokes code TURNS (Transonic Unsteady Rotor Navier-Stokes) was chosen as a test bed because of its wide use by universities and industry. For the efficient implementation of TURNS on parallel computing systems, two algorithmic changes are developed. First, main modifications to the implicit operator, Lower-Upper Symmetric Gauss Seidel (LU-SGS) originally used in TURNS, is performed. Second, application of an inexact Newton method, coupled with a Krylov subspace iterative method (Newton-Krylov method) is carried out. Both techniques have been tried previously for the Euler equations mode of the code. In this work, we have extended the methods to the Navier-Stokes mode. Several new implicit operators were tried because of convergence problems of traditional operators with the high cell aspect ratio (CAR) grids needed for viscous calculations on structured grids. Promising results for both Euler and Navier-Stokes cases are presented for these operators. For the efficient implementation of Newton-Krylov methods to the Navier-Stokes mode of TURNS, efficient preconditioners must be used. The parallel implicit operators used in the previous step are employed as preconditioners and the results are compared. The Message Passing Interface (MPI) protocol has been used because of its portability to various parallel architectures. It should be noted that the proposed methodology is general and can be applied to several other CFD codes (e.g. OVERFLOW).

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

NASA Astrophysics Data System (ADS)

Jacquette, Dale

2014-09-01

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

Newton's Use of the Pendulum to Investigate Fluid Resistance: A Case Study and Some Implications for Teaching about the Nature of Science

ERIC Educational Resources Information Center

Gauld, Colin F.

2009-01-01

Books I and III of Newton's "Principia" develop Newton's dynamical theory and show how it explains a number of celestial phenomena. Book II has received little attention from historians or educators because it does not play a major role in Newton's argument. However, it is in Book II that we see most clearly Newton both as a theoretician and an…

High effective inverse dynamics modelling for dual-arm robot

NASA Astrophysics Data System (ADS)

Shen, Haoyu; Liu, Yanli; Wu, Hongtao

2018-05-01

To deal with the problem of inverse dynamics modelling for dual arm robot, a recursive inverse dynamics modelling method based on decoupled natural orthogonal complement is presented. In this model, the concepts and methods of Decoupled Natural Orthogonal Complement matrices are used to eliminate the constraint forces in the Newton-Euler kinematic equations, and the screws is used to express the kinematic and dynamics variables. On this basis, the paper has developed a special simulation program with symbol software of Mathematica and conducted a simulation research on the a dual-arm robot. Simulation results show that the proposed method based on decoupled natural orthogonal complement can save an enormous amount of CPU time that was spent in computing compared with the recursive Newton-Euler kinematic equations and the results is correct and reasonable, which can verify the reliability and efficiency of the method.

An historical survey of computational methods in optimal control.

NASA Technical Reports Server (NTRS)

Polak, E.

1973-01-01

Review of some of the salient theoretical developments in the specific area of optimal control algorithms. The first algorithms for optimal control were aimed at unconstrained problems and were derived by using first- and second-variation methods of the calculus of variations. These methods have subsequently been recognized as gradient, Newton-Raphson, or Gauss-Newton methods in function space. A much more recent addition to the arsenal of unconstrained optimal control algorithms are several variations of conjugate-gradient methods. At first, constrained optimal control problems could only be solved by exterior penalty function methods. Later algorithms specifically designed for constrained problems have appeared. Among these are methods for solving the unconstrained linear quadratic regulator problem, as well as certain constrained minimum-time and minimum-energy problems. Differential-dynamic programming was developed from dynamic programming considerations. The conditional-gradient method, the gradient-projection method, and a couple of feasible directions methods were obtained as extensions or adaptations of related algorithms for finite-dimensional problems. Finally, the so-called epsilon-methods combine the Ritz method with penalty function techniques.

Global Asymptotic Behavior of Iterative Implicit Schemes

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1994-01-01

The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing three models of 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed using the theory of dynamical systems. The iterative procedures include simple iteration and full and modified Newton iterations. The results are compared with standard Runge-Kutta explicit methods, a noniterative implicit procedure, and the Newton method of solving the steady part of the ODEs. Studies showed that aside from exhibiting spurious asymptotes, all of the four implicit LMMs can change the type and stability of the steady states of the differential equations (DEs). They also exhibit a drastic distortion but less shrinkage of the basin of attraction of the true solution than standard nonLMM explicit methods. The simple iteration procedure exhibits behavior which is similar to standard nonLMM explicit methods except that spurious steady-state numerical solutions cannot occur. The numerical basins of attraction of the noniterative implicit procedure mimic more closely the basins of attraction of the DEs and are more efficient than the three iterative implicit procedures for the four implicit LMMs. Contrary to popular belief, the initial data using the Newton method of solving the steady part of the DEs may not have to be close to the exact steady state for convergence. These results can be used as an explanation for possible causes and cures of slow convergence and nonconvergence of steady-state numerical solutions when using an implicit LMM time-dependent approach in computational fluid dynamics.

The Beta-Geometric Model Applied to Fecundability in a Sample of Married Women

NASA Astrophysics Data System (ADS)

Adekanmbi, D. B.; Bamiduro, T. A.

2006-10-01

The time required to achieve pregnancy among married couples termed fecundability has been proposed to follow a beta-geometric distribution. The accuracy of the method used in estimating the parameters of the model has an implication on the goodness of fit of the model. In this study, the parameters of the model are estimated using the Method of Moments and Newton-Raphson estimation procedure. The goodness of fit of the model was considered, using estimates from the two methods of estimation, as well as the asymptotic relative efficiency of the estimates. A noticeable improvement in the fit of the model to the data on time to conception was observed, when the parameters are estimated by Newton-Raphson procedure, and thereby estimating reasonable expectations of fecundability for married female population in the country.

Distance majorization and its applications.

PubMed

Chi, Eric C; Zhou, Hua; Lange, Kenneth

2014-08-01

The problem of minimizing a continuously differentiable convex function over an intersection of closed convex sets is ubiquitous in applied mathematics. It is particularly interesting when it is easy to project onto each separate set, but nontrivial to project onto their intersection. Algorithms based on Newton's method such as the interior point method are viable for small to medium-scale problems. However, modern applications in statistics, engineering, and machine learning are posing problems with potentially tens of thousands of parameters or more. We revisit this convex programming problem and propose an algorithm that scales well with dimensionality. Our proposal is an instance of a sequential unconstrained minimization technique and revolves around three ideas: the majorization-minimization principle, the classical penalty method for constrained optimization, and quasi-Newton acceleration of fixed-point algorithms. The performance of our distance majorization algorithms is illustrated in several applications.

Computation of Quasiperiodic Normally Hyperbolic Invariant Tori: Rigorous Results

NASA Astrophysics Data System (ADS)

Canadell, Marta; Haro, Àlex

2017-12-01

The development of efficient methods for detecting quasiperiodic oscillations and computing the corresponding invariant tori is a subject of great importance in dynamical systems and their applications in science and engineering. In this paper, we prove the convergence of a new Newton-like method for computing quasiperiodic normally hyperbolic invariant tori carrying quasiperiodic motion in smooth families of real-analytic dynamical systems. The main result is stated as an a posteriori KAM-like theorem that allows controlling the inner dynamics on the torus with appropriate detuning parameters, in order to obtain a prescribed quasiperiodic motion. The Newton-like method leads to several fast and efficient computational algorithms, which are discussed and tested in a companion paper (Canadell and Haro in J Nonlinear Sci, 2017. doi: 10.1007/s00332-017-9388-z), in which new mechanisms of breakdown are presented.

A monolithic homotopy continuation algorithm with application to computational fluid dynamics

NASA Astrophysics Data System (ADS)

Brown, David A.; Zingg, David W.

2016-09-01

A new class of homotopy continuation methods is developed suitable for globalizing quasi-Newton methods for large sparse nonlinear systems of equations. The new continuation methods, described as monolithic homotopy continuation, differ from the classical predictor-corrector algorithm in that the predictor and corrector phases are replaced with a single phase which includes both a predictor and corrector component. Conditional convergence and stability are proved analytically. Using a Laplacian-like operator to construct the homotopy, the new algorithm is shown to be more efficient than the predictor-corrector homotopy continuation algorithm as well as an implementation of the widely-used pseudo-transient continuation algorithm for some inviscid and turbulent, subsonic and transonic external aerodynamic flows over the ONERA M6 wing and the NACA 0012 airfoil using a parallel implicit Newton-Krylov finite-difference flow solver.

First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Nishikawa, Hiroaki

2014-01-01

A time-dependent extension of the first-order hyperbolic system method for advection-diffusion problems is introduced. Diffusive/viscous terms are written and discretized as a hyperbolic system, which recovers the original equation in the steady state. The resulting scheme offers advantages over traditional schemes: a dramatic simplification in the discretization, high-order accuracy in the solution gradients, and orders-of-magnitude convergence acceleration. The hyperbolic advection-diffusion system is discretized by the second-order upwind residual-distribution scheme in a unified manner, and the system of implicit-residual-equations is solved by Newton's method over every physical time step. The numerical results are presented for linear and nonlinear advection-diffusion problems, demonstrating solutions and gradients produced to the same order of accuracy, with rapid convergence over each physical time step, typically less than five Newton iterations.

GlobiPack v. 1.0

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bartlett, Roscoe

2010-03-31

GlobiPack contains a small collection of optimization globalization algorithms. These algorithms are used by optimization and various nonlinear equation solver algorithms.Used as the line-search procedure with Newton and Quasi-Newton optimization and nonlinear equation solver methods. These are standard published 1-D line search algorithms such as are described in the book Nocedal and Wright Numerical Optimization: 2nd edition, 2006. One set of algorithms were copied and refactored from the existing open-source Trilinos package MOOCHO where the linear search code is used to globalize SQP methods. This software is generic to any mathematical optimization problem where smooth derivatives exist. There is nomore » specific connection or mention whatsoever to any specific application, period. You cannot find more general mathematical software.« less

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

NASA Astrophysics Data System (ADS)

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

2016-05-01

Context. Thanks to the large collecting area (3 ×~1500 cm2 at 1.5 keV) and wide field of view (30' across in full field mode) of the X-ray cameras on board the European Space Agency X-ray observatory XMM-Newton, each individual pointing can result in the detection of up to several hundred X-ray sources, most of which are newly discovered objects. Since XMM-Newton has now been in orbit for more than 15 yr, hundreds of thousands of sources have been detected. Aims: Recently, many improvements in the XMM-Newton data reduction algorithms have been made. These include enhanced source characterisation and reduced spurious source detections, refined astrometric precision of sources, greater net sensitivity for source detection, and the extraction of spectra and time series for fainter sources, both with better signal-to-noise. Thanks to these enhancements, the quality of the catalogue products has been much improved over earlier catalogues. Furthermore, almost 50% more observations are in the public domain compared to 2XMMi-DR3, allowing the XMM-Newton Survey Science Centre to produce a much larger and better quality X-ray source catalogue. Methods: The XMM-Newton Survey Science Centre has developed a pipeline to reduce the XMM-Newton data automatically. Using the latest version of this pipeline, along with better calibration, a new version of the catalogue has been produced, using XMM-Newton X-ray observations made public on or before 2013 December 31. Manual screening of all of the X-ray detections ensures the highest data quality. This catalogue is known as 3XMM. Results: In the latest release of the 3XMM catalogue, 3XMM-DR5, there are 565 962 X-ray detections comprising 396 910 unique X-ray sources. Spectra and lightcurves are provided for the 133 000 brightest sources. For all detections, the positions on the sky, a measure of the quality of the detection, and an evaluation of the X-ray variability is provided, along with the fluxes and count rates in 7 X-ray energy bands, the total 0.2-12 keV band counts, and four hardness ratios. With the aim of identifying the detections, a cross correlation with 228 catalogues of sources detected in all wavebands is also provided for each X-ray detection. Conclusions: 3XMM-DR5 is the largest X-ray source catalogue ever produced. Thanks to the large array of data products associated with each detection and each source, it is an excellent resource for finding new and extreme objects. Based on observations obtained with XMM-Newton, an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA.The catalogue is available at http://cdsarc.u-strasbg.fr/viz-bin/VizieR?-meta.foot&-source=IX/46

Toward milli-Newton electro- and magneto-static microactuators

NASA Technical Reports Server (NTRS)

Fan, Long-Sheng

1993-01-01

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

XMM-Newton Remote Interface to Science Analysis Software: First Public Version

NASA Astrophysics Data System (ADS)

Ibarra, A.; Gabriel, C.

2011-07-01

We present the first public beta release of the XMM-Newton Remote Interface to Science Analysis (RISA) software, available through the official XMM-Newton web pages. In a nutshell, RISA is a web based application that encapsulates the XMM-Newton data analysis software. The client identifies observations and creates XMM-Newton workflows. The server processes the client request, creates job templates and sends the jobs to a computer. RISA has been designed to help, at the same time, non-expert and professional XMM-Newton users. Thanks to the predefined threads, non-expert users can easily produce light curves and spectra. And on the other hand, expert user can use the full parameter interface to tune their own analysis. In both cases, the VO compliant client/server design frees the users from having to install any specific software to analyze XMM-Newton data.

Using CAS to Solve Classical Mathematics Problems

ERIC Educational Resources Information Center

Burke, Maurice J.; Burroughs, Elizabeth A.

2009-01-01

Historically, calculus has displaced many algebraic methods for solving classical problems. This article illustrates an algebraic method for finding the zeros of polynomial functions that is closely related to Newton's method (devised in 1669, published in 1711), which is encountered in calculus. By exploring this problem, precalculus students…

The XMM-Newton Survey of the Small Magellanic Cloud

NASA Technical Reports Server (NTRS)

Haberl, F.; Sturm, R.; Ballet, J.; Bomans, D. J.; Buckley, D. A. H.; Coe, M. J.; Corbet, R.; Ehle, M.; Filipovic, M. D.; Gilfanov, M.;

Solution des systemes de controle de grandes dimensions basee sur les boucles de retroaction dans la simulation des reseaux electriques

NASA Astrophysics Data System (ADS)

Mugombozi, Chuma Francis

The generation of electrical energy, as well as its transportation and consumption, requires complex control systems for the regulation of power and frequency. These control systems must take into account, among others, new energy sources such as wind energy and new technologies for interconnection by high voltage DC link. These control systems must be able to monitor and achieve such regulation in accordance with the dynamics of the energy source, faults and other events which may induce transients phenomena into the power network. Such transients conditions have to be analyzed using the most accurate and detailed hence, complex models of control system. In addition, in the feasibility study phase, the calibration or the setup of equipment as well as in the operation of the power network, one may require decision aid tools for engineers. This includes, for instance, knowledge of energy dissipated into the arresters in transient analysis. These tools use simulation programs data as inputs and may require that complex functions be solved with numerical methods. These functions are part of control system in computer simulator. Moreover, the simulation evolves in a broader context of the development of digital controller, distributed and parallel high performance computing and rapid evolutions in computer (multiprocessor) technology. In such context, a continuing improvement of the control equations solver is welcomed. Control systems are modelled using ax=b simultaneous system of equations. These equations are sometimes non-linear with feedback loops and thus require iterative Newton methods, including the formation of a Jacobian matrix and ordering as well as processing by graph theory tools. The proposed approach is based on the formulation of a reduced rank Jacobian matrix. The dimension is reduced up to the count of feedback loops. With this new approach, gains in computation speed are expected without compromising its accuracy when compared to classical full rank Jacobian matrix representation. A directed graph representation is adopted and a proper approach for detecting and removing cycles within the graph is introduced. A condition of all zero eigenvalues of adjacency matrix of the graph is adopted. The transformation of the graph of controls with no cycle permits a formulation of control equations for only feedback points. This yields a general feedback interconnection (GFBI) representation of control, which is the main contribution of this thesis. Methods for solving (non-linear) equations of control systems were deployed into the new GFBI approach. Five variants of the new approach were illustrated including firstly, a basic Newton method (1), a more robust one, the Dogleg method (2) and a fixed-point iterations method (3). I. The presented approach is implemented in Electromagnetic Transient program EMTP-RV and tested on practical systems of various types and levels of complexity: the PLL, an asynchronous machine with 87 blocks reduced to 23 feedback equations by GFBI, and 12 wind power plants integrated to the IEEE-39 buses system. Further analysis, which opens up avenues for future research includes comparison of the proposed approach against existing ones. With respect to the sole representation, it is shown that the proposed approach is equivalent to full classic representation of system of equations through a proper substitution process which complies with topological sequence and by skipping feedback variable identified by GFBI. Moreover, a second comparison with state space based approach, such as that in MATLAB/Simulink, shows that output evaluation step in state-space approach with algebraic constraints is similar to the GFBI. The algebraic constraints are similar to feedback variables. A difference may arise, however, when the number of algebraic constraints is not the optimal number of cuts for the GFBI method: for the PLL, for example, MATLAB/Simulink generated 3 constraints while the GFBI generated only 2. The GFBI method may offer some advantages in this case. A last analysis axis prompted further work in initialization. It is shown that GFBI method may modifies the convergence properties of iterations of the Newton method. The Newton- Kantorovich theorem, using bounds on the norms of the Jacobian, has been applied to the proposed GFBI and classic full representation of control equations. The expressions of the Jacobian norms have been established for generic cases using Coates graph. It appears from the analysis of a simple case, for the same initial conditions, the behaviour of the Newton- Kantorovich theorem differs in both cases. These differences may also be more pronounced in the non-linear case. Further work would be useful to investigate this aspect and, eventually, pave the way to new initialization approaches. Despite these limitations, not to mention areas for improvement in further work, one notes the contribution of this thesis to improve the gain of time on simulation for the solution of control systems. (Abstract shortened by UMI.).

PIXIE3D: A Parallel, Implicit, eXtended MHD 3D Code.

NASA Astrophysics Data System (ADS)

Chacon, L.; Knoll, D. A.

2004-11-01

We report on the development of PIXIE3D, a 3D parallel, fully implicit Newton-Krylov extended primitive-variable MHD code in general curvilinear geometry. PIXIE3D employs a second-order, finite-volume-based spatial discretization that satisfies remarkable properties such as being conservative, solenoidal in the magnetic field, non-dissipative, and stable in the absence of physical dissipation.(L. Chacón , phComput. Phys. Comm.) submitted (2004) PIXIE3D employs fully-implicit Newton-Krylov methods for the time advance. Currently, first and second-order implicit schemes are available, although higher-order temporal implicit schemes can be effortlessly implemented within the Newton-Krylov framework. A successful, scalable, MG physics-based preconditioning strategy, similar in concept to previous 2D MHD efforts,(L. Chacón et al., phJ. Comput. Phys). 178 (1), 15- 36 (2002); phJ. Comput. Phys., 188 (2), 573-592 (2003) has been developed. We are currently in the process of parallelizing the code using the PETSc library, and a Newton-Krylov-Schwarz approach for the parallel treatment of the preconditioner. In this poster, we will report on both the serial and parallel performance of PIXIE3D, focusing primarily on scalability and CPU speedup vs. an explicit approach.

Flow properties of concentrated suspensions

NASA Technical Reports Server (NTRS)

Hattori, K.; Izumi, K.

1984-01-01

The viscosity and flow behavior of a concentrated suspension, with special emphasis on fresh concrete containing a superplasticizer, is analyzed according to Newton's law of viscosity. The authors interpreted Newton's law in a new way, and explain non-Newton flow from Newton's law. The outline of this new theory is given. Viscosity of suspensions, and the effect of dispersants are analyzed.

Measurement of Newton's constant using a torsion balance with angular acceleration feedback.

PubMed

Gundlach, J H; Merkowitz, S M

2000-10-02

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) x 10(-11) m3 kg(-1) s(-2); the Earth's mass is, therefore, M = (5.972245+/-0.000082) x 10(24) kg and the Sun's mass is M = (1.988435+/-0.000027) x 10(30) kg.

From the Landgrave in Kassel to Isaac Newton

NASA Astrophysics Data System (ADS)

Høg, E.

2018-01-01

Landgrave Wilhelm IV established in 1560 the first permanent astronomical observatory in Europe. When he met the young Tycho Brahe in 1575 he recognized the genius and recommended him warmly to the Danish king Frederik II. Wilhelm and Tycho must share the credit for renewing astronomy with very accurate observations of positions of stars by new instrumentation and new methods. Tycho's observations of planets during 20 years enabled Johannes Kepler to derive the laws of planetary motion. These laws set Isaac Newton in a position to publish the laws of physical motion and universal gravitation in 1687 - the basis for the technical revolution.

Interior-Point Methods for Linear Programming: A Challenge to the Simplex Method

DTIC Science & Technology

1988-07-01

subsequently found that the method was first proposed by Dikin in 1967 [6]. Search directions are generated by the same system (5). Any hint of quadratic...1982). Inexact Newton methods, SIAM Journal on Numerical Analysis 19, 400-408. [6] I. I. Dikin (1967). Iterative solution of problems of linear and

On the use of finite difference matrix-vector products in Newton-Krylov solvers for implicit climate dynamics with spectral elements

DOE PAGES

Woodward, Carol S.; Gardner, David J.; Evans, Katherine J.

2015-01-01

Efficient solutions of global climate models require effectively handling disparate length and time scales. Implicit solution approaches allow time integration of the physical system with a step size governed by accuracy of the processes of interest rather than by stability of the fastest time scales present. Implicit approaches, however, require the solution of nonlinear systems within each time step. Usually, a Newton's method is applied to solve these systems. Each iteration of the Newton's method, in turn, requires the solution of a linear model of the nonlinear system. This model employs the Jacobian of the problem-defining nonlinear residual, but thismore » Jacobian can be costly to form. If a Krylov linear solver is used for the solution of the linear system, the action of the Jacobian matrix on a given vector is required. In the case of spectral element methods, the Jacobian is not calculated but only implemented through matrix-vector products. The matrix-vector multiply can also be approximated by a finite difference approximation which may introduce inaccuracy in the overall nonlinear solver. In this paper, we review the advantages and disadvantages of finite difference approximations of these matrix-vector products for climate dynamics within the spectral element shallow water dynamical core of the Community Atmosphere Model.« less

Iteration with Spreadsheets.

ERIC Educational Resources Information Center

Smith, Michael

1990-01-01

Presents several examples of the iteration method using computer spreadsheets. Examples included are simple iterative sequences and the solution of equations using the Newton-Raphson formula, linear interpolation, and interval bisection. (YP)

Ellipsoidal terrain correction based on multi-cylindrical equal-area map projection of the reference ellipsoid

NASA Astrophysics Data System (ADS)

Ardalan, A. A.; Safari, A.

2004-09-01

An operational algorithm for computation of terrain correction (or local gravity field modeling) based on application of closed-form solution of the Newton integral in terms of Cartesian coordinates in multi-cylindrical equal-area map projection of the reference ellipsoid is presented. Multi-cylindrical equal-area map projection of the reference ellipsoid has been derived and is described in detail for the first time. Ellipsoidal mass elements with various sizes on the surface of the reference ellipsoid are selected and the gravitational potential and vector of gravitational intensity (i.e. gravitational acceleration) of the mass elements are computed via numerical solution of the Newton integral in terms of geodetic coordinates {λ,ϕ,h}. Four base- edge points of the ellipsoidal mass elements are transformed into a multi-cylindrical equal-area map projection surface to build Cartesian mass elements by associating the height of the corresponding ellipsoidal mass elements to the transformed area elements. Using the closed-form solution of the Newton integral in terms of Cartesian coordinates, the gravitational potential and vector of gravitational intensity of the transformed Cartesian mass elements are computed and compared with those of the numerical solution of the Newton integral for the ellipsoidal mass elements in terms of geodetic coordinates. Numerical tests indicate that the difference between the two computations, i.e. numerical solution of the Newton integral for ellipsoidal mass elements in terms of geodetic coordinates and closed-form solution of the Newton integral in terms of Cartesian coordinates, in a multi-cylindrical equal-area map projection, is less than 1.6×10-8 m2/s2 for a mass element with a cross section area of 10×10 m and a height of 10,000 m. For a mass element with a cross section area of 1×1 km and a height of 10,000 m the difference is less than 1.5×10-4m2/s2. Since 1.5× 10-4 m2/s2 is equivalent to 1.5×10-5m in the vertical direction, it can be concluded that a method for terrain correction (or local gravity field modeling) based on closed-form solution of the Newton integral in terms of Cartesian coordinates of a multi-cylindrical equal-area map projection of the reference ellipsoid has been developed which has the accuracy of terrain correction (or local gravity field modeling) based on the Newton integral in terms of ellipsoidal coordinates.

How Two Differing Portraits of Newton Can Teach Us about the Cultural Context of Science

ERIC Educational Resources Information Center

Tucci, Pasquale

2015-01-01

Like several scientists, Isaac Newton has been represented many times over many different periods, and portraits of Newton were often commissioned by the scientist himself. These portraits tell us a lot about the scientist, the artist and the cultural context. This article examines two very different portraits of Newton that were realized more…

The Cooling Law and the Search for a Good Temperature Scale, from Newton to Dalton

ERIC Educational Resources Information Center

Besson, Ugo

2011-01-01

The research on the cooling law began with an article by Newton published in 1701. Later, many studies were performed by other scientists confirming or confuting Newton's law. This paper presents a description and an interpretation of Newton's article, provides a short overview of the research conducted on the topic during the 18th century, and…

A preconditioner for the finite element computation of incompressible, nonlinear elastic deformations

NASA Astrophysics Data System (ADS)

Whiteley, J. P.

2017-10-01

Large, incompressible elastic deformations are governed by a system of nonlinear partial differential equations. The finite element discretisation of these partial differential equations yields a system of nonlinear algebraic equations that are usually solved using Newton's method. On each iteration of Newton's method, a linear system must be solved. We exploit the structure of the Jacobian matrix to propose a preconditioner, comprising two steps. The first step is the solution of a relatively small, symmetric, positive definite linear system using the preconditioned conjugate gradient method. This is followed by a small number of multigrid V-cycles for a larger linear system. Through the use of exemplar elastic deformations, the preconditioner is demonstrated to facilitate the iterative solution of the linear systems arising. The number of GMRES iterations required has only a very weak dependence on the number of degrees of freedom of the linear systems.

Idea Bank.

ERIC Educational Resources Information Center

Science Teacher, 1990

1990-01-01

Eight activities for use in the science classroom are presented. Included are insect collecting, laboratory procedures and safety, recycling, current events, variable manipulation, scientific method, electricity, and mechanics (Newton's Second Law of Motion). (KR)

A quasi-Newton algorithm for large-scale nonlinear equations.

PubMed

Huang, Linghua

2017-01-01

In this paper, the algorithm for large-scale nonlinear equations is designed by the following steps: (i) a conjugate gradient (CG) algorithm is designed as a sub-algorithm to obtain the initial points of the main algorithm, where the sub-algorithm's initial point does not have any restrictions; (ii) a quasi-Newton algorithm with the initial points given by sub-algorithm is defined as main algorithm, where a new nonmonotone line search technique is presented to get the step length [Formula: see text]. The given nonmonotone line search technique can avoid computing the Jacobian matrix. The global convergence and the [Formula: see text]-order convergent rate of the main algorithm are established under suitable conditions. Numerical results show that the proposed method is competitive with a similar method for large-scale problems.

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

NASA Technical Reports Server (NTRS)

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

1972-01-01

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

Stochastic modification of the Schrödinger-Newton equation

NASA Astrophysics Data System (ADS)

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

2015-07-01

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

XMM-Newton publication statistics

NASA Astrophysics Data System (ADS)

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

2014-02-01

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

Comparing Three Methods for Teaching Newton's Third Law

ERIC Educational Resources Information Center

Smith, Trevor I.; Wittman, Michael C.

2007-01-01

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

Dielectric constant extraction of graphene nanostructured on SiC substrates from spectroscopy ellipsometry measurement using Gauss–Newton inversion method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Maulina, Hervin; Santoso, Iman, E-mail: iman.santoso@ugm.ac.id; Subama, Emmistasega

2016-04-19

The extraction of the dielectric constant of nanostructured graphene on SiC substrates from spectroscopy ellipsometry measurement using the Gauss-Newton inversion (GNI) method has been done. This study aims to calculate the dielectric constant and refractive index of graphene by extracting the value of ψ and Δ from the spectroscopy ellipsometry measurement using GNI method and comparing them with previous result which was extracted using Drude-Lorentz (DL) model. The results show that GNI method can be used to calculate the dielectric constant and refractive index of nanostructured graphene on SiC substratesmore faster as compared to DL model. Moreover, the imaginary partmore » of the dielectric constant values and coefficient of extinction drastically increases at 4.5 eV similar to that of extracted using known DL fitting. The increase is known due to the process of interband transition and the interaction between the electrons and electron-hole at M-points in the Brillouin zone of graphene.« less

Turning around Newton's Second Law

ERIC Educational Resources Information Center

Goff, John Eric

2004-01-01

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

Nonlinear and parallel algorithms for finite element discretizations of the incompressible Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Arteaga, Santiago Egido

1998-12-01

The steady-state Navier-Stokes equations are of considerable interest because they are used to model numerous common physical phenomena. The applications encountered in practice often involve small viscosities and complicated domain geometries, and they result in challenging problems in spite of the vast attention that has been dedicated to them. In this thesis we examine methods for computing the numerical solution of the primitive variable formulation of the incompressible equations on distributed memory parallel computers. We use the Galerkin method to discretize the differential equations, although most results are stated so that they apply also to stabilized methods. We also reformulate some classical results in a single framework and discuss some issues frequently dismissed in the literature, such as the implementation of pressure space basis and non- homogeneous boundary values. We consider three nonlinear methods: Newton's method, Oseen's (or Picard) iteration, and sequences of Stokes problems. All these iterative nonlinear methods require solving a linear system at every step. Newton's method has quadratic convergence while that of the others is only linear; however, we obtain theoretical bounds showing that Oseen's iteration is more robust, and we confirm it experimentally. In addition, although Oseen's iteration usually requires more iterations than Newton's method, the linear systems it generates tend to be simpler and its overall costs (in CPU time) are lower. The Stokes problems result in linear systems which are easier to solve, but its convergence is much slower, so that it is competitive only for large viscosities. Inexact versions of these methods are studied, and we explain why the best timings are obtained using relatively modest error tolerances in solving the corresponding linear systems. We also present a new damping optimization strategy based on the quadratic nature of the Navier-Stokes equations, which improves the robustness of all the linearization strategies considered and whose computational cost is negligible. The algebraic properties of these systems depend on both the discretization and nonlinear method used. We study in detail the positive definiteness and skewsymmetry of the advection submatrices (essentially, convection-diffusion problems). We propose a discretization based on a new trilinear form for Newton's method. We solve the linear systems using three Krylov subspace methods, GMRES, QMR and TFQMR, and compare the advantages of each. Our emphasis is on parallel algorithms, and so we consider preconditioners suitable for parallel computers such as line variants of the Jacobi and Gauss- Seidel methods, alternating direction implicit methods, and Chebyshev and least squares polynomial preconditioners. These work well for moderate viscosities (moderate Reynolds number). For small viscosities we show that effective parallel solution of the advection subproblem is a critical factor to improve performance. Implementation details on a CM-5 are presented.

SIMULATIONS OF 2D AND 3D THERMOCAPILLARY FLOWS BY A LEAST-SQUARES FINITE ELEMENT METHOD. (R825200)

EPA Science Inventory

Numerical results for time-dependent 2D and 3D thermocapillary flows are presented in this work. The numerical algorithm is based on the Crank-Nicolson scheme for time integration, Newton's method for linearization, and a least-squares finite element method, together with a matri...

Inverts permittivity and conductivity with structural constraint in GPR FWI based on truncated Newton method

NASA Astrophysics Data System (ADS)

Ren, Qianci

2018-04-01

Full waveform inversion (FWI) of ground penetrating radar (GPR) is a promising technique to quantitatively evaluate the permittivity and conductivity of near subsurface. However, these two parameters are simultaneously inverted in the GPR FWI, increasing the difficulty to obtain accurate inversion results for both parameters. In this study, I present a structural constrained GPR FWI procedure to jointly invert the two parameters, aiming to force a structural relationship between permittivity and conductivity in the process of model reconstruction. The structural constraint is enforced by a cross-gradient function. In this procedure, the permittivity and conductivity models are inverted alternately at each iteration and updated with hierarchical frequency components in the frequency domain. The joint inverse problem is solved by the truncated Newton method which considering the effect of Hessian operator and using the approximated solution of Newton equation to be the perturbation model in the updating process. The joint inversion procedure is tested by three synthetic examples. The results show that jointly inverting permittivity and conductivity in GPR FWI effectively increases the structural similarities between the two parameters, corrects the structures of parameter models, and significantly improves the accuracy of conductivity model, resulting in a better inversion result than the individual inversion.

Close Encounters of a Sparse Kind.

ERIC Educational Resources Information Center

Westerberg, Arthur W.

1980-01-01

By providing an example problem in solving sets of nonlinear algebraic equations, the advantages and disadvantages of two methods for its solution, the tearing approach v the Newton-Raphson approach, are elucidated. (CS)

"On Second Thoughts…": Changes of Mind as an Indication of Competing Knowledge Structures

NASA Astrophysics Data System (ADS)

Wilson, Kate F.; Low, David J.

2015-09-01

A review of student answers to diagnostic questions concerned with Newton's Laws showed a tendency for some students to change their answer to a question when the following question caused them to think more about the situation. We investigate this behavior and interpret it in the framework of the resource model; in particular, a weak Newton's Third Law structure being dominated by an inconsistent Newton's Second Law (or "Net Force") structure, in the absence of a strong, consistent Newtonian structure. This observation highlights the hidden problem in instruction where the implicit use of Newton's Third Law is dominated by the explicit conceptual and mathematical application of Newton's Second Law, both within individual courses and across a degree program. To facilitate students' development of a consistent Newtonian knowledge structure, it is important that instructors highlight the interrelated nature of Newton's Laws in problem solving.

MHOST: An efficient finite element program for inelastic analysis of solids and structures

NASA Technical Reports Server (NTRS)

Nakazawa, S.

1988-01-01

An efficient finite element program for 3-D inelastic analysis of gas turbine hot section components was constructed and validated. A novel mixed iterative solution strategy is derived from the augmented Hu-Washizu variational principle in order to nodally interpolate coordinates, displacements, deformation, strains, stresses and material properties. A series of increasingly sophisticated material models incorporated in MHOST include elasticity, secant plasticity, infinitesimal and finite deformation plasticity, creep and unified viscoplastic constitutive model proposed by Walker. A library of high performance elements is built into this computer program utilizing the concepts of selective reduced integrations and independent strain interpolations. A family of efficient solution algorithms is implemented in MHOST for linear and nonlinear equation solution including the classical Newton-Raphson, modified, quasi and secant Newton methods with optional line search and the conjugate gradient method.

Multiscale Multilevel Approach to Solution of Nanotechnology Problems

NASA Astrophysics Data System (ADS)

Polyakov, Sergey; Podryga, Viktoriia

2018-02-01

The paper is devoted to a multiscale multilevel approach for the solution of nanotechnology problems on supercomputer systems. The approach uses the combination of continuum mechanics models and the Newton dynamics for individual particles. This combination includes three scale levels: macroscopic, mesoscopic and microscopic. For gas-metal technical systems the following models are used. The quasihydrodynamic system of equations is used as a mathematical model at the macrolevel for gas and solid states. The system of Newton equations is used as a mathematical model at the mesoand microlevels; it is written for nanoparticles of the medium and larger particles moving in the medium. The numerical implementation of the approach is based on the method of splitting into physical processes. The quasihydrodynamic equations are solved by the finite volume method on grids of different types. The Newton equations of motion are solved by Verlet integration in each cell of the grid independently or in groups of connected cells. In the framework of the general methodology, four classes of algorithms and methods of their parallelization are provided. The parallelization uses the principles of geometric parallelism and the efficient partitioning of the computational domain. A special dynamic algorithm is used for load balancing the solvers. The testing of the developed approach was made by the example of the nitrogen outflow from a balloon with high pressure to a vacuum chamber through a micronozzle and a microchannel. The obtained results confirm the high efficiency of the developed methodology.

From Newton to Einstein.

ERIC Educational Resources Information Center

Ryder, L. H.

1987-01-01

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

Implicit integration methods for dislocation dynamics

DOE PAGES

Gardner, D. J.; Woodward, C. S.; Reynolds, D. R.; ...

2015-01-20

In dislocation dynamics simulations, strain hardening simulations require integrating stiff systems of ordinary differential equations in time with expensive force calculations, discontinuous topological events, and rapidly changing problem size. Current solvers in use often result in small time steps and long simulation times. Faster solvers may help dislocation dynamics simulations accumulate plastic strains at strain rates comparable to experimental observations. Here, this paper investigates the viability of high order implicit time integrators and robust nonlinear solvers to reduce simulation run times while maintaining the accuracy of the computed solution. In particular, implicit Runge-Kutta time integrators are explored as a waymore » of providing greater accuracy over a larger time step than is typically done with the standard second-order trapezoidal method. In addition, both accelerated fixed point and Newton's method are investigated to provide fast and effective solves for the nonlinear systems that must be resolved within each time step. Results show that integrators of third order are the most effective, while accelerated fixed point and Newton's method both improve solver performance over the standard fixed point method used for the solution of the nonlinear systems.« less

Newton and Colour: The Complex Interplay of Theory and Experiment.

ERIC Educational Resources Information Center

Martins, Roberto De Andrade; Silva, Cibelle Celestino

2001-01-01

Elucidates some aspects of Newton's theory of light and colors, specifically as presented in his first optical paper in 1672. Analyzes Newton's main experiments intended to show that light is a mixture of rays with different refrangibilities. (SAH)

An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions

NASA Technical Reports Server (NTRS)

Peters, B. C., Jr.; Walker, H. F.

1975-01-01

A general iterative procedure is given for determining the consistent maximum likelihood estimates of normal distributions. In addition, a local maximum of the log-likelihood function, Newtons's method, a method of scoring, and modifications of these procedures are discussed.

J. F. C. Fuller: His Methods, Insights, and Vision

DTIC Science & Technology

1999-04-01

contributed immensely to the body of knowledge concerning warfare. As a military scientist, MG Fuller attempted to do for warfare what Copernicus did for... astronomy , Newton for physics, and Darwin for natural history: establish a higher order for the study warfare based on scientific analysis and methods

Estimating the Parameters of the Beta-Binomial Distribution.

ERIC Educational Resources Information Center

Wilcox, Rand R.

1979-01-01

For some situations the beta-binomial distribution might be used to describe the marginal distribution of test scores for a particular population of examinees. Several different methods of approximating the maximum likelihood estimate were investigated, and it was found that the Newton-Raphson method should be used when it yields admissable…

PEOPLE IN PHYSICS: Newton's apple

NASA Astrophysics Data System (ADS)

Sandford Smith, Daniel

1997-03-01

This essay has a long history. It was triggered at university by one of my tutors describing the dispute between Robert Hooke and Isaac Newton. He conjured up an image of Newton sitting at his desk doing calculations while Hooke went down mineshafts trying to detect a change in the strength of gravity. To someone who was finding the maths content of a physics degree somewhat challenging this was a symbolic image. I believe that the story of Newton and the apple illustrates the complex nature of scientific discovery.

XMM-Newton On-demand Reprocessing Using SaaS Technology

NASA Astrophysics Data System (ADS)

Ibarra, A.; Fajersztejn, N.; Loiseau, N.; Gabriel, C.

2014-05-01

We present here the architectural design of the new on-the-fly reprocessing capabilities that will be soon developed and implemented in the new XMM-Newton Science Operation Centre. The inclusion of processing capabilities into the archive, as we plan, will be possible thanks to the recent refurbishment of the XMM-Newton science archive, its alignment with the latest web technologies and the XMM-Newton Remote Interface for Science Analysis (RISA), a revolutionary idea of providing processing capabilities through internet services.

Dissecting the structural determinants for the difference in mechanical stability of silk and amyloid beta-sheet stacks.

PubMed

Xiao, Senbo; Xiao, Shijun; Gräter, Frauke

2013-06-14

Stacking of β-sheets results in a protein super secondary structure with remarkable mechanical properties. β-Stacks are the determinants of a silk fiber's resilience and are also the building blocks of amyloid fibrils. While both silk and amyloid-type crystals are known to feature a high resistance against rupture, their structural and mechanical similarities and particularities are yet to be fully understood. Here, we systematically compare the rupture force and stiffness of amyloid and spider silk poly-alanine β-stacks of comparable sizes using Molecular Dynamics simulations. We identify the direction of force application as the primary determinant of the rupture strength; β-sheets in silk are orientated along the fiber axis, i.e. the pulling direction, and consequently require high forces in the several nanoNewton range for shearing β-strands apart, while β-sheets in amyloid are oriented vertically to the fiber, allowing a zipper-like rupture at sub-nanoNewton forces. A secondary factor rendering amyloid β-stacks softer and weaker than their spider silk counterparts is the sub-optimal side-chain packing between β-sheets due to the sequence variations of amyloid-forming proteins as opposed to the perfectly packed poly-alanine β-sheets of silk. Taken together, amyloid fibers can reach the stiffness of silk fibers in spite of their softer and weaker β-sheet arrangement as they are missing a softening amorphous matrix.

Evidence for a decay of the faint flaring rate of Sgr A* from 2013 Aug., 13 months before a rise of the before a rise of the bright one

NASA Astrophysics Data System (ADS)

Mossoux, E.; Grosso, N.

2017-10-01

Thanks to the overall 1999-2015 Chandra, XMM-Newton and Swift observations of the supermassive black hole at the center of our Galaxy, Sgr A*, we tested the significance and persistence of the increase of 'bright and very bright' X-ray flaring rate (FR) argued by Ponti et al. (2015). We detected the flares observed with Swift using the binned light curves whereas those observed by XMM-Newton and Chandra were detected using the two-steps Bayesian blocks (BB) algorithm with a prior number of change-points properly calibrated. We then applied this algorithm on the flare arrival times corrected from the detection efficiency computed for each observation thanks to the observed distribution of flare fluxes and durations. We confirmed a constant overall FR and a rise of the FR for the faintest flares from 2014 Aug. 31 and identified a decay of the FR for the brightest flares from 2013 Aug. and Nov. A mass transfer from the Dusty S-cluster Object/G2 to Sgr A* is not required to produce the rise of bright FR since the energy saved by the decay of the number of faint flares during a long time period may be later released by several bright flares during a shorter time period.

Evaluation of retention and fracture resistance of different fiber reinforced posts: An in vitro study.

PubMed

Pruthi, Varun; Talwar, Sangeeta; Nawal, Ruchika Roongta; Pruthi, Preeti Jain; Choudhary, Sarika; Yadav, Seema

2018-01-01

The aim of this study was to evaluate retention & fracture resistance of different fibre posts. 90 extracted human permanent maxillary central incisors were used in this study. For retention evaluation, after obturation, post space preparation was done in all root canals and posts were cemented under three groups. Later, the posts were grasped & pulled out from the roots with the help of a three-jaw chuck at a cross-head speed of 5mm/min. Force required to dislodge each post was recorded in Newtons. To evaluate the fracture behavior of posts, artificial root canals were drilled into aluminium blocks and posts were cemented. Load required to fracture each post was recorded in Newtons. The results of the present study show the mean retention values for Fibrekleer Parallel post were significantly greater than those for Synca Double tapered post & Bioloren Tapered post. The mean retention values of the Double tapered post & the tapered post were not statistically different. The Synca Double tapered post had the highest mean load to fracture, and this value was significantly higher than those of FibreKleer Parallel & Bioloren Tapered post. The mean fracture resistance values of Parallel & tapered post were not statistically different. This study showed parallel posts to have better retention than tapered and double tapered posts. Regarding the fracture resistance, double tapered posts were found to be better than parallel and tapered posts.

Large-scale 3-D EM modelling with a Block Low-Rank multifrontal direct solver

NASA Astrophysics Data System (ADS)

Shantsev, Daniil V.; Jaysaval, Piyoosh; de la Kethulle de Ryhove, Sébastien; Amestoy, Patrick R.; Buttari, Alfredo; L'Excellent, Jean-Yves; Mary, Theo

2017-06-01

We put forward the idea of using a Block Low-Rank (BLR) multifrontal direct solver to efficiently solve the linear systems of equations arising from a finite-difference discretization of the frequency-domain Maxwell equations for 3-D electromagnetic (EM) problems. The solver uses a low-rank representation for the off-diagonal blocks of the intermediate dense matrices arising in the multifrontal method to reduce the computational load. A numerical threshold, the so-called BLR threshold, controlling the accuracy of low-rank representations was optimized by balancing errors in the computed EM fields against savings in floating point operations (flops). Simulations were carried out over large-scale 3-D resistivity models representing typical scenarios for marine controlled-source EM surveys, and in particular the SEG SEAM model which contains an irregular salt body. The flop count, size of factor matrices and elapsed run time for matrix factorization are reduced dramatically by using BLR representations and can go down to, respectively, 10, 30 and 40 per cent of their full-rank values for our largest system with N = 20.6 million unknowns. The reductions are almost independent of the number of MPI tasks and threads at least up to 90 × 10 = 900 cores. The BLR savings increase for larger systems, which reduces the factorization flop complexity from O(N2) for the full-rank solver to O(Nm) with m = 1.4-1.6. The BLR savings are significantly larger for deep-water environments that exclude the highly resistive air layer from the computational domain. A study in a scenario where simulations are required at multiple source locations shows that the BLR solver can become competitive in comparison to iterative solvers as an engine for 3-D controlled-source electromagnetic Gauss-Newton inversion that requires forward modelling for a few thousand right-hand sides.

Estimation of parameters in rational reaction rates of molecular biological systems via weighted least squares

NASA Astrophysics Data System (ADS)

Wu, Fang-Xiang; Mu, Lei; Shi, Zhong-Ke

2010-01-01

The models of gene regulatory networks are often derived from statistical thermodynamics principle or Michaelis-Menten kinetics equation. As a result, the models contain rational reaction rates which are nonlinear in both parameters and states. It is challenging to estimate parameters nonlinear in a model although there have been many traditional nonlinear parameter estimation methods such as Gauss-Newton iteration method and its variants. In this article, we develop a two-step method to estimate the parameters in rational reaction rates of gene regulatory networks via weighted linear least squares. This method takes the special structure of rational reaction rates into consideration. That is, in the rational reaction rates, the numerator and the denominator are linear in parameters. By designing a special weight matrix for the linear least squares, parameters in the numerator and the denominator can be estimated by solving two linear least squares problems. The main advantage of the developed method is that it can produce the analytical solutions to the estimation of parameters in rational reaction rates which originally is nonlinear parameter estimation problem. The developed method is applied to a couple of gene regulatory networks. The simulation results show the superior performance over Gauss-Newton method.

Efficient combination of a 3D Quasi-Newton inversion algorithm and a vector dual-primal finite element tearing and interconnecting method

NASA Astrophysics Data System (ADS)

Voznyuk, I.; Litman, A.; Tortel, H.

2015-08-01

A Quasi-Newton method for reconstructing the constitutive parameters of three-dimensional (3D) penetrable scatterers from scattered field measurements is presented. This method is adapted for handling large-scale electromagnetic problems while keeping the memory requirement and the time flexibility as low as possible. The forward scattering problem is solved by applying the finite-element tearing and interconnecting full-dual-primal (FETI-FDP2) method which shares the same spirit as the domain decomposition methods for finite element methods. The idea is to split the computational domain into smaller non-overlapping sub-domains in order to simultaneously solve local sub-problems. Various strategies are proposed in order to efficiently couple the inversion algorithm with the FETI-FDP2 method: a separation into permanent and non-permanent subdomains is performed, iterative solvers are favorized for resolving the interface problem and a marching-on-in-anything initial guess selection further accelerates the process. The computational burden is also reduced by applying the adjoint state vector methodology. Finally, the inversion algorithm is confronted to measurements extracted from the 3D Fresnel database.

Tensor-GMRES method for large sparse systems of nonlinear equations

NASA Technical Reports Server (NTRS)

Feng, Dan; Pulliam, Thomas H.

1994-01-01

This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.

Astronomical and Cosmological Symbolism in Art Dedicated to Newton and Einstein

NASA Astrophysics Data System (ADS)

Sinclair, R.

2013-04-01

Separated by two and a half centuries, Isaac Newton (1642-1727) and Albert Einstein (1879-1955) had profound impacts on our understanding of the universe. Newton established our understanding of universal gravitation, which was recast almost beyond recognition by Einstein. Both discovered basic patterns behind astronomical phenomena and became the best-known scientists of their respective periods. I will describe here how artists of the 18th and 20th centuries represented the achievements of Newton and Einstein. Representations of Newton express reverence, almost an apotheosis, portraying him as the creator of the universe. Einstein, in a different age, is represented often as a comic figure, and only rarely do we find art that hints at the profound view of the universe he developed.

Enlarging the bounds of moral philosophy: Why did Isaac Newton conclude the Opticks the way he did?

PubMed Central

Henry, John

2017-01-01

This paper draws attention to the remarkable closing words of Isaac Newton's Optice (1706) and subsequent editions of the Opticks (1718, 1721), and tries to suggest why Newton chose to conclude his book with a puzzling allusion to his own unpublished conclusions about the history of religion. Newton suggests in this concluding passage that the bounds of moral philosophy will be enlarged as natural philosophy is ‘perfected’. Asking what Newton might have had in mind, the paper first considers the idea that he was foreshadowing the ‘moral Newtonianism’ developed later in the eighteenth century; then it considers the idea that he was perhaps pointing to developments in natural theology. Finally, the paper suggests that Newton wanted to at least signal the importance of attempting to recover the true original religion, and perhaps was hinting at his intention to publish his own extensive research on the history of the Church.

3, 2, 1 … Discovering Newton's Laws

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

Large radius of curvature measurement based on the evaluation of interferogram-quality metric in non-null interferometry

NASA Astrophysics Data System (ADS)

Yang, Zhongming; Dou, Jiantai; Du, Jinyu; Gao, Zhishan

2018-03-01

Non-null interferometry could use to measure the radius of curvature (ROC), we have presented a virtual quadratic Newton rings phase-shifting moiré-fringes measurement method for large ROC measurement (Yang et al., 2016). In this paper, we propose a large ROC measurement method based on the evaluation of the interferogram-quality metric by the non-null interferometer. With the multi-configuration model of the non-null interferometric system in ZEMAX, the retrace errors and the phase introduced by the test surface are reconstructed. The interferogram-quality metric is obtained by the normalized phase-shifted testing Newton rings with the spherical surface model in the non-null interferometric system. The radius curvature of the test spherical surface can be obtained until the minimum of the interferogram-quality metric is found. Simulations and experimental results are verified the feasibility of our proposed method. For a spherical mirror with a ROC of 41,400 mm, the measurement accuracy is better than 0.13%.

Multi-Sensor Data Fusion Identification for Shearer Cutting Conditions Based on Parallel Quasi-Newton Neural Networks and the Dempster-Shafer Theory.

PubMed

Si, Lei; Wang, Zhongbin; Liu, Xinhua; Tan, Chao; Xu, Jing; Zheng, Kehong

2015-11-13

In order to efficiently and accurately identify the cutting condition of a shearer, this paper proposed an intelligent multi-sensor data fusion identification method using the parallel quasi-Newton neural network (PQN-NN) and the Dempster-Shafer (DS) theory. The vibration acceleration signals and current signal of six cutting conditions were collected from a self-designed experimental system and some special state features were extracted from the intrinsic mode functions (IMFs) based on the ensemble empirical mode decomposition (EEMD). In the experiment, three classifiers were trained and tested by the selected features of the measured data, and the DS theory was used to combine the identification results of three single classifiers. Furthermore, some comparisons with other methods were carried out. The experimental results indicate that the proposed method performs with higher detection accuracy and credibility than the competing algorithms. Finally, an industrial application example in the fully mechanized coal mining face was demonstrated to specify the effect of the proposed system.

Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting

DOE PAGES

Carlberg, Kevin; Ray, Jaideep; van Bloemen Waanders, Bart

2015-02-14

Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most model-reduction techniques for nonlinear ODEs exploit knowledge of system's spatial behavior to reduce the computational complexity of each linear-system solve. However, the number of linear-system solves for the reduced-order simulation often remains roughly the same as that for the full-order simulation. We propose exploiting knowledge of the model's temporal behavior to (1) forecast the unknown variable of the reduced-order system of nonlinear equationsmore » at future time steps, and (2) use this forecast as an initial guess for the Newton-like solver during the reduced-order-model simulation. To compute the forecast, we propose using the Gappy POD technique. As a result, the goal is to generate an accurate initial guess so that the Newton solver requires many fewer iterations to converge, thereby decreasing the number of linear-system solves in the reduced-order-model simulation.« less

Why Did Newton See Indigo in the Spectrum?

ERIC Educational Resources Information Center

Biernson, George

1972-01-01

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

The Treatment of the Laws of Dynamics in Higher Level Schools.

ERIC Educational Resources Information Center

Kikoin, I. K.

1979-01-01

Describes how Newton's three laws of dynamics are taught in high school in the Soviet Union. Rejects introducing Newton's second law as an equation defining mass as a proportionality constant. Shows how the concept of mass can be introduced independently of Newton's Law. (GA)

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

NASA Technical Reports Server (NTRS)

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

1977-01-01

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

Newton's laws of motion in the form of a Riccati equation.

PubMed

Nowakowski, Marek; Rosu, Haret C

2002-04-01

We discuss two applications of a Riccati equation to Newton's laws of motion. The first one is the motion of a particle under the influence of a power law central potential V(r)=kr(epsilon). For zero total energy we show that the equation of motion can be cast in the Riccati form. We briefly show here an analogy to barotropic Friedmann-Robertson-Lemaitre cosmology where the expansion of the universe can be also shown to obey a Riccati equation. A second application in classical mechanics, where again the Riccati equation appears naturally, are problems involving quadratic friction. We use methods reminiscent to nonrelativistic supersymmetry to generalize and solve such problems.

A nonlinear relaxation/quasi-Newton algorithm for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Edwards, Jack R.; Mcrae, D. S.

1992-01-01

A highly efficient implicit method for the computation of steady, two-dimensional compressible Navier-Stokes flowfields is presented. The discretization of the governing equations is hybrid in nature, with flux-vector splitting utilized in the streamwise direction and central differences with flux-limited artificial dissipation used for the transverse fluxes. Line Jacobi relaxation is used to provide a suitable initial guess for a new nonlinear iteration strategy based on line Gauss-Seidel sweeps. The applicability of quasi-Newton methods as convergence accelerators for this and other line relaxation algorithms is discussed, and efficient implementations of such techniques are presented. Convergence histories and comparisons with experimental data are presented for supersonic flow over a flat plate and for several high-speed compression corner interactions. Results indicate a marked improvement in computational efficiency over more conventional upwind relaxation strategies, particularly for flowfields containing large pockets of streamwise subsonic flow.

A computer-assisted study of pulse dynamics in anisotropic media

NASA Astrophysics Data System (ADS)

Krishnan, J.; Engelborghs, K.; Bär, M.; Lust, K.; Roose, D.; Kevrekidis, I. G.

2001-06-01

This study focuses on the computer-assisted stability analysis of travelling pulse-like structures in spatially periodic heterogeneous reaction-diffusion media. The physical motivation comes from pulse propagation in thin annular domains on a diffusionally anisotropic catalytic surface. The study was performed by computing the travelling pulse-like structures as limit cycles of the spatially discretized PDE, which in turn is performed in two ways: a Newton method based on a pseudospectral discretization of the PDE, and a Newton-Picard method based on a finite difference discretization. Details about the spectra of these modulated pulse-like structures are discussed, including how they may be compared with the spectra of pulses in homogeneous media. The effects of anisotropy on the dynamics of pulses and pulse pairs are studied. Beyond shifting the location of bifurcations present in homogeneous media, anisotropy can also introduce certain new instabilities.

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

NASA Astrophysics Data System (ADS)

Andrea, Caliciotti; Giovanni, Fasano; Massimo, Roma

2016-10-01

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

3-D minimum-structure inversion of magnetotelluric data using the finite-element method and tetrahedral grids

NASA Astrophysics Data System (ADS)

Jahandari, H.; Farquharson, C. G.

2017-11-01

Unstructured grids enable representing arbitrary structures more accurately and with fewer cells compared to regular structured grids. These grids also allow more efficient refinements compared to rectilinear meshes. In this study, tetrahedral grids are used for the inversion of magnetotelluric (MT) data, which allows for the direct inclusion of topography in the model, for constraining an inversion using a wireframe-based geological model and for local refinement at the observation stations. A minimum-structure method with an iterative model-space Gauss-Newton algorithm for optimization is used. An iterative solver is employed for solving the normal system of equations at each Gauss-Newton step and the sensitivity matrix-vector products that are required by this solver are calculated using pseudo-forward problems. This method alleviates the need to explicitly form the Hessian or Jacobian matrices which significantly reduces the required computation memory. Forward problems are formulated using an edge-based finite-element approach and a sparse direct solver is used for the solutions. This solver allows saving and re-using the factorization of matrices for similar pseudo-forward problems within a Gauss-Newton iteration which greatly minimizes the computation time. Two examples are presented to show the capability of the algorithm: the first example uses a benchmark model while the second example represents a realistic geological setting with topography and a sulphide deposit. The data that are inverted are the full-tensor impedance and the magnetic transfer function vector. The inversions sufficiently recovered the models and reproduced the data, which shows the effectiveness of unstructured grids for complex and realistic MT inversion scenarios. The first example is also used to demonstrate the computational efficiency of the presented model-space method by comparison with its data-space counterpart.

Dynamics of magnetic particles in cylindrical Halbach array: implications for magnetic cell separation and drug targeting.

PubMed

Babinec, Peter; Krafcík, Andrej; Babincová, Melánia; Rosenecker, Joseph

2010-08-01

Magnetic nanoparticles for therapy and diagnosis are at the leading edge of the rapidly developing field of bionanotechnology. In this study, we have theoretically studied motion of magnetic nano- as well as micro-particles in the field of cylindrical Halbach array of permanent magnets. Magnetic flux density was modeled as magnetostatic problem by finite element method and particle motion was described using system of ordinary differential equations--Newton law. Computations were done for nanoparticles Nanomag-D with radius 65 nm, which are often used in magnetic drug targeting, as well as microparticles DynaBeads-M280 with radius 1.4 microm, which can be used for magnetic separation. Analyzing snapshots of trajectories of hundred magnetite particles of each size in the water as well as in the air, we have found that optimally designed magnetic circuits of permanent magnets in quadrupolar Halbach array have substantially shorter capture time than simple blocks of permanent magnets commonly used in experiments, therefore, such a Halbach array may be useful as a potential source of magnetic field for magnetic separation and targeting of magnetic nanoparticles as well as microparticles for delivery of drugs, genes, and cells in various biomedical applications.

Edme Mariotte and Newton's Cradle

ERIC Educational Resources Information Center

Cross, Rod

2012-01-01

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

Teaching Newton's Third Law of Motion in the Presence of Student Preconception

ERIC Educational Resources Information Center

Poon, C. H.

2006-01-01

The concept of interaction that underlies Newton's Laws of Motion is compared with the students' commonsense ideas of force and motion. An approach to teaching Newton's Third Law of Motion is suggested that focuses on refining the student's intuitive thinking on the nature of interaction.

Gravitation in Material Media

ERIC Educational Resources Information Center

Ridgely, Charles T.

2011-01-01

When two gravitating bodies reside in a material medium, Newton's law of universal gravitation must be modified to account for the presence of the medium. A modified expression of Newton's law is known in the literature, but lacks a clear connection with existing gravitational theory. Newton's law in the presence of a homogeneous material medium…

76 FR 24489 - Privacy Act of 1974; Amendment to System of Records

Federal Register 2010, 2011, 2012, 2013, 2014

2011-05-02

... message). Fax: 202-482-9237, Attention: Elaine Newton, Privacy Officer. Mail, Hand Delivery/Courier...: Elaine Newton, Privacy Officer. FOR FURTHER INFORMATION CONTACT: Ms. Newton at the Office of Government... 4685 (Jan. 26, 2009); and in support of this Administration's core principles of the business of...

Telecommunications Handbook: Connecting to Newton.

ERIC Educational Resources Information Center

Baker, Christopher; And Others

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

Electric and Plug-In Hybrid Electric Vehicle Publications | Transportation

Science.gov Websites

, Kandler Smith, and Kevin Walkowicz. (2016) Medium-Duty Plug-in Electric Delivery Truck Fleet Evaluation . (2014) Smith Newton Electric Delivery Trucks Smith Newton Vehicle Performance Evaluation (Gen 1 ), Cumulative Report: November 2011-June 2014. Adam Ragatz. (2014) Smith Newton Vehicle Performance Evaluation

Neural Generalized Predictive Control: A Newton-Raphson Implementation

NASA Technical Reports Server (NTRS)

Soloway, Donald; Haley, Pamela J.

1997-01-01

An efficient implementation of Generalized Predictive Control using a multi-layer feedforward neural network as the plant's nonlinear model is presented. In using Newton-Raphson as the optimization algorithm, the number of iterations needed for convergence is significantly reduced from other techniques. The main cost of the Newton-Raphson algorithm is in the calculation of the Hessian, but even with this overhead the low iteration numbers make Newton-Raphson faster than other techniques and a viable algorithm for real-time control. This paper presents a detailed derivation of the Neural Generalized Predictive Control algorithm with Newton-Raphson as the minimization algorithm. Simulation results show convergence to a good solution within two iterations and timing data show that real-time control is possible. Comments about the algorithm's implementation are also included.

Development of A Thrust Stand to Meet LISA Mission Requirements

NASA Technical Reports Server (NTRS)

Willis, William D., III; Zakrzwski, C. M.; Bauer, Frank H. (Technical Monitor)

2002-01-01

A thrust stand has been built and tested that is capable of measuring the force-noise produced by electrostatic micro-Newton (micro-Newton) thrusters. The LISA mission's Disturbance Reduction System (DRS) requires thrusters that are capable of producing continuous thrust levels between 1-100 micro-Newton with a resolution of 0.1 micro-Newton. The stationary force-noise produced by these thrusters must not exceed 0.1 pN/4Hz in a 10 Hz bandwidth. The LISA Thrust Stand (LTS) is a torsion-balance type thrust stand designed to meet the following requirements: stationary force-noise measurements from 10(exp-4) to 1 Hz with 0.1 micro-Newton resolution, absolute thrust measurements from 1-100 micro-Newton with better than 0.1 micro-Newton resolution, and dynamic thruster response from 10(exp -4) to 10 Hz. The ITS employs a unique vertical configuration, autocollimator for angular position measurements, and electrostatic actuators that are used for dynamic pendulum control and null-mode measurements. Force-noise levels are measured indirectly by characterizing the thrust stand as a spring-mass system. The LTS was initially designed to test the indium FEEP thruster developed by the Austrian Research Center in Seibersdorf (ARCS), but can be modified for testing other thrusters of this type.

New Method of Calibrating IRT Models.

ERIC Educational Resources Information Center

Jiang, Hai; Tang, K. Linda

This discussion of new methods for calibrating item response theory (IRT) models looks into new optimization procedures, such as the Genetic Algorithm (GA) to improve on the use of the Newton-Raphson procedure. The advantages of using a global optimization procedure like GA is that this kind of procedure is not easily affected by local optima and…

Probing the nature of AX J0043-737: Not an 87 ms pulsar in the Small Magellanic Cloud

NASA Astrophysics Data System (ADS)

Maitra, C.; Ballet, J.; Esposito, P.; Haberl, F.; Tiengo, A.; Filipović, M. D.; Acero, F.

2018-05-01

Aims: AX J0043-737 is a source in the ASCA catalogue whose nature is uncertain. It is most commonly classified as a Crab-like pulsar in the Small Magellanic Cloud (SMC) following apparent detection of pulsations at 87 ms from a single ASCA observation. A follow-up ASCA observation was not able to confirm this, and the X-ray detection of the source has not been reported since. Methods: We studied the nature of the source with a dedicated XMM-Newton observation. We ascertained the source position, searched for the most probable counterpart, and studied the X-ray spectrum. We also analysed other archival observations with the source in the field of view to study its long-term variability. Results: With the good position localisation capability of XMM-Newton, we identify the counterpart of the source as MQS J004241.66-734041.3, an active galactic nucleus (AGN) behind the SMC at a redshift of 0.95. The X-ray spectrum can be fitted with an absorbed power law with a photon-index of Γ = 1.7, which is consistent with that expected from AGNs. By comparing the current XMM-Newton observation with an archival XMM-Newton and two other ASCA observations of the source, we find signatures of long-term variability, another common phenomenon in AGNs. All of the above are consistent with AX J0043-737 being an AGN behind the SMC.

A Numerical Comparison of Barrier and Modified Barrier Methods for Large-Scale Bound-Constrained Optimization

NASA Technical Reports Server (NTRS)

Nash, Stephen G.; Polyak, R.; Sofer, Ariela

1994-01-01

When a classical barrier method is applied to the solution of a nonlinear programming problem with inequality constraints, the Hessian matrix of the barrier function becomes increasingly ill-conditioned as the solution is approached. As a result, it may be desirable to consider alternative numerical algorithms. We compare the performance of two methods motivated by barrier functions. The first is a stabilized form of the classical barrier method, where a numerically stable approximation to the Newton direction is used when the barrier parameter is small. The second is a modified barrier method where a barrier function is applied to a shifted form of the problem, and the resulting barrier terms are scaled by estimates of the optimal Lagrange multipliers. The condition number of the Hessian matrix of the resulting modified barrier function remains bounded as the solution to the constrained optimization problem is approached. Both of these techniques can be used in the context of a truncated-Newton method, and hence can be applied to large problems, as well as on parallel computers. In this paper, both techniques are applied to problems with bound constraints and we compare their practical behavior.

Fully-Implicit Orthogonal Reconstructed Discontinuous Galerkin for Fluid Dynamics with Phase Change

DOE PAGES

Nourgaliev, R.; Luo, H.; Weston, B.; ...

2015-11-11

A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method’s capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing (AM). We focus on the method’s accuracy (in both space and time), as wellmore » as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver.« less

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

PubMed Central

Asgharzadeh, Hafez; Borazjani, Iman

2016-01-01

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 nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42 – 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80–90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future. PMID:28042172

Measurement-based perturbation theory and differential equation parameter estimation with applications to satellite gravimetry

NASA Astrophysics Data System (ADS)

Xu, Peiliang

2018-06-01

The numerical integration method has been routinely used by major institutions worldwide, for example, NASA Goddard Space Flight Center and German Research Center for Geosciences (GFZ), to produce global gravitational models from satellite tracking measurements of CHAMP and/or GRACE types. Such Earth's gravitational products have found widest possible multidisciplinary applications in Earth Sciences. The method is essentially implemented by solving the differential equations of the partial derivatives of the orbit of a satellite with respect to the unknown harmonic coefficients under the conditions of zero initial values. From the mathematical and statistical point of view, satellite gravimetry from satellite tracking is essentially the problem of estimating unknown parameters in the Newton's nonlinear differential equations from satellite tracking measurements. We prove that zero initial values for the partial derivatives are incorrect mathematically and not permitted physically. The numerical integration method, as currently implemented and used in mathematics and statistics, chemistry and physics, and satellite gravimetry, is groundless, mathematically and physically. Given the Newton's nonlinear governing differential equations of satellite motion with unknown equation parameters and unknown initial conditions, we develop three methods to derive new local solutions around a nominal reference orbit, which are linked to measurements to estimate the unknown corrections to approximate values of the unknown parameters and the unknown initial conditions. Bearing in mind that satellite orbits can now be tracked almost continuously at unprecedented accuracy, we propose the measurement-based perturbation theory and derive global uniformly convergent solutions to the Newton's nonlinear governing differential equations of satellite motion for the next generation of global gravitational models. Since the solutions are global uniformly convergent, theoretically speaking, they are able to extract smallest possible gravitational signals from modern and future satellite tracking measurements, leading to the production of global high-precision, high-resolution gravitational models. By directly turning the nonlinear differential equations of satellite motion into the nonlinear integral equations, and recognizing the fact that satellite orbits are measured with random errors, we further reformulate the links between satellite tracking measurements and the global uniformly convergent solutions to the Newton's governing differential equations as a condition adjustment model with unknown parameters, or equivalently, the weighted least squares estimation of unknown differential equation parameters with equality constraints, for the reconstruction of global high-precision, high-resolution gravitational models from modern (and future) satellite tracking measurements.

Making More Plausible What is Hard To Believe: Historical Justifications and Illustrations of Newton's Third Law.

ERIC Educational Resources Information Center

Gauld, Colin

1998-01-01

Reports that many students do not believe Newton's law of action and reaction and suggests ways in which its plausibility might be enhanced. Reviews how this law has been made more plausible over time by Newton and those who succeeded him. Contains 25 references. (DDR)

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

ERIC Educational Resources Information Center

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…

Can Newton's Third Law Be "Derived" from the Second?

ERIC Educational Resources Information Center

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…

27 CFR 9.152 - Malibu-Newton Canyon.

Code of Federal Regulations, 2010 CFR

2010-04-01

....” (2) Then south along Kanan Dume Road to the point where an unnamed, unimproved dirt road referred to... Canyon Road to an unnamed, unimproved dirt road referred to by the petitioner as Newton Mountain Way at... southeastern ridgeline of Newton Canyon, to an unnamed, unimproved dirt road referred to by the petitioner as...

Newton's Cradle in Physics Education

ERIC Educational Resources Information Center

Gauld, Colin F.

2006-01-01

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

Higher symmetries of the Schrödinger operator in Newton-Cartan geometry

NASA Astrophysics Data System (ADS)

Gundry, James

2017-03-01

We establish several relationships between the non-relativistic conformal symmetries of Newton-Cartan geometry and the Schrödinger equation. In particular we discuss the algebra sch(d) of vector fields conformally-preserving a flat Newton-Cartan spacetime, and we prove that its curved generalisation generates the symmetry group of the covariant Schrödinger equation coupled to a Newtonian potential and generalised Coriolis force. We provide intrinsic Newton-Cartan definitions of Killing tensors and conformal Schrödinger-Killing tensors, and we discuss their respective links to conserved quantities and to the higher symmetries of the Schrödinger equation. Finally we consider the role of conformal symmetries in Newtonian twistor theory, where the infinite-dimensional algebra of holomorphic vector fields on twistor space corresponds to the symmetry algebra cnc(3) on the Newton-Cartan spacetime.

Isaac Newton learns Hebrew: Samuel Johnson's Nova cubi Hebræi tabella

PubMed Central

Joalland, Michael; Mandelbrote, Scott

2016-01-01

This article concerns the earliest evidence for Isaac Newton's use of Hebrew: a manuscript copy by Newton of part of a work intended to provide a reader of the Hebrew alphabet with the ability to identify or memorize more than 1000 words and to begin to master the conjugations of the Hebrew verb. In describing the content of this unpublished manuscript and establishing its source and original author for the first time, we suggest how and when Newton may have initially become acquainted with the language. Finally, basing our discussion in part on an examination of the reading marks that Newton left in the surviving copies of Hebrew grammars and lexicons that he owned, we will argue that his interest in Hebrew was not intended to achieve linguistic proficiency but remained limited to particular theological queries of singular concern.

An efficient method for solving the steady Euler equations

NASA Technical Reports Server (NTRS)

Liou, M. S.

1986-01-01

An efficient numerical procedure for solving a set of nonlinear partial differential equations is given, specifically for the steady Euler equations. Solutions of the equations were obtained by Newton's linearization procedure, commonly used to solve the roots of nonlinear algebraic equations. In application of the same procedure for solving a set of differential equations we give a theorem showing that a quadratic convergence rate can be achieved. While the domain of quadratic convergence depends on the problems studied and is unknown a priori, we show that firstand second-order derivatives of flux vectors determine whether the condition for quadratic convergence is satisfied. The first derivatives enter as an implicit operator for yielding new iterates and the second derivatives indicates smoothness of the flows considered. Consequently flows involving shocks are expected to require larger number of iterations. First-order upwind discretization in conjunction with the Steger-Warming flux-vector splitting is employed on the implicit operator and a diagonal dominant matrix results. However the explicit operator is represented by first- and seond-order upwind differencings, using both Steger-Warming's and van Leer's splittings. We discuss treatment of boundary conditions and solution procedures for solving the resulting block matrix system. With a set of test problems for one- and two-dimensional flows, we show detailed study as to the efficiency, accuracy, and convergence of the present method.

Conformal and projective symmetries in Newtonian cosmology

NASA Astrophysics Data System (ADS)

Duval, C.; Gibbons, G. W.; Horváthy, P. A.

2017-02-01

Definitions of non-relativistic conformal transformations are considered both in the Newton-Cartan and in the Kaluza-Klein-type Eisenhart/Bargmann geometrical frameworks. The symmetry groups that come into play are exemplified by the cosmological, and also the Newton-Hooke solutions of Newton's gravitational field equations. It is shown, in particular, that the maximal symmetry group of the standard cosmological model is isomorphic to the 13-dimensional conformal-Newton-Cartan group whose conformal-Bargmann extension is explicitly worked out. Attention is drawn to the appearance of independent space and time dilations, in contrast with the Schrödinger group or the Conformal Galilei Algebra.

Quasi-periodic Pulse Amplitude Modulation in the Accreting Millisecond Pulsar IGR J00291+5934

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bult, Peter; Doesburgh, Marieke van; Klis, Michiel van der

We introduce a new method for analyzing the aperiodic variability of coherent pulsations in accreting millisecond X-ray pulsars (AMXPs). Our method involves applying a complex frequency correction to the time-domain light curve, allowing for the aperiodic modulation of the pulse amplitude to be robustly extracted in the frequency domain. We discuss the statistical properties of the resulting modulation spectrum and show how it can be correlated with the non-pulsed emission to determine if the periodic and aperiodic variability are coupled processes. Using this method, we study the 598.88 Hz coherent pulsations of the AMXP IGR J00291+5934 as observed with themore » Rossi X-ray Timing Explorer and XMM-Newton . We demonstrate that our method easily confirms the known coupling between the pulsations and a strong 8 mHz quasi-periodic oscillation (QPO) in XMM-Newton observations. Applying our method to the RXTE observations, we further show, for the first time, that the much weaker 20 mHz QPO and its harmonic are also coupled with the pulsations. We discuss the implications of this coupling and indicate how it may be used to extract new information on the underlying accretion process.« less

Quasi-Periodic Pulse Amplitude Modulation in the Accreting Millisecond Pulsar IGR J00291+5934

NASA Technical Reports Server (NTRS)

Bult, Peter; van Doesburgh, Marieke; van der Klis, Michiel

2017-01-01

We introduce a new method for analyzing the a periodic variability of coherent pulsations in accreting millisecond X-ray pulsars (AMXPs). Our method involves applying a complex frequency correction to the time-domain lightcurve, allowing for the aperiodic modulation of the pulse amplitude to be robustly extracted in the frequency domain. We discuss the statistical properties of the resulting modulation spectrum and show how it can be correlated with the non-pulsed emission to determine if the periodic and a periodic variability are coupled processes. Using this method, we study the 598.88 Hz coherent pulsations of the AMXP IGR J00291+5934 as observed with the Rossi X-ray Timing Explorer and XMM-Newton. We demonstrate that our method easily confirms the known coupling between the pulsations and a strong 8 mHz quasi-periodic oscillation (QPO) in XMM-Newton observations. Applying our method to the RXTE observations, we further show, for the first time, that the much weaker 20 mHz QPO and its harmonic are also coupled with the pulsations. We discuss the implications of this coupling and indicate how it may be used to extract new information on the underlying accretion process.

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

ERIC Educational Resources Information Center

Boulos, Pierre J.

2006-01-01

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

On the Shoulders of Sir Isaac Newton and Arthur Storer

ERIC Educational Resources Information Center

Martin, Helen E.; Evans-Gondo, Bonita

2013-01-01

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

Science and Society: The Case of Acceptance of Newtonian Optics in the Eighteenth Century

ERIC Educational Resources Information Center

Silva, Cibelle Celestino; Moura, Breno Arsioli

2012-01-01

The present paper presents a historical study on the acceptance of Newton's corpuscular theory of light in the early eighteenth century. Isaac Newton first published his famous book "Opticks" in 1704. After its publication, it became quite popular and was an almost mandatory presence in cultural life of Enlightenment societies. However, Newton's…

Jan Hudde and the Quotient Rule before Newton and Leibniz

ERIC Educational Resources Information Center

Curtin, Daniel J.

2005-01-01

This article describes some of the work of Jan Hudde who anticipated some results of calculus. Prior to a career as a Burgomaster of Amsterdam, Hudde engaged in mathematics. His method of finding maxima and minima is especially interesting.

A NUMERICAL ALGORITHM FOR MODELING MULTIGROUP NEUTRINO-RADIATION HYDRODYNAMICS IN TWO SPATIAL DIMENSIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Swesty, F. Douglas; Myra, Eric S.

It is now generally agreed that multidimensional, multigroup, neutrino-radiation hydrodynamics (RHD) is an indispensable element of any realistic model of stellar-core collapse, core-collapse supernovae, and proto-neutron star instabilities. We have developed a new, two-dimensional, multigroup algorithm that can model neutrino-RHD flows in core-collapse supernovae. Our algorithm uses an approach similar to the ZEUS family of algorithms, originally developed by Stone and Norman. However, this completely new implementation extends that previous work in three significant ways: first, we incorporate multispecies, multigroup RHD in a flux-limited-diffusion approximation. Our approach is capable of modeling pair-coupled neutrino-RHD, and includes effects of Pauli blocking inmore » the collision integrals. Blocking gives rise to nonlinearities in the discretized radiation-transport equations, which we evolve implicitly in time. We employ parallelized Newton-Krylov methods to obtain a solution of these nonlinear, implicit equations. Our second major extension to the ZEUS algorithm is the inclusion of an electron conservation equation that describes the evolution of electron-number density in the hydrodynamic flow. This permits calculating deleptonization of a stellar core. Our third extension modifies the hydrodynamics algorithm to accommodate realistic, complex equations of state, including those having nonconvex behavior. In this paper, we present a description of our complete algorithm, giving sufficient details to allow others to implement, reproduce, and extend our work. Finite-differencing details are presented in appendices. We also discuss implementation of this algorithm on state-of-the-art, parallel-computing architectures. Finally, we present results of verification tests that demonstrate the numerical accuracy of this algorithm on diverse hydrodynamic, gravitational, radiation-transport, and RHD sample problems. We believe our methods to be of general use in a variety of model settings where radiation transport or RHD is important. Extension of this work to three spatial dimensions is straightforward.« less

Time domain contact model for tyre/road interaction including nonlinear contact stiffness due to small-scale roughness

NASA Astrophysics Data System (ADS)

Andersson, P. B. U.; Kropp, W.

2008-11-01

Rolling resistance, traction, wear, excitation of vibrations, and noise generation are all attributes to consider in optimisation of the interaction between automotive tyres and wearing courses of roads. The key to understand and describe the interaction is to include a wide range of length scales in the description of the contact geometry. This means including scales on the order of micrometres that have been neglected in previous tyre/road interaction models. A time domain contact model for the tyre/road interaction that includes interfacial details is presented. The contact geometry is discretised into multiple elements forming pairs of matching points. The dynamic response of the tyre is calculated by convolving the contact forces with pre-calculated Green's functions. The smaller-length scales are included by using constitutive interfacial relations, i.e. by using nonlinear contact springs, for each pair of contact elements. The method is presented for normal (out-of-plane) contact and a method for assessing the stiffness of the nonlinear springs based on detailed geometry and elastic data of the tread is suggested. The governing equations of the nonlinear contact problem are solved with the Newton-Raphson iterative scheme. Relations between force, indentation, and contact stiffness are calculated for a single tread block in contact with a road surface. The calculated results have the same character as results from measurements found in literature. Comparison to traditional contact formulations shows that the effect of the small-scale roughness is large; the contact stiffness is only up to half of the stiffness that would result if contact is made over the whole element directly to the bulk of the tread. It is concluded that the suggested contact formulation is a suitable model to include more details of the contact interface. Further, the presented result for the tread block in contact with the road is a suitable input for a global tyre/road interaction model that is also based on the presented contact formulation.

On the Latent Regression Model of Item Response Theory. Research Report. ETS RR-07-12

ERIC Educational Resources Information Center

Antal, Tamás

2007-01-01

Full account of the latent regression model for the National Assessment of Educational Progress is given. The treatment includes derivation of the EM algorithm, Newton-Raphson method, and the asymptotic standard errors. The paper also features the use of the adaptive Gauss-Hermite numerical integration method as a basic tool to evaluate…

Anderson acceleration and application to the three-temperature energy equations

NASA Astrophysics Data System (ADS)

An, Hengbin; Jia, Xiaowei; Walker, Homer F.

2017-10-01

The Anderson acceleration method is an algorithm for accelerating the convergence of fixed-point iterations, including the Picard method. Anderson acceleration was first proposed in 1965 and, for some years, has been used successfully to accelerate the convergence of self-consistent field iterations in electronic-structure computations. Recently, the method has attracted growing attention in other application areas and among numerical analysts. Compared with a Newton-like method, an advantage of Anderson acceleration is that there is no need to form the Jacobian matrix. Thus the method is easy to implement. In this paper, an Anderson-accelerated Picard method is employed to solve the three-temperature energy equations, which are a type of strong nonlinear radiation-diffusion equations. Two strategies are used to improve the robustness of the Anderson acceleration method. One strategy is to adjust the iterates when necessary to satisfy the physical constraint. Another strategy is to monitor and, if necessary, reduce the matrix condition number of the least-squares problem in the Anderson-acceleration implementation so that numerical stability can be guaranteed. Numerical results show that the Anderson-accelerated Picard method can solve the three-temperature energy equations efficiently. Compared with the Picard method without acceleration, Anderson acceleration can reduce the number of iterations by at least half. A comparison between a Jacobian-free Newton-Krylov method, the Picard method, and the Anderson-accelerated Picard method is conducted in this paper.

Terrain Correction on the moving equal area cylindrical map projection of the surface of a reference ellipsoid

NASA Astrophysics Data System (ADS)

Ardalan, A.; Safari, A.; Grafarend, E.

2003-04-01

An operational algorithm for computing the ellipsoidal terrain correction based on application of closed form solution of the Newton integral in terms of Cartesian coordinates in the cylindrical equal area map projected surface of a reference ellipsoid has been developed. As the first step the mapping of the points on the surface of a reference ellipsoid onto the cylindrical equal area map projection of a cylinder tangent to a point on the surface of reference ellipsoid closely studied and the map projection formulas are computed. Ellipsoidal mass elements with various sizes on the surface of the reference ellipsoid is considered and the gravitational potential and the vector of gravitational intensity of these mass elements has been computed via the solution of Newton integral in terms of ellipsoidal coordinates. The geographical cross section areas of the selected ellipsoidal mass elements are transferred into cylindrical equal area map projection and based on the transformed area elements Cartesian mass elements with the same height as that of the ellipsoidal mass elements are constructed. Using the close form solution of the Newton integral in terms of Cartesian coordinates the potential of the Cartesian mass elements are computed and compared with the same results based on the application of the ellipsoidal Newton integral over the ellipsoidal mass elements. The results of the numerical computations show that difference between computed gravitational potential of the ellipsoidal mass elements and Cartesian mass element in the cylindrical equal area map projection is of the order of 1.6 × 10-8m^2/s^2 for a mass element with the cross section size of 10 km × 10 km and the height of 1000 m. For a 1 km × 1 km mass element with the same height, this difference is less than 1.5 × 10-4 m^2}/s^2. The results of the numerical computations indicate that a new method for computing the terrain correction based on the closed form solution of the Newton integral in terms of Cartesian coordinates and with accuracy of ellipsoidal terrain correction has been achieved! In this way one can enjoy the simplicity of the solution of the Newton integral in terms of Cartesian coordinates and at the same time the accuracy of the ellipsoidal terrain correction, which is needed for the modern theory of geoid computations.

UNBIASED CORRECTION RELATIONS FOR GALAXY CLUSTER PROPERTIES DERIVED FROM CHANDRA AND XMM-NEWTON

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhao, Hai-Hui; Li, Cheng-Kui; Chen, Yong

2015-01-20

We use a sample of 62 clusters of galaxies to investigate the discrepancies between the gas temperature and total mass within r {sub 500} from XMM-Newton and Chandra data. Comparisons of the properties show that (1) both the de-projected and projected temperatures determined by Chandra are higher than those of XMM-Newton and there is a good linear relationship for the de-projected temperatures: T {sub Chandra} = 1.25 × T {sub XMM}–0.13. (2) The Chandra mass is much higher than the XMM-Newton mass with a bias of 0.15 and our mass relation is log{sub 10} M {sub Chandra} = 1.02 × log{sub 10}more » M {sub XMM}+0.15. To explore the reasons for the discrepancy in mass, we recalculate the Chandra mass (expressed as M{sub Ch}{sup mo/d}) by modifying its temperature with the de-projected temperature relation. The results show that M{sub Ch}{sup mo/d} is closer to the XMM-Newton mass with the bias reducing to 0.02. Moreover, M{sub Ch}{sup mo/d} are corrected with the r {sub 500} measured by XMM-Newton and the intrinsic scatter is significantly improved with the value reducing from 0.20 to 0.12. These mean that the temperature bias may be the main factor causing the mass bias. Finally, we find that M{sub Ch}{sup mo/d} is consistent with the corresponding XMM-Newton mass derived directly from our mass relation at a given Chandra mass. Thus, the de-projected temperature and mass relations can provide unbiased corrections for galaxy cluster properties derived from Chandra and XMM-Newton.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Goodwin, D. L.; Kuprov, Ilya, E-mail: i.kuprov@soton.ac.uk

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 (matrixmore » 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.« less

A Strassen-Newton algorithm for high-speed parallelizable matrix inversion

NASA Technical Reports Server (NTRS)

Bailey, David H.; Ferguson, Helaman R. P.

1988-01-01

Techniques are described for computing matrix inverses by algorithms that are highly suited to massively parallel computation. The techniques are based on an algorithm suggested by Strassen (1969). Variations of this scheme use matrix Newton iterations and other methods to improve the numerical stability while at the same time preserving a very high level of parallelism. One-processor Cray-2 implementations of these schemes range from one that is up to 55 percent faster than a conventional library routine to one that is slower than a library routine but achieves excellent numerical stability. The problem of computing the solution to a single set of linear equations is discussed, and it is shown that this problem can also be solved efficiently using these techniques.

Newton shows the light: a commentary on Newton (1672) 'A letter … containing his new theory about light and colours…'.

PubMed

Fara, Patricia

2015-04-13

Isaac Newton's reputation was initially established by his 1672 paper on the refraction of light through a prism; this is now seen as a ground-breaking account and the foundation of modern optics. In it, he claimed to refute Cartesian ideas of light modification by definitively demonstrating that the refrangibility of a ray is linked to its colour, hence arguing that colour is an intrinsic property of light and does not arise from passing through a medium. Newton's later significance as a world-famous scientific genius and the apparent confirmation of his experimental results have tended to obscure the realities of his reception at the time. This paper explores the rhetorical strategies Newton deployed to convince his audience that his conclusions were certain and unchallengeable. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

Blazing the trail to a service-driven culture.

PubMed

Pollison, Ruth

2002-01-01

Newton Memorial Hospital, Newton, New Jersey, decided it was time to aim for excellence when Press-Ganey ranked it in the 13th percentile for customer satisfaction. Newton management recommitted to the hospital's vision to be the premier, community-based health-care provider, not just in its area but in the nation. Its Press-Ganey score then skyrocketed to the 82nd percentile. In this article, the author explains how Newton changed its culture for the better by taking eight actions: committing to service, committing to leadership training, committing to employees, measuring only important things, aligning behaviors to the organization, building individual accountability, communicating, and rewarding and recognizing employees. To start the change, Newton chose a new strategic direction that put the hospital's mission into practical terms for management and staff. The hospital also would strive to decrease patient length of stay, to decrease cost per Case Mix Index adjusted, and to increase volume.

Fully-Implicit Reconstructed Discontinuous Galerkin Method for Stiff Multiphysics Problems

NASA Astrophysics Data System (ADS)

Nourgaliev, Robert

2015-11-01

A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method's capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing. We focus on the method's accuracy (in both space and time), as well as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, and funded by the LDRD at LLNL under project tracking code 13-SI-002.

Conservation properties of numerical integration methods for systems of ordinary differential equations

NASA Technical Reports Server (NTRS)

Rosenbaum, J. S.

1976-01-01

If a system of ordinary differential equations represents a property conserving system that can be expressed linearly (e.g., conservation of mass), it is then desirable that the numerical integration method used conserve the same quantity. It is shown that both linear multistep methods and Runge-Kutta methods are 'conservative' and that Newton-type methods used to solve the implicit equations preserve the inherent conservation of the numerical method. It is further shown that a method used by several authors is not conservative.

Newton's Investigation of the Resistance to Moving Bodies in Continuous Fluids and the Nature of "Frontier Science"

ERIC Educational Resources Information Center

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…

Solutions To the Problem of Impact in the 17th and 18th Centuries and Teaching Newton's Third Law Today.

ERIC Educational Resources Information Center

Gauld, Colin

1998-01-01

Compares the ideas of young people about Newton's third law, focusing on youth of today and youth of the 17th and 18th centuries. Examines the use of Newton's third law in understanding impact phenomena in the 17th and 18th centuries. Contains 46 references. (DDR)

Newton's Apple Teachers Guides. Seasons 9-10-11-12: A Collection of Lessons and Activities.

ERIC Educational Resources Information Center

Twin Cities Public Television, St. Paul, MN.

Newton's Apple is a PBS family science program that explores basic science through high-energy, hands-on demonstrations. This volume is a collection of the teacher's guides from four seasons of Newton's Apple which were originally broadcast from 1991 through 1994. Each of the four seasons in the volume contains 26 lessons and a combination of…

Weight, the Normal Force and Newton's Third Law: Dislodging a Deeply Embedded Misconception

ERIC Educational Resources Information Center

Low, David; Wilson, Kate

2017-01-01

On entry to university, high-achieving physics students from all across Australia struggle to identify Newton's third law force pairs. In particular, less than one in ten can correctly identify the Newton's third law reaction pair to the weight of (gravitational force acting on) an object. Most students incorrectly identify the normal force on the…

A systematic analysis of the XMM-Newton background: I. Dataset and extraction procedures

NASA Astrophysics Data System (ADS)

Marelli, Martino; Salvetti, David; Gastaldello, Fabio; Ghizzardi, Simona; Molendi, Silvano; Luca, Andrea De; Moretti, Alberto; Rossetti, Mariachiara; Tiengo, Andrea

2017-12-01

XMM-Newton is the direct precursor of the future ESA ATHENA mission. A study of its particle-induced background provides therefore significant insight for the ATHENA mission design. We make use of ˜12 years of data, products from the third XMM-Newton catalog as well as FP7 EXTraS project to avoid celestial sources contamination and to disentangle the different components of the XMM-Newton particle-induced background. Within the ESA R&D AREMBES collaboration, we built new analysis pipelines to study the different components of this background: this covers time behavior as well as spectral and spatial characteristics.

Supporting the learning of Newton's laws with graphical data

NASA Astrophysics Data System (ADS)

Piggott, David

Teaching physics provides the opportunity for a very unique interaction between students and instructor that is not found in chemistry or biology. Physics has a heavy emphasis on trying to alter students' misconceptions about how things work in the real word. In chemistry and microbiology this is not an issue because the topics of discussion in those classes are a new experience for the students. In the case of physics the students have everyday experience with the different concepts discussed. This causes the students to build incorrect mental models explaining how different things work. In order to correct these mental models physics teachers must first get the students to vocalize these misconceptions. Then the teacher must confront the students with an example that exposes the false nature of their model. Finally, the teacher must help the student resolve these discrepancies and form the correct model. This study attempts to resolve these discrepancies by giving the students concrete evidence via graphs of Newton's laws. The results reported here indicate that this method of eliciting the misconception, confronting the misconception, and resolving the misconception is successful with Newton's third law, but only marginally successful for first and second laws.

Teaching Newton's Laws with the iPod Touch in Conceptual Physics

NASA Astrophysics Data System (ADS)

Kelly, Angela M.

2011-04-01

One of the greatest challenges in teaching physics is helping students achieve a conceptual understanding of Newton's laws. I find that students fresh from middle school can sometimes recite the laws verbatim ("An object in motion stays in motion…" and "For every action…"), but they rarely demonstrate a working knowledge of how to apply them to observable phenomena. As a firm believer in inquiry-based teaching methods, I like to develop activities where students can experiment and construct understandings based on relevant personal experiences. Consequently, I am always looking for exciting new technologies that can readily demonstrate how physics affects everyday things. In a conceptual physics class designed for ninth-graders, I created a structured activity where students applied Newton's laws to a series of free applications downloaded on iPod Touches. The laws had been introduced during the prior class session with textual descriptions and graphical representations. The course is offered as part of the Enlace Latino Collegiate Society, a weekend enrichment program for middle and high school students in the Bronx. The majority of students had limited or no prior exposure to physics concepts, and many attended high schools where physics was not offered at all.

Iterative Methods for Solving Nonlinear Parabolic Problem in Pension Saving Management

NASA Astrophysics Data System (ADS)

Koleva, M. N.

2011-11-01

In this work we consider a nonlinear parabolic equation, obtained from Riccati like transformation of the Hamilton-Jacobi-Bellman equation, arising in pension saving management. We discuss two numerical iterative methods for solving the model problem—fully implicit Picard method and mixed Picard-Newton method, which preserves the parabolic characteristics of the differential problem. Numerical experiments for comparison the accuracy and effectiveness of the algorithms are discussed. Finally, observations are given.

On the method of least squares. II. [for calculation of covariance matrices and optimization algorithms

NASA Technical Reports Server (NTRS)

Jefferys, W. H.

1981-01-01

A least squares method proposed previously for solving a general class of problems is expanded in two ways. First, covariance matrices related to the solution are calculated and their interpretation is given. Second, improved methods of solving the normal equations related to those of Marquardt (1963) and Fletcher and Powell (1963) are developed for this approach. These methods may converge in cases where Newton's method diverges or converges slowly.

Multi-Sensor Data Fusion Identification for Shearer Cutting Conditions Based on Parallel Quasi-Newton Neural Networks and the Dempster-Shafer Theory

PubMed Central

Si, Lei; Wang, Zhongbin; Liu, Xinhua; Tan, Chao; Xu, Jing; Zheng, Kehong

2015-01-01

In order to efficiently and accurately identify the cutting condition of a shearer, this paper proposed an intelligent multi-sensor data fusion identification method using the parallel quasi-Newton neural network (PQN-NN) and the Dempster-Shafer (DS) theory. The vibration acceleration signals and current signal of six cutting conditions were collected from a self-designed experimental system and some special state features were extracted from the intrinsic mode functions (IMFs) based on the ensemble empirical mode decomposition (EEMD). In the experiment, three classifiers were trained and tested by the selected features of the measured data, and the DS theory was used to combine the identification results of three single classifiers. Furthermore, some comparisons with other methods were carried out. The experimental results indicate that the proposed method performs with higher detection accuracy and credibility than the competing algorithms. Finally, an industrial application example in the fully mechanized coal mining face was demonstrated to specify the effect of the proposed system. PMID:26580620

Solving regularly and singularly perturbed reaction-diffusion equations in three space dimensions

NASA Astrophysics Data System (ADS)

Moore, Peter K.

2007-06-01

In [P.K. Moore, Effects of basis selection and h-refinement on error estimator reliability and solution efficiency for higher-order methods in three space dimensions, Int. J. Numer. Anal. Mod. 3 (2006) 21-51] a fixed, high-order h-refinement finite element algorithm, Href, was introduced for solving reaction-diffusion equations in three space dimensions. In this paper Href is coupled with continuation creating an automatic method for solving regularly and singularly perturbed reaction-diffusion equations. The simple quasilinear Newton solver of Moore, (2006) is replaced by the nonlinear solver NITSOL [M. Pernice, H.F. Walker, NITSOL: a Newton iterative solver for nonlinear systems, SIAM J. Sci. Comput. 19 (1998) 302-318]. Good initial guesses for the nonlinear solver are obtained using continuation in the small parameter ɛ. Two strategies allow adaptive selection of ɛ. The first depends on the rate of convergence of the nonlinear solver and the second implements backtracking in ɛ. Finally a simple method is used to select the initial ɛ. Several examples illustrate the effectiveness of the algorithm.

Algorithms for the computation of solutions of the Ornstein-Zernike equation.

PubMed

Peplow, A T; Beardmore, R E; Bresme, F

2006-10-01

We introduce a robust and efficient methodology to solve the Ornstein-Zernike integral equation using the pseudoarc length (PAL) continuation method that reformulates the integral equation in an equivalent but nonstandard form. This enables the computation of solutions in regions where the compressibility experiences large changes or where the existence of multiple solutions and so-called branch points prevents Newton's method from converging. We illustrate the use of the algorithm with a difficult problem that arises in the numerical solution of integral equations, namely the evaluation of the so-called no-solution line of the Ornstein-Zernike hypernetted chain (HNC) integral equation for the Lennard-Jones potential. We are able to use the PAL algorithm to solve the integral equation along this line and to connect physical and nonphysical solution branches (both isotherms and isochores) where appropriate. We also show that PAL continuation can compute solutions within the no-solution region that cannot be computed when Newton and Picard methods are applied directly to the integral equation. While many solutions that we find are new, some correspond to states with negative compressibility and consequently are not physical.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Paul T.; Shadid, John N.; Tsuji, Paul H.

Here, this study explores the performance and scaling of a GMRES Krylov method employed as a smoother for an algebraic multigrid (AMG) preconditioned Newton- Krylov solution approach applied to a fully-implicit variational multiscale (VMS) nite element (FE) resistive magnetohydrodynamics (MHD) formulation. In this context a Newton iteration is used for the nonlinear system and a Krylov (GMRES) method is employed for the linear subsystems. The efficiency of this approach is critically dependent on the scalability and performance of the AMG preconditioner for the linear solutions and the performance of the smoothers play a critical role. Krylov smoothers are considered inmore » an attempt to reduce the time and memory requirements of existing robust smoothers based on additive Schwarz domain decomposition (DD) with incomplete LU factorization solves on each subdomain. Three time dependent resistive MHD test cases are considered to evaluate the method. The results demonstrate that the GMRES smoother can be faster due to a decrease in the preconditioner setup time and a reduction in outer GMRESR solver iterations, and requires less memory (typically 35% less memory for global GMRES smoother) than the DD ILU smoother.« less

A multi-reference filtered-x-Newton narrowband algorithm for active isolation of vibration and experimental investigations

NASA Astrophysics Data System (ADS)

Wang, Chun-yu; He, Lin; Li, Yan; Shuai, Chang-geng

2018-01-01

In engineering applications, ship machinery vibration may be induced by multiple rotational machines sharing a common vibration isolation platform and operating at the same time, and multiple sinusoidal components may be excited. These components may be located at frequencies with large differences or at very close frequencies. A multi-reference filtered-x Newton narrowband (MRFx-Newton) algorithm is proposed to control these multiple sinusoidal components in an MIMO (multiple input and multiple output) system, especially for those located at very close frequencies. The proposed MRFx-Newton algorithm can decouple and suppress multiple sinusoidal components located in the same narrow frequency band even though such components cannot be separated from each other by a narrowband-pass filter. Like the Fx-Newton algorithm, good real-time performance is also achieved by the faster convergence speed brought by the 2nd-order inverse secondary-path filter in the time domain. Experiments are also conducted to verify the feasibility and test the performance of the proposed algorithm installed in an active-passive vibration isolation system in suppressing the vibration excited by an artificial source and air compressor/s. The results show that the proposed algorithm not only has comparable convergence rate as the Fx-Newton algorithm but also has better real-time performance and robustness than the Fx-Newton algorithm in active control of the vibration induced by multiple sound sources/rotational machines working on a shared platform.

High-Order Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza R.; Nishikawa, Hiroaki

2014-01-01

In this paper, spatially high-order Residual-Distribution (RD) schemes using the first-order hyperbolic system method are proposed for general time-dependent advection-diffusion problems. The corresponding second-order time-dependent hyperbolic advection- diffusion scheme was first introduced in [NASA/TM-2014-218175, 2014], where rapid convergences over each physical time step, with typically less than five Newton iterations, were shown. In that method, the time-dependent hyperbolic advection-diffusion system (linear and nonlinear) was discretized by the second-order upwind RD scheme in a unified manner, and the system of implicit-residual-equations was solved efficiently by Newton's method over every physical time step. In this paper, two techniques for the source term discretization are proposed; 1) reformulation of the source terms with their divergence forms, and 2) correction to the trapezoidal rule for the source term discretization. Third-, fourth, and sixth-order RD schemes are then proposed with the above techniques that, relative to the second-order RD scheme, only cost the evaluation of either the first derivative or both the first and the second derivatives of the source terms. A special fourth-order RD scheme is also proposed that is even less computationally expensive than the third-order RD schemes. The second-order Jacobian formulation was used for all the proposed high-order schemes. The numerical results are then presented for both steady and time-dependent linear and nonlinear advection-diffusion problems. It is shown that these newly developed high-order RD schemes are remarkably efficient and capable of producing the solutions and the gradients to the same order of accuracy of the proposed RD schemes with rapid convergence over each physical time step, typically less than ten Newton iterations.

Algorithms for Solvents and Spectral Factors of Matrix Polynomials

DTIC Science & Technology

1981-01-01

spectral factors of matrix polynomials LEANG S. SHIEHt, YIH T. TSAYt and NORMAN P. COLEMANt A generalized Newton method , based on the contracted gradient...of a matrix poly- nomial, is derived for solving the right (left) solvents and spectral factors of matrix polynomials. Two methods of selecting initial...estimates for rapid convergence of the newly developed numerical method are proposed. Also, new algorithms for solving complete sets of the right

Newton's Apple

ERIC Educational Resources Information Center

Hendry, Archibald W.

2007-01-01

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

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

NASA Astrophysics Data System (ADS)

Borazjani, Iman; Asgharzadeh, Hafez

2015-11-01

Flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates with explicit and semi-implicit schemes. Implicit schemes can be used to overcome these restrictions. However, implementing implicit solver for nonlinear equations including Navier-Stokes is not straightforward. Newton-Krylov subspace methods (NKMs) are one of the most advanced iterative methods to solve non-linear equations such as implicit descritization of the Navier-Stokes equation. The efficiency of NKMs massively depends on the Jacobian formation method, e.g., automatic differentiation is very expensive, and matrix-free methods slow down as the mesh is refined. Analytical Jacobian is inexpensive method, but derivation of analytical Jacobian for Navier-Stokes equation on staggered grid is challenging. The NKM with a novel analytical Jacobian was developed and validated against Taylor-Green vortex and pulsatile flow in a 90 degree bend. The developed method successfully handled the complex geometries such as an intracranial aneurysm with multiple overset grids, and immersed boundaries. It is shown that the NKM with an analytical Jacobian is 3 to 25 times faster than the fixed-point implicit Runge-Kutta method, and more than 100 times faster than automatic differentiation depending on the grid (size) and the flow problem. The developed methods are fully parallelized with parallel efficiency of 80-90% on the problems tested.

Effects of Method of Instruction and Frequency of Response on Criterion Performance

ERIC Educational Resources Information Center

Troost, Cornelius J.; Morris, Stanley

1971-01-01

Grade six students were taught Newton's Second Law of Motion by a linear program, a lecture, or a video-taped lecture, with three different response modes: written responses to all questions, to one-third of the questions, or to no questions. There was no significant difference between teaching method, but the higher the overt response rate, the…

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

Code of Federal Regulations, 2013 CFR

2013-07-01

... 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 60.43...

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

Code of Federal Regulations, 2014 CFR

2014-07-01

... 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 60.43...

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

Code of Federal Regulations, 2012 CFR

2012-07-01

... 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 60.43...

A contracting-interval program for the Danilewski method. Ph.D. Thesis - Va. Univ.

NASA Technical Reports Server (NTRS)

Harris, J. D.

1971-01-01

The concept of contracting-interval programs is applied to finding the eigenvalues of a matrix. The development is a three-step process in which (1) a program is developed for the reduction of a matrix to Hessenberg form, (2) a program is developed for the reduction of a Hessenberg matrix to colleague form, and (3) the characteristic polynomial with interval coefficients is readily obtained from the interval of colleague matrices. This interval polynomial is then factored into quadratic factors so that the eigenvalues may be obtained. To develop a contracting-interval program for factoring this polynomial with interval coefficients it is necessary to have an iteration method which converges even in the presence of controlled rounding errors. A theorem is stated giving sufficient conditions for the convergence of Newton's method when both the function and its Jacobian cannot be evaluated exactly but errors can be made proportional to the square of the norm of the difference between the previous two iterates. This theorem is applied to prove the convergence of the generalization of the Newton-Bairstow method that is used to obtain quadratic factors of the characteristic polynomial.

Investigation on imperfection sensitivity of composite cylindrical shells using the nonlinearity reduction technique and the polynomial chaos method

NASA Astrophysics Data System (ADS)

Liang, Ke; Sun, Qin; Liu, Xiaoran

2018-05-01

The theoretical buckling load of a perfect cylinder must be reduced by a knock-down factor to account for structural imperfections. The EU project DESICOS proposed a new robust design for imperfection-sensitive composite cylindrical shells using the combination of deterministic and stochastic simulations, however the high computational complexity seriously affects its wider application in aerospace structures design. In this paper, the nonlinearity reduction technique and the polynomial chaos method are implemented into the robust design process, to significantly lower computational costs. The modified Newton-type Koiter-Newton approach which largely reduces the number of degrees of freedom in the nonlinear finite element model, serves as the nonlinear buckling solver to trace the equilibrium paths of geometrically nonlinear structures efficiently. The non-intrusive polynomial chaos method provides the buckling load with an approximate chaos response surface with respect to imperfections and uses buckling solver codes as black boxes. A fast large-sample study can be applied using the approximate chaos response surface to achieve probability characteristics of buckling loads. The performance of the method in terms of reliability, accuracy and computational effort is demonstrated with an unstiffened CFRP cylinder.

Water Rockets and Indirect Measurement.

ERIC Educational Resources Information Center

Inman, Duane

1997-01-01

Describes an activity that teaches a number of scientific concepts including indirect measurement, Newton's third law of motion, manipulating and controlling variables, and the scientific method of inquiry. Uses process skills such as observation, inference, prediction, mensuration, and communication as well as problem solving and higher-order…

The Computer Simulation of Liquids by Molecular Dynamics.

ERIC Educational Resources Information Center

Smith, W.

1987-01-01

Proposes a mathematical computer model for the behavior of liquids using the classical dynamic principles of Sir Isaac Newton and the molecular dynamics method invented by other scientists. Concludes that other applications will be successful using supercomputers to go beyond simple Newtonian physics. (CW)

Function Invariant and Parameter Scale-Free Transformation Methods

ERIC Educational Resources Information Center

Bentler, P. M.; Wingard, Joseph A.

1977-01-01

A scale-invariant simple structure function of previously studied function components for principal component analysis and factor analysis is defined. First and second partial derivatives are obtained, and Newton-Raphson iterations are utilized. The resulting solutions are locally optimal and subjectively pleasing. (Author/JKS)

Solving coupled groundwater flow systems using a Jacobian Free Newton Krylov method

NASA Astrophysics Data System (ADS)

Mehl, S.

2012-12-01

Jacobian Free Newton Kyrlov (JFNK) methods can have several advantages for simulating coupled groundwater flow processes versus conventional methods. Conventional methods are defined here as those based on an iterative coupling (rather than a direct coupling) and/or that use Picard iteration rather than Newton iteration. In an iterative coupling, the systems are solved separately, coupling information is updated and exchanged between the systems, and the systems are re-solved, etc., until convergence is achieved. Trusted simulators, such as Modflow, are based on these conventional methods of coupling and work well in many cases. An advantage of the JFNK method is that it only requires calculation of the residual vector of the system of equations and thus can make use of existing simulators regardless of how the equations are formulated. This opens the possibility of coupling different process models via augmentation of a residual vector by each separate process, which often requires substantially fewer changes to the existing source code than if the processes were directly coupled. However, appropriate perturbation sizes need to be determined for accurate approximations of the Frechet derivative, which is not always straightforward. Furthermore, preconditioning is necessary for reasonable convergence of the linear solution required at each Kyrlov iteration. Existing preconditioners can be used and applied separately to each process which maximizes use of existing code and robust preconditioners. In this work, iteratively coupled parent-child local grid refinement models of groundwater flow and groundwater flow models with nonlinear exchanges to streams are used to demonstrate the utility of the JFNK approach for Modflow models. Use of incomplete Cholesky preconditioners with various levels of fill are examined on a suite of nonlinear and linear models to analyze the effect of the preconditioner. Comparisons of convergence and computer simulation time are made using conventional iteratively coupled methods and those based on Picard iteration to those formulated with JFNK to gain insights on the types of nonlinearities and system features that make one approach advantageous. Results indicate that nonlinearities associated with stream/aquifer exchanges are more problematic than those resulting from unconfined flow.

A fast, time-accurate unsteady full potential scheme

NASA Technical Reports Server (NTRS)

Shankar, V.; Ide, H.; Gorski, J.; Osher, S.

1985-01-01

The unsteady form of the full potential equation is solved in conservation form by an implicit method based on approximate factorization. At each time level, internal Newton iterations are performed to achieve time accuracy and computational efficiency. A local time linearization procedure is introduced to provide a good initial guess for the Newton iteration. A novel flux-biasing technique is applied to generate proper forms of the artificial viscosity to treat hyperbolic regions with shocks and sonic lines present. The wake is properly modeled by accounting not only for jumps in phi, but also for jumps in higher derivatives of phi, obtained by imposing the density to be continuous across the wake. The far field is modeled using the Riemann invariants to simulate nonreflecting boundary conditions. The resulting unsteady method performs well which, even at low reduced frequency levels of 0.1 or less, requires fewer than 100 time steps per cycle at transonic Mach numbers. The code is fully vectorized for the CRAY-XMP and the VPS-32 computers.

Molecular dynamics simulation of a needle-sphere binary mixture

NASA Astrophysics Data System (ADS)

Raghavan, Karthik

This paper investigates the dynamic behaviour of a hard needle-sphere binary system using a novel numerical technique called the Newton homotopy continuation (NHC) method. This mixture is representative of a polymer melt where both long chain molecules and monomers coexist. Since the intermolecular forces are generated from hard body interactions, the consequence of missed collisions or incorrect collision sequences have a significant bearing on the dynamic properties of the fluid. To overcome this problem, in earlier work NHC was chosen over traditional Newton-Raphson methods to solve the hard body dynamics of a needle fluid in random media composed of overlapping spheres. Furthermore, the simplicity of interactions and dynamics allows us to focus our research directly on the effects of particle shape and density on the transport behaviour of the mixture. These studies are also compared with earlier works that examined molecular chains in porous media primarily to understand the differences in molecular transport in the bulk versus porous systems.

Signing off

NASA Astrophysics Data System (ADS)

2001-11-01

How much do we value our physicists? Some banknotes carry pictures of great physicists. It seems obvious to conduct an investigation using this data to find out how much we value them. Research can be carried out by finding what denomination a country uses for its physicists and using some simple currency conversions. All discussions of the relative merits of physicists have so far ignored this data. Newton, so often the baseline of physics greatness, was once represented on the English one-pound note. Although he has since been shredded and replaced by coins we will use the Newton as our base unit of currency, where one Newton is equal to one pound [those making a dimensional analysis should remember we are talking about currency]. The Danes value Bohr at 42 Newtons, whilst the Austrians consider Schrödinger to be worth 46 Newtons At this point the research becomes interesting because an (only slightly varying) constant emerges. The Danes value Bohr at 42 Newtons, whilst the Austrians consider Schrödinger to be worth 46 Newtons. Obviously, as with all quantum physics effects, those spending Schrödingers (as well as anyone who has retired) will find that when you have money to spend there is not time, and when you have the time there is no money to spend. These figures clearly show a trend that all physicists trade at about 45 Newtons. And they also seem to show how much the UK has undervalued Newton. However, this result may well be a feature of a newly suggested inverse square law of being famous, that the longer ago you lived the less important you seem. Physicists are working hard to reconcile this with the 'never famous before you are dead' postulate. More data is needed. With Marie Curie on the 500 French Franc note, one Curie is worth 48 Newtons, supporting the theory. However, Pierre Curie also appeared on this note so Marie can only really be valued at 24 Newtons. Quite how two physicists superpose in their currency valuations is unknown by theorists. Appearing on two notes also raises questions about the effect on value of working in several countries. The idea is yet to be fully formulated, but it would be nice if it were exponential. Certainly the fact that New Zealand's hero Rutherford has been represented on the one hundred dollar note, valuing him at 28 Newtons, adds to the idea of an attenuation coefficient. There also seem to be transient effects on value, resulting from the personality of the physicist involved. It seems entirely appropriate that the mercurial Tesla should be represented by the ten billion dollar Yugoslavian note, which was nevertheless worth almost nothing. But of course any discussions of great physicists always involve Einstein. Amazingly he has been seen represented on the Israeli five-pound note, valuing him at about 0.08 Newtons. Before rushing off, in support of the great man, to prove that this is clearly a relativistic aberration, just pause. Perhaps calculating your salary in Einsteins could be really rather good for morale... More about physicists on money can be found at www2.physics.umd.edu/~redish/Money/ Philip Britton Head of Physics, Leeds Grammar School, UK

Soil heating and evaporation under extreme conditions: Forest fires and slash pile burns

NASA Astrophysics Data System (ADS)

Massman, W. J.

2011-12-01

Heating any soil during a sufficiently intense wild fire or prescribed burn can alter soil irreversibly, resulting in many significant and well known, long term biological, chemical, and hydrological effects. To better understand how fire impacts soil, especially considering the increasing probability of wildfires that is being driven by climate change and the increasing use of prescribe burns by land managers, it is important to better understand the dynamics of the coupled heat and moisture transport in soil during these extreme heating events. Furthermore, improving understanding of heat and mass transport during such extreme conditions should also provide insights into the associated transport mechanisms under more normal conditions as well. Here I describe the development of a new model designed to simulate soil heat and moisture transport during fires where the surface heating often ranges between 10,000 and 100,000 Wm-2 for several minutes to several hours. Model performance is tested against laboratory measurements of soil temperature and moisture changes at several depths during controlled heating events created with an extremely intense radiant heater. The laboratory tests employed well described soils with well known physical properties. The model, on the other hand, is somewhat unusual in that it employs formulations for temperature dependencies of the soil specific heat, thermal conductivity, and the water retention curve (relation between soil moisture and soil moisture potential). It also employs a new formulation for the surface evaporation rate as a component of the upper boundary condition, as well as the Newton-Raphson method and the generalized Thomas algorithm for inverting block tri-diagonal matrices to solve for soil temperature and soil moisture potential. Model results show rapid evaporation rates with significant vapor transfer not only to the free atmosphere above the soil, but to lower depths of the soil, where the vapor re-condenses ahead of the heating front. Consequently the trajectory of the solution (soil volumetric water content versus soil temperature) is very unusual and highly nonlinear, which may explain why more traditional methods (i.e., those based on finite difference or finite element approaches) tend to show more numerical instabilities than the Newton-Raphson method when used to model these extreme conditions. But, despite the intuitive and qualitative appeal of the model's numerical solution, it underestimates the rate of soil moisture loss observed during the laboratory trials, although the soil temperatures are reasonably well simulated.

An X-Ray Investigation of the NGC346 Field in the SMC (3): XMM-Newton Data

NASA Technical Reports Server (NTRS)

Naze, Yael; Manfroid, Jean; Corcoran, Michael F.; Stevens, Ian R.

2004-01-01

We present new XMM-Newton results on the field around the NGC346 star cluster in the SMC. This continues and extends previously published work on Chandra observations of the same field. The two XMM-Newton observations were obtained, respectively, six months before and six months after the previously published Chandra data. Of the 51 X-ray sources detected with XMM-Newton, 29 were already detected with Chandru. Comparing the properties of these X-ray sources in each of our three datasets has enabled us to investigate their variability on times scales of a year. Changes in the flux levels and/or spectral properties were observed for 21 of these sources. In addition, we discovered long-term variations in the X-ray properties of the peculiar system HD5980, a luminous blue variable star, that is likely to be a colliding wind binary system, which displays the largest luminosity during the first XMM-Newton observation.

Newton shows the light: a commentary on Newton (1672) ‘A letter … containing his new theory about light and colours…’

PubMed Central

Fara, Patricia

2015-01-01

Isaac Newton's reputation was initially established by his 1672 paper on the refraction of light through a prism; this is now seen as a ground-breaking account and the foundation of modern optics. In it, he claimed to refute Cartesian ideas of light modification by definitively demonstrating that the refrangibility of a ray is linked to its colour, hence arguing that colour is an intrinsic property of light and does not arise from passing through a medium. Newton's later significance as a world-famous scientific genius and the apparent confirmation of his experimental results have tended to obscure the realities of his reception at the time. This paper explores the rhetorical strategies Newton deployed to convince his audience that his conclusions were certain and unchallengeable. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society. PMID:25750143

Integrating Gender and Group Differences into Bridging Strategy

NASA Astrophysics Data System (ADS)

Yılmaz, Serkan; Eryılmaz, Ali

2010-08-01

The main goal of this study was to integrate gender and group effect into bridging strategy in order to assess the effect of bridging analogy-based instruction on sophomore students' misconceptions in Newton's Third Law. Specifically, the authors developed and benefited from anchoring analogy diagnostic test to merge the effect of group and gender into the strategy. Newton's third law misconception test, attitude scale toward Newton's third law, and classroom observation checklists were the other measuring tools utilized throughout this quasi-experimental study. The researchers also developed or used several teaching/learning materials such as gender and group splitted concept diagrams, lesson plans, gender splitted frequency tables, make sense scales, PowerPoint slides, flash cards, and demonstrations. The convenience sample of the study chosen from the accessible population involved 308 students from two public universities. The results of multivariate analysis of covariance indicated that the bridging strategy had a significant effect on students' misconceptions in Newton's third law whereas it had no significant effect on students' attitudes toward Newton's third law.

There is grandeur in this view of Newton: Charles Darwin, Isaac Newton and Victorian conceptions of scientific virtue.

PubMed

Bellon, Richard

2014-01-01

For Victorian men of science, the scientific revolution of the seventeenth century represented a moral awakening. Great theoretical triumphs of inductive science flowed directly from a philosophical spirit that embraced the virtues of self-discipline, courage, patience and humility. Isaac Newton exemplified this union of moral and intellectual excellence. This, at least, was the story crafted by scientific leaders like David Brewster, Thomas Chalmers, John Herschel, Adam Sedgwick and William Whewell. Not everyone accepted this reading of history. Evangelicals who decried the 'materialism' of mainstream science assigned a different meaning to Newton's legacy on behalf of their 'scriptural' alternative. High-church critics of science like John Henry Newman, on the other hand, denied that Newton's secular achievements carried any moral significance at all. These debates over Newtonian standards of philosophical behavior had a decisive influence on Charles Darwin as he developed his theory of evolution by natural selection. Copyright © 2014 Elsevier Ltd. All rights reserved.

Structures and microfabrics of the Franciscan Complex (California): Inferences on the rheology and kinematics of a subduction channel

NASA Astrophysics Data System (ADS)

Krohe, A.; Wassmann, S.; Trepmann, C.; Stoeckhert, B.

2009-12-01

The characteristic feature of the Franciscan Subduction Complex (FSC) is a chaotic mélange structure with centimeter- to about one kilometer-sized tectonic blocks composed of metabasalts, floating in a matrix of oceanic meta-sediments or, locally, serpentinites. Investigating map scale structures, microfabrics, and P-T-histories of the FSC, we try to gain information on the mechanical properties of rocks and their influence on the kinematics of material transport in a subduction channel. Structures and microfabrics indicate that metabasalts from the oceanic crust as well as mantle-derived ultramafic rocks (i) underwent fragmentation and sealing under high pore fluid pressure, (ii) remaining internally undeformed, or (iii) deform by dissolution precipitation creep. Importantly, microfabrics which would indicate crystal plastic deformation or dislocation creep are systematically absent. This means that, during the entire P-T history, differential stresses generally remained too low to activate crystal plastic deformation or dislocation creep. Hence the material in the subduction channel is characterized by a low strength, being either limited by brittle failure at high pore fluid pressure, or a Newton viscosity, which is expected for dissolution precipitation creep. We interpret the characteristic mélange structure as to reflect this mechanical state of the system: Brittle failure at quasi-lithostatic fluid pressures down to great depths is recorded in the tectonic blocks by the widespread occurrence of aragonite-bearing veins. This leads to fragmentation into the blocks of variable size and moderate aspect ratios, which behave as rigid inclusions in a flowing matrix with distributed deformation by dissolution precipitation creep. In contrast, a power law rheology characteristic for dislocation creep, would favor strain localization into shear zones at sites of stress concentration. However, such shear zones formed at high-P metamorphic conditions are not identified. Mechanical contrasts within the mélange are presumably governed by variations in grain sizes and the nature of interphase boundaries, which both control viscous deformation by dissolution precipitation creep. As such, huge viscosity contrasts between matrix and rigid blocks can persist during burial to HP metamorphic conditions and decompression, while the mélange is deformed to very high bulk strain. These findings pose constraints on the large scale properties of a subduction channel presently active at depth, to be identified by geophysical methods.

Realistic soft tissue deformation strategies for real time surgery simulation.

PubMed

Shen, Yunhe; Zhou, Xiangmin; Zhang, Nan; Tamma, Kumar; Sweet, Robert

2008-01-01

A volume-preserving deformation method (VPDM) is developed in complement with the mass-spring method (MSM) to improve the deformation quality of the MSM to model soft tissue in surgical simulation. This method can also be implemented as a stand-alone model. The proposed VPDM satisfies the Newton's laws of motion by obtaining the resultant vectors form an equilibrium condition. The proposed method has been tested in virtual surgery systems with haptic rendering demands.

Design and characterization of a nano-Newton resolution thrust stand

NASA Astrophysics Data System (ADS)

Soni, J.; Roy, S.

2013-09-01

The paper describes the design, calibration, and characterization of a thrust stand capable of nano-Newton resolution. A low uncertainty calibration method is proposed and demonstrated. A passive eddy current based damper, which is non-contact and vacuum compatible, is employed. Signal analysis techniques are used to perform noise characterization, and potential sources are identified. Calibrated system noise floor suggests thrust measurement resolution of the order of 10 nN is feasible under laboratory conditions. Force measurement from this balance for a standard macroscale dielectric barrier discharge (DBD) plasma actuator is benchmarked with a commercial precision balance of 9.8 μN resolution and is found to be in good agreement. Published results of a microscale DBD plasma actuator force measurement and low pressure characterization of conventional plasma actuators are presented for completeness.

Force Sensing Applications of DNA Origami Nanodevices

NASA Astrophysics Data System (ADS)

Hudoba, Michael William

Mechanical forces in biological systems vary in both length and magnitude by orders of magnitude making them difficult to probe and characterize with existing experimental methodologies. From molecules to cells, forces can act across length scales of nanometers to microns at magnitudes ranging from picoNewtons to nanoNewtons. Although single-molecule techniques such as optical traps, magnetic tweezers, and atomic force microscopy have improved the resolution and sensitivity of such measurements, inherent drawbacks exist in their capabilities due to the nature of the tools themselves. Specifically, these techniques have limitations in their ability to measure forces in realistic cellular environments and are not amenable to in vivo applications or measurements in mimicked physiological environments. In this thesis, we present a method to develop DNA force-sensing nanodevices with sub-picoNewton resolution capable of measuring forces in realistic cellular environments, with future applications in vivo. We use a design technique known as DNA origami to assemble devices with nanoscale geometric precision through molecular self-assembly via Watson-Crick base pairing. The devices have multiple conformational states, monitored by observing a Forster Resonance Energy Transfer signal that can change under the application of force. We expanded this study by demonstrating the design of responsive structural dynamics in DNA-based nanodevices. While prior studies have relied on external inputs to drive relatively slow dynamics in DNA nanostructures, here we developed DNA nanodevices with thermally driven dynamic function. The device was designed with an ensemble of conformations, and we establish methods to tune the equilibrium distribution of conformations and the rate of switching between states. We also show this nanodynamic behavior is responsive to physical interactions with the environment by measuring molecular crowding forces in the sub-picoNewton range, which are known to play a critical role in regulating molecular interactions and processes. Broadly, this work establishes a foundation for nanodevices with thermally driven dynamics that enable new measurement and control functions. We also examine the effect that forces have on the mechanical properties of DNA origami devices by developing a method to automate mesh generation for Finite Element Analysis. With this approach we are able to determine how defects that arise during assembly affect mechanical strain within structures during force application that can ultimately lead to device failure.

Calculus Demonstrations Using MATLAB

ERIC Educational Resources Information Center

Dunn, Peter K.; Harman, Chris

2002-01-01

The note discusses ways in which technology can be used in the calculus learning process. In particular, five MATLAB programs are detailed for use by instructors or students that demonstrate important concepts in introductory calculus: Newton's method, differentiation and integration. Two of the programs are animated. The programs and the…

Space-Time, Relativity, and Cosmology

NASA Astrophysics Data System (ADS)

Wudka, Jose

2010-06-01

Acknowledgements; 1. The scientific method; 2. From antiquity to Aristotle; 3. From the Middle Ages to heliocentrism; 4. Galileo and Newton; 5. The clouds gather; 6. The Special Theory of Relativity; 7. The General Theory of Relativity; 8. The relativistic universe; 9. The lives of a star; Bibliography; Index.

Computerized Business Calculus Using Calculators, Examples from Mathematics to Finance.

ERIC Educational Resources Information Center

Vest, Floyd

1991-01-01

After discussing the role of supercalculators within the business calculus curriculum, several examples are presented which allow the reader to examine the capabilities and codes of calculators specific to different major manufacturers. The topics examined include annuities, Newton's method, fixed point iteration, graphing, solvers, and…

Testing Pattern Hypotheses for Correlation Matrices

ERIC Educational Resources Information Center

McDonald, Roderick P.

1975-01-01

The treatment of covariance matrices given by McDonald (1974) can be readily modified to cover hypotheses prescribing zeros and equalities in the correlation matrix rather than the covariance matrix, still with the convenience of the closed-form Least Squares solution and the classical Newton method. (Author/RC)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cao, Yong; Chu, Yuchuan; He, Xiaoming

This paper proposes a domain decomposition method for the coupled stationary Navier-Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition in order to improve the efficiency of the finite element method. The physical interface conditions are directly utilized to construct the boundary conditions on the interface and then decouple the Navier-Stokes and Darcy equations. Newton iteration will be used to deal with the nonlinear systems. Numerical results are presented to illustrate the features of the proposed method.

Pilot investigation - Nominal crew induced forces in zero-g

NASA Technical Reports Server (NTRS)

Klute, Glenn K.

1992-01-01

This report presents pilot-study data of test subject forces induced by intravehicular activities such as push-offs and landings with both hands and feet. Five subjects participated in this investigation. Three orthogonal force axes were measured in the NASA KC-135 research aircraft's 'zero-g' environment. The largest forces were induced during vertical foot push-offs, including one of 534 newtons (120 lbs). The mean vertical foot push-off was 311 newtons (70 lbs). The vertical hand push-off forces were also relatively large, including one of 267 newtons (60 lbs) with a mean of 151 newtons (34 lbs). These force magnitudes of these forces would result in a Shuttle gravity environment of about 1 x exp 10 -4 g's.

Non-Relativistic Twistor Theory and Newton-Cartan Geometry

NASA Astrophysics Data System (ADS)

Dunajski, Maciej; Gundry, James

2016-03-01

We develop a non-relativistic twistor theory, in which Newton-Cartan structures of Newtonian gravity correspond to complex three-manifolds with a four-parameter family of rational curves with normal bundle O oplus O(2)}. We show that the Newton-Cartan space-times are unstable under the general Kodaira deformation of the twistor complex structure. The Newton-Cartan connections can nevertheless be reconstructed from Merkulov's generalisation of the Kodaira map augmented by a choice of a holomorphic line bundle over the twistor space trivial on twistor lines. The Coriolis force may be incorporated by holomorphic vector bundles, which in general are non-trivial on twistor lines. The resulting geometries agree with non-relativistic limits of anti-self-dual gravitational instantons.

Resonating group method as applied to the spectroscopy of α-transfer reactions

NASA Astrophysics Data System (ADS)

Subbotin, V. B.; Semjonov, V. M.; Gridnev, K. A.; Hefter, E. F.

1983-10-01

In the conventional approach to α-transfer reactions the finite- and/or zero-range distorted-wave Born approximation is used in liaison with a macroscopic description of the captured α particle in the residual nucleus. Here the specific example of 16O(6Li,d)20Ne reactions at different projectile energies is taken to present a microscopic resonating group method analysis of the α particle in the final nucleus (for the reaction part the simple zero-range distorted-wave Born approximation is employed). In the discussion of suitable nucleon-nucleon interactions, force number one of the effective interactions presented by Volkov is shown to be most appropriate for the system considered. Application of the continuous analog of Newton's method to the evaluation of the resonating group method equations yields an increased accuracy with respect to traditional methods. The resonating group method description induces only minor changes in the structures of the angular distributions, but it does serve its purpose in yielding reliable and consistent spectroscopic information. NUCLEAR STRUCTURE 16O(6Li,d)20Ne; E=20 to 32 MeV; calculated B(E2); reduced widths, dσdΩ extracted α-spectroscopic factors. ZRDWBA with microscope RGM description of residual α particle in 20Ne; application of continuous analog of Newton's method; tested and applied Volkov force No. 1; direct mechanism.

Rapid computation of chemical equilibrium composition - An application to hydrocarbon combustion

NASA Technical Reports Server (NTRS)

Erickson, W. D.; Prabhu, R. K.

1986-01-01

A scheme for rapidly computing the chemical equilibrium composition of hydrocarbon combustion products is derived. A set of ten governing equations is reduced to a single equation that is solved by the Newton iteration method. Computation speeds are approximately 80 times faster than the often used free-energy minimization method. The general approach also has application to many other chemical systems.

Biomechanical comparison of fixation methods in transverse patella fractures.

PubMed

Scilaris, T A; Grantham, J L; Prayson, M J; Marshall, M P; Hamilton, J J; Williams, J L

1998-01-01

To compare monofilament wire versus braided cable for stabilizing transverse patella fractures using the modified AO tension band technique. A randomized blocked (paired) study comparing two fixation methods. Statistical analysis was performed using a nested repeated measures analysis, followed by Bonferroni post hoc testing. Seven paired embalmed knees (mean age 71.8 years, SD 14.6 years) were dissected, and transverse fractures were simulated. The knees were reduced and randomly fixed by either two parallel 0.062-inch Kirschner wires with a 1.0-millimeter-diameter 316L stainless steel monofilament wire tension loop or two Kirschner wires with a 1.0-millimeter-diameter 316L stainless steel braided cable tension loop. Knees were tested by applying a cyclic load through the suprapatellar tendon between twenty and 300 newtons for thirty cycles. The maximum fracture displacement increased with each cycle of loading for both the braided cable and monofilament wire tension loop configurations (p = 0.0001). The average peak displacement at the thirtieth cycle was 2.25 millimeters for monofilament wire and 0.73 millimeters for the cable. When comparing both methods for all cycles, the braided cable allowed less fracture displacement than did the monofilament wire (p = 0.002), and the rate of increase per cycle of maximum fracture displacement was less for the cable than for the wire (p = 0.0001). In transverse, noncomminuted patella fractures, fixation with two Kirschner wires and a 1.0-millimeter braided cable tension loop was superior to the monofilament wire tension loop. Most importantly, the braided cable afforded more predictable results during cyclic loading.

An effective solution to the nonlinear, nonstationary Navier-Stokes equations for two dimensions

NASA Technical Reports Server (NTRS)

Gabrielsen, R. E.

1975-01-01

A sequence of approximate solutions for the nonlinear, nonstationary Navier-Stokes equations for a two-dimensional domain, from which explicit error estimates and rates of convergence are obtained, is described. This sequence of approximate solutions is based primarily on the Newton-Kantorovich method.

Some Surprising Errors in Numerical Differentiation

ERIC Educational Resources Information Center

Gordon, Sheldon P.

2012-01-01

Data analysis methods, both numerical and visual, are used to discover a variety of surprising patterns in the errors associated with successive approximations to the derivatives of sinusoidal and exponential functions based on the Newton difference-quotient. L'Hopital's rule and Taylor polynomial approximations are then used to explain why these…

Univariate and Bivariate Loglinear Models for Discrete Test Score Distributions.

ERIC Educational Resources Information Center

Holland, Paul W.; Thayer, Dorothy T.

2000-01-01

Applied the theory of exponential families of distributions to the problem of fitting the univariate histograms and discrete bivariate frequency distributions that often arise in the analysis of test scores. Considers efficient computation of the maximum likelihood estimates of the parameters using Newton's Method and computationally efficient…

Magneto-hydrodynamical model for plasma

NASA Astrophysics Data System (ADS)

Liu, Ruikuan; Yang, Jiayan

2017-10-01

Based on the Newton's second law and the Maxwell equations for the electromagnetic field, we establish a new 3-D incompressible magneto-hydrodynamics model for the motion of plasma under the standard Coulomb gauge. By using the Galerkin method, we prove the existence of a global weak solution for this new 3-D model.

Research in nonlinear structural and solid mechanics

NASA Technical Reports Server (NTRS)

Mccomb, H. G., Jr. (Compiler); Noor, A. K. (Compiler)

1980-01-01

Nonlinear analysis of building structures and numerical solution of nonlinear algebraic equations and Newton's method are discussed. Other topics include: nonlinear interaction problems; solution procedures for nonlinear problems; crash dynamics and advanced nonlinear applications; material characterization, contact problems, and inelastic response; and formulation aspects and special software for nonlinear analysis.

Primal-dual and forward gradient implementation for quantitative susceptibility mapping.

PubMed

Kee, Youngwook; Deh, Kofi; Dimov, Alexey; Spincemaille, Pascal; Wang, Yi

2017-12-01

To investigate the computational aspects of the prior term in quantitative susceptibility mapping (QSM) by (i) comparing the Gauss-Newton conjugate gradient (GNCG) algorithm that uses numerical conditioning (ie, modifies the prior term) with a primal-dual (PD) formulation that avoids this, and (ii) carrying out a comparison between a central and forward difference scheme for the discretization of the prior term. A spatially continuous formulation of the regularized QSM inversion problem and its PD formulation were derived. The Chambolle-Pock algorithm for PD was implemented and its convergence behavior was compared with that of GNCG for the original QSM. Forward and central difference schemes were compared in terms of the presence of checkerboard artifacts. All methods were tested and validated on a gadolinium phantom, ex vivo brain blocks, and in vivo brain MRI data with respect to COSMOS. The PD approach provided a faster convergence rate than GNCG. The GNCG convergence rate slowed considerably with smaller (more accurate) values of the conditioning parameter. Using a forward difference suppressed the checkerboard artifacts in QSM, as compared with the central difference. The accuracy of PD and GNCG were validated based on excellent correlation with COSMOS. The PD approach with forward difference for the gradient showed improved convergence and accuracy over the GNCG method using central difference. Magn Reson Med 78:2416-2427, 2017. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Adaptive and iterative methods for simulations of nanopores with the PNP-Stokes equations

NASA Astrophysics Data System (ADS)

Mitscha-Baude, Gregor; Buttinger-Kreuzhuber, Andreas; Tulzer, Gerhard; Heitzinger, Clemens

2017-06-01

We present a 3D finite element solver for the nonlinear Poisson-Nernst-Planck (PNP) equations for electrodiffusion, coupled to the Stokes system of fluid dynamics. The model serves as a building block for the simulation of macromolecule dynamics inside nanopore sensors. The source code is released online at http://github.com/mitschabaude/nanopores. We add to existing numerical approaches by deploying goal-oriented adaptive mesh refinement. To reduce the computation overhead of mesh adaptivity, our error estimator uses the much cheaper Poisson-Boltzmann equation as a simplified model, which is justified on heuristic grounds but shown to work well in practice. To address the nonlinearity in the full PNP-Stokes system, three different linearization schemes are proposed and investigated, with two segregated iterative approaches both outperforming a naive application of Newton's method. Numerical experiments are reported on a real-world nanopore sensor geometry. We also investigate two different models for the interaction of target molecules with the nanopore sensor through the PNP-Stokes equations. In one model, the molecule is of finite size and is explicitly built into the geometry; while in the other, the molecule is located at a single point and only modeled implicitly - after solution of the system - which is computationally favorable. We compare the resulting force profiles of the electric and velocity fields acting on the molecule, and conclude that the point-size model fails to capture important physical effects such as the dependence of charge selectivity of the sensor on the molecule radius.

Effects of two grading techniques of zirconia material on the fatigue limit of full-contour 3-unit fixed dental prostheses

PubMed Central

Villefort, Regina Furbino; Amaral, Marina; Pereira, Gabriel Kalil Rocha; Campos, Tiago Moreira Bastos; Zhang, Yu; Bottino, Marco Antonio; Valandro, Luiz Felipe; de Melo, Renata Marques

2017-01-01

Objective This study evaluated the effects of two grading zirconia techniques on the fatigue limit of 3-unit fixed dental prostheses (FDPs). Methods Presintered blocks of 3Y-TZP were milled to obtain sixty-nine 3-unit FDPs, which were divided into three groups (n = 23). The control group (CTL) was sintered and glazed following manufacturer’s instructuctions. The two experimental groups presintered FDPs received a surface silica/glass infiltration treatment before the sintering process. Silica sol-gel group (SSG) was graded by the sol-gel processing route, while the glass-zirconia-glass group (GZG) was graded by an enameling technique. Graded groups did not receive a glaze layer after sintering. All FDPs were then luted with a dual-curing resin cement on composite abutments, embedded in polyurethane and stored in water for five days. The initial load of the fatigue test was calculated based on the results of the monotonic testing applied on three specimens of each group. To determine the fatigue limit, 20 samples of each group were subjected to staircase testing (100,000 cycles/5 Hz). Results The fatigue limits (in Newtons) were CTL = 1607.27, SSG = 1824.31, and GZG = 2006.57, and the Dixon and Mood test indicated statistically significant differences among groups (95% confidence interval). Significance The infiltration of silica and glass on bulk zirconia, by two different grading methods, increased the fatigue limits of monolithic zirconia FDPs. PMID:28118929

Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation

NASA Astrophysics Data System (ADS)

Agarwal, P.; El-Sayed, A. A.

2018-06-01

In this paper, a new numerical technique for solving the fractional order diffusion equation is introduced. This technique basically depends on the Non-Standard finite difference method (NSFD) and Chebyshev collocation method, where the fractional derivatives are described in terms of the Caputo sense. The Chebyshev collocation method with the (NSFD) method is used to convert the problem into a system of algebraic equations. These equations solved numerically using Newton's iteration method. The applicability, reliability, and efficiency of the presented technique are demonstrated through some given numerical examples.

Infinity and Newton's Three Laws of Motion

NASA Astrophysics Data System (ADS)

Lee, Chunghyoung

2011-12-01

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

Émilie Du Châtelet's interpretation of the laws of motion in the light of 18th century mechanics.

PubMed

Reichenberger, Andrea

2018-06-01

Émilie Du Châtelet is well known for her French translation of Newton's Philosophiae Naturalis Principia Mathematica. It is the first and only French translation of Newton's magnum opus. The complete work appeared in 1759 under the title Principes mathématiques de la philosophie naturelle, par feue Madame la Marquise Du Chastellet. Before translating Newton's Principia, Du Châtelet worked on her Institutions de physique. In this book she defended the Leibnizian concept of living forces - vis viva. This paper argues that both of these works were part of a critical transformation and consolidation of post-Newtonian mechanics in the early 18th century, beyond Newton and Leibniz. This will be shown by comparing Du Châtelet's translation of Newton's axioms with her own formulations of the laws of motion in light of Thomas Le Seur's and François Jacquier's Geneva edition which holds a special place among the several editions of the Principia that appeared in the early 18th century. Copyright © 2018 Elsevier Ltd. All rights reserved.

Dramatic (and Simple!) Demonstration of Newton's Third Law

NASA Astrophysics Data System (ADS)

Feldman, Gerald

2011-02-01

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 about what is going on. In the case of magnetic forces, however, the notion of action at a distance actually requires a careful inspection of the forces involved and thereby promotes a more detailed analysis of the situation. In this paper, a simple demonstration of Newton's third law is presented in the context of a magnet falling through a hollow conducting tube. The results are unambiguous and lead the students to an irrefutable verification of Newton's third law.

Short distance modification of the quantum virial theorem

NASA Astrophysics Data System (ADS)

Zhao, Qin; Faizal, Mir; Zaz, Zaid

2017-07-01

In this letter, we will analyse the deformation of a semi-classical gravitational system from minimal measurable length scale. In the semi-classical approximation, the gravitational field will be analysed as a classical field, and the matter fields will be treated quantum mechanically. Thus, using this approximation, this system will be represented by a deformation of Schrödinger-Newton equation by the generalised uncertainty principle (GUP). We will analyse the effects of this GUP deformed Schrödinger-Newton equation on the behaviour of such a semi-classical gravitational system. As the quantum mechanical virial theorem can be obtained using the Schrödinger-Newton equation, a short distance modification of the Schrödinger-Newton equation will also result in a short distance modification of the quantum mechanical virial theorem.

Logistic regression for circular data

NASA Astrophysics Data System (ADS)

Al-Daffaie, Kadhem; Khan, Shahjahan

2017-05-01

This paper considers the relationship between a binary response and a circular predictor. It develops the logistic regression model by employing the linear-circular regression approach. The maximum likelihood method is used to estimate the parameters. The Newton-Raphson numerical method is used to find the estimated values of the parameters. A data set from weather records of Toowoomba city is analysed by the proposed methods. Moreover, a simulation study is considered. The R software is used for all computations and simulations.

SIERRA Multimechanics Module: Aria User Manual Version 4.44

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sierra Thermal /Fluid Team

2017-04-01

Aria is a Galerkin fnite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process fows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ( %3C 1 ) regime. Enhanced modeling support of manufacturing processing is made possible through use of eithermore » arbitrary Lagrangian- Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton- Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h -adaptivity and dynamic load balancing are some of Aria's more advanced capabilities. Aria is based upon the Sierra Framework.« less

NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christensen, Max La Cour; Villa, Umberto E.; Engsig-Karup, Allan P.

The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, ourmore » FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sierra Thermal/Fluid Team

Aria is a Galerkin fnite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process fows via the incompressible Navier-Stokes equations specialized to a low Reynolds number ( %3C 1 ) regime. Enhanced modeling support of manufacturing processing is made possible through use of eithermore » arbitrary Lagrangian- Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton- Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h -adaptivity and dynamic load balancing are some of Aria's more advanced capabilities. Aria is based upon the Sierra Framework.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sierra Thermal /Fluid Team

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re %3C 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrarymore » Lagrangian- Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton- Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h-adaptivity and dynamic load balancing are some of Aria's more advanced capabilities. Aria is based upon the Sierra Framework.« less

Minimal norm constrained interpolation. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Irvine, L. D.

1985-01-01

In computational fluid dynamics and in CAD/CAM, a physical boundary is usually known only discreetly and most often must be approximated. An acceptable approximation preserves the salient features of the data such as convexity and concavity. In this dissertation, a smooth interpolant which is locally concave where the data are concave and is locally convex where the data are convex is described. The interpolant is found by posing and solving a minimization problem whose solution is a piecewise cubic polynomial. The problem is solved indirectly by using the Peano Kernal theorem to recast it into an equivalent minimization problem having the second derivative of the interpolant as the solution. This approach leads to the solution of a nonlinear system of equations. It is shown that Newton's method is an exceptionally attractive and efficient method for solving the nonlinear system of equations. Examples of shape-preserving interpolants, as well as convergence results obtained by using Newton's method are also shown. A FORTRAN program to compute these interpolants is listed. The problem of computing the interpolant of minimal norm from a convex cone in a normal dual space is also discussed. An extension of de Boor's work on minimal norm unconstrained interpolation is presented.

Vortex breakdown simulation

NASA Technical Reports Server (NTRS)

Hafez, M.; Ahmad, J.; Kuruvila, G.; Salas, M. D.

1987-01-01

In this paper, steady, axisymmetric inviscid, and viscous (laminar) swirling flows representing vortex breakdown phenomena are simulated using a stream function-vorticity-circulation formulation and two numerical methods. The first is based on an inverse iteration, where a norm of the solution is prescribed and the swirling parameter is calculated as a part of the output. The second is based on direct Newton iterations, where the linearized equations, for all the unknowns, are solved simultaneously by an efficient banded Gaussian elimination procedure. Several numerical solutions for inviscid and viscous flows are demonstrated, followed by a discussion of the results. Some improvements on previous work have been achieved: first order upwind differences are replaced by second order schemes, line relaxation procedure (with linear convergence rate) is replaced by Newton's iterations (which converge quadratically), and Reynolds numbers are extended from 200 up to 1000.

The architecture of Newton, a general-purpose dynamics simulator

NASA Technical Reports Server (NTRS)

Cremer, James F.; Stewart, A. James

1989-01-01

The architecture for Newton, a general-purpose system for simulating the dynamics of complex physical objects, is described. The system automatically formulates and analyzes equations of motion, and performs automatic modification of this system equations when necessitated by changes in kinematic relationships between objects. Impact and temporary contact are handled, although only using simple models. User-directed influence of simulations is achieved using Newton's module, which can be used to experiment with the control of many-degree-of-freedom articulated objects.

PEOPLE IN PHYSICS: 'Lady Newton' - an eighteenth century Marquise

NASA Astrophysics Data System (ADS)

Badilescu, Simona

1996-07-01

The contribution of Voltaire and Mme du Châtelet to the diffusion of Newtonian physics in eighteenth century France is outlined. Their most important writings in the realm of physics (Philosophical Letters, Elements de la philosophie de Newton, Institutions de Physique) are analysed and the impact of the new ideas on the traditional Cartesian physics is emphasized. The genesis of the first French translation of Newton's Principia is described. The usefulness of the historically connected stories in the teaching of physics is envisaged.

Variational nature, integration, and properties of Newton reaction path

NASA Astrophysics Data System (ADS)

Bofill, Josep Maria; Quapp, Wolfgang

2011-02-01

The distinguished coordinate path and the reduced gradient following path or its equivalent formulation, the Newton trajectory, are analyzed and unified using the theory of calculus of variations. It is shown that their minimum character is related to the fact that the curve is located in a valley region. In this case, we say that the Newton trajectory is a reaction path with the category of minimum energy path. In addition to these findings a Runge-Kutta-Fehlberg algorithm to integrate these curves is also proposed.

Variational nature, integration, and properties of Newton reaction path.

PubMed

Bofill, Josep Maria; Quapp, Wolfgang

2011-02-21

The distinguished coordinate path and the reduced gradient following path or its equivalent formulation, the Newton trajectory, are analyzed and unified using the theory of calculus of variations. It is shown that their minimum character is related to the fact that the curve is located in a valley region. In this case, we say that the Newton trajectory is a reaction path with the category of minimum energy path. In addition to these findings a Runge-Kutta-Fehlberg algorithm to integrate these curves is also proposed.

Automated Design of a High-Velocity Channel

DTIC Science & Technology

2006-05-01

using Newton’s method. 2.2.2 Groundwater Applications Optimization methods are also very useful for solving groundwater problems. Townley et al... Townley 85] apply present computational algorithms to steady and transient models for groundwater °ow. The aquifer storage coe±cients, transmissivities...Reliability Analysis", Water Resources Research, Vol. 28, No. 12, December 1992, pp. 3269-3280. [ Townley 85] Townley , L. R. and Wilson, J. L

Dynamic Supersonic Base Store Ejection Simulation Using Beggar

DTIC Science & Technology

2008-12-01

selected convergence tolerance. Beggar accomplishes this is by using the symmetric Gauss - Seidel relaxation scheme implemented as follows [26]: [ ln+1,m...scheme (Section 2.3.3). To compute a time accurate solution to an unsteady flow problem, Beggar ap- plies Newtons Method to Eq. 2.15. The full method ...3.6. Separation Distance (x/D) . . . . . . . . . . . . . . . . . . . . 46 4.1. Drag Coefficient of Static Solutions Compared to Dynamic Solu- tions

Tensor-product preconditioners for a space-time discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Diosady, Laslo T.; Murman, Scott M.

2014-10-01

A space-time discontinuous Galerkin spectral element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is presented. A diagonalized alternating direction implicit preconditioner is extended to a space-time formulation using entropy variables. The effectiveness of this technique is demonstrated for the direct numerical simulation of turbulent flow in a channel.

Unsteady Flow Simulation: A Numerical Challenge

DTIC Science & Technology

2003-03-01

drive to convergence the numerical unsteady term. The time marching procedure is based on the approximate implicit Newton method for systems of non...computed through analytical derivatives of S. The linear system stemming from equation (3) is solved at each integration step by the same iterative method...significant reduction of memory usage, thanks to the reduced dimensions of the linear system matrix during the implicit marching of the solution. The

Algorithms for accelerated convergence of adaptive PCA.

PubMed

Chatterjee, C; Kang, Z; Roychowdhury, V P

2000-01-01

We derive and discuss new adaptive algorithms for principal component analysis (PCA) that are shown to converge faster than the traditional PCA algorithms due to Oja, Sanger, and Xu. It is well known that traditional PCA algorithms that are derived by using gradient descent on an objective function are slow to converge. Furthermore, the convergence of these algorithms depends on appropriate choices of the gain sequences. Since online applications demand faster convergence and an automatic selection of gains, we present new adaptive algorithms to solve these problems. We first present an unconstrained objective function, which can be minimized to obtain the principal components. We derive adaptive algorithms from this objective function by using: 1) gradient descent; 2) steepest descent; 3) conjugate direction; and 4) Newton-Raphson methods. Although gradient descent produces Xu's LMSER algorithm, the steepest descent, conjugate direction, and Newton-Raphson methods produce new adaptive algorithms for PCA. We also provide a discussion on the landscape of the objective function, and present a global convergence proof of the adaptive gradient descent PCA algorithm using stochastic approximation theory. Extensive experiments with stationary and nonstationary multidimensional Gaussian sequences show faster convergence of the new algorithms over the traditional gradient descent methods.We also compare the steepest descent adaptive algorithm with state-of-the-art methods on stationary and nonstationary sequences.

Newton's Experimentum Crucis Reconsidered

ERIC Educational Resources Information Center

Holtsmark, Torger

1970-01-01

Certain terminological inconsistencies in the teaching of optical theory at the elementary level are traced back to Newton who derived them from Euclidean geometrical optics. Discusses this terminological ambiguity which influenced later textbooks. (LS)

The importance of being equivalent: Newton's two models of one-body motion

NASA Astrophysics Data System (ADS)

Pourciau, Bruce

2004-05-01

As an undergraduate at Cambridge, Newton entered into his "Waste Book" an assumption that we have named the Equivalence Assumption (The Younger): "If a body move progressively in some crooked line [about a center of motion] ..., [then this] crooked line may bee conceived to consist of an infinite number of streight lines. Or else in any point of the croked line the motion may bee conceived to be on in the tangent". In this assumption, Newton somewhat imprecisely describes two mathematical models, a "polygonal limit model" and a "tangent deflected model", for "one-body motion", that is, for the motion of a "body in orbit about a fixed center", and then claims that these two models are equivalent. In the first part of this paper, we study the Principia to determine how the elder Newton would more carefully describe the polygonal limit and tangent deflected models. From these more careful descriptions, we then create Equivalence Assumption (The Elder), a precise interpretation of Equivalence Assumption (The Younger) as it might have been restated by Newton, after say 1687. We then review certain portions of the Waste Book and the Principia to make the case that, although Newton never restates nor even alludes to the Equivalence Assumption after his youthful Waste Book entry, still the polygonal limit and tangent deflected models, as well as an unspoken belief in their equivalence, infuse Newton's work on orbital motion. In particular, we show that the persuasiveness of the argument for the Area Property in Proposition 1 of the Principia depends crucially on the validity of Equivalence Assumption (The Elder). After this case is made, we present the mathematical analysis required to establish the validity of the Equivalence Assumption (The Elder). Finally, to illustrate the fundamental nature of the resulting theorem, the Equivalence Theorem as we call it, we present three significant applications: we use the Equivalence Theorem first to clarify and resolve questions related to Leibniz's "polygonal model" of one-body motion; then to repair Newton's argument for the Area Property in Proposition 1; and finally to clarify and resolve questions related to the transition from impulsive to continuous forces in "De motu" and the Principia.

Imbalance of Ecosystems and the Modified Newton's 3 Laws of Change

NASA Astrophysics Data System (ADS)

Lin, H.

2013-12-01

Sustainability calls for the unity of human knowledge that bridges the present "two cultures" gulf between the sciences and the humanities, and the transition from the age of machine to the age of the environment quests for harmony with nature (so-called eco-civilization). Ecosystems are fundamentally different from machines, where individual components contain complex organisms instead of identical nonliving entities. Because of heterogeneity, diversity, self-organization, and openness, imbalances abound in nature. These are reflected in entropy increase over time (S > 0) and gradient persistence over space (F > 0). In this paper, three modified Newton's laws of change for ecosystems are suggested, and examples of imbalances from landscape-soil-water-ecosystem-climate will be illustrated. ● Newton's 1st law of motion: ∑F=0 → dv/dt=0. i.e., if net force acting on an object is zero, then the object's velocity remains unchanged. Modified Newton's 1st law of change (imbalance #1): ∑F>0 → dv/dt≥0. i.e., unavoidable forcing exists in nature (∑F>0), thus change always happens; however, with inertia/resistance in some systems or minimum threshold needed to change, dv/dt≥0. ● Newton's 2nd law of motion: ∑F=ma. i.e., acceleration is inversely proportional to body mass. Modified Newton's 2nd law of change (imbalance #2): ∑F≠ma. i.e., either 1) it is hard to make change because of resilience, self-adjustment, nonlinearity of interactions-feedbacks in living systems (∑F≥ma), or 2) there is possible threshold behavior or sudden collapse of a system (∑F

Airfoil optimization for unsteady flows with application to high-lift noise reduction

NASA Astrophysics Data System (ADS)

Rumpfkeil, Markus Peer

The use of steady-state aerodynamic optimization methods in the computational fluid dynamic (CFD) community is fairly well established. In particular, the use of adjoint methods has proven to be very beneficial because their cost is independent of the number of design variables. The application of numerical optimization to airframe-generated noise, however, has not received as much attention, but with the significant quieting of modern engines, airframe noise now competes with engine noise. Optimal control techniques for unsteady flows are needed in order to be able to reduce airframe-generated noise. In this thesis, a general framework is formulated to calculate the gradient of a cost function in a nonlinear unsteady flow environment via the discrete adjoint method. The unsteady optimization algorithm developed in this work utilizes a Newton-Krylov approach since the gradient-based optimizer uses the quasi-Newton method BFGS, Newton's method is applied to the nonlinear flow problem, GMRES is used to solve the resulting linear problem inexactly, and last but not least the linear adjoint problem is solved using Bi-CGSTAB. The flow is governed by the unsteady two-dimensional compressible Navier-Stokes equations in conjunction with a one-equation turbulence model, which are discretized using structured grids and a finite difference approach. The effectiveness of the unsteady optimization algorithm is demonstrated by applying it to several problems of interest including shocktubes, pulses in converging-diverging nozzles, rotating cylinders, transonic buffeting, and an unsteady trailing-edge flow. In order to address radiated far-field noise, an acoustic wave propagation program based on the Ffowcs Williams and Hawkings (FW-H) formulation is implemented and validated. The general framework is then used to derive the adjoint equations for a novel hybrid URANS/FW-H optimization algorithm in order to be able to optimize the shape of airfoils based on their calculated far-field pressure fluctuations. Validation and application results for this novel hybrid URANS/FW-H optimization algorithm show that it is possible to optimize the shape of an airfoil in an unsteady flow environment to minimize its radiated far-field noise while maintaining good aerodynamic performance.

Newton's Strange Collisions.

ERIC Educational Resources Information Center

Erlichson, Herman

1995-01-01

Discusses Newton's apparent oversight of the role of energy considerations in collisions between two spherical bodies related to the third corollary of his "Laws of Motion." Investigates several theories that provide solutions to the mysterious oversight. (LZ)

Newton-Cartan gravity and torsion

NASA Astrophysics Data System (ADS)

Bergshoeff, Eric; Chatzistavrakidis, Athanasios; Romano, Luca; Rosseel, Jan

2017-10-01

We compare the gauging of the Bargmann algebra, for the case of arbitrary torsion, with the result that one obtains from a null-reduction of General Relativity. Whereas the two procedures lead to the same result for Newton-Cartan geometry with arbitrary torsion, the null-reduction of the Einstein equations necessarily leads to Newton-Cartan gravity with zero torsion. We show, for three space-time dimensions, how Newton-Cartan gravity with arbitrary torsion can be obtained by starting from a Schrödinger field theory with dynamical exponent z = 2 for a complex compensating scalar and next coupling this field theory to a z = 2 Schrödinger geometry with arbitrary torsion. The latter theory can be obtained from either a gauging of the Schrödinger algebra, for arbitrary torsion, or from a null-reduction of conformal gravity.

Newton, Goethe and the process of perception: an approach to design

NASA Astrophysics Data System (ADS)

Platts, Jim

2006-06-01

Whereas Newton traced a beam of white light passing through a prism and fanning out into the colours of the rainbow as it was refracted, Goethe looked through a prism and was concerned with understanding what his eye subjectively saw. He created a sequence of experiments which produced what appeared to be anomalies in Newton's theory. What he was carefully illustrating concerns limitations accepted when following a scientifically objective approach. Newton was concerned with the description of 'facts' derived from the analysis of observations. Goethe was concerned with the synthesis of meaning. He then went on to describe subjective techniques for training 'the mind's eye' to work efficiently in the subjective world of the imagination. Derided as 'not science', what he was actually describing is the skill which is central to creative design.

Newton Methods for Large Scale Problems in Machine Learning

ERIC Educational Resources Information Center

Hansen, Samantha Leigh

2014-01-01

The focus of this thesis is on practical ways of designing optimization algorithms for minimizing large-scale nonlinear functions with applications in machine learning. Chapter 1 introduces the overarching ideas in the thesis. Chapters 2 and 3 are geared towards supervised machine learning applications that involve minimizing a sum of loss…

The Dynamic Force Table

ERIC Educational Resources Information Center

Geddes, John B.; Black, Kelly

2008-01-01

We examine an experimental apparatus that is used to motivate the connections between the basic properties of vectors, potential functions, systems of nonlinear equations, and Newton's method for nonlinear systems of equations. The apparatus is an adaptation of a force table where we remove the center-pin and allow the center-ring to move freely.…

Descartes' Calculus of Subnormals: What Might Have Been

ERIC Educational Resources Information Center

Boudreaux, Gregory Mark; Walls, Jess E.

2013-01-01

Rene Descartes' method for finding tangents (equivalently, subnormals) depends on geometric and algebraic properties of a family of circles intersecting a given curve. It can be generalized to establish a calculus of subnormals, an alternative to the calculus of Newton and Leibniz. Here we prove subnormal counterparts of the well-known…

16 CFR 1207.5 - Design.

Code of Federal Regulations, 2011 CFR

2011-01-01

...±340 newtons/sq. meter) and the pallet does not tip over when in motion. Attach a felt pen or other... following methods or their equivalent: 1 See reference (f) of § 1207.11 for full discussion. (A) Motion..., feet and/or legs. The slider's starting reactions with the slide shall be only as strong as necessary...

16 CFR 1207.5 - Design.

Code of Federal Regulations, 2010 CFR

2010-01-01

...±340 newtons/sq. meter) and the pallet does not tip over when in motion. Attach a felt pen or other... following methods or their equivalent: 1 See reference (f) of § 1207.11 for full discussion. (A) Motion..., feet and/or legs. The slider's starting reactions with the slide shall be only as strong as necessary...

Gender, Science and Modernity in Seventeenth-Century England

ERIC Educational Resources Information Center

Watts, Ruth

2005-01-01

The seventeenth century in England, bounded by the scientific stimulus of Francis Bacon at the beginning and Isaac Newton at the end, seemingly saw a huge leap from the Aristotelian dialectic of the past to a reconstruction of knowledge based on inductive methods, empirical investigation and cooperative research. In mid-century, Puritan reformers…

Connecting in Space: Docking with the International Space Station. Educational Brief.

ERIC Educational Resources Information Center

National Aeronautics and Space Administration, Washington, DC.

This brief discusses the space shuttle and the docking procedures used with the International Space Station (ISS). Using this activity designed for grades 5-12, students demonstrate and identify procedures for determining the best method for completing the docking activity. Students will also study and identify Newton's Laws of Motion. A mockup…

NEWSUMT: A FORTRAN program for inequality constrained function minimization, users guide

NASA Technical Reports Server (NTRS)

Miura, H.; Schmit, L. A., Jr.

1979-01-01

A computer program written in FORTRAN subroutine form for the solution of linear and nonlinear constrained and unconstrained function minimization problems is presented. The algorithm is the sequence of unconstrained minimizations using the Newton's method for unconstrained function minimizations. The use of NEWSUMT and the definition of all parameters are described.

GRIZZLY

DOE Office of Scientific and Technical Information (OSTI.GOV)

2012-12-17

Grizzly is a simulation tool for assessing the effects of age-related degradation on systems, structures, and components of nuclear power plants. Grizzly is built on the MOOSE framework, and uses a Jacobian-free Newton Krylov method to obtain solutions to tightly coupled thermo-mechanical simulations. Grizzly runs on a wide range of hardware, from a single processor to massively parallel machines.

Applying the Socratic Method to Physics Education

NASA Astrophysics Data System (ADS)

Corcoran, Ed

2005-04-01

We have restructured University Physics I and II in accordance with methods that PER has shown to be effective, including a more interactive discussion- and activity-based curriculum based on the premise that developing understanding requires an interactive process in which students have the opportunity to talk through and think through ideas with both other students and the teacher. Studies have shown that in classes implementing this approach to teaching as compared to classes using a traditional approach, students have significantly higher gains on the Force Concept Inventory (FCI). This has been true in UPI. However, UPI FCI results seem to suggest that there is a significant conceptual hole in students' understanding of Newton's Second Law. Two labs in UPI which teach Newton's Second Law will be redesigned replacing more activity with students as a group talking through, thinking through, and answering conceptual questions asked by the TA. The results will be measured by comparing FCI results to those from previous semesters, coupled with interviews. The results will be analyzed, and we will attempt to understand why gains were or were not made.

A Differential Evolution Based Approach to Estimate the Shape and Size of Complex Shaped Anomalies Using EIT Measurements

NASA Astrophysics Data System (ADS)

Rashid, Ahmar; Khambampati, Anil Kumar; Kim, Bong Seok; Liu, Dong; Kim, Sin; Kim, Kyung Youn

EIT image reconstruction is an ill-posed problem, the spatial resolution of the estimated conductivity distribution is usually poor and the external voltage measurements are subject to variable noise. Therefore, EIT conductivity estimation cannot be used in the raw form to correctly estimate the shape and size of complex shaped regional anomalies. An efficient algorithm employing a shape based estimation scheme is needed. The performance of traditional inverse algorithms, such as the Newton Raphson method, used for this purpose is below par and depends upon the initial guess and the gradient of the cost functional. This paper presents the application of differential evolution (DE) algorithm to estimate complex shaped region boundaries, expressed as coefficients of truncated Fourier series, using EIT. DE is a simple yet powerful population-based, heuristic algorithm with the desired features to solve global optimization problems under realistic conditions. The performance of the algorithm has been tested through numerical simulations, comparing its results with that of the traditional modified Newton Raphson (mNR) method.

Achievement of learning outcome after implemented physical modules based on problem based learning

NASA Astrophysics Data System (ADS)

Isna, R.; Masykuri, M.; Sukarmin

2018-03-01

Implementation of Problem BasedLearning (PBL) modules can grow the students' thinking skills to solve the problems in daily life and equip the students into higher education levels. The purpose of this research is to know the achievement of learning outcome after implementation physics module based on PBL in Newton,s Law of Gravity. This research method use the experimental method with posttest only group design. To know the achievement of student learning outcomes was analyzed using t test through application of SPSS 18. Based on research result, it is found that the average of student learning outcomes after appliying physics module based on PBL has reached the minimal exhaustiveness criteria. In addition, students' scientific attitudes also improved at each meeting. Presentation activities which contained at learning sync are also able to practice speaking skills and broaden their knowledge. Looking at some shortcomings during the study, it is suggested the issues raised into learning should be a problem close to the life of students so that, the students are more active and enthusiastic in following the learning of physics.

Genetic algorithm-based improved DOA estimation using fourth-order cumulants

NASA Astrophysics Data System (ADS)

Ahmed, Ammar; Tufail, Muhammad

2017-05-01

Genetic algorithm (GA)-based direction of arrival (DOA) estimation is proposed using fourth-order cumulants (FOC) and ESPRIT principle which results in Multiple Invariance Cumulant ESPRIT algorithm. In the existing FOC ESPRIT formulations, only one invariance is utilised to estimate DOAs. The unused multiple invariances (MIs) must be exploited simultaneously in order to improve the estimation accuracy. In this paper, a fitness function based on a carefully designed cumulant matrix is developed which incorporates MIs present in the sensor array. Better DOA estimation can be achieved by minimising this fitness function. Moreover, the effectiveness of Newton's method as well as GA for this optimisation problem has been illustrated. Simulation results show that the proposed algorithm provides improved estimation accuracy compared to existing algorithms, especially in the case of low SNR, less number of snapshots, closely spaced sources and high signal and noise correlation. Moreover, it is observed that the optimisation using Newton's method is more likely to converge to false local optima resulting in erroneous results. However, GA-based optimisation has been found attractive due to its global optimisation capability.

Use of Picard and Newton iteration for solving nonlinear ground water flow equations

USGS Publications Warehouse

Mehl, S.

2006-01-01

This study examines the use of Picard and Newton iteration to solve the nonlinear, saturated ground water flow equation. Here, a simple three-node problem is used to demonstrate the convergence difficulties that can arise when solving the nonlinear, saturated ground water flow equation in both homogeneous and heterogeneous systems with and without nonlinear boundary conditions. For these cases, the characteristic types of convergence patterns are examined. Viewing these convergence patterns as orbits of an attractor in a dynamical system provides further insight. It is shown that the nonlinearity that arises from nonlinear head-dependent boundary conditions can cause more convergence difficulties than the nonlinearity that arises from flow in an unconfined aquifer. Furthermore, the effects of damping on both convergence and convergence rate are investigated. It is shown that no single strategy is effective for all problems and how understanding pitfalls and merits of several methods can be helpful in overcoming convergence difficulties. Results show that Picard iterations can be a simple and effective method for the solution of nonlinear, saturated ground water flow problems.

Optimal Control of Micro Grid Operation Mode Seamless Switching Based on Radau Allocation Method

NASA Astrophysics Data System (ADS)

Chen, Xiaomin; Wang, Gang

2017-05-01

The seamless switching process of micro grid operation mode directly affects the safety and stability of its operation. According to the switching process from island mode to grid-connected mode of micro grid, we establish a dynamic optimization model based on two grid-connected inverters. We use Radau allocation method to discretize the model, and use Newton iteration method to obtain the optimal solution. Finally, we implement the optimization mode in MATLAB and get the optimal control trajectory of the inverters.

Decoupling the Stationary Navier-Stokes-Darcy System with the Beavers-Joseph-Saffman Interface Condition

DOE PAGES

Cao, Yong; Chu, Yuchuan; He, Xiaoming; ...

2013-01-01

This paper proposes a domain decomposition method for the coupled stationary Navier-Stokes and Darcy equations with the Beavers-Joseph-Saffman interface condition in order to improve the efficiency of the finite element method. The physical interface conditions are directly utilized to construct the boundary conditions on the interface and then decouple the Navier-Stokes and Darcy equations. Newton iteration will be used to deal with the nonlinear systems. Numerical results are presented to illustrate the features of the proposed method.

An efficient and general numerical method to compute steady uniform vortices

NASA Astrophysics Data System (ADS)

Luzzatto-Fegiz, Paolo; Williamson, Charles H. K.

2011-07-01

Steady uniform vortices are widely used to represent high Reynolds number flows, yet their efficient computation still presents some challenges. Existing Newton iteration methods become inefficient as the vortices develop fine-scale features; in addition, these methods cannot, in general, find solutions with specified Casimir invariants. On the other hand, available relaxation approaches are computationally inexpensive, but can fail to converge to a solution. In this paper, we overcome these limitations by introducing a new discretization, based on an inverse-velocity map, which radically increases the efficiency of Newton iteration methods. In addition, we introduce a procedure to prescribe Casimirs and remove the degeneracies in the steady vorticity equation, thus ensuring convergence for general vortex configurations. We illustrate our methodology by considering several unbounded flows involving one or two vortices. Our method enables the computation, for the first time, of steady vortices that do not exhibit any geometric symmetry. In addition, we discover that, as the limiting vortex state for each flow is approached, each family of solutions traces a clockwise spiral in a bifurcation plot consisting of a velocity-impulse diagram. By the recently introduced "IVI diagram" stability approach [Phys. Rev. Lett. 104 (2010) 044504], each turn of this spiral is associated with a loss of stability for the steady flows. Such spiral structure is suggested to be a universal feature of steady, uniform-vorticity flows.

VizieR Online Data Catalog: XMM-Newton Bright Serendipitous Survey (Della Ceca+, 2004)

NASA Astrophysics Data System (ADS)

Della Ceca, R.; Maccacaro, T.; Caccianiga, A.; Severgnini, P.; Braito, V.; Barcons, X.; Carrera, F. J.; Watson, M. G.; Tedds, J. A.; Brunner, H.; Lehmann, I.; Page, M. J.; Lamer, G.; Schwope, A.

2005-09-01

We present here "The XMM-Newton Bright Serendipitous Survey", composed of two flux-limited samples: the XMM-Newton Bright Source Sample (BSS, hereafter) and the XMM-Newton "Hard" Bright Source Sample (HBSS, hereafter) having a flux limit of fX~7x10-14erg/cm2/s in the 0.5-4.5keV and 4.5-7.5keV energy band, respectively. After discussing the main goals of this project and the survey strategy, we present the basic data on a complete sample of 400 X-ray sources (389 of them belong to the BSS, 67 to the HBSS with 56 X-ray sources in common) derived from the analysis of 237 suitable XMM-Newton fields (211 for the HBSS). At the flux limit of the survey we cover a survey area of 28.10 (25.17 for the HBSS) sq. deg. The extragalactic number-flux relationships (in the 0.5-4.5keV and in the 4.5-7.5keV energy bands) are in good agreement with previous and new results making us confident about the correctness of data selection and analysis. (5 data files).

Can Newton's Third Law Be "Derived" from the Second?

NASA Astrophysics Data System (ADS)

Gangopadhyaya, Asim; Harrington, James

2017-04-01

Newton's laws have engendered much discussion over several centuries. Today, the internet is awash with a plethora of information on this topic. We find many references to Newton's laws, often discussions of various types of misunderstandings and ways to explain them. Here we present an intriguing example that shows an assumption hidden in Newton's third law that is often overlooked. As is well known, the first law defines an inertial frame of reference and the second law determines the acceleration of a particle in such a frame due to an external force. The third law describes forces exerted on each other in a two-particle system, and allows us to extend the second law to a system of particles. Students are often taught that the three laws are independent. Here we present an example that challenges this assumption. At first glance, it seems to show that, at least for a special case, the third law follows from the second law. However, a careful examination of the assumptions demonstrates that is not quite the case. Ultimately, the example does illustrate the significance of the concept of mass in linking Newton's dynamical principles.

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

NASA Astrophysics Data System (ADS)

Alkharji, Mohammed N.

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

Dark Flows in Newton Crater Extending During Summer Six-Image Sequence

NASA Image and Video Library

2011-08-04

This image comes from observations of Newton crater by the HiRISE camera onboard NASA Mars Reconnaissance Orbiter where features appear and incrementally grow during warm seasons and fade in cold seasons.

Students' Concepts of Force: The Importance of Understanding Newton's Third Law.

ERIC Educational Resources Information Center

Brown, David E.

1989-01-01

Reports various misconceptions of Newton's third law obtained from interviews and written tests of high school students. Suggests putting emphasis on the third law in physics teaching. Ten references are listed. (YP)

Patterning by area selective oxidation

DOEpatents

Nam, Chang-Yong; Kamcev, Jovan; Black, Charles T.; Grubbs, Robert

2015-12-29

Technologies are described for methods for producing a pattern of a material on a substrate. The methods may comprise receiving a patterned block copolymer on a substrate. The patterned block copolymer may include a first polymer block domain and a second polymer block domain. The method may comprise exposing the patterned block copolymer to a light effective to oxidize the first polymer block domain in the patterned block copolymer. The method may comprise applying a precursor to the block copolymer. The precursor may infuse into the oxidized first polymer block domain and generate the material. The method may comprise applying a removal agent to the block copolymer. The removal agent may be effective to remove the first polymer block domain and the second polymer block domain from the substrate, and may not be effective to remove the material in the oxidized first polymer block domain.

An improved algorithm for the determination of the system paramters of a visual binary by least squares

NASA Astrophysics Data System (ADS)

Xu, Yu-Lin

The problem of computing the orbit of a visual binary from a set of observed positions is reconsidered. It is a least squares adjustment problem, if the observational errors follow a bias-free multivariate Gaussian distribution and the covariance matrix of the observations is assumed to be known. The condition equations are constructed to satisfy both the conic section equation and the area theorem, which are nonlinear in both the observations and the adjustment parameters. The traditional least squares algorithm, which employs condition equations that are solved with respect to the uncorrelated observations and either linear in the adjustment parameters or linearized by developing them in Taylor series by first-order approximation, is inadequate in our orbit problem. D.C. Brown proposed an algorithm solving a more general least squares adjustment problem in which the scalar residual function, however, is still constructed by first-order approximation. Not long ago, a completely general solution was published by W.H Jefferys, who proposed a rigorous adjustment algorithm for models in which the observations appear nonlinearly in the condition equations and may be correlated, and in which construction of the normal equations and the residual function involves no approximation. This method was successfully applied in our problem. The normal equations were first solved by Newton's scheme. Practical examples show that this converges fast if the observational errors are sufficiently small and the initial approximate solution is sufficiently accurate, and that it fails otherwise. Newton's method was modified to yield a definitive solution in the case the normal approach fails, by combination with the method of steepest descent and other sophisticated algorithms. Practical examples show that the modified Newton scheme can always lead to a final solution. The weighting of observations, the orthogonal parameters and the efficiency of a set of adjustment parameters are also considered. The definition of efficiency is revised.

XMM-Newton Mobile Web Application

NASA Astrophysics Data System (ADS)

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

2013-10-01

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

The General History of Astronomy

NASA Astrophysics Data System (ADS)

Taton, René; Wilson, Curtis; Hoskin, editor Michael, , General

2009-09-01

Part V. Early Phases in the Reception of Newton's Theory: 14. The vortex theory in competition with Newtonian celestial dynamics Eric J. Aiton; 15. The shape of the Earth Seymour L. Chapin; 16. Clairaut and the motion of the lunar apse: The inverse-square law undergoes a test Craig B. Waff; 17. The precession of the equinoxes from Newton to d'Alembert and Euler Curtis Wilson; 18. The solar tables of Lacaille and the lunar tables of Mayer Eric G. Forbes and Curtis Wilson; 19. Predicting the mid-eighteenth-century return of Halley's Comet Craig B. Waff; Part VI. Celestial Mechanics During the Eighteenth Century: 20. The problem of perturbation analytically treated: Euler, Clairaut, d'Alembert Curtis Wilson; 21. The work of Lagrange in celestial mechanics Curtis Wilson; 22. Laplace Bruno Morando; Part VII. Observational Astronomy and the Application of Theory in the Late Eighteenth and Early Nineteenth Century: 23. Measuring solar parallax: The Venus transits of 1761 and 1769 and their nineteenth-century sequels Albert Van Helden; 24. The discovery of Uranus, the Titius-Bode and the asteroids Michael Hoskin; 25. Eighteenth-and nineteenth century developments in the theory and practice of orbit determination Brian G. Marsden; 26. The introduction of statistical reasoning into astronomy: from Newton to Poincaré Oscar Sheynin; 27. Astronomy and the theory of errors: from the method of averages to the method of least squares F. Schmeidler; Part VIII. The Development of Theory During the Nineteenth Century: 28. The golden age of celestial mechanics Bruno Morando; Part IX. The Application of Celestial Mechanics to the Solar System to the End of the Nineteenth Century: 29. Three centuries of lunar and planetary ephemerides and tables Bruno Morando; 30. Satellite ephemerides to 1900 Yoshihide Kozai; Illustrations; Combined index for Parts 2A and 2B.

The calibration of read-out-streak photometry in the XMM-Newton Optical Monitor and the construction of a bright-source catalogue

NASA Astrophysics Data System (ADS)

Page, M. J.; Chan, N.; Breeveld, A. A.; Talavera, A.; Yershov, V.; Kennedy, T.; Kuin, N. P. M.; Hancock, B.; Smith, P. J.; Carter, M.

2017-04-01

The dynamic range of the XMM-Newton Optical Monitor (XMM-OM) is limited at the bright end by coincidence loss, the superposition of multiple photons in the individual frames recorded from its micro-channel-plate (MCP) intensified charge-coupled device (CCD) detector. One way to overcome this limitation is to use photons that arrive during the frame transfer of the CCD, forming vertical read-out streaks for bright sources. We calibrate these read-out streaks for photometry of bright sources observed with XMM-OM. The bright-source limit for read-out-streak photometry is set by the recharge time of the MCPs. For XMM-OM, we find that the MCP recharge time is 5.5 × 10-4 s. We determine that the effective bright limits for read-out-streak photometry with XMM-OM are approximately 1.5 mag brighter than the bright-source limits for normal aperture photometry in full-frame images. This translates into bright-source limits in Vega magnitudes of UVW2=7.1, UVM2=8.0, UVW1=9.4, U=10.5, B=11.5, V=10.2, and White=12.5 for data taken early in the mission. The limits brighten by up to 0.2 mag, depending on filter, over the course of the mission as the detector ages. The method is demonstrated by deriving UVW1 photometry for the symbiotic nova RR Telescopii, and the new photometry is used to constrain the e-folding time of its decaying ultraviolet (UV) emission. Using the read-out-streak method, we obtain photometry for 50 per cent of the missing UV source measurements in version 2.1 of the XMM-Newton Serendipitous UV Source Survey catalogue.

Conservative tightly-coupled simulations of stochastic multiscale systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Taverniers, Søren; Pigarov, Alexander Y.; Tartakovsky, Daniel M., E-mail: dmt@ucsd.edu

2016-05-15

Multiphysics problems often involve components whose macroscopic dynamics is driven by microscopic random fluctuations. The fidelity of simulations of such systems depends on their ability to propagate these random fluctuations throughout a computational domain, including subdomains represented by deterministic solvers. When the constituent processes take place in nonoverlapping subdomains, system behavior can be modeled via a domain-decomposition approach that couples separate components at the interfaces between these subdomains. Its coupling algorithm has to maintain a stable and efficient numerical time integration even at high noise strength. We propose a conservative domain-decomposition algorithm in which tight coupling is achieved by employingmore » either Picard's or Newton's iterative method. Coupled diffusion equations, one of which has a Gaussian white-noise source term, provide a computational testbed for analysis of these two coupling strategies. Fully-converged (“implicit”) coupling with Newton's method typically outperforms its Picard counterpart, especially at high noise levels. This is because the number of Newton iterations scales linearly with the amplitude of the Gaussian noise, while the number of Picard iterations can scale superlinearly. At large time intervals between two subsequent inter-solver communications, the solution error for single-iteration (“explicit”) Picard's coupling can be several orders of magnitude higher than that for implicit coupling. Increasing the explicit coupling's communication frequency reduces this difference, but the resulting increase in computational cost can make it less efficient than implicit coupling at similar levels of solution error, depending on the communication frequency of the latter and the noise strength. This trend carries over into higher dimensions, although at high noise strength explicit coupling may be the only computationally viable option.« less

AZTEC: A parallel iterative package for the solving linear systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hutchinson, S.A.; Shadid, J.N.; Tuminaro, R.S.

1996-12-31

We describe a parallel linear system package, AZTEC. The package incorporates a number of parallel iterative methods (e.g. GMRES, biCGSTAB, CGS, TFQMR) and preconditioners (e.g. Jacobi, Gauss-Seidel, polynomial, domain decomposition with LU or ILU within subdomains). Additionally, AZTEC allows for the reuse of previous preconditioning factorizations within Newton schemes for nonlinear methods. Currently, a number of different users are using this package to solve a variety of PDE applications.

Advancing Detached-Eddy Simulation

DTIC Science & Technology

2007-01-01

fluxes leads to an improvement in the stability of the solution . This matrix is solved iteratively using a symmetric Gauss - Seidel procedure. Newtons sub...model (TLM) is a zonal approach, proposed by Balaras and Benocci (5) and Balaras et al. (4). The method involved the solution of filtered Navier...LES mesh. The method was subsequently used by Cabot (6) and Diurno et al. (7) to obtain the solution of the flow over a backward facing step and by

First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

DTIC Science & Technology

2014-03-01

accuracy, with rapid convergence over each physical time step, typically less than five Newton iter - ations. 1 Contents 1 Introduction 3 2 Hyperbolic...however, we employ the Gauss - Seidel (GS) relaxation, which is also an O(N) method for the discretization arising from hyperbolic advection-diffusion system...advection-diffusion scheme. The linear dependency of the iterations on Table 1: Boundary layer problem ( Convergence criteria: Residuals < 10−8.) log10Re

A 2D electrostatic PIC code for the Mark III Hypercube

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ferraro, R.D.; Liewer, P.C.; Decyk, V.K.

We have implemented a 2D electrostastic plasma particle in cell (PIC) simulation code on the Caltech/JPL Mark IIIfp Hypercube. The code simulates plasma effects by evolving in time the trajectories of thousands to millions of charged particles subject to their self-consistent fields. Each particle`s position and velocity is advanced in time using a leap frog method for integrating Newton`s equations of motion in electric and magnetic fields. The electric field due to these moving charged particles is calculated on a spatial grid at each time by solving Poisson`s equation in Fourier space. These two tasks represent the largest part ofmore » the computation. To obtain efficient operation on a distributed memory parallel computer, we are using the General Concurrent PIC (GCPIC) algorithm previously developed for a 1D parallel PIC code.« less

Colloid micro-Newton thruster development for the ST7-DRS and LISA missions

NASA Technical Reports Server (NTRS)

Ziemer, John K.; Gamero-Castano, Manuel; Hruby, Vlad; Spence, Doug; Demmons, Nate; McCormick, Ryan; Roy, Tom

2005-01-01

We present recent progress and development of the Busek Colloid Micro-Newton Thruster (CMNT) for the Space Technology 7 Disturbance Reduction System (ST7-DRS) and Laser Interferometer Space Antenna (LISA) Missions.

Demonstrating Newton's Third Law: Changing Aristotelian Viewpoints.

ERIC Educational Resources Information Center

Roach, Linda E.

1992-01-01

Suggests techniques to help eliminate students' misconceptions involving Newton's Third Law. Approaches suggested include teaching physics from a historical perspective, using computer programs with simulations, rewording the law, drawing free-body diagrams, and using demonstrations and examples. (PR)

On Time-II: Newton's Time.

ERIC Educational Resources Information Center

Raju, C. K.

1991-01-01

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

Science and Society: The Case of Acceptance of Newtonian Optics in the Eighteenth Century

NASA Astrophysics Data System (ADS)

Silva, Cibelle Celestino; Moura, Breno Arsioli

2012-09-01

The present paper presents a historical study on the acceptance of Newton's corpuscular theory of light in the early eighteenth century. Isaac Newton first published his famous book Opticks in 1704. After its publication, it became quite popular and was an almost mandatory presence in cultural life of Enlightenment societies. However, Newton's optics did not become popular only via his own words and hands, but also via public lectures and short books with scientific contents devoted to general public (including women) that emerged in the period as a sort of entertainment business. Lectures and writers stressed the inductivist approach to the study of nature and presented Newton's ideas about optics as they were consensual among natural philosophers in the period. The historical case study presented in this paper illustrates relevant aspects of nature of science, which can be explored by students of physics on undergraduate level or in physics teacher training programs.

Bohlin transformation: the hidden symmetry that connects Hooke to Newton

NASA Astrophysics Data System (ADS)

Saggio, Maria Luisa

2013-01-01

Hooke's name is familiar to students of mechanics thanks to the law of force that bears his name. Less well-known is the influence his findings had on the founder of mechanics, Isaac Newton. In a lecture given some twenty years ago, W Arnol'd pointed out the outstanding contribution to science made by Hooke, and also noted the controversial issue of the attribution of important discoveries to Newton that were actually inspired by Hooke. It therefore seems ironic that the two most famous force laws, named after Hooke and Newton, are two geometrical aspects of the same law. This relationship, together with other illuminating aspects of Newtonian mechanics, is described in Arnol'd's book and is worth remembering in standard physics courses. In this didactical paper the duality of the two forces is expounded and an account of the more recent contributions to the subject is given.

The Newtonian Moment - Isaac Newton and the Making of Modern Culture

NASA Astrophysics Data System (ADS)

Feingold, Mordechai

2004-12-01

Isaac Newton is a legendary figure whose mythical dimension threatens to overshadow the actual man. The story of the apple falling from the tree may or may not be true, but Isaac Newton's revolutionary discoveries and their importance to the Enlightenment era and beyond are undeniable. The Newtonian Moment , a companion volume to a forthcoming exhibition by the New York Public Library, investigates the effect that Newton's theories and discoveries had, not only on the growth of science, but also on the very shape of modern culture and thought. Newton's scientific work at Cambridge was groundbreaking. From his optical experiments with prisms during the 1660s to the publication of both Principia (1687) and Opticks (1704), Newton's achievements were widely disseminated, inciting tremendous interest and excitement. Newtonianism developed into a worldview marked by many tensions: between modernity and the old guard, between the humanities and science, and the public battles between great minds. The Newtonian Moment illuminates the many facets of his colossal accomplishments, as well as the debates over the kind of knowledge that his accomplishments engendered. The book contributes to a greater understanding of the world today by offering a panoramic view of the profound impact of Newtonianism on the science, literature, art, and religion of the Enlightenment. Copiously illustrated with items drawn from the collections of the New York Public Library as well as numerous other libraries and museums, The Newtonian Moment enlightens its audience with a guided and in-depth look at the man, his world, and his enduring legacy.

Minimum Description Length Block Finder, a Method to Identify Haplotype Blocks and to Compare the Strength of Block Boundaries

PubMed Central

Mannila, H.; Koivisto, M.; Perola, M.; Varilo, T.; Hennah, W.; Ekelund, J.; Lukk, M.; Peltonen, L.; Ukkonen, E.

2003-01-01

We describe a new probabilistic method for finding haplotype blocks that is based on the use of the minimum description length (MDL) principle. We give a rigorous definition of the quality of a segmentation of a genomic region into blocks and describe a dynamic programming algorithm for finding the optimal segmentation with respect to this measure. We also describe a method for finding the probability of a block boundary for each pair of adjacent markers: this gives a tool for evaluating the significance of each block boundary. We have applied the method to the published data of Daly and colleagues. The results expose some problems that exist in the current methods for the evaluation of the significance of predicted block boundaries. Our method, MDL block finder, can be used to compare block borders in different sample sets, and we demonstrate this by applying the MDL-based method to define the block structure in chromosomes from population isolates. PMID:12761696

Minimum description length block finder, a method to identify haplotype blocks and to compare the strength of block boundaries.

PubMed

Mannila, H; Koivisto, M; Perola, M; Varilo, T; Hennah, W; Ekelund, J; Lukk, M; Peltonen, L; Ukkonen, E

2003-07-01

We describe a new probabilistic method for finding haplotype blocks that is based on the use of the minimum description length (MDL) principle. We give a rigorous definition of the quality of a segmentation of a genomic region into blocks and describe a dynamic programming algorithm for finding the optimal segmentation with respect to this measure. We also describe a method for finding the probability of a block boundary for each pair of adjacent markers: this gives a tool for evaluating the significance of each block boundary. We have applied the method to the published data of Daly and colleagues. The results expose some problems that exist in the current methods for the evaluation of the significance of predicted block boundaries. Our method, MDL block finder, can be used to compare block borders in different sample sets, and we demonstrate this by applying the MDL-based method to define the block structure in chromosomes from population isolates.

Discovery Science: Newton All around You.

ERIC Educational Resources Information Center

Prigo, Robert; Humphrey, Gregg

1993-01-01

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

I ``Saw'' Newton's Three Laws

NASA Astrophysics Data System (ADS)

Shaw, Mike

2012-11-01

Would you like to build an inexpensive, highly visible, quickly assembled device that dramatically illustrates Newton's three laws of motion? This model incorporates sturdiness, high-profile visibility, and a student interest component that is sure to capture and hold their attention.

Apparatus for Teaching Physics: Giant Newton's Rings.

ERIC Educational Resources Information Center

Cheung, Kai-yin; Mak, Se-yuen

1996-01-01

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

Newtons's Thermometry: The Role of Radiation.

ERIC Educational Resources Information Center

French, A. P.

1993-01-01

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

The Earth, the Moon and Conservation of Momentum

ERIC Educational Resources Information Center

Brunt, Marjorie; Brunt, Geoff

2013-01-01

We consider the application of both conservation of momentum and Newton's laws to the Moon in an assumed circular orbit about the Earth. The inadequacy of some texts in applying Newton's laws is considered.

Dome and Barchan Dunes in Newton Crater

NASA Image and Video Library

2014-10-01

This observation from NASA Mars Reconnaissance Orbiter shows both dome and barchan dunes in a small sand dune field on the floor of Newton Crater, an approximately 300 kilometer 130 mile wide crater in the Southern hemisphere of Mars.

The Use of Blended Learning to Facilitate Critical Thinking in Entry Level Occupational Therapy Students

ERIC Educational Resources Information Center

Rodriguez, Eva L.

2009-01-01

The popularity of using online instruction (both in blended and complete distance learning) in higher education settings is increasing (Appana, 2008; Newton, 2006; Oh, 2006). Occupational therapy educators are using blended learning methods under the assumption that this learning platform will facilitate in their students the required level of…

Roller Coasters without Differential Equations--A Newtonian Approach to Constrained Motion

ERIC Educational Resources Information Center

Muller, Rainer

2010-01-01

Within the context of Newton's equation, we present a simple approach to the constrained motion of a body forced to move along a specified trajectory. Because the formalism uses a local frame of reference, it is simpler than other methods, making more complicated geometries accessible. No Lagrangian multipliers are necessary to determine the…

Application of Newtonian Physics to Predict the Speed of a Gravity Racer

ERIC Educational Resources Information Center

Driscoll, H. F.; Bullas, A. M.; King, C. E.; Senior, T.; Haake, S. J.; Hart, J.

2016-01-01

Gravity racing can be studied using numerical solutions to the equations of motion derived from Newton's second law. This allows students to explore the physics of gravity racing and to understand how design and course selection influences vehicle speed. Using Euler's method, we have developed a spreadsheet application that can be used to predict…

A Comparative Study of Two Types of Ball-on-Ball Collision

ERIC Educational Resources Information Center

White, Colin

2017-01-01

This paper describes three methods of measuring the coefficient of restitution (CoR) for two different types of ball-on-ball collision. The first collision type (for which two different CoR measurement procedures are described) is a static, hanging steel ball forming part of a Newton's cradle arrangement, which is then hit by its adjacent…

On nonsingular potentials of Cox-Thompson inversion scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Palmai, Tamas; Apagyi, Barnabas

2010-02-15

We establish a condition for obtaining nonsingular potentials using the Cox-Thompson inverse scattering method with one phase shift. The anomalous singularities of the potentials are avoided by maintaining unique solutions of the underlying Regge-Newton integral equation for the transformation kernel. As a by-product, new inequality sequences of zeros of Bessel functions are discovered.

An incremental block-line-Gauss-Seidel method for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Napolitano, M.; Walters, R. W.

1985-01-01

A block-line-Gauss-Seidel (LGS) method is developed for solving the incompressible and compressible Navier-Stokes equations in two dimensions. The method requires only one block-tridiagonal solution process per iteration and is consequently faster per step than the linearized block-ADI methods. Results are presented for both incompressible and compressible separated flows: in all cases the proposed block-LGS method is more efficient than the block-ADI methods. Furthermore, for high Reynolds number weakly separated incompressible flow in a channel, which proved to be an impossible task for a block-ADI method, solutions have been obtained very efficiently by the new scheme.

Modified Interior Distance Functions (Theory and Methods)

NASA Technical Reports Server (NTRS)

Polyak, Roman A.

1995-01-01

In this paper we introduced and developed the theory of Modified Interior Distance Functions (MIDF's). The MIDF is a Classical Lagrangian (CL) for a constrained optimization problem which is equivalent to the initial one and can be obtained from the latter by monotone transformation both the objective function and constraints. In contrast to the Interior Distance Functions (IDF's), which played a fundamental role in Interior Point Methods (IPM's), the MIDF's are defined on an extended feasible set and along with center, have two extra tools, which control the computational process: the barrier parameter and the vector of Lagrange multipliers. The extra tools allow to attach to the MEDF's very important properties of Augmented Lagrangeans. One can consider the MIDFs as Interior Augmented Lagrangeans. It makes MIDF's similar in spirit to Modified Barrier Functions (MBF's), although there is a fundamental difference between them both in theory and methods. Based on MIDF's theory, Modified Center Methods (MCM's) have been developed and analyzed. The MCM's find an unconstrained minimizer in primal space and update the Lagrange multipliers, while both the center and the barrier parameter can be fixed or updated at each step. The MCM's convergence was investigated, and their rate of convergence was estimated. The extension of the feasible set and the special role of the Lagrange multipliers allow to develop MCM's, which produce, in case of nondegenerate constrained optimization, a primal and dual sequences that converge to the primal-dual solutions with linear rate, even when both the center and the barrier parameter are fixed. Moreover, every Lagrange multipliers update shrinks the distance to the primal dual solution by a factor 0 less than gamma less than 1 which can be made as small as one wants by choosing a fixed interior point as a 'center' and a fixed but large enough barrier parameter. The numericai realization of MCM leads to the Newton MCM (NMCM). The approximation for the primal minimizer one finds by Newton Method followed by the Lagrange multipliers update. Due to the MCM convergence, when both the center and the barrier parameter are fixed, the condition of the MDF Hessism and the neighborhood of the primal ninimizer where Newton method is 'well' defined remains stable. It contributes to both the complexity and the numerical stability of the NMCM.

Atomism from Newton to Dalton.

ERIC Educational Resources Information Center

Schofield, Robert E.

1981-01-01

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

Isaac Newton Olympics.

ERIC Educational Resources Information Center

Cox, Carol

2001-01-01

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

Gravitation in material media

NASA Astrophysics Data System (ADS)

Ridgely, Charles T.

2011-03-01

When two gravitating bodies reside in a material medium, Newton's law of universal gravitation must be modified to account for the presence of the medium. A modified expression of Newton's law is known in the literature, but lacks a clear connection with existing gravitational theory. Newton's law in the presence of a homogeneous material medium is herein derived on the basis of classical, Newtonian gravitational theory and by a general relativistic use of Archimedes' principle. It is envisioned that the techniques presented herein will be most useful to graduate students and those undergraduate students having prior experience with vector analysis and potential theory.

How Pressure Became a Scalar, Not a Vector

NASA Astrophysics Data System (ADS)

Chalmers, Alan

2018-06-01

The gradual emergence of a science of hydrostatics during the course of the seventeenth century is testament to the fact that a technical concept of pressure that was up to the task was far from obvious. The first published version of a theory of hydrostatics containing the essentials of the modern theory appeared in book 2 of Isaac Newton's Principia. Newton derived the propositions of hydrostatics from a definition of a fluid as a medium unable to withstand a distorting force. Newton's reasoning required that pressure be understood as a force per unit area acting on either side of imaginary planes within the body of a fluid. For a fluid in equilibrium, the forces at some location within a fluid are independent of the orientation of such planes. As Newton came to realize, within the body of a liquid, pressure acts equally in all directions so that there is no resultant pressing in any direction. Pressure has an intensity but not a direction. In modern terms, it is a scalar, not a vector. Although earlier scholars such as Simon Stevin, Blaise Pascal, and Robert Boyle helped set the scene for Newton's innovations, they were unable to transcend the common sense of pressure as a directed force acting on the solid surfaces bounding a fluid.

Testing Bayesian and heuristic predictions of mass judgments of colliding objects

PubMed Central

Sanborn, Adam N.

2014-01-01

Mass judgments of colliding objects have been used to explore people's understanding of the physical world because they are ecologically relevant, yet people display biases that are most easily explained by a small set of heuristics. Recent work has challenged the heuristic explanation, by producing the same biases from a model that copes with perceptual uncertainty by using Bayesian inference with a prior based on the correct combination rules from Newtonian mechanics (noisy Newton). Here I test the predictions of the leading heuristic model (Gilden and Proffitt, 1989) against the noisy Newton model using a novel manipulation of the standard mass judgment task: making one of the objects invisible post-collision. The noisy Newton model uses the remaining information to predict above-chance performance, while the leading heuristic model predicts chance performance when one or the other final velocity is occluded. An experiment using two different types of occlusion showed better-than-chance performance and response patterns that followed the predictions of the noisy Newton model. The results demonstrate that people can make sensible physical judgments even when information critical for the judgment is missing, and that a Bayesian model can serve as a guide in these situations. Possible algorithmic-level accounts of this task that more closely correspond to the noisy Newton model are explored. PMID:25206345

How Pressure Became a Scalar, Not a Vector

NASA Astrophysics Data System (ADS)

Chalmers, Alan

2018-04-01

The gradual emergence of a science of hydrostatics during the course of the seventeenth century is testament to the fact that a technical concept of pressure that was up to the task was far from obvious. The first published version of a theory of hydrostatics containing the essentials of the modern theory appeared in book 2 of Isaac Newton's Principia. Newton derived the propositions of hydrostatics from a definition of a fluid as a medium unable to withstand a distorting force. Newton's reasoning required that pressure be understood as a force per unit area acting on either side of imaginary planes within the body of a fluid. For a fluid in equilibrium, the forces at some location within a fluid are independent of the orientation of such planes. As Newton came to realize, within the body of a liquid, pressure acts equally in all directions so that there is no resultant pressing in any direction. Pressure has an intensity but not a direction. In modern terms, it is a scalar, not a vector. Although earlier scholars such as Simon Stevin, Blaise Pascal, and Robert Boyle helped set the scene for Newton's innovations, they were unable to transcend the common sense of pressure as a directed force acting on the solid surfaces bounding a fluid.

Fully Implicit, Nonlinear 3D Extended Magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Chacon, Luis; Knoll, Dana

2003-10-01

Extended magnetohydrodynamics (XMHD) includes nonideal effects such as nonlinear, anisotropic transport and two-fluid (Hall) effects. XMHD supports multiple, separate time scales that make explicit time differencing approaches extremely inefficient. While a fully implicit implementation promises efficiency without sacrificing numerical accuracy,(D. A. Knoll et al., phJ. Comput. Phys.) 185 (2), 583-611 (2003) the nonlinear nature of the XMHD system and the numerical stiffness associated with the fast waves make this endeavor difficult. Newton-Krylov methods are, however, ideally suited for such a task. These synergistically combine Newton's method for nonlinear convergence, and Krylov techniques to solve the associated Jacobian (linear) systems. Krylov methods can be implemented Jacobian-free and can be preconditioned for efficiency. Successful preconditioning strategies have been developed for 2D incompressible resistive(L. Chacón et al., phJ. Comput. Phys). 178 (1), 15- 36 (2002) and Hall(L. Chacón and D. A. Knoll, phJ. Comput. Phys.), 188 (2), 573-592 (2003) MHD models. These are based on ``physics-based'' ideas, in which knowledge of the physics is exploited to derive well-conditioned (diagonally-dominant) approximations to the original system that are amenable to optimal solver technologies (multigrid). In this work, we will describe the status of the extension of the 2D preconditioning ideas for a 3D compressible, single-fluid XMHD model.

Applications of Sharp Interface Method for Flow Dynamics, Scattering and Control Problems

DTIC Science & Technology

2012-07-30

Reynolds number, Advances in Applied Mathematics and Mechanics, to appear. 17. K. Ito and K. Kunisch, Optimal Control of Parabolic Variational ...provides more precise and detailed sensitivity of the solution and describes the dynamical change due to the variation in the Reynolds number. The immersed... Inequalities , Journal de Math. Pures et Appl, 93 (2010), no. 4, 329-360. 18. K. Ito and K. Kunisch, Semi-smooth Newton Methods for Time-Optimal Control for a

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

HyeongKae Park; Robert Nourgaliev; Vincent Mousseau

2008-07-01

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

Galileo on Two Wheels: Why Does Newton Make Me Keep Pedaling This Thing?

NASA Astrophysics Data System (ADS)

Gardner, Dave; Osenbach, Kate; Connolly, Joseph

2010-02-01

As part of an effort to use examples for the bicycle to illustrate basic physics principles, we have been exploring the application of Newton's laws of motion to a moving bicycle. In particular, we have developed methods to measure the bicycle's two primary forces of resistance-tire rolling resistance and air resistance on rider and bike. With the use of minimal equipment such as stopwatches and bicycle speedometers, we have obtained data that provide a very good fit to simple models and closed differential equation solutions. We have also found that the bicycle affords a simple, low tech, and convenient method to study concepts of terminal velocity and rolling resistance. Just as Galileo made use of inclined planes to study falling objects, we used gently sloping hills to determine forces on the moving bicycle. Our methods make use of a novel technique to determine the bicycle and rider frontal cross sectional area. We hope our methods and results will be of interest to students of physics and mathematics and to the general cycling community. We have found it is possible for a cyclist to easily measure; without the use of expensive time in a wind tunnel; the effects of various body positions on wind resistance. This paper also examines the force and power consequences of riding at high speeds. )

Movement of Landslide Triggered by Bedrock Exfiltration with Nonuniform Pore Pressure Distribution

NASA Astrophysics Data System (ADS)

Jan, C. D.; Jian, Z. K.

2014-12-01

Landslides are common phenomena of sediment movement in mountain areas and usually pose severe risks to people and infrastructure around those areas. The occurrence of landslides is influenced by groundwater dynamics and bedrock characteristics as well as by rainfall and soil-mass properties. The bedrock may drain or contribute to groundwater in the overlying soil mass, depending on the hydraulic conductivity, degree of fracturing, saturation, and hydraulic head. Our study here is based on the model proposed by Iverson (2005). The model describes the relation between landslide displacement and the shear-zone dilation/contraction of pore water pressure. To study landslide initiation and movement, a block soil mass sliding down an inclined beck-rock plane is governed by Newton's equation of motion, while both the bedrock exfiltration and excess pore pressure induced by dilatation or contraction of basal shear zone are described by diffusion equations. The Chebyshev collocation method was used to transform the governing equations to a system of first-order ordinary differential equations, without the need of iteration. Then a fourth-order Runge-Kutta scheme was used to solve these ordinary differential equations. The effects of nonuniform bedrock exfiltration pressure distributions, such as the delayed peak, central peak, and advanced peak distributions, on the time of landslide initiation and the speed of landslide movement were compared and discussed.

Implicit time accurate simulation of unsteady flow

NASA Astrophysics Data System (ADS)

van Buuren, René; Kuerten, Hans; Geurts, Bernard J.

2001-03-01

Implicit time integration was studied in the context of unsteady shock-boundary layer interaction flow. With an explicit second-order Runge-Kutta scheme, a reference solution to compare with the implicit second-order Crank-Nicolson scheme was determined. The time step in the explicit scheme is restricted by both temporal accuracy as well as stability requirements, whereas in the A-stable implicit scheme, the time step has to obey temporal resolution requirements and numerical convergence conditions. The non-linear discrete equations for each time step are solved iteratively by adding a pseudo-time derivative. The quasi-Newton approach is adopted and the linear systems that arise are approximately solved with a symmetric block Gauss-Seidel solver. As a guiding principle for properly setting numerical time integration parameters that yield an efficient time accurate capturing of the solution, the global error caused by the temporal integration is compared with the error resulting from the spatial discretization. Focus is on the sensitivity of properties of the solution in relation to the time step. Numerical simulations show that the time step needed for acceptable accuracy can be considerably larger than the explicit stability time step; typical ratios range from 20 to 80. At large time steps, convergence problems that are closely related to a highly complex structure of the basins of attraction of the iterative method may occur. Copyright

Optimal sixteenth order convergent method based on quasi-Hermite interpolation for computing roots.

PubMed

Zafar, Fiza; Hussain, Nawab; Fatimah, Zirwah; Kharal, Athar

2014-01-01

We have given a four-step, multipoint iterative method without memory for solving nonlinear equations. The method is constructed by using quasi-Hermite interpolation and has order of convergence sixteen. As this method requires four function evaluations and one derivative evaluation at each step, it is optimal in the sense of the Kung and Traub conjecture. The comparisons are given with some other newly developed sixteenth-order methods. Interval Newton's method is also used for finding the enough accurate initial approximations. Some figures show the enclosure of finitely many zeroes of nonlinear equations in an interval. Basins of attractions show the effectiveness of the method.

Prolonged Ponding Episode in C-Newton Crater in Recent Geological Times on Mars

NASA Technical Reports Server (NTRS)

Grin, E. A.; Cabrol, N. A.; Wynn-Williams, D. D.

2001-01-01

We present the morphological evidence that supports the existence of a lake in a recent past in C-Newton crater. We assess the astrobiological potential of this environment. Additional information is contained in the original extended abstract.

Atmospheric Blocking and Intercomparison of Objective Detection Methods: Flow Field Characteristics

NASA Astrophysics Data System (ADS)

Pinheiro, M. C.; Ullrich, P. A.; Grotjahn, R.

2017-12-01

A number of objective methods for identifying and quantifying atmospheric blocking have been developed over the last couple of decades, but there is variable consensus on the resultant blocking climatology. This project examines blocking climatologies as produced by three different methods: two anomaly-based methods, and the geopotential height gradient method of Tibaldi and Molteni (1990). The results highlight the differences in blocking that arise from the choice of detection method, with emphasis on the physical characteristics of the flow field and the subsequent effects on the blocking patterns that emerge.

Characterization and Implementation of a Real-World Target Tracking Algorithm on Field Programmable Gate Arrays with Kalman Filter Test Case

DTIC Science & Technology

2008-03-01

to predict its exact position. To locate Ceres, Carl Friedrich Gauss , a mere 24 years old at the time, developed a method called least-squares...dividend to produce the quotient. This method converges to the reciprocal quadratically [11]. For the special case of: 1 H × P (:, :, k)×H ′ + R (3.9) the...high-speed computation of reciprocals within the overall system. The Newton-Raphson method is also expanded for use in calculat- ing square-roots in

Iterative algorithms for computing the feedback Nash equilibrium point for positive systems

NASA Astrophysics Data System (ADS)

Ivanov, I.; Imsland, Lars; Bogdanova, B.

2017-03-01

The paper studies N-player linear quadratic differential games on an infinite time horizon with deterministic feedback information structure. It introduces two iterative methods (the Newton method as well as its accelerated modification) in order to compute the stabilising solution of a set of generalised algebraic Riccati equations. The latter is related to the Nash equilibrium point of the considered game model. Moreover, we derive the sufficient conditions for convergence of the proposed methods. Finally, we discuss two numerical examples so as to illustrate the performance of both of the algorithms.

Ramsey's method of separated oscillating fields and its application to gravitationally induced quantum phase shifts

DOE Office of Scientific and Technical Information (OSTI.GOV)

Abele, H.; Jenke, T.; Leeb, H.

2010-03-15

We propose to apply Ramsey's method of separated oscillating fields to the spectroscopy of the quantum states in the gravity potential above a horizontal mirror. This method allows a precise measurement of quantum mechanical phaseshifts of a Schroedinger wave packet bouncing off a hard surface in the gravitational field of the Earth. Measurements with ultracold neutrons will offer a sensitivity to Newton's law or hypothetical short-ranged interactions, which is about 21 orders of magnitude below the energy scale of electromagnetism.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weston, Brian T.

This dissertation focuses on the development of a fully-implicit, high-order compressible ow solver with phase change. The work is motivated by laser-induced phase change applications, particularly by the need to develop large-scale multi-physics simulations of the selective laser melting (SLM) process in metal additive manufacturing (3D printing). Simulations of the SLM process require precise tracking of multi-material solid-liquid-gas interfaces, due to laser-induced melting/ solidi cation and evaporation/condensation of metal powder in an ambient gas. These rapid density variations and phase change processes tightly couple the governing equations, requiring a fully compressible framework to robustly capture the rapid density variations ofmore » the ambient gas and the melting/evaporation of the metal powder. For non-isothermal phase change, the velocity is gradually suppressed through the mushy region by a variable viscosity and Darcy source term model. The governing equations are discretized up to 4th-order accuracy with our reconstructed Discontinuous Galerkin spatial discretization scheme and up to 5th-order accuracy with L-stable fully implicit time discretization schemes (BDF2 and ESDIRK3-5). The resulting set of non-linear equations is solved using a robust Newton-Krylov method, with the Jacobian-free version of the GMRES solver for linear iterations. Due to the sti nes associated with the acoustic waves and thermal and viscous/material strength e ects, preconditioning the GMRES solver is essential. A robust and scalable approximate block factorization preconditioner was developed, which utilizes the velocity-pressure (vP) and velocity-temperature (vT) Schur complement systems. This multigrid block reduction preconditioning technique converges for high CFL/Fourier numbers and exhibits excellent parallel and algorithmic scalability on classic benchmark problems in uid dynamics (lid-driven cavity ow and natural convection heat transfer) as well as for laser-induced phase change problems in 2D and 3D.« less

Measurement Uncertainty of Dew-Point Temperature in a Two-Pressure Humidity Generator

NASA Astrophysics Data System (ADS)

Martins, L. Lages; Ribeiro, A. Silva; Alves e Sousa, J.; Forbes, Alistair B.

2012-09-01

This article describes the measurement uncertainty evaluation of the dew-point temperature when using a two-pressure humidity generator as a reference standard. The estimation of the dew-point temperature involves the solution of a non-linear equation for which iterative solution techniques, such as the Newton-Raphson method, are required. Previous studies have already been carried out using the GUM method and the Monte Carlo method but have not discussed the impact of the approximate numerical method used to provide the temperature estimation. One of the aims of this article is to take this approximation into account. Following the guidelines presented in the GUM Supplement 1, two alternative approaches can be developed: the forward measurement uncertainty propagation by the Monte Carlo method when using the Newton-Raphson numerical procedure; and the inverse measurement uncertainty propagation by Bayesian inference, based on prior available information regarding the usual dispersion of values obtained by the calibration process. The measurement uncertainties obtained using these two methods can be compared with previous results. Other relevant issues concerning this research are the broad application to measurements that require hygrometric conditions obtained from two-pressure humidity generators and, also, the ability to provide a solution that can be applied to similar iterative models. The research also studied the factors influencing both the use of the Monte Carlo method (such as the seed value and the convergence parameter) and the inverse uncertainty propagation using Bayesian inference (such as the pre-assigned tolerance, prior estimate, and standard deviation) in terms of their accuracy and adequacy.

Intuitive Physics.

ERIC Educational Resources Information Center

McCloskey, Michael

1983-01-01

Although Newton's laws of motion are well known, studies have shown that many people have misconceptions about the motions of objects. Subjects of these studies tend to follow a theory held in the three centuries before Newton (impetus theory). This theory and studies examining misconceptions about motion are discussed. (JN)

Analysis of Newton's Third Law Questions on the Force Concepts Inventory at Georgia State University

NASA Astrophysics Data System (ADS)

Oakley, Christopher; Thoms, Brian

2012-03-01

A major emphasis of the Physics Education Research program at Georgia State University is an effort to assess and improve students' understanding of Newton's Laws concepts. As part of these efforts the Force Concepts Inventory (FCI) has been given to students in both the algebra-based and calculus-based introductory physics sequences. In addition, the algebra-based introductory physics sequence is taught in both a SCALE-UP and a traditional lecture format. The results of the FCI have been analyzed by individual question and also as categorized by content. The analysis indicates that students in both algebra and calculus-based courses are successful at overcoming Aristotelian misconceptions regarding Newton's Third Law (N3) in the context of a stationary system. However, students are less successful on N3 questions involving objects in constant motion or accelerating. Interference between understanding of Newton's Second and Third Laws as well as other possible explanations for lower student performance on N3 questions involving non-stationary objects will be discussed.

The role of competing knowledge structures in undermining learning: Newton's second and third laws

NASA Astrophysics Data System (ADS)

Low, David J.; Wilson, Kate F.

2017-01-01

We investigate the development of student understanding of Newton's laws using a pre-instruction test (the Force Concept Inventory), followed by a series of post-instruction tests and interviews. While some students' somewhat naive, pre-existing models of Newton's third law are largely eliminated following a semester of teaching, we find that a particular inconsistent model is highly resilient to, and may even be strengthened by, instruction. If test items contain words that cue students to think of Newton's second law, then students are more likely to apply a "net force" approach to solving problems, even if it is inappropriate to do so. Additional instruction, reinforcing physical concepts in multiple settings and from multiple sources, appears to help students develop a more connected and consistent level of understanding. We recommend explicitly encouraging students to check their work for consistency with physical principles, along with the standard checks for dimensionality and order of magnitude, to encourage reflective and rigorous problem solving.

Implementation of an improved adaptive-implicit method in a thermal compositional simulator

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tan, T.B.

1988-11-01

A multicomponent thermal simulator with an adaptive-implicit-method (AIM) formulation/inexact-adaptive-Newton (IAN) method is presented. The final coefficient matrix retains the original banded structure so that conventional iterative methods can be used. Various methods for selection of the eliminated unknowns are tested. AIM/IAN method has a lower work count per Newtonian iteration than fully implicit methods, but a wrong choice of unknowns will result in excessive Newtonian iterations. For the problems tested, the residual-error method described in the paper for selecting implicit unknowns, together with the IAN method, had an improvement of up to 28% of the CPU time over the fullymore » implicit method.« less

Efficiency trade-offs of steady-state methods using FEM and FDM. [iterative solutions for nonlinear flow equations

NASA Technical Reports Server (NTRS)

Gartling, D. K.; Roache, P. J.

1978-01-01

The efficiency characteristics of finite element and finite difference approximations for the steady-state solution of the Navier-Stokes equations are examined. The finite element method discussed is a standard Galerkin formulation of the incompressible, steady-state Navier-Stokes equations. The finite difference formulation uses simple centered differences that are O(delta x-squared). Operation counts indicate that a rapidly converging Newton-Raphson-Kantorovitch iteration scheme is generally preferable over a Picard method. A split NOS Picard iterative algorithm for the finite difference method was most efficient.

A unified convergence theory of a numerical method, and applications to the replenishment policies.

PubMed

Mi, Xiang-jiang; Wang, Xing-hua

2004-01-01

In determining the replenishment policy for an inventory system, some researchers advocated that the iterative method of Newton could be applied to the derivative of the total cost function in order to get the optimal solution. But this approach requires calculation of the second derivative of the function. Avoiding this complex computation we use another iterative method presented by the second author. One of the goals of this paper is to present a unified convergence theory of this method. Then we give a numerical example to show the application of our theory.

An improved computer program for calculating the theoretical performance parameters of a propeller type wind turbine. An appendix to the final report on feasibility of using wind power to pump irrigation water (Texas). [PROP Code

DOE Office of Scientific and Technical Information (OSTI.GOV)

Barieau, R.E.

1977-03-01

The PROP Program of Wilson and Lissaman has been modified by adding the Newton-Raphson Method and a Step Wise Search Method, as options for the method of solution. In addition, an optimization method is included. Twist angles, tip speed ratio and the pitch angle may be varied to produce maximum power coefficient. The computer program listing is presented along with sample input and output data. Further improvements to the program are discussed.

Newton's Method and the Wada Property: A Graphical Approach

ERIC Educational Resources Information Center

Frame, Michael; Neger, Nial

2007-01-01

Imagine trying to paint a picture with three colors--say red, blue, and yellow--with a blue region between any red and yellow regions, a red region between any blue and yellow regions, and a yellow region between any red and blue regions, down to infinitely fine details. Regions arranged in this way satisfy what is called the Wada property. At…

Measuring, Understanding, and Responding to Covert Social Networks: Passive and Active Tomography

DTIC Science & Technology

2017-11-29

Methods for generating a random sample of networks with desired properties are important tools for the analysis of social , biological, and information...on Theoretical Foundations for Statistical Network Analysis at the Isaac Newton Institute for Mathematical Sciences at Cambridge U. (organized by...Approach SOCIAL SCIENCES STATISTICS EECS Problems span three disciplines Scientific focus is needed at the interfaces

Uncalibrated Three-Dimensional Microrobot Control

DTIC Science & Technology

2016-05-11

environment is essential. While many groups have already demonstrated the ability to control a microrobot in three dimensions through magnetically...or “uncalibrated”) controller which can dynamically adjust to changes in the operation environment is essential. While many groups have already...error squared and drive the microrobot to the desired position, [2]. The control signal is computed via a quasi -Newton method operating an

Effect of Prior Exposure at Elevated Temperatures on Tensile Properties and Stress-Strain Behavior of Four Non-Oxide Ceramic Matrix Composites

DTIC Science & Technology

2015-06-18

x 4 inch square plates. All six plates of each COIC CMC were cut from the same mother panel of the respective material system. Definitive 30...Bibliography [1] W. L. Harper, Isaac Newton’s Scientific Method: Turning Data Into Evidence about Gravity and Cosmology , New York: Oxford University

[Odontology and the beginning of cartesianism (1673--1650) (Rene Descartes)].

PubMed

Gysel, C

1979-01-01

In the seventeenth century the universities of the Netherlands underwent the influence of Descartes in all the faculties. In medicine three periods can be distinguished: in the first, pathology and therapy are still galenic; the second, by the application of the cartesian method, triumphs in physiology; and the third, corrected by the views of Newton is integrated in a moderate biomechanism.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

HyeongKae Park; Robert Nourgaliev; Vincent Mousseau

2008-07-01

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

{lambda} elements for singular problems in CFD: Viscoelastic fluids

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wong, K.K.; Surana, K.S.

1996-10-01

This paper presents two dimensional {lambda} element formulation for viscoelastic fluid flow containing point singularities in the flow field. The flow of viscoelastic fluid even without singularities are a difficult class of problems for increasing Deborah number or Weissenburg number due to increased dominance of convective terms and thus increased hyperbolicity. In the present work the equations of fluid motion and the constitutive laws are recast in the form of a first order system of coupled equations with the use of auxiliary variables. The velocity, pressure and stresses are interpolated using equal order C{sup 0} {lambda} element approximations. The Leastmore » Squares Finite Element Method (LSFEM) is used to construct the integral form (error functional I) corresponding to these equations. The error functional is constructed by taking the integrated sum of the squares of the errors or residuals (over the whole discretization) resulting when the element approximation is substituted into these equations. The conditions resulting from the minimization of the error functional are satisfied by using Newton`s method with line search. LSFEM has much superior performance when dealing with non-linear and convection dominated problems.« less

Mapping the hot gas temperature in galaxy clusters using X-ray and Sunyaev-Zel'dovich imaging

NASA Astrophysics Data System (ADS)

Adam, R.; Arnaud, M.; Bartalucci, I.; Ade, P.; André, P.; Beelen, A.; Benoît, A.; Bideaud, A.; Billot, N.; Bourdin, H.; Bourrion, O.; Calvo, M.; Catalano, A.; Coiffard, G.; Comis, B.; D'Addabbo, A.; Désert, F.-X.; Doyle, S.; Ferrari, C.; Goupy, J.; Kramer, C.; Lagache, G.; Leclercq, S.; Macías-Pérez, J.-F.; Maurogordato, S.; Mauskopf, P.; Mayet, F.; Monfardini, A.; Pajot, F.; Pascale, E.; Perotto, L.; Pisano, G.; Pointecouteau, E.; Ponthieu, N.; Pratt, G. W.; Revéret, V.; Ritacco, A.; Rodriguez, L.; Romero, C.; Ruppin, F.; Schuster, K.; Sievers, A.; Triqueneaux, S.; Tucker, C.; Zylka, R.

2017-10-01

We propose a method to map the temperature distribution of the hot gas in galaxy clusters that uses resolved images of the thermal Sunyaev-Zel'dovich (tSZ) effect in combination with X-ray data. Application to images from the New IRAM KIDs Array (NIKA) and XMM-Newton allows us to measure and determine the spatial distribution of the gas temperature in the merging cluster MACS J0717.5+3745, at z = 0.55. Despite the complexity of the target object, we find a good morphological agreement between the temperature maps derived from X-ray spectroscopy only - using XMM-Newton (TXMM) and Chandra (TCXO) - and the new gas-mass-weighted tSZ+X-ray imaging method (TSZX). We correlate the temperatures from tSZ+X-ray imaging and those from X-ray spectroscopy alone and find that TSZX is higher than TXMM and lower than TCXO by 10% in both cases. Our results are limited by uncertainties in the geometry of the cluster gas, contamination from kinetic SZ ( 10%), and the absolute calibration of the tSZ map (7%). Investigation using a larger sample of clusters would help minimise these effects.

Interpreting Recoil for Undergraduate Students

NASA Astrophysics Data System (ADS)

Elsayed, Tarek A.

2012-04-01

The phenomenon of recoil is usually explained to students in the context of Newton's third law. Typically, when a projectile is fired, the recoil of the launch mechanism is interpreted as a reaction to the ejection of the smaller projectile. The same phenomenon is also interpreted in the context of the conservation of linear momentum, which is closely related to Newton's third law. Since the actual microscopic causes of recoil differ from one problem to another, some students (and teachers) may not be satisfied with understanding recoil through the principles of conservation of linear momentum and Newton's third law. For these students, the origin of the recoil motion should be presented in more depth.

Schools Can Provide Help for the Children of Divorce.

ERIC Educational Resources Information Center

Holzman, Terry

1984-01-01

Since the mid-1970s, Newton, Massachusetts, schools have developed support groups and curricular offerings to help children of divorced parents. Newton's Ad-Hoc Committee on Separation and Divorce, developed under the leadership of John Cullinane, now serves as a systemwide clearinghouse for teacher resources. (JBM)

Steady potential solver for unsteady aerodynamic analyses

NASA Technical Reports Server (NTRS)

Hoyniak, Dan

1994-01-01

Development of a steady flow solver for use with LINFLO was the objective of this report. The solver must be compatible with LINFLO, be composed of composite mesh, and have transonic capability. The approaches used were: (1) steady flow potential equations written in nonconservative form; (2) Newton's Method; (3) implicit, least-squares, interpolation method to obtain finite difference equations; and (4) matrix inversion routines from LINFLO. This report was given during the NASA LeRC Workshop on Forced Response in Turbomachinery in August of 1993.

Teaching students about informatics and astronomy using real data for detection of asteroids

NASA Astrophysics Data System (ADS)

Boldea, A. L.; Vaduvescu, O.

2017-09-01

In this paper we approach the astronomy teaching process for students in computer sciences through a controlled investigation method using real astronomical data, including data reduction and quality control of the astrometry of near-Earth asteroids. The method used data collected on the Isaac Newton Telescope located at the ORM observatory on the island of La Palma in the Spanish Canary Islands and was successfully tested with a group of students in their second year of study.

Numerical solution of the two-dimensional time-dependent incompressible Euler equations

NASA Technical Reports Server (NTRS)

Whitfield, David L.; Taylor, Lafayette K.

1994-01-01

A numerical method is presented for solving the artificial compressibility form of the 2D time-dependent incompressible Euler equations. The approach is based on using an approximate Riemann solver for the cell face numerical flux of a finite volume discretization. Characteristic variable boundary conditions are developed and presented for all boundaries and in-flow out-flow situations. The system of algebraic equations is solved using the discretized Newton-relaxation (DNR) implicit method. Numerical results are presented for both steady and unsteady flow.

Adaptive Implicit Non-Equilibrium Radiation Diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Philip, Bobby; Wang, Zhen; Berrill, Mark A

2013-01-01

We describe methods for accurate and efficient long term time integra- tion of non-equilibrium radiation diffusion systems: implicit time integration for effi- cient long term time integration of stiff multiphysics systems, local control theory based step size control to minimize the required global number of time steps while control- ling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton-Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.

Ambiguity resolution in systems using Omega for position location

NASA Technical Reports Server (NTRS)

Frenkel, G.; Gan, D. G.

1974-01-01

The lane ambiguity problem prevents the utilization of the Omega system for many applications such as locating buoys and balloons. The method of multiple lines of position introduced herein uses signals from four or more Omega stations for ambiguity resolution. The coordinates of the candidate points are determined first through the use of the Newton iterative procedure. Subsequently, a likelihood function is generated for each point, and the ambiguity is resolved by selecting the most likely point. The method was tested through simulation.

On pendulums and air resistance. The mathematics and physics of Denis Diderot

NASA Astrophysics Data System (ADS)

Dahmen, Sílvio R.

2015-09-01

In this article Denis Diderot's Fifth Memoir of 1748 on the problem of a pendulum damped by air resistance is discussed in its historical as well as mathematical aspects. Diderot wrote the Memoir in order to clarify an assumption Newton made without further justification in the first pages of the Principia in connection with an experiment to verify the Third Law of Motion using colliding pendulums. To explain the differences between experimental and theoretical values, Newton assumed the bob was traversed. By giving Newton's arguments a mathematical scaffolding and recasting his geometrical reasoning in the language of differential calculus, Diderot provided a step-by-step solution guide to the problem. He also showed that Newton's assumption was equivalent to having assumed F R proportional the bob's velocity v, when in fact he believed it should be replaced by F R ˜ v 2. His solution is presented in full detail and his results are compared to those obtained from a Lindstedt-Poincaré approximation for an oscillator with quadratic damping. It is shown that, up to a prefactor, both results coincide. Some results that follow from his approach are presented and discussed for the first time. Experimental evidence to support Diderot's or Newton's claims is discussed together with the limitations of their solutions. Some misprints in the original memoir are pointed out.

High-bandwidth prefetcher for high-bandwidth memory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mehta, Sanyam; Kohn, James Robert; Ernst, Daniel Jonathan

A method for prefetching data into a cache is provided. The method allocates an outstanding request buffer ("ORB"). The method stores in an address field of the ORB an address and a number of blocks. The method issues prefetch requests for a degree number of blocks starting at the address. When a prefetch response is received for all the prefetch requests, the method adjusts the address of the next block to prefetch and adjusts the number of blocks remaining to be retrieved and then issues prefetch requests for a degree number of blocks starting at the adjusted address. The prefetchingmore » pauses when a maximum distance between the reads of the prefetched blocks and the last prefetched block is reached. When a read request for a prefetched block is received, the method resumes prefetching when a resume criterion is satisfied.« less

On multilevel RBF collocation to solve nonlinear PDEs arising from endogenous stochastic volatility models

NASA Astrophysics Data System (ADS)

Bastani, Ali Foroush; Dastgerdi, Maryam Vahid; Mighani, Abolfazl

2018-06-01

The main aim of this paper is the analytical and numerical study of a time-dependent second-order nonlinear partial differential equation (PDE) arising from the endogenous stochastic volatility model, introduced in [Bensoussan, A., Crouhy, M. and Galai, D., Stochastic equity volatility related to the leverage effect (I): equity volatility behavior. Applied Mathematical Finance, 1, 63-85, 1994]. As the first step, we derive a consistent set of initial and boundary conditions to complement the PDE, when the firm is financed by equity and debt. In the sequel, we propose a Newton-based iteration scheme for nonlinear parabolic PDEs which is an extension of a method for solving elliptic partial differential equations introduced in [Fasshauer, G. E., Newton iteration with multiquadrics for the solution of nonlinear PDEs. Computers and Mathematics with Applications, 43, 423-438, 2002]. The scheme is based on multilevel collocation using radial basis functions (RBFs) to solve the resulting locally linearized elliptic PDEs obtained at each level of the Newton iteration. We show the effectiveness of the resulting framework by solving a prototypical example from the field and compare the results with those obtained from three different techniques: (1) a finite difference discretization; (2) a naive RBF collocation and (3) a benchmark approximation, introduced for the first time in this paper. The numerical results confirm the robustness, higher convergence rate and good stability properties of the proposed scheme compared to other alternatives. We also comment on some possible research directions in this field.

Variation block-based genomics method for crop plants.

PubMed

Kim, Yul Ho; Park, Hyang Mi; Hwang, Tae-Young; Lee, Seuk Ki; Choi, Man Soo; Jho, Sungwoong; Hwang, Seungwoo; Kim, Hak-Min; Lee, Dongwoo; Kim, Byoung-Chul; Hong, Chang Pyo; Cho, Yun Sung; Kim, Hyunmin; Jeong, Kwang Ho; Seo, Min Jung; Yun, Hong Tai; Kim, Sun Lim; Kwon, Young-Up; Kim, Wook Han; Chun, Hye Kyung; Lim, Sang Jong; Shin, Young-Ah; Choi, Ik-Young; Kim, Young Sun; Yoon, Ho-Sung; Lee, Suk-Ha; Lee, Sunghoon

2014-06-15

In contrast with wild species, cultivated crop genomes consist of reshuffled recombination blocks, which occurred by crossing and selection processes. Accordingly, recombination block-based genomics analysis can be an effective approach for the screening of target loci for agricultural traits. We propose the variation block method, which is a three-step process for recombination block detection and comparison. The first step is to detect variations by comparing the short-read DNA sequences of the cultivar to the reference genome of the target crop. Next, sequence blocks with variation patterns are examined and defined. The boundaries between the variation-containing sequence blocks are regarded as recombination sites. All the assumed recombination sites in the cultivar set are used to split the genomes, and the resulting sequence regions are termed variation blocks. Finally, the genomes are compared using the variation blocks. The variation block method identified recurring recombination blocks accurately and successfully represented block-level diversities in the publicly available genomes of 31 soybean and 23 rice accessions. The practicality of this approach was demonstrated by the identification of a putative locus determining soybean hilum color. We suggest that the variation block method is an efficient genomics method for the recombination block-level comparison of crop genomes. We expect that this method will facilitate the development of crop genomics by bringing genomics technologies to the field of crop breeding.

Demonstrating Kinematics and Newton's Laws in a Jump

ERIC Educational Resources Information Center

Kamela, Martin

2007-01-01

When students begin the study of Newton's laws they are generally comfortable with static equilibrium type problems, but dynamic examples where forces are not constant are more challenging. The class exercise presented here helps students to develop an intuitive grasp of both the position-velocity-acceleration relation and the force-acceleration…

Newton's Apple: 15th Season. Free Educational Materials.

ERIC Educational Resources Information Center

Twin Cities Public Television, St. Paul, MN.

This guide helps teachers use the 15th season of the television program "Newton's Apple" in the classroom and lists show segments on asthma, car engines, glacier climbing, glass blowing, glaucoma, gliders, gold mine, greenhouse effect, kids on Mars, lightning, "Lost World" dinosaurs, mammoth dig, NASA robots, Novocain (TM),…

XMM-Newton X-ray spectra of V407 Lup (Nova Lup 2016)

NASA Astrophysics Data System (ADS)

Ness, Jan-Uwe; Starrfield, Sumner; Woodward, Chick E.; Kuin, Paul; Page, Kim; Beardmore, Andy; Osborne, Julian; Sala, Gloria; Hernanz, Margarita; Orio, Marina; Williams, Bob

2017-09-01

Nova Lup 2016 (V407 Lup) was observed by XMM-Newton from 11 March 2017, 11:45 to 17:08 UT, 168 days after outburst (ATel #9538) with an exposure duration of 23,000 s. The EPIC pn was operated in Timing Mode with Medium filter.

Newton Algorithms for Analytic Rotation: An Implicit Function Approach

ERIC Educational Resources Information Center

Boik, Robert J.

2008-01-01

In this paper implicit function-based parameterizations for orthogonal and oblique rotation matrices are proposed. The parameterizations are used to construct Newton algorithms for minimizing differentiable rotation criteria applied to "m" factors and "p" variables. The speed of the new algorithms is compared to that of existing algorithms and to…

A Class Inquiry into Newton's Cooling Curve

ERIC Educational Resources Information Center

Bartholow, Martin

2007-01-01

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

Newton's Law of Cooling Revisited

ERIC Educational Resources Information Center

Vollmer, M.

2009-01-01

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

Fighting domestic violence. Newton-Wellesley Hospital Hospital recognized as major advocate, role model for others.

PubMed

1996-01-01

Newton-Wellesley Hospital wanted to be a major advocate in its region in detecting and helping domestic violence victims. It did that and more. In the process, the hospital attained significant recognition as a leader in community benefits and advocacy for domestic violence survivors.

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

ERIC Educational Resources Information Center

Wichmann, Sue, Ed.

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

Gamow on Newton: Another Look at Centripetal Acceleration

ERIC Educational Resources Information Center

Corrao, Christian

2012-01-01

Presented here is an adaptation of George Gamow's derivation of the centripetal acceleration formula as it applies to Earth's orbiting Moon. The derivation appears in Gamows short but engaging book "Gravity", first published in 1962, and is essentially a distillation of Newton's work. While "TPT" contributors have offered several insightful…

Proving Newton Right or Wrong with Blur Photography

ERIC Educational Resources Information Center

Davidhazy, Andrew

2012-01-01

Sir Isaac Newton determined that the acceleration constant for gravity was 32 ft./per/sec/sec. This is a fact that most students become familiar with over time and through various means. This article describes how this can be demonstrated in a technology classroom using simple photographic equipment. (Contains 5 figures.)

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

NASA Astrophysics Data System (ADS)

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

2012-08-01

The use of increasingly strong magnetic fields in magnetic resonance imaging (MRI) improves sensitivity, susceptibility contrast, and spatial or spectral resolution for functional and localized spectroscopic imaging applications. However, along with these benefits come the challenges of increasing static field (B0) and rf field (B1) inhomogeneities induced by radial field susceptibility differences and poorer dielectric properties of objects in the scanner. Increasing fields also impose the need for rf irradiation at higher frequencies which may lead to elevated patient energy absorption, eventually posing a safety risk. These reasons have motivated the use of multidimensional rf pulses and parallel rf transmission, and their combination with tailoring of rf pulses for fast and low-power rf performance. For the latter application, analytical and approximate solutions are well-established in linear regimes, however, with increasing nonlinearities and constraints on the rf pulses, numerical iterative methods become attractive. Among such procedures, optimal control methods have recently demonstrated great potential. Here, we present a Krotov-based optimal control approach which as compared to earlier approaches provides very fast, monotonic convergence even without educated initial guesses. This is essential for in vivo MRI applications. The method is compared to a second-order gradient ascent method relying on the Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton method, and a hybrid scheme Krotov-BFGS is also introduced in this study. These optimal control approaches are demonstrated by the design of a 2D spatial selective rf pulse exciting the letters "JCP" in a water phantom.

Directional filtering for block recovery using wavelet features

NASA Astrophysics Data System (ADS)

Hyun, Seung H.; Eom, Il K.; Kim, Yoo S.

2005-07-01

When images compressed with block-based compression techniques are transmitted over a noisy channel, unexpected block losses occur. Conventional methods that do not consider edge directions can cause blocked blurring artifacts. In this paper, we present a post-processing-based block recovery scheme using Haar wavelet features. The adaptive selection of neighboring blocks is performed based on the energy of wavelet subbands (EWS) and difference between DC values (DDC). The lost blocks are recovered by linear interpolation in the spatial domain using selected blocks. The method using only EWS performs well for horizontal and vertical edges, but not as well for diagonal edges. Conversely, only using DDC performs well for diagonal edges with the exception of line- or roof-type edge profiles. Therefore, we combine EWS and DDC for better results. The proposed directional recovery method is effective for the strong edge because exploit the varying neighboring blocks adaptively according to the edges and the directional information in the image. The proposed method outperforms the previous methods that used only fixed blocks.

XMM-Newton and INTEGRAL view of the hard state of EXO 1745-248 during its 2015 outburst

NASA Astrophysics Data System (ADS)

Matranga, M.; Papitto, A.; Di Salvo, T.; Bozzo, E.; Torres, D. F.; Iaria, R.; Burderi, L.; Rea, N.; de Martino, D.; Sanchez-Fernandez, C.; Gambino, A. F.; Ferrigno, C.; Stella, L.

2017-07-01

Context. Transient low-mass X-ray binaries (LMXBs) often show outbursts that typically last a few weeks and are characterized by a high X-ray luminosity (Lx ≈ 1036-1038 erg s-1), while most of the time they are found in X-ray quiescence (LX ≈ 1031-1033 erg s-1). The source EXO 1745-248 is one of them. Aims: The broad-band coverage and sensitivity of the instrument on board XMM-Newton and INTEGRAL offers the opportunity of characterizing the hard X-ray spectrum during the outburst of EXO 1745-248. Methods: We report on quasi-simultaneous XMM-Newton and INTEGRAL observations of the X-ray transient EXO 1745-248 located in the globular cluster Terzan 5, performed ten days after the beginning of the outburst (on 2015 March 16) of the source between March and June 2015. The source was caught in a hard state, emitting a 0.8-100 keV luminosity of ≃ 1037 erg s-1. Results: The spectral continuum was dominated by thermal Comptonization of seed photons with temperature kTin ≃ 1.3 keV, by a cloud with a moderate optical depth τ ≃ 2, and with an electron temperature of kTe ≃ 40 keV. A weaker soft thermal component at temperature kTth ≃ 0.6-0.7 keV and compatible with a fraction of the neutron star radius was also detected. A rich emission line spectrum was observed by the EPIC-pn on board XMM-Newton; features at energies compatible with K-α transitions of ionized sulfur, argon, calcium, and iron were detected, with a broadness compatible with either thermal Compton broadening or Doppler broadening in the inner parts of an accretion disk truncated at 20 ± 6 gravitational radii from the neutron star. Strikingly, at least one narrow emission line ascribed to neutral or mildly ionized iron is needed to model the prominent emission complex detected between 5.5 and 7.5 keV. The different ionization state and broadness suggest an origin in a region located farther from the neutron star than where the other emission lines are produced. Seven consecutive type I bursts were detected during the XMM-Newton observation, none of which showed hints of photospheric radius expansion. A thorough search for coherent pulsations from the EPIC-pn light curve did not result in any significant detection. Upper limits ranging from a few to 15% on the signal amplitude were set, depending on the unknown spin and orbital parameters of the system.

Spatially resolved spectroscopy analysis of the XMM-Newton large program on SN1006

NASA Astrophysics Data System (ADS)

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

2016-04-01

We perform analysis of the XMM-Newton large program on SN1006 based on our newly developed methods of spatially resolved spectroscopy analysis. We extract spectra from low and high resolution meshes. The former (3596 meshes) is used to roughly decompose the thermal and non-thermal components and characterize the spatial distributions of different parameters, such as temperature, abundances of different elements, ionization age, and electron density of the thermal component, as well as photon index and cutoff frequency of the non-thermal component. On the other hand, the low resolution meshes (583 meshes) focus on the interior region dominated by the thermal emission and have enough counts to well characterize the Si lines. We fit the spectra from the low resolution meshes with different models, in order to decompose the multiple plasma components at different thermal and ionization states and compare their spatial distributions. In this poster, we will present the initial results of this project.

A numerical study of steady crystal growth in a vertical Bridgman device

NASA Astrophysics Data System (ADS)

Jalics, Miklos Kalman

Electronics based on semiconductors creates an enormous demand for high quality semiconductor single crystals. The vertical Bridgman device is commonly used for growing single crystals for a variety of materials such as GaAs, InP and HgCdTe. A mathematical model is presented for steady crystal growth under conditions where crystal growth is determined strictly by heat transfer. The ends of the ampoule are chosen far away from the insulation zone to allow for steady growth. A numerical solution is sought for this mathematical model. The equations are transformed into a rectangular geometry and appropriate finite difference techniques are applied on the transformed equations. Newton's method solves the nonlinear problem. To improve efficiency GMRES with preconditioning is used to compute the Newton iterates. The numerical results are used to compare with two current asymptotic theories that assume small Biot numbers. Results indicate that one of the asymptotic theories is accurate for even moderate Biot numbers.